The young mill-wright & miller's guide. In five parts --embellished with twenty five [i.e., twenty-six] plates ... / By Oliver Evans, of Philadelphia.

THE YOUNG Mill-wright's & Miller's GUIDE.

PART THE FIRST.

CHAPTER I.

Art. 1. OF THE FIRST PRINCIPLES OF MECHANICS.

MOTION may be said to be the Beginning or Foundation of all Mechanics, because no Mechanical Operation can be performed without Motion.

AXIOMS, or Self-evident Truths.

1. A body at rest will continue so for ever, un∣less it is put in motion by some force impressed.* 1.1

2. A body in motion will continue so for ever, with the same velocity in the same direction, un∣less resisted by some force.† 1.2

3. The impulse that gives motion,* 1.3 and the re∣sistance that destroys it, are equal.

4. Causes and effects are equal, or directly pro∣portional.

POSTULATUMS, or Positions without Proof.

A quadruple impulse, or moving power, is re∣quisite to communicate double velocity to a bo∣dy* 1.4; therefore a quadruple resistance is requisite to destroy double velocity in a body, by axiom 3d.

The impulse we may call power, and the re∣sistance that it overcomes, the effect produced by that power.

COROLLARY.

Consequently, the powers of bodies in motion, to produce effects, are as the squares of their velo∣cities; that is, a double velocity, in a moving bo∣dy, produces 4 times the effect.

Art. 2. OF THE PRINCIPLES OF MECHANICS.

THERE are two principles, which are the foundation of all mechanical motion and mechani∣cal powers, viz. Gravity and Elasticity; or Weight and Spring.

By one or the other of these principles or pow∣ers every mechanical operation is performed.

Gravity,* 1.5 in the extent of the word, means every species of attraction; but more especially that species which is common to, and mutual be∣tween, all bodies; and is evident between the sun and its planetary attendants, as also the earth and moon.* 1.6 But we will only consider it, as it relates to that tendency which all bodies on this earth has to fall towards its centre; thus far it concerns the mechanical arts, and its laws are as follows, viz.

Laws of Gravity.

1. Gravity is common to all bodies, and mutual between them.

2. It is in proportion to the quantity of matter in bodies.

3. It is exerted every way from the centre of attracting bodies, in right-lined directions; there∣fore all bodies on the earth tend to the centre of gravity of the earth.† 1.7

4. It decreases as the squares of the distance in∣crease; that is, if a body, on the earth, was to be removed to double the distance from the centre of gravity of the earth, about 4000 miles high, it would there have but 1-4 of the gravity or weight it had when on the ground: but a small height from the surface of the earth (50,100, or 500 feet) will make no sensible difference in gra∣vity.‡ 1.8

By the 3d law,* 1.9 it follows, that all bodies de∣scending freely by their gravity, tend towards the earth, in right lines, perpendicular to its surface, and with equal velocities (abating for the resist∣ance of the air) as is evident by the 2d law.* 1.10

Art. 3. ELASTICITY.

Elasticity is that strength or power, which any body or quantity of matter, being confined or compressed, has to expand itself; such as a spring that is bent or wound up, heated air or steam con∣fined in a vessel, &c. and by it many mechanical operations are performed.

Elasticity, in the full sense of the word, here means every species of repulsion.

The limits of the prodigious power of repulsion, which takes place between the particles of heated air and steam, are not yet known. Their effects are seen in the explosion of gunpowder, the burst∣ing and cracking of wood in the fire, &c. In short, in every instance, where steam could not find room to expand itself, it has burst the vessel that confined it, endangering the lives of those who were near it.† 1.11

Having premised what was necessary to the right understanding of the science of mechanics,* 1.12 which mostly depends upon the principles of gra∣vitation,

We come to consider the Objects thereof, viz. the Nature, Kinds, and various Effects of Motion and moving Bodies, and the Structure and Me∣chanism of all Kinds of Machines, called Mecha∣nical Powers, whether Simple or Compound.

CHAPTER II.

Art. 4. OF MOTION AND ITS GENERAL LAWS.

MOTION is the continual and successive change of space or place,* 1.13 and is either ab∣solute or relative.

Absolute motion is the change of space or place of bodies,* 1.14 such as the flight of a bird, or the mo∣tion of a ball projected in the air.

Relative motion is the motion one body has with respect to another,* 1.15 such as the difference of mo∣tion of the flight of two birds, or of two ships sailing.* 1.16

Art. 5.

MOTION is either Equable, Accelerated,* 1.17 〈◊〉〈◊〉 Retarded.

Equable motion is when a body passes over equal distances in equal times.* 1.18

Accelerated motion,* 1.19 is that which is continually increased; such is the motion of falling bodies.* 1.20

Retarded motion,* 1.21 is that which continually de∣creases; such is the motion of a cannon-ball throw perpendicularly upwards.† 1.22

Art. 6.

THE Momentum or quantity of motion, is 〈◊〉〈◊〉 the power or force which a moving body has 〈◊〉〈◊〉 strike an obstacle to produce effects, and is equal to that impressed force by which a body is com∣pelled to change its place, by axiom 3, art. 1••

which,* 1.23 I think, ought to be distinguished by two names, viz. Instant and Effective Momentums.

1. The Instant Momentum, or force of moving bodies,* 1.24 is in the compound ratio of their quantities of matter and simple velocities conjointly; that is, as the weight of the body A, multiplied into its velocity, is to the weight of the body B, mul∣tiplied into its velocity, so is the instant force of A to the instant force of B. If A has 4lbs. of matter, and 1 degree of velocity, and B has 2lbs. of matter, and 4 degrees of velocity; then the momentum of their strokes will be as 4 is to 8; that is, supposing them to be instantaneously stop∣ped by an obstacle.

2. The Effective Momentum, or force of moving bodies, is all the effect they will produce by im∣pinging on any yielding obstacle, and is in the compound duplicate ratio of their quantities (or weights) multiplied into the squares of their ve∣locities; that is, as the weight of the body A, multiplied into the square of its velocity, is to the weight of the body B, multiplied into the square of its velocity, so is the effective momen∣tum of A to that of B. If A has 2lbs of matter and 2 degrees of velocity, and B 2lbs of matter and 4 degrees of velocity, then their effective mo∣mentums are as 8 to 32; that is, a double velocity produces a quadruple effect.

Art. 7.

THE general Laws of Motion are the three following, viz.

Law 1. Every body will continue in its present ••••ate,* 1.25 whether it be at rest or moving uniformly 〈◊〉〈◊〉 a right line, except it be compelled to change that state by some force impressed.* 1.26

Law 2.* 1.27 The change of motion or velocity is always proportional to the square root of the moving force impressed,* 1.28 and in a right line with that force, and not as the force directly.* 1.29

Law 3. Action and re-action are always equal, and in contrary directions to each other.† 1.30

CHAPTER III. Art. 8.

OF THE MOMENTUM OR FORCE OF BODIES IN MOTION.

IF two non-elastic bodies, A and B, fig. 1,* 1.31 each having the same quantity of matter, move with equal velocities against each other, they will de∣stroy each other's motion, and remain at rest after the stroke:* 1.32 because their momentums will be equal; that is, if each has 2lbs of matter and 10 degrees of celerity, their instantaneous momen∣tums will each be 20.

But if the bodies be perfectly elastic, they will recede from each other with the same velocity with which they meet; because action and re-action are equal, by the 3d general law of motion, art. 7.* 1.33

2. If two non-elastic bodies, A and B, fig. 2,* 1.34 moving in the same direction with different veloci∣ties, impinge on each other, they will (after the stroke) move on together with such velocity, as, being multiplied into the sum of their weights, will produce the sum of their instant momentums which they had before the stroke; that is, if each weigh 1lb. and A has 8 and B 4 degrees of cele∣rity, the sum of their instant momentums will be 12, then, after the stroke, their velocity will be 6; which, multiplied into their quantity of mat∣ter

2,* 1.35 produces 12, the sum of their instant mo∣mentums. But if they had been elastic, then A would have moved with 4 and B with 8 degrees of velocity after the stroke, and the sum of their instant momentums would be 12, as before.* 1.36

3. If a non-elastic body A, with quantity of matter 1, and 10 degrees of velocity, strike B at rest, of quantity of matter 1, they will both move on together with velocity 5; but if they be elastic, B flies off with velocity 10, and A re∣mains at rest, by 3d general law of motion, art. 7.† 1.37 It is universally true, that whatever instant mo∣mentum is communicated to a body, is lost by the body that communicates it.

4. If the body A,* 1.38 fig. 4,* 1.39 receive two strokes or impulses at the same time, in different direc∣tions, the one sufficient to propel it from A to B, and the other to propel it from A to D, in equal time, then this compound force will propel it in the diagonal line A C, and it will arrive at C in the same time that it would have arrived at B or D, by one impulse only; and the projectile force of these strokes are as the squares of the sides of the parallelogram, by law 2, art. 7.‡ 1.40

5. If a perfect elastic body be let fall 4 feet,* 1.41 to strike a perfect elastic plain,* 1.42 by the laws of falling bodies, art. 9, it will strike the plain with a ve∣locity of 16, 2 feet per second, and rise, by its re-action, to the same height from whence it fell, in half a second: If it falls 16 feet, it will strike with a velocity of 32, 4 feet, and rise 16 feet in one second. Now, if we call the rising of the body the effect, we shall find that a double velo∣city, in this case, produces a quadruple effect in double time. Hence it appears, that a body moving through a resisting medium, with a dou∣ble velocity, will continue in motion a double time, and go 4 times the distance; which will be a quadruple effect.* 1.43

OF NON-ELASTICITY IN IMPINGING BODIES.* 1.44

1. IF A and B, fig. 3,* 1.45 fig. 3, be two columns of matter in motion, meeting each other, and equal in non-elasticity, quantity, and velocity, they will meet at the dotted line e e, destroy each other's motion, and remain at rest, provided none of their parts separate.

2. But if A is elastic, and B non-elastic, they will meet at ee, but B will give way by battering up, and both will move a little further; that is, half the distance that B shortens.

3. But if B is a column of fluid, and, when it strikes A, flies off in a lateral perpendicular direc∣tion, then whatever is the sum total of the mo∣mentums of these particles laterally, has not been communicated to A; therefore A will continue to move, after the stroke, with that said momen∣tum.

4. But with what proportion of the striking ve∣locity the fluid, after the stroke, will move in the lateral direction, I do not find determined; but, from small experiments I have made (not fully to be relied on) I suppose it to be more than one half; because water falling 4 feet, and striking a horizontal plain, with 16,2 feet velocity, will cast some few drops to the distance of 9 feet (say 10 feet, allowing one foot to be lost by friction, &c.) which we must suppose take their direction at an angle of 45 degrees; because it is shewn, in Martin's philosophy, page 135, Vol. I, that a body projected at an angle of 45 degrees, will de∣scribe the greatest possible horizontal randum; also, that a body falling 4 feet, and reflected with its acquired velocity 16,2 feet, at 45 degrees,

will reach 16 feet horizontal randum,* 1.46 or 4 times the distance of the fall. Therefore, by this, 1-4 of 10 feet, equal to 2,5 feet, is the fall that will produce the velocity that produced it, viz. Velo∣city 12,64 feet per second, about 3-4 of the strik∣ing velocity.

5. And if the force of striking fluids be as the squares of their velocities, * 1.47 as proved in art. 67; by experiment, and demonstrated by art. 46; then the ratio of the force of this side velocity, 12,64 feet per second, is to the force of forward velocity, as 160 to 256, more than half (about, 6) of the whole force is here lost by non-elasti∣city.

6. This side force cannot be applied to produce any further forward force, after it has struck the first obstacle; because its action and re-action ba∣lance each other afterwards: which I demonstrate by fig. 27.

Let A be an obstacle, against which the column of water G A, of quantity 16 and velocity per second 16, strikes; as it strikes A, suppose it to change its direction, at right angles, with 3-4 ve∣locity, and strike B B; then change again, and strike forward against C C, and backwards against D D; then again in the side direction E E; and again in the forward and backward directions all of which counteract each other, and balance exactly.

Therefore, if we suppose the obstacle A to be the float of an undershot water-wheel, the water can be of no further service, in propelling it, after the first impulse, but rather a disadvantage; be∣cause the elasticity of the float will cause it to re∣bound in a certain degree, and not keep fully up with the float it struck, but re-act back against the float following; therefore it will be better to let it escape freely as soon as it has fully made the stroke, but not sooner, as it will require a certain

space to act in,* 1.48 which will be in direct proportion to the distance between the floats.

7. From these considerations,* 1.49 we may conclude, that the greatest effect to be obtained from striking fluids, will not amount to more than half the power that gives them motion; but much less, if they be not applied to the best advantage: And that the force of non-elastic bodies, striking to pro∣duce effects, will be in proportion to their non-elasticity.

CHAPTER IV. OF FALLING BODIES. Art. 9.

BODIES descending freely by their gravity, in vacuo, or in an unresisting medium, are subject to the following laws:

1st. They are equably accelerated.* 1.50

2d. Their velocity is always in proportion to the time of their fall, and the time is as the square root of the distance fallen.† 1.51

3d. The spaces through which they pass, are as the square of the times or velocities.‡ 1.52 There∣fore,

4th.* 1.53 Their velocities are as the square root of the space descended through;* 1.54 and their force, to produce effects, as their distances fallen direct∣ly.

5th. The space passed through the first second, is very nearly 16,2 feet, and the velocity ac∣quired, at the lowest point, is 32,4 feet per se∣cond.

6th. A body will pass through twice the space, in a horizontal direction, with the last acquired velocity of the descending body, in the same time of its fall.† 1.55

7th. The total sum of the effective impulse act∣ing on them to give them velocity, is in direct proportion to the space descended through,‡ 1.56 and their velocity being as the square root of the space descended through; or, which is the same, as the square root of the total impulse. There∣fore,

8th. Their momentums, or force to produce effects, are as the squares of their velocities,‖ 1.57 or directly as their distances fell through; and the times expended in producing the effects, are as the square root of the distance fallen through.§ 1.58

9th.* 1.59 The resistance they meet with in any given time, in passing through a resisting medium, is as their surfaces, and as the cubes of their ve∣locities.* 1.60

A TABLE OF THE MOTION OF FALLING BODIES, SUPPOSED IN VACUO.

Distance passed thro' in feet.	The velocity acquir∣ed by the fall, in feet and parts, counted per second.	Seconds of time that a body is supposed to be falling.	Distance passed thro' in said time, in feet and parts.	Velocity per second acquired at the end of every second, in feet and parts.
1	8.1	.125	.25	4.
2	11.4	.25	1.01	8.1
3	14.	.5	4.05	16.2
4	16.2	.75	9.11	24.3
5	18.	1	16.2	32.4
6	19.84	2	64.8	64.8
7	21.43	3	145.8	97.2
8	22.8	4	259.2	129.6
9	24.3	5	305.	162.
10	25.54	6	583.2	194.4
11	26.73	7	793.8	226.8
12	28.	8	1036.8	259.2
13	29.16	9	1312.2	291.6
14	30.2	10	1620.	324.
15	31.34	30	14580.	972.
16	32.4	60	58320.	1944.
17	33.32
18	34.34
19	35.18
20	36.2
21	37.11
36	48.6
49	56.7
64	64.8
100	81.
144	97.2

A SCALE OF THE MOTION OF FALLING BODIES.* 1.61

		16.2 feet is the space fallen through the 1st second, by law 5, which let be equal to			1
		Which is also the whole space fallen through at the end of the 1st second, which let be equal to	1
	16.2	32.4 feet per second is the velocity ac∣quired by the fall, ditto		1
1	—.—.a
	64.8	48.6 feet is the space fallen through the 2d second, ditto			3
	64.8 feet do. at the end of 2 seconds, do.	4
b	64.8 feet is the velocity per second, ac∣quired at the end of the 2d second, do.		2
3		—.—.—.—.c
		81. feet is the space fallen through the 3d second of time, ditto			5
		145.8 feet ditto in 3 seconds of time, do.	9
d		97.2 feet is the velocity acquired by the fall at the end of 3 seconds, ditto		3
5		—.—.—.—.—.—.e
		113.4 feet is the space fallen through in the 4th second of time, ditto			7
		259.2 feet ditto in 4 seconds, ditto	16
f		129.6 feet per second, is the velocity acquired at the end of 4 seconds, do.		4
7		—.—.—.—.—.—.—.—.g

This scale shews,* 1.62 at one view, all the laws to be performed by the falling body o, which falls from o to 1, 16, 2 feet, the first second, and ac∣quires a velocity that would carry it 32,4 feet, from 1 to a, the next second, by laws 5 and 6; this velocity would also carry it down to b in the same time, but its gravity, producing equal effects in equal times, will accelerate it so much as to take it to 3 in the same time, by law 1. It will now have a velocity of 64,8 feet per second, that will take it to c horizontally, or down to d, but gravity will help it on to 5 in the same time. Its velocity will now be 97,2 feet, which will take it horizontally to c, or down to f, but gravity will help it on to 7; and its last acquired veloci∣ty will be 129,6 feet per second from 7 to g.

If either of these horizontal velocities be con∣tinued, the body will pass over double the distance it fell, in the same time, by law 6.

Again, if o be perfectly elastic, and, falling, strikes a perfect elastic plain, either at 1, 3, 5 or 7, the effective force of its stroke will cause it to rise again to o in the same space of time it took to fall.

Which shews, that in every equal part of dis∣tance, it received an equal effective impulse from gravity, and that the total sum of their effective impulse is as the distance fallen directly—and the effective force of their strokes will be as the squares of their velocities, by laws 7 and 8.

CHAPTER V. OF BODIES DESCENDING, INCLINED PLAINS AND CURVED SURFACES. Art. 10.

BODIES descending inclined plains and curved surfaces, are subject to the following laws:

1. They are equably accelerated, because their motion is the effect of gravity.

2. The force of gravity propelling the body A,* 1.63 fig. 5, to descend an inclined plain A D, is to the absolute gravity of the body, as the height of the plain A C is to its length A D.

3. The spaces descended thro' are as the squares of the times.

4. The times, in which the different plains A D, A H, and A I, or the altitude A C, are passed over, are as their lengths respectively.

5. The velocities acquired in descending such plains, in the lowest points D, H, I or C, are all equal.

6. The times and velocities of bodies descend∣ing through plains alike inclined to the horizon, are as the square roots of their lengths.

7. Their velocities, in all cases, are as the square roots of their perpendicular descent.

From these laws or properties of bodies descend∣ing inclined plains, are deduced the following co∣rollaries, viz.

1. That the time, in which a body descends through the diameter A C, or any cord A a, A e or A i, are equal.Hence,

2. All the cords of a circle are described in equal times.* 1.64

3. The velocity acquired in descending thro' any arch, or cord of an arch, of a circle, as a C, in the lowest point C, is equal to the velocity that would be acquired in falling through the per∣pendicular height F C.

The motion of pendulums have the same pro∣perties, the rod or string acting as the smooth curved surface.

For demonstration of these properties, see Mar∣tin's Philosophy, vol. I, page 111—117.

CHAPTER VI. OF THE MOTION OF PROJECTILES. Art. 12.

A PROJECTILE is a body thrown or pro∣jected in any direction; such as a stone from the hand, water spouting from any vessel, a ball from a cannon, &c. fig. 6.* 1.65

Every projectile is acted on by two forces at the same time, viz. the Impulse and the Gra∣vity.

By the impulse,* 1.66 or projectile force, the body will pass over equal distances, A B, B C, &c. in equal times, by 1st general law of motion, art. 7, and, by gravity, it descends through the spaces A G, G H, &c. which are as the squares of the times, by 3d law of falling bodies, art. 9. There∣fore, by these forces compounded, the body will describe the curve A Q, called a parabola; and

this will be the case in all directions,* 1.67 except per∣pendicular; but the curve will vary with the elevation, yet it will still be what is called a pa∣rabola.

If the body is projected at an angle of 45 de∣grees elevation, it will be thrown to the greater horizontal distance possible; and, if projected with double velocity, it will describe a quadruple ran∣dom.

For a full account and demonstration, see Mar∣tin's Phil. vol. I, p. 128—135.

CHAPTER VII. OF CIRCULAR MOTION & CENTRAL FORCES. Art. 13.

IF a body A,* 1.68 fig, 7,* 1.69 be suspended by a string A C, and caused to move round the centre C that tendency which it has to fly off from the centre, is called the centrifugal force; and the action of the string upon the body, which con∣stantly solicits it towards the centre, and keep it in the circle A M, is called the centripital force. Speaking of these two forces indefinitely, they are called central forces.* 1.70

The particular laws of this species of motion, are,

1. Equal bodies describing equal circles in equal times,* 1.71 have equal central forces.* 1.72

2. Unequal bodies describing equal circles in unequal times, their central forces are as their quantities of matter multiplied into their velo∣cities.

3. Equal bodies describing unequal circles in equal times, their velocities and central forces are as their distances from their centres of motion, or as the radius of their circles.* 1.73

4. Unequal bodies describing unequal circles in equal times, their central forces are as their quan∣tities of matter multiplied into their distance from ••he centre or radius of their circles.

5. Equal bodies describing equal circles in un∣equal times, their central forces are as the squares of their velocities; or, in other words, a double velocity generates a quadruple central force.† 1.75 Therefore,

6. Unequal bodies describing equal circles i•• unequal times,* 1.76 their central forces are as their quantities multiplied into the squares of their velocities.

7. Equal bodies describing unequal circles 〈◊〉〈◊〉 equal celerities, their central forces are inverse•••• as their distances from the centre of motion 〈◊〉〈◊〉 radius of the circles.* 1.77

8. Equal bodies describing unequal circles having their central forces equal, their periodical times are as the square roots of their distances.

9. Therefore the squares of the periodical time are proportional to the cubes of their distances when neither the periodical times nor the cele••••∣ties are given. In that case,

10.* 1.78 The central forces are as the squares of the distances inversely.* 1.79

CHAPTER VIII. OF THE CENTRES OF MAGNITUDE, MOTION, AND GRAVITY. Art. 14.

THE centre of magnitude is that point which is equally distant from all the external parts of a body.

2. The centre of motion is that point which remains at rest,* 1.81 while all other parts of the body move round it.

3. The centre of gravity of bodies, is of great consequence to be well understood, it being the principle of much mechanical motion, and pos∣sesses the following particular properties:

1. If a body is suspended on this point, as its centre of motion, it will remain at rest in any po∣sition.

2. If a body is suspended on any other point than its centre of gravity, it can rest only in such position, that a right line drawn from the centre of the earth, through the centre of gravity, will intersect the point of suspension.

3. When this point is supported, the whole bo∣dy is kept from falling.

4. When this point is at liberty to descend, the whole body will fall.

5. The centre of gravity of all homogeneal bodies, as squares, circles, spheres, &c. is the middle point in a line connecting any two opposite points or angles.

6. In a triangle, it is in a right line drawn from any angle to bisect the opposite side, at the distance of one third of its length from the side bisected.

7. In a hollow cone, it is in a right line passing from the apex to the centre of the base, and at the distance of one third of the side from the base.

8. In a solid cone, it is one fourth the side from the base, in a line drawn from the apex to the centre of the base.

Hence the solution of many curious phaenomena, as, why many bodies stand more firmly on their bases than others; and all bodies will fall, when their centre of gravity falls without their base.

Hence appears the reason,* 1.82 why wheel-carriages, loaded with stones,* 1.83 iron, or any heavy matter, will not overturn so easy, as when loaded with wood, hay, or any light matter; for when the load is not higher than a b, the centre of gravity will fall within the centre of the base at c; but if the load is as high as d, it will then fall outside the base of the wheels at e, consequently it will overturn. From this appears the error of those, who hastily rise in a coach or boat, when likely to overset, thereby throwing the centre of gravi∣ty more out of the base, and increasing the dan∣ger.

CHAPTER IX. OF THE MECHANICAL POWERS.

Art. 15.

HAVING now premised and considered all that is necessary for the better understand∣ing those machines called Mechanical Powers, we come to treat of them, and they are six in number, viz.

The Lever, the Pulley, the Wheel and Axle, the Inclined Plain, the Wedge, and the Screw.

They are called Mechanical Powers, because they increase our power of raising or moving hea∣vy bodies; and,* 1.84 although they are six in number, they seem to be reducible to one, viz. the Lever, and appear to be governed by one simple principle, which I shall call the First General Law of Me∣chanical Powers; which is this,* 1.85 viz. the Momen∣tums

of the power and weight are always equal when the engine is in equilibrio.* 1.86

Momentum, her•• means the product of 〈◊〉〈◊〉 weight of the body multiplied into the distance 〈◊〉〈◊〉 moves; that is, the power multiplied into its dis∣tance moved, or into its distance from the centre of motion, or into its velocity, is equal to 〈◊〉〈◊〉 weight multiplied into its distance moved, or into its distance from the centre of motion, or ••nto 〈◊〉〈◊〉 velocity; or, the power multiplied into its per∣pendicular descent, is equal to the weight multi∣plied into its perpendicular ascent.

The Second General Law of Mechanical Pow∣ers, is,

The power of the engine, and velocity of the weight moved, are always in the inverse propor∣tion to each other; that is, the greater the velo∣city of the weight moved, the less it must be; and the less the velocity, the greater the weight may be; and that universally in all cases. There∣fore,

The Third General Law is,

Part of the original power is always lost in over coming friction, inertia, &c. but no power can be gained by engines, when time is considered i•• the calculation.

IN the theory of this science, we suppose al•••• plains to be perfectly smooth and even, levers 〈◊〉〈◊〉 have no weight, cords to be perfectly pliable, and machines to have no friction; in short, all imper∣fections are to be laid aside, until the theory 〈◊〉〈◊〉 established, and then proper allowances are to be made.

Art. 16. Of the Lever.

A Lever is a bar of iron, wood, &c. one part of which is supported by a prop, and all other parts turn or move on that prop, as their centre of motion; and its length, on each side of the prop, is called its arms: the velocity or motion of every part of these arms, is directly as its dis∣tance from its centre of motion, by 3d law of cir∣cular motion.

The Lever—Observe the following laws:

1. The power and weight are to each other,* 1.87 as their distances from the centre of motion, or from the prop, respectively.* 1.88

2. The power is to the weight, as the distance the weight moves is to the distance the power moves, respectively.† 1.89

3. The power is to the weight, as the perpen∣dicular ascent of the weight is to the perpendicu∣lar descent of the power.‡ 1.90

4. Their velocities are as their distances from their centre of motion, by 3d law of circular mo∣tion.

These simple laws hold universally true in all mechanical powers or engines;* 1.91 therefore it is easy (from these simple principles) to compute the power of any engine, either simple or com∣pound; for it is only to find how much swifter the power moves than the weight, or how much farther it moves in the same time; and so much is the power, (and time of producing it) increased by the help of the engine.

Art. 17. GENERAL RULES FOR COMPUTING THE POWER OF ANY ENGINE.

1. DIVIDE either the distance of the power from its centre of motion, by the distance of the weight from its centre of motion. Or,

2. Divide the space passed through by the pow∣er, by the space passed through by the weight. This space may be counted either on the arch de∣scribed, or perpendiculars. And the quotient will shew how much the power is increased by the help of the engine.

Then multiply the power applied to the en∣gine, by that quotient, and the product will be the power of the engine, whether simple or com∣pound.

EXAMPLES.

Let A B C, fig. 8,* 1.92 represent a lever; then, to compute its power, divide the distance of the power P from its centre of motion B C 12, by the distance of the weight W, A B 1; and the quoti∣ent is 12: the power is increased 12 times by the engine; which, multiply by the power applied 1, produces 12, the power of the engine at A, or the weight W, that will balance P, and hold the engine in equilibrio. But suppose the arm A B to be continued to E, then, to find the power of the engine, divide the distance B C 12, by B E 6; and the quotient is two; which multiplied by 1, the power applied, produces 2, the power of the en∣gine, or weight w to balance P.

Or divide the perpendicular descent of the pow∣er C D equal 6, by the perpendicular ascent E F equal 3; and the quotient 2, multiplied by the power P equal 1, produces 2, the power of the en∣gine at E.

Or divide the velocity of the power P equal 6,* 1.93 by the velocity of the weight w equal 3; and the quotient 2, multiplied by the power 1, produces 2, the power of the engine at E. If the power P had been applied at 8, then it would have re∣quired to have been 1 1-2 to balance W, or w; because 1 1-2 times 8 is 12, which is the momen∣tum of both weights W and w. If it had been applied at 6, it must have been 2; if at 4, it must have been 3; and so on for any other distance from the prop or centre of motion.

Art. 18. There are Four kinds of Levers.

1. THE common kind,* 1.94 where the prop is placed between the weight and power, but gene∣rally nearest the weight.

2. When the prop is at one end, the power at the other, and the weight between them.

3. When the prop is at one end, the weight at the other, and the power applied between them.

4. The bended lever, which differs only in form, but not in properties, from the others.

Those of the first and second kind have the same properties and powers, and are real mechanical powers, because they increase the power; but the third kind is a decrease of power, and only used to increase velocity, as in clocks, watches, and mills, where the first mover is too slow, and the velocity increased by the gearing of the wheels.

The machinery of the human frame is composed of the last kind of lever;* 1.95 for when we lift a weight by the hand, resting the elbow on any thing, the muscle that exerts the force to raise the weight, is fastened at about one tenth of the distance from

the elbow to the hand,* 1.96 and must exert a for•• ten times as great as the weight raised; there∣fore, he that can lift 56lbs with his arm at•• right angle at the elbow, exerts a force equal 〈◊〉〈◊〉 560lbs. by the muscles of his arm. Wonder•••• is the power of the muscles in these cases. He•• appears the reason, why men of low stature stronger than those of high, in proportion to the thickness, as is generally the case.

Art. 19. Compound Lever.

IF several levers are applied to act one upon another,* 1.97 as 2 1 3, in fig. 9, where No. 1 is 〈◊〉〈◊〉 the first kind, No. 2 of the second, and No. 3 〈◊〉〈◊〉 the third. The power of these levers, united act on the weight w, is thus found by the follow∣ing rule, which will hold universally true in an•• number of levers united, or wheels (which is si∣milar thereto) acting upon one another.

RULE.

1st. Multiply the power P,* 1.98 into the length 〈◊〉〈◊〉 all the driving levers successively, and note the product.

2d. Then multiply all the leading levers in•••• one another successively, and note the product.

3d. Divide the first product by the last, and the quotient will be the weight w, that will hold the machine in equilibrio.

This rule is founded on the first law of the lever, art. 16, and on this principle, viz.

If the weight w,* 1.99 and power P, are such, tha•• when suspended on any compound machine, whe∣ther

of levers united,* 1.100 or of wheels and axles, they hold the machine in equilibrio. Then, 〈◊〉〈◊〉 the power P, is multiplied into the radius of all the driving wheels, or lengths of the driving le∣vers, and the product noted; and the weight w multiplied into the radius of all the leading wheels, or length of the leading levers, and the product noted; these products will be equal. If we had taken the velocities or circumferences of the wheels, instead of their radius, they would have been equal also.

On this principle is founded all rules for calcu∣lating the power and motion of wheels in mills, &c. See art. 20 & 74.

EXAMPLES.

Given, the power P equal to 4,* 1.101 on lever 2, at 8 distance from the centre of motion. Required, with what force lever 1, fastened at 2 from the centre of motion of lever 2, must act, to hold the lever 2 in equilibrio.* 1.102

By the rule, 4×8 the length of the long arm, is 32, and divided by 2, the length of the short arm, quotes 16, the force required.

Then 16 on the long arm, lever 1, at 6 from the centre of motion. Required, the weight on the short arm, at 2, to balance it.

By the rule, 16×6=96, which divided by 2,* 1.103 the short arm, quotes 48, for the weight re∣quired.

Then 48 is on the lever 3, at 2 from the cen∣tre. Required, the weight at 8 to balance it.

Then 48×2=96, which, divided by 8, the length of the long arm, quotes 12, the weight required.

Given, the power P=4, on one end of the com∣bination of levers. Required, the weight w, o•• the other end, to hold the whole in equilibrio.

Then by the rule, 4×8×6×2=384 the product 〈◊〉〈◊〉 the power multiplied into the length of all the driving levers, and 2×2×8=32 the product of all the leading levers, and 384|32=12 the weight w required.

Art. 20. Foundation of the rules for finding the motion of wheels, or number of cogs to pro∣duce motions.

THE same rule holds good in calculating the powers of machines, consisting of wheels whether simple or compound, by counting the radius of the wheels as the levers; and because the diame∣ters and circumferences of circles are proportional; we may take the circumference instead of the ra∣dius, and it will be the same. Then again, be∣cause the number of cogs in the wheels, constitute the circle, we may take the number of cogs and rounds instead of the circle or radius, and the re∣sult will be the same.

Let Fig. 11 represent a water-mill (for grind∣ing grain) double geared:* 1.104

• Number 8 The water-wheel,
• 4 The great cog-wheel,
• 2 The wallower,
• 3 The counter cog-wheel,
• 1 The trundle.
• 2 The mill-stones,

And let the above numbers also represent the radius of the wheels in feet.* 1.105

Now suppose there be a power of 500lb. on the water-wheel, required what will be the force ex∣erted on the mill-stone, 2 feet from the centre,

Then,* 1.106 by the rule, 500×8×2×1=8000, and 4×3×2=24, by which divide 8000, and it quotes 333,33 lb. the power or force required, exerted on the mill-stone two feet from its centre, which is the mean circle of a 6 feet stone.—And as the velocities are as the distance from the centre of mo∣tion, by 3d law of circular motion, art. 13, there∣fore, to find the velocity of the mean circle of the stone 2, deduce the following rule, viz.

1st. Multiply the velocity of the water-wheel into the radius or circumference of all the driving wheels,* 1.107 successively, and note the product.

2. Multiply the radius or circumference of all the leading wheels, successively, and note the pro∣duct; divide the first by the last product, and the quotient will be the answer.

But observe here, that the driving wheels in this rule, are the leading levers in the last rule.

EXAMPLES.

Suppose the velocity of the water-wheel to be 12 feet per second; then by the rule 12×4×3×2=288 and 8×2×1=16 by which divide the first pro∣duct 288, and it quotes 18 feet per second, the ve∣locity of the stone, 2 feet from its centre.

Art. 21. Power decreases as motion increases.

IT may be proper to observe here, that as the velocity of the stone is increased, the power to move it is decreased, and as its velocity is decreas∣ed,

the power 〈◊〉〈◊〉 it to move it is increased,* 1.108 by 2d general law of mechanical powers. This 〈◊〉〈◊〉 universally true in all engines that can possibly 〈◊〉〈◊〉 contrived; which is evident from the 1st law of the lever, viz. the power multiplied into its ve∣locity or distance moved, is equal to the weight multiplied into its velocity or distance moved.

Hence the general rule to compute the power of any engine,* 1.109 simple or compo••nd, art. 17. 〈◊〉〈◊〉 you have the moving power, and its velocity o•• distance moved, given, and the velocity or dis∣tance of the weight, then, to find the weight (which, in mills, is the force to move the stone, &c.) divide that product by the velocity of the weight or mill-stone, &c. and it quotes the weight or force exerted on the stone to move it: But a certain quantity or proportion of this force is lost, in order to obtain a velocity to the stone; which is shewn in art. 29.* 1.110

Art. 22. No Power gained by enlarging Undershot Water-Wheels.

THIS seems a proper time to shew the absurdi∣ty of the idea of increasing the power of the mill,* 1.111 by enlarging the diameter of the water-wheel, on the principle of lengthening the lever, or by dou∣ble gearing mills where single gears will do; be∣cause the power can neither be increased nor di∣minished by the help of engines, while the velo∣city of the body moved is to remain the same.

EXAMPLE.

Suppose we enlarge the diameter of the water-wheel from 8 to 16 feet radius, fig. 11,* 1.112 and leave

the other wheels the same; then,* 1.113 to find the ve∣locity of the stone, allowing the velocity of the periphery of the water-wheel to be the same (12 feet per second); by the rule, 12×4×3×2=288, and 16×2×1=32, by which divide 288, it quotes 9 feet in a second, for the velocity of the stone.

Then, to find the power by the rule for that purpose, art. 20, 500×16×2×1=16000, and 4×3×2=24, by which divide 16000, it quotes 666,66lb. the power. But as velocity as well as power, is necessary in mills, we shall be obliged, in order to restore the velocity, to enlarge the great cog-wheel from 4 to 8 radius.

Then, to find the velocity, 12×8×3×2=576, and 16×2×1=32, by which divide 576, it quotes 18, the velocity as before.

Then, to find the power by the rule, art. 20, it will be 333,33, as before.

Therefore no power can be gained, upon the principle of lengthening the lever, by enlarging the water-wheel.

The true advantages that large wheels have over small one••,* 1.114 arises from the width of the buc∣kets bearing but a small proportion to the radius of the wheel; because if the radius of the wheel be ••8 feet, and the width of the bucket or float-board but 1 foot, the float takes up but 1-8 of the arm, and the water may be said to act fairly upon the end of the arm and to advantage. But if the radius of the wheel be but 2 feet, and the width of the float 1 foot, part of the water will act on the middle of the arm, and act to dis∣advantage, as the float takes up half the arm. The large wheel also serves the purpose of a fly∣wheel; (art. 30) it likewise keeps a more regular motion, and casts off back water b••tter. See art. 70.

But the expence of these large wheels is to be taken into consideration, and then the builder

will find that there is a maximum size,* 1.115 (see art▪ 44) or a size that will yield him the greatest pro∣fit.

Art. 23. No Power gained by double gearing Mills, but some lost.

I might also go on to shew that no power or advantage is to be gained by double gearing Mills,* 1.116 upon any other principles than the following, viz.

1. The motion necessary for the stone, can sometimes be obtained without having the trun∣dle too small, because we are obliged to have the pitch of the cogs and rounds, and the size of the spindle large enough, to bear the stress of the power. This pitch of gear and size of spindle may bear too great a proportion to the radius of the trundle (as does the size of the float to the ra∣dius of the water-wheel, art 22) and may work hard. Therefore there may be a loss of power on that account; as there can be a loss but no gain, by 3. general law of mechanical powers, art. 15.

2. The mill may be made more convenient for two pair of stones to one water-wheel.* 1.117

Art. 24. Of the Pulley.

2. The pulley is a mechanical power well-known. One pulley,* 1.118 if it be moveable by the

weight doubles the power,* 1.119 because each rope sus∣tains half the weight.

But if two or more pulleys be joined together in the common way,* 1.120 then the easiest way of com∣puting their power is, to count the number of ropes that join to the lower or moveable block, and so many times is the power increased; because all these ropes have to be shortened, and all run into one rope (called the fall) to which the mov∣ing power is applied. If there be 4 ropes the power is increased fourfold.* 1.121 See plate 1, fig. 10.

Art. 25. Of the Wheel and Axle.

3. THE wheel and axle, fig. 17, is a mechanical power, the same as the lever of the first kind; there fore the power is to the weight, as the diameter of the axle is to the diameter of the wheel; or the pow∣er multiplied into the radius of the wheel, is equal to the weight multiplied into the radius of the axle,† 1.122 in an equilibrium of this engine.

Art. 26. Of the inclined Plain.

4. The inclined plain is the fourth mechanical power: and in this the power is to the weight,* 1.123 as the height of the plain is to its length. This

is of use in rolling heavy bodies,* 1.124 such as barreled hogsheads, &c. into wheel-carriages, &c. and for letting them down again. See plate V, fig. 1. If the height of the plain be half its length, the•••• half the force will roll the body up the plain, that would lift it perpendicularly.

Art. 27. Of the Wedge.

5. The wedge is only a•• inclined plain. Whence,* 1.125 in the common form of it, the power applied will be to the resistance to be overcome as the thickness of the wedge is to the length thereof. This is a very great mechanical power, and may be said to excel all the rest; because wi•••• it we can effect, what we cannot with any 〈◊〉〈◊〉 in the same time, and I think may be comput•••••• in the following manner.

If the wedge be 12 inches long and 2 inches thick,* 1.126 then the power to hold it in equilibrio 〈◊〉〈◊〉 as 1 to balance 12 resistance; that is, 12 resistance pressing on each side of the wedge,* 1.127 and whe•• struck with a mallet, the whole force of the gra∣vity of the mallet, added to the whole force 〈◊〉〈◊〉 the agent exerted in the stroke, is communicated to the wedge in the time it continues to move 〈◊〉〈◊〉 and this force to produce effect, is as the square of the velocity, with which the mallet strike••

multiplied into its weight;* 1.128 therefore the mallet should not be too large, (see art. 44) because it may be too heavy for the workman's strength, and will meet too much resistance from the air, so that it will loose more by lessening the veloci∣ty, than it will gain by its weight. Suppose a mallet of 10lb. strike with 5 velocity, its effect∣ive momentum 250; but if it strike with 10 ve∣locity, then its effective momentum is 1000. The effects produced by the strokes will be as 250 to 1000; and all the force of each stroke, ex∣cept what may be destroyed by the friction of the wedge, is added in the wedge, until the sum of these forces amount to more than the resistance of the body to be split, therefore it must give way; but when the wedge does not move the whole force is destroyed by the friction. Therefore the less the inclination of the sides of the wedge, the greater resistance we can overcome by it, because it will be easier moved by the stroke.

Art. 28. Of the Screw.

6. THE Screw is the last mentioned mechani∣cal power,* 1.129 and is a circular inclined plain (which will appear by wrapping a paper, cut in form of an inclined plain round a cylinder) and the lever of the first kind combined (the lever being applied to force the weight up in the inclined plain) and is a great mechanical power; its use is both for pres∣sure and raising great weights. The power ap∣plied is to the weight it will raise, as the distance through which the weight moves, is to the dis∣tance through which the power moves; that is, as the distance of the threads of the screw, is to the cir∣cle the power describes: so is the power to the weight it will raise. If the distance of the thread

be half an inch,* 1.130 and the lever be 15 inches radius and the power applied be 10lb. then the power will describe a circle of 94 inches, while the weight raises half an inch; then, as half an inch is to 94 inches, so is 10lb to 1888lb the weight•• the engine would raise with 10lb power. But this is supposing the screw to have no friction, 〈◊〉〈◊〉 which it has a great deal.

Perhaps an improvement might be made on the screw, for some particular uses, by introducing rollers to take off the friction. See art. 33.

WE have hitherto considered the action 〈◊〉〈◊〉 effect of these engines,* 1.131 as they would answer 〈◊〉〈◊〉 the strictness of mathematical theory, were the•• no such thing as friction or rubbing of parts upon each other; by which means, philosophers have allowed, that one third of the effect of the ma∣chine is, at a medium, destroyed: which bring us to treat of it next in course.* 1.132

Art. 30. Of the Fly-wheel, and its Use.

BEFORE I dismiss the subject of mechanics powers, I shall take notice of the fly-wheel, 〈◊〉〈◊〉

use of which is to regulate the motion of engines,* 1.133 and should be made of cast metal, of a circular form, that it may not meet with much resistance from the air.

Many have taken this wheel for an increaser of power, whereas it is, in reality, a considerable de∣stroyer of it; which appears evident, when we consider that it has no motion of its own, but re∣ceives all its motion from the first mover, and, as the friction of the gudgeons and resistance of the air are to be overcome, it cannot be done without some power; yet this wheel is of great use in many cases, viz.

1st. For regulating the power,* 1.134 where it is ir∣regularly applied, such as the treadle or crank moved by foot or hand, as spinning-wheels, turn∣ing lathes, flax-mills, or where steam is applied, by a crank, to produce a circular motion.

2d. Where the resistance is irregular, by jerks, &c. such as saw-mills, forges, flitting-mills, pow∣der-mills, &c.

The fly-wheel, by its inertia, regulates the motion; because, if it be very heavy, it will re∣quire a great many little shocks or impulses of power to give it a considerable velocity, and it will require as many equal shocks of resistance to destroy said velocity, by axiom 3, art. 1.

While a rolling or flitting mill is running emp∣ty, the force of the water is employed in generating velocity to the fly-wheel [a heavy water-wheel will have the same effect] which force, summed up in the fly, will be sufficient to continue the motion, without much abatement, while the sheet is running between the rollers; whereas, had the force of the water been lost while the mill was empty, she would have slack∣••ned in motion too much before the sheet got through. This may be the case where water is ••carce.

CHAPTER X. OF FRICTION.

Art. 31.

FROM what I can gather from different authors,* 1.135* 1.136 and by my own experiments, 〈◊〉〈◊〉 conclude that the doctrine of friction is as follows and we may say it is subject to the following laws 〈◊〉〈◊〉 viz.

Laws of Friction.

1. It is neither increased nor decreased by in∣creasing or decreasing the surfaces of contact 〈◊〉〈◊〉 the moving body.* 1.137† 1.138

2. It is in proportion to the weight and veloci∣ty, conjointly, of the moving body.‡ 1.139

3. This proportion decreases as the weight and velocity increases,* 1.140 but by what ratio, is not de∣termined.* 1.141

4. It is greatly varied by the smoothness or roughness,* 1.148 hardness or softness, of the surfaces of contact of the moving bodies.

5. A body without motion has no friction; therefore, the less the motion, the less the fric∣tion.

Art. 32. Of reducing Friction.

TO reduce friction, we must, by mechanical contrivances,* 1.149 reduce the motion of the rubbing parts as much as possible; which is done, either by making the gudgeons small and the diameter of wheels large, or by fixing the gudgeons to run o•• friction-wheels.* 1.150 Thus, let A, fig. 14, represent the gudgeon of a wheel set to run on the ver•••••• of two wheels of cast metal passing each other 〈◊〉〈◊〉 little, and the gudgeon laying between them. It is evident, that as A turns, it will turn both friction-wheels; and, if the diameter of gudgeon A is 2 inches, and that of the wheels 12, then the wheels will turn once while A turns 6 times, so that the velocity of the gudgeons C C of the wheels, is to the velocity of the gudgeon A, as 〈◊〉〈◊〉 is to 6, supposing them to be equal in size; but 〈◊〉〈◊〉 there are 4 of them to bear A, they may be bu•• half the diameter, and then their velocity will be to that of A, as 1 is to 12; or A might be set on one wheel, as at B, with supporters to keep it on; and, if friction-wheels are added to friction wheels, the friction may be reduced to almost no∣thing by that means.

Art. 33. Late Invention to reduce Friction.

WHEEL-CARRIAGES,* 1.151 pullies, and such wheels as have large axles in proportion to their diameters, have much friction. There has been a late discovery, in England, of applying the prin∣ciple of the roller to them; which may be so done as almost totally to destroy the friction.

The easiest method possible, of moving heavy bodies horizontally, is the roller.

Let A B, fig. 15,* 1.152 represent a body of 100 tons weight (with the underside perfectly smooth and even) set on two rollers, perfectly hard, smooth, and round, rolling on the horizontal plain C D,* 1.153 perfectly hard, smooth, and even; it is evident that this body is supported by two lines perfectly perpendicular, and, if globes were used instead of rollers, the least force would move it in any horizontal direction; even a spider's web would be sufficient, giving it time to overcome the visinertia of the body: But as perfect hard∣ness, smoothness, &c. are not attainable, a little friction will still remain.

This principle is, or may be, applied to wheel-carriages, in the following manner:

Let the outside ring B C D, fig. 16,* 1.154 represent the box of a carriage-wheel, the inside circle A the axle, the circles a a a a a a the rollers round the axle between it and the box, and the inner ••ring a thin plate for the pivots of the rollers to run in, to keep them at a proper distance from each other. When the wheel turns the rollers pass round on the axle, and on the inside of the box, and we may say without friction, because there is no rubbing of the parts past one another.* 1.155

CHAPTER XI. OF MAXIMUMS, OR THE GREATEST EFFECTS OF ANY MACHINE.

Art. 34.

THE effect of a machine,* 1.156 is the distance which it moves or the velocity with which i•• moves any body to which it is applied to give mo∣tion, in a given time; and the weight of the body multiplied into its distance moved, or into its ve∣locity, shews the effect.

The theory published by philosophers,* 1.157 and re∣ceived and taught as true, for several centuries past, is, that any machine will work with its greatest perfection when it is charged with 〈◊〉〈◊〉

4-9 of the power that would hold it in equilibrio,* 1.158 and then its velocity will be just 1-3 of the great∣est velocity of the moving power.

To explain this, they suppose the water-wheel, fig.17,* 1.159 to be of the undershot kind, 16 feet dia∣meter, turned by water issuing from under a 4 feet head, with a gate 1. foot wide, 1 foot high drawn; then the force will be 250lbs. because that is the weight of the column of water above the gate, and its velocity will be 16,2 feet per second, as shall be shewn under the head of Hydraulics; then the wheel will be moved by a power of 250lbs. and if let run empty, will move with a velocity of 16 feet per second; but if we hang the weight W to the axle (of 2 feet diameter) with a rope, and continue to add to it until it stops the wheel, and holds it in equilibrio, the weight will be found to be 2000lbs. by the rule, art. 19; and then the effect of the machine is nothing, because the velocity is nothing: But as we decrease the weight W, the wheel begins to move, and its velocity increases accordingly; and then the pro∣duct of the weight multiplied into its velocity, will increase until the weight is decreased to 4-9 of 2000=888,7, which, multiplied into its dis∣tance moved or velocity, will produce the great∣est effect, and the velocity of the wheel will then be 1-3 of 16 feet, or 5,33 feet per second. So say those who have treated of it.

This will appear plainer to a young learner,* 1.160 if he will conceive this wheel to be applied to work an elevator, as E, fig. 17, to hoist wheat, and suppose that the buckets, when all full, contain 9 pecks, and will hold the wheel in equilibrio, it is evident it will then hoist none, because it has no motion; then, in order to obtain motion, we must lessen the quantity in the buckets, when the wheel will begin to move, and hoist faster and

faster until the quantity is decreased to 4-9,* 1.161 or 4 pecks, and then, by the theory, the velocity of the machine will be 1-3 of the greatest velocity, when it will hoist the greatest quantity possible in a given time: for if we lessen the quantity in the buckets below 4 pecks, the quantity hoisted in any give•• time will be lessened.

This is the theory established, for demonstra∣tion of which, see Martin's Philosophy, vol. 1, page 185-187.

Art. 35. Old Theory investigated.

IN order to investigate this theory,* 1.162 and the better to understand what has been said, let us consider as follows, viz.

1. That the velocity of spouting water, under 4 feet head, is 16 feet per second, nearly.

2. The section or area of the gate drawn, in feet, multiplied by the height of the head in feet, gives the cubic feet in the whole column, which multiplied by 62,5 (the weight of a cubic foot of water) gives the weight or force of the whole column pressing on the wheel.

3. That the radius of the wheel, multiplied by the force, and that product divided by the radius of the axle, gives the weight that will hold the wheel in equilibrio.

4. That the absolute velocity of the wheel, subtracted from the absolute velocity of the wa∣ter, leaves the relative velocity with which the water strikes the wheel in motion.

5. That as the radius of the wheel is to the ra∣dius of the axle, so is the velocity of the wheel to the velocity of the weight hoisted on the axle.

6. That the effects of spouting fluids are as the squares of their velocities (see art. 45, law 6) but the instant force of striking fluids,* 1.163 are as their velocities simply. See art. 8.

7. That the weight hoisted, multiplied into its perpendicular ascent, gives the effect.

8. That the weight of water expended, multi∣plied into its perpendicular descent, gives the power used per second.

On these pinciples I have calculated the follow∣ing scale; first supposing the force of striking fluids to be as the square of their striking or rela∣tive velocity, which brings out the maximum a∣greeably to the old theory, viz.

When the load, at equilibrio, is 2000, then the maximum load is 888,7=4/9; of 2000, when the effect is at its greatest, viz. 591,98, as appears in the 6th column, and then the velocity of the wheel is 5,333 feet per second, equal to 1-3 of 16, the velocity of the water, as appears in the 5th line of the scale: but as there is an evi∣dent error in the first principle of this theory,* 1.164 by counting the instant force of the water on the wheel to be as the square of its striking velocity, therefore it cannot be true. See art. 41.

I then calculate upon this principle, viz. That the instant force of striking fluids is as their velo∣city simply, then the load that the machine will carry, with its different velocities, will be as the velocity simply, as appears in the 7th column, and the load, at a maximum, is 1000lb=½ of 2000, the load at equilibrio, when the velocity of the wheel is 8 feet=½ of 16 the velocity of the water per second; and then the effect is at its greatest, as shewn in the 8th column, viz. 1000, as appears in the 4th line of the scale.

This I call the new theory,* 1.165 (because I found that William Waring had also, about the same time, established it, see art. 38) viz. That when

any machine is charged with just 1-2 of the load that will hold it in equilibrio,* 1.166 its velocity will be just 1-2 of the natural velocity of the moving power, and then its effect will be at a maximum, or greatest possible.

This appears to be the way by which this great error has been so long overlooked by philosophers, and which has rendered the theory of no use in practice, but led many into expensive errors, thereby bringing great discredit upon philoso∣phy.

For demonstrations of the old theory, see Mar∣tin's Phil. vol. I, page 185—187.

A SCALE FOR DETERMINING THE MAXIMUM CHARGE AND VELOCITY OF UNDERSHOT MILLS.

		Velocity of the wheel per second, by supposition.	Velocity with which the water strikes the wheel in motion, or relative velocity.	Velocity of the weight ascending.	Weight hoisted, accord∣ing to the old theory.	Effect, by the old theory	Weight hoisted, accord∣ing to new theory.	Effect, by new theory.	Ratio of the power and effect at a maximum, the power being 4000 in each case.
	feet.	feet.	feet.	feet.	lbs.	feet.	lbs.	feet.
Radius of the wheel	8	16	0	2	0	0			Maxi∣mum by new the∣ory▪
Radius of the axle	1	12	4	1, 5	125	187, 5	500	750
Section of the gate in square feet	1	10	6	1, 25	281	351	750	937
8	8	1	500	500	1000	1000	4 to 1
Height of the head of water	4	6	10	,75	781,2	585,9	1250	937
Velocity of the water per second	16	5,333	10,666	,666	888,7	591,98	1332	878	10 to 1,47
Weight of the column of water pressing on the wheel	1bs.	5	11	,625	945	590,6	1375	859	Maximum by old theo∣ry
250	4	12	,5	1125	562,5	1500	750
The weight that holds the wheel in equilibrio	2000	2	14	,25	1531	382,7	1750	375
0	16	0	2000		2000

Art. 36. New Theory doubted.

BUT although I know that the velocity of the wheel, by this new theory is much nearer prac∣tice than the old, (tho' rather slow) yet I am led to doubt the theory, for the following reasons, viz.

When I consider that there are 16 cubic feet of water, equal 1000lbs. expended in a second, which multiplied by its perpendicular descent, 4 feet, pro∣duces the power 4000. The ratio of the power and effect by the old theory is as 10 to 1,47, and by the new as 4 to 1; as appears in the 9th co∣lumn of the scale; which is a proof that the old theory is a great error, and sufficient cause of doubt that there is yet some error in the new. And as the subject is of the greatest consequence in prac∣tical mechanics. Therefore I proceed, to endea∣vour to discover a true theory, and will shew my work in order, that if I establish a theory it may be the easier understood, if right; or detected, if wrong.

Attempts made to discover a true Theory.

In the search, I constructed Fig 18,pl. II. which represents a simple wheel with a rope passing over it and the weight P, of 100 lbs. at one end to act by its gravity, as a power to produce effects, by hoisting the weight w at the other end.

This seems to be on the principles of the lever, and overshot wheel; but with this exception, that the quantity of descending matter, acting as pow∣er, will still be the same, although the velocity will be accelerated, whereas in overshot wheels, the power on the wheel is inversely, as the velo∣city of the wheel.

Here we must consider,

• 1. That the perpendicular descent of power P,

• ... 〈◊〉〈◊〉 second,* 1.167 multiplied into its weight, shews the ••••wer.
• 2. That the weight w when multiplied into perpendicular ascent gives the effect.
• 3. That the natural velocity of the falling bo∣•• P, is 16 feet the first second, and the distance has to fall 16 feet.
• 4. That we do suppose that the weight w, or ••istance will occupy its proportional part of the velocity. That is if w be=1/2 P, the velocity ••••th which P will then descend, will be ½ 16=8 〈◊〉〈◊〉 per second.
• 5. If w be = P, there can be no velocity, consequently no effect; and if w = o then P will de∣••nd 16 feet in a second, but produces no effect; because, the power, although 1600 per second, applied to hoist nothing.

Upon these principles I have calculated the fol∣lowing scale.

A SCALE for determining the Maximum Charge, Velocity of 100lbs. descending by its Gravity.

Power applied on the wheel.	Natural velocity in feet per second, of the power falling freely.	Weight w hoisted, or the resistan•• in lbs.	Proportion of the velocity occupied by the resistance or weight w hoisted.	Proportion of velocity left in motion. which is the velocity of both power and weight.	Effect, which is the weight w multipli∣ed into its ascent per second.	Power, which is the power?, multi∣plied into its descent per second.	Ratio of the power and effect.
lb. 100	feet. 16	lb.	feet.	feet.	°	1600	10:0
		1	,16	15, 84	15,84	1584	10:,01
		10	1,6	14, 4	144	1440	10:1
		20	3,2	12, 8	256	1280	10:2
		30	4,8	11, 2	336	1120	10:3
		40	6,4	9, 6	384	960	10:4
		50	,8	8,	400	800	10:5	maximum by new th••••
		60	9,6	6, 4	384	640	10:6
		70	11,2	4, 8	336	480	10:7
		80	12,8	3, 2	256	320	10:8
		90	14,4	1, 6	144	160	10:9
		99	15, 84	,16	15,8	16	10:9,9
		100	16,	0,	0	0

By this scale it appears,* 1.168 that when the weight w is=50=½ P the power; the effect is at a max∣imum, viz. 400, as appears in the 6th column, when the velocity is half the natural velocity, viz. 8 feet per second; and then the ratio of the power to the effect is as 10 to 5, as appears in the 8th line.

By this scale it appears,* 1.169 that all engines that are moved by one constant power, which is equably accelerated in their velocity (if any such there be) as appears to be the case here must be charg∣ed with weight or resistance equal to half the moving power, in order to produce the greatest effect in a given time; but if time be not regard∣ed, then the greater the charge, so as to leave any velocity, the greater the effect, as appears by the 8th column. So that it appears, that an over∣shot wheel, if it be made immensely capacious, and to move very slow, may produce effects in the ratio of 9,9 to 10 of the power.

Art. 37. Scale of Experiments.

THE following scale of actual experiments were made to prove whether the resistance occu∣pies its proportion of the velocity, in order that I might judge whether the foregoing scale was foun∣ded on true principles; the experiments were not very accurately performed, but often repeated, and proved always nearly the same. See plate II, fig. 18.

A SCALE OF EXPERIMENTS.

Power applied on the wheel, in pounds.	Distance it had to descend, in feet.	Weight, in pounds, hoisted the whole distance.	Equal parts of time (each being 2 beats of a watch) in which the weight was hoisted the whole distance.	Distance, in feet, that the weight moved in 1 of the equal parts of time, found by dividing 40, the whole distance, by the number of equal parts of time taken up in the ascent.	Effect, found by multiplying the weight w into the velo∣city or distance ascended in one of those parts of time.	Power, found by multiplying the weight of P into its descent in one of those parts of time	Ratio of the power and effect.	Effect, supposing it to be as the square of the velocity of the weight, found by multiplying the weight into the square of the velocity.
7	40	7		0	0
		6	20	2×6	12	14	10:8,5	24
		5	15,5	2, 6×5	13	18,2	10:7,1	33, 8
		4	12	3, 33×4	13,32	23,31	10:5,7	44, 35
		3,5	10	4×3, 5	14	28	10:5,	max. new theor••
		3	9	4, 44×3	13,32	31,08	10:4,2	59, 14
		2	6, 5	6×2	12	42	10:2,8	72 maximum.
		1	6	6,6×1	6,6	46,2	10:1,4	33,56
		0	5	8	0	56

By this scale it appears,* 1.170 that when the power P falls freely without any load, it descends 40 feet in five equal parts of time, but when charged with 3,5lbs.=1/2 P, which was 7lbs. it then took up 10 of those parts of time to descend the same distance; which seems to shew, that the charge occupies its proportional part of the whole velocity, which was wanted to be known, and the maximum ap∣pear as in the last scale.* 1.171 It also shews, that the effect is not as the weight multiplied into the square of its ascending velocity, this being the measure of the effect that would be produced by the stroke on a non-elastic body.

This experiment partly confirmed me in what I have called the New Theory; but still doubt∣ing, and after I had formed the foregoing tables, I called on the late ingenius and worthy friend, William Waring, teacher in the Friends' Acade∣my, Philadelphia, for his assistance. He told me he had discovered the error in the old theory, and corrected it in a paper which he had laid be∣fore the Philosophical Society of Philadelphia, wherein he had shewn that the velocity of the undershot water-wheel, to produce a maximum effect, must be just one half the velocity of the water.

Art. 38. William Waring's Theory.

The following are extracts from the above mentioned paper,* 1.172 published in the third volume of the Transactions of the American Philosophical Society, held at Philadelphia, p. 144.

After his learned and modest introduction, in which he shews the necessity of correcting so great an error as the old theory, he begins with these words, viz.

"But,* 1.173 to come to the point, I would just pro∣mise these

DEFINITIONS.

If a stream of water impinge against a wheel is motion, there are three different velocities to be considered appertaining thereto, viz.

First,* 1.174 The absolute velocity of the water.

Second, The absolute velocity of the wheel.

Third, The relative velocity of the water to that of the wheel; i.e. the difference of the ab∣solute velocities, or the velocity with which the water overtakes or strikes the wheel.

Now the mistake consists in supposing the mo∣mentum, or force of the water against the wheel, to be in the duplicate ratio of the relative veloci∣ty: Whereas,

PROP. I.

The force of an invariable stream, impinging against a mill-wheel in motion, is in the simple proportion of the relative velocity.

For,* 1.175 if the relative velocity of a fluid against 〈◊〉〈◊〉 single plain, be varied, either by the motion 〈◊〉〈◊〉 the plain, or of the fluid from a given aperture, or both, then the number of particles acting on the plain, in a given time, and likewise the mo∣mentum of each particle being respectively as the relative velocity, the force, on both these ac∣counts, must be in the duplicate ratio of the rela∣tive velocity, agreeable to the common theory with respect to this single plain; but the number of these plains, ••wowrd•• parts of the wheel, acted on 〈◊〉〈◊〉 a given time, will be as the velocity of the wheel or inversely as the relative velocity; therefore the moving force of the wheel must be as the sim∣ple ratio of the relative velocity Q. E. D.

Or the proposition is manifest from this consi∣deration, that while the stream is invariable, whatever be the velocity of the wheel, the same number of particles, or quantity of the fluid, must strike it somewhere or other in a given time; con∣sequently, the variation of the force is only on account of the varied impingent velocity of the same body, occasioned by a change of motion in the wheel; that is, the momentum is as the rela∣tive velocity.

Now this true principle, substituted for the er∣roneous one in use, will bring the theory to agree remarkably with the notable experiments of the ingenius Smeaton, published in the Philosophical Transactions of the Royal Society of London, for the year 1751, vol. ••I; for which the honorary annual medal was adjudged by the society, and presented to the author by their president.

A•• instance or two of the importance of this correction, may be adduced, as follows:

PROP. II.

The velocity of a wheel, moved by the impact of a stream, must be half the velocity of the fluid, to produce the greatest effect possible.

V=the velocity, M=the momentum, of the fluid.

v=the velocity, P=the power, of the wheel.

Then V—v=their relative velocity, by defini∣tion 3^d.

And, as V:V—v::M:M / Vx√V—v= P, (Prop. I) whichXv=P, v=M / VxV / Vv—v²=a maximum; hence Vv—v²=a maximum and its fluction (v being a variable quantity=Vv—2vv=o; therefore=1/2V; that is, the velocity of the wheel=half that of the fluid, at the place of impact, when the effect is maximum, Q. E. D.

The usual theory gives v=1/3V,* 1.176 where the ••••∣ror is not less than one sixth of the true velo∣city!"

WM. WARING.

Philadelphia, 7th 9th mo. 1790.

Note,* 1.177 I omit quoting prop. III. as it is in alge∣bra, and refers to a figure, because I am not wr••∣ing so particularly to men of science, as to practi∣cal Mechanics.

Art. 39. Extract from a further paper, read in the phi∣losophical society, April 5th, 1793.

"Since the philosophical society were pleased favour my crude observations on the theory mills,* 1.178 with a publication in their transaction 〈◊〉〈◊〉 am apprehensive some part thereof may be ••••••••∣plied, it being therein demonstrated, that '〈◊〉〈◊〉 force of an invariable stream, impinging against mill-wheel in motion, is in the simple direct ratio of the relative velocity.' Some may suppose that the effect produced, should be in the 〈◊〉〈◊〉 proportion, and either fall into an error, or ••••••∣ing by experiment, the effect to be as the sq•••••• of the velocity, conclude the new theory to be 〈◊〉〈◊〉 well founded; I therefore wish there had been little added, to prevent such misapplication, ••••••••∣fore the society had been troubled with the ••••••∣ing of my paper on that subject: perhaps some∣thing like the following.

The maximum effect of an undershot wh•••• produced by a given quantity of water,* 1.179 in a ••••∣en time, is in the duplicate ratio, of the velocity of the water; for the effect must be as the ime∣tus acting on the wheel, multiplied into the ve∣locity thereof: but this impetus is demonstrate to be simply as the relative velocity, prop

and the velocity of the wheel,* 1.180 producing a max∣imum, being half of the water by prop. II. is likewise as the velocity of the water; hence the power acting on the wheel, multiplied into the velocity of the wheel, or the effect produc∣ed, must be in the duplicate ratio of the velocity of the water. Q. E. D.

COROL. Hence the effect of a given quantity of water, in a given time, will be as the height of the head, because this height is as the square of the velocity. This also agrees with experi∣ment.

If the force, acting on the wheel, were in duplicate ratio of the water's velocity, as usual∣ly asserted, then the effect would be as the cube thereof, when the quantity of water and time are given, which is contrary to the result of experi∣ment."

Art. 40. Waring's Theory doubted.

From the time I first called on William Waring,* 1.181 until I read his publication on the subject (after his death) I had rested partly satisfied, with the new theory, as I have called it, with respect to the velocity of the wheel, at least; but finding that he had not determined the charge, as well as the velocity, by which we might have compared the ratio of the power and the effect produced,* 1.182 and that he had assigned reasons somewhat different for the error; and having found the motion to be rather too slow to agree with practice, I began to suspect the whole, and resumed the search for a true theo∣ry, thinking that perhaps no person had ever yet considered every thing that affects the calcula∣tion, I therefore premised the following

POSTULATES.* 1.183

1. A given quantity of perfect elastic or 〈◊〉〈◊〉 matter, impinging on a fixed obstacle, its e••••∣tive force is as the squares of its different vel••∣ties, although its instant force may be as its ve••∣ties simply, by annotation, art. 8.* 1.184

2. An equal quantity of elastic matter, imp••∣ing on a fixt obstacle with a double velocity, re∣duces a quadruple effect, art. 8; i.e. their 〈◊〉〈◊〉 are as the squares of their velocities Conse∣quently,

3. A double quantity of said matter, impin•••• with a double velocity, produces an octuble 〈◊〉〈◊〉 or their effects are as the cubes of their velocity art. 47 & 67.

4. If the impinging matter be non-elastic, as fluids, then the instant force will be but in each case, but the ratio will be the same in case.

5. A double velocity, through a given ••••∣ture, gives a double quantity to strike the ••∣cle or wheel, therefore the effects, by post•••••• 3, will be as the cubes of the velocity. See 〈◊〉〈◊〉 47.

6. But a double relative velocity cannot incr•• the quantity that is to act on the wheel, there∣fore the effect can only be as the square of the ve∣locity, by postulate 2.

7. Although the instant force and effect striking fluids, on fixt obstacles, are only as 〈◊〉〈◊〉 simple velocities, yet their effects, on mo•••• wheels, are as the squares of their velocities; cause, 1, a double striking velocity gives a do•• instant force, which bears a double load on wheel; and 2, a double velocity moves the 〈◊〉〈◊〉

a double distance in an equal time,* 1.185 and a double load moved a double distance, is a quadruple ef∣fect.

Art: 41. Search for a true Theory, commenced on a new Plan.

IT appears, that we have applied wrong prin∣ciples in our search after a true theory of the max∣imum velocity and load of undershot water-wheels, or other engines moved by a constant power, that does not increase or decrease in quantity on the engine, as on an overshot water-wheel, as the ve∣locity varies.

Let us suppose water to issue from under a head of 16 feet, on an undershot water-wheel; then, if the wheel moves freely with the water, its velo∣city will be 32, 4 feet per second; but will bear no load.

Again, suppose we load it, so as to reduce its motion to be equal the velocity of water spouting from under 15 feet; it appears evident that the load will then be just equal to that 1 foot of the head, the velocity of which is checked; and this load multiplied into the velocity of the wheel, viz. 31, 34×1=31,34 for the effect.

This appears to be the true principle, from which we must seek the maximum velocity and load, for such engines as are moved by one constant power; and on this principle I have calculated the following scale.

A SCALE FOR DETERMINING THE TRUE MAXIMUM VELOCITY AND LOAD FOR UNDERSHOT WHEELS.

Total head of water in action.	Head of water 〈◊〉〈◊〉 unbalanced to give motion to the wheel.	Velocity of the wheel in feet per second, being 〈◊〉〈◊〉 the veloci∣ty of the water from under the head left unbalanced.	Load of the wheel being equal that part of the total head, the motion of which is checked.	Effect per second, being the ve∣locity of the wheel, multipli∣ed by the lo••d.
feet.	feet.	feet.			Maximum motion 〈◊〉〈◊〉 load.
16	16	32,4	0	0
	15	31,34	1,	3••,34
	14	30,2	2,	60,4
	12	28,	4	112
	10	25,54	6	153,24
	8	22,8	8	182,4
	7	21,43	9	192,87
	6	19,84	10	198,4
	5,66	19,27	10,33	198,95
	5,33	18,71	10,66	199,44
	5	18,	11	198
	4	16,2	12	194,4
	3	14	13	172
	2	11,4	14	159,6
	1	8,1	15	120,
	0	0	16	0

In this scale,* 1.186 let us suppose the aperture of the gate to be a square foot; then the greatest load that will balance the head, will be 16 cubic feet of water, and the different loads will be shewn in cubic feet of water.

And then it appears, by this scale, that when the wheel is loaded with 10,66 cubic feet of wa∣ter, just 2-3 of the greatest load, its velocity will be 18,71 feet per second, just ,577 parts of the velo∣city of the water, and the effect produced is at a maximum, or the greatest possible, viz. 199,44.

To make this more plain,* 1.187 let us suppose A B, plate II, fig. 19, to be a fall of water 16 feet, which we wish to apply to produce the greatest effect possible, by hoisting water on its side oppo∣site to the power applied; first, on the undershot principle, where the water acts by its impulse on∣ly. Now let us suppose the water to strike the wheel at I, then, if we let the wheel move free∣ly without any load, it will move with the velo∣city of the water, viz. 32,4 feet per second, but will produce no effect, if the water issue at C; al∣though there be 32,4 cubic feet of water expend∣ed, under 16 feet perpendicular descent. Let the weight of a cubic foot of water be represented by unity or 1, for ease in counting; then 32,4×16 will shew the power expended, per second, viz. 518,4; and the water it hoists multiplied into its perpendicular ascent, or height hoisted, will shew the effect. Then, in order to obtain effect from the power, we load the wheel; the simplest way of doing which, is, to cause the tube of water C D to act on the back of the bucket at I; then, if CD be equal to AB, the wheel will be held in equili∣brio; this is the greatest load, and the whole of the fall AB is balanced, and no part left to give the wheel velocity; therefore the effect=0. But if we make C D=12 feet of A B, then from 4 to A=4 feet, is left unbalanced, to give velocity to the wheel, which is now loaded with 12 feet, and

exactly balanced by 12 on the other side,* 1.188 and per∣fectly free to move either way by the least for 〈◊〉〈◊〉 applied: Therefore it is evident, that the 〈◊〉〈◊〉 pressure or force of 4 feet of A B will act to 〈◊〉〈◊〉 velocity to the wheel, and, as there is no re••••••∣ance to oppose the pressure of these 4 feet, 〈◊〉〈◊〉 velocity will be the same that water will 〈◊〉〈◊〉 from under 4 feet head, viz. 16,2 feet per second which is shewn by the horizontal line 4=16 〈◊〉〈◊〉 and the perpendicular line 12=12 represents 〈◊〉〈◊〉 load of the wheel; the rectangle or product of the 〈◊〉〈◊〉 two lines, form a parallelogram, the area of 〈◊〉〈◊〉 is a true representation of the effect, viz. the 〈◊〉〈◊〉 12 multiplied into 16,2 the distance it moves 〈◊〉〈◊〉 second=194,4, the effect. In like manner we 〈◊〉〈◊〉 try the effect of different loads; the less the 〈◊〉〈◊〉 the greater will be the velocity. The horizon lines all shew the velocity of the wheel, produ•••• by the respective heads left unbalanced, and the per∣pendicular lines shew the load on the wheel; 〈◊〉〈◊〉 we find that when the load is 10,66=⅔ 16,〈◊〉〈◊〉 load at equilibrio, the velocity of the wheel 〈◊〉〈◊〉 be 18,71 feet per second; which is 577/1000 parts, 〈◊〉〈◊〉 a little less than 6 tenths, or 2/4 the velocity the water,* 1.189 and the effect is 199,44, the maximum or greatest possible; and if the aperture of 〈◊〉〈◊〉 gate be 1 foot, the quantity will be 18,71 〈◊〉〈◊〉 feet per second. The power being 18,71 〈◊〉〈◊〉 feet expended per second, multiplied by 16 〈◊〉〈◊〉 the perpendicular descent, produces 299,36, 〈◊〉〈◊〉 the ratio of the power and effect being 10 to 6 5/〈◊〉〈◊〉 as 3: 2; but this is supposing none of the 〈◊〉〈◊〉 lost by non-elasticity.

This may appear plainer, if we suppose the wa∣ter to descend the tube A B, and, by its pressure to raise the water in the tube C D; now it is ••••••∣dent, that if we raise the water to D, we 〈◊〉〈◊〉 no velocity, therefore effect=o. Then again, we open the gate at C, we have 32,4 feet per se∣cond velocity, but because we do not hoist 〈◊〉〈◊〉

water any distance,* 1.190 effect=o. Therefore the maximum is somewhere between C and D. Then suppose we open gates of 1 foot area, at different heights, the velocity will shew the quantity of cubic feet raised; which multiplied by the per∣pendicular height of the gate from C, or height raised, gives the effect as before, and the maxi∣mum as before. But here we must consider, that in both these cases, the water acts as a perfect definite quantity, which will produce effects equal to elastic bodies, or equal to its gravity (see art.59) which is impracticable in practice: Whereas when it acts by percussion only, it communicates only half of its original force, on account of its non-elasticity, the other half being spent in splashing about (see art. 8); therefore the true effect will be 33/100,(a little more than 1-3) of the moving pow∣er; because nearly 1-3 is lost to obtain velocity, and half of the remaining 2-3 is lost by non-elasti∣city. These are the reasons, why the effects pro∣duced by an undershot wheel is only half of that produced by an overshot wheel, the perpendicu∣lar descent and quantity of water being equal. And this agrees with Smeaton's experiments (see art.68); but if we suppose the velocity of the wheel to be 1-3 that of the water-10,8, and the load to be 4-9 of 16, the greatest load at equilibrio; which is-7, 111, as by old theory, then the effect will be 10,8×4-9 of 16-76,79 for the effect, which is quite too little, the moving power be∣ing 32,4 cubic feet of water, multiplied by 16 feet descent-518,4, the effect by this theory be∣ing less than , 15/100 of the power, about half equal to the effect by experiment, which effect is set on the outside of the dotted circle in the fig.(19.) The dotted lines join the corner of the parallelo∣grams, formed by the lines that represent the loads and velocities, in each experiment or sup∣position, the areas of which truly represent the effect, and the dotted line A a d x, meeting the

perpendicular line x E in the point x,* 1.191 formi•••• the parallelogram ABCx, truly represents the power=518,4.

Again, if we suppose the wheel to move w•• half the velocity of the water, viz. 16,2 feet 〈◊〉〈◊〉 second, and be loaded with half the greatest 〈◊〉〈◊〉=8, according to Waring's theory, then the ef∣fect will be 16,2×8=129,6 for the effect, abo•••• 23/100 of the power, which is still less than by ex∣periment. All this seems to confirm the maxi∣mum brought out on the new principles.

But, if we suppose according to the new prin∣ciple, that, when the wheel moves with the ve∣locity of 16,2 feet per second, which is the velo∣city of a 4 feet head, that it will then bear as load the remaining 12 feet, then the effect 〈◊〉〈◊〉 be 16,2×12=194,4, which nearly agrees wi•••• practice: but as most mills in practice move ••••∣ter, rather than slower, than what I call the 〈◊〉〈◊〉 maximum, shews it to be nearest the truth, 〈◊〉〈◊〉 true maximum velocity being, 577 of the veloci∣ty of the water, and the mills in practice movi•• with 2-3, and generally quicker.* 1.192

This scale also establishes a true maximum charge for an overshot wheel,* 1.193 when the case is such,* 1.194 that the power or quantity of water on the wheel at once, is always the same, even although the velocity vary, which would be the case, if the buckets were kept always full: for, suppose the water to be shot into the wheel at a, and by its gravity to raise the whole water again on the opposite side; then, as soon as the water rises in the wheel to d, it is evident that the wheel will stop, and effect=o; therefore we must let the water out of the wheel, before it rises to 〈◊〉〈◊〉, which will be in effect to loose part of the power to obtain velocity. If the buckets both descending and ascending, carry a column of wa∣ter 1 foot square, then the velocity of the wheel will shew the quantity hoisted as before, which, multiplied by the perpendicular ascent, shews the effect, and the quantity expended, multiplied by the perpendicular descent shews the power; and we find, that when the wheel is loaded with 2-3 of the power, the effect will be at a maximum, i. e. the whole of the water is hoisted, 2-3 of its whole descent, or 2-3 of the water the whole of the descent, therefore the ratio of the power to the effect is as 3 to 2, double to the effect of an undershot wheel: but this is, supposing the quan∣tity in the buckets to be always the same; where∣••••, in overshot wheels, the quantity in the buck∣ets is universally as the velocity of the wheel, i.e. the slower the motion of the wheel, the greater the quantity in the buckets, and the greater the velocity the less the quantity: but, ••gain, as we are obliged to let the overshot wheel love with a considerable velocity, in order to obtain a steady, regular motion to the mill, we will find this charge to be always nearly right; hence I deduce the following theory.

THEORY.* 1.195

This scale seems to have shewn,* 1.196

1. That when an undershot mill moves 〈◊〉〈◊〉 ,577 or nearly ,6 of the velocity of the wa•••• it will then bear a charge, equal to 2-3 of the 〈◊〉〈◊〉 that will hold the wheel in equilibrio, and 〈◊〉〈◊〉 the effect will be at a maximum. The ratio 〈◊〉〈◊〉 the power to the effect will be as 3 to 1, nearly.

2. That, when an overshot wheel is charg•• with 2-3 of the weight of the water acting up the wheel, then the effect will be at a maximum i. e. the greatest effect, that can be produced said power in a given time, and the ratio of the power to the effect will be as 3 to 2, nearly.

3. That 1-3 of the power is necessarily lost obtain velocity, or to overcome the visinertia the matter, and this will hold true with all 〈◊〉〈◊〉 chinery that requires velocity as well as pow••••. This I believe to be the true theory of wat•••• mills, for the following reasons, viz.

1. The theory is deduced from original reas••∣ing, without depending much on calculation.

2. It agrees better than any other theory with the ingenious Smeaton's experiments.

3. It agrees best with real practice, from 〈◊〉〈◊〉 best of my information.

Yet I do not wish any person to receive it ••••∣plicitly, without first informing himself, wheth•• it be well founded, and agrees with practice•• for this reason I have quoted said Smeaton's ex∣periments at full length, in this work, that reader may compare them with the theory.

Art. 42.

Theorem for finding the Maximum Charge for 〈◊〉〈◊〉 shot Wheels.

As the square of the velocity of the water 〈◊〉〈◊〉 wheel empty, is to the height of the 〈◊〉〈◊〉

or pressure,* 1.197 which produced that velocity, so is the square of the velocity of the wheel, to the head, pressure, or force, which will produce the velocity; and this pressure, deducted from the whole pressure or force, will leave the load moved by the wheel, on its periphery or verge, which load, multiplied by the velocity of the wheel, shews the effect.

PROBLEM.

Let V-32,4, the velocity of the water or wheel, P-16, the pressure, force or load, at equili∣brio,
v=the velocity of the wheel, supposed to be 16,2 feet per second,
p-the pressure, force or head, to produce said velocity,
l=the load on the wheel,
Then, to find I, the load, we must first find p;
Then, by
Theorem VV:P::vv:p,
And P-p=1
VVp=vvP
P=vvP / VV=4
l=P-p=12, the load.
Which, in words at length, is, The square of the velocity of the wheel, multiplied by the whole force, pressure, or head of the water, and divided by the square of the velocity of the wa∣ter, quotes the pressure, force or head of water, ••hat is left unbalanced by the load, to produce the velocity of the wheel, which pressure, force or head, subtracted from the whole pressure, force 〈◊〉〈◊〉 head, leaves the load that is on the wheel.

Art. 42. Theorem for finding the Velocity of the Wheel, when we have the Velocity of the Water, Load at Equi∣librio, and Load on the Wheel given.

As the square root of the whole pressure, force or load at equilibrio, is to the velocity of the water, so is the square root of the difference, be∣tween the load on the wheel, and the load at equilibrio, to the velocity of the wheel.

PROBLEM.

Let V=velocity of the water-32,4,
P=pressure, force, head, or load at equili∣brio=16,
l=the load on the wheel, suppose 12,
v=velocity of the wheel,
Then by the
Theorem √P:V::√P—l:v
And √pXv=V√p—l
v=V√p—l / √P=16,2. The velocity of the wheel.
That is, in words at length, the velocity of the water 32,4, multiplied by the square root of th•• difference, between the load on the wheel, 〈◊〉〈◊〉 and the load at equilibrio 16-2-64,8, divided 〈◊〉〈◊〉 the square root of the load at equilibrio, quote•• 16,2, the velocity of the wheel.

Now, if we seek for the maximum, by eith•••• of these theorems, it will be found as in the 〈◊〉〈◊〉 fig. 19.

Perhaps here may now appear the true 〈◊〉〈◊〉 of the error of the old theory, art. 35, by 〈◊〉〈◊〉 posing the load on the wheel, to be as the squ•••• of the relative velocity, of the water and when••

And of the error of what I have called the 〈◊〉〈◊〉 theory, by supposing the load to be in the simp••

ratio of the relative or striking velocity of the water,* 1.198 art. 38; whereas it is to be found by nei∣ther of these proportions.

Neither the old nor new theories agree with practice; therefore we may suspect they are founded on error.

But if, what I call the true theory, should con∣tinue to agree with practice, the practitioner need not care on what it is founded.

Art. 43. Of the Maximum velocity for Overshot Wheels, or those that are moved by the weight of the Wa∣ter.

BEFORE I dismiss the subject of maximums, I think it best to consider, whether this doctrine will apply to the motion of the overshot wheels. It seems to be the general opinion of those, who consider the matter, that it will not; but, that the slower the wheel moves, provided it be ca∣pacious enough to hold all the water, without losing any until it be delivered at the bottom of the wheel, the greater will be the effect, which appears to be the case in theory (see art. 36); but how far this theory will hold good in practice, is to be considered. Having met with the ingeni∣ous James Smeaton's experiments, where he shews, that, when the circumference of his lit∣tle wheel, of 24 inches diameter, (head 6 inches) moved with about 3,1 feet per second (although the greatest effect was diminished about 1/20 of the whole) he obtained the best effect, with a steady, regular motion. Hence he concludes about 3 feet to be the best velocity for the circumference of overshot mills. See art. 68. I undertook to compare this theory of his, with the best mills

in practice,* 1.199 and, finding that those of about 17 feet diameter, generally moved about 9 feet per second,* 1.200 being treble the velocity assigned by Smea∣ton, I began to doubt the theory, which led 〈◊〉〈◊〉 to inquire into the principle, that moves an over∣shot wheel, and this I found to be a body descend∣ing by its gravity, and subject to all the laws of falling bodies, (art. 9.) or of bodies descending in∣clined plains,* 1.201 and curved surfaces (art. 10, 11,) the motion being equably accelerated in the who•••• of its descent, its velocity being as the square ro•••• of the distance descended through, and that the diameter of the wheel was distance the water descended through.* 1.202 From thence I concluded that the velocity of the circumference of the overshot wheels, was, as the square root of their diameters, and of the distance the water has 〈◊〉〈◊〉 descend, if it be a breast of pitch-back wheel•• then, taking Smeaton's experiments, with 〈◊〉〈◊〉 wheel of 2 feet diameter, for a foundation, 〈◊〉〈◊〉 say, As the square root of the diameter of Smea∣ton's wheel, is to its maximum velocity, so is the square root of the diameter of any other wheel to its maximum velocity. Upon these principles I have calculated the following table;* 1.203 and, hav∣ing compared it with at least 50 mills in practice found it to agree so nearly with all the best con∣structed ones, that I have reason to believe it is founded on true principles.

If an overshot wheel moves freely without re∣sistance,* 1.204 it will acquire a mean velocity, between that of the water coming on the wheel, and the greatest velocity it would acquire, by falling free∣ly through its whole descent: therefore this mean velocity will be greater, than the velocity of the water coming on the wheel; consequent∣ly the backs of the buckets will overtake the wa∣ter, and drive a great part of it out of the wheel. But, the velocity of the water being accelerated by its gravity, overtakes the wheel, perhaps ha••••

way down,* 1.205 and presses on the buckets, until it leaves the wheel:* 1.206 therefore the water presses harder upon the buckets in the lower, than in the upper quarter of the wheel. Hence appears the reason why some wheels cast their water, which is always the case, when the head is not sufficient to give it velocity enough to enter the buckets. But this depends also much on the po∣sition of the buckets, and direction of the shute into them. It, however, appears evident that the head of water above the wheel, should be nicely adjusted, to suit the velocity of the wheel. Here we may consider, that the head above the wheel acts by percussion, or on the same principles with the undershot wheel, and, as we have shewn (art. 41) that the undershot wheel should move with nearly 2-3 of the velocity of the water, it appears, that we should allow a head over the wheel, that will give such velocity to the water, as will be to that of the wheel as 3 to 2. Thus the whole descent of the water of a mill-seat should be nicely divided,* 1.207 between head and fall, to suit each other, in order to obtain the best effect, and a steady-moving mill. First find the velocity that the wheel will move with, by the weight of the water, for any diameter you may suppose you will take for the wheel, and divide said velocity into two parts; then try if your head is such, as will cause the water to come on with a velocity of 3 such parts, mak∣ing due allowances for the friction of the water, according to the aperture. See art. 55. Then, if the buckets and direction of the shute be right, the wheel will receive the water well, and move to the best advantage, keeping a steady, regular motion when at work, loaded or charged with a resistance equal to 2-3 of its power, (art. 41. 42.)

A TABLE OF VELOCITIES OF THE CIRCUMFERENCE OF UNDERSHOT WHEELS, Suitable to their Diameters, or rather to the Fall, after the Water strikes the Wheel; and of the head of Water above the Wheel, suitable to said Velocities, also of the Number of Revolutions the Wheel will Per∣form in a Minute, when rightly charged.

Diameter of the wheel in feet.	Velocity of its circumference in feet and parts, per second.	Head of water above the wheel to give velocity as 3 to 2 of the wheel, in feet and parts.	Additional head to overcome the friction of the aperture, by conjecture only.	Total head of water.	No. of revolutions of the wheel per minute.
2	3,1
3	3,78
4	4,38
5	4,88
6	5,36
7	5,8
8	6,19
9	6,57	1,41	,1	1,51	14,3
10	6,92	1,64	,1	1,74	13,
11	7,24	1,84	,1	1,94	12,6
12	7,57	2,	,2	2,2	12
13	7,86	2,17	,3	2,47	11,54
14	8,19	2,34	,4	2,74	11,17
15	8,47	2,49	,5	2,99	10,78
16	8,76	2,68	,6	3,28	10,4
17	9,	2,8	,7	3,5	10,1
18	9,28	3,	,8	3, 8	9,8
19	9,5	3,13	,9	4,03	9,54
20	9,78	3,34	1,	4,34	9,3
21	10,	3,49	1,05	4,54	9,1
22	10,28	3,76	1,1	4,86	8,9
23	10,5	3,84	1,15	4,99	8,7
24	10,7	4,07	1,2	5,27	8,5
25	10,95	4,2	1,25	5,45	8,3
26	11,16	4,27	1,3	5,57	8,19
27	11,36	4,42	1,35	5,77	8,03
28	11,54	4,56	3,4	5,96	7,93
29	11,78	4,7	1,45	6,15	7,75
30	11,99	4,9	1,5	6,4	7,63

Art. 44. Application of the doctrine of maxi∣mums.

THIS doctrine of maximums is very interest∣ing, and is to be met with in many occurrences through life.

1. It has been shewn, that there is a maximum load and velocity for all engines, to suit the pow∣er and velocity of the moving power.

2. There is also a maximum size, velocity and feed for mill-stones, to suit the power; and velo∣city for rolling-screens, and bolting-reels, by which the greatest work can be done in the best manner, in a given time.

3. A maximum degree of perfection and close∣ness, with which grain is to be manufactured in∣to flour, so as to yield the greatest profit by the mill in a day or week, and this maximum is con∣tinually changing with the prices in the market, so that what would be the greatest profit at one time, will sink money at another. See art. 113.

4. A maximum weight for mallets, axes, sledges, &c. according to the strength of those that use them.

A true attention to the principles of maxi∣mums, will prevent us from running into many errors.

CHAPTER XII. HYDRAULICS.

UNDER the head of Hydraulics we shall on∣ly consider such parts of this science, as im∣mediately relate to our purpose, viz. such as m••••∣lead to the better understanding of the principle and powers of water, acting on mill-wheels, 〈◊〉〈◊〉 conveying water to them.

Art. 45. Of Spouting Fluids.

SPOUTING Fluids observe the following laws:

1. Their velocities and powers, under equal pressures, or equal perpendicular heights, and equal apertures, are equal in all cases.* 1.208

2. Their velocities under different pressures or perpendicular heights, are as the square roots of those pressures or heights; and their perpendicu∣lar

heights or pressures,* 1.209 are as the squares of their velocities.* 1.210

3. Their quantities expended through equal apertures, in equal times, under equal pressures, are as their velocities simply.† 1.211

4. Their pressures or heights being the same, their effects are as their quantities expended.‡ 1.212

5. Their quantities expended being the same, their effects are as their pressure, or height of their head directly.‖ 1.213

6. Their instant forces with equal apertures, are as the squares of their velocities, or as the height of their heads directly.

7. Their effects are as their quantities, multi∣plied into the squares of their velocities.sect 1.214

8. Therefore their effects or powers with 〈◊〉〈◊〉* 1.219

appertures,* 1.220 are as the cubes of their velocities.* 1.221

ASCALE founded on the 3rd, 6th and 7th laws, shewing the effects of striking Fluids, with different Velocities.

Aperture.	Multiplied by the	Velocity.	Is equal the	Quantity expended.	Which multiplied by the	Square of the velo∣city,	Is equal the	Effect.	Which is as the	Cube of the velo∣city.
1	X	1	=	1	X	1	=	1	as	1
1	X	2	=	2	X	4	=	8	as	8
1	X	3	=	3	X	9	=	27	as	27
1	X	4	=	4	X	16	=	64	as	64

9. Their velocity under any head is equal to the velocity that a heavy body would acquire, in falling from the same height.† 1.222

10. Their velocity is such under any head or height, as will pass over a distance equal to twice the height of the head, in a horizontal direction, in the time that a heavy body falls the distance of the height of the head.

11. Their action and reaction are equal.‡ 1.223

12. They being non-elastic, communicate only half their real force by impulse, in striking obsta∣cles;

but by their gravity produce effects,* 1.224 equal to elastic or solid bodies.* 1.225

Art. 47. Application of the Laws of Motion to Undershot Wheels.

To give a short and comprehensive detail of the ideas, I have collected from the different authors, and from the result of my own reasoning on the laws of motion, and of spouting fluids, as they ap∣ply. to move undershot mills, I constructed fig. 44 plate V.

Let us suppose two large wheels, one of 1•• feet, and the other of 24 feet radius, then the cir∣cumference of the largest, will be double that 〈◊〉〈◊〉 the smallest: and let A 16, and C 16, be two 〈◊〉〈◊〉 stocks of water, of 16 feet head, each.

1. Then, if we open a gate of 1 square foot at, 〈◊〉〈◊〉 to issue from the penstock A 16,* 1.226 and impinge 〈◊〉〈◊〉 the small wheel at I, the water being pressed by 4 feet head, will move 16 feet per second.(we omit fractions) The instant pressure or force on that gate, being 4 cubic feet of water, it will require a resistance of 4 cubic feet of water, from the head C 16 to stop it, and hold it in equilibrio (but we suppose the water cannot escape unless the wheel moves, so that no force be lost by non-elasticity) Here equal quantities of matter, with equal velocities, have their momentums equal.

2. Again, suppose we open a gate of 1 square foot at A 16 under 16 feet head, it will strike the large wheel at k, with velocity 32, its instant force or pressure being 16 cubic feet of water, it will require 16 cubic feet resistance, from the head C 16, to stop or balance it. In this case the

pressure or instant force is quadruple,* 1.227 and so is the resistance, but the velocity only double, to the first case. In these two cases the forces and resistances being equal quantities, with equal ve∣locities, their momentums are equal.

3. Again, suppose the head C 16 to be raised to E, 16 feet above 4, and a gate drawn ¼ of a square foot, then the instant pressure on the float I of the small wheel, will be 4 cubic feet, pressing on ¼ of a square foot, and will exactly balance 4 cu∣bic feet, pressing on 1 square foot, from the head A 16; and the wheel will be in equilibrio, (sup∣posing the water cannot escape until the wheel moves as before) although the one has power of velocity 32, and the other only 16 feet per se∣cond. Their loads at equilibrio are equal, conse∣quently their loads at a maximum velocity and charge, will be equal, but their velocities differ∣ent.

Then, to try their effects, suppose, first, the wheel to move by the 4 feet head, its maximum velocity to be half the velocity of the water, which is 16, and its maximum load to be half its greatest load, which is 4, by Waring's theory; then the velocity 16|2 × by the load 4|2=16, the effect of the 4 feet head, with 16 cubic feet expended; because the velocity of the water is 16, and the gate 1 foot.

Again, suppose it to move by the 16 feet head and gate of ¼ of a foot; then the velocity 32|2X by the load 4|2=32, the effect, with but 8 cu∣bic feet expended, because the velocity of the water is 32, and the gate but ¼ of a foot.

In this case the instant forces are equal, each being 4; but the one moving a body only 〈◊〉〈◊〉 as heavy as the other, moves with velocity 32, and produces effect 32, while the other, moving with velocity 16, produces effect 16. A double velo∣city, with equal instant pressure, produces a dou∣ble effect, which seems to be according to the Newtonian theory. And in this sense the

momentums of bodies in motion,* 1.228 are as th•••• quantities, multiplied into their simple velocities, and this I call the instant momentums.

But when we consider, that in the above case, it was the quantity of matter put in motion, 〈◊〉〈◊〉 water expended, that produced the effect, we find that the quantity 16, with velocity 16, pro∣duced effect 16; while qu. 8, with velocity 32 produced effect 32. Here the effects are as the•••• quantities, multiplied into the squares of their velocities; and this I call the effective momen∣tums.

Again, if the quantity expended under each head, had been equal, their effects would have been 16 and 64, which is as the squares of their velocities, 16 and 32.

4. Again, suppose both wheels to be on one shaft, and let a gate of ½ of a square foot be drawn at 16 C, to strike the wheel at k, the head being 16 feet, the instant pressure on the gate will be 2 cu∣bic feet of water, which is half of the 4 feet head with 1 foot gate, from A 4 striking at I; but the 16 feet head, with instant pressure 2, acting 〈◊〉〈◊〉 the great wheel, will balance 4 feet on the small one, because the lever is of double length, and the wheels will be in equilibrio. Then, by Wa∣ring's theory, the greatest load of the 16 feet head being 2, its load at a maximum will be 4 and the velocity of the water being 32, the max∣imum velocity of the wheel will be 16. Now the velocity 16×1=16, the effect of the 16 feet head, and gate of 1/8 of a foot. The greatest load of the 4 feet head being 4, its maximum load 〈◊〉〈◊〉 the velocity of the water 16, and the velocity of the wheel 8, now 8×2=16, the effect. Here the effects are equal: and here again the effects are as the instant pressures, multiplied into their simple velocities; and the resistances that would instant∣ly stop them, must be equal thereto, in the same ratio.

But when we consider,* 1.229 that in this case, the 4 feet head expended 16 cubic feet of water, with velocity 16, and produced effect 16; while the 16 feet head expended only 4 cubic feet of water, with velocity 32, and produced effect 16, we find, that the effects are as their quantities, multiplied into the squares of their velocities.

And when we consider, that the gate of ⅓ of a square foot, with velocity 32, produced effects equal to the gate of 1 square foot, with velocity 16, it is evident, that if we make the gates equal, the effects will be as 8 to 1; that is, the effects of spouting fluids, with equal apertures, are as the cubes of their velocities; because, their instant forces are as the squares of their velocities by 6th law.

Art. 48. The Hydrostatic Paradox.

THE pressure of fluids is as their perpendicu∣lar heights, without any regard to their quanti∣ty: and their pressure upwards is equal to their pressure downwards. In short, their pressure is every way equal, at any equal distance from their surface.* 1.230

In a vessel of a cubic form,* 1.234 whose sides and bot∣tom are equal, the pressure on each side is just half the pressure on the bottom; therefore the pressure on the bottom and sides, is equal to 〈◊〉〈◊〉 times its pressure on the bottom.* 1.235

And in this sense fluids may be said to act with three times the force of solids. Solids act by gravity only, but fluids by gravity and pressure jointly. Solids act with a force proportional to their quantity of matter; but fluids act with 〈◊〉〈◊〉 pressure proportional to their altitude only.

Art. 50.

The weight of a cubic foot of water is found by experience, to be 1000 ounces avoirdupoise, or 62,5lb. On these principles is founded the following theorem.

THEOREM I.

The area of the base or bottom,* 1.236 or any part of a vessel, of whatever form, multiplied by the greatest perpendicular height of any part of the fluid, above the centre of the base or bottom,

whatever be its position with the horizon,* 1.237 pro∣duces the pressure on the bottom of said vessel.

PROBLEM. I.

Given, the length of the sides of the cubic vessel (fig. 22. pl. III.) 6 feet, required the pres∣sure on the bottom when full of water.

Then 6×6=36 feet, the area, multiplied by 6, the altitude,=216, the quantity, or cubic feet of water, pressing on the bottom; which multiplied by 62,5=13500lb. the whole pressure on the bot∣tom.

PROBLEM. II.

Given, the height of a penstock of water 31,5 feet, and its dimensions at bottom 3 by 3 feet, inside, required the pressure on 3 feet high of one of its sides.

Then,* 1.238 3×3=9 the area, multiplied by 30 feet, the perpendicular height or head above its centre=270 cubic feet of water pressing, which ×62,5=16875lb. the pressure on one yard square, which shews what great strength is required, to hold the water under such great heads.

Art. 51. Rule for finding the Velocity of spouting Water.

BY experiments it has been found, that water will spout from under a 4 feet head, with a velocity equal to 16,2 feet per second, and from under 16 feet head, with a velocity equal to 32,4 feet per second.

On these experiments, and the 2nd law of spout∣ing fluids, is founded the following theorem, or

general rule for finding the velocity of water un∣der any given head.* 1.239

THEOREM II.

As the square root of a 4 feet head (=2) is to 16,2 feet,* 1.240 the velocity of the water, spouting un∣der it, so is the square root of any other head, to the velocity of the water spouting under it.

PROBLEM. I.

Given, the head of water 16 feet, required the velocity of water spouting under it.

Then, as the square root of 4(=2) is to 16,2, so is the square root of 16,(=4) to 32,4, the velocity of the water under the 16 feet head.

PROBLEM II.

Given, a head of water of 11 feet, required the velocity of water spouting under it.

Then, as 2:16, 2::3, 316:26,73 feet per second, the velocity required.

Art. 52.

FROM the laws of spouting fluids, theorems I. and II. the theory for finding the maximum charge and velocity of undershot wheels, (art. 42) and the principle of non-elasticity, is deduc∣ed the following theorem for finding the effect of any gate, drawn under any given head, upon an undershot water-wheel.

THEOREM III.* 1.241

Find,* 1.242 by theorem I. (art. 50) the instantane∣ous pressure of the water, which is the load at equilibrio, and ⅔ thereof is the maximum load, which, multiplied by ,577 of the velocity of the water, under the given head, (found by theo. II.) produces the effect.

PROBLEM.

Given, the head 16 feet, gate 4 feet wide, 25 of a foot drawn, required the effect on an un∣dershot wheel, per second. The measure of the effect to be the quantity, multiplied into its dis∣tance moved, (velocity) or into its perpendicular ascent.

Then, by theorem I. (art. 50) 4X,25=1 square foot, the area of the gate ×16=16 the cubic feet pressing; but, for the sake of round numbers, we call each cubic foot 1, and although 32,4 cubic feet strike the wheel per second, yet, on ac∣count of non-elasticity, only 16 cubic feet is the load at equilibrio, and ⅔ of 16 is 10,666, the max∣imum load.

Then, by theorem II. the velocity is 32, 4,,577 of which is=18,71, the maximum velocity of the wheel X 10,66, the load=199,4, the effect.

This agrees with Smeaton's observations, where he says, (art. 67) "It is somewhat remarkable, that though the velocity of the wheel, in relation to the velocity of the water, turn out to be more than 1/3, yet the impulse of the water, in case of the maximum, is more than double of what is assigned by theory; that is, instead of 4/8; of the column, it is nearly equal to the whole column." Hence I conclude, that non-elasticity does not operate so much against this application, as to

reduce the load to be less than ⅔. And when we consider, that 32,4 cubic feet of water, or a co∣lumn 32,4 feet long, strike the wheel while it moves only 18,71 feet, the velocity of the wheel being to the velocity of the water as 577 to 1000. May not this be the reason why the load is just 2/3 of the head, which brings the effect to be just ,38 (a little more than 1/3 of the power.) This I admit, because it agrees with experiment, altho' it be difficult to assign the true reason thereof. See annotation, art. 42.

Therefore ,577 the velocity of the water=18,71, multiplied by 2/3 of 16, the whole column, or instantaneous pressure, pressing on the wheel—art. 50—which is 10,66, produces 199,4, the effect. This appears to be the true effect, and if so the true theorem will be as follows, viz.

THEOREM.

Find, by theorem I. art. 50, the instantane∣ous pressure of the water, and take ⅔ for the max∣imum load; multiply by ,577 of the velocity of the water—which is the velocity of the wheel—and the product will be the effect.

Then 16 cubic feet, the column, multiplied by 2/3=10,66, the load, which, multiplied by 18,71, the velocity of the wheel, produces 199,4, for the effect; and if we try different heads and dif∣ferent apertures, we find the effects to bear the ratio to each other, that is agreeable to the laws of spouting fluids.

Art. 53. Water applied on Wheels to act by Gravity.

BUT when fluids are applied to act on wheels to produce effects by their gravity, they act on very different principles, producing double ef∣fects, to what they do by percussion, and then

their powers are directly as their quantity or weight,* 1.243 multiplied into their perpendicular de∣scent.

DEMONSTRATION

Let fig. 19,* 1.244 plate III. be a lever, turning on its centre or fulcrum A. Let the long arm A B represent the perpendicular descent,* 1.245 16 feet, the short arm A D a descent of 4 feet, and suppose water to issue from the trunk F, at the rate of 50 lb, in a second, falling into the buckets fastened to the lever at B. Now, from the principles of the lever—art. 16—it is evident, that 50lb. in a second, at B, will balance 200lb. in a second, at D, issuing from the trunk G, on the short arm; because 50×16=4×200=800, each. Perhaps it may appear plainer if we suppose the perpendicu∣lar line or diameter FC, to represent the descent of 16 feet and the diameter G I a descent of 4 feet. By the laws of the lever—art. 16—it is shewn, that, to multiply 50 into its perpendicu∣lar descent 16 feet or distance moved, is=200, multiplied into its perpendicular descent 4 feet, or distance moved; that is, 50×16=200×4=800; that is, their power is as their quantity, multi∣plied into their perpendicular descent; or, in other words, a fall of 4 feet will require 4 times as much water, as a fall of 16 feet, to produce equal power and effects. Q. E. D.

Upon these principles is founded the following simple theorem, for measuring the power of an overshot mill, or of a quantity of water, acting upon any mill-wheel by its gravity.

THEOREM IV.

Cause the water to pass along a regular canal, and multiply its depth in feet and parts, by its

width in feet and parts,* 1.246 for the area of its sec∣tion, which product multiply by its velocity per second in feet and parts,* 1.247 and the product is the cubic feet used per second, which multiplied by 62,5lb. the weight of 1 cubic foot, produces the weight of water per second, that falls on the wheel, which multiplied by its whole perpendi∣cular descent, gives a true measure of its power.

PROBLEM I.

Given, a mill-seat with 16 feet fall, width of the canal 5,333 feet, depth 3 feet, velocity of the water passing along it 2,03 feet per second, required the power per second.

Then, 5,333×3=15,999 feet, the area of the section of the stream, multiplied by 2,03 feet, the velocity, is equal 32,4 cubic feet, the quantity per second, multiplied by 62,5 is equal 2025lb. the weight of the water per second, multiplied by 16, the perpendicular descent, is equal 32400, for the power of the seat per second.

PROBLEM II.

Given, the perpendicular descent 18,3, width of the gate 2,66 feet, height, 145 of a foot, ve∣locity of the water per second, issuing on the wheel 15,76 feet, required the power.

Then, 2,66X,145=,3857 the area of the gate, ×15,76 the velocity=6,178 cubic feet, expended per second×62,5=375,8lb. per second×18,3 feet perpendicular descent=6877 for the measure of the power per second, which ground 3,75lb. per minute, equal 3,75 bushels in an hour, with a five feet pair of bur stones.

Art. 54. Investigation of the Principles of Overshot Mills

SOME have asserted, and many believed, that water is applied to great disadvantage on

the principle of an overshot mill;* 1.248 because, say they, there are never more than two buckets, at once* 1.249 that can be said to act fairly on the end of the lever, as the arms of the wheel are called in these arguments. But we must consider well the laws of bodies, descending inclined plains, and curved surfaces. See art. 10, 11. This matter will be cleared up, if we consider the circumference of the wheel to be the curved surface: for the fact is, that the water acts to the best advantage, and produces effects equal to what it would, in case the whole of it acted upon the very end of the lever, in the whole of its perpendicular descent.* 1.250

DEMONSTRATION.

Let A B C, fig. 20,* 1.251 represent a water-wheel, and F H a trunk, bringing water to it from a 16 feet head.* 1.252 Now suppose F G and 16 H to be two penstocks under equal heads, down which the water descends, to act on the wheel at C, on the principle of an undershot, on opposite sides of the float C, with equal apertures. Now it is evident from the principles of hydrostatics, shewn by the paradox (art. 48, and the 1st law of spouting fluids art. 45.) that the impulse and pressure will be equal from each penstock respectively. Although the one be an inclined plain, and the other a perpen∣dicular their forces are equal, because their per∣pendicular heights are; (art. 48) therefore the wheel will remain at rest, because each side of the float is pressed on by a column of water of equal size and height, as represented by the lines on each side of the float. Then suppose we shut the penstock F G, and let the water down the circular one rx, which is close to the point

of the buckets; this makes it obvious, from the same principles, that the wheel will be held in equilibrio, if the columns of each side be equal. For, although the column in the circular pen∣stock is longer than the perpendicular one, yet, because part of its weight presses on the lower side of the penstock, its pressure on the float is 〈◊〉〈◊〉 equal to the perpendicular.

Then, again, suppose the column of water is the circular penstock, to be instantly thrown into the buckets, it is evident, that the wheel will still be held in equilibrio, and each bucket will then bear a proportional part of the column, that the bucket C bore before; and that pa••t of the weight of the circular column, which rested on the under side of the circular penstock, is now on the gudgeons of the wheel. This shews that the effect of a stream, applied on an overshot wheel, is equal to the effect of the same stream, applied on the end of the lever, in its whole per∣pendicular descent,* 1.253 as in fig. 21, where the wa∣ter is shot into the buckets fastened to a strap or chain,* 1.254 revolving over two wheels; and here the whole force of the gravity of the column acts on the very end of the lever, in the whole of its descent. Yet, because the length of the column in action, in this case, is only 16 feet; whereas on a 16 feet wheel the length of the column in action is 25,15, therefore the powers are equal.

Again, if we divide the half circle into 3 arch∣es Ab, bc, eC, the centre of gravity of the up∣per and lower arches, will fall near the point a, 3,9 feet from the centre of motion, and centre of gravity of the middle arch, near the point 6,7,6 feet from the centre of motion. Now each of these arches is 8,38 feet, and 8,38×2×3,9-65,36, and 8,38×7,6 feet—63,07, which two pro∣ducts added—128,43, for the momentum of the circular column, by the laws of the lever and for the perpendicular column 16×8 the radius of

the wheel=128, for the momentum;* 1.255 by which it appears, that if we could determine the exact points on which the arches act, the momentums would be equal, all which shews, that the power of water on overshot wheels, is equal to the whole power it can any way produce, through the whole of its perpendicular descent, except what may be lost to obtain velocity, (art. 41) overcome friction, or by part of the water spilling, before it gets to the bottom of the wheel. Q. E. D.

I may add,* 1.256 that I have made the following ex∣periment, viz. I fixed a truly circular wheel on nice pivots, to evade friction, and took a cylindric rod of thick wire, cutting one piece exactly the length of half the circumference of the wheel, and fastening it to one side, close to the rim of the wheel its whole length, as at G X r A. I then took another piece of the same wire, of a length equal to the diameter of the wheel, and hung it ••n the opposite side, on the end of the lever or arm, as at B, and the wheel was in equilibrio. Q. E. D.

Art. 55. Of the Friction of the Apertures of Spouting Fluids.

THE doctrine of this species of friction ap∣pears to be as follows:* 1.257

1. The ratio of the friction of round apertures are as their diameters, nearly, while their quanti∣ties expended, are as the squares of their diameters.

2. The friction of an aperture, of any re∣gular or irregular figure, is as the length of the sum of the circumscribing lines, nearly; the

quantities being as the areas of the aperture.* 1.258 Therefore,

3. The less the head or pressure, and the large the aperture, the less the ratio of the friction therefore,

4. This friction need not be much regards in the large openings or apertures of undershot mills,* 1.259 where the gates are from 2 to 15 inches 〈◊〉〈◊〉 their shortest sides; but it very sensibly affect the small apertures of high overshot or undershot mills, with great heads, where their shortest 〈◊〉〈◊〉 are from five tenths of an inch to two inches.† 1.260

Art. 56. Of the Pressure of the Air on Fluids.

THE second cause of the motion or rise fluids,* 1.261 is the pressure of the air on the surface them, in the fountain or reservoir; and this 〈◊〉〈◊〉 sure is equal to a head of water 33; feet per∣pendicular height, under which pressure or 〈◊〉〈◊〉 of head, the velocity of spouting water is 46.•• feet per second.

* 1.262

Therefore,* 1.263 if we could by any means take off the pressure of the atmosphere, from any one part of the surface of a fluid, that part would spout up with a velocity of 46,73 feet per second, and rise to the height of 331/3 feet, nearly.* 1.264

On this principle act all syphons or cranes, and all pumps for raising water by suction, as it is called.—Let fig. 23,* 1.265 pl. III. represent a cask of water, with a syphon therein, to extend 33⅓ feet above the surface of the water in the cask.* 1.266 Now if the bung be made perfectly air-tight, round the syphon, so that no air can get into the cask, and the cask be full, then, if all the air be drawn cut of the syphon, at the bended part A, the fluid will not rise in the syphon, because the air can∣not get to it to press it up; but take out the plug P, and let the air into the cask, to press on the surface of the water, and it will spout up the short leg of the syphon B A, with the same force and velocity, as if it had been pressed with a head of water 33⅓ feet high, and will run into the long leg and will fill it. Then if we turn the cock c, and let the water run out, its weight in the long leg will overbalance the weight in the short one, drawing the water out of the cask, until the water sink so low, that the leg B A will be 33⅓ feet high, above the surface of the water in the cask; then it will stop, because the weight of water in the leg, in which it rises, will be equal to the weight of a column of the air of equal size, and of the whole height of the atmosphere. The water will not run out of the leg

A c, but will stand full 33⅓ feet above its mouth because the air will press up the mouth c,* 1.267 with force that will balance 33⅓ feet of water 〈◊〉〈◊〉 the leg c A. This will be the case, let the ••••∣per part of the leg be any size whatever—〈◊〉〈◊〉 there will be a small vacuum in the top of the long leg.

Art. 57. Of Pumps.

LET fig. 24,* 1.268 pl. III. represent a pump of the common kind, used for drawing water out 〈◊〉〈◊〉 wells. The moveable valve or bucket A,* 1.269 is cas•• with leather, which springs outwards, and 〈◊〉〈◊〉 the tube so nicely, that neither air nor water 〈◊〉〈◊〉 pass freely by it. When the lever L is worked the valve A opens as it descends, letting the 〈◊〉〈◊〉 or water pass through it. As it ascends again the valve shuts; the water which is above the bucket A is raised, and there would be a vacuum between the valves, but the weight of the 〈◊〉〈◊〉 presses on the surface of the water in the well at W, forcing it up through the valve B to 〈◊〉〈◊〉 the space between the buckets; and as the valve. A descends, B shuts, and prevents the water 〈◊〉〈◊〉 descending again: But if the upper valve A be 〈◊〉〈◊〉 more than 33⅓ feet above the surface of the water in the well, the pump cannot be made to draw because the pressure of the atmosphere will not cause the water to rise more than 33⅓ feet.

A TABLE FOR PUMP-MAKERS.

Height of the pump in feet above the sur∣face of the well.	Diameter of the bore.	Water discharged in a minute in wine measure.
inches.	1••0 parts of an in.	Galls.	Pints.
10	6	93	81	6
15	5	66	54	4
20	4	90	40	7
25	4	38	32	6
30	4	00	27	2
35	3	70	23	3
40	3	46	20	3
45	3	27	18	1
50	3	10	16	3
55	2	95	14	7
60	2	84	13	5
65	2	72	12	4
70	2	62	11	5
75	2	53	10	7
80	2	45	10	2
85	2	38	9	5
90	2	31	9	1
95	2	25	8	5
100	2	19	8	1

"All pumps should be so constructed as to work with equal ease, in rais∣ing the water to any given height above the surface of the well: and this may be done by observing adue proportion between the diameter of that part of the pump bore in which the piston or bucket works, and the height to which the water must be raised.

"For this purpose I have calculated the above table, in which the han∣dle of the pump is supposed to be a lever, increasing the power five times: that is, the distance or length of that part of the handle that lies between the pin on which it moves, and the top of the pump-rod to which it is fixed, to be only one fifth part of the length of the handle, from the said pin to the part where the man (who works the pump) applies his force or power.

"In the first column of the table, find the height at which the pump must discharge the water above the surface of the well; then in the second co∣lumn, you have the diameter of that part of the bore in which the piston or bucket works, in inches and hundredth parts of an inch; in the third column is the quantity of water, (in wine measure) that a man of common strength can raise in a minute.—And by constructing according to this me∣thod, pumps of all heights may be wrought by a man of ordinary strength so as to be able to hold out for an hour."

JAMES FERGUSON.

Art. 58. Of conveying Water under Valleys and over Hills.

WATER, by its pressure, and the pressure of the atmosphere,* 1.270 may be conveyed under val∣leys and over hills, to supply a family, a mill, or a town.* 1.271 See fig. 20. pl. III. F H is a canal for conveying water to a mill-wheel. Now let us suppose F G 16 H to be a tight tube or trunk—the water being let in at F, it will descend from F to G, and its pressure at F will cause it to rise to H, passing along if permitted, and may be conveyed over a hill by a tube, acting on the principle of the syphon. (art. 56) But where some have had occasion thus to convey water under any obstacle for the convenience of a mill, which often occurs in practice they have gone into the following expensive error: They make the tube at G 16 smaller than if it had been on a level, because, say they, a greater quantity will pass through a tube, pressed by the head G F, than on a level. But they should consider that the head G F is balanced by the head H 16, and the ve∣locity through the tube G 16 will only be such that a head equal to the difference between the perpendicular height of G F and H 16 would give it; (see art. 41, fig. 19) therefore it should be as large at G 16 as if on a level.

Art. 59. Of the Difference of the Force of indefinite and de∣finite Quantities of Water Striking a Wheel. DEFINITIONS.

1. BY an indefinite quantity of water we here mean a river or large quantity, much larger than

the float of the wheel, so that,* 1.272 when it strikes the float, it has liberty to move or escape from it in every lateral direction.* 1.273

2. By a definite quantity of water we mean a quantity passing through a given aperture along a shute to strike, a wheel; but as it strikes the float, it has liberty to escape in every lateral direc∣tion.

3. By a perfectly definite quantity, we mean a quantity passing along a close tube so confined, that when it strikes the float it has not liberty to escape in any lateral direction.

First,* 1.274 when a float of a wheel is struck by an indefinite quantity, the float is struck by a co∣lumn of water, the section of which is equal to the area of the float; and as this column is con∣fined on every side by the surrounding water, which has equal motion, it cannot escape freely sideways; therefore more of its force is commu∣nicated to the float than would be, in case it had free liberty to escape sideways in every direction.

Secondly,* 1.275 The float being struck by definite quantity, with liberty to escape freely in every side direction, it acts as the most perfect non-elas∣tic body; therefore (by art. 8) it communicates only a part of its force, the other part being spent in the lateral direction. Hence it appears, that in the application of water to act by impulse, we should draw the gate as near as possible to the float-board, and confine it as much as possible from escaping sideways as it strikes the float; but, taking care at the same time, that we do not bring the principle of the Hydrostatic Paradox into ac∣tion, (art 48).

What proportion of the force of the water is spent in a lateral direction is not yet determined, but see Art. 8.

3. A perfectly definite quantity striking a plain, communicates its whole force; because no part can escape sideways, and is equal in power to an

elastic body,* 1.276 or the weight of the water on 〈◊〉〈◊〉 overshot wheel, in its whole perpendicular de∣scent.* 1.277 But this application of water to 〈◊〉〈◊〉 has been hither to impracticable; for whenever we attempt to confine the water totally from escap∣ing sideways, we bring the paradoxical principle into action which defeats the scheme.* 1.278

To make this plain, let fig. 25, pl. III, be a wa∣ter-wheel; and first, let us suppose the water is be brought to it by the penstock 4. 16 to act by im∣pulse on the float b, and have free liberty to e∣scape every way as it strikes; then by art. 8 〈◊〉〈◊〉 will communicate but half its force. But if it be confined both at sides and bottom and can escape only upwards, to which the gravity will make some opposition, it will communicate perhaps more than half its force, and will not 〈◊〉〈◊〉 back against the float c. But if we put soali•••• to the wheel to prevent the water from escaping upwards, then the space between the floats 〈◊〉〈◊〉 be filled, as soon as the wheel begins to be retard∣ed,* 1.279 and the paradoxical principle art. 48 is brought fully into action, viz. the pressure of water is 〈◊〉〈◊〉 way equal, and presses backwards against the bottom of the float c, with a force equal to 〈◊〉〈◊〉 pressure on the top of the float b, and the wheel will immediately stop and be held in equilibrio and will not start again although all resistance 〈◊〉〈◊〉 removed. This we may call the paradoxical mill. There are many mills, where this princi∣ple is, in part, brought into action, which very much lessens their power.

Art. 60. Of the Motion of Breast and Pitch-back wheels.

MANY have been of opinion,* 1.280 that when wa∣ter is put to act on the wheel as at a (called 〈◊〉〈◊〉

low breast) with 12 feet head,* 1.281 that then the 4 feet fall below the point of impact a, is totally lost,* 1.282 because, say they, the impulse of the 12 feet head, will require the wheel to move with such velocity to suit the motion of the water as to move before the action of gravity, therefore the water cannot act after the stroke. But if they will consider well the principles of gravity act∣ing on falling bodies (art. 9) they will find, that, if the velocity of a falling body be ever so great, the action of gravity is still the same to cause it to move faster, so that, although an overshot wheel may move before the power of the gravity, of the water thereon, yet no impulse downwards can give a wheel such velocity, as that the gravi∣ty of the water acting thereon can be lessened thereby.* 1.283

Hence it appears, that when a greater head is used,* 1.284 than what is necessary to shoot the water fairly into the wheel, the impulse should be direct∣ed downward a little as at D (which is called pitch-back) and have a circular sheeting to pre∣vent the water from leaving the wheel, because if it be shot horizontally on the top of the wheel, the impulse in that case will not give the water any greater velocity downwards, then, in this case, the fall would be lost, if the head was very great, and the wheel moved to suit the velocity of the impulse, the water would be thrown out of the buckets by the centrifugal force; and if we attempt to retard the wheel, so as to retain the water the mill will be so ticklish and unsteady, that it will be almost impossible to attend it.

Hence may appear the reason why breast-wheels generally run quicker than overshots, al∣though the fall after the water strikes be not so great.

1. There is generally more head allowed to breast-mills than overshots, and the wheel will incline to move with nearly 2/3 the velocity of the water, spouting from under the head, (art. 41).

2. If the water was permitted to fall freely after it issues from the gate, it would be accele∣rated by the fall, so that its velocity at the low∣est point, would be equal to its velocity, had it spouted from under a head equal to its whole per∣pendicular descent. This accelerated velocity of the water, tends to accelerate the wheel; hence, to find the velocity of a breast-wheel, where the water is struck on in a tangent direc∣tion as in fig. 31, 32, I deduce the following.

THEOREM.

1. Find the difference of the velocity of the water under the head allowed to the wheel, above the point of impact, and the velocity of a falling body, having fell the whole perpendicular de∣scent of the water. Call this difference the ac∣celeration by the fall: Then say, As the veloci∣ty of a falling body acquired in falling through the diameter of any overshot wheel, is to the pro∣per velocity of that wheel by the scale, (art. 43) so is the acceleration by the fall, to the accelera∣tion of the wheel by the fall, after the water strikes the wheel.

2. Find the velocity of the water issuing on the wheel; take, 577 of said velocity, to which 〈◊〉〈◊〉 the accelerated velocity, and that sum will be the velocity of the breast-wheel.

This rule will hold nearly true, when the head is considerably greater than is assigned by the

scale (art. 43); but as the head approaches that assigned by the scale,* 1.285 this rule will give the mo∣tion too quick.

EXAMPLE.

Given, a high breast-wheel, f••ig. 25, where the water is shot on at d, the point of impact—6 feet head, and 10 feet fall—required the mo∣tion of the circumference of the wheel, work∣ing to the best advantage, or maximum effect.

Then, the velocity of the water is∣suing on the wheel, 6 feet head,	19,34 feet.
The velocity of a falling body, hav∣ing 16 feet fall, the whole descent,	32,4•• feet.
Difference,	13,06 feet.

Then as the velocity under a 16 feet fall (32,4 feet) is to the velocity of an overshot wheel=8,76 feet, so is 13,06 feet, to the 16 feet diameter velocity accelerated, which is equal 3,5 feet, to which add ,577 of 19,34 feet (being 11,15 feet); this amounts to 14,65 feet per second, the velo∣city of the breast-wheel.

Art. 61. Rule for calculating the Power of any Mill-Seat.

THE only loss of power sustained by using too much head, in the application of water to turn a mill-wheel, is from the head producing only half its power. Therefore, in calculating the power of 16 cubic feet per second, on the different ap∣plications of fig. 25, pl. III. we must add half the head to the whole fall, and count that sum

the virtual perpendicular descent.* 1.286 Then by the∣orem IV. (art. 53) multiply the weight of the water per second by its perpendicular descent, and you have the true measure of its power.

But to reduce the rule to a greater simplicity,* 1.287 let us call each cubic foot 1, and the rule will be simply this—Multiply the cubic feet expended per second, by its virtual perpendicular descent in feet, and the product will be a true measure of the power per second. This measure 〈◊〉〈◊〉 have a name, which I call Cuboch; that is, 〈◊〉〈◊〉 cubic foot of water, multiplied by 1 foot descent, is one cuboch, or the unit of power.

EXAMPLES.

1. Given, 16 cubic feet of water per second to be applied by percussion alone, under 16 feet head, required the power per second.

Then, half 16=8×16=128 cubochs, for the mea∣sure of the power per second.

2. Given, 16 cubic feet per second, to be ap∣plied to a half breast of 4 feet fall and 12 〈◊〉〈◊〉 head, required the power.

Then, half 12=6+4=10×16=160 cubochs, 〈◊〉〈◊〉 the power.

3. Given, 16 cubic feet per second, to be ap∣plied to a pitch-back or high breast—fall 10, he•• 6 feet, required the power.

Then, half 6=3+10=13×16=208 cubochs, 〈◊〉〈◊〉 the power per second.

4. Given, 16 cubic feet of water per 〈◊〉〈◊〉 to be applied as an overshot—head 4, fall 12 〈◊〉〈◊〉 required the power.

Then, half 4=2+12=14×16=224 cubochs, 〈◊〉〈◊〉 the power.

The powers of equal quantities of water 〈◊〉〈◊〉 cubic feet per second, and equal total perpendicu∣lar descents by the different applications 〈◊〉〈◊〉

The undershot,

• 16 feet head,* 1.288* 1.289
• 0 fall,
• 128 cubochs power.* 1.290

The half breast,

• 12 feet head,
• 4 feet fall,
• 160 cubochs of power.

The high breast

• 6 feet head,
• 10 feet fall,
• 208 cubochs of power.

The overshot,

• 4 feet head.
• 12 feet fall,
• 224 cubochs of power.

Ditto,

• 2,5 feet head,
• 13,5 feet fall,
• 236 cubochs of power.

The last being the head necessary to shoot the water fairly into the buckets, may be said to be the best application. See art. 43.

On these simple rules, and the rule laid down in art. 43, for proportioning the head and fall, I have calculated the following table or scale of the different quantities of water expend∣ed per second, with different perpendicular de∣scents, to produce a certain power, in order to present at one view to the reader the ratio of in∣crease or decrease of quantity, as the perpendi∣cular descent increases or decreases.

A TABLE shewing the quantity of water required with different falls, to produce by its gravity, 112 cubochs of pow∣er, which will drive a five feet stone about 97 revoluti∣ons in a minute, grinding wheat about 5 bushels in an hour.

The virtual descent of the water being half the head added to all the fall after it strikes the wheel.	Cubic feet of water required per second, &c.	The virtual descent of the water being half the head added to all the fall after it strikes the wheel.	Cubic feet of water required per second.
1	112	16	7
2	56	17	6,58
3	37,3	18	6,22
4	28	19	5,99
5	22,4	20	5,6
6	18,6	21	5,33
7	16,	22	5,1
8	14	23	4,87
9	12,4	24	4,66
10	11,2	25	4,48
11	10,2	26	4,3
12	9,33	27	4,15
13	8,6	28	4,
14	8,	29	3,86
15	7,46	30	3,73

Art. 62. Theory and Practice compared.

I WILL here give a table of 18 mills in actual practice out of about 50 that I have taken an ac∣count of, in order to compare theory with prac∣tice, and in order to ascertain the power requir∣ed

on each superficial foot of the acting parts of the stone:* 1.291 But I must premise the following

THEOREMS.

1. To find the circumference by the diameter,* 1.292 or the diameter by the circumference of a circle given; say, As 7 is to 22, so is the diameter of the stone to the circumference,i.e. Multiply the diameter by 22, and divide the product by 7, for the circumference; or, multiply the circumfer∣ence by 7, and divide the product by 22, for the diameter.

To find the area of circle by the diameter given: As I, squared,* 1.293 is to, 7854, so is the square of the diameter to the area; i.e. Multiply the square of the diameter by ,7854, and deduct 1 foot for the eye and you have the area of the stone.

3. To find the quantity of surface passed by a mill-stone:* 1.294 The area, squared, multiplied by the revolutions of the stone, gives the number of superficial feet, passed in a given time.

Observations on the following Table of Experiments.* 1.295

I have asserted in art. 44, that the head above the gate of a wheel, on which the water acts by its gravity, should be such, as to cause the water to issue on the wheel, with a velocity to that 〈◊〉〈◊〉 the wheel as 3 to 2, to compare this with the following table of experiments.

1. EXP. Overshot. Velocity of the water 12,〈◊〉〈◊〉 feet per second, velocity of the wheel 8,〈◊〉〈◊〉 feet per second, which is a little less than ⅔ 〈◊〉〈◊〉 the velocity of the water. This wheel received the water well. It is at Stanton, in Delaware state.

2. Overshot. Velocity of the water 11,17 feet per second, ⅔ of which is 7,44 feet, velocity 〈◊〉〈◊〉 the wheel 8,5 feet per second. This received the water pretty well. It is at the abovemention place.

3. Overshot. Velocity of the water 12,16 feet per second, velocity of wheel 10,2; 〈◊〉〈◊〉 out great part of the water by the back of the buckets; strikes it and makes a thumping 〈◊〉〈◊〉 It is allowed to run too fast; revolves faster th•••• my theory directs. It is at Brandiwine, in Dela∣ware state.

4. Overshot. Velocity of the water 14,4 feet per second, velocity of the wheel 9,3 feet, a little less than ⅔ of the velocity of the water. It re∣ceives the water very well; has a little 〈◊〉〈◊〉 head than assigned by theory, and runs a little faster; it is a very good mill, situate at Brandi∣wine, in the state of Delaware.

6. Undershot. Velocity of the wheel, loaded 16, and when empty 24 revolutions per minute which confirms the theory of motion for under shot wheels. See art. 42.

7. Overshot. Velocity of the water 15,79 feet velocity of the wheel 7,8 feet; less than ⅔ 〈◊〉〈◊〉

the velocity of the water; motion slower and head more than assigned by theory.* 1.296 The miller said the wheel ran too slow, and would have her altered; and that she worked best when the head was conside∣rably sunk. She is at Bush, Hartford county, Maryland.

8. Overshot. Velocity of the water 14,96 feet per second, velocity of the wheel 8,8 feet, less than ⅔, very near the velocity assigned by the theory; but the head is greater, and she runs best when the head is sunk a little; is counted the best mill; and is at the same place with the last mentioned.

9,10,11,12. Undershot, open wheels. Velo∣city of the wheels when loaded 20 and 40, and when empty 28 and 56 revolutions per minute, which is faster than my theory for the motion of undershot mills. Ellicott's mills, near Baltimore, in Maryland, serves to confirm the theory.

14. Overshot. Velocity of the water 16,2 feet, velocity of the wheel 9,1 feet, less than ⅔ of the water, revolutions of the stone 114 per minute, the head near the same as by theory, the velocity of the wheel less, stone more. This shews her to be too high geared. She receives the water well, and is counted a very good mill, situate at Alexandria, in Virginia.

15. Undershot. Velocity of the water 24,3 per second, velocity of the wheel 16,67 feet, more than ⅔ the velocity of the water. Three of these mills are in one house, at Richmond, Virginia—they confirm the theory of undershots, being very good mills.

16. Undershot. Velocity of the water 25,63 feet per second, velocity of the wheel 19,05 feet, being more than ⅔. Three of these mills are in one house, at Petersburg, in Virginia—they are very good mills, and confirm the theory. See art. 43.

18. Overshot wheel. Velocity of the water 11, 〈◊〉〈◊〉 feet per second, velocity of the wheel 10,96 feet, nearly as fast as the water. The backs of the buckets strike the water, and drive great 〈◊〉〈◊〉 over: and as the motion of the stone is 〈◊〉〈◊〉 right, and the motion of the wheel faster 〈◊〉〈◊〉 assigned by the theory, it shews the mill to be 〈◊〉〈◊〉 low geared, all which confirms the theory. 〈◊〉〈◊〉 art. 43.

In the following table I have counted the dia∣meter of the mean circle to be two thirds of the diameter of the great circle of the stone, which is not strictly true. The mean circle to continue half the area of any other circle must be, 70•• parts of the diameter of the said circle, or nearly ,7 or ⅔.

Hence the following theorem for finding the mean circle of any stone.

THEOREM.

Multiply the diameter of the stone by, 70•• and it produces the diameter of the mean circle.

EXAMPLE.

Given, the diameter of the stone 5 feet, re∣quired a mean circle that shall contain half in area.

Then, 5X,707=3,535 feet the diameter of the mean circle.

Art. 63. Further observations on the following Table.

1. The mean power used to turn the 5 feet stones in the Experiments (No. 1. 7. 14. 17.) is 87,5 cubochs of the measure established art.* 1.297 61, and the mean velocity is 104 revolutions of the stones in a minute, the velocity of the mean cir∣cle being 18,37 feet per second, and their mean quantity ground is 3,8lb. per minute, which is 3,8 bushels per hour, and the mean power used to each foot of the area of the stone is 4,69 of the measure aforesaid, done by 36582 superficial feet passing each other in a minute. Hence we may conclude, until better informed,

1. That 87,5 cubochs of power per second will turn a 5 feet stone 104 revolutions in a minute, and grind 3,8 bushels an hour.

2. That 4,69 cubochs of power is required to every superficial foot of a mill-stone, when their mean circles move with a velocity of 18,37 feet per second. Or,

3. That for every 36582 feet of the face of stones that pass each other we may expect 3,8lb. will be ground, when the stones, grain, &c. are in the state and condition, as were the above stones in the experiments.

A TABLE of Experiments of

Numb. of Exp.	Virtual or effective descent of the water.	Head above the centre of the gate.	Area of the gate, abating for contraction occasioned by friction.	Velocity of the water per second, by theory.	Cubic feet expended per se∣cond, abating for friction by conjecture.	power per second, by simple theorem, Art. 61.	Diameter of the wheel.	No. of revolutions per mi∣nute.	Velocity of the 〈…〉〈…〉 per second.
	feet.	feet.	feet.	feet.	cub.ft.	chs.	feet.
1	20,	2,67	,385	12,9	3,8	76	18	8,5	8,2
2	19,2	1,9	,325	11,17	3,5	67	18	9,1	8,5
3	16,2	2,2		12,16			15	13	10,2
				14,4
4	16,6	3,1					15	12	9,3
5	19,25	3		13,8			17,75	105	9,8
								16	loaded
6							16	24	unload
7	17,8	3,83	,345	15,79	5,18	92	16,4	9,5	7,8
8	17,8	3,5	,425	14,96	6,16	110	16,4	10	8,8
9	11			26,73			15	20	loaded
								28	unload
10							7,5	40	loaded
								56	unload
11							15	20	loaded
								28	unload
12							7,5	40	loaded
								56	unload
13	20,6	4		16,2			18,6	8	7,8
14	21,5	4		16,2	3,57	86	19,3	9	9,1
15	9,5			24,3			10	32	16,67
16	10			25,63			8	45,5	19,05
17	12,5	3	,567	14	7,6	96	11	16	9,2
18		2		11,4			14	14	10,96

Note, the above table being large, obliged us to put it on two pages folding of which may set it a little out of place. In the 3rd, 4th, 〈◊〉〈◊〉 18th experiments, there is two pair of stones to one water-wheel, the 〈◊〉〈◊〉 &c. of which, are shewn by the braces. If the reader will by a rule 〈◊〉〈◊〉 small lines between the experiments, the table will be easier read.

Eighteen Mills in Practice.

〈…〉〈…〉	Cogs in the counter cog∣whipp••e.	Rounds in the trundles.	Revolutions of the stones per minute.	Diameter of the stones in feet and inches.	Area of the stones.	Power required to each foot of face.	Velocity of the mean circle.	Superficial feet passed in a minute.	Quantity ground per minute in lbs. or pr hour in bush.
				f. in.	sup.ft.		feet.
〈◊〉〈◊〉	••4	15	99,7	5	18,63	4,1	17,3	34594	3,5
〈◊〉〈◊〉	48	14	124,8	4 3	13,13	4,34	18,5	21514	2,5
〈◊〉〈◊〉	44	14	122	4 2
〈◊〉〈◊〉	44	14	122	4 8
〈◊〉〈◊〉	44	14	104	4 6
〈◊〉〈◊〉	44	14	108	4 6			16,97
〈◊〉〈◊〉	48	13	126	4 3			18,6
〈◊〉〈◊〉	44	14	105	5	18,63	4,9	18,32	36435	3,75
〈◊〉〈◊〉	44	14	103	5	18,63	5,9	17,97	35741
		23	73	7	38,48		17,84	108091
		16	105	5			18,32	36435
		16	105	4 10
		16	105	5	18,63		18,32	36435
••5	44	19	71	6 10	36,63		16,92	95264
••4	44	16	88	5 6	23,76		16,89	49678
••5	54	16	114	5	18,63	4,67	19,89	39558	4,5
		17	113	5 4			20,75
		21	95	6	28,38		19,9	74850
〈◊〉〈◊〉	44	14	103	5	18,63	5,15	17,97	35741	3,5
〈◊〉〈◊〉	48	15	124	4 4
••6	48	16	116	4 8

Observations continued from Page 115.* 1.298

But as we cannot attain to a mathematical ••••∣actness in those cases, and as it is evident 〈◊〉〈◊〉 all the stones in the said experiments have been working with too little power, because it 〈◊〉〈◊〉 known that a pair of good bur stones of 5 〈◊〉〈◊〉 diameter, will grind sufficiently well about 12 bushels in 24 hours; that is 5,2 bushels in 〈◊〉〈◊〉 hour, which would require 6,4 power per se∣cond—we may say 6 cubochs per second, when 〈◊〉〈◊〉 feet stones grind 5 bushels per hour, for the 〈◊〉〈◊〉 of simplicity. Hence we deduce the following simple theorem for determining the size of 〈◊〉〈◊〉 stones to suit the power of any given seat, or 〈◊〉〈◊〉 power required to any size of a stone.

THEOREM.* 1.299

Find the power by the theorem in art. 61; 〈◊〉〈◊〉 divide the power by 6, which is the power re∣quired, by 1 foot, and it will give you the 〈◊〉〈◊〉 of the stone that the power will drive, to which add 1 foot for the eye, and divide by ,7854, 〈◊〉〈◊〉 the quotient will be the square of the diameter or, if the power be great, divide by the product 〈◊〉〈◊〉 the area of any size stones you choose, multiplied by 6, and the quotient will be the number 〈◊〉〈◊〉 stones the power will drive: or, if the size of the stone be given,* 1.300 multiply the area by 6 cuboch•• and the product is the power required to drive 〈◊〉〈◊〉

EXAMPLES.

1. Given, 9 cubic feet per second, 12 feet per∣pendicular, virtual, or effective descent, requir∣ed the diameter of the stone suitable thereto.

Then, by art. 61, 9×12=108, the power, and 108|6=18, the area, and 18+1 | 7854=24,2 the root of which is 4,9 feet, the diameter of the stone required.

Observation 5th.* 1.301 The velocities of the mean circles of these stones in the table are some below and some above 18 feet per second,* 1.302 the mean of them all being nearly 18 feet; therefore I con∣clude that 18 feet per second is a good velocity in general, for the mean circle of any sized stone.

Of the different quantity of Surfaces that are passed by Mill-stones of different diameters with different velocities.

Supposing the quantity ground by mill-stones and power required to turn them to be as the pas∣sing surfaces of their faces, each superficial foot that passes over another foot requires a certain power to grind a certain quantity: Then to explain this let us premise,

1. The circumference and diameter of circles are directly proportional. That is, a double dia∣meter gives a double circumference.

2. The areas of circles are as the squares of their diameters. That is, a double diameter gives 4 times the area.

3. The square of the diameter of a circle mul∣tiplied by ,7854 gives its area.

4. The square of the area of a mill-stone multi∣plied by its number of revolutions, gives the sur∣face passed. Consequently,

5. Stones of unequal diameters revolving in equal times. Their passing surfaces, quantity ground, and power required to drive them, will be as the squares of their areas, or as the biquadrate of their diameters. That is, a double diameter will pass 16 times the surface.* 1.303

6. If the velocity of their mean circles or cir∣cumferences be equal their passing surfaces, quan∣tity

ground,* 1.304 and power required to move then will be as the cubes of their diameters.† 1.305

7. If the diameters and velocities be unequal their passing surfaces and quantity ground, &c. will be as the squares of their areas, multiplied by their revolutions.

8. If their diameters be equal the quantity 〈◊〉〈◊〉 surfaces passed, &c. are as their velocities or revo∣lutions simply.

But we have been supposing theory and prac∣tice to agree strictly which they will by no me•• do in this case. The quantity ground and power used by large stones more than by small ones 〈◊〉〈◊〉 not be in the ratio assigned by the theory; be∣cause the meal having to pass a greater distance through the stone, is operated upon often•••• which operations must be lighter, else it will 〈◊〉〈◊〉 overdone; by which means large stones may 〈◊〉〈◊〉 equal quantities with small ones, and with equal power, and do it with less pressure; therefore 〈◊〉〈◊〉 flour will be better.‡ 1.306 See art. III.

From these considerations added to experi∣ments I conclude, that the power required 〈◊〉〈◊〉 quantity ground, will nearer approach to be 〈◊〉〈◊〉 the area of the stones, multiplied into the veloci∣ty of the mean circles; or, which is nearly the same: As the squares of their diameters. But 〈◊〉〈◊〉 the velocities of their mean circles or circumfer∣ences be equal, then it will be as their area, ••••••∣ply.

On these principles I have calculated the fol∣lowing table, shewing the power required 〈◊〉〈◊〉 quantity ground both by theory, and what I sup∣pose to be the nearest practice.

A TABLE of the area of MILL-STONES with their different diameters, deducting 1 foot for the eye; and of the power required to move them with a mean velocity of 18 feet per second, &c.

Diameter of the stone in feet and parts.	Area of the stone in feet and parts deducting 1 foot for the eye.	Power required to drive the stone with mean velocity 18 ft. per second allowing 6 cubochs to each foot of its area.	Circumference of the mean circle to con∣tain half the area of the stone.	Revolutions of the stone per minute, with 18 feet velocity of mean circle.	No. of superficial feet passed per minute, be∣ing the square of the area of the stones mul∣tiplied by the number of revolutions.	Quantity ground in lbs. per minute, or bush∣els per hour, supposing it to be as the num∣ber of superficial feet passed.	Power required supposing it to be as the no. of superficial feet passed.	Quantity ground supposing it to be simply as the area of the stone with equal velocity.	Quantity ground supposing it to be as the squares of the diameter of the stone, which appears to come nearest the true quantity.
feet.	su. ft.	cuhs.	feet.		sup. ft.	lbs.	cuhs.	lbs.	lbs.
3,5	8.62	51,72	7,777	138,8	10312	1,49	33,1	2,3	2,45
3,75	9,99	59,94							2,8
4,	11,56	69,36	8,888	121,5	16236	2,3	52	3,1	3,2
4,25	13,18	79,							3,6
4▪5	14,9	89,4	9,99	108,1	23999	3,46	77	4,	4,05
4,75	16,71	100,26							4,5
5,	18,63	111,78	11,09	97,4	34804	5,	111,78	5,	5,
5,25	20,64	123,84							5,53
5,5	22,76	136,5							6,05
5,75	24,96	153,7							6,6
6,	27,27	163,6	13,37	80,7	60012	8,6	192	7,3	7,2
6,25	29,67	178,							7,8
6,5	32,18	196,							8,4
6,75	34,77	208,6							9,1
7,	37 48	255,	15,55	69,4	97499	14,06	313	10	9,8
1	2	3	4	5	6	4	8	9	10

Note—The reason why the quantity ground in the 7th column, is not exactly as the cubes of the diameter of the stone, and in the 9th column not exactly as the squares of its diameter, is the deduction for the eye, being equal in each stone, de∣stroys the proportion.

The engine of a paper-mill, roll 2 feet diameter, 2 feet long, revolving 160 times in a minute, requires equal power with a 4 feet stone, grinding 5 bushels an hour.

Having now laid down in art.* 1.307 61, 62, and 63, a theory for measuring the power of any mill-seat, and for ascertaining the quantity of that power that mill-stones of different diameters will require, by which we can find the diameter of the stones to suit the power of the seat: and, having fixed on six cubochs of that power per second to every superficial foot of the mill-stone, as requisite to move the mean circle of the stone 18 feet per second, when in the act of grinding with moderate and sufficient feed, and having al∣lowed the passing of 34804 feet per minute to grind 5lb. in the same time, which is the effect of the five feet stone in the table, by which, if right, we can calculate the quantity that a stone of any size will grind with any velocity.

I have chosen a velocity of 18 feet per second, for the mean circle of all stones, which is slower than common practice, but not too slow for making good flour. See art. 111. Here will appear the advantage of large stones over small ones; for if we will make small stones grind as fast as large ones, we must give them such velocity as to heat the meal.

But I wish to inform the reader, that the expe∣riments, from which I have deduced the quantity of power to each superficial foot to be six cubochs, have not been sufficiently accurate to be fully re∣lied on; but it will be easy for every ingenious mill-wright to make accurate experiments to sa∣tisfy himself as to this.

Art. 64. Of Canals for conveying Water to Mills.

IN digging canals we must consider that water will come to a level on its surface, be the form of the bottom as it may. If we have once de∣termined

on the area of the section of the canal necessary to convey a sufficient quantity of water to the mill,* 1.308* 1.309 we need only mind to keep to that area in the whole distance, and need not pay much regard to the depth or width, if there be rocks in the way. Much expence may be often-times saved, by making the canal deep where it cannot easily be got wide enough, and wide where it cannot easily be got deep enough. Thus, sup∣pose we have determined it to be 4 feet deep and 6 feet wide, then the area of its section will be 24.—Let fig. 36, pl. IV. represent a canal,* 1.310 the line A B the level or surface of the water, C D the side, E F the bottom, A C the width 6 feet,* 1.311 A E the depth 4 feet. Then, if there be rocks at G, so that we cannot without great expence obtain more than 3 feet width, but 8 feet depth at a small expence: then 8×3=24, the section required. Again, suppose a flat rock to be at H, so that we cannot,* 1.312 without great expence obtain more than 2 feet depth, but can, with small ex∣pence obtain 12 feet width: then 2×12=24, the section required; and the water will come on equally well, even if it were not more than, 5 of a foot deep, provided it be proportionably wide. One disadvantage however arises in having canals too shallow in places, because the water in very dry seasons, may be too low to rise over them; but if the water was always to be of one height, the disadvantage would be but little. The cur∣rent will keep the deep places open; light sand or mud will not settle in them. This will seem paradoxical to some, but seeing the experiment may be a saving of expence, it may be worth try∣ing.

Art. 65. Of the Size and Fall of Canals.

AS to the size and fall necessary to convey any quantity of water required, to a mill, I do not find any rule laid down for either. But in order to establish one let us consider, that the size de∣pends entirely upon the quantity of water and the velocity with which it is to pass: therefore, 〈◊〉〈◊〉 we can determine on the velocity, which I 〈◊〉〈◊〉 suppose to be from 1 to 2 feet per second—〈◊〉〈◊〉 the slower the better, as there will be the less fall lost. We can find the size of the canal by the following theorem.

THEOREM.

Divide the quantity required in cubic feet 〈◊〉〈◊〉 second,* 1.313 by the velocity in feet per second, and the quotient will be the area of the section of the canal. Divide that area by the proposed depth▪ and the quotient is the width: or, divide by the width, and the quotient is the depth.

PROBLEM. I.

Given, a 5 feet mill stone to be moved 〈◊〉〈◊〉 feet per second, velocity of its mean circle 〈◊〉〈◊〉 seat of 10 feet virtual or effective descent, requir∣ed the size of the canal, with a velocity of 1 〈◊〉〈◊〉 per second.

Then, by theorem in art. 63: The area of the stone 18,63 feet, multiplied by 6 cubochs of pow∣er, is equal 111, 78 cubochs for the power (in com∣mon practice say 112 cubochs) which, divided by 10 the fall, quotes 11,178 cubic feet required per second, which, divided by one, the velocity

proposed per second,* 1.314 quotes 11,178 feet, the area of the section, which divided by the depth pro∣posed, two feet, quotes 5,58 feet for the width.

PROBLEM. II.

Given, a mill stone 6 feet diameter, to be moved with a velocity of 18 feet per second of its mean circle, to be turned by an undershot wheel on a seat of 8 feet perpendicular descent, requir∣ed the power necessary per second to drive them, and the quantity of water per second, to produce said power, likewise the size of the canal to con∣vey the water with a velocity of 1,5 feet per se∣cond.

Then, by art. 61, 8 feet perpendicular descent, on the undershot principle, is only=4 feet virtual or effective descent: and the area of the stone by the table (art. 63)=27,27 feet ×6 cubochs=163,62 cubochs, for the power per second, which di∣vided by 4, the effective descent =40,9 cubic feet, the quantity required per second, which divided by the velocity proposed 1,5 feet per second =20,45, for the area of the section of the canal, which divided by 2,25 feet, the depth of the ca∣nal proposed =9,1 feet, the width.* 1.315

As to the fall necessary in the canal I may ob∣serve,* 1.316 that all the fall should be in the bottom of the canal and none on the top, which should be all the way on a level with the water in the dam, in order that when the gate is shut down at the mill, the water will not overflow the banks, but stand at a level with the water in the dam; that is, as much fall as there is to be in the whole

length of the canal,* 1.317 so much deeper must the ca∣nal be at the mill than at the dam. From obser∣vations I conclude that about 3 inches to 〈◊〉〈◊〉 yards will be sufficient, if the canal be long, but more will be better if it be short, and the head apt to run down when water is scarce, for the shallower the water the greater must be the velo∣city, and more fall is required.—A French author M. Fabre, allows 1 inch to 500 feet.

Art. 66. Of Air-pipes to prevent tight Trunks from 〈◊〉〈◊〉 when filled with water.

WHEN water is to be conveyed under ground or in a tight trunk below the surface of the wa∣ter in the reservoir,* 1.318 to any considerable length, there must be air-pipes (as they have been called to prevent the trunk from bursting. To under∣stand their use let us suppose a trunk 100 feet long, 16 feet below the surface of the water, 〈◊〉〈◊〉 fill which we draw a gate at one end of equal size with the trunk. Then the water, in passing to the other end acquires great velocity if it meets 〈◊〉〈◊〉 resistance, which velocity is suddenly to be stop∣ped when the trunk is full. This great column of water in motion, in this case, would strike with a force equal to a solid body of equal weight and velocity, the shock of which would be suffi∣cient to burst any trunk that ever was made of wood.* 1.319 Many having thought the use of these pipes to be to let out the air, have made then too small, so that they would vent the air fa•••• enough to let the water in with considerable ve∣locity, but would not vent the water fast enough when full, to cheek its motion easily, in which case they are worse than none at all, for if the

air cannot escape freely,* 1.320 the water cannot enter freely.

Whenever the air has been compressed in the trunk by the water coming in,* 1.321 it has made a great blowing noise in escaping through the crevices, and therefore has been blamed as the cause of the bursting of the trunk; whereas it acted by its elastic principle as a great preventative against it. For I do suppose, that if we were to pump the air all out of a trunk, 100 feet long, and 3 by 3 feet wide, and let the water in with full force, that it would burst, if as thick as a cannon of cast me∣tal: because in that case there would be 900 cu∣bic feet of water, equal to 56250lbs. pressed on by the weight of the atmosphere, with a velocity of 47 feet per second, to be suddenly stopped, the shock would be inconceivable.* 1.322

Therefore I do conclude it best, to make an air-pipe for every 20 or 30 feet, of the full size of the trunk; but this will depend much on the depth of the trunk below the surface of the re∣servoir, and many other circumstances.

Having now said what was necessary in order the better to understand the theory of the power and principles of mechanical engines, and water acting on the different principles on water-wheels, and for the establishing new and true theories of the motion of the different kinds of water-wheels, I here quote many of the ingenious Smeaton's ex∣periments, that the reader may compare them with the theories established, and judge for him∣self.

Art. 67. An experimental Enquiry, read in the Philosophical Society in London, May 3rd and 10, 1759, con∣cerning the Natural Powers of Water to 〈◊〉〈◊〉 Mills and other Machines, depending on a circu∣lar Motion, by James Smeaton, F.R.S.

WHAT I have to communicate on this sub∣ject was originally deduced from experiment made on working models, which I look upon 〈◊〉〈◊〉 the best means of obtaining the outlines in mecha∣nical enquiries. But in this case it is necessary to distinguish the circumstances in which a 〈◊〉〈◊〉 differ from a machine in large: otherwise a ••••••∣del is more apt to lead us from the truth than ••••∣wards it. Hence the common observation, 〈◊〉〈◊〉 a thing may do very well in a model that 〈◊〉〈◊〉 not do in large. And indeed though the 〈◊〉〈◊〉 circumspection be used in this way the best struc∣ture of machines cannot be fully ascertained, 〈◊〉〈◊〉 by making trials with them of their proper 〈◊〉〈◊〉 It is for this purpose that though the model ••••∣ferred to, and the greatest part of the following experiments, were made in the year 1752 〈◊〉〈◊〉 1753 yet deferred offering them to the 〈◊〉〈◊〉 till I had an opportunity of putting the deduction made therefrom in real practice in a variety 〈◊〉〈◊〉 cases and for various purposes, so as to be able assure the society, that I have found them to ••••∣swer.

PART I. Concerning Undershot Water-wheels.

Plate XII is a view of the machine for experiments, on water-wheels, wherein

ABCD is the lower cistern or magazine for receiving the water after it has left the wheel and for supplying

DE the upper cistern or head,* 1.323 wherein the water being raised to any height by a pump, that height is shewn by

FG a small rod divided into inches and parts, with a float at the bottom to move the rod up and down, as the surface of the water rises and falls.

HI is a rod by which the sluice is drawn, and stopped at any height required, by means of

••K a pin or peg, which fits several holes placed in the manner of a diagonal scale upon the face of the rod HI.

GL is the upper part of the rod of the pump for drawing the water out of the lower cistern, in order to raise and keep up the surface thereof to its desired height in the head DE, thereby to supply the water expended by the aperture of the sluice.

NM is the arch and handle of the pump, which is limited in its stroke by

N a piece for stopping the handle from raising the piston too high, that also being prevented from going too low, by meeting the bottom of the bar∣rel.

O is the cylinder upon which the cord winds, and which being conducted over the pulleys P and Q, raises

R the scale, into which the weights are put for trying the power of the water.

W the beam, which supports the scale that is placed 15 or 16 feet higher than the wheel.

XX is the pump-barrel 5 inches diameter and 11 inches long.

Y is the piston, and

Z is the fixed valve.

G V is a cylinder of wood fixed upon the pump-rod, and reaches above the surface of the water, this piece of wood being of such a thick∣ness that its section is half the area of the pump-barrel, will cause the water to rise in the head as

much while the piston is descending as while is rising,* 1.324 and will thereby keep the gauge F G more equally to its height.

aa shews one of the two wires that serves 〈◊〉〈◊〉 a director to the float.

b is the aperture of the sluice.

ca is a kant-board for kanting the water down the opening cd into the lower cistern.

ce is a sloping board for bringing back the ••••∣ter that is thrown up by the wheel.

There is a contrivance for engaging and disen∣gaging the scale and weight instantaneously from the wheel, by means of a hollow cylinder 〈◊〉〈◊〉 which the cord winds by slipping it on the 〈◊〉〈◊〉 and when it is disengaged it is held to its place 〈◊〉〈◊〉 a ratchet-wheel, for without this experiment could not be made with any degree of exacted.

The apparatus being now explained I think necessary to assign the sense in which I use 〈◊〉〈◊〉 term Power.

The word power is used in practical mecha∣nics I apprehend to signify the exertion 〈◊〉〈◊〉 strength, gravity, impulse, or pressure, so a•• 〈◊〉〈◊〉 produce motion.

The raising of a weight relative to the height to which it can be raised in a given time, is 〈◊〉〈◊〉 most proper measure of power. Or in 〈◊〉〈◊〉 words, if the weight raised, is multiplied by the height to which it can be raised in a given time the product is the measure of the power raising it, and consequently all those powers are equal. But note all this is to be understood in case of slow or equable motion of the body raised, for in quick, accelerated, or retarded motions, the visinertia of the matter moved will make a variation.

In comparing the effects produced by water-wheels with the powers producing them; or in other words to know what part of the original power is necessarily lost in the application, we must previously know how much of the power is

spent in overcoming the friction of the machinery and the resistance of the air,* 1.325 also what is the real velocity of the water at the instant it strikes the wheel, and the real quantity of water expended in a given time.

From the velocity of the water at the instant that it strikes the wheel, given; the height of the head productive of such velocity can be de∣duced, from acknowledged and experienced prin∣ciples of hydrostatics: so that by multiplying the quantity or weight of water really expended in a given time, by the height of head so obtained; which must be considered as the height from which that weight of water had descended, in that given time; we shall have a product equal to the origin∣al power of the water, and clear of all uncertain∣ty that would arise from the friction of the water in passing small apertures, and from all doubts, arising from the different measure of spouting wa∣ters, assigned by different authors.

On the other hand the sum of the weights rais∣ed by the action of this water, and of the weight required to overcome the friction and resistance of the machine; multiplied by the height to which the weight can be raised in the time given, the product will be the effect of that power; and the proportion of the two products will be the pro∣portion of the power to the effect: so that by loading the wheel with different weights succes∣sively, we shall be able to determine at what par∣ticular load and velocity of the wheel the effect is a maximum.

To determine the Velocity of the Water striking the Wheel.

First let the wheel be put in motion by the water, but without any weight in the scale; and let the number of turns in a minute be 60: now

it is evident,* 1.326 that was the wheel free from fric∣tion and resistance, that 60 times the circumfer∣ence of the wheel would be the space through which the water would have passed in a minute; with that velocity wherewith it struck the wheel: But the wheel being incumbered with friction and resistance and yet moving 60 turns in a minute, it is plain that the velocity of the wa∣ter must have been greater than 60 circumferen∣ces, before it met with the wheel. Let the cord now be wound round the cylinder but contrary to the usual way, and put as much weight in th•• scale as will without any water turn the wheel somewhat faster than 60 turns in a minute, sup∣pose 63, and call this the counter-weight, th•••• let it be tried again with the water assisted by this counter-weight, the wheel therefore will now make more than 60 turns in a minute, sup∣pose 64, hence we conclude the water still exerts some power to turn the wheel. Let the weight be increased so as to make 64½ turns in a minute without the water, then try it with the water and the weight as before, and suppose it now makes the same number of turns with the water, as without, viz. 64½, hence it is evident, that 〈◊〉〈◊〉 this case the wheel makes the same number of turns as it would with the water if the wheel had no friction or resistance at all, because the weight is equivalent thereto, for if the counter weight was too little to overcome the friction, the water would accelerate the wheel, and if too great it would retard it, for the water in this case becomes a regulator of the wheel's motion, and the velocity of its circumference becomes a mea∣sure of the velocity of the water.

In like manner in seeking the greatest product or maximum of effect; having found by trials what weight gives the greatest product, by simply mul∣tiplying the weight in the scale, by the number of turns of the wheel, find what weight in the

scale,* 1.327 when the cord is on the contrary side of the cylinder, will cause the wheel to make the same number of turns, the same way without water: it is evident that this weight will be nearly equal to all friction and resistance taken together; and consequently that the weight in the scale, with twice* 1.328 the weight of the scale, added to the back or counter-weight, will be equal to the weight that could have been raised supposing the machine had been without friction or resistance, and which multiplied by the height to which it was raised, the product will be the greatest effect of that power.

The Quantity of Water expended is found thus.

The pump was so carefully made, that no wa∣ter escaped back through the leathers, it deliver∣ed the same quantity each stroke, whether quick or slow, and by ascertaining the quantity of 12 strokes and counting the number of strokes in a minute, that was sufficient to keep the surface of the water to the same height, the quantity ex∣pended was found.

These things will be further illustrated by go∣ing over the calculations of one set of experi∣ments.

Specimen of a Set of Experiments.

The sluice drawn to the 1st hole,
The water above the floor of the sluice	30 inch.
Strokes of the pump in a minute,	39½
The head raised by 12 strokes,	21 inch.
The wheel raised the empty scale and made turns in a minute,	80

With a counter-weight of 1lb.8 oz.* 1.329 it made	85
Ditto, tried with water,	86

No.	lbs. oz.	turns in a min.	product.
1	4: 0	45	180
2	5: 0	42	210
3	6: 0	36¼	217½
4	7: 0	33¾	236¼
5	8:0	30	240 m••••.
6	9: 0	26½	238½
7	10: 0	22	220
8	11: 0	16½	1••1½
9	12: 0	* 1.330 ceased working.

Counter-weight for 30 turns without water oz. in the scale.

N. B. The area of the head was 105,8 〈◊〉〈◊〉 inches, weight of the empty scale and pulley 〈◊〉〈◊〉 ounces, circumference of the cylinder 9 inches and circumference of the water-wheel 75 do.

Reduction of the above Set of Experiments.

The circumference of the wheel 75 inches multiplied by 86 turns, gives 6450 inches for 〈◊〉〈◊〉 velocity of the water in a minute, 1/〈◊〉〈◊〉; of which will be the velocity in a second, equal to 〈◊〉〈◊〉

inches,* 1.331 or 8,96 feet, which is due to a head of 15 inches,* 1.332 and this we call the virtual or effective head.

The area of the head being 105,8 inches, this multiplied by the weight of water of one cubic inch, is equal to the decimal of ,579 of the ounce avoirdupois, gives 61,26 ounces for the weight of as much water as is contained in the head upon one inch in depth, 1⅙ of which is 3,83lb. this mul∣tiplied by the depth 21 inches gives 80,43lb. for the value of 12 strokes, and by proportion 39⅓ (the number made in a minute) will give 264,7lb. the weight of water expended in a minute.

Now, as 264,7lb. of water may be considered as having descended through a space of 15 inches in a minute, the product of these two numbers 3970 will express the power of the water to pro∣duce mechanical effects; which are as follows.

The velocity of the wheel at the maximum as appears above, was 30 turns in a minute; which multiplied by 9 inches, the circumference of the cylinder, makes 270 inches: but as the scale was hung by a pulley and double line, the weight was only raised half of this, viz.135 inches.

The weight in the scale at the maximum	8lb. 0 oz.
Weight of the scale and pulley,	0lb. 10 oz.
Counter-weight, scale, and pulley,	0lb. 12 oz.
Sum of the resistance	9lb. 6 oz. or 9,375lb

Now, as 9,375lb. is raised 135 inches, these two numbers being multiplied together produces 266, which expresses the effect produced at a

maximum:* 1.333 so that the proportion of the power to the effect is as 3970:1266, or as 10:3,18.

But though this is the greatest single effect ••••••••∣ducible from the power mentioned, by the 〈◊〉〈◊〉 pulse of the water upon an undershot wheel 〈◊〉〈◊〉 as the whole power of the water is not extra 〈◊〉〈◊〉 thereby, this will not be the true ratio between the power and the sum of all the effects procura∣ble therefrom: for the water must necessary leave the wheel with a velocity equal to 〈◊〉〈◊〉 circumference, it is plain that some part of 〈◊〉〈◊〉 power of the water must remain after 〈◊〉〈◊〉 the wheel.

The velocity of the wheel at a maximum 〈◊〉〈◊〉 turns a minute, and consequently its circumfer∣ence moves at the rate of 3,123 feet per second which answers to a head of 1,82 inches: this 〈◊〉〈◊〉 multiplied by the expence of water in a mi∣nute, viz. 264,7lb. produces 4••1 for the power remaining, this being deducted from the 〈◊〉〈◊〉 power 3970, leaves 3489 which is that 〈◊〉〈◊〉 the power that is spent in producing the 〈◊〉〈◊〉 1266, so that the power spent 3489 is 〈◊〉〈◊〉 greatest effect 1266, as 10:3,62, or as 11:4.

The velocity of the water striking the 〈◊〉〈◊〉 86 turns in a minute, is to the velocity at a ••••••∣imum 30 turns a minute, as 10:3,5 or as 20 〈◊〉〈◊〉 so that the velocity of the wheel is a little 〈◊〉〈◊〉 than ⅓ of the velocity of the water.

The load at a maximum has been shewn 〈◊〉〈◊〉 equal to 9lb. 6 oz. and that the wheel ceased ••••••••∣ing with 12lb. in the scale: to which if the 〈◊〉〈◊〉 of the scale be added, viz.10 oz.* 1.334 the proper 〈◊〉〈◊〉 will be nearly as 3 to 4, between the load at the maximum and that by which the wheel is ••••••••∣ped.† 1.335

It is somewhat remarkable,* 1.336 that though the ve∣locity of the wheel in relation to the water turns out greater than 1-3 of the velocity of the water, yet the impulse of the water in case of the maxi∣mum is more than double of what is assigned by theory; that is, instead of 4/9 of the column it is nearly equal to the whole column.* 1.337

It must be remembered, therefore, that in the present case, the wheel was not placed in an open river where the natural current after it has com∣municated its impulse to the float, has room on all sides to escape, as the theory supposes; but in a conduit or race, to which the float being adapted, the water cannot otherwise escape than by mov∣ing along with the wheel. It is observable, that a wheel working in this manner as soon as the wa∣ter meets the float, it receiving a sudden check rises up against the float, like a wave against a fix∣ed object, insomuch, that when the sheet of wa∣ter is not a quarter of an inch thick, before it meets the float, yet this sheet will act upon the whole surface of a float, whose height is three inches; consequently, was the float no higher than the thickness of the sheet of water, as the theory al∣so supposes, a great part of the force would be lost by the water dashing over the float.

In confirmation of what is already delivered, I have adjoined the following table, containing the result of 27 experiments made and reduced in the manner above specified. What remains of the theory of undershot wheels, will naturally follow from a comparison of the different expe∣riments together.

A TABLE of Experiments, No. 1.

Number.	〈◊〉〈◊〉 of the water in the cistern.	Turns of the wheel, unloaded.	Virtual head deduced therefrom.	Turns at a maximum.	Load at the equilibrium.	Load at the maximum.	Water expended in a minute.	Power.	Effect.	Ratio of the power and effect.	Ratio of the velocities of the water and wheel.	〈…〉〈…〉 to the load at the 〈◊〉〈◊〉.
	in		inchs.		lb. oz.	lb. oz.	lbs.
1	33	88	15,85	30	13 10	10 9	275	4358	1411	10:3, 24	10:3,4	10:7,〈◊〉〈◊〉
2	30	86	15,	30	12 10	9 6	264, 7	3970	1266	10:3,2	10:3,5	10:7,4
3	27	••2	13, 7	28	11 2	8 6	243	3329	1044	10:3,15	10:3,4	10:7,〈◊〉〈◊〉
4	••4	78	12,3	27,7	9 10	7 5	235	2890	901,4	10:3,12	10:3,55	10:7,5
5	21	75	11,4	25,9	8 10	6 5	214	2439	735,7	10:3, 02	10:3,45	10:7,〈◊〉〈◊〉
6	18	70	9,95	23,5	6 10	5 5	199	1970	561,8	10:2, 85	10:3,36	10:8,〈◊〉〈◊〉
7	••5	65	8,54	23, 4	5 2	4 4	178,5	1524	442,5	10:2,9	10:3,6	10:8,〈◊〉〈◊〉
8	〈◊〉〈◊〉	••0	7,29	22	3 10	3 5	161	1173	328	10:2,8	10:3, 77	10:〈◊〉〈◊〉,〈◊〉〈◊〉
9	••9	52	5,47	19	2 12	2 8	134	733	213,7	10:2, 9	10:3,65	10:〈◊〉〈◊〉,〈◊〉〈◊〉
10	〈◊〉〈◊〉	42	3,55	16	1 12	1 10	114	404,7	117	10:2, 82	10:3,8	10:〈◊〉〈◊〉,〈◊〉〈◊〉
11	••4	84	14,2	30,75	13 10	10 14	342	4890	1505	10:3,07	10:3,66	10:〈◊〉〈◊〉,〈◊〉〈◊〉
12	21	81	13,5	29	11 10	9 6	297	4009	1223	10:3,01	10:3,6••	10:〈◊〉〈◊〉,〈◊〉〈◊〉
13	1••	••2	10,5	26	9 10	8 7	285	2993	975	10:3,25	10:3,6	10:〈◊〉〈◊〉,〈◊〉〈◊〉
14	15	••0	9,6	25	7 10	6 14	277	2659	774	10:2,92	10:3,62	10:〈◊〉〈◊〉,〈◊〉〈◊〉
15	12	13	8,0	25	5 10	4 14	234	1872	549	10:2,94	10:3,97	10:〈◊〉〈◊〉,〈◊〉〈◊〉
16	〈◊〉〈◊〉	16	6,37	23	4 0	3 13	201	1280	390	10:3, 05	10:4,1	10:〈◊〉〈◊〉,〈◊〉〈◊〉
17	••6	16	4,25	21	2 8	2 4	167,5	712	212	10:2, 98	10:4,55	10:〈◊〉〈◊〉,〈◊〉〈◊〉
18	15	72	10 5	29	11 10	9 6	357	3748	1201	10:3,23	10:4,02	10:〈◊〉〈◊〉,〈◊〉〈◊〉
19	12	••6	8,75	26,75	8 10	7 6	330	2887	878	10:3,05	10:4,05	10:〈◊〉〈◊〉,〈◊〉〈◊〉
20	9	59	6,8	24, 5	5 8	5 0	255	1734	541	10:3 01	10:4,22	10:〈◊〉〈◊〉,〈◊〉〈◊〉
21	6	48	4,7	23,5	3 2	3 0	228	1064	317	10:2,99	10:4,9	10:〈◊〉〈◊〉,〈◊〉〈◊〉
22	12	68	9, 3	27	9 2	8 6	359	3338	1006	10:3,02	10:3,97	10:〈◊〉〈◊〉,〈◊〉〈◊〉
23	9	58	6,8	26,25	6 2	5 13	332	1257	686	10:3,04	10:4,52	10:〈◊〉〈◊〉,〈◊〉〈◊〉
24	6	••8	4,7	24,5	3 12	3 8	262	1231	385	10:3,13	10:5,1	10:〈◊〉〈◊〉,〈◊〉〈◊〉
25	9	60	7,29	27,3	6 12	6 〈◊〉〈◊〉	355	2588	783	10:3,03	10:4, 55	10:〈◊〉〈◊〉,〈◊〉〈◊〉
26	〈◊〉〈◊〉	50	5,03	24,6	4 6	〈◊◊〉〈◊◊〉	307	1544	456	10:2,92	10:4,9	10:〈◊〉〈◊〉,〈◊〉〈◊〉
27	6	50	5,03	26	4 15	4 9	360	1811	534	10:2,95	10:5,2	10:〈◊〉〈◊〉,〈◊〉〈◊〉
1	2	3	4	5	6	7	8	9	10	11	12	13

Maxims and Observations deduced from the forego∣ing Table of Experiments.* 1.338

MAX. 1. That the virtual or effective head be∣ing the same, the effect will be nearly as the quantity of water expended.

This will appear by comparing the contents of the columns 4, 8 and 10, in the foregoing sets of experiments, as for

Example I. taken from No. 8 and 25, viz.

No.	Virtual head.	Water expended.	Effect.
8	7, 29	161	328
25	7, 29	355	785

Now the heads being equal if the effects are proportioned to the water expended, we shall have by maxim I. as 161:355::328:723; but 723 falls short of 785, as it turns out in experiment, according to No. 25 by 62. The effect therefore of No. 25, compared with No. 8, is greater than according to the present maxim, in the ratio of 14 to 13.

The foregoing example with four similar ones are seen at one view in the following table.

* 1.339

A TABLE of Experiments, No. 2.

Examples.	No. Table 1.	Virtual head,	Expence of water.	Effect.	COMPARISON.	Variation.	Proportional va∣riation,
1st	8	7,29	161	328	161: 355:: 328: 723	624	14: 13
25	7,29	355	785
2d	13	10, 5	285	975	285: 357:: 975: 1221	11—	121: 122
18	10,5	357	1210
3d	22	6,8	255	541	255: 332:: 541: 704	18—	38: 39
23	6,8	332	686
4th	21	4,7	228	317	228: 262:: 317: 364	214	18: 17
24	4,7	262	385
5th	26	5,03	307	450	307: 360:: 450: 531	3••	17••: 177
27	5,03	360	534

By this table of experiments it appears that some fall short,* 1.340 and others exceed the maximum, and all agree as near as can be expected in an af∣fair where so many different circumstances are concerned; therefore we may conclude the max∣im to be true.

MAX. II. That the expence of the water be∣ing the same, the effect will be nearly as the height of the virtual or effective head.

This also will appear by comparing the con∣tents of columns 4, 8 and 10 in any of the sets of experiments.

Example 1. of No. 2 and No. 24.

No.	Virt. head.	Expence.	Effect.
2	15	264,7	1266
24	4,7	262	385

Now as the expences are not quite equal, we must proportion one of the effects accordingly, thus:

By maxim I.	262:264,7:: 385:389
And by max. II.	15: 4,7::1266:397
	Difference 8

The effect therefore of No. 24, compared with No. 2, is less than according to the present max∣im in the ratio of 49: 50.

MAX. III. that the quantity of water expend∣ed being the same, the effect is nearly as the square root of its velocity.

This will appear by comparing the contents of columns 3, 8 and 10, in any set of experiments; 〈◊〉〈◊〉 for

Example I. of No. 2 with No. 24, viz.

No.	Turns in a min.	Expence.	Effect.
2	86	264,7	1266
24	48	262,	385

The velocity being as the number of turns,* 1.341 〈◊〉〈◊〉 shall have

By maxim I.	262: 264,7	::385:389
And by max. III.	862 482	::1266:394
7396:2304
		Difference 5.

The effect of No. 24, compared with No, 〈◊〉〈◊〉. less than by the present maxim in the ratio 〈◊〉〈◊〉 78:79.

MAX. IV. The aperture being the same, 〈◊〉〈◊〉 effect will be nearly as the cube of the velocity of the water.

This also will appear by comparing the con∣tents of columns 3, 8 and 10, as for

Example of No. 1 and No. 10, viz.

No.	Turns.	Expence.	Effect.
1	88	275	1411
10	42	114	117

LEMMA. It must here be observed, that, water passes out of an aperture in the same ••••••∣tion, but with different velocities, the exp•••••• will be proportional to the velocity; and there∣fore conversely, if the expence is not proportion∣al to the velocity, the section of water is not 〈◊〉〈◊〉 same.

Now comparing the water discharged with 〈◊〉〈◊〉 turns of No. 1 and 10, we shall have 88:42 〈◊〉〈◊〉 131,2; but the water discharged by No. 10 〈◊〉〈◊〉 114lb. therefore, tho' the sluice was drawn to 〈◊〉〈◊〉 same height in No. 10 as in No.1: yet the ••••••∣tion of the water passing out, was less in No. 〈◊〉〈◊〉 than No. 1, in the proportion of 114 to 131 consequently had the effective aperture or section of the water been the same in No. 10 as in No. 〈◊〉〈◊〉 so that 131, 2lb. of water had been discharged, in∣stead of 114lb. the effect would have been increas∣ed in the same proportion; that is,

By lemma	88: 42	::275:131, * 1.342 2
By maxim I.	114: 131,2	::117:134,5
And by max. IV.	883: 423	::1411:153,5
681472: 74088
		Difference 19

The effect therefore of No. 10, compared with No. 1, is less than it ought to be, by the present maxim, in the ratio of 7:8.

OBSERVATIONS.

OBSERV. 1st. On comparing column 2 and 4, table I, it is evident, that the virtual head bears no certain proportion to the head of water, but that when the aperture is greater or the velocity of the water issuing therefrom less, they approach nearer to a coincidence: and consequently, in the large opening of mills and sluices, where great quantities of water are discharged from moderate ••eads, the head of water and virtual head deter∣mined from the velocity will nearer agree, as ex∣perience confirms.

OBSERV. 2nd. Upon comparing the several proportions between the powers and effects in co∣lumn 11th, the most general is that of 10 to 3; the streams are 10 to 3,2 and 10 to 2,8; but as it is observable, that where the quantity of water or the velocity thereof is great, that is, where the power is greatest, the 2nd term of the ratio is greatest also, we may therefore well allow the proportion subsisting in large works as 3 to 1.

OBSERV. 3rd. The proportion of velocities between the water and wheel in column 12 are contained in the limits of 3 to 1 and 2 to 1; but as the greater velocities approach the limits of 3 to 〈◊〉〈◊〉, and the greater quantity of water approach to

that of 2 to 1,* 1.343 the best general proportion will be that of 5 to 2.* 1.344

OBSERV. 4th. On comparing the numbers 〈◊〉〈◊〉 column 13, it appears, that there is no certain ra∣tio between the load that the wheel will ca•••••• 〈◊〉〈◊〉 its maximum, and what will totally stop it; 〈◊〉〈◊〉 that they are contained within the limits of 〈◊〉〈◊〉 19 and of 20 to 15; but as the effect approach nearest to the ratio of 20 to 15 or of 4 to 3, 〈◊〉〈◊〉 the power is greatest, whether by increase of ve∣locity or quantity of water, this seems to be 〈◊〉〈◊〉 most applicable to large works: but as the 〈◊〉〈◊〉 that a wheel ought to have in order to work the best advantage, can be assigned by knowing 〈◊〉〈◊〉 effect it ought to produce, and the velocity, 〈◊〉〈◊〉 ought to have in producing it, the exact know∣ledge of the greatest load that it will bear is 〈◊〉〈◊〉 less consequence in practice.† 1.345

It is to be noted, that in almost all of the exam∣ples under the three last maxims (of the four pre∣ceding) the effect of the lesser power falls short 〈◊〉〈◊〉 its due proportion to the greater, when comp•••••••• by its maxim. And hence, if the experiment are taken strictly, we must infer that the 〈◊〉〈◊〉 increase and diminish in an higher ratio than 〈◊〉〈◊〉 maxims suppose; but as the deviations is not ve∣ry

considerable,* 1.346 the greatest being about ⅕ of the quantity in question, and as it is not easy to make experiments of so compound a nature, with abso∣lute precision, we may rather suppose that the lesser power is attended with some friction, or works under some disadvantage, not accounted for: and therefore we may conclude that these maxims will hold very nearly, when applied to works in large.

After the experiments abovementioned were tried, the wheel which had 24 floats was reduc∣ed to 12, which caused a diminution in the effect on account of a greater quantity of water escap∣ing between the floats and the floor, but a cricu∣lar sweep being adapted thereto, of such a length that one float entered the curve before the pre∣ceding one quitted it, the effect came so near to the former, as not to give hopes of increasing the effect by increasing the number of floats past 24, in this particular wheel.

PART II. Art. 68. Concerning Overshot Wheels.

IN the former part of this essay, we have consi∣dered the impulse of a confined stream, acting on undershot wheels; we now proceed to examine the power and application of water, when acting by its gravity on overshot wheels.

It will appear in the course of the following de∣ductions, that the effect of the gravity of de∣scending bodies, is very different from the effect of the stroke of such as are non-elastic, though ge∣nerated by an equal mechanical power.

The alterations of the machinery already de∣scribed,* 1.347 to accommodate the same for experiments on overshot wheels, were principally as follows.

Plate XII. The sluice I b being shut down, the rod H I was taken off. The undershot water wheel was taken off the axis, and instead thereof an overshot wheel of the same size and diameter was put in its place. Note, this wheel was 2 inches deep in the shroud or depth of the bucket, the number of buckets was 36.

A trunk for bringing the water upon the wheel was fixed according to the dotted lines fg, the aperture was adjusted by a shuttle, which also closed up the outer end of the trunk, when the water was to be stopped.

Specimen of a SET of EXPERIMENTS,* 1.348

Head 6 Inches—14 1-2 strokes of the Pump in a minute, 12 ditto=80 lb.* 1.349 weight of the scale (being wet) 10 1-2 ounces.

Counter weight for 20 turns besides the Scale, 3 ounces.

No.	wt.in the scale.	turns.	product.	observations.
1	0	60	—	threw most part of the water out of the wheel.
2	1	56	—
3	2	52	—
4	3	49	147	received the water more quietly.
5	4	47	188
6	5	45	225
7	6	42½	255
8	7	41	287
9	8	38½	308
10	9	36½	328½
11	10	35½	355
12	11	32¾	360½
13	12	31¼	375
14	13	28½	370½
15	14	27½	385
16	15	26	390
17	16	24½	392
18	17	22¼	386¾
19	18	21¼	391½
20	19	20¾	394¼	maximum.
21	20	19¾	395
22	21	18¼	383¼
23	22	18	396	worked irregular.
24	23	overset by its load.

Reduction of the preceding Specimen.* 1.350

In these experiments the head being 6 inches, and the height of the wheel 24 inches, the whole descent will be 30 inches: the expence of water was 14½ strokes of the pump in a minute, where of 12 contained 80lb. therefore the water ex∣pended in a minute, was 96⅔lb. which multiplied by 30 inches, gives the power =2900.

If we take the 20th experiment for the maxi∣mum, we shall have 20¾ turns a minute, each of which raised the weight 4½ inches, that is 93,37 inches, in a minute. The weight in the scale was 19lb. the weight of the scale 10½ oz. the counter-weight 3 oz. in the scale, which with the weight of the scale 10½ oz. makes in the whole 20½lb. which is the whole resistance or load, this multiplied by 93,37 makes 1914 for the effect.

The ratio therefore of the power and effect will be as 2900:1914, or as 10:6,6 or as 3 to 〈◊〉〈◊〉 nearly.

But if we compute the power from the height of the wheel only, we have 96⅔lb.×24 inches 〈◊〉〈◊〉 2320 for the power, and this will be to the effect as 2320:1914 or as 10:8,2 or as 5 to 4 nearly

The reduction of this specimen is set down in No. 9 of the following table, and the rest were deducted from a similar set of experiments, reduced in the same manner.

TABLE III.—Containing the result of 16 sets of Expe∣riments on Overshot-Wheels.

Number.	Whole descent.	Water expended per minute.	Turns at a maximum per minute.	Weight raised at a maximum.	Power of the whole descent.	Power of the Wheel.	Effect.	Ratio of the whole power and effect.	Ratio of the power of the wheel and effect.	Mean ratio.
	inc.	lb.		lbs.
1	27	30	19	6½	810	720	0556	10:6,9	10:7,7	Medium 10:8,1
2	27	56⅔	16¼	14½	1530	1360	1060	10:6,9	10:7,8
3	27	56⅔	20¾	12½	1530	1360	1167	10:7,6	10:8,4
4	27	63⅓	20½	13½	1710	1524	1245	10:7,3	10:8,2
5	27	76⅔	21½	15½	2070	1840	1500	10:7,3	10:8,2
6	28½	73⅓	18¾	17½	2090	1764	1476	10:7	10:8,4	10:8,2
7	28½	96⅔	20¼	20½	2755	2320	1868	10:6,8	10:8,1
8	30	90	20	19½	2700	2160	1755	10:6,5	10:8,1	10:8,2
9	30	96⅔	20¾	20½	2900	2320	1914	10:6,6	10:8,2
10	30	113⅓	21	23½	3400	2720	2221	10:6,5	10:8,2
11	33	56⅔	20¼	13½	1870	1360	1230	10:6,6	10:9	10:8,5
12	33	106⅔	22¼	21〈◊〉〈◊〉	3520	256	2153	10:6,1	10:8,4
13	33	146⅔	23	27〈◊〉〈◊〉	4840	3520	2846	10:5,9	10:8,1
14	35	65	19¾	16〈◊〉〈◊〉	2275	1560	1466	10:6,5	10:9,4	10:8,5
15	35	120	21½	25½	4200	2880	2467	10:5,9	10:8,6
16	35	163 1/2;	25	26½	5728	3924	2981	10:5,2	10:7,6
1	2	3	4	5	6	7	8	9	10	11

OBSERVATIONS AND DEDUCTION FROM THE FOREGOING EXPERIMENTS.

I. Concerning the Ratio between the Power and 〈◊〉〈◊〉 of Overshot Wheels.

The effective power of the water must be rec∣koned upon the whole descent, because it must be raised to that height in order to be in a condition of producing the same effect a second time.

The ratios between the powers so estimated and the effects at the maximum, deduced from the several sets of experiments are exhibited at 〈◊〉〈◊〉 view in column 9 of table III; and hence it ap∣pears, that those ratios differs from that of 10 to 7,6 to that of 10 to 5,2; that is, nearly from 〈◊〉〈◊〉 3 to 4:2. In those experiments where the head of water and quantities expended are least; the proportion is nearly as 4 to 3, but where the head and quantities are greatest, it approaches nearer to that of 4 to 2, and by a medium of the whole the ratio is that of 3:2 nearly. We have seen be∣fore in our observations upon the effects of under∣shot wheels, that the general ratio of the power to the effect when greatest, was as 3:1. The ef∣fect, therefore of overshot wheels, under the 〈◊〉〈◊〉 circumstances of quantity and fall, is at a medi∣um double to that of the undershot: and a con∣sequence thereof, that non-elastic bodies when acting by their impulse or collision, communication only a part of their original power; the other part being spent in changing their figure, in con∣sequence of the stroke.* 1.351

The powers of water computed from the height of the wheel only, compared with the 〈◊〉〈◊〉

as in column 10,* 1.352 appear to observe a more constant ratio: for if we take the medium of each class, which is set down in column 11. we shall find the extreme to differ no more than from the ratio of 10:8,1 to that of 10:8,5, and as the se∣cond terms of the ratio gradually increases from 8,1 to 8,5 by an increase of head from 3 inches to 11, the excess of 8,5 above 8,1 is to be imputed to the superior impulse of the water, at the head of 11 inches, above that of 3 inches, so that if we reduce 8,1 to 8, on account of the impulse of the 3 inch head, we shall have the ratio of the power computed upon the height of the wheel only, to the effect at a maximum, as 10:8 or as 5:4 nearly. And from the equality of the ratio, between pow∣er and effect, subsisting where the constructions are similar, we must infer that the effects 〈◊〉〈◊〉 well as the powers, are as the quantities of water and perpendicular heights, multiplied together re∣spectively.

II. Concerning the most proper Height of the Wheel in Proportion to the whole descent.

We have already seen in the preceding observ∣ation, that the effect of the same quantity of wa∣ter, descending through the same perpendicular space, is double, when acting by its gravity upon an overshot wheel, to what the same produces when acting by its impulse, upon an undershot. It also appears that by increasing the head from 3 to 11 inches, that is, the whole descent, from 27 to 35, or in the ratio of 7 to 9 nearly, the ef∣fect is advanced no more than in the ratio of 8,1 to 8,4; that is, as 7:7,26, and consequently the increase of the effect is not 1/7 of the increase of the perpendicular height. Hence it follows that the higher the wheel is in proportion to the whole descent, the greater will be the effect; because it depends less upon the impulse of the head, and

more upon the gravity of the water,* 1.353 in the buck∣ets: and if we consider how obliquely the water issuing from the head must strike the buckets, we shall not be at a loss to account for the little ad∣vantage that arises from the impulse thereof; and shall immediately see of how little conse∣quence his impulse is to the effect of an overshot wheel. However, as every thing has its limits, so has this: for thus much is desirable, that the water should have somewhat greater velocity, than the circumference of the wheel, in coming thereon: otherwise the wheel will not only be re∣tarded by the buckets striking the water, but thereby dashing a part of it over, so much of the power is lost.

The velocity that the circumference of the wheel ought to have being known, the head re∣quisite to give the water its proper velocity is ea∣sily found, by the common rules of Hydrostatics and will be found much less than what is comm••n∣ly practised.

III. Concerning the Velocity of the Circumferences of the Wheel in order to produce the greatest Ef∣fect.

If a body is let fall freely from the ••urface of the head to the bottom of the descent, it will take a certain time in falling; and in this case the whole action of gravity is spent in giving the body a cer∣tain velocity: But, if this body in falling is 〈◊〉〈◊〉 to act upon some other body, so as to produce 〈◊〉〈◊〉 mechanical effect, the falling body will be retard∣ed; because, a part of the action of gravity is the•• spent in producing the effect, and the remainder only giving motion to the falling body: and there∣fore, the slower a body descends, the greater will be the portion of the action of gravity applicable to the producing a mechanical effect. Hence we

are led to this general rule,* 1.354 that the less the velo∣city of the wheel, the greater will be the effect thereof. A confirmation of this doctrine, toge∣ther with the limits it is subject to in practice, may be deduced from the foregoing specimen of a set of experiments.

From these experiments it appears, that when the wheel made about 20 turns in a minute, the effect was near upon the greatest; when it made 30 turns, the effect was diminished about 1/20; part; but, that when it made 40, it was diminished a∣bout ¼ when it made less than 18¼, its motion was irregular; and when it was loaded so as not to admit its making 18 turns, the wheel was over∣powered by its load.

It is an advantage in practice, that the velocity of the wheel should not be diminished farther than what will procure some solid advantage in point of power; because, as the motion is slower, the buckets must be made larger; and the wheel be∣ing more loaded with water, the stress upon every part of the work will be increased in proportion: the best velocity for practice therefore will be such, as when the wheel here used made about 30 turns in a minute; that is, when the velocity of the circumference is a little more than 3 feet in a second.

Experience confirms, that this velocity of 3 feet in a second, is applicable to the highest overshot wheels as well as the lowest; and all other parts of the work being properly adapted thereto, will produce very nearly the greatest effect possible. However, this also is certain, from experience, that high wheels may deviate further from this rule, before they will loose their power, by a gi∣ven aliquot part of the whole, than low ones can be admitted to do: for a wheel of 24 feet high may move at the rate of 6 feet per second without loos∣ing

any considerable part of its power: and,* 1.355 on the other hand, I have seen a wheel of 33 feet high that has moved very steadily and well, with a ve∣locity but little exceeding 2 feet.* 1.356

[Said Smeaton has also made a model of a wind-mill, and a complete set of experiments on the power and effect of the wind, acting on wind-mill sails of different constructions. But as the ac∣counts thereof are quite too long for the compass of my work, I therefore only extract little more than a few of the principal maxims deduced from his experiments, which, I think, may not only be of good service, to those who are concerned in building wind-mills, but may serve to confirm some principles, deduced from his experiments on water-mills.]

PART III. Art. 69. On the Construction and Effects of Wind-mill Sails.† 1.357

IN trying experiments on wind-mill sails, the wind itself is too uncertain to answer the pur∣pose: we must therefore have recourse to artifi∣cial wind.

This may be done two ways; either by caus∣ing the air to move against the machine, or the machine to move against the air. To cause the air to move against the machine in a sufficient co∣lumn with steadiness and the requisite velocity, is not easily put in practice: To carry the ma∣chine forward in a right line against the air,

would require a larger room than I could conve∣niently meet with.* 1.358 What I found most practi∣cable therefore was, to carry the axis whereon the sails were to be fixed progressively round in the circumference of a large circle. Upon this idea the machine was constructed.* 1.359

Specimen of a Set of Experiments.

Radius of the sails	21 inches.
Length of the sails in cloth,	18
Breadth of the sails in the cloth,	5,6
‡ 1.360 Angle at the extremity,	10 degs.
Do. at the greatest inclination,	25
20 turns of the fails raised the weight	11,3 inch.
Velocity of the centre of the sails in the circumference of the great cir∣cle in a second, in which the ma∣chine was carried round,	6 feet.
Continuance of the experiment,	52 secs.

No.	Weight in the scale.	Turns.	Product.
1	0lb.	108	0
2	6	85	510
3	6½	81	526½
4	7	78	546
5	7½	73	547½ maxim.
6	8	65	520
7	9	0	0

The product is found by simply multiplying the weight in the scale by the number of turns.

By this set of experiments it appears that the maximum velocity is ⅔ of the greatest velocity,

and that the ratio of the greatest load to that of a maximum is,* 1.361 as 9 to 7,5, but by adding the weight of the scale and friction to the load the ratio turns out to be as 10:8,4, or as 5 to 4 nearly. The following table is the result of 19 similar sets of experiments.

By the following table it appears, that the most general ratio between the velocity of the sails un∣loaded and when loaded to a maximum, is 3 to 2 nearly.

And the ratio between the greatest load and the load at a maximum (taking such experiments where the sails answered best) is at a medium a∣bout as 6 to 5 nearly.

And that the kind of sails used in the 15th and 16th experiments is best of all, because they pro∣duce the greatest effect or product, in proportion to their quantity of surface, as appears in column 12.

TABLE IV. Containing Nineteen Sets of Experiments on Wind-mill Sails, of various structures, positions and quantities of surface.

The kind of sails made 〈◊〉〈◊〉	Number.	Angle at the extreme••ties.	Greatest angle.	Turos of the sails unloaded.	Ditto at a maximum.	Load at a maximum.	Greatest load.	Product.	Quantity of surface.	Ratio of the greatest veloci∣ty to the velocity at a max∣imum.	Ratio of the greatest load ••o the load at maximum.	Ratio of a surface to the product.
I 1.362		o	o			lb.	lb.		sq.in
1	35	35	66	42	7,56	12,59	318	404	10:7	10:6	10: 7,9
II 1.363	2	12	12		70	6,3	7,56	441	404		10:8,3	10:10,1
3	15	15	105	69	6,72	8,12	464	404	10:6,6	10:8,3	10:10,15
4	18	18	96	66	7,0	9,81	462	404	10:7	10:7,1	10:10,15
III 1.364	5	9	26,5		66	7,0		462	404			10:11,4
6	12	29,5		70,5	7,35		518	404			10:12,8
7	15	32,5		63,5	8,3		527	404			10:13,0
IV 1.365	8	0	15	120	93	4,75	5,31	442	404	10:7,7	10:8,9	10:11,0
9	3	18	120	79	7,0	8,12	553	404	10:6,6	10:8,6	10:13,7
10	5	20		78	7,5	8,12	585	404		10:9,2	10:14,5
11	7,5	22,5	113	77	8,3	9,81	639	404	10:6,8	10:8,5	10:15,8
12	10	25	108	73	8,69	10,37	634	404	10:6,8	10:8,4	10:15,7
13	12	27	100	66	8,41	10,94	580	404	10:6,6	10:7,7	10:14,4
V 1.366	14	7,5	22,5	123	75	10,65	12,59	799	505	10:6,1	10:8,5	10:15,8
15	10	25	117	74	11,08	13,69	820	505	10:6,3	10:8,1	10:16,2
16	12	27	114	66	12,09	14,23	799	505	10:5,8	10:8,4	10:15,8
17	15	30	96	63	12,09	14,78	762	505	10:6,6	10:8,2	10:15,1
VI 1.367	18	12	22	105	64,5	16,42	27,87	1059	854	10:6,1	10:5,9	10:12,4
19	12	22	99	64,5	18,06		1165	1146	10:5,9		10:10,1
	1	2	3	4	5	6	7	8	9	10	11	12

TABLE V. Containing the Result of 6 Sets of Experiments, made for determining the Dif∣ference of Effect according to the Differ∣ence of the Wind.

Number.	Angle at the ex∣tremity.	Velocity of the wind in a se∣cond.	Turns of the sails, unloaded.	Turns of the sails, at a maximum.	Load at the max∣imum.	Greatest load.	Product.	Maximum load for the half velocity.	Turns of the sails therewith.	Product of the less∣er load and great∣er velocity.	Ratio of the two products.	Ratio of the great∣est velocity to the velocity at a max∣imum.	Ratio of the great∣est load to the load at a maxi∣mum.
	degr	ft. in.			lb.	lb.
1	5	4 4,5	96	66	4,47	5,37	295					10:6,9	10:8,3
2	5	8 9	207	122	16,42	18,06	2003	4,47	180	805	10:27,3	10:5,9	10:9,1
3	7,5	4 4,5		65	4,62		300
4	7,5	8 9		130	17,52		2278	4,62	180	832	10:27,8
5	10	4 4,5	91	61	5,03	5,87	307					10:6,7	10:8,5
6	10	8 9	178	110	18,61	21,34	2047	5,03	158	795	10:26	10:6,2	10:8,7
1	2	3	4	5	6	7	8	9	10	11	12	13	14

N. B. The sails were of the same kind as those of Nos. 10,11 and 12, table IV. Continuance of the experiment one mi∣nute.

Concerning the Effects of Sails according to the differ∣ent Velocity of the Wind.* 1.368

From the foregoing table the following maxims deduced.

MAXIM I. The velocity of wind-mill sails, whe∣ther unloaded or loaded, so as to produce a maxi∣mum, is nearly as the velocity of the wind, their shape and position being the same.

This appears by comparing the respective num∣bers of columns 4 and 5, table V, wherein those numbers 2,4 and 6, ought to be double of No. 1,3 and 5, and are as nearly so as can be expected by the experiments.

MAXIM II. The load at the maximum is near∣ly but somewhat less than as the square of the ve∣locity of the wind, the shape and position of the sails being the same.

This appears by comparing No. 2,4 and 6, in column 6, with 1, 3 and 5, wherein the former ought to be quadruple of the latter (as the veloci∣ty is double) and are as nearly so as can be expect∣ed.

MAXIM III. The effects of the same sails at a maximum are nearly, but somewhat less than, as the cubes of the velocity of the wind.* 1.369

It has been shewn maxim I, that the velocity of sails at a maximum, is nearly as the velocity of the wind; and by maxim II, that the load at the maximum is nearly as the square of the same ve∣locity. If those two maxims would hold precise∣ly, it would be a consequence that the effect would 〈◊〉〈◊〉 in triplicate ratio thereof. How this agrees with experiment will appear by comparing the products in column 8, wherein those of No. 2, 4 and 6 (the velocity of the wind being double) ought to be octuble of those of No. 1, 3 and 5, and are nearly so.

MAXIM IV. The load of the same sails at the maximum is nearly as the squares of,* 1.370 and their ef∣fects as the cubes, of their number of turns in a given time.

This maxim may be esteemed a consequence of the three preceding ones.

[These 4 maxims agree with and confirm the 4 maxims concerning the effects of spouting 〈◊〉〈◊〉 acting on undershot mills; and, I think, sufficient∣ly confirms as a law of motion, that the effect pro∣duced if not the instant momentum of a body in motion, is as the square of its velocity, as asserted by the Dutch and Italian philosophers.

Smeaton says, that by several trials in large, he has found the following angles to answer as well as any:] The radius is supposed to be divided in∣to 6 parts, and ⅙ reckoning from the centre is cal∣led 1, the extremity being denoted 6.

No.	Angle with the axis.	Angle with the plain of motion.
1	72°	18°
2	71	19
3	72	18 middle.
4	74	16
5	77½	12½
6	83	7 extremity.

[He seems to prefer the sails being largest at the extremities.]

END OF PART FIRST.

INTRODUCTION.

WHAT has been said in the first part, was meant to establish theories and easy rules—In this part I mean to bring them into practice, in as concise a manner as possible, referring only to the articles in the first part, where the reasons and demonstrations are given.

This part is particularly intended for the help of Young and Practical Millwrights, whose time will not permit them fully to investigate the principles of theo∣ries, which requires a longer series of studies than most of them can possibly spare from their business; there∣fore I shall endeavour here to reduce the substance of all that has been said, to a few tables, rules, and short directions, which, if found to agree with practice, will be sufficient for the practitioner.

There are but two principles by which water acts on mill-wheels, to give them motion, viz. Percussion and Gravity.

That equal quantities of water, under equal per∣pendicular descents, will produce double the power by

gravity that it will by percussion, has been shewn in articles 8 and 68.

Therefore, when the water is scarce, we ought to endeavour to cause it to act by gravity, as much as possible, paying due regard to other circumstances noted in article 44, so as to obtain a steady motion, &c.

THE YOUNG Mill-wright's Guide. CHAPTER I. OF THE DIFFERENT KINDS OF MILLS.

Of Undershot Mills.

UNDERSHOT wheels move by the per∣cussion or stroke of the water, and are only half as powerful as other wheels that are moved by the gravity of the water. See art. 8. Therefore this construction ought not to be used, except where there is but little fall or great plenty of water. The undershot wheel, and all others that move by percussion, should move with a velocity nearly equal to two thirds of the velocity of the water. See art. 42. Fig. 28. plate iv. represents this con∣struction.

For a rule for finding the velocity of the water, under any given head, see art. 51.

Upon which principles,* 1.371 and by said rule, is formed the following table of the velocity of spouting water, under different heads, from one to twenty-five feet high above the centre of the issue; to which is added the velocity of

the wheel suitable thereto,* 1.372 and the number of revolutions a wheel of fifteen feet diameter (which I take to be a good size) will revolve in a minute; also, the number of cogs and rounds in the wheels, both for double and sin∣gle gears, so as to produce about ninety-seven or one hundred revolutions for a five feet stone per minute, which I take to be a good mo•••••• and size for a mill-stone, grinding for mer∣chantable flour.

That the reader may fully understand how the following table is calculated, let him ob∣serve,

1. That by art. 42, the velocity of the wheel must be just 577 thousandth parts of the velocity of the water; therefore, if the velo∣city of the water, per second, be multiplied by, 577 the product will be the maximum ve∣locity of the wheel, or velocity that will pro∣duce the greatest effect, which is the third co∣lumn in the table.

2. The velocity of the wheel per second, multiplied by 60, produces the distance the circumference moves per minute, which, di∣vided by 47,1 feet, the circumference of a 15 feet wheel, quotes the number of revolutions of the wheel per minute, which is the fourth column.

3. That by art. 20 and 74, the number of revolutions of the wheel per minute, multi∣plied by the number of cogs in all the driving wheels, successively, and that product divided by the product of the number of cogs in all the leading wheels, multiplied successively, the quotient is the revolutions of the stones per minute, which is the ninth and twelfth co∣lumns.

4. The cubochs of power required to drive the stone,* 1.373 being, by art. 61, equal to 111,78 cubochs per second, which, divided by half the head of water, added to all the fall (if any,) being the virtual or effective head by art. 61 quotes the quantity of water, in cubic feet, required per second, which is the thirteenth column.

5. The quantity required, divided by the velocity with which it is to issue, quotes the area of the aperture of the gate—fourteenth column.

6. The quantity required, divided by the velocity of the water proper for it to move a∣long the canal, quotes the area of a section of the canal—fifteenth column.

7. Having obtained their areas, it is easy, by art. 65, to determine the width and depth, as may suit other circumstances.

THE MILL-WRIGHT'S TABLE FOR UNDERSHOT MILLS, CALCULATED FOR A WATER-WHEEL OF FIFTEEN FEET, AND ST•••••• OF FIVE FEET DIAMETER.

Head of water above the point of im∣pact.	Velocity of the water per second at the point of impact.	Velocity of the wheel per second, load∣ed at a maximum.	Number of revolutions of the wheel of 15 feet diameter, per minute.	No. of cogs in the master cog-wheel.	Rounds in the wallower.	Cogs in the counter cog-wheel.	Rounds in the trundle.	Revolutions of the stone per minute.	Cogs in the cog-wheel for single gear.	Rounds in the trundle.	Revolutions of the stone per minute.	Cubic feet of water required per second to drive a 5 feet stone 97 revolutions per minute.	Area of the gate to vent the water, or rather of a section of the column of water at place of impact.	Area of a section 〈…〉〈…〉 to bring on the water with 1, 5 feet velocity.
feet	feet	feet										cub.ft.	sup. ft.	sup. ft.
1	8,1	4,67	5,94	112	22	54	16	101,6				223,5	27,5	149,〈◊〉〈◊〉
2	11,4	6,57	8,36	96	23	54	19	99,				111,78	9,8	74,〈◊〉〈◊〉
3	14,	8,07	10,28	88	25	54	19	100,5				74,52	4,6	43,
4	16,2	9,34	11,19	78	23	48	20	97,				55,89	3,45	37,26
5	18,	10,38	13,22	66	24	48	18	97,	112	15	98,66	44,7	2,48	29,8
6	19,84	11,44	14,6	66	24	48	20	96,2	112	17	96,2	37,26	1,9	24,84
7	21,43	12,36	15,74	66	25	44	19	96,2	104	17	96,2	31,9	1,48	21,26
8	22,8	13,15	16,75	66	25	44	20	97,2	96	16	100,	27,94	1,22	18,6
9	24,3	14,02	17,86	66	26	42	19	100,2	96	17	100,8	24,84	1,02	16,56
10	25,54	14,73	18,78	60	25	44	20	99,	96	18	100,	22,89	,9	15,26
11	26,73	15,42	19,7	60	26	44	20	100,	96	19	99,5	20,32	,76	13,54
12	28,	16,16	20,5	60	27	44	20	100,	96	20	98,4	18,63	,66	12,42
13	29,16	16,82	21,42	60	27	42	20	99,8	96	21	102,6	16,27	,56	10,8
14	30,2	17,42	22,19	60	28	42	20	99,	88	20	97,63	15,94	,53	10,6
15	31,34	18,08	23,03	60	29	42	20	99,	88	21	96,5	14,9	,47	9,93
16	32,4	18,69	23,8						88	21	99,7	13,97	,43	9,31
17	33,32	19,22	24,48						84	21	97,9	13,14	,39	8,76
18	34,34	19,81	25,23						80	21	96,1	12,42	,36	8,〈◊〉〈◊〉
19	35,18	20,29	25,82						80	21	98,3	11,76	,33	7,84
20	36,2	20,88	26,6						78	21	98,3	11,17	,3	7,4
21	37,11	21,41	27,26						78	22	97,	10,64	,29	7,1
22	37,98	21,86	27,84						78	22	98,6	10,16	,26	6,77
23	38,79	22,38	28,5						72	21	97,7	9,72	,25	6,48
24	39,69	2••,9	29,17						66	20	96,2	9,32	,23	6,21
25	40,5	23,36	29,75						60	18	99,	8,94	,22	5,96
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15

Note, that five feet fall is the least that a single gear can be built on,* 1.374 to keep the cog-wheel clear of the water, and give the stone sufficient motion.

Although double gear is calculated to fifteen feet fall, yet I do not recommend them above ten feet, unless for some particular conveni∣ence, such as two pair of stones to one wheel, &c. &c. The number of cogs in the wheels are even, and chosen to suit eight, fix, or four arms, so as not to pass through any of them, this being the common practice. But when the motion cannot be obtained without a trun∣dle that will cause the same cogs and rounds to meet too often, such as 16 into 96, which will meet every revolution of the cog-wheel, or 18 into 96, which will meet every third re∣volution—I advise rather to put in one more or less, as may best suit the motion, which will cause them to change oftener. See art. 82.

Note, that the friction at the aperture of the gate will greatly diminish both the veloci∣ty and power of the water in this application, where the head is great, if the gate be made of the usual form, wide and shallow. Where the head is great, the friction will be great. See art. 55. Therefore the wheel must be narrow, and the aperture of the gate of a square form, to evade the friction and loss that may be under a wide wheel, if it does not run close to the sheeting.

Use of the Table.

HAVING levelled your mill-seat carefully, and finding such fall and quantity of water as determines you to make choice of an under∣shot wheel; for instance, suppose 6 feet fall, and about 45 cubic feet of water per second, which you find as directed in art. 53; cast of about 1 foot for fall in the tale-race, below the bottom of the wheel, if subject to back∣water, leaves you 5 feet head; look for 5 feet head in the first column of the table, and a∣gainst it are all the calculations for a 15 feet water-wheel and 5 feet stones; in the thir∣teenth column you have 44,7 cubic feet of water; which shews you have enough for a 5 feet pair of stones; and the velocity of the water will be 18 feet per second, the velocity of the wheel 10,38 feet per second, and it will revolve 13,22 times per minute. And if you choose double gear, then 66 cogs in the master cog-wheel, 24 rounds in the wallower, 48 cogs in the counter cog-wheel, and 〈◊〉〈◊〉 rounds in the trundle, will give the stone 〈◊〉〈◊〉 revolutions in a minute; if single gear, 112 cogs and 15 rounds give 98,66 revolutions in a minute; it will require 44,7 cubic feet of water per second; the size of the gate must be 2,48 feet, which will be about 4 feet wide and, 62 feet deep, about 7 1-4 inches deep; the size of the canal must be 29,8 feet; that is, about 3 feet deep, and 9,93 or nearly 10 feet wide. If you choose single gear, you may make your water-wheel much less, say

7 1-2 feet, the half of 15 feet, then the cog-wheel must have half the number of cogs, the trundle-head the same, the spindle will be longer, husk lower, and the mill full as good; but, in this case, it will not do, because a cog-wheel of 66 cogs would reach the water; but where the head is 10 or 12 feet, it will do very well.

If you choose stones, or water-wheels, of other sizes, it will be easy, by the rules by which the table is calculated, to proportion the whole to suit, seeing you have the veloci∣ty of the periphery of a wheel of any size.* 1.375

Observations on the Table.

1. IT is calculated for an undershot wheel constructed,* 1.377 and the water shot on, as in plate IV, fig. 28. The head is counted from the point of impact I, and the motion of the wheel at a maximum, about ,58 of the velocity of the water; but when there is plenty of water, and great head, the wheel will run best at about, 66 or two thirds of the velocity of the water: therefore the stones will incline to run faster than in the table, in the ratio of 58 to 66, nearly; for which reason, I have set the motion of 5 feet stones under 100 revolutions in a minute, which is slower than common practice; they will incline to run between and 110 revolutions.

2. I have taken half of the whole head a∣bove the point of impact, for the virtual 〈◊〉〈◊〉 effective head, by art. 53; which appears 〈◊〉〈◊〉 me will be too little in very low heads, 〈◊〉〈◊〉 perhaps too much in high ones. As the prin∣ciple of non-elasticity does not appear to 〈◊〉〈◊〉 to operate against the power so much in 〈◊〉〈◊〉 as in high heads, therefore if the head be 〈◊〉〈◊〉.

1 foot,* 1.378 it may not require 223,5 cubic feet of water per second, and if 20 feet, may re∣quire more than 11,17 cubic feet of water per second, as in the table. See art. 8.

Art. 71. Of Tub Mills.

A TUB MILL has a horizontal water-wheel,* 1.379 that is acted on by the percussion of the water altogether; the shaft is verticle, carrying the stone on the top of it, and serves in place of a spindle; the lower end of this shaft is set in a step fixed in a bridge-tree, by which the stone is raised and lowered, as by the bridge-tree of other mills; the water is shot on the upper side of the wheel, in a tan∣gent direction with its circumference. See fig. 29, plate IV, which is a top view of the tub-wheel, and fig. 30 is a side view of it, with the stone on the top of the shaft, bridge-tree, &c. The wheel runs in a hoop, like a mill-stone hoop, projecting so far above the wheel as to prevent the water from shooting over the wheel, and whirls it about until it strikes the buckets, because the water is shot on in a deep narrow column, 9 inches wide and 18 inches deep, to drive a 5 feet stone, with 8 feet head—so that all this column can∣not enter the buckets until part has passed half way round the wheel, so 〈◊〉〈◊〉 there are always nearly half the buckets struck at once; the buckets are set obliquely, so that the water

may strike them at right angles.* 1.380 See fig. 30. As soon as it strikes it escapes under the wheel in every direction, as in fig. 29.* 1.381

The disadvantages of these wheels are,* 1.382

1. The water does not act to advantage on them, we being obliged to make them so small to obtain velocity to the stone (in most cases) that the buckets take up a third part of their diameter.

2. The water acts with less power than on undershot wheels,* 1.383 as it is less confined at the time of striking the wheel, and its non elastic principle takes place more fully. See art. 8.

3. It is with difficulty we can put a sufficient quantity of water to act on them to drive them with sufficient power, if the head be low; therefore I advise to strike the water on in two places, as in fig. 29; then the apertures need only be about 6 by 13 inches each, in∣stead of 9 by 18, and will act to more advan∣tage; and then, in this case, nearly all the buckets will be acted on at once.

Their advantages are,

Their exceeding simplicity and cheapness,* 1.384 having no cogs nor rounds to be kept in re∣pair; their wearing parts are few, and have but little friction; the step-gudgeon runs un∣der water, therefore, if well fixed, will not get out of order in a long time; and they will move with sufficient velocity and power with 9 or 10 feet total fall, and plenty of water; and, if they be well fixed, they will not re∣quire

much more water than undershot wheels; therefore they are vastly preferable in all seats with plenty of water, and above 8 feet fall.

In order that the reader may fully under∣stand how the following table is calculated, let him consider,

1. That as the tub-wheel moves altogether by percussion,* 1.385 the water flying clear of the wheel the instant it strikes, and it being better, by art. 70, for such wheels to move faster in∣stead of slower than the maximum velocity; therefore, instead of ,577 we will allow them to move ,66 velocity of the water;* 1.386 then mul∣tiplying the velocity of the water by ,66 gives the velocity of the wheel, at the centre of the buckets; which is the 3d column in the table.

2. And the velocity of the wheel per second,* 1.387 multiplied by 60, and divided by the number of revolutions the stone is to make in a minute, gives the circumference of the wheel at the centre of the buckets; which circumference, multiplied by 7, and divided by 22, gives the diameter from the centre of the buckets, to produce the number of revolutions required; which are the 4th, 5th, 6th and 7th columns.

3. The cubochs of power required,* 1.388 by art. 63, to drive the stone, divided by half the head, gives the cubic feet of water required to produce said power; which are the 8th and 10th columns.

4. The cubic feet of water,* 1.389 divided by the velocity, will give the sum of the apertures of the gates; which are the 9th and 11th co∣lumns.

5. The cubic feet of water, divided by 1,5 feet,* 1.390 the velocity of the water in the canal, gives the area of a section of the canal; which are the 12th and 13th columns.

6. For the quantity of water, aperture of gate, and size of canal, for 5 feet stones, see table for undershot Mills, in art. 70.

THE MILL-WRIGHT's TABLE FOR TUB MILLS.

Head of water above the point of impact or top of the wheel.	Velocity of the water per second.	Velocity of the wheel, counted at the centre of the buckets, and being, 66 velocity of the water.	Diameter of the wheel, to the centre of the buckets, for a stone 4 feet diameter, 122 revolutions in a minute.	Ditto for a 5 feet stone, to revolve 98 times in a minute.	Ditto for a 6 feet stone, to revolve 81 times in a minute.	Ditto for a 7 feet stone, to revolve 70 times in a minute.	Cubic feet of water per second, required to drive the 4 feet stones.	Sum of the areas of the apertures of the gate for a 4 feet stone.	Cubic feet of water required, per second, for a 6 feet stone.	Sum of the areas of the apertures for a 6 feet stone.	Area of a section of the canal sufficient to bring the water to 4 feet stones, with a velocity of 1,5 feet, per second.	Ditto of a 6 feet stone.
ft.	feet	feet	feet	feet	feet	feet	cub.ft	su.f	cub.ft	su.ft	sup.ft	sup.ft
8	22,8	15,04	2,17	2,73	3,3	3,9	17,34	,76	40,9	1,79	11,56	27,3
9	24,3	16,03	2,5	3,12	3,68	4,37	15,41	,64	36,35	1,5	10,3	24,23
10	25,54	16,85	2,63	3,28	3,97	4,59	13,87	,54	32,72	1,28	9,25	21,7
11	26,73	17,64	2,75	3,44	4,15	4,8	12,61	,47	29,74	1,11	8,4	19,83
12	28,	18,48	2,9	3,6	4,34	4,9	11,56	,41	27,26	,97	7,7	18,17
13	29,16	19,24	3,01	3,74	4,53	5,24	10,67	,36	25,17	,86	7,1	16,8
14	30,2	19,93	3,12	3,9	4,7	5,43	9,9	,33	23,36	,77	6,6	15,56
15	31,34	20,68	3,24	4,03	4,87	5,67	9,24	,29	21,93	,7	6,16	14,62
16	32,4	21,38	3,34	4,12	5,01	5,83	8,67	,27	20,45	,6	5,71	13,6
17	33,32	21,99	3,43	4,25	5,18	5,95	8,16	,24	19,24	,57	5,44	12,15
18	34,34	22,66	3,54	4,41	5,32	6,18	7,7	,22	18,18	,52	5,13	12,12
19	35,18	23,21	3,63	4,52	5,47	6,33	7,3	,2	17,	,48	4,9	11,33
20	36,2	23,89	3,71	4,62	5,49	6,47	6,93	,19	16,36	,45	4,62	10,9
1	2	3	4	5	6	7	8	9	10	11	12	13

Use of the Table for Tub Mills.

HAVING levelled your seat, and finding that you have above 8 feet fall, and plenty of water, and wish to build a mill on the sim∣plest, cheapest, and best construction to suit your seat; you will, of course, make choice of a tub mill.

Cast off 1 foot for fall in the tale-race below the bottom of the wheel, if it be subject to back-water, and 9 inches for the wheel: then suppose you have 9 feet left for head above the wheel; look in the table, against 9 feet head, and you have all the calculations neces∣sary for 4, 5, 6 and 7 feet stones, the quan∣tity of water required to drive them, the sum of the areas of the apertures, and the areas of the canals.

If you choose stones of any other size, you can easily proportion the parts to suit, by the rules by which the table is calculated.

Art.72. Of Breast Mills.

BREAST WHEELS, which have the water shot on them in a tangent direction,* 1.391 are acted on by the principles of both percussion and gravity; all that part above the point of impact, called head, acts by percussion, and all that part below said point, called fall, acts 〈◊〉〈◊〉 gravity.

We are obliged,* 1.392 in this structure of breast mills,* 1.393 to use more head than will act to advan∣tage; because we cannot strike the water 〈◊〉〈◊〉 the wheel, in a true tangent direction, higher than I, the point of impact in fig. 31, which is a breast-wheel, with 12 feet perpendicular descent, 6,5 feet of which is above the point I, as head, and 5,5 feet below, as fall. The upper end of the shute, that carries the water down to the wheel, must project some inches above the point of the gate when full dra•••• else the water will strike towards the centre of the wheel; and it must not project too high else the water in the penstock will not c•••••• fast enough into the shute when the head 〈◊〉〈◊〉 a little. The bottom of the penstock is a little below the top end of the shute, to leave room for stones and gravel to settle, and prevent them from getting into the gate.

We might lay the water on higher, by set∣ting the top of the penstock close to the whe•••• and using a sliding gate at bottom, as 〈◊〉〈◊〉 by the dotted lines; but this is not approved of in practice. See Ellicott's mode, part 〈◊〉〈◊〉 plate III, fig. 1.

But if the water in the penstock be nearly as high as the wheel,* 1.394 it may be carried over as by the upper dotted lines, and shot on ••••••••∣wards, making that part next the wheel 〈◊〉〈◊〉 shute to guide the water into the wheel, 〈◊〉〈◊〉 the gate very narrow or shallow, allowing 〈◊〉〈◊〉 water to run over the top of it when drawn by this method (called Pitchback) the 〈◊〉〈◊〉 may be reduced to the same as it is for 〈◊〉〈◊〉 overshot wheel; and then the motion of the circumference of the wheel will be equal

the motion of an overshot wheel,* 1.395 whose dia∣meter is equal to the fall below the point of impact, and their power will be equal.

This structure of a wheel,* 1.396 fig. 31, I take to be a good one, for the following reasons, viz.

1. The buckets,* 1.397 or floats, receive the per∣cussion of the water at right angles, which is the best direction possible.

2. It prevents the water from flying to∣wards the centre of the wheel, without re∣acting against the bottom of the buckets, and retains it in the wheel, to act by its gravity in its descent, after the stroke.

3. It admits air, and discharges the water freely, without lifting it at bottom; and this is an important advantage, because, if the buckets of a wheel be tight, and the wheel wades a little in back-water, they will lift the water a considerable distance as they empty; the pressure of the atmosphere prevents the water from leaving the buckets freely, and it requires a great force to lift them out of the water with the velocity of wheel; which may be proved by dipping a common water-bucket into water, and lifting it out, bot∣tom up, with a quick motion, you have to ••••ft not only the water in the bucket, but it appears to suck a deal more up after it; which is the effect of the pressure of the atmosphere, see art. 56. This shews the necessity of air-holes to let air into the buckets, that the wa∣ter may have liberty to get out freely.

Its disadvantages are,

1. It loses the water much, if it is not kept close to the sheeting. And,

2. It requires too great a part of the total fall to be used as head, which is a loss of pow∣er, one foot fall being equal in power to two feet head, by art. 8.

Fig. 32 is a draught,* 1.398 shewing the position of the shute for striking the water on a wheel in a tangent direction, for all the total perpen∣dicular descents from 6 to 15 feet; the points of impact are numbered inside the fig. with the number of the total fall, that each is for respectively. The top of the shute is only about 15 inches from the wheel, in order to set the point of impact as high as possible, al∣lowing 3 feet above the upper end of the 〈◊〉〈◊〉 to the top of the water in the penstock, which is little enough, when the head is often to be run down any considerable distance; but when the stream is steady, being always nearly the same height in the penstock, 2 feet would 〈◊〉〈◊〉 sufficient, especially in the greatest total 〈◊〉〈◊〉 where the quantity is less, raising the shute foot would raise the point of impact nearly the same, and increase the power, because I 〈◊〉〈◊〉 fall is equal in power to 2 feet head, by art 61.

On these principles, to suit the application of water, as represented by fig. 32, I have calculated the following table for breast mill. And, in order that the reader may fully un∣derstand the principles on which it is calcu∣lated, let him consider as follows:

1. That all the water above the point of im∣pact,* 1.399 called head, acts wholly by percussion and all below said point, called fall, acts wh••••∣ly by gravity (see art. 60) and form the 〈◊〉〈◊〉 and 3d columns.

2. That half the head, added to the whole fall,* 1.400 constitutes the virtual or effective descent, by art. 61; which is the 4th column.

3. That if the water was permitted to de∣scend freely down the circular sheeting,* 1.401 after it passes the point of impact,* 1.402 its velocity would be accelerated, by art. 60, to be, at the low∣est point, equal to the velocity of water spout∣ing from under a head equal to the whole de∣scent: therefore the maximum velocity of this wheel will be a compound of the velocity to suit the head and the acceleration after it passes the point of impact. Therefore, to find the velocity of this wheel, I first multiply the ve∣locity of the head, in column 5, by ,577 (as for the undershot mills) which gives the velo∣city suitable to the head; I then (by the rule for determining the velocity of overshots) say, as the velocity of water descending 21 feet, equal to 37,11 feet per second, is to the velo∣city of the wheel 10 feet per second, so is the acceleration of velocity, after it passes the point of impact, to the accelerated velocity of the wheel; and these two velocities added, gives the velocity of the wheel; which is the 6th column.

4. The velocity of the wheel per second,* 1.403 multiplied by 60, and divided by the circum∣ference of the wheel, gives the revolutions per minute: 7th column.

5. The number of cogs in the cog-wheel,* 1.404 multiplied by the number of revolutions of the wheel per minute, and divided by the rounds in the trundle-head, will give the number of revolutions of the stone per minute; and if we divide by the number of revolutions the stone

is to have,* 1.405 it gives the rounds in the trundle, and, when fractions arise, take the nearest whole number; columns 8, 9, and 10.

6. The cubochs of power required to turn the stone,* 1.406 by art. 63, divided by the virtual descent, gives the cubic feet of water required per second; column II.

7. The cubic feet,* 1.407 divided by the velocity of water allowed in the canal, suppose 1,5 feet per second, gives the area of the canal; column 12.

8. If the mill is to be double geared, take the revolutions of the wheel from column 7 of this table, and look in column 4 of the under∣shot table, art. 70, for the number of revo∣lutions nearest to it, and against that number you have the gears that will give a 5 feet stone the right motion.

THE MILL-WRIGHT's TABLE FOR BREAST MILLS, CALCULATED FOR A WATER-WHEEL FIFTEEN FEET, AND STONES FIVE FEET DIAMETER; THE WATER BEING SHOT ON IN A TANGENT DIRECTION TO THE CIR∣CUMFERENCE OF THE WHEEL.

Total perpendicular descent or fall of the water from the top of the water in the penstock, to ditto in tale-race.	Head above the point of impact.	Fall below the point of impact.	Virtual or effective descent, being half the head added to the fall.	Velocity of the water per second at the point of impact.	Velocity of the circumference of the wheel per second.	Number of revolutions of a wheel fifteen feet diameter per minute.	Cogs in the cog-wheel, for single gear.	Rounds in the trundle-head.	Revolutions of the stone per minute.	Cubic feet of water required per second.	Area of a section of the canal, allowing the velocity of the water in it to be 1,5 feet per second.
feet	feet	feet	feet	feet	feet	No.	No.	N.	No.	cub.ft	sup.ft
6	4,5	1,5	3,75	17,13	10,61	13,5	112	15	100,8	29,8	19,25
7	5,	2,	4,5	18,	11,3	14,4	112	16	100,8	24,83	16,55
8	5,5	2,5	5,25	18,99	12,07	15,3	104	16	99,4	21,29	14,19
9	5,9	3,1	6,05	19,48	12,53	16,	104	16	102,7	18,45	12,3
10	6,2	3,8	6,9	20,16	13,07	16,6	96	16	99,6	16,2	10,8
11	6,5	4,5	7,75	20,64	13,53	17,	96	16	102,	14,42	9,61
12	6,8	5,3	8,7	21,11	14,03	17,81	96	17	100,5	12,73	8,49
13	6,8	6,2	9,6	21,11	14,35	18,28	96	18	97,5	11,63	7,75
14	6,9	7,1	10,55	21,3	14,41	18,35	96	18	97,8	10,59	7,06
15	7,	8,	11,5	21,13	14,76	18,56	96	18	98,4	9,72	6,48
1	2	3	4	5	6	7	8	9	10	11	12

Use of the Table for Breast Mills.

HAVING a seat with above 6 feet fall but not enough for an overshot mill, and the water being scarce, so that you wish to make the best use of it, leads you to the choice of a breast mill.

Cast off about 1 foot for fall in the tale-race below the bottom of the wheel, if much subject to back-water; and suppose you have then 9 feet total descent; look for it in the first column of the table, and against it you have it divided into 5,9 feet head above, and 3,1 feet fall below the point of impact, which is the highest point that the water can be fair∣ly struck on the wheel, leaving the head 3 feet deep above the shute; which is equal to 6,05 feet virtual or effective descent: the velocity of the water striking the wheel 18,99 feet, velocity of the wheel 12,07 feet, per second, will revolve 16 times in a minute; and, if single geared, 104 cogs, and 16 rounds, gives the stone 99,4 revolutions in a minute, re∣quires 21,29 cubic feet of water per second; the area of a section of the canal must be 14,19 feet, about 3 feet deep, and 5 feet wide. If the stones be of any other size, it is easy to proportion the gears to give them any number of revolutions required.

If you wish to proportion the size of the stones to the power of your seat, multiply the cubic feet of water your stream affords per se∣cond, by the virtual descent in column 4, and that product is the power in cubochs; then

look in the table, in art. 63, for the size of the stone that nearest suits that power.

For instance, suppose your stream affords 14 cubic feet of water per second, then 14 multi∣plied by 6,05 feet virtual descent, produces 84,7 cubochs of power; which, in the table in art. 63, comes nearest to 4,5 feet for the dia∣meter of the stones; but, by the rules laid down in art. 63, the size may be found more exactly.

Note, 6 cubochs of power are required to every superficial foot of the stones.

Art. 73. Of Overshot Mills.

FIG. 33,* 1.408 plate IV, is an Overshot Wheel; the water is laid on at the top, so that the up∣per part of the column will be in a true tan∣gent direction with the circumference of the wheel, but so that all the water may strike with∣in the circle of the wheel.

The gate is drawn about 12 inches behind the perpendicular line from the centre of the wheel,* 1.409 and the point of the shute ends at said perpendicular, with a direction a little down∣wards, which gives the water a little velocity downwards to follow the wheel; for if it be directed horizontally, the head will give it no velocity downwards, and, if the head be great, the parabolic curve, which the spouting water forms, will extend beyond the outside of the

circle of the wheel, and it will incline to 〈◊〉〈◊〉 over. See art. 44 and 60.

The head above the wheel acts by per∣cussion,* 1.410 as on an undershot wheel, and we have shewn, art. 43, that the head should be such as to give the water velocity 3 for 2 of the wheel. After the water strikes the wheel it acts by gravity; therefore, to calculate the power, we must take half the head and add it to the fall, for the virtual descent, as in breast mills.

The velocity of overshot wheels are as the square roots of their diameters. See art. 43.

On these principles, I have calculated the following table for overshot wheels; and, in order that the reader may understand it fully, let him consider well the following premises:

1. That the velocity of the water spouting on the wheel must be one and a half the velo∣city of the wheel,* 1.411 by art. 43; then, to find the head that will give said velocity, say, 〈◊〉〈◊〉 the square of 16,2 feet per second, is to 4 feet, the head that gives that velocity, so is the square of the velocity required, to the hea•• that will give that velocity—But, to this head so found, we must add a little by conjecture to overcome the friction of the aperture. See art. 55.

In this table, I have added to the heads o•• wheels from 9 to 12 feet diameter, 1 of a foot and from 12 to 20 I have added, 1 tenth more for every foot increase of diameter, and from 20 to 30 feet I have added ,05 more to every foot diameter's increase; which gives a 30 feet wheel 1,5 feet additional head, while a 9 feet

wheel has only, 1 tenth of a foot, to overcome the friction. The reason of this great difference will appear when we consider that the friction increases as the aperture decreases, and as the velocity increases—But this much depends on the form of the gate, for if that be nearly square, there will be but little friction, but if very oblong, say 24 inches by half an inch, then it will be very great.

The heads, thus found, compose the 3d co∣lumn.

2. The head, added to the diameter of the wheel,* 1.412 makes the total descent, and is co∣lumn 1.

3. The velocity of the wheel per second,* 1.413 taken from the table in art. 43, and multiplied by 60, and divided by the circumference of the wheel, quotes the number of revolutions of the wheel per minute, and is column 4.

4. The number of revolutions of the wheel per minute,* 1.414 multiplied by the number of cogs in all the driving wheels successively, and that product divided by the product of all the lead∣ing wheels, quotes the number of revolutions of the stone per minute, and is column 9, double gear, for 5 feet stones; and column 12, single gear, for 6 feet stones.

5. The cubochs of power required to drive the stone,* 1.415 by table in art. 63, divided by the virtual or effective descent, which is half the head added to the (fall or) diameter of the wheel, quotes the cubic feet of water required per second to drive the stone, and is column 13.

6. The cubic feet required,* 1.416 divided by the velocity you intend the water to have in the canal, quotes the area of a section of the ca∣nal. The width multiplied by the depth, must always produce this area. See art. 64.

7. The number of cogs in the wheel, mul∣tiplied by the quarter inches in the pitch, pro∣duces the circumference of the pitch circle which, multiplied by 7, and divided by 22, quotes the diameter in quarter inches; which, reduced to feet and parts, is column 15. The reader may here at once observe how near the cog wheel, in the single gear, will be to the water; that is, how near it is, in size, equal to the water-wheel.

Use of the Table.

HAVING, with care, levelled the seat 〈◊〉〈◊〉 which you mean to build, and found, that af∣ter deducting 1 foot for fall below the wheel, and a sufficiency for the sinking of the head race, according to its length and size, and having a total descent remaining sufficient for an overshot wheel, suppose 17 feet; then 〈◊〉〈◊〉 in column 1 of the table, for the descent near∣est to it, we find 16,74 feet, and against it 〈◊〉〈◊〉 wheel 14 feet diameter; head above the wheel 2,7 feet; revolutions of the wheel per min•••••• 11,17; (and double gears, to give a 5 feet stone 98,7 revolutions per minute; also, single gears, to give a 6 feet stone 76,6 revolutions per mi∣nute) the cubic feet of water required for 〈◊〉〈◊〉

feet stone 7,2 feet per second, and the area of a section of the canal 5 feet, about 2 feet deep and 2,5 feet wide.

If you choose to proportion the size of the stones exactly to suit the power of the seat, do it as directed in art. 63. All the rest can be proportioned by the rules by which the table is calculated.

THE MILL-WRIGHT's TABLE FOR OVERSHOT MILLS. CALCULATED FOR FIVE FEET STONES, DOUBLE GEAR, AND SIX FEET STONES, SINGLE GEAR.

Total descent of the water, which is in this table, made to suit the diameter of the wheel and head above it.	Diameter of the wheel.	Head above the wheel, allowing for the friction of the aperture, so as to give the water velocity 3 for 2 of the wheel.	Number of revolutions of the wheel per minute.	Double gear, 5 feet stones.	Single gear, 6 feet stones.	Cubic feet of water required per second, for 5 feet stones.	Area of a section of the canal, allowing the velocity of the water in it to be 1 foot per second.	Diameter of the pitch 〈◊〉〈◊〉 of the 〈◊〉〈◊〉 cog-wheels for single gear, pitch 4 1-4 inches.
No of cogs in master cog wheel.	Rounds in the wallower	Cogs in the counter cog-wheel.	Rounds in the trundle.	Revolutions of the stone per minute.	Cogs in the cog-wheel.	Rounds in the trundle.	Revolutions of the stone per minute.
feet	ft.	feet										cu.ft.	sup.ft	ft.inch.
10,51	9	1,51	14,3	54	21	44	16	102,9	60	11	78,	11,46	11,46	6:9〈◊〉〈◊〉
11,74	10	1,74	13,	54	21	48	18	98,	60	10	78,	10,3	10,3
12,94	11	1,94	12,6	60	21	48	18	96,	66	11	75,6	9,34	9,34	7:5¼
14,2	12	2,2	12,	66	23	48	17	97,	66	10	79,2	8,53	8,53
15,47	13	2,47	11,54	66	21	48	17	99,3	84	12	80,7	7,92	7,92	9:5½
16,74	14	2,74	11,17	72	23	48	17	98,7	96	14	76,6	7,2	7,2	10:9¼〈◊〉〈◊〉
17,99	15	2,99	10,78	78	23	48	18	98,3	96	13	81,9	6,77	6,77
19,28	16	3,28	10,4	78	23	48	17	99,5	120	16	76,	6,4	6,4	13:6¼〈◊〉〈◊〉;
20,5	17	3,5	10,1	78	21	48	18	96,6	120	15	80,8	6,	6,
21,8	18	3,8	9,8	84	24	48	17	97,	128	16	78,4	5,56	5,56	14:5¼〈◊〉〈◊〉
23,03	19	4,03	9,54	84	23	48	17	98,3	128	15	81,4	5,32	5,32
24,34	20	4,34	9,3	88	23	48	17	100,	128	15	79,3	5,04	5,04
25,54	21	4,54	9,1	88	23	48	17	98,3	128	15	77,6	4,81	4,81
26,86	22	4,86	8,9	96	24	48	17	100,5	128	14	81,4	4,57	4,57
27,99	23	4,99	8,7	96	25	54	18	100,2				4,34	4,34
29,27	24	5,27	8,5	96	25	54	17	103,				4,19	4,19
30,45	25	5,45	8,3	96	25	54	17	101,				4,	4,
31,57	26	5,57	8,19	96	25	54	17	99,6				3,82	3,82
32,77	27	5,77	8,03	104	25	54	18	100,2				3,7	3,7
33,96	28	5,96	7,93	104	25	54	18	99,				3,6	3,6
35,15	29	6,15	7,75	112	26	54	18	100,1				3,4	3,4
36,1	30	6,4	7,63	112	26	54	18	98,6				3,36	3,36
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15

Observations on the Table.

1. IT appears,* 1.417 that single gear does not much suit this construction; because, where the water-wheels are low, their motion is so flow that the cog-wheels (if made large enough to give sufficient motion to the stone, without having the trundle too small, see art. 23) will touch the water: And again, when the water-wheels are high, above 20 feet, the cog-wheels require to be so high, in order to give motion to the stone without having the trundle too small, that they become unwieldy, and the ••••sk too high, spindle short, &c. so as to be inconvenient. Therefore, single gear seems to suit overshots only where the diameter of the water-wheel is between 12 and 18 feet; and even with them, the water-wheel will have to run rather too fast, or the trundle be ••••ther too small, and the stones should be 6 feet diameter at least.

2. I have, in the preceding tables, allowed the water to pass along the canal with 1,5 feet ••er second velocity; but have since concluded that 1 foot per second is nearer the proper mo∣tion; that is, about 20 yards per minute; then the cubic feet required per second, will be the area of a section of the canal, as in co∣lumn 14 of this table.

3. Although I have calculated this table for the velocities of the wheels to vary as the square roots of their diameters, which makes 〈◊〉〈◊〉 30 feet wheel move 11,99 feet per second, and a 12 feet wheel ••o move 7,57 feet per se∣cond;

yet they will do to have equal velocity, and head, which is the common practice among mill-wrights. But, for the reasons I have mentioned in art. 43, I prefer giving them the velocity and head assigned in the table, in order to obtain steady motion.

4. Many have been deceived, by observing the exceeding slow and steady motion of some very high overshot wheels working forge or furnace bellows, concluding therefrom, that they will work equally steady with a very slow as with any quicker motion, not considering perhaps, that it is the principle of the bellows that regulates the motion of the wheel, which is different from any other resistance, for it soon becomes perfectly equable: therefore the motion will be uniform, which is not the case with any kind of mills.

5. Many are of opinion, that water is not well applied by an overshot wheel; because, say they, those buckets near above or below the centre, act on too short a lever. In en∣deavouring to correct this error, I have di∣vided the fall of the overshot wheel, fig. 33. plate IV, into feet, by dotted lines. Now, by art. 53 and 54, every cubic foot of water on the wheel produces an equal quantity of power in descending each foot perpendicular, called a cuboch of power; because, where the lever is shortest, there is the greatest quantity of water within the foot perpendicular; or, in other words, each cubic foot of water is 〈◊〉〈◊〉 much longer time, and passes a greater dis∣tance, in descending a foot perpendicular, than where it is longest; which exactly com∣pensates

for the deficiency in the length of lever. And, considering that the upper and lower parts of the wheel does not run away from the gravity of the water, so much as the breast of the wheel, we must conclude, that the upper and lower feet of perpendicular de∣scent (in theory) actually produce more pow∣er than the middle two feet—But (in practice) the lower foot is entirely lost, by the spilling of the water out of the buckets. See this de∣monstrated, art 54.

Of Mills moved by Re-action.

WE have now treated of the four different kinds of mills that are in general use. There are others, the invention or improvements of the late ingenious James Rumsey, which move by the re-action of the water. One of these is said to do well where there is much back-water; it being small, and of a true circular form, the back-water does not resist it much. I shall say but little of these, supposing the pro∣prietors mean to treat of them; but may say, that there appears to me but two principles by which water can be applied to move mill-wheels, viz. Percussion and Gravity.

For the different effects of equal quantities of water, with equal perpendicular descents, applied by these different principles, fee art.8 and 68.

Water may be applied, by percussion two ways, viz. by action (which is when it strikes the floats of a wheel) and by re-action, which is when it issues from within the wheel, and, by its re-action, moves it round; and these two are equal, by 3d general law of motion, art. 7.

For the effects of centrifugal force, and the inertia of the water, on this application of re-ac∣tion, see axioms I and II, art. 1; and art. 13. The principle of inertia will operate in pro∣portion to the quantity of water used; there∣fore this application will suit high heads better than low ones.

Water may be applied, by gravity, two ways, viz. either by spouting it high on the wheel, into tight buckets, as on common over-shots, or by causing the whole head of water to press on the floats, at the lower side of the wheel, which is so constructed that the wa∣ter cannot escape, but as the wheel moves, and at the same time keeping clear of the paradoxical principle mentioned in arts.48 and 59; which cannot be done, unless the floats are made to move on pivots, so as to fold in on one side of the wheel, and open out, to re∣ceive the weight of the water, on the other. And these two applications are equal in theory, as will appear plain by art. 54, fig. 20; yet they may differ greatly in practice.* 1.418

CHAPTER II. RULES AND CALCULATIONS.

Art. 74.

THE fundamental principle,* 1.419 on which is founded all rules for calculating the mo∣tion of wheels, produced by a combination of wheels, and for calculating the number of cogs to be put in wheels, to produce any mo∣tion that is required, see in art. 20; which is as follows:

If the revolutions that the first moving wheel makes in a minute,* 1.420 be multiplied by the num∣ber of cogs in all the driving wheels succes∣sively, and the product noted; and the revo∣lutions of the last leading wheel be multiplied by the number of cogs in all the leading wheels successively, and the product noted; these pro∣ducts will be equal in all possible cases. Hence we deduce the following simple rules:

1st. For finding the motion of the mill-stone; the revolutions of the water-wheel, and cogs in the wheels, being given,

RULE.* 1.421

Multiply the revolutions of the water-wheel per minute,* 1.422 by the number of cogs in all the driving wheels successively, and note the pro∣duct; and multiply the number of cogs or rounds in all the leading wheels successively, and note the product; then divide the first product by the last, and the quotient is the number of revolutions 〈◊〉〈◊〉 the stone per mi∣nute.

EXAMPLE.

Given, the revolutions of the water-wheel per minute	10,4
No. of cogs in the master cog-wheel	78	Drivers.
No. of do. in the counter cog-wheel	48
No. of rounds in the wallower	23	Leaders.
No. of do. in the trundle	17

Then 10,4, the revolutions of the water-wheel, multiplied by 78, the cogs in the mas∣ter wheel, and 48, the cogs in the counter wheel, is equal to 38937,6; and 23 rounds in the wallower, multiplied by 17, rounds in the trundle, is equal to 391, by which we divide 38937,6, and it quotes 99,5, the revolutions of the stone per minute; which are the cal∣culations for a 16 feet wheel, in the overshot table.

2d. For finding the number of cogs to be put in the wheels, to produce any number of revolutions required to the millstone, or any wheel.

Take any suitable number of cogs for all the wheels,* 1.423 except one;* 1.424then multiply the revolutions of the first mover per minute, by all the drivers, except the one wanting (if it be a driver) and the revolutions of the wheel required, by all the leaders, and divide the greatest product by the least, and it will quote the number of cogs required in the wheel to produce the desired revolutions.

Note, If any of the wheels be for straps, take their diameter in inches and parts, and multiply and divide with them, as with the cogs.

EXAMPLE.

Given, the revolutions of the water-wheel		10,4
And we chuse cogs in master wheel	78	Drivers.
Ditto in the counter wheel	48
And rounds in the wallower	23

The number of the trundle is required, to give the the stone 99 revolutions.

Then 10,4 multiplied by 78, and 48, is equal to 38937,6; and 99, multiplied by 23, is equal to 2277, by which divide 38937,6, and it quotes 16,66; instead of which, I take the nearest whole number, 17, for the rounds in the trundle, and find, by rule 1st, that it pro∣duces 99,5 revolutions, as required.

For the exercise of the learner, I have con∣structed fig.7,* 1.425 plate XI; which I call a circle of motion, and which serves to prove the fun∣damental

principle on which the rules are founded;* 1.426 the first shaft being also the last of the circle.

• A is a cog-wheel of 20 cogs, and is a driver.
• B is a cog-wheel of 24 cogs, and is a leader.
• C is a cog-wheel of 24 cogs, and is a driver.
• D is a cog-wheel of 30 cogs, and is a leader.
• E is a cog-wheel of 25 cogs, and is a driver.
• F is a cog-wheel of 30 cogs, and is a leader.
• G is a cog-wheel of 36 cogs, and is a driver.
• H is a cog-wheel of 20 cogs, and is a leader.

But if we trace the circle the backward way, the leaders become drivers.

• I is a strap-wheel 14½ inches diameter, driver.
• K is a strap-wheel 30 inches diameter, leader.
• L is a cog-wheel 12 cogs, diameter, driver.
• M is a cog-wheel 29 cogs, diameter, leader.

MOTION OF THE SHAFTS.

• The upright shaft, and first driver,
• —AH 36 revs. in a min.
• BC 30 revs. in a min.
• DE 24 revs. in a min.
• FG 20 revs. in a min.
• HA 36 revs. in a min.
• M 4 revs. in a min. which is the shaft of a hopperboy.

If this circle be not so formed, as to give the first and last shafts (which are here the same) exactly the same motion, one of the shafts must break as soon as they are put in motion.

The learner may exercise the rules on this circle,* 1.427 until he can form a similar circle of his own; and then he need never be afraid to un∣dertake to calculate any motion, &c. after∣wards.

I omit shewing the work for finding the motion of the several shafts in this circle, and the wheels to produce said motion; but leave it for the learner to practise the rules on.

EXAMPLES.

1st. Given, the first mover AH 36 revolu∣tions per minute, and first driver A 20 cogs, leader B 24; required, the revolutions of shaft BC. Answer, 30 revolutions per minute.

2d. Given, first mover 36 revolutions per minute, drivers 20—24—25, and leaders 24—30—30; required, the revolutions of the last leader. Answer, 20 revolutions per mi∣nute.

3d. Given, first mover 20 revolutions per minute, and first driver, strap wheel, 14½ inches, cog-wheel 12, and leader, strap-wheel, 30 inches, cog-wheel 29; required, the revolu∣tions of the last leader, or last shaft. Answer, 4 revolutions.

4th. Given, first mover 36 revolutions, driver A 20, C 24, leader B 24, D 30; required, the number of leader F, to produce 20 revolutions per minute. Answer, 30 cogs.

5th. Given, first mover 36 revolutions per minute, driver A 20, C 24, E 25, driver pully 14½ inches diameter, L 12, and leader B 24, D 30, F 30, M 29; required, the diameter of strap-wheel K, to give shaft 4 four revolutions per minute. Answer, 30 inches diameter.

The learner may,* 1.428 for exercise, work the above questions, and every other that he can propose on the circle.

Art. 75.

MATHEMATICIANS have laid down the following proportions for finding the circum∣ference of a circle by its diameter, or the di∣ameter by the circumference given,* 1.429viz.

As 1 is to 3,1416, so is the diameter to the circumference;* 1.430 and as 3,1416 is to 1, so is the circumference to the diameter: Or, as 7 is to 22, so is the diameter to the circumfe∣rence; and as 22 is to 7, so is the circum∣ference to the diameter. The last proportion makes the diameter a little the largest; there∣fore it suits mill-wrights best for finding the pitch circle; because the sum of the distance, from centre to centre, of all the cogs in a wheel, makes the circle too short, especially where the number of cogs are few, because the distance is taken in strait lines, instead of the circle. In a wheel of 6 cogs only, the cir∣cle will be so much too short, as to give the diameter 2/22 parts of the pitch or distance of the cogs too short. Hence we deduce the fol∣lowing.

RULE FOR FINDING THE PITCH CIRCLE.

Multiply the number of cogs in the wheel,* 1.431 by the quarter inches in the pitch, and that product by 7, and divide by 22, and the quo∣tient is the diameter in quarter inches, which is to be reduced to feet.

EXAMPLE.* 1.432

Given, 84 cogs, 4½ inches pitch; required, the diameter of the pitch circle.

Then, by the rule, 84 multiplied by 18 and 7, is equal to 10584; which, divided by 22, is equal to 481 2/22 quarter inches, equal to 10 feet ¼ 2/22; inches, for the diameter of the pitch circle required.

Art. 76.

A TRUE, simple, and expeditious method of finding the diameter of the pitch circle, is to find it in measures of the pitch itself that you use.

RULE.

Multiply the number of cogs by 7,* 1.433and di∣vide by 22, and you have the diameter of the pitch circle, in measures of the pitch, and 22 parts of said pitch.

EXAMPLE.

Given, 78 cogs; required, the diameter of the pitch circle. Then, by the rule,

78
7
22)546(24 18/22 Measures of the pitch for the diameter of the circle required.
44
106
88
18

Half of which diameter,* 1.434 12 9/22 of the pitch, is the radius, or half diameter, by which the circle is to be swept.

To use this rule, Set a pair of compasses to the pitch, and screw them fast, not to be al∣tered until the wheel is pitched: divide the pitch into 22 equal parts: Then step 12 steps on a strait line with the pitch compasses, and 9 of these equal parts of the pitch, makes the radius that is to describe the circle.

To save the trouble of dividing the pitch for every wheel, the workman may mark the dif∣ferent pitch, which he commonly uses, on the edge of his two foot rule (or make a little rule for the purpose) and carefully divide then there, where they will be always ready for use.* 1.435 See plate IV, fig. 35.

By these rules, I have calculated the fol∣lowing table of the radius's of pitch circles of the different wheels commonly used, from 〈◊〉〈◊〉 to 136 cogs.

TABLE OF THE PITCH CIRCLES OF THE COG-WHEELS COMMONLY USED, FROM 6 TO 136 COGS, BOTH IN MEASURES OF THE PITCH, AND IN FEET, INCHES, AND PARTS.

Cogs in the wheel.	Radius of the pitch circle in measures of the pitch and 22 parts and tenths of parts of said pitch.	Radius of the pitch circle of the wheels in column 1, taken in inches, quar∣ters, and 22 parts of a quarter, when the pitch is 2 1-2 inches, for bolt∣ing gears, &c.	Cogs in the wheel.	Radius of the pitch circle in measurs of the pitch, and 22 parts of said pitch.	Radius of the pitch circle of the wheels in the 4th column, taken in feet, inches, quarters, and 22 parts of a quar∣ter, when the pitch is 4 1-4 inches, for large gears, &c.	Ditto, when the pitch is 4 1-2 inches.
No.	Pitch. 22 par	inches quar∣ters•• 22 pts	No.	Pitch. 22 pts.	feet. inches qrs. 22 pts.	feet. inches. qrs. 22 pts.
6	1	2: 2: 0	33	5 5½	1: 10: 1: 5½	1: 11: 2: 11
7	1 3,5	2: 3: 12	34	5 9	1: 10: 3: 21	2: 0: 1: 8
8	1 6,7	3: 1: 3	35	5 12½	1: 11: 2: 14½	2: 1: 0: 5
9	1 10,2	3: 2: 14	36	5 16	2: 0: 1: 8	2: 1: 3: 2
10	1 13,6	4: 0: 3	37	5 19½	2: 1: 0: 1½	2: 2: 1: 21
11	1 17,1	4: 1: 17	38	6 1	2: 1: 2: 17	2: 3: 0: 10
12	1 20,5	4: 3: 5	39	6 4½	2: 2: 1: 10½	2: 3: 3: 15
13	2 1,9	5: 0: 17	40	6 8	2: 3: 0: 4	2: 4: 2: 12
14	2 5,3	5: 2: 8	42	6 15	2: 4: 1: 13	2: 6: 0: 6
15	2 8,8	5: 3: 20	44	7	2: 5: 3: 0	2: 7: 2: 0
16	2 12,2	6: 1: 11	48	7 14	2: 8: 1: 18	2: 10: 1: 10
17	2 15,7	6: 3: 2	52	8 4	2: 11: 0: 14	3: 1: 0: 20
18	2 19,1	7: 0: 15	54	8 11	3: 0: 2: 1	3: 2: 2: 14
19	3 0,6	7: 2: 6	56	8 20	3: 1: 3: 10	3: 4: 0: 8
20	3 4,1	7: 3: 18	60	9 13	3: 4: 2: 6	3: 6: 3: 18
21	3 7,5	8: 1: 9	66	10 11	3: 8: 2: 11	3: 11: 1: 0
22	3, 11	8: 3: 0	72	11 10	4: 0: 2: 16	4: 3: 2: 4
23	3 14,5	9: 0: 13	78	12 9	4: 4: 2: 21	4: 7: 3: 8
24	3 18,	9: 2: 4	84	13 8	4: 8: 3: 4	5: 0: 0: 12
25	3 21,5	9: 3: 17	88	14 0	4: 11: 2: 0	5: 3: 0: 0
26	4 3,	10: 1: 8	90	14 7	5: 0: 3: 9	5: ••: 1: 16
27	4 6,5	10: 2: 21	96	15 6	5: 4: 3: 14	5: 8: 2: 20
28	4 10,	11: 0: 12	104	16 13	5: 10: 1: 6	6: ••: 1: 18
29	4 13,5	11: 2: 3	112	17 18	6: 3: 2: 20	6: 8: 0: 16
30	4 17,	11: 3: 16	120	19 2	6: 9: 0: 12	7: 1: 3: 14
31	4 20,5	12: 1: 7	128	20 8	7: 2: 2: 4	7: ••: ••: 12
32	5 2,	12: 2: 20	136	21 14	7: 7: 3: 1••	8: 1: 1: 1••
	2	3	4	5	6	7

Use of the foregoing Table.* 1.436

SUPPOSE you are making a cog-wheel with 66 cogs; look for the number in the 1st or 4th column, and against it, in the 2d or 5th column, you find 10,11; that is, 10 steps of the pitch (you use) on a strait line, and 11 of 22 equal parts of said pitch added, makes the radius that is to describe the pitch circle.

The 3d, 6th and 7th columns, contain the radius in feet, inches, quarters, and 22 parts of a quarter; which may be of use in roughing out timber, and fixing the centres that the wheels are to run in, so that they may gear to the right depth: But, on account of the difference in the parts of the same scales or rules, and the difficulty of setting the com∣passes exactly, they can never be true enough for the pitch circles.

RULE COMMONLY PRACTISED.

Divide the pitch into 11 equal parts, and take in your compasses 7 of those parts,* 1.437 and step on a strait line, counting 4 cogs for every step, until you come up to the number in your wheel; if there be an odd one at last, take 1-4 of a step, if 2 be left, take 1-2 of a step if 3 be left, take 3-4 of a step, for them; an•• these steps, added, makes the radius or sweep staff of the pitch circle: But on account of the difficulty of making these divisions sufficiently exact, there is little truth in this rule—and where the number of cogs are few, it w•••• make the diameter too short, for the reason mentioned before.

The following geometrical rule,* 1.438 is more true and convenient, in some instances.

RULE.

Draw the line AB, plate IV,* 1.439 fig. 34, and draw the line 22,0 at random;* 1.440 then take the pitch in your compasses, and beginning at the point 22, step 11 steps towards A, and 3 1-2 steps to point X, towards O; draw the line AC through the point X; draw the line DC parallel to AB; and, without having altered your compasses, begin at point O, and step both ways, as you did on AB; then, from the respective points, draw the cross lines pa∣rallel to 0 22; and the distance from the point, where they cross the line AC, to the line AB, will be the radius of the pitch circles for the number of cogs respectively, as in the figure. If the number of cogs be odd, say 21, the radi∣us will be between 20 and 22.

This will also give the diameter of all wheels, that have few cogs, too short; but where the number of cogs is above 20, the error is im∣perceptible.

All these rules are founded on the propor∣tion, as 22 is to 7, so is the circumference to the diameter.

Art. 77.

A TABLE OF ENGLISH DRY MEASURE.

Solid inches.
33,6	Pint.
268,8	8	Gallon.
537,6	••6	2	Peck.
2150,4	64	8	4	Bushel.

THE bushel con∣tains 2150,4 solid inches. Therefore to measure the con∣tents of any garner, take the following

RULE.

Multiply its length in inches,* 1.441 by its breadth in inches, and that product by its height in inches, and divide the last product by 2150,4, and it will quote the bushels it contains.

But to shorten the work, decimally; be∣cause 2150,4 solid inches are 1,244 solid feet, multiply the length, breadth, and height in feet, and decimal parts of a foot by each other, and divide by 1,244; and it will quote the contents in bushels.

EXAMPLE.

Given, a garner 6,25 feet long, 3,5 feet wide, 10,5 feet high; required, its contents in bushels. Then 6,25 multiplied by 3,5 and 10,5, is equal to 229,687; which, divided by 1,244, quotes 184 bushels and 6 tenths.

To find the contents of a hopper, take the following

RULE.

Multiply the length by the width at the top and that product by one third of the depth,* 1.442

measuring to the very point,* 1.443 and divide by the contents of a bushel, either in inches or decimals, as you have wrought, and the quo∣tient will be the contents in bushels.

EXAMPLE.

Given, a hopper 42 inches square at top, and 24 inches deep; required, the contents in bushels.

Then 42 multiplied by 42 and 8, is equal to 14112 solid inches; which, divided by 2150,4, quotes 6,56 bushels, or a little more than 6 1-2 bushels.

To make a garner to hold any given quan∣tity, having two of its sides given,* 1.444 take the following

RULE.

Multiply the contents of 1 bushel by the number of bushels the garner is to hold; then multiply the given sides into each other, and divide the first by the last product; and the quotient will be the side wanted, in the same measure you have wrought in.

EXAMPLE.

Given, two sides of a garner 6,25 by 10,5 feet; required, the other side, to hold 184,6 bushels.

Then 1,244 multiplied by 184,6, is equal to 229,642; which, divided by the product of the two sides 65,625, the quotient is 3,5 feet for the side wanted.

To make a hopper to hold any given quan∣tity,* 1.445 having the depth given.

RULE.* 1.446

Divide the inches contained in the bushels it is to hold, by 1-3 the depth in inches; and the quotient will be the square of one of the sides at the top in inches. Given, the depth 24 inches; required, the sides to hold 6,56 bushels.

Then 6,56 multiplied by 2150,4, is equal to 14107,624; which, divided by 8, quotes 1764, the square root of which is 42 inches; which is the length of the sides of the hopper wanted.

CHAPTER III.

Art. 78. OF THE DIFFERENT KINDS OF GEARS, AND FORCE OF COGS.

IN order to conceive a just idea of the most suitable form or shape for cogs in cog-wheels,* 1.447 we must consider, that they describe, with respect to the pitch circles, a figure call∣ed an Epicycloid.

And when one wheel works in cogs set in a strait line, such as the carriage of a saw-mill the cogs or rounds,* 1.448 moving out and in, form a curve figure called a Cycloid.

To describe which,* 1.449 let us suppose the large circle in plate V, fig. 37, to move on the strait line from O to A; then the point O 〈◊〉〈◊〉

its periphery will describe the arch O D A,* 1.450 called a Cycloid; and we may conceive, by the way, that the curve joins the line, what should be the form of the point of the cog.

Again, suppose the small circle to run round the large one; then the point o in the small circle, will describe the arch o b c, called an Epicycloid; by which we may conceive the form the point of the cogs should be. But in common practice we generally let the cogs extend but a short distance past the pitch cir∣cle; so that the form of the cogs is not so par∣ticular.

Art. 79. Of Spur Gears.

THE principle of Spur Gears,* 1.451 is that of two cylinders rolling on each other, with their shafts or axis truly parallel to each other.—Here the touching parts move with equal ve∣locity, therefore have but little friction. And to prevent these cylinders from slipping, we are obliged to indent them, or to set in cogs.—And here it appears to me,* 1.452 that the pitch of the driving wheel should be a little larger than the leading wheel, for the following reasons:

1. If there is to be any slipping, it will be much easier for the driver to slip a little past the leader, than for the cogs to have to force the leader a little before the driver; which would be very hard on them.

2. If the cogs should bend any by the stress of the work (as they surely do; because 1lb. falling on a beam a foot square, will jar it,

which cannot be done without bending it a little) this will cause those that are coming into gear to touch too soon,* 1.453 and rub hard at entering.

3. It is much better for cogs to rub hard as they are going out of gear, than as they are coming in; because then they work with the grain of the wood; whereas at entering they work against it, and would wear much faster.

The advantage of this kind of gear is,* 1.454 we can make the cogs as wide as we please, so that their bearing may be so large that they will not cut each other, but only polish and wear smooth; therefore they will last a long time.

Their disadvantages are,* 1.455

1st. That if the wheels be of different sizes, and the pitch circles are not made to meet ex∣actly, they will not run smooth. And,

2d. We cannot change the direction of the shafts so conveniently

Fig. 38,* 1.456 plate IV, ••s two spur wheels work∣ing into each other; the dotted lines shew the pitch circles, which must always meet exact∣ly. The ends of the cogs are made circular, as is common; but if they were made of the true epicycloids that would suit the size of the wheels, they would work smoother, with less friction.

Fig. 39 is a spur and face wheel or wallow∣er;* 1.457 whose pitch circles should always mee•••• exactly also.

The rule for describing the sides of the cogs of a form near the figure of an epicycloid,* 1.458 is as follows, viz. Describe a circle a little inside

of the pitch circle,* 1.459 for the point of your com∣passes to be set in, so as to describe the sides of the cog as the four cogs at A, fig. 38—39, as near as you can to the curve of the epicycloid that is formed by the little wheel's moving round the great one; the greater the difference between the great and small wheels, the great∣er distance must this circle be inside of the pitch circle; of this the practitioner is to be the judge, as no certain rule is yet formed, that I know of.

Art. 80. Of Face Gears.

THE principle of Face Gears,* 1.460 is that of two cylinders rolling with the side of one on the end of the other, their axis being at right angles. Here the greater the bearing, and the less the diameter of the wheels,* 1.461 the great∣er will be the friction; because the touching parts move with different velocities, therefore the friction will be great.

The advantages of this kind of gear are,* 1.462

1st. Their cogs stand parallel to each other; therefore moving them out or in gear a little, does not alter the pitch of the bearing parts of the cogs, and they will run smoother when their centres are out of place, than spur gears.

2d. They serve for changing the direction of the shafts.

The disadvantages are,

1st. The smallness of the bearing,* 1.463 so that they wear out very fast.* 1.464

2d. Their great friction and rubbing of parts.* 1.465

The cogs for small wheels are generally round, and put in with round shanks. Great care should be taken in boring the holes for the cogs, with a machine to direct the auger strait, that the distance of the cogs may be equal, without dressing. And all the holes of all the small wheels in a mill should be bored with one auger, and made of one pitch; then the miller may keep by him a quantity of cogs ready turned, to a gauge to suit the auger, and when any fail, he can drive out the old ones, and put in a new set, without much loss of time.

Fig. 40, plate V, represents a face cog-wheel working into a trundle; shewing the necessity of having the corners of the sides of the cogs sniped off in a cycloidical form, to give liberty for the rounds to enter between the cogs, and pass out again freely. To de∣scribe the sides of the cogs of the right shape to meet the rounds when they get fairly into gear,* 1.466as at c, there must be a circle described on the ends of the cogs, a little outside of the pitch circle, for the point of the compasses to be set in, to scribe the ends of the cogs; for if the point be set in the pitch circle, it will leave the inner corners too full, and make the out∣er ones too scant. The middle of the cog is to be left strait from bottom to top, or nearly so, and the side nearly flat at the distance 〈◊〉〈◊〉 half the diameter of the round from the end,

the corners only being sniped off to make the ends of the shape in the figure;* 1.467 because when the cog comes into gear fully, as at c, there is the chief stress, and there the bearing should be as large as possible. The smaller the cog-wheel, the larger the trundle, and the wider the cogs, the more will the corners require to be sniped off. Suppose the cog-wheel to turn from 40 to b, the cog 40, as it enters, will bear on the lower corner, unless it be suffici∣ently sniped off; when it comes to c, it will be fully in gear, and if the pitch of the cog-wheel be a little larger than that of the trun∣dle, the cog a will bear as it goes out, and let c fairly enter before it begins to bear.

Suppose the plumb line A B to hang directly to the centre of the cog-wheel, the spindle is (by many mill-wrights) set a little before the line or centre, that the working round or stave of the trundle may be fair with said line, and meet the cog fairly as it comes to bear; it al∣so causes the cogs to enter with less, and go out with more friction. Whether there be any real advantage in thus setting the spindle foot before the centre plumb line, does not seem determined.

Art. 81. Of Bevel Gears.

THE principle of Bevel Gears,* 1.468 is that of two cones rolling on the surface of each other, their vertexes meeting in a point, as at A, fig. 41, plate V. Here the touching surfaces move with equal velocities in every part of the

cones;* 1.469 therefore there is but little friction, These cones being indented, or fluted with teeth diverging from the vertex to the base,* 1.470 to prevent them from slipping, become bevel gear; and as these teeth are very small at the point or vertex of the cone, they may be cut off 2 or 3 inches from the base, as 19 and 25, at B; they then have the appearance of wheels.

To make these wheels of a suitable size for any number of cogs you choose to have to work into one another, take the following

RULE.

Draw lines to represent your shafts,* 1.471 in the direction they are to be, with respect to each other, to intersect at A; then take from any scale of equal parts, either feet, inches, or quarters, &c. as many as your wheels are to have cogs, and at that distance from the re∣spective shafts, draw the dotted lines a b, c d, for 21 and 20 cogs; and from where they cross at e, draw e A. On this line, which makes the right bevel, the pitch circles of the wheels will meet, to contain that proportion of cogs of any pitch.

Then to determine the size of the wheels 〈◊〉〈◊〉 suit any particular pitch, take from the table of pitch circles, the radius in measures of th•• pitch, and apply it to the centre of the shaft and the bevel line A e, taking the distance 〈◊〉〈◊〉 right angles with the shaft; and it will 〈◊〉〈◊〉 the point in which the pitch circles will meet to suit that particular pitch.

By the same rule, the sizes of the wheels 〈◊〉〈◊〉 B and C are found.

These kind of wheels are frequently made of cast metal,* 1.472 and are said to do exceeding well.

The advantages of this kind of gear are,* 1.473

1. They have very little friction, or sliding of parts.

2. We can make the cogs of any width of bearing we chuse; therefore they will wear a great while.

3. By them we can set the shafts in any di∣rection desired, to produce the necessary move∣ments.

Their disadvantages are,

1. They require to be kept exactly of the right depth in gear,* 1.474 so that the pitch circles just meet, else they will not run smooth, as is the case with spur gears.

2. They are expensive to make of wood; therefore few in this country use them.

The universal joint,* 1.475 as represented fig. 43, may be applied to communicate motion, in∣stead of bevel gear,* 1.476 where the motion is to be the same, and the angle not more than 30 or 40 degrees. This joint may be constructed by a cross, as in the figure, or by 4 pins fasten∣ed at right angles on the circumference of a hoop or solid ball. It may sometimes serve to communicate the motion,* 1.477 instead of 2 or 3 face wheels. The pivots at the end of the cross play in the ends of the semicircles. It is best to screw the semicircles to the blades, that they may be taken apart.

Art. 82. Of matching Wheels, to make the Cogs wear Even.

GREAT care should be taken in matching or coupling the wheels of a mill, that their number of cogs be not such that the same cogs will often meet; because if two soft ones meet often, they will both wear away faster than the rest, and destroy the regularity of the pitch; whereas if they are continually changing, they will wear regular, even if they are at first a little irregular.

For finding how often they will revolve be∣fore the same cogs meet again, take the fol∣lowing

RULE.

1. Divide the cogs in the greater wheel by the cogs in the lesser; and if there be no re∣mainder, the same cogs will meet once every revolution of the great wheel.

2. If there be a remainder, divide the cogs in the lesser wheel by said remainder; and if it divide them equally, the quotient shews how often the great wheel will revolve before the same cogs meet.

3. But if it will not divide equally, the•••• the great wheel will revolve as often as the•••• are cogs in the small wheel, and the 〈◊〉〈◊〉 wheel as often as there are cogs in the large wheel, before the same cogs meet; often•• they can never be made to change.

EXAMPLES.

1. Given, wheels 13 and 17 cogs; required, how often each will revolve before the same cogs meet again.

Then 13)17(1
13
4)13(3
12 Answer, Great wheel 13, and Small do. 17 revs.
1

Art. 83. Theory of Rolling Screens and Fans, or Wind-mills for screening and fanning the Wheat in Mills.

LET fig. 42, plate V,* 1.478 represent a Rolling Screen and Fan, fixed for cleaning wheat in a merchant-mill. DA the screen, AF the fan, AB the wind tube, 3 feet deep from A to b, and 4 inches wide, in order that the grain may have a good distance to fall through the wind, to give time and opportunity for the light parts to be carried forward before the heavy parts. Suppose the tube to be of equal depth and width the whole of its length, except where it communicates with the tight boxes or garners under it, viz. c for the clean wheat, S for the screenings and light wheat, and C for the cheat, chaff, &c. Now it is evident, 〈◊〉〈◊〉 be by the fan drove into the tube at A, that, if it can escape no where, it will pass on to B, with the same force as at A, let the tube be of any length or direction; and any thing which it will move at A, it will carry out at B, if the tube be of an equal size all the way.

It is also evident, that if we shut the holes of the fan at A and F, and let no wind into it,

none can be forced into the tube;* 1.479hence, the best way to regulate the blast is, to fix shutters sliding at the air holes, to give more or less feed of air to the fan, so as to produce a blast sufficient to clean the grain.

The grain is let into the screen at D, into the inmost cylinder, in a small stream. The screen consists of two cylinders of sieve wire, the inmost one has the meshes so open, as to pass all the wheat through it to the outer one, retaining only the white caps, large garlick, and every thing larger than the grain of the wheat, which falls out at the tail A.

The outer cylinder is so close in the mesh, as to retain all good wheat, but sift out the cheat, cockle, small wheat, garlick, and every thing less than good grains of wheat; the wheat is delivered out at the tail of the 〈◊〉〈◊〉 cylinder, which is not quite as long as the in∣ner one, where it drops into the wind tube 〈◊〉〈◊〉 a, and as it falls from a to b, the wind car∣ries off every thing lighter than good wheat, viz. cheat, chaff, light garlic, dust, and light rotten grains of wheat; but, in order to effect this more completely, it should fall at least 〈◊〉〈◊〉 feet through the current of wind.

The clean wheat falls into the funnel b, 〈◊〉〈◊〉 thence into the garner c, over the stones 〈◊〉〈◊〉 light wheat, screenings, &c. fall into garner S, and the chaff settles into the chaff room C. The current slackens passing over this room and drops the chaff, but resumes its full forc•• as soon as it is over, and carries out the 〈◊〉〈◊〉 through the wall at B. To prevent the cur∣rent from slackening too much as it passes over

S and c,* 1.480and under the screen, make the pas∣sages, where the grain comes in and goes out, as small as possible, not more than half an inch wide, and as long as necessary. If the wind escapes any where but at B, it defeats the scheme, and carries out the dust into the mill. Or fix valves to shut the passages by a weight or spring, so that the weight of the wheat, &c. falling on will open them just enough to let it pass, without suffering any wind to escape.* 1.481

Note, The fan is set to blow both the wheat and screenings, and carry the dust out.

Note also, That the wind cannot escape in∣to the garners or screen room, if they are tight; for as soon as they are full, no more can enter.

By attending duly to the foregoing princi∣ple, we may fix fans to answer our purposes.

The principal things to be observed in fixing screens and fans, are,

1. Give the screen 1 inch to the foot fall, and between 15 and 18 revolutions in a mi∣nute.

2. To make the fan blow strong enough, let the wings be 3 feet wide, 20 inches long, and revolve 140 times in a minute.

3. Then regulate the blast, by giving more or less feed of wind.

4. Leave no place for the wind to escape, but at the end through the wall.

5. Wherever you want it to blow hardest, there make the tube narrowest.

6. Where you want the chaff and cheat to fall,* 1.482there make the tube sufficiently wider.

7. Make them blow both the wheat and screenings, and carry the dust clear out of the mill.

8. The wind tube may be of any length and either crooked or strait, as may best suit; but no where less than where the wheat falls.

CHAPTER IV. Art. 84. OF GUDGEONS, THE CAUSE OF THEIR HEAT∣ING AND GETTING LOOSE, AND REMEDIES THEREFOR.

THE cause of Gudgeons heating, is the excessive friction of their rubbing parts, which generates the heat in proportion to the weight that presses the rubbing surfaces toge∣ther, and the velocity with which they more See art. 31.

The cause of their getting loose is, then heating, and burning the wood, or drying it so that it shrinks in the bands, and gives 〈◊〉〈◊〉 gudgeon room to work.

To avoid the effects, we must remove the causes.

1. Increase the surface of contact or rubbing parts, and, if possible, decrease their velocity the heat will not then be generated so much.

2. Conduct the heat away from the gudgeon as fast as generated,* 1.483if possible.

To increase the surface of contact•• without increasing its velocity, make the 〈◊〉〈◊〉 or bear∣ing part of the gudgeon longer. 〈◊〉〈◊〉 the length be doubled, the weight will be sustained by a double surface, and velocity the same; there will not then be so much heat generated: and even supposing the same quantity of heat ge∣nerated, there will be a double space of sur∣face exposed to air, to convey it away.* 1.484

To convey the heat away as fast as gene∣rated cause a small quantity of water to drop slowly on the gudgeon, to carry off the heat by evaporation.† 1.485A small quantity is better than a large; because it should be just suffici∣ent to keep up the evaporation, and not de∣stroy the polish made by the grease; which it

will do if the quantity be too great,* 1.486 and will let the bare stone and gudgeon come in con∣••••••; which will cause both to wear away very fast.* 1.487

The best form that I have seen for large gudgeons for heavy wheels, is made of cast iron. Fig. 6, plate XI, is a perspective view of one; a a a a, are four wings at right angles with each other, extending from side to side of the shaft. These wings are larger, every way, at the end that is farthest in the shaft, than at the outer end, for convenience in cast∣ing them, and also that the bands may drive on tight, one over each end of the wings. Fig. 4 is an end view of the shaft, with the gudgeon in it, and a band on the end; these bands, being put on hot, become very tight as they cool, and if the shaft is dry will not, get loose, but will if it is green; but by driving a few wedges along side of each wing, it can be easily fastened, by any ordinary hand, without danger of moving it much from the centre.

One great use of these wings is, to convey away the heat from the gudgeon to the bank, which are in contact with the air; and by

thus distributing the heat through so much metal,* 1.488with so large a surface exposed to the air, the heat is carried off as fast as generated; therefore can never accumulate to a degree sufficient to burn loose, as it will often do in common gudgeons of wrought iron. Wood will not conduct the heat as well as the wings of metal; therefore it accumulates in the small space of the gudgeon, to such a degree as to burn loose.

These gudgeons should be made of the best hard metal, well refined, in order that they may wear well, and not be subject to break; but of this there is but little danger, if the metal is good: should it prove to be the case, I propose to have wings cast separate from the neck, as represented by fig. 4; where the in∣side light square shews a mortice for the steeled gudgeon, fig. 7, to be fitted into, with an iron key behind the wings, to draw the gudgeon in tight, if ever it should work loose; by which means it may be taken out, at any time, to repair.

This plan would do well for step gudgeons for heavy upright shafts, such as tub mills, &c.

When the neck is cast with the wings, the square part in the shaft need not be larger than the light square representing the mortice.

CHAPTER V.

Art. 85. ON BUILDING MILL-DAMS, LAYING FOUN∣DATIONS, AND BUILDING MILL-WALLS.

THERE are several things to be consider∣ed, and dangers to be guarded against, in building mill-dams.

1. Construct them so, that the water tum∣bling over them, cannot undermine their foun∣dations at the lower side.* 1.489

2. So that heavy logs, large pieces of ice, &c. floating down, cannot catch against any part of them, but slide easily over.† 1.490

3. So that the pressure or force of the cur∣rent of the water will press their parts more firmly together,* 1.491* 1.492

4. Give them a sufficient tumbling space to vent all the water in time of freshes.* 1.493* 1.494

5. Make the abutments so high, that the water will not overflow them in time of freshes.

6. Let the dam and mill be a sufficient dis∣tance apart; so that the dam will not raise the water on the mill, in time of high floods.† 1.495

Art. 86. On building Mill-walls.

THE principal things to be considered in building mill-walls, are,

1. To lay the foundations with good large stones, so deep as to be out of danger of being undermined, in case of any accident of the wa∣ter breaking thro' at the mill.* 1.496

2. Set the centre of gravity, or weight of the wall, on the centre of its foundation.† 1.497

3. Use good mortar,* 1.498and it will, in time, petrify and become as hard as stone.* 1.499

4. Arch over all the windows, doors, &c.

5. Tie them well together by the timbers of the floors.

PART THE THIRD—Containing, EVANS's PATENTED IMPROVEMENTS ON THE ART OF MANUFACTURING GRAIN INTO MEAL AND FLOUR.

INTRODUCTION

THESE improvements consist of the invention, and various applications, of the following machines,viz.

• 1. The Elevator.
• 2. The Conveyer.
• 3. The Hopper-boy.
• 4. The Drill.
• 5. The Descender.

Which five machines are variously applied, in dif∣ferent mills, according to their construction, so as to perform every necessary movement of the grain and meal, from one part of the mill to another, or from one machine to another, through all the various ope∣rations, from the time the grain is emptied from the waggoner's bag, or from the measure on board the 〈◊〉〈◊〉, until it is completely manufactured into super∣fine flour, and other different qualities, and completely separated, ready for packing into barrels, for sale or ••••portation. All which is performed by the force of 〈◊〉〈◊〉 water, without the aid of manual labour, except 〈◊〉〈◊〉 set the different machines in motion, &c. Which ••••••sens the labour and expence of attendance of flour ••ills, fully one half. See the whole applied, plate III.

THE YOUNG Mill-Wright's Guide. PART THE THIRD. CHAPTER I. Art. 88. DESCRIPTION OF MACHINES.

1. Of the Elevator.

THE Elevator is an endless strap,* 2.1revolv∣ing over two pullies, one of which is set where the grain or meal, &c. is to be hoisted from, and the other where it is to be hoisted to; to this strap is fastened a number of small buckets, which fill themselves as they pass un∣der the lower pulley, and empty as they pass over the upper one. To prevent waste of what may spill out of these buckets, the strap, buckets and pullies, are all enclosed, and work in tight cases; so that what spills will descend to the place from whence it was hoisted. A B, in fig. 1, plate VI,* 2.2is an elevator for raising grain, which is let in at A, and discharged at B into the spouts leading to the different gar∣ners. Fig.2 is a perspective view of the strap,* 2.3

and different kinds of buckets,* 2.4and the various modes of fastening them to the strap.

2. Of the Conveyer.

The Conveyer K I,* 2.5fig. 1, is an endless screw of two continued spires, put in motion in a trough; the grain is let in at one end, and the screw drives it to the other, or collects it to the centre, as at y, to run into the eleva∣tor (see plate VIII, 37—36—4, and 44—45) or it is let in at the middle, and convey∣ed each way, as 15—16, plate VIII.

Fig. 3,* 2.6is a top view of the lower pully of a meal elevator in its case, and a meal convey∣er in its trough, for conveying meal from the stones, as fast as ground, into the elevator. This is an 8 sided shaft,* 2.7set on all sides with small inclining boards, called flights, for con∣veying the meal from one end of the trough to the other; these flights are set in a spiral line, as shewn by the dotted line; but being set across said line, changes the principle of the machine from a screw to that of plows, which is found to answer better for conveying warm meal.

Besides these conveying flights, half their number of others are sometimes necessary; which are called lifters, and set with their broadsides foremost, to raise the meal from one side, and let it fall on the other side of the shaft to cool: these are only used where the meal is hot, and the conveyer short. See 21—22, in plate VIII: which is a conveyer, carrying the meal from 3 pair of stones to the elevator, 23—24.

3. Of the Hopper-boy.

Fig. 12, plate VII,* 2.8is a Hopper-boy; which consists of a perpendicular shaft, AB, put in a slow motion, (not above 4 revolutions in a mi∣nute) carrying round with it the horizontal piece CD, which is called the arms, and set, on the under side, full of small inclining boards, call∣ed flights, so set as to gather the meal towards the centre, or spread it from the centre to that part of the arm which passes over the bolting hopper; at which part, one board is set broad-side foremost, as E (called a sweeper) which drives the meal before it, and drops it into the hoppers HH, as the arms pass over them. The meal is generally let fall from the eleva∣tor, at the extremity of the arm, at D, where there is a sweeper,* 2.9which drives the meal be∣fore it, trailing it in a circle the whole way round, so as to discharge nearly the whole of its load, by the time it returns to be loaded again: the flights then gather it towards the centre, from every part of the circle; which would not be the case, if the sweepers did not lay it round; but the meal would be gathered from only one side of the circle. These sweep∣ers are screwed on the back of the arm, so that they may be raised or lowered, in order to make them discharge sooner or later, as ne∣cessary.

The extreme flight of each end of the arms are put on with a screw passing through its centre, so that they may be turned to drive the meal outwards; the use of which is, to spread the warm meal as it falls from the ele∣vator,

in a ring round the hopper-boy, while it at the same time gathers the cool meal into the bolting hopper; so that the cold meal may be bolted, and the warm meal spread to cool, by the same machine, at the same time, if the miller chuses so to do. The foremost edge of these arms is sloped up, in order to make them rise over the meal, and its weight is nearly balanced by the weight w, hung to one end of a cord passing over the pulley P, and to the stay iron F. About 4 1-2 feet of the lower end of the upright shaft is made round, passing loosely through a round hole in the flight arm, giving it liberty to rise and fall freely, to suit any quantity of meal under it. The flight arm is led round by the leading arm LM, by a cord passing through the holes LM, at each end, and made fast to the flight arm DC. This cord is lengthened or shortened by a hitch-stick N, with two holes for the cord to pass through, the end of the cord being passed through a hole at D, and fastened to the end of the stick; this cord must reeve freely thro' the holes at the ends of the arms, in order that the ends may both be led equally. The flight arm falls behind the leader about 1-6th part of the circle. The stay-iron CFE, is a ring at F, which fits the shaft loosely, and is for keep∣ing the arm steady, and hanging the ends of an equal height by the screws. CE.

Fig. 13 is a perspective view of the under∣side of the flight arms. The arm a-c, with flights and sweepers complete; s s s shews the screws which fasten the sweepers to the arms. The arm c-b, is to shew the rule for laying

out for the flights.* 2.10When the sweeper at b, is turned in the position of the dotted line, it drives the meal outwards. Fig. 14 is a plate on the bottom of the shaft, to keep the arm from the floor, and 15 is the step gudgeon.

4. Of the Drill.

The Drill is an endless strap revolving over two pullies,* 2.11like an elevator, but set nearly horizontal, and instead of buckets, there are small rakes fixed to the strap, which draw the grain or meal along the bottom of the case. See GH, in plate VI, fig. 1. The grain is let in at H, and discharged at G. This can sometimes be applied with less expence than a conveyer; if it is set a little descending, it will move grain or meal with ease, and will do well even a little ascending.

5. Of the Descender.

The Descender is a broad endless strap of every thin pliant leather,* 2.12canvass, or flannel, &c. revolving over two pullies, which turn on small pivots, in a case or trough, to prevent waste, one end of which is to be lower than the other.* 2.13See EF, fig. 1. The grain or meal falls from the elevator on the upper strap, at E, and by its own gravity and fall, sets the machine in motion, and it discharges the load over the lower pulley F. There are two small buckets to bring up what may spill or fall off the strap, and lodge in the bottom of the case.

This machine moves on the principles of an overshot water-wheel, and will convey meal

a considerable distance,* 2.14with a small descent. Where a motion is easily obtained from the water, it is to be preferred to that of working itself, it being easily stopped, is apt to be trou∣blesome.

The Crain Spout is hung on a shaft to turn on pivots or a pin, so that it may turn every way, like a crane; into this spout the grain•• falls from the elevator, and, by turning, it can be directed into any garner. The spout is made to fit close, and play under a broad board, and the grain is let into it through the middle of this board, near the pin, so that it will always enter the spout. See it under B fig. 1. L is a view of the under side of it, and M is a top view of it. The pin or shaft 〈◊〉〈◊〉 reach down so low, that a man may stand 〈◊〉〈◊〉 the floor and turn it by the handle x.

CHAPTER II. APPLICATION OF THE MACHINES, IN THE PROCESS OF MANUFACTURING WHEAT INTO SUPERFINE FLOUR.

PLATE VIII, is not meant to shew 〈◊〉〈◊〉 plan of a mill; but merely the Applica∣tion and Use of the patented Machines.

Art. 89.

The grain is emptied from the waggon into the spout 1,* 2.15which is set in the wall, and con∣veys it into the scale 2,* 2.16that is made to hold 10, 20, 30, or 60 bushels, at pleasure.

There should, for convenience of counting, be weights of 60lbs. each; divided into 30, 15 and 7 1-2lbs. then each weight would shew a bushel of wheat, and the smaller ones halves, pecks, &c. which any one could count with case.

When the wheat is weighed, draw the gate at the bottom of the scale, and let it run into the garner▪ 3; at the bottom of which there is a gate to let it into the elevator 4—5, which 〈◊〉〈◊〉 it to 5, and the crane spout being turn∣ed over the great store garner 6, which com∣municates from floor to floor, to garner 7, over the stones 8, which suppose to be for ••••elling or rubbing the wheat, before it is ground, to take off all dust that sticks to the grain, to break smut or fly-eaten grain, lumps of dust, &c. As it is rubbed it runs, by the dotted lines, into 3 again; in its passage it goes through a current of wind blowing into the ••ight room 9, having only the spout a, through the lower floor, for the wind to escape; all the chaff will settle in the room, but most of the dust passes out with the wind at a. The wheat again runs into the elevator at 4, and the crane spout, at 5, is turned over the screen ••••ppers 10 or 11, and the grain lodged there, ••ut of which it runs into the rolling screen 12, and descends through the current of wind made by the fan 13, the clean heavy grain de∣scends, by 14, into the conveyer 15—16;

which conveys it into all the garners over the stones 7—17—18, and these regularly supply the stones 8—19—20, keeping always an equal quantity in the hoppers, which will cause them to feed regularly; as it is ground the meal falls to the conveyer 21—22, which collects it to the meal elevator, at 23, and it is raised to 24, whence it gently runs down the spout to the hopper-boy at 25, which spreads and cools it sufficiently, and gathers it into the bolting hoppers, both of which it attends regularly; as it passes through the superfine cloths 26, the superfine flour falls into the packing chest 28, which is on the second floor: If the flour is to be loaded on waggons, it should be packed 〈◊〉〈◊〉 this floor, that it may conveniently be 〈◊〉〈◊〉 into them; but if the flour is to be put 〈◊〉〈◊〉 board a vessel, it will be more convenience 〈◊〉〈◊〉 pack on the lower floor, out of chest 29, 〈◊〉〈◊〉 roll it into the vessel at 30. The shorts and bran should be kept on the second floor, 〈◊〉〈◊〉 they may be conveyed by spouts into the ves∣sel's hold, to save labour.

The rublings which fall from the tail of the 1st reel 26, are guided into the head of the 2d reel 27; which is in the same chest, near the floor, to save both room and machinery. On the head of this reel is 6 or 7 feet of 〈◊〉〈◊〉 cloth, for tail flour, and next to it the mid∣dling stuff, &c.

The tail flour which falls from the tail 〈◊〉〈◊〉 the 1st reel 26, and head of the 2d reel 27, and requires to be bolted over again, is guided by a spout, as shewn by dotted lines 31—2•• into the conveyer 22—23, to be hoisted again

with the ground meal;* 2.17a little bran may be let in with it,* 2.18to keep the cloth open in warm weather—But if there be not a fall sufficient for the tail flour to run into the lower convey∣er, there may be one set to convey it into the elevator, as 31—32. There is a little regu∣lating board, turning on the joint x under the tail of the first reels, to guide more or less with the tail flour.

The middlings,* 2.19as they fall, are conveyed into the eye of either pair of millstones by the conveyer 31—32, and ground over with the wheat; which is the best way of grinding them, because the grain keeps them from be∣ing killed, and there is no time lost in doing it,* 2.20and they are regularly mixed with the flour. There is a slanting sliding board, to guide the middlings over the conveyer, that the miller may take only such part, for grind∣ing over, as he shall judge fit; and a little re∣gulating board between the tail flour and mid∣dlings, to guide more or less into the stones or elevator.

The light grains of wheat, screenings, &c. after being blown by the fan 13, fall into the screenings garner 32; the chaff is driven fur∣ther on, and settles in the chaff-room 33; the greater part of the dust will be carried out with the wind through the wall. For the theory of fauning wheat, see are. 83.

To clean the Screenings.

Draw the little gate 34,* 2.21and let them into the elevator at 4, and be elevated into garner

10;* 2.22then draw gate 10, and shut 11 and 34, and let them pass through the rolling-screen 12 and fan 13, and as they fall at 14, guide them down a spout (shewn by dotted lines) into the elevator at 4, and elevate them into the screen-hopper 11; then draw gate 11, shut 10, and let them take the same course over again, and return into garner 10, &c. as often as necessary, and, when cleaned, guide them into the stones to be ground.

The screenings of the screenings are now in garner 32, which may be cleaned as before, and an inferior quality of meal made out of them.

By these means the wheat may be so effectu∣ally separated from the seed of weeds, &c as to leave none to be wasted, and all the chaff, cheat, &c. saved for food for cattle.

This completes the whole process from the waggon to the waggon again, without manual labour, except in packing the flour, and roll∣ing it in.

Art. 90. Of elevating Grain from Ships.

IF the wheat comes to the mill by ships,* 2.23No. 35, and requires to be measured at the mill, then a conveyer, 35—4, may be set 〈◊〉〈◊〉 motion by the great cog-wheel, and may be under or above the lower floor, as may be suit the height of the floor above high water. This conveyer must have a joint, as 36, in the middle, to give the end that lays on the side of the ship, liberty to raise and lower with

the tide.* 2.24 The wheat, as measured, is poured into the hopper at 35, and is conveyed into the elevator at 4; which conveyer will so rub the grain as to answer the end of rubbing stones. And, in order to blow away the dust, when rubbed off, before it enters the elevator, part of the wind 〈◊〉〈◊〉 by fan 13 may be brought down by a spout, ••3—36, and, when it en∣ters the case of the conveyer, will pass each way, and blow out the dust at 37 and 4.

In some instances, a short elevator, with the centre of the upper pulley, 38, fixed im∣movable, the other end standing on the deck, so much aslant as to give the vessel liberty to raise and lower, the elevator sliding a little on the deck. The case of the lower strap of this elevator must be considerably crooked, to pre∣vent the points of the buckets from wearing by rubbing in the descent. The wheat, as measured, is poured into a hopper, which lets it in at the bottom of the pulley.

But if the grain is not to be measured at the mill,* 2.25 then fix the elevator 35—39, to take it out of the hole, and elevate it into any door convenient. The upper pulley is fixed in a gate that plays up and down in circular rab∣bits, to raise and lower to suit the tide and depth of the hole to the wheat. 40 is a draft of the gate, and manner of hanging the eleva∣tor in it. See a particular description in the latter part of art. 95.

This gate is hung by a strong rope passing over a strong pulley or roller 41,* 2.26 and thence round the axis of the wheel 42; round the rim of which wheel there is a rope, which passes

round the axis of wheel 43,* 2.27round the rim of which wheel is a small rope, leading down over the pulley P, to the deck, and fastened to the cleet q; a man by pulling this rope can hoist the whole elevator; because if the diameter of the axis be 1 foot and the wheels 4 feet, the power is increased 16 fold, by art. 20. The elevator is hoisted up, and rested against the wall, until the ship comes too, and is fasten∣ed steady in the right place, then it is set in the hole on the top of the wheat,* 2.28then it is set in the hole on the top of the wheat, and the bottom being open, the buckets fill as they pass under the pulley; a man holds by the cord, and lets the elevator settle as the wheat sinks in the hole, until the lower part of the case rests on the bottom of the hole, it being so long as to keep the buckets from touching the vessel; by this time it will have hoisted 1, 2 or 300 bushels,* 2.29according to the size of the ship and depth of the hole, at the rate of 300 bushels per hour. When the grain ceases run∣ning in of itself, the man may shovel it up, till the load is discharged.

The elevator discharges the wheat into the conveyer at 44,* 2.30which conveys it into the screen-hoppers 10—11, or into any other gar∣ner, from which it may descend into the ele∣vator 4—5, or into the rubbing-stones 8.

This conveyer may serve instead of rubbing stones, and the dust rubbed off thereby may be, by a wind-spout from the fan 13, into the conveyer at 45, blown out through the wall at p. The holes at 44 and 10—11 are to be small, to let but little wind escape any where but out through the wall, where it will carry the dust.

A small quantity of wind might be let into the conveyer 15—16,* 2.31 to blow away the dust rubbed off by it.

The fan must be made to blow very strong, to be sufficient for all these purposes, and the strength of the blast regulated as directed by art. 83.

Art. 91. A Mill for grinding Parcels.

HERE each person's parcel is to be ••••ored in a separate garner,* 2.32 and kept separate thro' the whole process of manufacture, which oc∣casions much labour; almost all of which is performed by the machines. See plate VI. fig 1; which is a view of one side of a mill containing a number of garners holding par∣cels, and a side view of the wheat elevator.

The grain is emptied into the garner g, from the waggon, as shewn in plate VIII; and, by drawing the gate A, it is let into the elevator AB, and elevated into the crane-spout B, which being turned into the mouth of the garner-spout BC, which leads over the top of a number of garners, and has, in its bottom, a little gate over each garner; which gates and garners are all numbered with the same numbers re∣spectively.

Suppose we wish to deposit the grain in the garner No. 2, draw the gate 2 out of the bot∣tom, and shut it in the spout, to stop the wheat from passing along the spout past the hole, so that it must all fall into the garner; and thus for the other garners 3-4-5-6-&c. These

garners are all made like hoppers,* 2.33 about 4 inches wide at the floor, and nearly the length of the garner; but as it passes through the next story, it is brought to the form of a spout 4 inches square, leading down to the general spout KA, which leads to the eleva∣tor; in each of these spouts is a gate number∣ed; with the number of its garner; so that when we want to grind the parcel in garner 2, we draw the gate 2 in the lower spout, to let the wheat run into the elevator at A, to be elevated into the crane-spout B, which is to be turned over the rolling-screen, as shewn in plate VIII.

Under the upper tier of garners, there is an∣other tier in the next story, set so that the spouts from the bottom of the upper tier pass down the partitions of the lower tier, and the upper spouts of the lower tier pass between the partitions of the upper tier, to the garner-spout.

These garners, and the gates leading both into and out of them, are numbered as the others.

If it is not convenient to fix the descending spouts BC, to convey the wheat from the ele∣vator to the garners, and KA to convey it from the garners to the elevator again, then the conveyers r-s and l-k may be used for said purposes.

To keep the parcels separate,* 2.34 there should be a crane-spout to the meal elevator, or any other method, by which the meal of the se∣cond parcel may be guided to fall on another part of the floor, until the first parcel is 〈◊〉〈◊〉 bolted, and the chests cleared out, when the

meal of the second parcel may be guided into the hopper-body.* 2.35

I must here observe, that in mills for grind∣ing parcels, the tail flour must be hoisted by a separate elevator to the hopper-boy, to be bolted over, and not run into the conveyer, as shewn in plate VIII; because then the parcels could not be kept separate.

The advantages of the machinery,* 2.36 applied to a mill for grinding parcels, are very great.

1. Because without them there is much la∣bour in moving the different parcels from place to place, all which is done by the machinery.

2. The meal, as it is ground, is cooled by the machinery, in so short a time, and bolted, that when the grinding is done, the bolting is also nearly finished: Therefore,

3. It saves room, because the meal need not be spread over the floor to cool, there to lay 12 hours as usual, and none but one parcel need be on the floor at once.

4. It gives greater dispatch, as the mill need never stop either stones or bolts, in order to keep parcels separate. The screenings of each parcel may be cleaned, as directed in art. 89, with very little trouble; and the flour may be nearly packed before the grinding is finished. So that if a parcel of 60 bushels arrive at the mill in the evening, the owner may wait till morning, when he may have it all finished; he may use the off all for feed for his team, and proceed with his load to market.

Art. 92. A Grist-mill for grinding very small Parcels.

FIG. 16, plate VII, is a representation of a grist-mill,* 2.37 so constructed that the grist being put into the hopper, it will be ground and bolted, and return into the bags again.

The grain is emptied into the hopper at A, and as it is ground it runs into the elevator at B, and is elevated and let run into the bolt∣ing hopper down a broad spout at C, and as bolted, it falls into the bags at d. The chef is made to come to a point like a funnel, and a division made to separate the fine and coarse, if wanted, and a bag put under each part; 〈◊〉〈◊〉 the top of this division is set a regulating board on a joint, as x, by which the fine and coarse can be regulated at pleasure.

If the bran requires to be ground over (〈◊〉〈◊〉 it often does) it is made to fall into a box over the hopper, and by drawing the little gate 〈◊〉〈◊〉 it may be let into the hopper, as soon as the grain is all ground, and as it is bolted the se∣cond time, it is let run into the bag by shutting the gate b, and drawing the gate c.

If the grain is put into the hopper F, then as it is ground it falls into the drill, which draws it into the elevator at B, and it asce•••• as before.

To keep the different grists separate—Who the miller sees the first grist fall into the eleva∣tor,* 2.38 he shuts the gate B or d, and gives 〈◊〉〈◊〉 for it to get all into the bolting reel; he 〈◊〉〈◊〉 stops the knocking of the shoe by pulling 〈◊〉〈◊〉 shoe line, which hangs over the pullies pp, from the shoe to near his hand, making it fast 〈◊〉〈◊〉

peg; he then draws the gate B or d,* 2.39 and lets the second grist into the elevator, to fall into the shoe or bolting hopper, giving time for the first grist to be all into the bags, and the bags of the second grist put in their places; he then unhitches the line from the peg, and lets the shoe knock again, and begin to bolt the second grist.

If he does not choose to let the meal run immediately into the bags, he may have a box made with feet to stand in the place of the bags, for the meal to fall in, out of which it may be taken, and put into the bags, by the miller or the owner, as fast as it is bolted, and mixed as desired; and as soon as the first parcel is bolted, the little gates at the mouth of the bags may be shut, while the meal is fill∣ed out of the box, and the second grist may be bolting.

The advantages of this improvement on a grist-mill are,* 2.40

1. It saves the labour of hoisting, spreading, and cooling the meal, and carrying up the ran to be ground over, sweeping the chest, and filling the bags.

2. It does all with greater dispatch, and 〈◊〉〈◊〉 waste, without having to stop the stones or ••••lting-reel, to keep the grists separate, and he bolting is finished almost as soon as the ••••inding; therefore the owner will be the less 〈◊〉〈◊〉 detained.

The chest and spouts should be made steep prevent the meal from lodging in them,* 2.41 so 〈◊〉〈◊〉 the miller, by striking the bottom of the 〈◊〉〈◊〉, will shake out all the meal.

The elevator and drill should be so made as to clean out at one revolution.* 2.42 The drill might have a brush or two, instead of rakes, which would sweep the case clean at a revo∣lution; and the shoe of the bolting-hopper should be short and steep, so that it will clean out soon.

The same machinery may be used for mer∣chant-work, by having a cranespout at C, or a small gate, to turn the meal into the hopper-boy that tends the merchant bolt.

A mill thus constructed, might grind grists in the day-time, and merchant-work at night.

A drill is preferable to a conveyer for grist-mills, because they will clean out much sooner and better. The lower pulley of the elevator is twice as large in diameter as the pullies of the drill; the lower pulley of the elevator, and one pulley of the drill, are on the same shaft, close together, the elevator moves the drill, and the pulley of the drill being small∣est, gives room for the meal to fall into the buck∣ets of the elevator.

Art. 93. Of elevating Grain, Salt, or any granulous Sub∣stance, from Ships into Store-houses, by the Strength of a Horse.

FIG. 17 represents the elevator, and the manner of giving it motion; the horse is hitch∣ed to the end of the sweep-beam A, by which he turns the upright shaft, on the top of which is the driving cog-wheel, of 96 cogs,

2 1-2 inches pitch,* 2.43 to gear into the leading wheel of 20 cogs, on the same shaft with which is another driving wheel of 40 cogs, to gear into another leading wheel of 19 cogs, which is on the same shaft with the elevator pulley; then if the horse makes about 3 revolutions in a minute (which he will do if he walk in a circle of 20 feet diameter) the elevator pulley will make about 30 revolutions in a minute; and if the pulley is 2 feet in diameter, and a bucket be put on every foot of the strap, to hold a quart each, the elevator will hoist a∣bout 187 quarts per minute,* 2.44 or 320 bushels in an hour, 3840 bushels in 12 hours; and for every foot the elevator is high, the horse will have to sustain the weight of a quart of wheat; say 48 feet, which is the height of the highest store-houses, then the horse would have to move 1 1-2 bushels of wheat upwards, with a velocity equal to his own walk; which I presume he can do with ease, and overcome the friction of the machinery: By which will appear the great advantages of this applica∣tion.

The lower end of the elevator should stand near the side of the ship, and the grain, salt, &c &c. be emptied into a hopper; the upper end may pass through a door or window, as may be most convenient; the lower case should be a little crooked to prevent the buckets from rubbing in their descent.

Art. 94. Of an Elevator applied to elevate Grain, &c. wrought by a Man.

FIG. 18, AB, are two Ratchet Wheels,* 2.45 with two deep grooves in each of them, for ropes to run in; they are fixed close together, on the same shaft with the upper pulley of the elevator, so that they will turn easily on the shaft the backward way, but a click falls in∣to the ratchet, and prevents them from turn∣ing forwards. Fig. 19 is a side view of the wheel, ratchet and click. C D are two levers, like weavers treadles, and from lever C there is a light staff passes to the foreside of the groove wheel B, and made fast by a rope half way round the wheel; and from said lever C there is a rope passing to the backside of the wheel A; and from lever D there is a light staff pas∣sing to the foreside of the groove wheel A, and a rope to the backside of the groove wheel B.

The man,* 2.46 who is to work this machine, stands on the treadles, and holds by the staffs with his hands; and as he treads on D it de∣scends, and the staff pulls forward the wheel A, and the rope pulls backwards the wheel B, and as he treads on C the staff pulls forward the wheel B, and the rope pulls backward the wheel A; but as the click falls into the ratch∣et so that the wheels cannot move forward without turning the elevator pulley, thus it is moved one way by the treadles; and in or∣der to keep up a regular motion, F is a heavy fly-wheel, which should be of cast metal, to prevent much obstruction from the air.

To calculate what quantity a man can raise 〈◊〉〈◊〉 any height,* 2.47 let us suppose his weight to be 150lbs. which is the power to be applied,* 2.48 and suppose he is able to walk about 70 feet 〈◊〉〈◊〉 stairs in a minute, by the strength of both 〈◊〉〈◊〉 legs and arms, or, which is the same thing, 〈◊〉〈◊〉 move his weight on the treadles 70 steps 〈◊〉〈◊〉 a minute; then suppose we allow, as by 〈◊〉〈◊〉. 29—42, to lose 1-3 of the power to gain ve∣locity and overcome friction (which will be a 〈◊〉〈◊〉 plenty in this case, because in the ex∣periment in the table in art. 37, when 7lbs were charged with 6lbs. they moved with a velocity of 2 feet in half a second) then there 〈◊〉〈◊〉 remain 100lbs. raised 70 feet in a minute, 〈◊〉〈◊〉 to 200lbs. raised 35 feet to the top of the 〈◊〉〈◊〉 story per minute, equal to 200 bushels 〈◊〉〈◊〉 hour, 2400 bushels in 12 hours.

The great advantages of this application of 〈◊〉〈◊〉 elevator,* 2.49 and of this mode of applying 〈◊〉〈◊〉 strength, will appear from these consi∣derations, viz. he uses the strength of both 〈◊〉〈◊〉 legs and arms, to move his weight only, 〈◊〉〈◊〉 one treadle to the other, which weight 〈◊〉〈◊〉 the work; whereas in carrying bags on a back, he uses the strength of his legs only, 〈◊〉〈◊〉 raise both the weight of his body and the 〈◊〉〈◊〉, add to this that he generally tak••s a 〈◊〉〈◊〉 circuitous rout to the place where he is 〈◊〉〈◊〉 empty the bag, and returns empty: where∣•••• the elevator takes the shortest direction to 〈◊〉〈◊〉 place of emptying, and is always steadily 〈◊〉〈◊〉 work.

The man must sit on a high bench, as a ••eaver does, on which he can rest part of his

weight,* 2.50 and rest himself occasionally, when the machine moves lightly, and have a 〈◊〉〈◊〉 above his head, that he may push his head a∣gainst, to overcome extraordinary resistance. This is probably the best means of applying man's strength to produce rotary motions.

DESCRIPTION OF PLATE IX.

THE grain is emptied into the spout A, 〈◊〉〈◊〉 which it descends into the garner B; which by drawing the gate at C, it passes into 〈◊〉〈◊〉 elevator C D, which raises it to D, and emp∣ties it into the Crane-spout E, which is so 〈◊〉〈◊〉 on gudgeons that it may be turned to 〈◊〉〈◊〉 surrounding granaries, into the Screen-••••••∣per F, for instance, (which has two parts and G) out of which it is let into the Roll Screen, at H, by drawing the small gate. It passes through the F an I, and falls into 〈◊〉〈◊〉 little Sliding-Hopper K, which may be ••••••ed, so as to guide it into either of the 〈◊〉〈◊〉-Garners, over the stones, L or M, and is let into the Stone-Hoppers by the little 〈◊〉〈◊〉 bb, as fast as it can be ground. When 〈◊〉〈◊〉 it falls into the Conveyor N N, which 〈◊〉〈◊〉 it into the Elevator at O O, this raises 〈◊〉〈◊〉 empties it into the Hopper-Boy at P, who is so constructed as to carry it round in a 〈◊〉〈◊〉 gathering it gradually towards the centre, 〈◊〉〈◊〉 it sweeps it into the Boulting-Hoppers Q Q.

The tail flour, as it falls, is guided into Elevator, to ascend with the meal, and, 〈◊〉〈◊〉 a proper quantity may be elevated, there 〈◊〉〈◊〉 regulating board R, set under the super•••••• cloths, on a joint x, so that it will turn 〈◊〉〈◊〉

the head or tail of the Reel,* 2.51 and send more or less into the Elevator, as may be re∣••••••ed.

There may be a piece of coarse cloth or ••ire put on the tails of the superfine reels, ••••at will let all pass through except the bran, which falls out at the tail, and a part of which 〈◊〉〈◊〉 guided into the elevator with the tail flour, 〈◊〉〈◊〉 assist the boulting in warm weather; the quantity is regulated by a small board r, set 〈◊〉〈◊〉 a joint under the ends of the reels. Beans may be used to keep the cloths open, and still 〈◊〉〈◊〉 returned into the elevator to ascend again. That passes through the course cloth, or wire, 〈◊〉〈◊〉 the remainder of the bran, are guided in∣•••• the reel S, to be boulted.

To clean Wheat several Times.

Suppose the grain to be in the screen-hopper 〈◊〉〈◊〉 Draw the gate a; shut the gate e; move 〈◊〉〈◊〉 ••••iding hopper K over the spout K c d; and 〈◊〉〈◊〉 it run into the elevator to be raised again. 〈◊〉〈◊〉 the crane spout over the empty hopper 〈◊〉〈◊〉 and the wheat will be all deposited there early as soon as it is out of the hopper F. 〈◊〉〈◊〉 draw the gate e, shut the gate a, and in the crane spout over F; and so on alter∣nately, as often as necessary. When the grain sufficiently cleaned, slide the hopper K over 〈◊〉〈◊〉 hole that lead into the stones.

The screenings fall into a garner, hopper-••••se, to clean them draw the gate f, and let ••••em run into the elevator, to be elevated to the screen hopper F. Then proceed with 〈◊〉〈◊〉 as with the wheat, till sufficiently clean.

To clean the fannings,* 2.52 draw the little gate a, and let them into the elevator, &c. as before.

Fig. II. is a perspective view of the Con∣veyer, as it lies in its trough, at work; and shews the manner in which it is joined to the pulleys, at each side of the elevator.

Fig. III. exhibits a view of the pulley of the meal elevator, as it is supported on each side, with the strap and buckets descending 〈◊〉〈◊〉 be filled.

Fig. IV. is a perspective view of the under side of the arms of the hopper-boy, with flights complete. The dotted lines show the tra•••• of the flights of one arm; those of the other following, and tracking between them. All are the sweepers. These carry the meal 〈◊〉〈◊〉 in a ring, trailing it regularly all the way, 〈◊〉〈◊〉 flights drawing it to the centre, as already mentioned. B B are the sweepers that dri•••••• it into the boulting hoppers.

Fig. V. is a perspective view of the 〈◊〉〈◊〉 of the wheat-elevator; and shows the 〈◊〉〈◊〉 in which it is fastened, by a broad piece 〈◊〉〈◊〉 leather, which passes through and under the ••••••∣vator-strap, and is nailed to the sides with 〈◊〉〈◊〉 tacks.

CHAPTER III. OF THE CONSTRUCTION OF THE SEVERAL MACHINES.

Art. 95. Of the Wheat-Elevator.

FIRST determine how many bushels it should hoist in an hour,* 2.53 and where it shall be set, so as to answer all the following pur∣poses if possible.

1. To elevate the grain from a waggon or 〈◊〉〈◊〉

2. From the different garners into which it ••ay be stored.

3. If it be a two story mill, to hoist the wheat from the tail of the fan, as it is cleaned, to a garner over the stones.

4. To hoist the screenings to clean them se∣veral times.

5. To hoist the wheat from a shelling-mill, if there be one.

One elevator may do all this in a mill right∣ly planned, and most of it can be done in mills ready built.

Then if you wish it to hoist about 300 bush∣els in an hour,* 2.54 make the strap 4 1-2 inches

wide,* 2.55 of good, strong, white harness-leather, only one thickness. It must be cut and joined together in a straight line, with the thickest and consequently the thinnest ends together, so that if they be too thin they may be lapped over and doubled, until they are thick enough singly.—Then,* 2.56 to make wooden buckets, take the but of a willow or water-birch, that will split freely, cut it in bolts 15 inches long, and rive and shave it into staves 5 1-2 inches wide, and three eigths of an inch thick; these will make one bucket each. Set a pair of compass∣ses to the width of the strap, and make the sides and middle of the bucket equal thereto at the mouth, but let the sides be only two third of that width at the bottom, which will make it of the form of fig. 9. plate 6; the ends be∣ing cut a little circular to make the buckets by closer to the strap and wheel.* 2.57 As it passes over, make a pattern of the form of fig. 9 to describe all the rest by. This makes a buc∣ket of a neat form, to hold about 75 solid inch∣es, or somewhat more than a quart. Then 〈◊〉〈◊〉 make them bend to a square at the corners 〈◊〉〈◊〉 cut a mitre square across where they are to bend, about 2-3 through; boil them and be•••• them hot, tacking a strip of leather acros•• them, to hold them in that form until they 〈◊〉〈◊〉 cold, and then put bottoms to them of the 〈◊〉〈◊〉 skirts of the harness-leather. These botto•••• are to extend from the lower end to the 〈◊〉〈◊〉 that binds it on. Then, to fasten them on 〈◊〉〈◊〉 and with dispatch, prepare a number of first 1 3-4 inches wide, of the best cuttings of 〈◊〉〈◊〉 harness-leather, wet them and stretch them hard as possible, which reduces their width

about 1 1-2 inches.* 2.58 Nail one of these straps to the side of a bucket, with 5 or 6 strong tacks that will reach through the bucket and clinch inside. Then take a 1 1-2 inch chisel, and strike it through the main strap about a quarter of an inch from each edge, and put one end of the binding-strap through the slits, draw the buc∣ket very closely to the strap, and nail it on the other side of the bucket, which will finish it. See B in fig. 2, plate 6.* 2.59 C is a meal-bucket fastened in the same manner,* 2.60 but is bottom∣ed only with leather at the lower end, the main strap making the bottom side of it. This is the best way I have yet discovered to make wooden buckets. The scraps of the harness-leather, out of which the elevator-straps are 〈◊〉〈◊〉, are generally about enough to complete the buckets, which works it all up.

To make Sheet-Iron Buckets.

CUT the sheet in the form of fig. 8,* 2.61 plate VI.* 2.62 making the middle part c, and the sides 〈◊〉〈◊〉 and b nearly equal to the width of the strap, and nearly 5 1-2 inches long, as before. Bend them to a right angle at every dotted line, and 〈◊〉〈◊〉 bucket will be formed. c will be the bot∣tom side next to the strap; and the little holes 〈◊〉〈◊〉 and b b will meet, and must be rivetted a hold it together. The two holes c are for ••••stening it to the straps by rivets. The part 〈◊〉〈◊〉 is the part that dips up the wheat, and the 〈◊〉〈◊〉 being doubled back strengthens it, and 〈◊〉〈◊〉 to make it wear well. The bucket be∣ing completely formed, and the rivet-holes 〈◊〉〈◊〉, spread one out again as fig. 8, to de∣scribe

all the rest by,* 2.63 and to mark for the holes, which will meet again when folded up. They are fastened to the strap by two rivets with thin heads put inside the bucket, and a double bur of sheet-iron put on the under side of the strap, which fastens them on very tightly. See A fig. 2. These buckets will hold about 1,3 quarts, or 88 cubic inches. This is the best way I have found to make sheet-iron buc∣kets.* 2.64 D is a meal-bucket of sheet-iron, ri∣vetted on by two rivets, with their heads in∣side the strap; the sides of the buckets are turned a little out, and holes made in them for the rivets to pass through. Fig. 11 is the form of one spread out, and the dotted lines show where they are bent to right angles to form them. The strap forms the bottom 〈◊〉〈◊〉 of these buckets.

Make the pulleys 24 inches diameter,* 2.65 as thick as the strap is wide, and half an inch higher in the middle than at the sides, to make the strap keep on; give them a motion of 25 revolutions in a minute, and put on a sheet-iron bucket for every 15 inches; then 12 buckets will pass per minute, which will carry 162 quarts,* 2.66 and hoist 300 bushels in an hour, and 3600 bushels in 12 hours. If you wish it to hoist faster make the strap wider, the buc∣kets larger in proportion, and increase the ve∣locity of the pulley, but not above 35 revolu∣tions in a minute, nor more buckets than one for every 12 inches, otherwise they will not empty well. A strap of 5 inches, with buck∣ets 6 inches long, and of a width and propor∣tion suiting the strap (4 1-2 inches wide) 〈◊〉〈◊〉 hold 1, 8 quarts each; and 35 revolutions of 〈◊〉〈◊〉

pulley will pass 175 buckets,* 2.67 which will carry 315 quarts in a minute,* 2.68 and 590 bushels in an hour. If the strap be 4 inches wide, and the wooden buckets 5 inches deep, and in propor∣tion to the strap, they will hold, 8 of a quart: then, if there be one for every 15 inches, and the pulley revolves 27 revolutions in a minute, it will hoist 200 bushels in an hour,* 2.69 where there is a good garner to empty the wheat in∣to. This is sufficient for unloading waggons, and the size they are commonly made.

Fig. 6 represents the gudgeon of the lower pulley; fig. 7 the gudgeon for the shaft, on which the upper pulley is fixed. Fix both the pulleys in their places, but not firmly, so that a line stretched from one pulley to the other, will cross the shafts or gudgeons at right an∣gles. This must always be the case to make the straps work fairly. Put on the strap with the buckets; draw it tightly and buckle it; put it in motion, and if it does not keep fairly 〈◊〉〈◊〉 the pulleys their position may be altered a little. Observe how much the descending strap swags by the weight of the buckets,* 2.70 and make the case round it so crooked, that the points of the buckets will not rub in their de∣scent, which will cause them to wear much longer and work easier. The side boards need not be made crooked in dressing out, but may be bent sufficiently by sawing them half way or two thirds through, beginning at the upper edge, holding the saw very much aslant, the point downwards and inwards, so that in bend∣ing the parts will slip past each other. The 〈◊〉〈◊〉 case must be nearly straight; for if it 〈◊〉〈◊〉 much crooked, the buckets will in∣cline

to turn under the strap.* 2.71 Make the cases 3-4 of an inch wider than the strap and buck∣ets inside, and 1 1-2 inch deeper, that they may play freely; but do not give them room to turn upside down. If the strap and buckets be 4 inches,* 2.72 then make the side boards 5 1-2, and the top and bottom boards 6 3-4 inches wide, of inch boards. Be careful that no shoulders nor nail-points be left inside of the ca∣ses, for the buckets to catch in. Make the ends of each case, where the buckets enter as they pass over the pulleys, a little wider than the rest of the case. Both the pulleys are to be nicely cased round to prevent waste, not leaving room for a grain to escape, continu∣ing the case of the same width round the 〈◊〉〈◊〉 of the upper, and bottom of the lower pulley, then if any of the buckets should ever get loose and stand askew, they will be kept right by the case; whereas, if there were any ends of boards or shoulders, they would catch against them. See A B,* 2.73 plate VI. fig. 1. The bottom of the case of the upper pulley must be descend∣ing,* 2.74 so that what grain may be falling out of the buckets in passing over the pulleys, may be guided into the descending case. The shaft passing through this pulley is made round where the case fits to it: half circles are cut out of two boards, so that they meet and em∣brace it closely. The undermost board, where it meets the shaft, is ciphered off inside next the pulley, to guide the grain inward. But it is full as good a way to have a strong gud∣geon to pass through the upper pulley, with a tenon at one end, to enter a socket, 〈◊〉〈◊〉 may be in the shaft, that is to give it 〈◊〉〈◊〉.

This will best suit where the shaft is short,* 2.75 and has to be moved to put the elevator out, and in gear.

The way that I have generally cased the pulleys is as follows,* 2.76 viz. The top board of the upper strap-case, and the bottom board of the lower strap-case are extended past the lower pulley to rest on the floor; and the lower ends of these boards are made two inches narrower, as far as the pulley-case ex∣tends; the side board of the pulley is nailed, or rather screwed, to them with wooden screws. The rest of the case boards join to the top of the pulley-case, both being of one width. The blocks which the gudgeons of 〈◊〉〈◊〉 pulley run in, are screwed fast to the out∣side of the case boards; the gudgeons do not pass quite through, but reach to the bottom of the hole, which keeps the pulley in its place.

The said top and bottom boards, and also the side boards of the strap-cases, are extend∣ed; past the upper pulley, and the side boards of the pulley-case are screwed to them; but this leaves a vacancy between the top of the side boards of the strap-cases, and shoul∣ders for the buckets to catch against. This vacancy is to be filled up by a short board, guiding the buckets safely over the upper pul∣ley. The case must be as close to the points of the buckets, where they empty, as is safe, that as little as possible may fall down again. There is to be a long hole cut into the case at B, for the wheat to fall out at,* 2.77 and a short spout guiding it into the crane-spout. The top of the short spout next B, should be loosely fastened in with a button, that it may be ta∣ken

off,* 2.78 to examine if the buckets empty well, &c. Some neat workmen have a much better way of casing the pulleys, that I can∣not here describe; what I have described is the cheapest, and does very well.

The wheat should be let in at the bottom,* 2.79 as meet the buckets, and a gate to shut as near the point of them as possible, as at A, fig. 1. Then if the gate be drawn sufficiently to fill the buckets, and the elevator be stopped, the wheat will stop running in, and the elevator will be free to start again; but if it had been let in any distance up, then, when the eleva∣tor stopped, it would fill from the gate to the bottom of the pulley, and the elevator could not start again. If it be in any case let in 〈◊〉〈◊〉 distance up, the gate should be so fixed, 〈◊〉〈◊〉 it cannot be drawn so far, as to let in the 〈◊〉〈◊〉 faster than the buckets can take it, else 〈◊〉〈◊〉 case will fill and stop the buckets. If it be 〈◊〉〈◊〉 in faster at the hindmost side of the pulley, 〈◊〉〈◊〉 the buckets will carry it, the same evil 〈◊〉〈◊〉 occur; because the buckets will push 〈◊〉〈◊〉 wheat before them, being more than they 〈◊〉〈◊〉 hold, and give room for too much to come 〈◊〉〈◊〉 therefore there should be a relief-gate at 〈◊〉〈◊〉 bottom to let the wheat out, if ever it happen to get too much of it in.

The motion is to be given to the upper pul∣ley of all elevators,* 2.80 if it can be done, 〈◊〉〈◊〉 the weight in the buckets, causes the strap 〈◊〉〈◊〉 hang tighter on the upper, and slacker on 〈◊〉〈◊〉 lower pulley; therefore the upper pulley 〈◊〉〈◊〉 carry the greatest quantity without slipp••••••. All elevators should stand a little 〈◊〉〈◊〉 because they will discharge the better. 〈◊〉〈◊〉

boards for the cases should be of any unequal lengths,* 2.81 so that two joints will never come close together, which makes the case strong. Some have joined the cases at every floor, which is a great error. There must be a door in the ascending case, at the most conveni∣ent place, to buckle the strap, &c. &c.

Of the Crane-Spout.

TO make a Crane-Spout,* 2.82 fix a board 18 or 20 inches broad truly horizontal or level, as a under B, in plate VI. fig. 1. Through the middle of this board the wheat is conveyed, by a short spout from the elevator. Then make the spout of 4 boards, 12 inches wide 〈◊〉〈◊〉 the upper, and about 4 or 5 inches at the 〈◊〉〈◊〉 end. Cut the upper end off aslant, so 〈◊〉〈◊〉 to fit nicely to the bottom of the board; 〈◊〉〈◊〉 it to a strong pin, passing through the 〈◊〉〈◊〉 board near the hole through which the wheat passes, so that the spout may be turned in any direction and still cover the hole, at the some time it is receiving the wheat, and guid∣ing it into any garner, at pleasure. In order that the pin may have a strong hold of the board and spout, there must be a piece of can••ling, 4 inches thick, nailed on the top of the board, for the pin to pass through; and 〈◊〉〈◊〉 to the bottom, for the head of the pin 〈◊〉〈◊〉 rest on. But if the spout be long and heavy, 〈◊〉〈◊〉 is best to hang it on a shaft, that may ex∣••••••d down to the floor, or below the collar-beams, with a pin through it, as x, to turn the spout by. In crane-spouts for meal it is

sometimes best to let the lower board reach to,* 2.83 and rest of the floor. If the elevator ca∣ses and crane-spout be well fixed, there 〈◊〉〈◊〉 neither grain nor meal escape or be washed that enters the elevator, until it comes out at the end of the crane-spout again.

Of an Elevator to elevate Wheat from a Ship's Hold.* 2.84

MAKE the Elevator complete (as it ap∣pears 35-39 plate 8) on the ground,* 2.85 (〈◊〉〈◊〉 raise it afterwards.) The pulleys are to 〈◊〉〈◊〉 both fixed in their places and cased; and 〈◊〉〈◊〉 blocks that the gudgeon of the upper 〈◊〉〈◊〉 is to run in, are to be rivetted fast to the 〈◊〉〈◊〉 boards of the pulley, and these case 〈◊〉〈◊〉 screwed to the strap-cases by long screw reaching through the case boards edge 〈◊〉〈◊〉 Both sides of the pulley-case are fastened one set of screws. On the outside of the blocks, round the centre of the gudgeons, 〈◊〉〈◊〉 circular knobs, 6 inches diameter, and 3 inch∣es long, strongly rivetted to keep them 〈◊〉〈◊〉 splitting off, because by these knobs the 〈◊〉〈◊〉 weight of the elevator is to hang. In 〈◊〉〈◊〉 moveable frame 40. 00, 00, are these 〈◊〉〈◊〉 with their knobs, let into the pieces of 〈◊〉〈◊〉 frame BC rs. The gudgeons of the 〈◊〉〈◊〉 pulley p pass through these knobs, and 〈◊〉〈◊〉 them. Their use is to bear the weight of 〈◊〉〈◊〉 elevator that hangs by them; the gudgeons by this means, bear only the weight of 〈◊〉〈◊〉 strap and its load, as is the case with out

elevators.* 2.86 Their being circular gives the ele∣vator liberty to swing out from the wall to the ••old of the ship.

The frame 40 is made as follows: The top ••iece A B is 9 by 8, strongly tenoned into the 〈◊〉〈◊〉 pieces A D and B C with double tenons, which side pieces are 8 by 6. The piece r s 〈◊〉〈◊〉 put in with a tenon, 3 inches thick, which 〈◊〉〈◊〉 dovetailed, keyed, and drawpinned, with 〈◊〉〈◊〉 iron pin, so that it can easily be taken out. In each side piece A D and B C there is a row 〈◊〉〈◊〉 cogs, set in a circle, that are to play in cir∣cular rabbits in the posts p 41. These circles 〈◊〉〈◊〉 to be described with a radius, whose length 〈◊〉〈◊〉 the centre of the joint gudgeon G, to 〈◊〉〈◊〉 centre of the pulley 39; and the posts must 〈◊〉〈◊〉 up, so that the centre of the circle, will 〈◊〉〈◊〉 the centre of the gudgeon G; then the 〈◊〉〈◊〉 will be always right, although the ele∣vator rise and fall to suit the ship or tide. The 〈◊〉〈◊〉 of these circular rabbits ought to be so fix∣ing that the lower end of the elevator may 〈◊〉〈◊〉 near the wall. This may be regulat∣ing by fixing the centre of gudgeon G. The 〈◊〉〈◊〉 of these rabbits is regulated by the 〈◊〉〈◊〉 the vessel is to rise and fall, to allow the elevator to swing clear of the vessel light at 〈◊〉〈◊〉 water. The best way to make the cir∣cular rabbits is, to dress two pieces of 2 inch 〈◊〉〈◊〉 for each rabbit, of the right-circle, and 〈◊〉〈◊〉 them to the posts, at such a distance, leav∣•••••• the rabbit between them.

When the gate and elevator are completed, 〈◊〉〈◊〉 tryed together; the gate hung in its rab∣bits and played up and down, then the eleva∣tor may be raised by the same power; that is, to raise and lower it as described, art. 4.

Art. 96. Of the Meal-Elevator.

LITTLE may be said of the manner of constructing the Meal-Elevator,* 2.87 after what has been said in art. 90, except giving the ••••∣mensions. Make the pulleys 3 1-2 inches thick, and 18 inches diameter. Give them no 〈◊〉〈◊〉 than 20 revolutions in a minute. Make the strap 3 1-2 inches wide, of good, pliant, white harness-leather; make the buckets either of wood or sheet-iron, to hold about half a 〈◊〉〈◊〉 each; put one for every foot of the strap; make the cases tight, especially round the up∣per pulley, slanting much at bottom, so that the meal which falls out of the buckets, may be guided into the descending case. 〈◊〉〈◊〉 lean a little, that it may discharge the better. The spout that conveys the meal from the ele∣vator to the hopper-boy, should not 〈◊〉〈◊〉 much more than 45 degrees descent, that 〈◊〉〈◊〉 meal may run easily down, and not cause dust; fix it so that the meal will spread 〈◊〉〈◊〉 over its bottom: in its descent it will 〈◊〉〈◊〉 the better. Cover the top of the spout 〈◊〉〈◊〉 way down, and hang a thin, light cloth at 〈◊〉〈◊〉 end of this cover, to check all the dust 〈◊〉〈◊〉 may raise, by the fall of the meal from the buckets. Remember to take a large 〈◊〉〈◊〉 off the inside of the board, where it fits to 〈◊〉〈◊〉 undermost side of the shaft of the upper pulley else the meal will work out along the 〈◊〉〈◊〉. Make all tight, as directed, and it will effect∣tually prevent waste.

In letting meal into an elevator,* 2.88 it must be let in some distance above the centre of the pulley,* 2.89 that it may fall clear from the spout that conveys it in; otherwise it will clog and ••hoke. Fig. 4 is the double socket gudgeon of the lower pulley, to which the Conveyer joins. Fig. 3, ab cd is a top view of the case that the pulley runs in, which is constructed 〈◊〉〈◊〉: a b is a strong plank, 14 by 3 inches, steped i•• the fill, dovetailed and keyed in the meal∣••••am,* 2.90 and is called the main bearer. In this, at the determined height, is framed the gud∣geon bearers ac bd, which are planks 15 by 1 1-2 inches, set 7 1-2 inches apart, the pul∣ley running between, and resting on them. The end piece c d 7 inches wide and 2 thick, 〈◊〉〈◊〉 in the direction of the strap-case, and 〈◊〉〈◊〉 5 inches above the top of the pulley; to this the bearers are nailed. On the top of the bearers, above the gudgeons, are set two 〈◊〉〈◊〉 planks 13 by 1 1-2 inches, rabitted into the main bearer, and screwed fast to the end piece c d; these are 4 inches above the pulley. The bottom piece of this case slides in between the bearers, resting on two cleets, so that it 〈◊〉〈◊〉 be drawn out to empty the case, if it should ever by any means be overcharged with meal: this completes the case. In the gudgeon bearer under the gudgeons are mor∣••••••, made about 12 by 2 inches, for the meal 〈◊〉〈◊〉 pass from the conveyer into the elevator; the bottom board of the conveyer trough rests as the bearer in these mortises. The strap cases joins to the top of the pulley case, but is not made fast, but the back board of the de∣scending case is steped into the inside of the

top of the end piece c d.* 2.91 The bottom of the ascending case is to be supported steady to its place, and the board at the bottom must be ci∣phered off at the inside, with long and large ciphers, making them at the point only 〈◊〉〈◊〉 inch thick; this to make the bottom of the case wide, for the buckets to enter, if any of them should be a little askew, because the pul∣ley-case is wider than the strap-cases, to give room for the meal from the conveyer to 〈◊〉〈◊〉 into the buckets; and in order to keep the pas∣sage open,* 2.92 there is a piece 3 inches wide, and 1-3-4 inch thick, put on each side of the pul∣ley, to stand at right angles with each other extending 3 1-2 inches at each end past 〈◊〉〈◊〉 pulley, and are cyphered off, so as to clear the strap, and draw the meal under the bucket•• these are called Bangers.

Art. 97. Of the Meal-Conveyer.

SEE it described,* 2.93 art. 88. Fig. 3, a Conveyer joined to the pulley of the Elevator. Fig. 4 is the gudgeon that is put 〈◊〉〈◊〉 the lower pulley, to which the conveyer 〈◊〉〈◊〉 joined by a socket, as represented. Fig 5 〈◊〉〈◊〉 view of said socket and the band, as it appears on the end of the shaft. The tenon of the gudgeon is square, that the socket may fit to every way alike. Make the shaft 5 1-2 inches diameter, of eight equal sides, and put on the socket and the gudgeon:* 2.94 then, to lay it 〈◊〉〈◊〉 for the flights, begin at the pulley, mark

near the end as possible, on the one side,* 2.95 and turning the shaft the way it is to work, at the distance of 1 1-2 inch towards the other end, set a flight on the next side; and thus go on to mark for a flight on every side, still advancing 1 1-2 inchs to the other end, which will form the dotted spiral line, which would drive the meal the wrong way; but the flights are to be set across this spiral line, at an angle of a∣bout 30 degrees, with a line square across the left; and then they will drive the meal the right way, the flights operating like plows.

To make the flights, take good maple,* 2.96 or other smooth hard wood; saw it in 6 inch lengths; split it always from the sap to the 〈◊〉〈◊〉; make pieces 2 1-2 inches wide, and 3-4 〈◊〉〈◊〉 inch thick; plane them smooth on one 〈◊〉〈◊〉, and make a pattern to describe them by, and make a tenon 2 1-2 inches long, to suit a 〈◊〉〈◊〉 inch augre. When they are perfectly by, having the shaft bored, and the inclina∣tion of the flights marked by a scribe, drive them in and cut them off 2 1-2 inches from the shaft, dress them with their foremost edge sharp, taking all off from the back side, leav∣ing the face smooth and straight, to push for∣ward the meal; make their ends nearly circu∣lar. If the conveyer be short,* 2.97 put in lifting flights, with their broad side foremost, half the 〈◊〉〈◊〉of the others, between the spires of them; they cool the meal by lifting and let∣ting it fall over the shaft.

To make the trough for it to run in, take 3 wards, the bottom one 11, back 15, and 〈◊〉〈◊〉 ••3 inches. Fix the block for the gud∣geon to run in at one end, and fill the comers

with cleets,* 2.98 to make the bottom nearly circu∣lar, that but little meal may lay in it; join it neatly to the pulley-case, resting the bottom on the bottom of the hole cut for the meal to enter, and the other end on a supporter, that it can be removed and put to its place again with ease, without stopping the elevator.

A meal-elevator and conveyer thus made of good materials, will last 50 years, with very little repair, and save more meal fresh waste, than will pay for building and repair∣ing them for ever. The top of the trough must be left open, to let the steam of the meal out; and a door may be made in the ascend∣ing case of the elevator, about 4 feet long to buckle the strap tighter, &c. The stra•••••• the elevator turns the conveyer, so that it 〈◊〉〈◊〉 be easily stopped if any thing should be ca•••••• in it, being dangerous to turn it by ca••••. This machine is often applied to cool the 〈◊〉〈◊〉 without the hopper-boy,* 2.99 and attend the b••••∣ing-hopper, by extending it to a great length and conveying the meal immediately into 〈◊〉〈◊〉 hopper, which does very well, and some pre∣fer it; but a hopper-boy is preferable with there is room for one.

Art. 98. Of a Grain-Conveyer.

THIS machine has been constructed in variety of ways,* 2.100 the best I take to be as fol∣lows, viz. Make a round shaft, 9 inches dia∣meter. Then, to make the spire, take strong

sheet-iron,* 2.101 make a pattern 3 inches broad and of the true arch of a circle;* 2.102 the diameter of which (being the inside of the pattern) is to be 12 inches; this will give it room to stretch along a 9 inch shaft, so as to make a hasty spire, that will advance about 21 inches along the shaft every revolution. By this pattern cut the sheet-iron into circular pieces, and join the ends together by riveting, lapping them so as to let the grain run freely over the joints; then they are joined together they will form several circles, one above the other, ••lip it on the shaft, and stretch it along as far as you can, till it comes tight to the shaft, and fast∣er it to its place, by pins, set in the shaft at the back side of the spire, and nail it to the 〈◊〉〈◊〉: it will now form a beautiful spire 21 inches apart, which is too great a distance; therefore there should be two or three of these fires made, and wound into each other, and all be put on together, because if one be put on first, the others cannot be got on so well af∣terwards; they will then be 7 inches apart, and will convey wheat very fast. If these spires 〈◊〉〈◊〉 punched full of holes like a grater, and the ••••ough lined with sheet-iron punched full of small holes, it will be an excellent rubber; will clean the wheat of the dust and down, that adheres to it, and supersede the necessity of any other rubbing-machine.

The spires may also be formed with either wooden or iron flights,* 2.103 set so near to each other in the spiral lines, as to convey the wheat from one to another.

Art. 99. Of the Hopper-Boy

THIS machine has appeared in various constructions, the best of which is represented by fig. 12:* 2.104see the description art. 88.* 2.105

To make the flight-arms C D, take a piece of dry poplar, or other soft scantling 14 feet long, 8 by 2 1-2 inches in the middle, 5 by 1 1-2 inches at the end, and straight at the bottom;* 2.106 on this strike the middle line a b, fig. 13. Consider which way it is to revolve, and ••••∣pher off the under side of the foremost edge from the middle line, leaving the edge 3-4 of an inch thick, as appears by the shaded part. Then, to lay out the flights, take the follow∣ing

RULE.

Set your compasses at 4 1-2 distance,* 2.107and beginning with one foot in the centre c, 〈◊〉〈◊〉 towards the end b, observing to lessen the dis∣tance one sixteenth part of an inch every feet this will set the flights closer together at the end than at the centre.* 2.108 Then, to set the flights of one arm to track truly between 〈◊〉〈◊〉 of the other, and to find their inclination with one point in the centre c, sweep the ••••••∣ted circles across every point in one arm, 〈◊〉〈◊〉 without altering the centre or distance, into the little dotted marks on the other arm, 〈◊〉〈◊〉 between them the circles are to be swept 〈◊〉〈◊〉 the flights in it.* 2.109 Then, to vary their inclina∣tion regularly from the end to the centre strike the dotted line c d half an inch from the centre c, and 2 1-2 inches from the middle.

line at d. Then with the compasses set to half an inch,* 2.110 set off the inclination from the dotted circles on the line c d. Then, because the line c d approaches the middle line, the inclination is greater near the centre than at the end, and vary regularly. Dovetail the flights into the arm,* 2.111 observing to put the side that is to drive the meal to the line of inclination. The bot∣toms of them should not extend past the mid∣dle line, the ends being all rounded and dres∣sed off at the back side to make the point sharp, leaving the driving side quite straight like the 〈◊〉〈◊〉 r. See them complete in the end c a. The sweepers should be 5 or 6 inches long,* 2.112 〈◊〉〈◊〉 on behind the flights, at the back side of the arms, one at each end of the arm, and 〈◊〉〈◊〉 at the part that passes over the hopper: 〈◊〉〈◊〉 use is described art. 88.

The upright shaft should be 4 by 4 inches,* 2.113 and 〈◊〉〈◊〉 round for about 4 1-2 feet at the lower end to pass lightly through the centre of the 〈◊〉〈◊〉. To keep the arm steady, there is a 〈◊〉〈◊〉 iron 15 inches high, its legs 1-2 inch by 〈◊〉〈◊〉 to stride 2 feet: The ring at the top should fit the shaft neatly, and be smooth and ••••••ded inside, that it may slide easily up and down: by this the arm hangs to the rope that fits over a pulley at the top of the shaft 8 〈◊〉〈◊〉 diameter, with a deep groove for the 〈◊〉〈◊〉 or cord to run in. Make the leading 〈◊〉〈◊〉 6 by 1 1-4 inches in the middle, 2 by inch at the end, and 8 feet long. This arm 〈◊〉〈◊〉 be braced to the cog-wheel above, to ••••ep it from splitting the shaft by any extra 〈◊〉〈◊〉.

The weight of the balance w must be so near equal to the weight of the arm,* 2.114 that when is raised to the top it will descend quietly.

In the bottom of the upright shaft is the step-gudgeon (fig. 15) which passes through the square plate 4 by 4 inches, (fig. 14) on this plate the arm rests, before the flight touch the floor. The ring on the lower end of the shaft is less than the shaft, that it may pass through the arm: this gudgeon 〈◊〉〈◊〉 out every time the shaft is taken out of the arm.

If the machine is to attend but one boulting hopper,* 2.115 it need not be above 12 or 13 feet long. Set the upright shaft close to the hop∣per, and the flights all gather as the end the fig. 13.* 2.116 But if it is to attend for the grind of two pair of stones, and two hoppers, 〈◊〉〈◊〉 it 15 feet long, and set it between them a lit∣tle to one side of both, so that the two 〈◊〉〈◊〉 may not both be over the hoppers at the same time, which would make it run unsteady then the flights between the hoppers and the centre must drive the meal outwards to the sweepers, as the end c a, fig. 13.

If it is to attend two hoppers, and 〈◊〉〈◊〉 be set between them for want of room, 〈◊〉〈◊〉 set the shaft near to one of them; make 〈◊〉〈◊〉 flights that they all gather to the centre, 〈◊〉〈◊〉 put sweepers over the outer hopper which 〈◊〉〈◊〉 be first supplied, and the surplus carried to other. The machine will regulate itself attend both, although one should feed the times as fast as the other.

If it be to attend three hoppers,* 2.117 set the near the middle one, and put sweepers to

the other two, the surplus will come to the centre one,* 2.118 and it will regulate to feed all three; but should the centre hopper ever stand while the others are going (of either these last applications) the flights next the centre must be moveable that they may be turned, and set to drive the meal out, from the centre; hop∣per-boys should be moved by a strap in some part of their movement,* 2.119 that they may easily stop if any thing catch in them; but several ingenious mill-wrights do prefer cogs; they should not revolve more than 4 times in a mi∣nute.

This machine may be made of a great ma∣ny different forms and constructions on the same principles, to answer the same end, in lesser degree of perfection.

Art. 100. Of the Drill.

SEE the description art. 1. The pulleys should not be less than 10 inches diameter for meal, and more for wheat. The case they run in is a deep narrow trough, say 16 inches deep, 4 wide, pulleys and strap 3 inches. The rakes are little square blocks of willow or pop∣ular, or any soft wood, that will not split with the nails, all of one size that each may take an equal quantity, nailed to the strap with long, small nails, with broad heads, which are inside the strap: the meal should be let into them al∣ways above the centre of the pulley, or at the top of it, to prevent its choking,

which it is apt to do,* 2.120 if let in low. The mo∣tion should be slow for meal; but may be more lively for wheat.

Directions for using a Hopper-Boy.

1. When the meal-elevator is set in motion to elevate the meal, the hopper-boy must be set in motion also, to spread and cool it; and as soon as the circle is full, the boults may be started; the grinding and boulting may like∣wise be carried on together regularly, which is the best way of working.

2. But if you do not choose to boult as you grind, turn up the feeding sweepers, and let the hopper-boy spread and cool the meal, and rise over it; and when you begin to boult turn them down again.

3. If you choose to keep the warm meal se∣parate from the cool, shovel about 18 inches of the outside of the circle in towards the centre, and turn the end flights, to drive the meal outwards, it will spread the warm meal out∣wards, and gather the cool meal in the boult∣ing-hopper. As soon as the ring is full with warm meal, rake it out of the reach of the hopper-boy, and let it fill again.

4. To mix tail-flour or bran, &c. with a quantity of meal that is under the hopper-boy, make a hole for it in the meal quite to the floor, and put it in; and the hopper-boy will mix it regularly with the whole.

5. If it does not keep the hopper full, turn the feeding sweeper a little lower, and throw a little meal on the top of the arm, to make it sink deeper into the meal. If the spread∣ing

sweepers discharge their loads too soon,* 2.121 and do not trail the meal all around the circle, turn them a little lower; if they do not dis∣charge, but keep too full raise them a little.

CHAPTER IV. Art. 101. OF THE UTILITY OF THESE INVENTIONS AND IMPROVEMENTS.

DR. Wistar,* 2.122 of Philadelphia, had discovered and proved by many experiments (which he communicated to the American philosophical society, and which they have published in the 3rd volume of their transactions) that cold is 〈◊〉〈◊〉 principal agent in causing moisture to eva∣porate from bodies; and the fact is evident from daily observation, viz. that it is the dif∣ferent degrees of heat and cold, between the air and bodies, that causes them to cast off or contract moisture.

1st. We see in all sudden transitions from an extreme cold air to a warm, that the walls of houses, stones, ground, and every thing that retains cold, contracts moisture; and it certainly has the same effect on meal.

2. In all sudden changes from warm to cold, 〈◊〉〈◊〉 thing casts off its moisture; for instance, what great quantities of water will disappear

from the ground,* 2.123 in one cold night: this is the reason why meal being warm gets so dry in cold weather, and bolts so free; whereas it is always harder to bolt when there is a change from cold to warm.

3. If you warm a razor, or a glass, warm∣er than your breath, neither of them will be sullied by it.

4. Fill a glass-bottle with cold water in a warm day, and wipe it dry, and there will be presently seen on its outside large drops, col∣lected from the moisture of the air, though the bottle still continues full.

From these instances,* 2.124 it is evident, that the meal should be spread as thin as possible, and be kept in motion from the moment it leaves the stones, until it is cold, that it may have a fair opportunity of casting off its moisture, which will be done more effectually in that time, that can possibly be effected in warm weather, in any reasonable time, after it has grown out in a heap and retained its moisture; and there is no time for insects to deposit their eggs that may in time breed the worms, that are often found in the heart of barrels of flour are packed,* 2.125 and by the moisture being cast and more effectually, it will not be so apt to found.* 2.126 Therefore one great advantage is that the meal is better prepared for boulting, packing and keep∣ing in much less time.

2. They do the work to much greater perfection by cleaning the grain and screenings more ef∣fectually, hoisting and bolting over great parts of the flour, and grinding and boulting 〈◊〉〈◊〉 the middlings, all at one operation, mixing those parts that are to be mixed, and separat∣ing

such as are to be separated more effectu∣ally.* 2.127

3. They save much meal from being wasted,* 2.128 if they be well constructed, because there is no necessity of trampling in it, which trails it wherever we walk, **nor shoveling it about to raise a dust that flies away, &c. This article of saving will soon pay the first cost of building, and keep them in repair afterwards.

4. They afford more room than they take up,* 2.129 because the whole of the meal-loft that here∣tofore was little enough to cool the meal on, may now be spared for other uses, except the circle described by the hopper-boy; and the wheat-garners may be filled from one sto∣ry to another, up to the crane-spout, above the collar-beams; so that a small part of the house will hold a great quantity of wheat, and it may be drawn from the bottom into the ele∣vator as wanted.

5. They tend to dispatch business by finishing as they go;* 2.130 so that there is not as much time ••••ended in grinding over middlings, which will not employ the power of the mill, nor in cleaning and grinding the screenings, they be∣ing cleaned every few days, and mixed with the wheat; and as the labour is easier the miller can keep the stones in better order, and more regularly and steady at work, especi∣ally in the night time, when they fre∣quently stop for want of help, whereas one 〈◊〉〈◊〉, for a time, would be sufficient to attend 〈◊〉〈◊〉 pair of stones running (in one house) well attended by machinery.

6.* 2.131 They last a long time with but little expence of repair,* 2.132 because their motions are slow and easy.

7. They hoist the grain and meal with less pow∣er,* 2.133 and disturb the motion of the mill much less than the old way, because the descending strap balances the ascending one, so that there is no more power used, than to hoist the grain or meal itself; whereas in the old way for every 3 bushels of wheat, which fills a 4 bushel tub with meal, the tub has to be hoisted, the weight of which is equal to a bushel of wheat, consequently the power used, is as 3 for the elevator to 4 for the tubs, which is one fourth less with elevators than tubs: besides, the weight of 4 bushels of wheat, thrown at once on the wheel, always checks the motion, be∣fore the tub is up; the stone sinks a little, and the mill is put out of tune every tub-full, which makes a great difference in a year's grinding; this is worthy of notice when water is scarce.

8. They save a great expence of attendance.* 2.134 One half of the hands that were formerly re∣quired are now sufficient, and their labour is easier. Formerly one hand was required for every 10 barrels of flour that the mill made daily; now one for every 20 barrels is suffici∣ent. A mill that made 40 barrels a day, re∣quired four men and a boy; two men are now sufficient.

Two men's wages,* 2.135 at 7 dolls. each, per month,	168 dolls.
Boarding &c. for do. at 15l. per year,	80
One boy's board, cloathing, &c.	50
	208

There appears a saving of 298 dollars a year,* 2.136 in the article of wages and board, in one double mill.

In support of what is here said, I add the following certificates.

I.

WE do certify that we have erected Oliver Evans's new-invented mode of elevat∣ing,* 2.137 conveying, and cooling meal, &c. As far as we have experienced, we have found them to answer a valuable purpose, well wor∣thy the attention of any person concerned in merchant, or even extensive country mills, who wishes to lessen the labour and expence of manufacturing wheat into flour.

• JOHN ELLICOTT,
• JONATHAN ELLICOTT,
• GEORGE ELLICOTT,
• NATHANIEL ELLICOTT.

Ellicott's mills, Baltimore county, state of Maryland, Aug. 4, 1790.

II.

WE the subscribers do hereby certify, that we have introduced Oliver Evans's im∣provements into our mills at Brandiwine, and have found them to answer, as represented to us by a plate and description: also to be a great saving of waste, labour and expence, and not subject to get out of order. We there∣fore recommend them as well worthy the at∣tention

of those concerned in manufacturing grain into flour.* 2.138

• JOSEPH TATNALL,
• THOMAS LEA,
• SAMUEL HOLLINGSWORTH,
• THOMAS SHALLCROSS,
• CYRUS NEWLIN.

Brandywine mills, 3rd month, 28th, 1791.

III.

WE do certify, that we have used Oliver Evans's machinery, for the space of two years, in our mills, at Petersburg, in Virginia, consisting of three water-wheels, and three pair of stones: and we judge that they have been, and will continue to be, a saving of 300 dollars per year.

N. ELLICOTT, & Co.

Feb. 20, 1794.

IV.

WE do certify, that we have used Oliver Evans's patent machinery in our mills, at Manchester, in the state of Virginia, con∣sisting of three water-wheels, and three pair of stones, for the space of one year, and we judge upon fair calculations, that they are saving to us of 300 dollars per annum.

NICHOLSON & TAYLOR.

Many more to the same purpose might be added, but these may suffice.

Supposing the reader is now fully convinced of the utility of these improvements,* 2.139 I pro∣ceed to give the following bills of materials.

CHAPTER V. BILLS OF MATERIALS TO BE PROVIDED FOR BUILD∣ING AND CONSTRUCTING THE MACHINERY.

Art. 102. For a Wheat-Elevator 43 Feet high, with a Strap 4 inches wide.

THREE sides of good,* 2.140 firm white harness leather.

••20 feet of inch pine, or other boards, that are dry, of about 12 1-2 inches wide, for the cases: these are to be dressed, as follows: ••6 feet in length, 7 inches wide, for the top and bottom.

••6 feet in length, 5 inches wide, with the edges truly squared, for the side boards.

A quantity of inch boards for the garners, as they may be wanted.

A good but of willow or sheet-iron, for the buckets.

••000 tacks, 14 and 16 ounce size, the larg∣est about half an inch long, for the buckets.

3lb.* 2.141 of 8d. and 1lb. of 10d. nails, for 〈◊〉〈◊〉 cases.

2 dozen of large wood screws (but nails 〈◊〉〈◊〉 do) for pulley-cases.

16 feet of 2 inch plank for pulleys.

16 feet of ditto, for cog-wheels, and dry pi•• scantling 4 1-2 by 4 1-2, or 5 by 5 inche to give it motion.

Smith's Bill of Iron.

1 double gudgeon 3-4 inch,* 2.142 (such as fig. 6. pl. VI) 5 inches between the shoulders, 3 3-4 inches between the holes, the necks, or gudgeon-part, 3 inches.

1 small gudgeon, of the common size, 3-•• inch thick.

1 gudgeon an inch thick, (fig. 7) neck 3 1-4 tang 10 inches, to be next the upper pul∣ley.

2 small bands, 4 1-4 inches from the outsides.

1 harness-buckle, 4 inches from the outsides with 2 tongues, of the form of fig. 12.

Add whatever more may be wanting for the gears, that are for giving it motion.

For a Meal-Elevator 43 Feet high, strap 3 1-•• Inches wide, and a Conveyer for two pair 〈◊〉〈◊〉 Stones.

270 feet of dry pine,* 2.143 or other inch board most of them 11 1-2 or 12 inches width of any length, that they may suit to be dres∣sed for the case-boards, as follows:

••6 feet in length, 6 1-2 inches wide,* 2.144 for tops and bottoms of the cases.

••6 feet in length, 4 1-2 inches wide, for the side boards, truly squared at the edges.

The back board of the conveyer trough 15 inches, bottom do. 11 inches, and front 13 inches wide.

Some two inch plank for the pulleys and cog-wheels.

Scantling for conveyers 6 by 6, or 5 1-2 by 5 1-2 inches, of dry pine or yellow poplar; (prefer light wood) pine for shafts, 4 1-2 by 4 1-2 or 5 by 5 inches.

2 1-2 sides of good, pliant harness-leather. 1500 of 14 ounce tacks.

A good, clean but of willow for buckets, un∣less the pieces that are left, that are too small for the wheat-buckets, will make the meal-buckets.

〈◊〉〈◊〉 of 8d. and 1lb. of 10d. nails.

〈◊〉〈◊〉 dozen of large wooden screws (nails will do) for the pulley-cases.

Smith's Bill of Iron.

double gudgeon,* 2.145 (such as fig. 4.pl. VI.) 1 1-2 inch thick, 7 1-2 inches between the necks, 3 1-4 between the key-holes, the necks 1 1-2 inch long, and the tenons at each end of the same length, exactly square, that the socket may fit every way alike.

sockets, one for each tenon, such as ap∣pears on one end of fig. 4. The distance between the outside of the straps with the nails in, must be 5 1-4 inches: fig. 5 is an end view of it, and the band that drives

over it at the end of the shaft,* 2.146 as they ap∣pear on the end of the conveyer.

2 small 3-4 inch gudgeons for the other end of the conveyers.

4 thin bands 5 1-2 inches from the outsides, for the conveyers.

1 gudgeon an inch thick, neck 3 1-4 inches, and tang. 10 inches, for the shaft in the upper pulley and next to it; but if a gud∣geon be put through the pulley, let it be of the form of fig. 6, with a tenon and socket at one end, like fig. 4.

1 harness-buckle, 3 1-2 inches from the out∣sides, with two tongues: such as fix. 12, pl. 6.

Add whatever more small gudgeons and bands may be necessary for giving motion.

For a Hopper-Boy.

1 piece of dry,* 2.147 hard, clean pine scantling 4 1-2 by 4 1-2 inches, and 10 feet long, for the upright shaft.

1 piece of dry poplar, soft pine, or other for light wood, not subject to crack and split i•• working, 8 by 2 1-2 inches, 15 or 16 feet long, for the flight arms.

Some 2 inch plank for wheels to give it mo∣tion, and scantling 4 1-2 by 4 1-2 inches for the shafts.

60 flights 6 inches long, 3 inches wide, and 1-2 inch at one, and 1-4 at the other edge thinner at the fore than hind end, that they may drive in tight like a dovetail wedge. These may be made out of green hard ma∣ple, split from sap to heart, and set to dry

Half a common bed-cord,* 2.148 for a leading line, and balance rope.

Smith's Bill of Iron.

1 stay-iron, C F E, plate VII, fig. 12. The height from the top of the ring F, to the bottom of the feet C E, is 15 inches: distance of the points of the feet C E 24 inches; size of the legs 1-2 by 3-4 inch; size of the ring F 1 by 1-4 inches, round and smooth inside; 4 inch∣es diameter, the inside corners rounded off, to keep it from cutting the shaft; there must be two little loops or eyes, one in each quarter, for the balance-rope to be hung to either, that may suit best.

2 screws (with thumb-burs that are turned by the thumb and fingers) 1-4 of an inch thick, and 3 inches long, for the feet of the stay-iron.

2 do. for the end flights, 3 1-2 inches long, rounded 1 1-2 inch next the head, and square 1 1-4 inch next the screw, the round part thickest.

2 do. for the end sweepers, 6 1-4 inches long, rounded 1 inch next the head, 1-4 inch thick.

2 do. for the hopper sweepers, 8 1-2 inches long and 1-4 inch thick, (long nails with rivet heads will do.)

1 step-gudgeon (fig. 15) 2 1-2 inches long below the ring, and tang 9 inches, 3-4 inch thick.

1 plate 4 by 4, and 1-8 inch thick, for the step-gudgeon to pass through (fig. 14.)

1 band for the step-gudgeon,* 2.149 3 3-4 inches di∣ameter; from the outsides it has to pass thro' the stay-iron.

1 gudgeon and band, for the top of the shaft, gudgeon 3-4 inch, band 4 inches diameter from the outsides.

The smith can, by the book, easily under∣stand how to make these irons: and the read∣er may, from these bills of materials, make a rough estimate of the whole expence, which he will find very low compared with their utility.

Art. 103. A Mill for hulling and cleaning Rice.

PLATE X. fig. 2. The rice brought to the mill in boats, is to be emptied into the hopper 1, out of which it is conveyed, by the conveyer, into the elevator at 2, which ele∣vates it into the garner 3; on the third floor it descends into the garner 4, that hangs over the stones 5, and supplies them regularly. The stones are to be dressed with a few deep furrows, with out little draught, and picked full of large holes; they must be set more than the length of the grain apart. The hoop should be lined inside with strong sheet-iron, and if punched full of holes it will do better. The grain is kept under the stone as long as neces∣sary, by causing it to rise some distance up the hoop, to get out through a hole, which is to be made higher or lower by a gate, slid∣ing in the bottom of it.

The principle by which the grain is hulled,* 2.150 is that of rubbing them against one another with great force, between the stones, by which means they hull one another, without being broke by the stones, near as much as by the usual way.* 2.151 As it passes through the stones 5, it should fall into a rolling-screen or shak∣ing-sieve 6, made of wire, with such mashes as will let out, at the head, all the sand and dust, which may be let run through the floor into the water, if convenient: and to let the rice and most of the heavy chaff fall through into the conveyer, which will convey it into the elevator at 2. The light chaff, &c. that does not pass through the sieve, will fall out at the tail, and if useless may also run into the water, and float away. There may be a fan put on the spindle, above the trundle, to make a light blast, to blow out the light chaff and dust, which should be conveyed out through the wall: and this fan may supersede the necessity of the shaking-sieve. The grain and heavy chaff are elevated into garner 7, thence it de∣scends into garner 8, and passes through the stones 9, which are to be fixed and dressed the same way as the others, and are only to rub the grain harder: the sharpness on the outside of the chaff (which nature seems to have pro∣vided for the pupose) will cut off all the inside hull from the grain, and leave it perfectly clean; then, as it falls from these stones

it passes through the wind of the fan 10,* 2.152 fixed on the spindle of the stones 9, which will blow ••ut the chaff and dust, and drop them in the room 21: the wind should escape through the wall. There is a regulating board that moves on a joint at 21, so as to take all the grain into the conveyer, which will con∣vey it into the elevator at 11, which elevates it into the garner 12, to pass through the roll∣ing-screen 13, which should have wire of 3 sized mashes: first, to take out the dust, to fall into a part 17, by itself; second, the small rice into an apartment 16; the whole grains fall into garner 14, perfectly clean, and are drawn into barrels at 15. The fan 18 blows out the dust, and lodges it in the room 19, and the wind passes out at 20; the head rice falls at the tail of the screen, and runs into the hopper of the stones 5, to go through the whole operation again. Thus the whole is completely done by the water, by the help of the machinery from the boat, until ready to put into the barrel, without the least manual labour.

Perhaps it may be necessary to make a few furrows in the edge of the stone, slanting, at an angle of about 30 degrees with a perpendicu∣lar line, these furrows will throw up the grain next the stone, on the top of that in the hoop which will change its position continually, by which means it will be better cleaned: but this may probably be done without.

END OF PART THIRD

PART THE FOURTH.

THE Young Miller's Guide: CONTAINING, THE WHOLE PROCESS OF THE ART OF MANUFACTURING GRAIN INTO FLOUR: EXPLAINED IN ALL ITS BRANCHES, ACCORDING TO THE MOST IM∣PROVED PLANS PRACTISED IN THE BEST MERCHANT AND FLOUR MILLS, IN AMERICA.

CONTENTS OF PART THE FOURTH.

• CHAP. I. The principles of grinding, and rules for draughting the furrows of Mill-stones.
• CHAP. II. Directions for furrowing & hanging ready for grinding a new pair of bur-stones, and keeping them in good face, for sharp∣ening them and grinding to the right fine∣ness; so as to clean the bran well, and make but little coarse flour.
• CHAP. III. Of Garlick—with directions for grinding wheat mixed with it, and dressing the stones suitable thereto.
• CHAP. IV. Of grinding the Middlings, and other coarse flour over again, to make the best profit of them.
• CHAP. V. Of the quality of stones to suit the quality of the wheat.
• CHAP. VI. Of bolting-reels and cloths, with directions for bolting and inspecting flour.
• CHAP. VII. Of the duty of the miller, in keeping the business in order.
• Peculiar accidents by which Mills are subject to take fire.
• Of improving Mill-feats.

THE Young Miller's Guide. CHAPTER I. THE PRINCIPLES OF GRINDING EXPLAINED, WITH SOME OBSERVATIONS ON LAYING OUT THE FUR∣ROWS IN THE STONES, WITH A PROPER DRAUGHT.

Art. 104.

THE end we have in view, in grinding the grain, is, to reduce it to such a de∣gree of fineness, as is found by experience to make the best bread, and to put it in such a state, that the flour may be most effectually separated from the bran or skin of the grain, by means of sifting or bolting: and it has been proved by experience, that to grind the grain fine with dull mill-stones, will not answer said purpose well, because it kills or destroys that lively quality of the grain, that causes it

to ferment and raise in the baking:* 2.153 it also makes the meal so clammy, that it sticks to the cloth, and chokes up the mashes in bolt∣ing. Hence it appears, that it should be made fine with as little pressure as possible; and it is evident, that this cannot be done without sharp instruments. Let us suppose we under∣take to operate on one single grain, I think it seems reasonable, that we should first cut it into several pieces, with a sharp instrument, to put it in a state, suitable for being passed between two plains, in order to be reduced to one regular fineness. The planes should have on their faces a number of little sharp edges, to-scrape off the meal from the bran, and be set at such a distance, as to reduce the meal to the required fineness, and no finer, so that no part can escape unground. The same rules or principles will serve for a quanti∣ty, that will serve for one grain.

Therefore, to prepare the stones for grind∣ing to the greatest perfection, we may con∣clude that their faces must be put in such or∣der, that they will first cut the grain into se∣veral pieces, and then pass it between them, in such a manner, that none can escape with∣out being ground to a certain degree of fine∣ness, and at the same time scrape the meal off clean from the bran or skin.

1. The best way that I have yet found to effect this is,* 2.154 (after the stones are faced with the staff and the pick) to grind a few quarts of sharp fine sand; this will face them to fit each other so exactly, that no meal can pass between them, without being ground: it is also the best way of sharpening all the little

edges on the face,* 2.155 that are formed by the pores of the stone, (but instead of sand, water may be used, the stones then face each other) so that they will scrape the meal off of the bran, without too much pressure being applied. But as the meal will not pass from the centre to the periphery or verge of the stones, soon enough, without some assistance, there must be a number of furrows,* 2.156 to assist it in its egress; and these furrows must be set with such a draught, that the meal will not pass too far along them at once, without passing over the land or plain, le••t it should get out unground. They should also be of sufficient depths, to ad∣mit air enough to pass though the stones to carry out the heat generated by the friction of grinding;* 2.157 but if they have too much draught, they will not bear to be deep, for the meal will escape along them unground. These furrows ought to be made sharp at the feather edge (which is the hinder edge of the furrow, and the foremost edge of the land) which serves the purpose of cutting down the 〈◊〉〈◊〉; they should be more numerous near the centre, because there the office of the stone is to cut the grain, and near the periphe∣ry their office is (that of the two plains) to reduce the flour to its required fineness, and scrape the bran clean by the edges, formed by the numerous little pores with which the burr stone abounds.* 2.158 However, we must consider, 〈◊〉〈◊〉 it is not best to have the stones too sharp near the eye, because they then cut the bran 〈◊〉〈◊〉 fine. The stones incline to keep open near the eye, unless they are too close. If they are porous (near the eye) and will keep open

without picking,* 2.159 they will always be a little dull, which will flatten the bran, without cut∣ting it too much. Again, if they be soft next the eye, they will keep too open, and that part of the stone will be nearly useless. There∣fore they should be very hard and porous.

It is also necessary, that we dress the 〈◊〉〈◊〉 of the stone in such a form, as to allow 〈◊〉〈◊〉 for the grain or meal, in every stage of its passage between the stones. In order to un∣derstand this, let us conceive the stream•••••• wheat, entering the eye of the stone, to 〈◊〉〈◊〉 about the thickness of a man's finger, but in∣stantly spreading every way over the 〈◊〉〈◊〉 face of the stone; therefore this stream 〈◊〉〈◊〉 get thinner, as it approaches the periph•••••• (where it would be thinner than a fine hair,* 2.160 〈◊〉〈◊〉 it did not pass slower as it becomes finer, 〈◊〉〈◊〉 if the stones were not kept apart by the 〈◊〉〈◊〉 for this reason the stones must be dressed 〈◊〉〈◊〉 that they will not touch at the centre, 〈◊〉〈◊〉 about a 16th or 20th part of an inch, but to 〈◊〉〈◊〉 closer gradually, till within about 10 or 〈◊〉〈◊〉 inches from the verge of the stone, proportion∣ed to the diameter, and from that part 〈◊〉〈◊〉 they must fit nicely together. This close part is called the flouring of the stone. The 〈◊〉〈◊〉 rows should be deep near the centre, to admit the wheat in its chopt state, and the air, which tends to keep the stones cool.* 2.161

Art. 105. Of the Draught necessary to be given to the Fur∣rows of Mill-Stones.

FROM these principles and ideas,* 2.163 and the 〈◊〉〈◊〉 of central forces, explained art. 13, I 〈◊〉〈◊〉 my judgment of the proper draught of 〈◊〉〈◊〉 furrows, and the manner of dress, in which I find but few of the best millers to agree; 〈◊〉〈◊〉 prefer one kind, and some another, with shews that this necessary part of the 〈◊〉〈◊〉 art, is not yet generally well under∣stood. In order that this matter may be more 〈◊〉〈◊〉 discussed and better understood, I have ••••••••ructed fig. 3, plate XI. A B represents 〈◊〉〈◊〉 eight quarter, C D the twelve quarter, 〈◊〉〈◊〉 E A the central dress. Now we observe 〈◊〉〈◊〉 in the eight quarter dress, the short fur∣•••••• at F have about five times as much draught 〈◊〉〈◊〉 long ones, and cross one another like a 〈◊〉〈◊〉 of sheers, opened so wide that they will 〈◊〉〈◊〉 all before them, and cut nothing; and 〈◊〉〈◊〉 these furrows be deep they will drive out the 〈◊〉〈◊〉 as soon as it gets into them, and thereby 〈◊〉〈◊〉 much coarse meal, such as middlings and 〈◊〉〈◊〉-stuff or carnell; the twelve quarter dress appears to be better;* 2.164 but the short furrows at ••••ve about four times as much draught as 〈◊〉〈◊〉 long ones, the advantage of which I can∣not yet see, because if we have once found the 〈◊〉〈◊〉 that is right for one furrow, so as to 〈◊〉〈◊〉 the meal to pass through the stone in a ••••••per time, it apppears reasonable that the draught of every other furrow should be equal to it.

In the central dress E A the furrows have all one draught,* 2.165 and if we could once determine how much is necessary exactly, then we might expect to be right, and I presume we will find it to be in a certain proportion to the size and velocity of the stone; because, the centrifugal force that the circular motion of the stone gives the meal, has a tendency to move it out∣ward, and this force will be in inverse propor∣tion to the diameter of the stones; their veloci∣ties being the same by the 4th law of circular motion. E e is a furrow of the running stone, and we may see by the figure, that the fur∣rows cross one another at the centre in a 〈◊〉〈◊〉 greater angle than near the periphery, 〈◊〉〈◊〉 I conceive to be right, because the centrifugal force is much less nearer the centre than the periphery. But we must also consider, that the grain, whole or but little broken, requires less draught and central force to send it out, than it does when ground fine; which shews, that we must here differ in practice from the theories laid down in art. 13, founded on the laws of circular motion and central forces 〈◊〉〈◊〉 be∣cause, the grain as it is ground into meal, is 〈◊〉〈◊〉 effected by the central force to drive it out, therefore the angles with which the furrows cross each other must be greater near the verge or skirt of the stone, and less near its centre than assigned by theory, and this variation from theory can be formed only by conjecture, and ascertained by practice.

From the whole of my speculations on the difficult subject, added to my observations on my own and others practice and experience. I attempt to form the following rule for laying out a 5 foot mill-stone. See fig. 1. PI. XI.

1 Describe a circle with 3 inches,* 2.166 and another with 6 inches radius, round the centre of the stone.

2 Divide the 3 inch space between these two circles, into 4 spaces, by 3 circles equi-dis∣tant, call these 5 circles, draught circles.

3 Divide the stone into 5 parts, by describing 4 circles equi-distant between the eye and verge.

4 Divide the circumference of the stone into 18 equal parts, called quarters.

5 Then take a straight edged rule, lay one end at one of the quarters at 6, at the verge of the stone, and the other end at the outside draught circle, 6 inches from the centre of the stone, and draw a line for the furrow 〈◊〉〈◊〉 the verge of the stone to the circle 5. Then shift the rule from draught circle 6, in the draught circle 5, and continue the furrow line towards the centre, from circle 〈◊〉〈◊〉 to 4: then shift in the rule to draught circle 4, and continue to 3; shift to 3 and continue to 2; shift to 2 and continue to 1, and the curve of the furrow is formed, as 1—6 in the figure.

To this curve form a pattern to lay out all the rest by.

The furrows with this curve will cross each other with the following angles, shewn fig. I, 〈◊〉〈◊〉 circle 1, which is the eye

〈◊〉〈◊〉—〈◊〉〈◊〉	of the stone	at 75	degrees angle.
〈◊〉〈◊〉—2		45	—
〈◊〉〈◊〉—3		35	—
〈◊〉〈◊〉—4		31	—
〈◊〉〈◊〉—5		27	—
〈◊〉〈◊〉—6		23	—

These angles,* 2.167 I think, will do well in prac∣tice, will grind smooth, and make but little coarse meal, &c. as shewn by the lines 〈◊〉〈◊〉, Hr, Gs, Hs, &c. &c.

Supposing the greatest draught circle to be 6 inches radius, then by theory the angles would have been

at circle 1		138	degrees angles
—2		69	—
—3		46	—
—4		34,5	—
—5		27,5	—
—6		23	—

If the draught circle had been 5 inches radius, and the furrows straight, the angles would then have been at

	circle		degrees
	1	about	180
And 6 inches from centre, as shewn by lines G 1, H 1.		—	110
	2	—	60
	3	—	38
	4	—	29
	5	—	2••
	6	—	18

The angles near the centre here, are 〈◊〉〈◊〉 too great to grind, they will push the 〈◊〉〈◊〉 before them; therefore, to remedy all 〈◊〉〈◊〉 disadvantages, take the aforesaid rule, 〈◊〉〈◊〉 forms the furrows, as shewn at 6—7, fig. 〈◊〉〈◊〉 which is 4 of 18 qrs. H 8 represents a furrow 〈◊〉〈◊〉 the runner, shewing the angles where 〈◊〉〈◊〉 cross those of the bed-stone, in every 〈◊〉〈◊〉. Here I have supposed the extremes of the draught to be 6 inches for the verge, and 〈◊〉〈◊〉 inches for the eye of the stone, to be right for

••••••one 5 feet diameter,* 2.168 revolving 100 times in a minute; but of this we cannot be certain. Yet by experience and practice the extreams may be ascertained in time for all sizes of stones, with different velocities, no kind of dress that 〈◊〉〈◊〉 conceive, appearing to me likely to be brought to a truth except this, and it certain∣ly appears both by inspecting the figure, and reason, that it will grind the smoothest of all the different kinds exhibited in the plate.

The principle of grinding is partly that of ••ears clipping. The plains of the face of the stones serving as guides to keep the grain, &c. 〈◊〉〈◊〉 the edge of the shears, the furrows and 〈◊〉〈◊〉, forming the edges; if the shears cross one another too short, they cannot cut; this shews 〈◊〉〈◊〉 all strokes of the pick should be parallel to the furrows.

To give two stones of different diameters the same draught, we must make their draught 〈◊〉〈◊〉 in direct proportion to their diameters; 〈◊〉〈◊〉 the furrows of the upper and lower stones ••••ch size, will cross each other with equal 〈◊〉〈◊〉 in all proportional distances, from their ••••res, to their periphery: See art. 13. But 〈◊〉〈◊〉 we come to consider that the mean cir∣cle of all stones are to have nearly equal veloci∣ty and that their central forces will be in in∣•••••• proportion to the diameters;* 2.169 we must 〈◊〉〈◊〉, that small stones must have much less 〈◊〉〈◊〉, than large ones, in proportion to their 〈◊〉〈◊〉 ••••••ters. See the proportion for determin∣ing the draught, art. 13.

It is very necessary that the true draught of 〈◊〉〈◊〉 furrows, should be determined to suit the

velocity of the stone;* 2.170 because the centrifugal force of the meal will vary, as the squares of the velocity of the stone, by the 5th law of cir∣cular motion. But the error of the draught may be corrected, in some measure, by the depth of the furrows. The less the draught, the deeper the furrow; and the greater the draught, the shallower must the furrow be to prevent the meal from escaping unground. But if the furrows be too shallow, there will not 〈◊〉〈◊〉 sufficient quantity of air pass through the stones to keep them cool. But in the central dress the furrows meet so near together that they cut the stone too much away at the centre,* 2.171 unless they are made too narrow; therefore, I pre∣fer what is called the quarter dress; but divi∣ded into so many quarters, that there will be little difference between the draught of the furrows; suppose about 18 quarters in a 5 foot stone; then each quarter takes up about 〈◊〉〈◊〉 1-2 inches of the circumference of the stone; which suits to be divided into about 4 furrows and 4 lands, if the stone be close; but if 〈◊〉〈◊〉 open, 2 or 3 furrows to each quarter will 〈◊〉〈◊〉 enough. This rule will give 4 feet 6 inch stones, 16; and 5 feet 6 inch stones, 21; and 6 feet stones, 23 quarters. But the number of quarters is not so particular, but better more than less. If the quarters be few, the disad∣vantage of the short furrows crossing at 〈◊〉〈◊〉 great an angle, and throwing out the meal 〈◊〉〈◊〉 coarse, may be remedied; by making the 〈◊〉〈◊〉 widest next the verge, thereby turning 〈◊〉〈◊〉 furrows towards the centre, when they 〈◊〉〈◊〉 have less draught, as in the quarter H I, fig. 〈◊〉〈◊〉.

CHAPTER II. DIRECTIONS FOR FACING A PAIR OF NEW BUR STONES, LAYING OUT THE FUR∣ROWS, HANGING THEM FOR GRINDING, AND FOR KEEPING THEM IN GOOD FACE; PICKING AND SHARPENING THEM; FOR GRINDING TO THE RIGHT FINENESS, SO AS TO CLEAN THE BRAN WELL, AND MAKE BUT LITTLE MIDDLINGS, &c.

Art. 106. Of facing Mill-Stones.

THE bur mill-stones are generally left in 〈◊〉〈◊〉 such face by the maker,* 2.172 that the miller 〈◊〉〈◊〉 not spend much labour and time on 〈◊〉〈◊〉 with picks, before he may hang, and 〈◊〉〈◊〉 water or dry sand, with them, because 〈◊〉〈◊〉 can make much better speed by this me∣••••••. After they have ground a quantity, 〈◊〉〈◊〉 may be judged sufficient, they must be 〈◊〉〈◊〉 up, and the red staff tried over their 〈◊〉〈◊〉,* 2.173 and if it touches in circles, the red 〈◊〉〈◊〉 should be well cracked with picks, then

put them to grind a small quantity of water or sand again;* 2.174 after this take them up, and try the staff on them, picking off the red parts as before, and repeat this operation, until the staff will touch nearly alike all the way across, and until the stone comes to a face in every part, that the quality thereof may plainly ap∣pear: then, with a red or black line proceed to lay out the furrows, in the manner deter∣mined upon, from the observations already laid down in chap. I. But here we must ob∣serve that the edges does the grinding,* 2.175 and that the quantity ground will be in proportion to the number of edges that are to do it. Af∣ter having a fair view of the face and quality of the stone, we can judge of the number of furrows most suitable, observing, that where the stone is most open and porous, few fur∣rows will be wanted; but where it is close and smooth, the furrows ought to be more nume∣rous, and both they and the lands narrow, (about 1 & 1-8 of an inch wide) that they may form the more edges,* 2.176 to perform the grind∣ing. The furrows, at the back, should be made nearly the depth of the thickness of a grain of wheat, but sloped up to a feather edge, not deeper than the thickness of a fin∣ger-nail;* 2.177 this edge is to be made as sharp

as possible,* 2.178 which cannot be done without a very sharp, hard pick. When the furrows are all made, try the red staff over them, and if it touches near the centre,* 2.179 the marks must be quite taken off about a foot next to it, but observing to crack lighter the farther from it, so that when the stones are laid together, they will not touch at the centre, by about one twen∣tieth part of an inch, and close gradually, so as to touch and fit exactly, for about 10 or 12 inches from the verge.* 2.180 If the stones be now well hung, having the facing and furrowing neatly done, they will be found in the most excellent order for grinding wheat, that they can possibly be put in, because they are in good 〈◊〉〈◊〉, fitting so neatly together, that the wheat cannot escape unground, and all the edges being at their sharpest, so that the grain can of ground into flour, with the least pressure possible.

Art. 107. Of hanging Mill-Stones.

IF the stone have a balance-ryne it is an easy matter to hang it,* 2.181 for we have only to 〈◊〉〈◊〉 the spindle perpendicular to the face of the 〈◊〉〈◊〉-stone; which is done by fastening a staff on 〈◊〉〈◊〉 cock-head of the spindle, so that the end may reach to the edge of the stone, and be near the face. In this end we put a piece of a whale-bone or quill, so as to touch the 〈◊〉〈◊〉, that, when one turns the trundle-head,

the quill will move round the edge of the stone,* 2.182 and when it is made to touch alike all the way round, by altering the wedges of the bridge: the stone may be laid down and it will be ready hung:* 2.183 but if we have a stiff-ryne, it will be much more difficult, because we have not only to fix the spindle perpendi∣cular to the face of the bed-stone, but we must set the face of the runner perpendicular to the spindle, and all this must be done to the greatest exactness,* 2.184 because the ryne being still, will not give way to suffer the runner to form itself to the bed-stone, as will the ba∣lance-ryne.

The bed of the ryne being first carefully cleaned out,* 2.185 the ryne is put into it and tied, until the stone is laid down on the cock-head; then we find the part that hangs lowest, and by putting the hand thereon, we press the stone down a little, turning it about at the same time, and observing, whether that low∣est

part touches the bed-stone equally all the way round;* 2.186 if it does not, it is adjusted by altering the wedges of the bridge-tree, un∣til it touches equally, and then the spindle will stand perpendicular to the face of the bed-stone. Then, to set the face of the runner perpendicular or square to the spindle, we stand in one place, turning the stone, and pressing on it at every horn of the ryne, as it passes, and observing whether the runner will touch the bed-stone equally, at every horn, which, if it does not, we strike with an iron bar on the horn, that bears the stone highest, which, by its jaring, will settle itself better 〈◊〉〈◊〉 its bed, and thereby let the stone down a little in that part; but if this be not suffici∣ent there must be paper put on the top of the horn, that lets the stone too low; observ∣ing to mark the high horns, that when the 〈◊〉〈◊〉 is taken up, a little may be taken off 〈◊〉〈◊〉 the bed, and the ryne will soon become 〈◊〉〈◊〉 neatly beded, that the stone will hang very easily. But I have ever found the bridge 〈◊〉〈◊〉 a little out of place, or in other words, 〈◊〉〈◊〉 spindle moved a little from its true per∣pendicular position, with respect to the face of the bed-stone, at every time the stone is taken 〈◊〉〈◊〉 which is a great objection to the stiff horn 〈◊〉〈◊〉; for if the spindle be but very little out 〈◊〉〈◊〉, the stones cannot come together 〈◊〉〈◊〉; whereas, if it be considerably out of 〈◊〉〈◊〉 with a balance ryne, it will be little or 〈◊〉〈◊〉 injury to the grinding, because the running 〈◊〉〈◊〉 has liberty to form itself to the bed-stone.

Art. 108. Of regulating the Feed and Water in Grinding.

The stone being well hung,* 2.187 proceed to grind, and when all things are ready, draw as much water as is judged to be sufficient; then observe the motion of the stone, by the noise of the damsel, and feel the meal; and if it be too coarse, and the motion too slow, give less feed, and she will grind finer, and the mo∣tion will be quicker; if it grind too coarse yet, lower the stone, then if the motion be too slow draw a little more water; but if the meal feel to be too low ground, and the motion right, raise the stone a little, and give a little more feed. If the motion and feed be too great, and the meal be ground too low, shut off part of the water.

But if the motion be too slow, and feed be too small, draw more water.

To regulate the grinding to suit the quanti∣ty of water, the following rule is set in verse; that it may be more easily remembered.* 2.188

RULE.

If the motion be too great, Then add a little feed and weight: But if the motion be too slow, Less feed and weight will let her go.

But here the miller must remember, that there is a certain portion of feed that the stones

will bear and grind it well;* 2.189 which will be in pro∣portion to the size, velocity and sharpness of them, and if this be exceeded, there will be a loss by not having the grinding well done. But no rule can be laid down, to ascertain this portion of feed; it must be attained by prac∣tice:* 2.190 as must also the art of judging of the right fineness. I may, however, lay down such rules and directions as may be of some assist∣ance to the young beginner.

Art. 109. Rules for judging of good Grinding.

CATCH your hand full of the meal as it falls from the stones,* 2.191 and feel it lightly between your fingers and thumb; and if it feels smooth and not oily or clammy, and will not stick much 〈◊〉〈◊〉 the hand, it shews it to be fine enough, 〈◊〉〈◊〉 the stones to be sharp. If there be no 〈◊〉〈◊〉 to be felt larger than the rest, but all of 〈◊〉〈◊〉 fineness, it shews the stones to be well 〈◊〉〈◊〉, and the furrows to have not too much ••••••ught, as none has escaped unground.

But if the meal feels very smooth and oily, and sticks much to the hand, it shews it to be ••••low ground, hard pressed and the stones dull. But if it feels part oily, and part coarse and 〈◊〉〈◊〉, and will stick much to the hand, it

shews that the stones has too much feed;* 2.192 or, that they are dull, and badly faced, or have some furrows that has too much draught; or are too deep, or perhaps too steep at the back edge, as part has escaped unground, and part too much pressed and low.

Catch your hand full, and holding the palm up, shut it briskly, if the greatest quantity of the meal fly out and escape between your fingers, it shews it to be in a fine and lively state, the stones sharp, the bran thin, and will bolt well: But the greater the quantity that stays in the hand, the more it shews the reverse.

Catch a hand full of meal in a sieve, and 〈◊〉〈◊〉 the meal clean out of the bran; then feel it, and if it feels soft and springing, or elastic, and also feels thin, with but little sticking to the inside of the bran, and no pieces found much thicker than the rest, will shew the stones 〈◊〉〈◊〉 be sharp, and the grinding well done.* 2.193

But if it is broad and stiff, and the 〈◊〉〈◊〉 white, it is a sure sign that the stones are 〈◊〉〈◊〉 or overfed. If you find some parts that are much thicker and harder than the rest, such 〈◊〉〈◊〉 almost half or quarter grains, it shews 〈◊〉〈◊〉 there are some furrows that have too much draught, or are too deep or steep, at the 〈◊〉〈◊〉 edge; else, that you are grinding with less fee•• than the depth of the furrows, and velocity of the stone will bear.

Art. 110. Of Dressing and Sharpening the Stones when Dull.

WHEN the stones get dull they must be ta∣ken up,* 2.194 that they may be sharpened; to do this in the best manner, we must be provided with sharp hard picks, with which the feather edge of the furrows are to be dressed as sharp as pos∣sible; which cannot be done with soft or dull picks. The bottoms of the furrows are like∣wise to be dressed, to keep them of the pro∣per depth;* 2.195 but here the dull picks may be 〈◊〉〈◊〉.* 2.196 The straight staff must now also be 〈◊〉〈◊〉 over the face carefully, and if there be any 〈◊〉〈◊〉 harder or higher than the rest, the red will be left on them; which must be cracked 〈◊〉〈◊〉, with many cracks, to make them wear 〈◊〉〈◊〉 fast as the softer parts, in order to keep the 〈◊〉〈◊〉 good. These cracks do also form edges 〈◊〉〈◊〉 help to clean the bran; and the harder and 〈◊〉〈◊〉 the stone, the more numerous are they 〈◊〉〈◊〉 be. They are to be made with a ve∣ry sharp pick, parallel to the furrows; and the ••••per the grain, the more the stone is to be ••••ked, and the drier and harder, the smoother 〈◊〉〈◊〉 the face be. The stone will never be in the 〈◊〉〈◊〉 order for cleaning the bran, without first ••inding a little sand, to sharpen all the little edges formed by the pores of the stone: the 〈◊〉〈◊〉 sand may be used several times. The 〈◊〉〈◊〉 may be sharpened without being taken 〈◊〉〈◊〉 or even stopped, viz. take a half a pint of

sand,* 2.197 and hold the shoe from knocking, to 〈◊〉〈◊〉 them run empty; then pour in the sand, 〈◊〉〈◊〉 this will take the glaze off of the face, 〈◊〉〈◊〉 whet up the edges so that they will grind con∣siderably better:* 2.198 this ought to be often done.* 2.199

Some are in the practice of letting stones run for months, without being dressed; but I am well convinced that, those who dress them well twice a week, are well paid for their trouble.

Art.111. Of the Most proper Degree of Fineness for Flour.

AS to the most proper degree of fineness for flour,* 2.200 millers differ in their opinion; but a great majority, and many of the longest experience, and best judgment, agree in this; that, if 〈◊〉〈◊〉 flour be made very fine, it will be killed; 〈◊〉〈◊〉 it is termed) so that it will not raise, or ••••••∣ment so well in baking; but I have heard se∣veral millers of good judgment, give it as 〈◊〉〈◊〉 opinion, that flour cannot be made too fine 〈◊〉〈◊〉 ground with sharp clean stones; provided th•••• are not suffered to rub against each other: 〈◊〉〈◊〉

〈◊〉〈◊〉 of those millers do actually reduce almost all the meal they get out of the wheat into su∣perfine flour;* 2.201 by which means they have but 〈◊〉〈◊〉 kinds, viz. superfine flour, and horse-feed, which is what is left after the flour is made, and is not fit to make even the coarsest kind of 〈◊〉〈◊〉-bread.

I have tryed the following experiment,* 2.202 viz. I contrived to catch as much of the dust of flour that was floating about in the mill, as made a large loaf of bread, which was raised with the same yeast, and baked in the same oven, with other loaves, that were made out of the most ••••vely meal; when the loaf made of the dust of the flour was equally light, and as good, if not better than any of the others; it being the ••••••stest, pleasantest tasted, though made of 〈◊〉〈◊〉 that felt like oil, it being so very fine.

I therefore conclude, that it is not the de∣•••• of fineness that destroys the life of the 〈◊〉〈◊〉, but the degree of pressure applied on it 〈◊〉〈◊〉 grinding; and that flour may be reduced to 〈◊〉〈◊〉 greatest degree of fineness, without injur∣ing the quality; provided, it be done with 〈◊〉〈◊〉 clean stones, and little pressure.* 2.203

CHAPTER. III. Art. 112. OF GARLIC, WITH DIRECTIONS FOR GRINDING WHEAT MIXED THEREWITH; AND FOR DRESSING THE STONE SUITABLE THERETO.

IN many parts of America there is a species of onion called garlic,* 2.205 that grows spontane∣ously with the wheat. It bears a head resem∣bling a seed onion, which contains a number of grains about the size of a grain of wheat, near∣ly as heavy, but somewhat lighter.* 2.206 It is of a

••••tinous substance,* 2.207 which very soon adheres 〈◊〉〈◊〉 stone (in grinding) in such a manner, as 〈…〉〈…〉 the edges, that they will not grind to 〈◊〉〈◊〉 degree of perfection. Therefore, as often at the stones become dull, we are obliged to 〈◊〉〈◊〉 the runner up, and wash the glaze off 〈◊〉〈◊〉 water, scrubbing the faces with stiff brush∣e•• and drying up the water with cloths or ••••nges; this laborious operation must be ••••••eated twice, or perhaps four times, in 24 hours; if there be about 10 grains of garlic 〈◊〉〈◊〉 a handful of wheat.

To put the stones in the best order to grind ••••••cky wheat, they must be cracked roughly 〈◊〉〈◊〉 the face; and dressed more open about 〈◊〉〈◊〉 eye, that they may not break the grains 〈◊〉〈◊〉 garlic too suddenly, but gradually giving 〈◊〉〈◊〉 glutinous substance of the garlic more 〈◊〉〈◊〉 to incorporate itself with the meal, that 〈◊〉〈◊〉 not adhere to the stone.* 2.208 The rougher 〈◊〉〈◊〉, the longer will the stones grind, be∣•••••• the longer will the garlic be in filling all ••••••ges.

〈◊〉〈◊〉 best method that I have yet discover∣•••• manufacturing garlicky wheat,* 2.209 is as 〈◊〉〈◊〉 viz.

〈◊〉〈◊〉, clean it over several times, in order 〈◊〉〈◊〉 out all the garlic that can be got out of the machinery, (which is easily done if you 〈◊〉〈◊〉 a wheat elevator well fixed, as directed 〈◊〉〈◊〉. 94. pl. IX.) then chop or half grind it, 〈◊〉〈◊〉 will break the garlic, (it being softer 〈◊〉〈◊〉 the wheat) the moisture of which, will so

diffuse itself through the chopt wheat,* 2.210 that it will not injure the stones so much, in the 〈◊〉〈◊〉 grinding.* 2.211 By this means a considerable quan∣tity can be ground, without taking up the stones. The chopping may be done at the rate of 15 or 20 bushels in an hour; and with 〈◊〉〈◊〉 little trouble or loss of time; provided the•• 〈◊〉〈◊〉 a meal-elevator that will hoist it up to the me••••∣loft, from whence it may descend to the hop∣per by spouts, to be ground a second time, 〈◊〉〈◊〉 it will grind foster than if it had not been chopp∣ed. Great care should be taken, that it is not chopped so fine that it will not feed by the knocking of the shoe;* 2.212 (which would make 〈◊〉〈◊〉 very troublesome) as likewise, that it be not too coarse, left the garlic be not sufficiently broken. If the chopt grain could lay a con∣siderable time, that the garlic may dry, 〈◊〉〈◊〉 would grind much better.

But although every precaution be tak•• if there be much garlic in the wheat, the 〈◊〉〈◊〉 will not be well cleaned; besides, there 〈◊〉〈◊〉 be much coarse meal made: such as 〈◊〉〈◊〉 and stuff; which will require to be 〈◊〉〈◊〉 over again, in order to make the most 〈◊〉〈◊〉 of the grain: this I shall treat of in the 〈◊〉〈◊〉 chapter.* 2.213

CHAPTER IV. Art. 113. GRINDING OVER THE MIDDLINGS, STUFF & BRAN, 〈◊〉〈◊〉 SHORTS, IF NECESSARY; TO MAKE THE MOST 〈◊〉〈◊〉 THEM.

ALTHOUGH we grind the grain in the best 〈◊〉〈◊〉 manner we possibly can, so as to make a∣•••• reasonable dispatch; yet there will appear 〈◊〉〈◊〉 the bolting, a species of coarse meal, called ••••••ings; and stuff, a quality between super∣•••••• and shorts; which will contain a por∣tion of the best part of the grain: but in 〈◊〉〈◊〉 coarse state they will make very coarse 〈◊〉〈◊〉 consequently, will command but a low 〈◊〉〈◊〉. For which reason it is oftentimes more 〈◊〉〈◊〉 ••••••ble to the miller to grind and bolt such 〈◊〉〈◊〉 ••gain, and make them into superfine flour, 〈◊〉〈◊〉 middlings; this may easily be done by 〈◊〉〈◊〉 management.

〈◊〉〈◊〉 middlings is generally hoisted by tubs,* 2.214 ••aid in a convenient place on the floor, in meal-loft, near the hopper-boy, until there 〈◊〉〈◊〉 large quantity gathered: when the first 〈◊〉〈◊〉 opportunity offers it is bolted over, with∣•••• ••ny bran or shorts, mixed with it: in order 〈◊〉〈◊〉 take out all that is already fine enough; which will pass through the superfine cloth. 〈◊〉〈◊〉 middlings will pass through the middlings' 〈◊〉〈◊〉 and will then be round and lively, and in

a state ••it for grinding;* 2.215 being freed from the fine part that would have prevented it from seeding freely. The small specks of bran that were before mixed with it, being lighter than the rich round part, will not pass through the middlings' cloth, but will pass on to the stuff's cloth. The middlings will, by this means, be richer than before; and when made fine, may be mixed with the ground meal, and bolted into superfine flour.

The middlings may now be put into the hanging garner,* 2.216 over the hopper of the stones; out of which it will run into the hopper, and keep it full, as does the wheat; provided the garner be rightly constructed, and a hole, a∣bout 6 by 6 inches made for it to issue out at. There must be a rod put through the bar that supports the upper end of the damsel, the low∣er end of which must reach into the eye of the stone, near to the bottom, and on one side thereof, to prevent the meal from sticking in the eye, which if it does it will not feed. The hole in the bottom of the hopper must not be less than four inches square. Things being thus prepared, and the stones being sharp and clean, and nicely hung; draw a small quanti∣ty of water, (for meal does not require a∣bove one tenth part that grain does) taking great care to avoid pressure, because the bran is not between the stones now to prevent their coming too close together. If you lay on as much weight, as when grinding grain, the flour will be killed. But if the stones be well hung, and it be pressed lightly, the flour will be lively, and will make much better bread, without being bolted, than it would be∣fore

it was ground.* 2.217 As fast as it is ground, it may be elevated and bolted; but a little bran will now be necessary to keep the cloth open; and all that passes through the superfine cloth in this operation, may be mixed with what pas∣sed through in the first bolting of the middlings; and be hoisted up and mixed (by the hop∣per-boy) regularly with the ground meal, and bolted into superfine flour; as directed, art. 89.* 2.218

The stuff,* 2.219 which is a degree coarser than middlings, if it be too poor for ship bread, and 〈◊〉〈◊〉 rich to feed cattle on, is to be ground over, i•• the same manner as the middlings. But if it be mixed with fine flour, (as it sometimes is) so that it will not feed freely, it must be bolted over first, this will take out the 〈◊〉〈◊〉 flour; and also the fine specks of bran, which being lightest, will come through the 〈◊〉〈◊〉 last. When it is bolted, the part that 〈◊〉〈◊〉 through the middlings' and stuff's parts of the cloth, are to be mixed and ground to∣gether; by which means, the rich particles will 〈◊〉〈◊〉 reduced to flour; and when bolted, will pass ••••ough the finer cloths, and will make tole∣rable good bread. What passes through the middlings' cloth, will make but indifferent ship∣••••••••, and what passes through the ship-stuff's 〈◊〉〈◊〉 will be what is called brown-stuff, roug∣••••, or horse-feed.

The bran and shorts seldom are worth the trouble of grinding over,* 2.220 unless the stones have been very dull;* 2.221 or the grinding been but slight∣ly performed; or the wheat very garlic∣ky. For this purpose, the stones are to be ve∣ry sharp; and more water and pressure is here required, than in grinding grain. The flour that is made thereof, is generally of an indif∣ferent quality, being made of that part of the grain that lies next the skin, and great part thereof being the skin itself, cut fine.

* 2.222

CHAPTER V. Art. 114. Of the Quality of Mill-Stones, to Suit the Quality of the Wheat.

IT has been found by experience,* 2.223 that differ∣ent qualities of wheat, require different qua∣lities of stones, to grind it to the best per∣fection.

Although there be several species of wheat of different qualities; yet with respect to the

grinding,* 2.224 we may take notice of but the three following qualities, viz.

• 1. The dry and hard.
• 2. The damp and soft.
• 3. Wheat that is mixed with garlic.* 2.225

When the grain that is to be ground be dry and hard, such as is raised on high, and clay lands; threshed in barns, and kept dry;* 2.226 the stones for grinding such wheat, should be of that quality of the bur, that is called close and hard, with few large pores; in order that they may have more face. The grain being brittle and easy broken into pieces, requires more face or plain parts (spoken of in art. 104.) to re∣duce it to the required fineness.

When the grain that is to be ground is a lit∣tle damp and soft; such as is raised on a light, sandy soil; tread out on the ground, and car∣ried in the hold of ships to market,* 2.227 which tends to increase the dampness, the stones is required to be more open, porous and sharp; because the grain is tough, difficult to be broke into pie∣ces, and requires more sharpness, and less face (or plain surface) to reduce it to the required fineness:† 2.228 See art. 104.

When there is more or less of the garlic,* 2.229 or wild onion,* 2.230 (mentioned Art. III;) mixed with the wheat; the stones will require to be open, porous, and sharp: because the glutinous sub∣stance of the garlic adheres to the face of the stones, and blunts the edges; by which means little can be ground, before the stones get so dull that they will require to be taken up, and sharp∣ened: and the more porous and sharp the stones are, the longer will they run, and the more will they grind, without getting dull:* 2.231 See Art. 111.

CHAPTER VI. Art. 115. OF BOLTING-REELS, AND CLOTHS; WITH DIRECTI∣ONS FOR BOLTING AND INSPECTING THE FLOUR.

* 2.233THE effect we wish to produce by sifting, or bolting, is to separate the different 〈◊〉〈◊〉 of flour from each other; and from 〈◊〉〈◊〉 skin, shorts, or bran. For this reason let 〈◊〉〈◊〉 consider the most rational means, that we 〈◊〉〈◊〉 use to attain this end.

Queries concerning Bolting.

1. Suppose that we try a sieve; the mash∣•••• of which are so large, as to let all the bran 〈◊〉〈◊〉 meal through: now it is evident, that we 〈◊〉〈◊〉 never attain to the end, proposed by the 〈◊〉〈◊〉 thereof.

2. Suppose we try a finer sieve, that will let the meal through, but none of the bran: 〈◊〉〈◊〉 by this we cannot separate the different ••••••lities of flour.

3. We provide as many sieves of the differ∣ent degrees of fineness, as we intend to make different qualities of flour; and which for dis∣••••••tion, we name—Superfine, Middlings, and Carnell.

The superfine sieve,* 2.234 of mashes, so fine 〈◊〉〈◊〉 to let through the superfine flour, but none of the middlings: the middling's sieve, so fine as to let the middlings pass through, but none of the carnell: the carnell sieve, so fine as to let none of the shorts or bran pass through.

Now it is evident, that if we would conti∣nue the operation long enough, with each sieve, beginning with the superfine, that we 〈◊〉〈◊〉 effect a complete separation.* 2.235 But if we 〈◊〉〈◊〉 not continue the operation a sufficient length of time, with each sieve, the separation will 〈◊〉〈◊〉 be complete. For part of the superfine will 〈◊〉〈◊〉 left, and will pass through with the middlings and part of the middlings with the carnell, 〈◊〉〈◊〉 part of the carnell with the shorts; and 〈◊〉〈◊〉 would be a laborious and tedious work, if per∣formed by the hand.

To facilitate this business, many has been 〈◊〉〈◊〉 improvements; amongst which, the circ•••• sieve or bolting-reel, is one of the fore•••••••• and which was, at first, turned and 〈◊〉〈◊〉 hand; though afterwards contrived to be 〈◊〉〈◊〉 by water.

But many have been the errors in the appli∣cation of this machine; either by having 〈◊〉〈◊〉 cloths too coarse, by which means the middlings and small pieces of bran will pass through 〈◊〉〈◊〉 the superfine flour, and part of the carnell 〈◊〉〈◊〉

the middlings:* 2.236 or by having the cloths too h••rt, when they are fine enough; so that the operation cannot be continued a sufficient time 〈◊〉〈◊〉 take all the superfine out, before it reaches 〈◊〉〈◊〉 middlings' cloth, and all the middlings, be∣fore it reaches the carnell cloth.

The late improvements made on bolting, 〈◊〉〈◊〉 to be wholly as follows, viz.

1. By using finer cloths—but they were 〈◊〉〈◊〉 to clog,* 2.237 or choke up, when put on small 〈◊〉〈◊〉 of 22 inches diameter.

2. By enlarging the diameter of the reels 〈◊〉〈◊〉 1-2 inches, which gives the meal greater 〈◊〉〈◊〉 to fall, and causes it to strike harder 〈◊〉〈◊〉 the cloth, which keeps it open.

3. By lengthening the cloths, that the ope∣•••••• may be continued a sufficient length of 〈◊〉〈◊〉.

4. By bolting a greater part of the flour over 〈◊〉〈◊〉 than was done formerly.

〈◊〉〈◊〉 meal, as it is ground, must be hoisted to ••eal-loft, where it is spread thin, and of∣•••• 〈◊〉〈◊〉, that it may cool and dry, to pre∣•••• it for bolting. After it is bolted, the ••••our,* 2.238 or that part of the superfine that falls and which is too full of specks of bran to for superfine flour, is to be hoisted up a∣•••••• and mixed with the ground meal, to be 〈◊〉〈◊〉 over again. This hoisting, spreading, 〈◊〉〈◊〉, and attending the bolting hoppers, in ••••••chant-mills, creates a great deal of hard 〈◊〉〈◊〉, if done by hand; and never complete∣•••••• at last: But all this, and much more 〈◊〉〈◊〉 labour of mills, can now de done by ma∣••••ery, moved by water: See part 3.

Of Inspecting Flour.* 2.239

THE miller must by some means attain a knowledge of the standard quality, passable in the markets—

He holds a clean piece of board under the bolt, moving it from head to tail, so as to catch a proportional quantity all the way, as far as is taken for superfine: then, having smoothed it well, by pressing an even surface on it, to make the specks and colour more plainly ap∣pear; if it be not good enough, turn a little more of the tail to be bolted over.

If the flour appears darker than expected from the quality of the grain, it shews the grinding to be high, and bolting too near; be∣cause the finer the flour, the whiter its co∣lour.* 2.240

But this mode requires good light; there∣fore, the best way, is for the miller to observe to what degree of poorness he may reduce his tail flour, or middlings, so as to be safe; by which he may judge with much more safety in 〈◊〉〈◊〉 night. But the quality of the tale flour, mid∣dlings, &c. will greatly vary in different 〈◊〉〈◊〉 for those that have the late improvements 〈◊〉〈◊〉 bolting over the tale flour, grinding over 〈◊〉〈◊〉 middlings, &c. can make nearly all into ••••∣perfine.

Whereas those that have them not—the qua∣••••ty that remains next to superfine,* 2.241 is common, 〈◊〉〈◊〉 fine flour; then rich middlings, ship-stuff, &c. Those who have experience will conceive the difference in the profits. If the flour feel soft, 〈◊〉〈◊〉, and oily, yet white; it shews the stones 〈◊〉〈◊〉 have been dull, and too much pressure used.

If it appear lively, yet dark coloured, and 〈◊〉〈◊〉 full of very fine specks; this shews the stones 〈◊〉〈◊〉 have been too rough, sharp, and that it 〈◊〉〈◊〉 ground and bolted too close.

CHAPTER VII. DIRECTIONS FOR KEEPING THE MILL; AND THE BUSINESS OF IT IN GOOD ORDER.

Art. 116. The Duty of the Miller.

THE mill is supposed to be completely finish∣ed for merchant work, on the new plan; 〈◊〉〈◊〉 with a stock of grain flour casks, nails, 〈◊〉〈◊〉, picks, shovels, scales, weights, &c. 〈◊〉〈◊〉 the millers enters on their duty—If there be two of them capable of standing 〈◊〉〈◊〉, or taking charge of the mill, the time ••••••erally divided as follows: In the day time 〈◊〉〈◊〉 ••oth attend to business, but one of them 〈◊〉〈◊〉 the chief direction: The night is divided 〈◊〉〈◊〉 two watches, the first of which ends at ••'clock in the morning; when the master 〈◊〉〈◊〉 should enter on his watch, and continue

till morning;* 2.242 that he may be ready to direct other hands to their business early. The first thing he should do, when his watch begins, is to see whether the stones are grinding, and the cloths bolting well.

And 2ndly, to review all the moving gudge∣ons of the mill, to see whether any of them want grease, &c. that he may know what care may be necessary for them during his watch; for want of this the gudgeons often run dry, and heat, which brings on heavy losses of time and repairs; for when they heat, they get a little loose, and the stones they run on crack; after which they cannot be kept cool. He should also see what quantity of grain is over the stones, and if there be not enough to supply them till morning, set the cleaning machines in motion.

All things being set right, his duty is very easy—he has only to see the machinery, the grinding, and bolting, once in an hour; he has therefore plenty of time to amuse himself in reading, &c. rather than going to sleep, which is not safe.

Early in the morning, all the floors should be swept, and the flour dust collected. The cas•••••• nailed, weighed, marked and branded, and the packing began, that it may be completed in the forepart of the day; by this means, should a∣ny unforeseen thing occur, there will be spare time. Besides, to leave the packing till the af∣ternoon, is a lazy practice, and keeps the busi∣ness out of order.

When the stones are to be sharpened, every thing necessary should be prepared, before the mill is stopped, (especially if there be but one

pair of stones to a water wheel) that as little 〈◊〉〈◊〉 as possible may be lost:* 2.243 the picks made right sharp, not less than 12 in number. Things being ready, take up the stone; set one hand to each, and dress them as soon as possible, that they may be set to work again; not forgetting to grease the gears, and spindle foot.

In the after part of the day, a sufficient quan∣tity of grain is cleaned down, to supply the 〈◊〉〈◊〉 the whole night; because it is best to have nothing to do in the night, more than at∣tend to the grinding, bolting, gudgeons, &c.

Art. 117. Peculiar Accidents by which Mills are subject to Catch Fire.

1. THERE being many moving parts in a 〈◊〉〈◊〉, if any piece of timber fall, and lay on 〈◊〉〈◊〉 moving wheel, or shaft, and the velocity 〈◊〉〈◊〉 pressure be great, it will generate fire, and ••••••∣haps consume the mill.

2. Many people use wooden candlesticks, that 〈◊〉〈◊〉 be set on a cask, bench, or the floor, and ••••getting them, the candle burns down, sets ••••stick, cask, &c. on fire, which, perhaps 〈◊〉〈◊〉 not be seen until the mill is in a flame.

3. Careless millers, sometimes, stick a can∣dle to a cask, or post, and forget it, until it 〈◊〉〈◊〉 a hole in the post, or sets the cask on 〈◊〉〈◊〉.

4. Great quantities of grain sometimes bend the floor so as to press the head blocks,* 2.244 against the top of the upright shafts, and generate fire: (unless the head blocks have room to rise as the floor settles) mill-rights should consider this, and be careful to guard against it as they build.

5. Branding irons, carelessly laid down, when hot, and left; might set something on fire.

6. I have heard of bran falling from the tail of a bolt, round a shaft, the friction of which burnt the shaft off.

7. The foot of the mill-stone spindle, and gudgeons, frequently heat, and set the bridge-tree or shaft on fire. It is probable, that from such causes mills have taken fire, when no per∣son could discover how.

Art. 118. Observations on improving of Mill-Scats.

I MAY end this Part with a few observati∣ons on improving mill-seats. The improving of a mill-seat at 1000l. expence, is an under∣taking worthy of mature deliberation, as wro•••• steps may increase it to 1100l. and the improve∣ment be incomplete: whereas, right steps ma•• reduce it to 900l. and perfect them.

Strange as it may appear, yet it is a rea•••• fact, that those who have least experience 〈◊〉〈◊〉 the milling-business, generally build the 〈◊〉〈◊〉 and completest mills.—The reasons are evi∣dent—

The experienced man is bound to old sys∣••••••s;* 2.245 he relies on his own judgment in laying all his plans: whereas,

The unexperienced man, being conscious of his deficiency, is at liberty; perfectly free from 〈◊〉〈◊〉 prejudice, to call on all his experienced ••••••ads, and to collect all the improvements 〈◊〉〈◊〉 are extant.

A merchant who knows but little of the millers 〈◊〉〈◊〉, or of the structure or mechanism of mills, 〈◊〉〈◊〉 naturally led to the following steps, viz.

He calls several of the most experienced ••••ers and mill-wrights, to view the seat sepa∣rately, and point out the spot for the mill-house, dam, &c. and notes their reasonings in 〈◊〉〈◊〉 of their opinion. The first perhaps 〈◊〉〈◊〉 on a pretty level spot for the mill-house, 〈◊〉〈◊〉 a certain rock, that nature seems to have ••••pared, to support the breast of the dam, and 〈◊〉〈◊〉 easy piace to dig the race, mill-seat, &c.

The second passes by these places without ••••icing them; explores the stream to the secondary line; fixes on another place, the on∣•••• one he thinks appointed by nature for build∣ing a lasting dam, the foundation a solid rock, 〈◊〉〈◊〉 cannot be undermined by the tumbling ••••••ter; fixing on a rugged spot for the seat of 〈◊〉〈◊〉 house: assigning for his reasons, that the 〈◊〉〈◊〉 fall must be taken in, that all may be 〈◊〉〈◊〉 in a future day. He is then informed of 〈◊〉〈◊〉 opinion of the other, against which he gives ••••stantial reasons.

The mill-wright, carpenter and mason, that 〈◊〉〈◊〉 to undertake the building, are now called ••••ther, to view the seat, fix on the spot for 〈◊〉〈◊〉 house, dam, &c. After their opinion and

4. Great quantities of grain sometimes bend the floor so as to press the head blocks,* 2.246 against the top of the upright shafts, and generate fire: (unless the head blocks have room to rise as the floor settles) mill-rights should consider this, and be careful to guard against it as they build.

5. Branding irons, carelessly laid down, when hot, and left; might set something on fire.

6. I have heard of bran falling from the tail of a bolt, round a shaft, the friction of which burnt the shaft off.

7. The foot of the mill-stone spindle, and gudgeons, frequently heat, and set the bridge-tree or shaft on fire. It is probable, that from such causes mills have taken fire, when no per∣son could discover how.

Observations on improving of Mill-Scats.* 2.247

I MAY end this Part with a few observati∣ons on improving mill-seats. The improving of a mill-seat at 1000l. expence, is an under∣taking worthy of mature deliberation, as wrong steps may increase it to 1100l. and the improve∣ment be incomplete: whereas, right steps may reduce it to 900l. and perfect them.

Strange as it may appear, yet it is a real fact, that those who have least experience 〈◊〉〈◊〉 the milling-business, generally build the 〈◊〉〈◊〉 and completest mills.—The reasons are evi∣dent—

The experienced man is bound to old sys∣tems;* 2.248 he relies on his own judgment in laying all his plans: whereas,

The unexperienced man, being conscious of his deficiency, is at liberty; perfectly free from all prejudice, to call on all his experienced friends, and to collect all the improvements that are extant.

A merchant who knows but little of the millers art, or of the structure or mechanism of mills, is naturally led to the following steps, viz.

He calls several of the most experienced millers and mill-wrights, to view the seat sepa∣rately, and point out the spot for the mill-house, dam, &c. and notes their reasonings in favour of their opinion. The first perhaps 〈◊〉〈◊〉 on a pretty level spot for the mill-house, and a certain rock, that nature seems to have prepared, to support the breast of the dam, and as easy place to dig the race, mill-seat, &c.

The second passes by these places without noticing them; explores the stream to the secondary line; fixes on another place, the on∣ly one he thinks appointed by nature for build∣ing a lasting dam, the foundation a solid rock, 〈◊〉〈◊〉 cannot be undermined by the tumbling ••••ter; fixing on a rugged spot for the seat of 〈◊〉〈◊〉 house: assigning for his reasons, that the ••hole fall must be taken in, that all may be 〈◊〉〈◊〉 in a future day. He is then informed of 〈◊〉〈◊〉 opinion of the other, against which he gives ••••••stantial reasons.

The mill-wright, carpenter and mason, that 〈◊〉〈◊〉 to undertake the building, are now called ••••••ether, to view the seat, fix on the spot for 〈◊〉〈◊〉 house, dam, &c. After their opinion and

reasons are heard,* 2.249 they are informed of the opinion and reasons of the others, all are joined together, and the places are fixed on. They are then desired to make out a com∣plete draught of the plan for the house, &c. and to spare no pains to plan all for the best; but alter and improve on paper, 〈◊〉〈◊〉 all appear to meet right, in the simplest and most convenient manner; (a week may be thus well spent) making out complete bills of every piece of timber, quantity of boards, stone, lime, &c. Bill of iron work, number of wheels, their diameters, number of cogs, &c. &c. in the whole work. Each person can then make out his charge, and the costs can be counted nearly. Every species of materials may be contracted for, to be delivered in due time: then the work goes on regularly without dis∣appointment, and when done, the improve∣ments are complete, and 100l. out of 1000l. at least saved by such steps.

END OF PART FOURTH.

[figure]

Plate I

[figure]

II

[figure]

III

[figure]

Plate IV

[figure]

[figure]

VI

[figure]

VII

[figure]

Plate VIII

[figure]

IX

[figure]

X.

[figure]

Plate XI

[figure]

XII

PART THE FIFTH.

THE Practical Mill-wright: CONTAINING, INSTRUCTIONS FOR BUILDING MILLS, WITH ALL THEIR PROPORTIONS; SUITABLE TO ALL FALLS FROM 3 TO 36 FEET.

RECEIVED FROM THOMAS ELLICOTT, Mill-wright.

CONTENTS.

THE Preface explains the Plate containing the new Im∣provements.

• ART. 1. Of undershot mills—directions for laying on the water.
• Art. 2. Draught of a forebay, with directions for mak∣ing them durable.
• Art. 3. Principles and practical experiments, to deter∣mine the proper motion for undershot wheels. 〈◊〉〈◊〉 table for gearing undershot wheels, suited to all falls, from 3 to 20 feet.
• Art.4. Of breast mills, with directions for proportion∣ing and gearing them, to give the stone the right mo∣tion.
• Art. 5. Of pitch-back mills, with directions for proportion∣ing and gearing them, to give the stone the right mo∣tion.
• Art 6. Of overshot mills, and their dimensions.
• Art 7. Of the proper motion for overshot mills.
• Art 8. Of gearing the water-wheel to the mill-stones, to give them the proper motion.
• Art 9. Rules for finding the diameter of the pitch cir∣cles. ••able of all the proportions for overshot mills, suitable for all falls, from 15 to 36 feet; for 4 and 4 feet 6 inches, and 5 and 5 feet 6 inch stones, diameter.
• Art 10. Directions for constructing undershot wheels.
• Art 11. do. for dressing shafts.
• Art 12. do. for laying out mortises for arms.
• Art 13. do. for putting in gudgeons.
• Art 14. do. for constructing cog-wheels.
• Art 15. do. for making spurs and head blocks.
• ...

• Art. 16. Of the best time for cutting cogs, and method of seasoning them.
• Art. 17. Of shanking, putting in, and dressing off the cogs.
• Art. 18. Of the little cog-wheel and shaft.
• Art. 19. Directions for making wallowers and trundles.
• Art. 20. do. for fixing the head blocks, and hang∣ing the wheels.
• Art. 21. do, for sinking the balance ryne.
• Art. 22. do. for bridging he spindle.
• Art. 23. do. for making the crain and lighter staff.
• Art. 24. do. for making a hoop for the mill-stones.
• Art. 25. do. for grinding sand to face the stones.
• Art. 26. do. for laying out the furrows in new stones.
• Art. 27. do. for making a hopper, shoe, and feeder.
• Art. 28. do. for making bolting chests and reels.
• Art. 29. do. for setting bolts to go by water.
• Art. 30. do. for making bolting wheels.
• Art. 31. Of rolling screens.
• Art. 32. Of fans.
• Art. 33. Of the shaking sieve.
• Art. 34. Of the use of draughting to build mills by.
• Art. 35. Directions for draughting and planning mills.
• Art. 36. Bills of scantling for a mill.
• Art. 37. Bills of iron work for a mill.
• Art. 38. Explanation of the plates.
• Art. 39. Of saw mills, with a table of the dimensions of flutter wheels, to suit all heads from 6 to 30 feet.
• Art. 40. Of fulling mills.

TO THE READER.

I BEING requested by Oliver Evans, to assist him in completeing his book, entitled, The Young Mill-wright and Miller's Guide—have thought proper to give 〈◊〉〈◊〉 reader a short history of the rise and progress of mer∣chant mills, towards their present state of perfection, ••••ce the beginning of my time.

It is now upwards of 38 years since I first began mill-wrighting: I followed it very constant for about ten years, ••••••king it my particular study. Several of my brothers 〈◊〉〈◊〉 also mill-wrights, we kept in company; and were 〈◊〉〈◊〉 called to different parts of this, and the adjacent ••••••••es, to build mills of the first rates, in their day. Some of them entered into the manufacturing line, but I con∣••••••ed at mill-wrighting, and other business connected ••herewith; such as rolling screens, and fans, and mak∣ing them to go by water, in merchant and grist mills; 〈◊〉〈◊〉 farmers fans, for cleaning grain; being the first, I ••••••eve that made these things in America: but for se∣veral years past, have done but little else, than build 〈◊〉〈◊〉, or draught to build by.

When I first began the business, mills were at a low 〈◊〉〈◊〉 in this country; neither burr-stones, nor rolling screens being used; and but few of the best merchant mills had a fan. Many carried the meal on their backs, and bolted it by hand, even for merchant work; and I have frequently heard, that a little before my beginning the business, it had been customary, in many instances, to have the bolting mill some distance from the grind∣ing mill, and there bolted by hand. It was counted ex∣traordinary

when they got their bolting to go by water: after this, fans by hand, and standing screens took place; then bur-stones, rolling-screens, and superfine bolting cloths, with a number of other improvements. Some of the latest are, the Elevators, hopper-boys, &c.—Invented by Oliver Evans, late of Delaware, tho' now of Philadelphia.

Being very desirous to improve in the art of building mills, and manufacturing grain into flour, I have fr•• frequently went a considerable distance to see new im∣provements, and have often searched the book-stores 〈◊〉〈◊〉 expectation of finding books that might instruct me, but never found any which was of use to me in that respect more than to learn the ancient names of some parts of the mills; for although they had been wrote by men of considerable learning, in other respects; yet, as they had never been mill-wrights themselves, they had neither practical, nor experimental knowledge to direct 〈◊〉〈◊〉 in the work. For instance, see the mill-wrights table, in Ferguson's lectures, page 79.; where the cog-wheel is to have 127 cogs, about 15½ feet diameter; trundle 6 staves, and stones 6 feet: And in Imison's introduction to useful knowledge, page 31, the water-wheel is to be 18 feet, cog-wheel 254 cogs, about 31 feet diameter, much higher than the water-wheel;—staves in the trun∣dle 6, and stones 4 2/1; feet. Besides, some have asserted, that water applied on an undershot wheel, will do 6 times as much as if applied on an overshot; others, that if applied on an overshot it will do 10 times as much as an undershot, the quantity and falls being equal: many other parts of their theories are equally wrong, in prac∣tice. So that what knowledge I have gained, has been by steady attention to the improvements of our own country; I have wondered, that no person of prac∣tical knowledge in the art, has yet attempted to write a treatise on it, seeing it is a subject worthy attention,

and such a book so much wanted. The manufacturing of our own country produce, in the most saving, ex∣peditious, and best manner, I have thought, is a sub∣••••••t worthy the attention of the legislatures. Mills are often laid under heavy taxes, being supposed to be very suitable; but if all the spare wheat was to be shipped, where would the miller's profit be. But to return to the subject—I have often thought, that if I could spare time would write a small treatise on mill-wrighting myself, ••••••king it would be of much use to young mill-wrights) 〈◊〉〈◊〉 fearing I was not equal to the task, I was ready to 〈◊〉〈◊〉 it up, but on further consideration, I called on Tho∣•••••• Dobson, printer of the Encyclopedia; and asked 〈◊〉〈◊〉 if he would accept of a small treatise on mill-wright••••: he said Oliver Evans had been there a few days 〈◊〉〈◊〉, and proposed such a work, which I thought 〈◊〉〈◊〉 save me the trouble. But some time afterwards, 〈◊〉〈◊〉 said Evans, applied to me, requesting my assistance 〈◊〉〈◊〉 undertaking; this I was the more willing to do, ha∣•••••• built several mills with his additional improvements; 〈◊〉〈◊〉 draughted several others—and without which im∣provements, I think a mill cannot now be said to be com∣••••••. By them the manufacture of grain into flour, carried on by water, with very little hand labour, 〈◊〉〈◊〉 much less waste, either in small or large busi∣••••••. And I do believe, that taking a large quantity of ••eat together, that we can make 2 or 3lbs. more 〈◊〉〈◊〉 of a bushel by the new, than by the old way, though it be equally well ground; because it is so 〈◊〉〈◊〉 more completely bolted, and with less waste. In 〈◊〉〈◊〉 old way, the wheat is weighed and carried up 〈◊〉〈◊〉 or two pair of stairs, and thrown into garners; the 〈◊〉〈◊〉 often having holes in, it is spilt and trampled un∣•••••••• foot; several lbs. being frequently lost in receiv∣ing a small quantity; and when it is taken from these ••••••ers, and carried to the rolling screens, some is again ••••••ed, and as it is ground, it is shoveled into tubs, a

dust is raised, and some spilt and trampled on; it is there hoisted, and spread, and tossed about with shovels, over a large floor, raked and turned to cool, and shoveled up again, and put into the bolting hopper; all which occa∣sions great labour, besides being spilt and trampled over the mill, which occasions a considerable waste. 〈◊〉〈◊〉 these disadvantages, there are others in attending the bolting hoppers; being often let run empty, then 〈◊〉〈◊〉 too hard, so that they choke, which occasions the 〈◊〉〈◊〉 to be very unevenly bolted; sometimes too poor, and at other times too rich, which is a considerable loss; 〈◊〉〈◊〉 when the flour is bolted, it is much finer at the head that the tail of the cloths: the fine goes through first, and has to be mixed by hand, with shovels or rakes; and 〈◊〉〈◊〉 labour is often neglected or only half done; by 〈◊〉〈◊〉 means; part of the flour will be condemned for being 〈◊〉〈◊〉 poor, and the rest be above the standard quality. 〈◊〉〈◊〉 hoisting of the tail flour, mixing it with bran, by 〈◊〉〈◊〉 and bolting it over, is attended with so much labour, 〈◊〉〈◊〉 it is seldom done to perfection.

In the new way, all these inconveniences and disad∣vantages are completely provided against: See plate 〈◊〉〈◊〉 which is a representation of the machinery, as they 〈◊〉〈◊〉 applied in the whole process of the manufacture, 〈◊〉〈◊〉 the grain from the ship or waggon, and passing it 〈◊〉〈◊〉 the whole process by water, until it is completely manu∣factured into superfine flour. As they are applied in mill of my planning and draughting, now in actual prac∣tice, built on Occoquam river, in Virginia, with 3 water wheels, and 6 pair of stones.

If the wheat comes by water to the mill in the ship 〈◊〉〈◊〉 it is measured and poured into the hopper A, and 〈◊〉〈◊〉 conveyed into the elevator at B, which elevates it, 〈◊〉〈◊〉 drops it into the conveyer C D, which conveys it along under the joists of the second floor, and drops it into the hopper garner at D, out of which it is conveyed into

the main wheat elevator at E, which carries it up into the ••peak of the roof, and delivers it into the rolling screen at F, which (in this plan) is above the colar beams, out if which it falls into the hopper G, thence into the short ••••vator at H, which conveys it up into the fan I, from whence it runs down slanting into the middle of the long conveyer at j that runs towards both ends of the mill, and conveys the grain as cleaned into any garner K K K K K K, over all the stones, which is done by shifting a 〈◊〉〈◊〉 under the fan, to guide the grain to either side of the cog-wheel j, and although each of these garners ••••••uld contain 2000 bushels of wheat, over each pair of 〈◊〉〈◊〉, 12000 bushels in 6 garners, yet nearly all may 〈◊〉〈◊〉 ground out without handling it, and feed the stones 〈◊〉〈◊〉 even and regular than it is possible to do in the old 〈◊〉〈◊〉. As it is ground by the several pair of stones, the 〈◊〉〈◊〉 falls into the meal conveyer at M M M, and is con∣•••••• into the common meal elevator at N, which raises 〈◊〉〈◊〉 O, from thence runs down into the hopper-boy at which spreads and cools it over a circle of 10 or 15 〈◊〉〈◊〉 diameter, and (if thought best) will raise over it, 〈◊〉〈◊〉 form a heap two or three feet high, perhaps thirty ••••••els of flour or more at a time, which may be bolted 〈◊〉〈◊〉 at pleasure. When it is bolting the hopper-boy ••••••ers it into the bolting hoppers at Q▪ and attends them are regularly than is ever done by hand. As it is bolt∣•••••• the conveyer R in the bottom of the superfine chest, conveys the superfine flour to a hole through the floor 〈◊〉〈◊〉, into the packing chest, which mixes it completely. 〈◊〉〈◊〉 of the packing chest it is filled into the barrel at T, ••••ighed in the scale U, packed at W by water, headed 〈◊〉〈◊〉 X, and rolled to the door Y, then lowered down by 〈◊〉〈◊〉 and windlass into the ship again at Z.

If the wheat comes to the mill by land, in the waggon it is emptied from the bags into a spout that is in the all, and it runs in the scale 8, which is large enough hold a waggon load, and as it is weighed it is (by draw∣ing

a gate at bottom) let run into the garner D, out of which it is conveyed into the elevator at E, and so thro' the same process as before.

As much of the tail of the superfine reels 37 as we think will not pass inspection, we suffer to pass on into the short elevator. (by shutting the gates at the bottom of the con∣veyer next the elevator, and opening one further to∣wards the other end) The rubblings, which falls at the tail of said reels, is also hoisted into the bolting hoppers of the sifting reel 39, which is covered with a fine cloth, to take out all the fine flour dust, which will stick to the bran, in warm damp weather, and all that passes thro' it is conveyed by the conveyer 40, into the elevator 41, which elevates it so high that it will run freely into the hopper-boy at O, and is bolted over again with the ground meal. The rubblings that falls at the tail of the sifting reel 39, falls into the hopper of the middlings' reel 42; and the bran falls at the tail into the lower story. Thus you have it in your power either by day or night, without any hand labour except to shift the sliders, or some such trifle, to make your flour to suit the standard quality; and the most superfine possible made out of the grain, and finished complete at one operation.

These improvements are a curiosity worthy the no∣tice of the philosopher and statesman, to see with what harmony the whole machinery works in all their differ∣ent operations.

But to conclude, agreeable to request I attempt to shew the method of making and putting water on the several kinds of water-wheels commonly used, with their dimen∣sions &c. suited to falls and heads from 3 to 36 feet; and have calculated tables for gearing them to mill-stones; and made draughts* 2.250 of several water-wheels with their forebays and manner of putting on the water, &c.

THOMAS ELLICOTT.

THE Practical Mill-wright. Art. 1. OF UNDERSHOT MILLS.

FIG. 1, plate I, represents an undershot wheel 18 feet diameter, with 3 feet total head and fall. It should be 2 feet wide for every foot the mill-stones are in diameter; that is, 8 feet between the shrouds for a 4 feet, and 10 feet wide for a 5 feet stone. It should have three sets of arms and shrouds, on account of its great width. Its shaft should be at least 26 inches diameter. It requires 12 arms, 18 feet long, 3 1-2 inches thick, by 9 wide; and 24 shrouds 7 1-2 feet long, 10 inches deep, by 3 thick, and 32 floats 15 inches wide. Note, it may be geared the same as an overshot wheel, of equal diameter. Fig. 2 represents the forebay, with its ••ills, posts sluice and fall: I have in this case allowed 1 foot fall and 2 feet head.

Fig. 3 represents an undershot wheel 18 feet diameter, with 7 feet head and fall. It should be as wide between the shrouds as the stone is in diameter. Its shaft should be 2 feet diame∣ter. Requires 8 arms 18 feet long, 3 1-4 of an

inch thick,* 2.251 by 9 wide. And 16 shrouds, 7 1-2 feet long, 10 inches deep, by 3 thick. Note, it may be geared the same as an overshot wheel 13 feet diameter, because their revolutions per minute will be nearly equal.

Fig. 4 represents the forebay, sluice, and fall, the head and fall about equal.

Fig. 5 represents an undershot wheel 12 feet diameter, with 15 feet total head and fall. It should be 6 inches wide for every foot the stone is in diameter. Its shaft 20 inches dia∣meter. Requires 6 arms 12 feet long, 3 by 8 inches; and 12 shrouds, 6 1-2 feet long, 2 1-2 inches thick, and 8 deep. It suits well to be geared to a 5 feet stone with single gears, 60 cogs in the cog-wheel, and 16 rounds in the trundle; to a 4 1-2 feet stone, with 62 cogs and 15 rounds; and, to a 4 feet stone, with 64 cogs and 14 rounds. These gears will do well till the fall is reduced to 12 feet, only the wheel must be less as the falls are less, so as to make the same number of revolutions in a minute: but this wheel requires more water than a breast mill, with the same fall.

Fig. 6 is the forebay, gate, shute and fall. Forebays should be wide proportionable to the quantity of water they are to convey to the wheels; and should stand 8 or 10 feet in the bank, and be firmly joined, to prevent the wa∣ter from breaking through; which it will cer∣tainly do, unless they be well secured.

Art. 2. Directions for making Forebays.

THE best way that I know for making these kind of forebays, is shewn in plate V, fig. 7. Make a number of solid frames, consisting of a fill, two posts, and a cap each; set them cross-wise, (as shewn in the figure) 2 1-2 or 3 feet apart; to these the plank are to be spiked, for there should be no sills lengthwise, as the wa∣ter is apt to find its way along them. The frame at the head next the water, and one 6 or 8 feet downwards in the bank, should extend 4 or 5 feet on each side of the forebay in the bank; and be planked in front to prevent the water and vermin from working round. Both of the fills of these long frames should be well secured, by driving down plank edge to edge, like piles, along the upperside, from end to end.

The sills being settled on good foundations, the earth or gravel must be rammed well on all sides, full to the top of the sills. Then lay the bottom with good sound plank, well joint∣ed and spiked to the sills. Lay your shute, ex∣tending the upper end a little above the point of the gate when full drawn, to guide the wa∣ter in a right direction to the wheel. Plank the head to its proper height, minding to leave a suitable sluice, to guide the water smoothly down. Fix the gate in an upright position—••••ang and wheel and finish it off ready for let∣ting on the water.

A rack must be made to keep off the floating trash that would break the floats and buckets of undershot, breast, and pitch-back wheels,

and injure the gates.* 2.252 See it at the head of fore∣bay, fig. 7, plate V. This is done by setting a frame 3 feet in front of the forebay, and lay∣ing a sill 2 feet in front of it, for the bottom of the rack: in it the staves are put, made of laths, set edgewise with the stream, 2 inches a∣part, their upper ends nailed to the cap of the last frame, which causes them to lean down steam. The bottom of the race must be planked between the forebay and rack, to prevent the water from making a hole by tumbling through the rack when choaked; and the sides be planked outside the posts to keep up the banks. This rack must be double as long as the forebay is wide, or else the wa∣ter will not come fast enough through it to keep the head up; for the head is the spring of motion of an undershot mill.

Art. 3. Of the Principle of Undershot Mills.

THEY differ from all others in principle, because the water looses all its force by the first stroke against the floats; and the time this force is spending, is in proportion to the difference of the velocities of the wheel and water, and the distance of the floats. Other mills have the weight of the water after the force of the head is spent, and will continue to move; but an undershot will stop as soon as the head is spent, as they depend not on the weight. They should be geared so, that when the stone goes with a proper motion, they will not run too fast with the water, so as not to receive its

force;* 2.253 nor too slow, so as to loose its power by rebounding and dashing over the buckets. This matter requires very close attention, and has puzzled our mechanical philoso∣phers to find it out by theory. They give us for a rule, that the wheel must move just 1-3 the velocity of the water;—perhaps this may suit where the head is not much higher than the float boards, but I am fully convinced it will not suit high heads.

Experiments for determining the proper Motion for Undershot Wheels.

I drew a full sluice of water on an undershot wheel with 15 feet head and fall, and counted its revolutions per minute; then geared it to a mill-stone, set it to work properly, and again counted its revolutions, and the difference was not more than one fourth slower. I believe, that if I had checked the motion of the wheel to be equal 1-3 the motion of the water, that the water would have rebounded the flew up to the shaft. Hence I conclude, that the moti∣on of the water must not be checked by the wheel more than 1-3, nor less than 1-4; else it will loose in power: for although the wheel will carry a greater load with a slow, than swift motion, yet it will not produce so great effect, its motion being too slow. And again, if the motion be too swift, the load or resist∣ance it will overcome will be so much less, that its effect will be lessened also. I conclude, that about 2-3 the velocity of the water is the proper motion for undershot wheels, the

water will then spend all its force in the distance of 2 float boards;* 2.254 notwithstanding, the learned authors have asserted it to be but 1-3. To confute them, suppose the floats 12 inches, and the column of water striking them, 8 inches deep; then, if 2-3 of the motion of this column be checked, it must instantly be∣come 24 inches deep, and rebound against the backs of the floats, and the wheel would be wallowing in this dead water: whereas, when 1-3 of its motion is checked, it becomes only 12 inches deep, and runs off from the wheel smooth and lively.

Directions for gearing Undershot Wheels, 18 feet Diameter, where the Head is above 3 and under 8 feet, with double Gears; counting the Head from the Point where the Water strikes the Floats.

1. For 3 feet head and 18 feet wheel, see 18 feet wheel in the overshot table.

2. For 3 feet 8 inches head, see 17 feet wheel in said table.

3. For 4 feet 4 inches head, see 16 feet wheel in said table.

4. For 5 feet head, see 15 feet wheel in said table.

5. For 5 feet 8 inches head, see 14 feet wheel in said table.

6. For 6 feet 4 inches head, see 13 feet wheel in said table.

7. For 7 feet head, see 12 feet wheel in said table.

The revolutions of the wheels ••ill be near∣ly equal; therefore the gears may be the same.

The following table is calculated to suit for any sized stone, from 4 to 6 feet diameter;

different sized water-wheels from 12 to 18 feet diameter,* 2.255 and different heads from 8 to 20 feet above the point it strikes the floats. And to make 5 feet stones revolve 88 times; 4 feet 6 inch stones 97 times; and 4 feet stones 106 times in a minute, when the water wheel moves 2-3 the velocity of the striking water.

Mill-wrights Table for Undershot-mills—Single Geared.

Height of the ••ead of wat. in f.	Diameter of the water-wheel in feet.	Velocity of the water per minute in feet.	Velocity of the water-wheel per minute in feet.	Revolutions of the water-wheel per minute.	Revolutions of the stone per minute.	No. cogs in the cog-wheel.	Number of rounds in the trun∣dle head.	Revolutions of the mill-stone for one of the water-wheel.	Diameter of the stones in feet.
8	12	1360	9••6	24	88	56	15	3¾	5
9	13	1448	965	23½	88	58	15	36/7;	5
10	14	1521	1014	231/7;	88	58	15	36/7;	5
11	15	1595	1061	22¾	88	58	15	3¾	5
12	16	1666	1111	22¼	88	58	15	37/8;	5
13	16	1735	1157	231/7;	88	60	16	3¾	5
14	16	1800	1200	24	88	59	16	3⅔	5
15	16	1863	1242	24⅘	88	60	17	3½	5
16	16	1924	1283	25⅔	88	59	17	33/8	5
17	17	1983	1322	25	88	62	17	3¾	5
18	17	2041	1361	25⅔	88	62	17	3¾	5
19	18	2097	1398	25	88	62	17	3¾	5
20	18	2152	1435	25½	88	60	17	3〈◊〉〈◊〉	5
1	2	3	4	5	6	7	8	9	10

Note that there is nearly 60 cogs in the cog-wheel, in the foregoing table, and 60 inch∣es is the diameter of a 5 feet stone; therefore, it will do without sensible error, to put 1 cog more in the wheel for every inch that the stone is less than 60 inches diameter, down to 4 feet; the trundle head and water-wheel the same.

And for every 3 inches that the stone in larg∣er than 60 inches in diameter, put 1 round more in the trundle, and the motion of the stone will be nearly right up to 6 feet diame∣ter.

Art. 4. Of Breast-Wheels.

BREAST wheels differ but little in their structure or motion from overshots, excepting only, the water passes under instead of over them, and they must be wider in proportion as their fall is less.

Fig. 1, plate II, represents a low breast with 8 feet head and fall. It should be 9 inch∣es wide for every foot of the diameter of the stone. Such wheels are generally 18 feet dia∣meter; the number and dimensions of their parts being as follows: 8 arms 18 feet long, 3 1-4 by 9 inches; 16 shrouds 8 feet long, 2 1-2 by 9 inches; 56 buckets; and shaft, 2 feet diameter.

Fig. 2 shews the forebay, water gate, and fall, and manner of striking on the water.

Fig. 3 is a middling breast-wheel 18 feet di∣ameter. with 12 feet head and fall. It should

be 8 inches wide for every foot the stone is in diameter.* 2.256

Fig. 4 shews the forebay, gate and fall, and manner of striking on the water.

Fig. 5 and 6 is a high breast-wheel, 16 feet diameter, with 3 feet head in the forebay, and 10 feet fall. It should be 7 inches wide for every foot the stone is in diameter. The num∣ber and dimensions of its parts are, 6 arms 16 feet long, 3 1-4 by 9 inches; 12 shrouds 8 feet ••6 inches long, 2 1-2 by 8 or 9 inches deep, and 48 buckets.

Art. 5. Of Pitch-back Wheels.

PITCH-BACK wheels are constructed ex∣actly similar to breast-wheels, only the water is struck on them higher. Fig. 1, plate III, is a wheel 18 feet diameter, with 3 feet head in the penstock, and 16 feet fall below it. It should be 6 inches wide for every foot of the diameter of the stone.

Fig. 2 shews the trunk, penstock, gate and fall, the gate sliding on the bottom of the pen∣stock, and drawn by the lever A, turning on a roller. This wheel is much recommended by some mechanical philosophers, for the saving of water; but I do not join them in opinion, but think that an overshot with equal head and fall, is fully equal in power: besides, the saving the expence of so high a wheel and fall, that are difficult to be kept in order.

Art. 6. Of Overshot Wheels.

OVERSHOT wheels receive their water on the top, being moved by its weight; and are much to be recommended where there is fall enough for them. Fig. 3 represents one 18 feet diameter, which should be about 6 inches wide for every foot the stone is in diameter. It should hang 8 or 9 inches clear of the tail water, because they draw it under them. The head in the penstock should be generally about 3 feet, which will spout the water about 1-3 faster than the wheel moves. Let the shute have about 3 inches fall, and direct the water into the wheel at the centre of its top.

I have calculated a table for gearing over∣shot wheels, which will equally well suit any of the others of equal diameter, that have equal heads above the point where the water strikes the wheel.

Dimensions of this wheel, 8 arms 18 feet long, 3 by 9 inches; 16 shrouds 7 feet 9 inches long, 2 1-2 by 7, or 8 inches; 56 buckets, and shaft, 24 inches diameter.

Fig. 4 represents the penstock and trunk, &c. the water being let on the wheel by draw∣ing the gate G.

Fig. 1 and 2, plate IV, represents a low overshot 12 feet diameter, which should be in width equal to the diameter of the stone. Its parts and dimensions are, 6 arms 12 feet long, 3 1-2 by 9 inches; 12 shrouds, 6 1-2 feet long, 2 1-2 by 8 inches; shaft 22 inches diameter, and 30 buckets.

Fig. 3 represents a very high overshot 30 feet diameter,* 2.257 which should be 3 1-2 inches wide for every foot of the diameter of the stone. Its parts and dimensions are, 6 main arms, 30 feet long, 3 1-4 inches thick, 10 inches wide at the shaft, and 6 at the end; 12 short arms 14 feet long, of equal dimensions; which are fram∣ed into the main arms near the shaft, as in the figure; for if they were all put through the shaft, they would make it too weak. The shaft should be 27 inches diameter, the wheel being very heavy and bearing a great load. Such high wheels require but little water.

Art. 7. Of the Motion of Overshot Wheels.

AFTER trying many experiments, I con∣cluded that the circumference of overshot wheels geared to mill-stones, grinding to the best advantage, should move 550 feet in a mi∣nute; and that of the stones 1375 feet in the same time; that is, while the wheel moves 12, the stone moves 30 inches, in the proportion of 2 to 5.

Then, to find how often the wheel we pro∣pose to make will revolve in a minute, take the following steps: 1st, Find the circumference of the wheel by multiplying the diameter by 22, and dividing by 7, thus:

Suppose the diameter to be 16 feet, then 16 multi∣plied by 22, produces 352; which, divided by 7, quotes 50 2/••; for the circumference.

16
22
32
32
7)352
50〈◊〉〈◊〉

By which we divide 550,* 2.258 the distance the wheel moves in a minute, and it quotes 11, for the revolu∣tions of the wheel per mi∣nute, casting off the frac∣tion 2/7, it being small.

5|0)55|0
11 times.

To find the revolutions of the stone per minute, 4 feet 6 inches (or 54 inches) diameter, multiply 54 inch∣es by 22, and divide by 7, and it quotes 1695/7; (say 170) inches, the circum∣ference of the stone.

54
22
108
108
7)1188
169 5/7

By which divide 1375 feet, or 16500 inches, the distance the skirt of the stone should move in a mi∣nute, and it quotes 97; the revolutions of a stone per minute, 4½ feet diameter.

1375
12
17|0)1650|0(9
153
120
119
1

To find how often the stone revolves for once of the water wheel, divide 97, the revolutions of the stone, by 10, the revolutions of the wheel, and it quotes 89/11, (say 9 times).

11)97(8 9/11
88
9

Art. 8. Of Gearing.

Now, if the mill was to be single geared, 99 cogs and 11 rounds, would give the stone

••he right motion,* 2.259 but the cog-wheel would be too large, and trundle too small, therefore it must be double geared.

Suppose we choose 66 cogs in the big cog-wheel and 48 in the little one, and 5 rounds in the wallower, and 15 in the trundle.

Then, to find the revo∣lutions of the stone for one of the water-wheel, multiply the cog-wheel, together, and the wallow∣er and trundle together, and divide one product by the other, and it will quote be answer, 8 168/375, not quite 〈◊〉〈◊〉 revolutions instead of 9.

25
15
125
25
375
66
48
528
264
375)3168(8 168/375
3000
168

Therefore we must make another proposition ▪Considering which of the wheels we had ••••est alter, and wishing not to alter the big cog-wheel nor trundle, we put one round less ••••n the wallower, and 2 cogs more in the little cog-wheel, and multiplying and dividing as be∣fore, we find the stone will turn 9⅙ times for once of the water-wheel, which is as near as we can get. The mill now stands thus, a 16 foot overshot wheel, that will revolve 11 times in a minute, geared to a stone 4 1-2 feet dia∣meter; the big cog-wheel 66 cogs, 4 1-2 inch∣es from centre to centre of the cogs; (which we call the pitch of the gear) little cog-wheel 50 cogs 4 1-4 pitch; wallower 24 rounds, 4 1-2 pitch, and trundle 15 rounds, 4 1-4 inches pitch.

Art. 9. Rules for finding the Diameter of the Pitch Circles.

To find the diameter of the pitch circle, that the cogs stand in, multiply the number of cogs by the pitch, which gives the cir∣cumference; which, mul∣tiplied by 7, and divided by 22, gives the diameter in inches; which, divided by 12, reduces it to feet and inches thus:

66
4 1/2
264
33
297
7
22)2079(94 11/22 inc.
198
99
88
11

For the cog-wheel of 66 cogs, 4 1-2 pitch, we find to be 7 feet 10 11/22 inches, the diameter of pitch circle; to which I add 8 inches, for the outside of the cogs, makes 8 feet 6 1-2 inches, the diameter from out to out.

By the same rules I find the diameters of the pitch circles of the other wheels, to be as fol∣lows, viz.

	ft.	in.
Little cog-wheel 50 cogs, 4 1-4 inches pitch,	5	7 110/222 p. circ.
I add for the outside of the circle,		7½
Total diamet. from out to out	6	3
Wallower 24 rounds 4 1-2 inches pitch.	2	11¾ 4/22
Add for outsides,	0	3 13/22; do.
Total diameter from the outsides.	3	3

Trundle head 15 rounds,* 2.260 4 1-4 inch pitch,	1	8¼ 3/22 p.circ.
Add for outsides		2½ 19/22
Total diameter for the outsides,	1	11

Thus we have completed the calculations for one mill, with a 16 feet overshot water-wheel, and stones 4 1-2 feet diameter. By the same rules we may calculate for wheels of all sizes from 12 to 30 feet, and stones from 4 to 6 feet diameter, and may form tables that may be of great use to many, even to master workmen that understand calculating well in dispatching of business, in laying out work for their apprentices and other hands, getting out timber, &c. but more especially 〈◊〉〈◊〉 those who are not learned in arithmetic sufficient to calculate, I being from long ex∣perience highly sensible of the need of such a ••••ble, have therefore undertaken the arduous 〈◊〉〈◊〉.

MILL-WRIGHTS TABLES,

Calculated to suit overshot water-wheels with suitable heads above them, of all sizes from 12 to 30 feet diameter, the velocity of their circumferences being about 550 feet per minute, shewing the number of cogs and rounds in all the wheels, double gear, to give the circumference of the stone a velocity of 375 feet per minute, also the diameter of their pitch-circles, the diameter of the out∣sides,

and revolutions of the water-wheel and stones per minute.

For particulars see what is written over the head of each table. Table I. is to suit a 4 feet stone, table II. a 4 1-2, table III. a 5 feet, and table IV. a 5 1-2 feet stone.

N. B. If the stones should be an inch or two bigger or less than those above described, make use of the table that comes nearest to it, and likewise for the water-wheels. For further particulars see draughting mills.

Use of the following Tables.

Having levelled your mill-seat and found the total fall, after making due allowances for the fall in the races, and below the wheel, Suppose there is 21 feet 9 inches, and the mill-stones are 4 feet diameter, then look in table I, (which is for 4 feet stones) column 2, for the fall that is nearest your's, and you find it in the 7th ex∣ample: and against it in column 3, is the head proper to be above the wheel 3 feet, in co∣lumn 4 is 18 feet, for the diameter of the wheel, &c. for all the proportions of the gears to make a steady moving mill, the stones to revolve 106 times in a minute.* 2.261

Table I. For Overshot Mills with Stones 4 feet Diameter to revolve 106 times in a minute, Pitch of the gear of great cog wheel and wallower 4½ and of lesser cog wheel and trundle 4¼ inches.

No of examples.	Total falls of water from the top of that in the penstock to that in the tail-race.	Different heads of water above the water wheels.	Diameters of water wheels from out to out.	Width of water wheels in the clear.	No. of cogs in the great and lesser cog wheels.	Diameters of pitch circles of great and lesser wheels.	Diameters of cog wheels from out to out.	No. of rounds in the wal∣lowers and trundles.	Diameters of pitch circles in wallowers and trundles.	Total diameters of wallow∣ers and trundles.	Revolutions of great wheel per minute nearly.
	ft. in.	f. i.	feet	f. i.		f. i.	f. i.		f. i.	f. i.
1	15,3	2,6	12	3,0	66	7,10〈◊〉〈◊〉	8,6〈◊〉〈◊〉	25	2,11¾	3,3	3
48	5,4〈◊〉〈◊〉	6,0〈◊〉〈◊〉;	15	1,8〈◊〉〈◊〉	1,11〈◊〉〈◊〉
2	16,4	2,7	13	2,10	69	8,2〈◊〉〈◊〉	8,10¼	25	2,11〈◊〉〈◊〉;	3,3	12½
48	5,4〈◊〉〈◊〉	6,0½	15	1,8〈◊〉〈◊〉	1,11¼
3	17,5	2,8	14	2,8	69	8,2〈◊〉〈◊〉	8,10〈◊〉〈◊〉	26	3,¼	3,5¼	12
48	5,4〈◊〉〈◊〉	6,0½	15	1,8〈◊〉〈◊〉	1,11¼
4	18,6	2,9	15	2,6	69	8,2〈◊〉〈◊〉	8,10⅓	25	2,111/4;	3,3	11½
50	5,7〈◊〉〈◊〉	6,3	15	1,8〈◊〉〈◊〉	1,11〈◊〉〈◊〉
5	19,7	2,10	16	2,4	72	8,7〈◊〉〈◊〉;	9,3	26	3,1¼	3,5¼	11
52	5,10⅓	6,6	15	1,8〈◊〉〈◊〉	1,11〈◊〉〈◊〉
6	20,8	2,11	17	2,3	72	8,7¼	9,3	25	2,11¾	3,3	10½
52	5,10¼	6,6	14	1,7	1,10
7	21,9	3,0	18	2,2	72	8,7〈◊〉〈◊〉	9,3	25	2,10¼	3,1½	10
52	5,10⅓	6,6	14	1,7	1,10
8	22,10	3,1	19	2,1	75	8,11⅓	9,7⅓	24	2,10⅓	3,1½	9⅔
52	5,10⅓	6,6	14	1,7	1,10
9	23,11	3,2	20	2,0	75	8,11⅓	9,7⅓	24	2,9	3,0	9¼
52	5,10⅓	6,6	14	1,7	1,10
10	25,1	3,4	21	1,11	78	9,3¼	9,11〈◊〉〈◊〉	23	2,10⅓	3,1½	87/6;
52	5,10⅓	6,6	14	1,7	1,10
11	26,3	3,6	22	1,10	78	9,3½	9,11½	24	2,9	3,0	8½
52	5,10½	6,6	14	1,7	1,10
12	27,5	3,8	23	1,9	78	9,3¼	9,11½	23	2,9	3,0	8¼
54	6,1	6,8½	14	1,7	1,10
13	28,7	3,10	24	1,8	81	9,8	10,4	23	2,9	3,0	8
54	6,1	6,8½	14	1,7	1,10
14	29,9	4,0	25	1,7	81	9,8	10,4	23	2,9	3,0	7¾
56	6,3〈◊〉〈◊〉	6,11〈◊〉〈◊〉	14	1,7	1,10
15	30,11	4,2	26	1,6	84	10,0〈◊〉〈◊〉	10,8¼	23	2,9	3,0	7½
56	6,3〈◊〉〈◊〉	6,11¼	14	1,7	1,10
16	32,1	4,4	27	1,5	84	10,0¼	10,8〈◊〉〈◊〉	23	2,9	3,0	6¾
6,6¼	7,1¾	14	1,7	1,10
17	33,3	4,6	28	1,4	84	10,0〈◊〉〈◊〉	10,8¼	23	2,9	3,0	6⅔
56	6,3¾	7,1¾	14	1,5¼	1,8¼
18	34,6	4,9	29	1,3	8〈◊〉〈◊〉	10,0¼	10,8¼	22	2,7½	2,10½	6½
56	6,3¾	7,1¾	13	1,5¼	1,8¼
19	35,9	5,9	13	1,2	37	10,5	11,1	22	2,7½	2,10½	6¼
56	6,3¾	7,1¾	13	1,6¼	1,8¼
1	2	3	4	5	6	7	8	9	10	11	12

TABLE II. For Overshot Mills with Stones 4 feet 6 inches Diameter to revolve 99 times in a minute, pitch of the gears 4½ and 4¼ inches.

No. of Examples.	Total falls of water from the top of that in the Pen∣stock to that in the tail ra••e.	Different head of water above the water wheel.	Diameters of water wheels from out to out.	Widths of water wheels in the Clear.	No. of Cogs in the great and lesser Cog wheels.	Diameters of Pitch Circles of great and lesser cog wheels.	Diameters of Cog wheels from out to out.	No. of rounds in wallower and trundle••.	Diameters of Pitch C••••eres in wallowers and trun∣dles.	Total diameters of wallow∣ers and trundles.	Revolutions of the great wheel per minute nearly.
	ft.in.	ft.in.	ft.in.	ft.in.		ft.in.	ft.in.		ft.in.	ft.in.
1	15,3	2,6	12	3,6	66	7,10〈◊〉〈◊〉	8,〈◊〉〈◊〉	20	3,〈◊〉〈◊〉;	3,〈◊〉〈◊〉	12½
48	5,4½	6,0½	15	1,8〈◊〉〈◊〉	1,11¼
2	16,4	2,7	13	3,4	66	7,10½	8,6½	25	2,11〈◊〉〈◊〉	3,3	12½
48	5,4〈◊〉〈◊〉	6,0½	15	1,8½	1,11⅓
3	17,5	2,8	14	3,2	69	8,2⅓	8,10〈◊〉〈◊〉	26	3,1¼	3,4¼	12
48	5,4〈◊〉〈◊〉	6,0½	15	1,8〈◊〉〈◊〉	1,11½
4	13,6	2,9	15	3,0	69	8,2⅓	8,10½	25	2,11〈◊〉〈◊〉	3,3	11½
48	5,4⅓	6,0½	15	1,8¼	1,11½
5	19,7	2,10	16	2,10	69	8,2〈◊〉〈◊〉	8,10½	25	2,11¼	3,3	11
50	5,7〈◊〉〈◊〉	6,3	15	1,8¾	1,11½
6	20,8	2,11	17	2,8	72	8,7〈◊〉〈◊〉	9,3	26	3,1¼	3,4¼	10¼
52	5,10¼	6,6	15	1,8¾	1,11½
7	21,9	3,0	18	2,6	72	8,7¼	9,3	25	2,11¼	3,3	10
52	5,10¼	6,6	14	1,8〈◊〉〈◊〉	1,11½
8	22,10	3,1	19	2,4	72	8,7¼	9,3	24	2,10⅓	3,2½	9½
52	5,10〈◊〉〈◊〉	6,6	14	1,8〈◊〉〈◊〉	〈◊〉〈◊〉, 11½
9	23,11	3,2	20	2,3	75	8,11⅓	9,7⅓	24	2,10〈◊〉〈◊〉	3,2½	9
52	5,10⅓	6,6	14	1,8¾	1,11½
10	25,1	3,4	21	2,2	75	〈◊〉〈◊〉,11⅓	9,7¼	••3	2,9	3,0	8¾
52	5,10⅓	6,6	14	1,8¾	1,11½
11	26,3	3,6	22	2,1	78	9,3½	9,11½	24	2,10〈◊〉〈◊〉	3,2½	8½
52	5,10⅓	6,6	14	1,8¾	1,11½
12	27,5	3,8	23	2,0	78	9,3½	9,11½	23	2,9	3,0	8¼
52	5,10⅓	6,6	14	1,8¼	1,11¼
13	28,7	3,10	24	1,11	78	9,3½	9,11½	23	2,9	3,0	8
54	6,1	6,8½	14	1,8½	1,11¼
14	29,9	4,0	25	1,10	81	9,8	10,4	23	2,9	3,0	7¾
54	6,1	6,8½	14	1,8½	1,11½
15	30,11	4,2	26	1,9	31	9,8	10,4	23	2,9	3,0	7½
56	6,3¼	6,11¼	14	1,8½	1,11½
16	32,1	4,4	27	1,8	84	10,0¼	10,8¼	23	2,9	3,0	6¾
〈◊〉〈◊〉	6,3¼	6,11¼	14	1,8½	1,11½
17	33,3	4,6	28	1,6	••4	10,0¼	10,8¼	23	2,9	3,0	6⅔
58	6,6¼	7,1¼	14	1,8½	1,11½
18	34,6	4,〈◊〉〈◊〉	29	1,5	84	10,0¼	10,8½	23	2,9	3,0	6½
6	6,3¼	6,11¼	13	1,5¼	1,8¼
19	35,9	〈◊〉〈◊〉	30	1,1	84	10,0¾	10,8¼	22	2,7½	2,10½	6¼
••6	6,3〈◊〉〈◊〉	6,11〈◊〉〈◊〉	13	1,5½	1,8〈◊〉〈◊〉
1	2	3	4	5	6	7	8	9	10	11	12

TABLE III. Stones 5 feet Diameter to revolve 86 times in a minute, the pitch of the gears 4½ and 4¼ inches.

No. of examples.	Total falls of water from the top of the Penstock to that in the tail race	Different heads of water above the water wheels.	Diameters of water wheels from out to out.	Widths of water wheels in the clear.	No. of Cogs in the great and lesser cog wheels.	Diameters of Pitch circles of great and lesser cog wheels.	Diameters of cog wheels from out to out,	No. of rounds in the wal∣lower and trundle.	Diameters of pitch circles in wallowers and trundles	Total Diameters of wallow∣ers and trundles.	Revolutions of the great wheel per minute Near∣ly.
	ft.in.	ft.in.	feet	ft.in.		ft.in.	ft.in.		ft.in.	ft.in.
1	15,3	2,6	12	4,0	63	7,6〈◊〉〈◊〉	8,2 〈◊〉〈◊〉	26	3,1¼	3,4¼	13
48	5,4〈◊〉〈◊〉	6,0½	16	1,9⅔	2,0⅔
2	16,4	2,7	13	3,10	66	7,10½	8,6½	26	3,1¼	3,4¼	12¼
48	5,4⅞	6,0½	16	1,9⅔	2,4¼
3	17,5	2,8	14	3,8	66	7,10½	8,6½	25	2,11〈◊〉〈◊〉	3,3	12
48	5,4〈◊〉〈◊〉	6,0½	15	1,8⅓	1,11⅓
4	18,6	2,9	15	3,6	69	8,2⅔	8,1〈◊〉〈◊〉	26	3,1¼	3,4¼	11½
48	5,4⅞	6,0½	15	1,8⅓ / 3;	1,11⅓;
5	19,7	2,10	16	3,4	69	8,2⅓	8,10⅓	25	2,11¾	3,3	21
48	5,4〈◊〉〈◊〉	6,0½	15	1,8⅓	1,11⅓
6	20,8	2,11	17	3,2	69	8,2⅓	8,10⅓	25	2,11〈◊〉〈◊〉	3,3	10½
50	5,7½	6,3	15	1,8⅓	1,11⅓
7	21,9	3,0	18	3,0	72	8,7¼	9,3	26	3,1¼	3,4¼	10
52	5,10¼	6,6	15	1,8¼	1,11⅓
8	22,10	3,1	19	2,10	72	8,7¼	9,3	25	2,11¼	3,3	9⅔
52	5,10〈◊〉〈◊〉	6,6	14	1,8〈◊〉〈◊〉	1,11½
9	23,11	3,2	20	2,8	72	8,7〈◊〉〈◊〉	9,3	24	2,10¼	3,2½	9¼
52	5,10〈◊〉〈◊〉	6,6	14	1,8¾	1,11½
10	25,1	3,4	21	2,6	75	8,11〈◊〉〈◊〉	9,7⅓	24	2,10⅓	3,2½	8⅞
52	5,10¼	6,6	14	1,8¾	1,11½
11	26,3	3,6	22	2,5	75	8,11⅓	9,7⅓	23	2,9	3,0	8½
52	5,10½	6,6	14	1,8¾	1,11½
12	27,5	3,8	23	2,4	78	9,3½	9,11½	24	2,10¼	3,2⅓	8¼
52	5,10⅓	6,6	14	1,8¾	1,11½
13	28,7	3,10	24	2,3	78	9,3½	9,11½	23	2,9	3,0	8
52	5,10⅓	6,6	14	1,8¾	1,11½
14	29,9	4,0	25	2,2	78	9,3½	9,11½	23	2,9	3,0	7¾
54	6,1	6,8½	14	1,8¾	1,11½
15	30,11	4,2	26	2,0	81	9,8	10,4	23	2,9	3,0	7½
54	6,1	6,8½	14	1,8¾	1,11½
16	32,1	4,4	27	1,11	81	9,8	10,4	23	2,9	3,0	6⅓
56	6,3¼	6,11¼	14	1,8¾	1,11½
17	33,3	4,6	28	1,9	84	10,0¼	10,8¼	23	2,9	3,0	6⅔
56	6,3¼	6,11¼	14	1,8¾	1,11½
18	34,6	4,9	29	1,7	84	10,0¼	10,8¼	23	2,9	3,0	6¼
58	6,6¼	7,1¼	14	1,8¾	1,11½
19	15••	5,0	30	1,6	84	10,〈◊〉〈◊〉	10,8¼	23	2,9	3,0	6¼
56	6,3¼	6,11¼	13	1,5¼	1,8¼
1	2	3	4	5	6	7	8	9	10	11	12

TABLE IV. For Overshot Mills with Stones 5 feet 6 inches Diameter to revolve 80 times in a minute the pitch of the gears 4¾ and 4½ inches.

No. of examples.	Total falls of water from the top of that in the pen∣stock to top of that in the tail race.	Different heads of water above the water wheels.	Diameters of water wheels from out to out.	Widths of water wheels in the clear.	No. of cogs in great and lesser cog wheels.	Diameters of pitch circles of great and lesser cog wheels.	Diameters of cog wheels from out to out.	No. of rounds in the wallowers and trundles.	Diameters of pitch circles in wallowers and trundles.	Total diameters of wallow∣ers and trundles.	Revolutions of the great wheel per minute nearly.
	ft. in.	ft.in.	feet.	ft. in.		ft.in.	ft. in.		ft. in.	ft. in.
1	15,3	2,6	12	4,6	60	7,6¾	8,2¾	26	3,3〈◊〉〈◊〉	3,6¼	13
48	5,8¾	6,4¼	16	1,11	2,2
2	16,4	2,7	13	4,4	63	7,11〈◊〉〈◊〉	8,7〈◊〉〈◊〉	26	3,3〈◊〉〈◊〉	3,6¼	12½
48	5,8〈◊〉〈◊〉	6,4¼	16	1,11	3,2
3	17,5	2,8	14	4,2	66	8,3¾	8,11¾	26	3,3¼	3,6¼	12
48	5,8¾	6,6¼	16	1,11	2,2
4	18,6	2,9	15	4,0	66	8,3¾	8,11¾	26	3,3¼	3,6¼	11½
48	5,8¾	6,4¼	15	1,9½	2,0½
5	19,7	2,10	16	3,10	69	8,8⅓	9,4⅓	26	3,3¼	3,6¼	11
48	5,8¾	6,4¼	15	1,9½	2,0½
6	20,8	2,11	17	3,8	69	8,8⅓	9,4⅓	25	3,1¾	3,4¾	10½
48	5,8¾	6,4¼	15	1,9½	2,0½
7	21,9	3,0	18	3,6	69	8,8⅓	9,4⅓	25	3,1¾	3,4¾	9
50	5,11½	6,2½	15	1,9½	2,0½
8	22,10	3,1	19	3,9	72	9,0¾	9,8¾	26	3,3¼	3,6¼	9⅔
52	6,2½	6,10⅓	14	1,8	1,11
9	23,11	3,2	20	3,2	72	9,0¾	9,8¾	25	3,1¾	3,4¾	9¼
52	6,2½	6,10⅓	14	1,8	1,11
10	25,1	3,4	21	3,0	72	9,0¾	9,8¾	24	3,0¾	3,3⅓	8¼
52	6,2½	6,10	14	1,8	1,11
11	26,3	3,6	22	2,10	75	9,5⅓	10,1⅓	24	3,0¾	3,3¾	3½
52	6,2½	6,10	14	1,8	1,11
12	27,5	3,8	23	2,8	75	9,5⅓	10,1〈◊〉〈◊〉;	23	2,10¾	3,1¾	8¼
52	6,2½	6,10	14	1,8	1,11
13	28,7	3,10	24	2,6	78	9,10	10,6	24	3,0¾	3,3¾	8
52	6,2½	6,10	14	1,8	1,11
14	29,9	4,0	25	2,4	78	9,10½	10,6	23	2,10¾	3,1¾	7¾
52	6,2〈◊〉〈◊〉	6,10	14	1,8	1,11
15	30,11	4,2	26	2,2	78	9,10½	10,6	23	2,10¾	3,1¾	7½
54	6,5¼	7,1	14	1,8	1,11
16	32,〈◊〉〈◊〉	4 4	27	2,0	81	10,2〈◊〉〈◊〉	10,10	13	2,10〈◊〉〈◊〉	3,1¾	6¾
54	6,5⅓	7,1	14	1,8	1,11
17	33,3	4,6	28	1,11	81	10,2½	10,10½	23	2,10¾	3,1¾	6⅔
56	6,8	7,3½	14	1,8	1,11
18	34,6	〈◊〉〈◊〉	29	1,10	84	10,7	11,3	23	2,10〈◊〉〈◊〉	3,1¾	6½
56	6,8	7,3½	14	1,8	1,11
19	35,9	5,0	30	1,9	84	10,7	11,3	23	2,10¾	3,1¾	6¼
58	6,11	7,6½	14	1,8	1,11
1	2	3	4	5	6	7	8	9	10	11	12

Art. 10. Directions for constructing Undershot Wheels, such as fig. 1, plate I.

1. Dress the arms straight and square on all sides, and find the centre of each; divide each into 4 equal parts on the side square centre scribe, and gauge them from the upper side a∣cross each point, on both sides, 6 inches each way from the centre.

2. Set up a truckle or centre-post, for a cen∣tre to frame the wheel on, in a level place of ground, and set a stake to keep up each end of the arms level with the truckle, of convenient height to work on.

3. Lay the first arm with its centre on the centre of the truckle, and take a square notch out of the upper side 3-4 of its depth, wide enough to receive the 2nd arm.

4. Make a square notch in the lower edge of the 2nd arm, 1-4 of its depth, and lay it in the other, and they will joint standing square across other.

5. Lay the 3rd arm just equi-distant be∣tween the others, and scribe the lower arms by the side of the upper, and the lower edge of the upper by the sides of the lower arms. Then, take the upper arm off and strike the square scribes, taking out the lower half of the 3rd arm, and the upper half of the lower arms, and fit and lay them together.

6. Lay the 4th arm on the others, and scribe as directed before; then take 3-4 of the lower edge of the 4th arm, and 1-4 out of the up∣per edge of the others, and lay them toge∣ther, and they will be locked together in the depth of one.

7. Make a sweep-staff with a gimblet hole for the centre at one end,* 2.262 which must be set by a gimblet in the centre of the arms. Measure from this hole half the diameter of the wheel, making a hole there, and another the depth of the shrouds towards the centre, making each edge of this sweep at the end next the shrouds, straight towards the centre hole, to scribe the ends of the shrouds by.

8. Circle both edges of the shrouds by the sweep, dress them to width and thickness, lay out the laps 5 inches long, set a gauge to a lit∣tle more than 1-3 their thickness, gauge all their ends for the laps from the outsides, cut them all out but the last, that it may be made a little longer, or shorter, as may suit to make the wheel the right diameter; sweep a circle on the arms to lay the shrouds to, while fitting them, put a small draw-pin in the middle of each lap, to draw the joints close, strike a true circle for both inside and outside the shrouds, and one 1 1-2 inch from the inside, where the arms are to be let in.

9. Divide the circle into 8 equal parts, com∣ing as near the middle of each shroud as possi∣ble; strike a scribe across each to lay out the notch by, that is to be cut 1 1-2 inch deep, to let in the arm at the bottom of where it is to be forked to take in the remainder of the shroud. Strike a scribe on the arms with the same sweep that the stroke on the shrouds for the notches was struck with.

10. Scribe square down each side of the arms, at the bottom of where they are to be forked; make a gauge to fit the arms, so wide as just to take in the shrouds, and leave 1 1-2

inch of wood outside of the mortise;* 2.263 bore 1 or 2 holes through each end of the arms to draw-pin the shrouds to the arms when hung; mark all the arms and shrouds to their places, and take them apart.

11. Fork the arms, put them together a∣gain, and put the shrouds into the arms; drawbore them, but not too much, which would be worse than too little; take the shrouds apart again, turn them the other side up, and draw the joints together with the pins, and lay out the notches for 4 floats between each arm, 32 in all, large enough for admit∣ting keys to keep them fast, but allowing them to drive in when any thing gets under the wheel. The ends of the floats must be dovetail∣ed a little into the shrouds; when one side is framed, frame the other to fellow it. This done, the wheel is ready to hang, but remem∣ber to face the shrouds between the arms with inch boards, nailed on with strong nails, to keep the wheel firm together.

Art. 11. Directions for Dressing Shafts, &c.

THE shaft for a water-wheel with 8 arms should be 16 square, or 16 sided, about two feet diameter, the tree to make it being 2 feet 3 inches at the top end. When cut down saw it off square at each end and roll it on level kids, and if it be not straight, lay the rounding side down and view it, to find the spot for the centre at each end. Set the big compasses to half its diameter and sweep a circle at each

end,* 2.264 plum a line across each centre, and at each side at the circle, striking chalk lines over the plum lines at each side from end to end, and dress the sides plum to these lines; turn it down on one side, setting it level; plum, line, and dress off the sides to a 4 square; set it exactly on one corner, and plum, line, and dress off the corner to 8 square. In the same manner dress it to 16 square.

To cut it square off to its exact length, stick a peg in the centre of each end, take a long square (that may be made of boards) lay it a∣long the corner, the short end against the end of the peg, mark on the square where the shaft is to be cut, and mark the shaft by it at every corner line, from mark to mark; then cut it off to the lines, and it will be truly square.

Art. 12. To lay out the Mortises for the Arms.

FIND the centre of the shaft at each end, and strike a circle, plum a line through the centre at each end to be in the middle of two of the sides; make another scribe square across it, divide the distance equally between them, so as to divide the circle into 8 equal parts, and strike a line from each of them, from end to end, in the middle of the sides; measure from the top end about 3 feet, and mark for the arm of the water-wheel, and the width of the wheel, and make another mark. Take a straight edge 10 feet pole, and put the end even

with the end of the shaft,* 2.265 and mark on it even with the marks on the shaft, and by these marks measure for the arm at every corner, marking and lining all the way round. Then take the uppermost arms of each rim, and by them lay out the mortises, about half an inch longer than they are wide, which is to leave key room; set the compasses a little more than half the thickness of the arms, and set one foot in the centre line at the end of the mortise, striking a scribe each way for to lay out the width by: this done, lay out 2 more on the opposite side, to complete the mortises through the shaft. Lay out 2 more square across the first, one quarter the width of the arm, longer inward, towards the middle of the wheel. Take no∣tice which way the locks of the arms wind, whether to right or left, and lay out the third mortises to suit, else it will be a chance whether they suit or not: these must be half the width of the arms, longer inwards.

The 4th set of mortises must be 3-4 longer in∣wards than the width of the arms: the mor∣tises should be made rather hollowing than rounding, that the arms may slip in easily and stand fair.

If there be 3 (which are called 6) arms to the cog-wheel, but 1 of them can be put thro' the sides of the shaft fairly; therefore, to lay out the mortises, divide the end of the shaft a∣••ew, into but 6 equal parts, by striking a circle and each end; and without altering the com∣passes, step from one of the old lines, six steps round the circle, and from these points strike chalk lines, and they will be the middle of the mortises, which may be laid out as before,

minding which way the arms lock,* 2.266 and mak∣ing 2 of the mortises 1-3 longer than the width of the arm, extending 1 on one side, and the other on the other side of the middle arm.

If there be but 2 (called 4) arms in the cog-wheel, (which will do where the number of cogs do not exceed 60) they will pass fairly through the sides, whether the shaft be 12 or 16 sided, One of these must be made one half longer than the width of the arms, to give room to put the arm in.

Art. 13. To put in the Gudgeons.

STRIKE a circle on the ends of the shaft to let on the end bands; make a circle all round 2 1-2 feet from each end, and saw a notch all round half an inch deep. Lay out a square round the centres the size of the gud∣geons, near the neck; lay the gudgeons straight on the shaft, and scribe round them for their mortises; let them down within an 1-8 of an inch of being in the centre. Dress off the ends to suit the bands; make 3 keys of good season∣ed white oak, to fill each mortise above the gudgeons, to key them in, those next to the gudgeons to be 3 1-4 inches deep at their inner end, and 1 1-2 inch at their outer end, the wedge or driving key 3 inches at the head, and 6 inches longer than the mortice, that it may be cut off if it batters in driving; the piece next the band so wide as to rise half an inch a∣bove the shaft, when all are laid in. Then take out all the keys and put on the bands,

and make 8 or 12 iron wedges about 4 inches long by 2 wide,* 2.267 1-3 inch thick at the end, not much tapered except half an inch at the small end, on one side next the wood; drive them in 〈◊〉〈◊〉 each side the gudgeon exceeding hard at a proper distance with a set. Then put in the keys again, and lay a piece of iron under each 〈◊〉〈◊〉 between it and the key 6 inches long, half an inch thick in the middle, and tapering off at the ends; then grease the keys well with allow and drive it well with a heavy sledge: after this drive an iron wedge half an inch from the two sides of each gudgeon 5 inches long, near half an inch thick, and as wide as the gudgeon.

Art. 14. Of Cog-wheels.

THE great face cog-wheels require 3 (cal•••••• 6) arms, if the number of cogs exceed 54, 〈◊〉〈◊〉 4 will do. We find by the table, exam∣ple 43, that the cog-wheel must have 69 cogs, with 4 1-2 inches pitch, the diameter of its pitch circle 8 feet 2 1-3 inches, and of its out∣sides 8 feet 10 1-3 inches. It requires 3 arms 〈◊〉〈◊〉 feet long, 14 by 3 3-4 inches; 12 cants 6 1-2 feet long, 16 by 4 inches. See it represented 〈◊〉〈◊〉 V, fig. 1.

To frame it, dress and lock the arms toge∣ther (as fig. 6) as directed art. 10, only mind 〈◊〉〈◊〉 leave 1-3 of each arm uncut, and to lock 〈◊〉〈◊〉 the right way to suit the winding of the mortises in the shaft, which is best found by fitting a strip of board in the middle mortise,

and, supposing it to be the arm, mark which way it should be cut, then apply the board to the arm and mark it, The arms being laid on a truckle as directed art. 10, make a sweep the sides directing to the centre, 2 feet from the out end to scribe by; measure on the sweep half the diameter of the wheel, and by it circle out the back edges of the cants, all of one width in the middle; dress them, keeping the best faces for the face side of the wheel; make a circle on the arms 1-2 an inch larger than the diameter of the wheel, laying 3 of the cants with their ends on the arms at this circle at equal distance apart. Lay the other three on the top of them, so as to lap equally, scribe them both under and top, and gauge all for the laps from the face side; dress them out and lay them together, and joint them close; drawpin them by an inch pin near their inside corners: this makes one half of the wheel shewn fig. 5. Raise the centre level with that half, strike a circle near the out∣side, and find the centre of one of the cants; then, with the sweep that described the circle, step on the circle six steps, beginning at the middle of the cant, and these steps will shew the middle of all the cants or places for the arms. Make a scribe from the centre across each; strike another circle exactly at the cor∣ners, to place the corners of the next half by, and another about 2 1-2 inches farther out than the inside of the widest part of the cant, to let the arms in by; lay on three of the up∣per cants, the widest part over the narrowest part of the lower half, the inside to be at the point where the corner circle crosses the cen∣tre

lines. Saw off the ends at the centre scribes,* 2.268 and fit them down to their places, doing the same with the rest. Lay them all on and joint their ends together; draw-pin them to the lower half by inch pins, 2 inches from their in∣most edges, and 9 inches from their ends. Raise the centre level with the wheel; plane a little of the rough off the face, and strike the pitch circle and another 4 inches inside for the width of the face; strike another very near it, in which drive a chisel half an inch deep all 〈◊〉〈◊〉, and strike lines with chalk in the middle of the edge of the upper cants, and cut out of the solid half of the upper cants, which raises the face; divide the pitch circle into 69 equal parts, 4 1-2 inches pitch, beginning and ending in a joint; strike two other circles each 2 1-2 inches from the pitch circle, and strike central scribes between the cogs, and where they cross the circles put in pins, as many as there is cogs, half on each circle; find the lowest part on the ••••ce, and make the centre level with it; look across in another place square with the first, and make it level with the centre also: then make the face straight from these 4 places, and it will be true.

Strike the pitch circle and divide it over a∣gain, and one of each side of it, 1 inch distance for the cog mortises; sweep the outside of the wheel and inside of the face, and two circles 3-4 of an inch from them, to dress off the cor∣ners; strike a circle of two inches diameter on the centre of each cog, and with the sweep strike central scribes at each side of these cir∣cles for the cog-mortises; bore and mortise half through; turn the wheel, dress and mor∣tise

the back side,* 2.269 leaving the arms from under it; strike a circle on the face edge of the arms, equal in diameter to that struck on the face of the half wheel, to let them in by; saw in square and take out 4 1-2 inches, and let them into the back of the wheel 1 1-4 inch deep, and bore a hole 1 1-2 inch into each arm, to pin it to the wheel.

Strike a circle on the arms one inch less than the diameter of the shaft, make a key 8 inches long, 1 1-2 thick, 3 1-4 at the but, and 2 1-2 inches at the top end, and by it lay out the mortises, two on each side of the shaft, in each arm to hang the wheel by.

Art. 15. Of Sills, Spur-blocks, and Head-blocks.

SEE a side view of them in plates I, II, III, and IV, and a top view of them with their keys at the end of the shaft, plate VI. The sills are generally 12 inches square. Lay them on the wall as firm as possible, and one 3 feet farther out, on these lay the spurs, which are 5 feet long, 7 by 7 inches, 3 feet apart, notched and pinned to the sills; on these are set the head-blocks, 14 by 12 inches, 5 feet long, let down with a dovetail shoulder be∣tween the spurs, to support keys to move it endways, and let 2 inches into the spurs with room for keys, to move it sideways, and hold it to its place; See fig. 33 and 34, plate VI. The ends of the shaft are let 2 inches into the headblocks, to throw the weight more on the centre.

Provide two stones 5 or 6 inches square,* 2.270 ve∣ry hard and clear of grit, for the gudgeons to 〈◊〉〈◊〉 on, let them into the head-blocks, put the cog-wheel into its place, and then put in the shaft on the head-blocks in its place.

Put in the cog-wheel arm, lock them to∣gether and pin the wheel to them; then hang the wheel first by the keys, to make it truly round, and then by side wedges, to make it true in face; turn the wheel and make two circles one on each side of the cog-mortises, half an inch from them, so that the head of the cogs may stand between them equally.

Art. 16. Of Cogs; the best Time for cutting and Way of seasoning them.

THEY should be cut 14 inches long, 3 1-4 inches square, when the sap runs at its fullest, which should be done at least a year before they are used, that they may dry without cracking. If either hickory or whiteoak is 〈◊〉〈◊〉 when the bark is set, they will worm-eat, and if dryed hastily will crack; to prevent which boil them and dry them slowly, or soak them in water, a year, (20 years in mud and water would not hurt them;) when they are taken out they should be put in a hay-mow under the hay, which, when foddered away they will dry without cracking; but this often takes too long time. I have discovered the following method of drying them in a few days without cracking: I have a malt-kiln

With a floor of laths two inches apart.* 2.271 I shank the cogs, hang them shank downwards, be∣tween the laths, cover them with the hair∣cloth, make a wood fire and the smoke pre∣serves them from cracking. Some dry them in an oven which ruins them. Boards, planks, or scantling are best dried in a kiln, covered so as to keep the smoke amongst them.

Art. 17. Of shanking, putting in, and dressing off Cogs.

STRAIGHTEN one of the heart sides for the shank, make a pattern the head 4, and shank 10 inches long, and 2 inches wide at the head, 1 3-4 at the point; lay it on the cog, scribe the shank and shoulders for the head, saw in and dress off the sides; make an∣other pattern of the shank, without the head, to scribe the sides and dress off the backs by, laying it even with the face, which is to have no shoulder; take great care in dressing them off, that the axe does not strike the shoulder, if it does it will crack there in drying (if they be green); fit and drive them in the mortises exceeding tight, with their shoulders foremost when at work. When the cogs are all in, ••ix two pieces of scantling for rests, to scribe the cogs by, one across the cog-pit near the cogs, another in front of them, fix them firm. Hold a pointed tool on the rest, and scribe for the length of the cogs by turning the wheel, and saw them off 3 1-2 inches long; then move the rest close to them, and fix it firm; find the pitch circle on the end of the cogs, and by turning the wheel describe it there.

Describe another 1-4 of an inch outside thereof,* 2.272 for to set compass in to describe the face of the cogs by, and another at each side of the cogs to dress them to their width; then pitch the cogs by dividing them equally, 〈◊〉〈◊〉 that in stepping round the compasses may 〈◊〉〈◊〉 in the point where they began; describe a circle in some particular place with the pitch that it may not be lost; these points must be as near as possible, of a proper dis∣tance for the centre from the back of the 〈◊〉〈◊〉; find the cog that this point comes near∣est to the back, and set the compasses from 〈◊〉〈◊〉 point to the back of the cog, and with 〈◊〉〈◊〉 distance set off the backs of all the cogs 〈◊〉〈◊〉, on the circle 1-4 of an inch outside of 〈◊〉〈◊〉 pitch circle, and from these points last 〈◊〉〈◊〉, set off the thickness of the cogs, which 〈◊〉〈◊〉 be 2 1-8 inches in this case.

Then describe the face and back of the cogs 〈◊〉〈◊〉 setting the compasses in the hindmost point 〈◊〉〈◊〉 one cog, and sweeping over the foremost 〈◊〉〈◊〉 of another for the face, and in the fore∣most point of one, sweeping over the hindmost 〈◊〉〈◊〉 the other, for the back part; dress them off 〈◊〉〈◊〉 all sides, tapering about 1-8 of an inch in an 〈◊〉〈◊〉 distance, try them by a gauge to make 〈◊〉〈◊〉 all alike, take a little of the corners off, 〈◊〉〈◊〉 they are finished.

Art. 18. Of the little Cog-wheel and Shaft.

THE process of making this is similar to 〈◊〉〈◊〉 of the big cog-wheel. Its dimensions we 〈◊〉〈◊〉 by the table, and the same example 43, to

be 52 cogs,* 2.273 4 1-4 pitch. Diameter of pitch cir∣cle 5 feet 10 1-3 inches, and from out to out 6 feet 6 inches.

It requires 2 arms 6 feet 6 inches long, 11 by 3 1-4 inches; 8 cants 5 feet 6 inches, 17 by 3 1-2 inches. See it plate V, fig. 4.

Of the Shaft.

Dress is 8 feet long, 14 by 14 square, and de∣scribe a circle on each end 14 inches diameter; strike two lines through the centre parallel to the sides and divide the quarters into 4 equal parts each; strike lines across the centre at each part at the end of these lines; strike chalk lines from end to end to hew off the corners by, and it will be 8 square; lay out the mortises for the arms, put on the bands, and put in the gud∣geons, as with the big shaft.

Art. 19. Directions for making Wallowers and Trundles.

By example 43 in the table, the wallower is to have 26 rounds 4 1-2 pitch. Diameter of its pitch circle is 3 feet 1 1-4 inch, and 3 feet 4 1-4 inches from outsides: see fig. 3 plate V. Its heads should be 3 1-2 inches thick, doweled truly together, or made double with plank crossing other. Make the bands 3 inches wide, 1-6 of an inch thick evenly drawn; the heads must be made to suit the bands, by setting the compasses so that they will step round the inside of the band in 6 steps; with this distance sweep

the head,* 2.274 allowing about 1/16 of an inch outside in dressing to make such a large band tight. Make them hot alike all round with a chip fire, which swells the iron; put them on the head while hot, and cool them with water to keep them from burning the wood too much, but not too fast, lest they snap: the same for hoop∣ing all kinds of heads.

Dress the head fair after banded, and strike the pitch circle and divide it by the same pitch of the cogs; bore the holes for the rounds with a•• auger at least 1 1-2 inch; make the rounds of the best wood 2⅜ inches diameter, and 11 inches between the shoulders, the tenons 4 inches, to fit the holes loosely until within one inch of the shoulder, then drive tight. Make the mortises for the shaft in the heads, with notches for the keys to hand it by. When the rounds are all drove in to the shoulders, observe whether they stand straight, if not, they may be set fair by putting the wedges nearest to one side of the tenon, so that the strongest part may incline to draw them straight: this should be done with both heads.

Art. 20. Of fixing the Head-blocks and hanging the Wheels.

THE head-blocks for the wallower shaft, are shewn in plate VI. Number 19 is one cal∣led a spur, 6 feet long and 15 inches deep, one end of which at 19 is let one inch into the 〈◊〉〈◊〉 of the husk-sill, which sill is 1 1-2 inch above 〈◊〉〈◊〉 floor, the other end tenoned strongly into

a strong post 14 by 14 inches,* 2.275 12 or 14 feet long, standing near the cog-wheel on a sill in the bottom of the cog-pit; the top is tenoned into the husk-plank; these are called the tom∣kin posts. The other head-blocks appears at 20 and 28. In these large head-blocks there is small ones let in, that are 2 feet long and 6 inches square, with a stone in each for the gud∣geons to run on. That one in the spur 19 is made to slide, to put the wallower out and in gear by a lever screwed to its side.

Lay the centre of the little shaft level with the big one, so as to put the wallower to gear 2-3 the thickness of the rounds deep into the cog-wheel; put the shaft into its place and hang the wallower, and gauge the rounds to equal distance where the cogs take. Hang the cog-wheel, put in the cogs, make the trundle as directed for the wallower. See plate V fig. 4.

Art. 21. Directions for putting in the Balance-Ryne.

LAY it in the eye of the stone, and fix it truly in the centre; to do which make a sweep by putting a long pin through the end to reach into and fit the pivot hole in the balance-ryne, by repeated trials on the opposite sides fix it in the centre; then make a particular mark on the sweep and others to suit it on the stone, scribe round the horns, and with picks and chisels sink the mortises to their proper depth, trying by the sweep if it be in the cen∣tre,

by the particular marks made for the pur∣pose.* 2.276 Put in the spindle with the foot up∣wards and the driver on in its place, while one holds it plum. Set the driver over two of the horns, if it has four, but between them if it has but two. When the neck is exactly in the centre of the stone, scribe round the horns of the driver, and let it into the stone, nearly to the balance, if it has four horns. Put the top of the spindle in the pivot-hole to try whether the mortises lets it down freely on both sides.

Make a tram to set the spindle square by, as follows: take a piece of board, cut a notch in one side, at one end, and hang it on the top of the spindle, by a little peg put in the shoulder of the notch, to go in the hole in the foot to keep it on, let the other end reach down to the edge of the stone, take another piece, circle out one end to fit the spindle neck, and make the other end fast to the low∣er end of the hanging piece near the stone, so as to play round level with the face of the stone, resting on the centre-hole in the foot, and against the neck, put a bit of quill through the end of the level piece, that will touch the edge of the stone as it plays round. Make little wedge and drive them in behind the horns of the driver, to keep both ends at once close to the sides of the mortises they bear against when at work, keeping the pivot or cock-head in its hole in the balance, try the tram gently round, and mark where the quill touches the stone first, and dress off the bear∣ing sides of the mortises for the driver until it will touch equally all round, giving the driver liberty to move endways and sideways to let

the stone rock an inch any way.* 2.277 The ryne and driver must be sunk 3-4 of an inch below the face of the stone. Then hang the trundle firmly and truly on the spindle, put it in its place to gear in the little cog-wheel.

Art. 22. To Bridge the Spindle.

MAKE a little tram of a piece of lath, 3 inches wide at one end, and 1 inch at the other, make a mortise in the wide end, and put it on the cock-head, and a piece of quill in the small end, to play round the face of the stone: then, while one turns the trundle, an∣other observes where the quill touches first, and alters the keys of the bridge-tree, driv∣ing the spindle-foot towards the part the quill touches, until it touches equally all round. Case the stone neatly round within 2 inches of the face.

Art. 23. Of the Crain and Lighter-Staff.

MAKE a crain for taking up and putting down the stone, with a screw and bale. See it represented in Evans's part, pl. XI. fig. 2 and 3. Set the post out of the way as much as possible, let it be 9 by 6 inches in the middle, the arm 9 by 6, brace 6 by 4, make a hole plum over the spindle, for the screw, put an iron washer on the arm under the female screw, nail it fast the screw should be above half the diameter of the stone, in the worm,

and 10 inches below it,* 2.278 the bale to touch only at the ends to give the stone liberty to turn, the pins to be 7 inches long, 1 1-8 thick, the able to be 2 1-2 inches wide in the middle, 〈◊〉〈◊〉 1 3-4 an inch thick at the end: all of the best iron, for if either of them break the danger would be great. The holes in the 〈◊〉〈◊〉 should be nearest the upper side of it. ••••ise the runner by the crane, screw and bale, turn it and lay it down, with the horns of the living-ryne in their right places, as marked, being down, as appears in pl. IX. fig. 9. 〈◊〉〈◊〉 the lighter staff C C to raise and lower 〈◊〉〈◊〉 stone in grinding, about 6 feet long, 3 1-2 〈◊〉〈◊〉 2 1-2 inches at the large end, and 2 inches 〈◊〉〈◊〉 at the small end, with a knob on the ••••••er side. Make a mortise through the butt 〈◊〉〈◊〉 for the bray-iron to pass through, which 〈◊〉〈◊〉 into a mortise 4 inches deep in the end of the bray at b, fastened with a pin; it may be 2 inches wide, 1-2 an inch thick, a plain 〈◊〉〈◊〉 with one hole at the lower end, and 5 or 6 〈◊〉〈◊〉 the upper end, set in a staggering position. This lighter is fixed in front of the meal-beam, 〈◊〉〈◊〉 a proper height to be handy to raise or lower 〈◊〉〈◊〉 pleasure; a weight of 4lb. is hung to the end 〈◊〉〈◊〉 it by a strap, that laps two or three times 〈◊〉〈◊〉 and the other end fastened to the post below, that keeps it in its place. Play the lighter up and down, and observe whether the stone rises and falls flat on the bed-stone, if it 〈◊〉〈◊〉, draw a little water, and let the stone ••••ve gently round, then see that all things be light, and draw a little more water, let the one run at a middling rate, and grind the faces a few minutes.

Art. 24. Directions for making a Hoop for the Mill-Stone.

TAKE a white pine or poplar board, 8 inch∣es longer than will go round the stone, and 2 inches wider than the top of the stone is high, dress it smooth, and gauge it one inch thick, run a gauge-mark 1-6 of an inch from the outside, divide the length into 52 parts, and saw as many saw-gates square across the in∣side to the gauge-line. Take a board of equal width, 1 foot long, nail one half of it on the outside at one end of the hoop, lay it in 〈◊〉〈◊〉 a day or two to soak, or sprinkle the outside well an hour or two with hot water. Read it round so that the ends meet, and nail the other end to the short board, put sticks 〈◊〉〈◊〉 inside in every direction to press out the 〈◊〉〈◊〉 that bend least, and make it truly round. Make a cover for the hoop such as is represent∣ed in plate VII, fig. 23,8 square inside, and 1 inch outside the hoop. It consists of 8 pieces lapped over one another, the black lines shew∣ing the joints as they appear when made, the dotted lines the under parts of the laps. De∣scribe it on the floor, and make a pattern to make all the rest by; dress all the laps, fit and nail them together by the circle on the floor, and then nail it on the hoop; put the hoop over the stone and scribe it to fit the floor in its place.

Art. 25. Of grinding Sand to Face the Stones.

LAY boards over the hoop to keep the dust 〈◊〉〈◊〉 flying, and take a bushel or two of dry, 〈◊〉〈◊〉 sharp sand, team it gently in the eye, 〈◊〉〈◊〉 the stones move at a moderate rate, con∣••••••ing to grind for an hour or two; then take of the stone, sweep them clean, and pick the smoothest hardest places, and lay the stone 〈◊〉〈◊〉 again, and grind more sand as before, 〈◊〉〈◊〉 off the back (if it be a bur) taking 〈◊〉〈◊〉 care that the chisel does not catch; 〈◊〉〈◊〉 up the stone again, and make a red 〈◊〉〈◊〉, in length the diameter of the stone, only 2 1-2 inches, paint it with red paint and 〈◊〉〈◊〉, and rub it over the face of the stones in directions, the red will be left on the highest and hardest parts, which must be pecked down, taking the bed-stone perfectly plain, and the 〈◊〉〈◊〉 a little concave about 1-6 of an inch at 〈◊〉〈◊〉 eye, and lessening gradually to about 8 inches from the skirt. If they be close and have much face they need not touch or flour so far, as if they are open and have but little face: those things are left to the judgment of the mill-wright and miller.

Art. 26. Directions for laying out the Furrows in the stones, &c.

IF they be 5 feet diameter, divide the skirt into 16 equal parts, called quarters, if 6 feet, into 18, if 7 feet, into 20 quarters. Make two strips of board, one an inch, and the other 2

inches wide;* 2.279 stand with your face to the eye, and if the stone turns to the right when at work, lay the strip at one of the quarter divisi∣ons, and the other at the left hand side close so the eye, and mark with a spike flated for a master furrow; they all are laid out the 〈◊〉〈◊〉 way in both stones, for when their faces are to∣gether the furrows should cross other like 〈◊〉〈◊〉 in the best position for cutting cloth. The•• having not less than 6 good picks, proceed to pick out all the master furrows, making the edge next the skirt and the other end next the eye the deepest, the feather edge not half so deep as the back.

When all the master furrows are picked out, lay the broad strip next to the feather edges of all the furrows, and mark the heal lands of the short furrows, then lay the same strip next the back edges, and mark for this lands, and lay the narrow strip, and mark for the furrows, and so on mark out all the lands and furrows, minding not to cross the hea•••• lands, but leaving it between the master fur∣rows and the short ones of each quarter. But if they be close country stones, lay out both fur∣rows and land with the narrow strip.

The neck of the spindle must not be wedg∣ed too tight else it will burn loose; bridge the spindle again; put a collar round the spindle neck, but under it put a piece of an old stock∣ing, with tallow rolled up in it, about a fin∣ger thick, tack it close round the neck; put a piece of stiff leather about 6 inches diameter on the cock-head under the driver, to turn with the spindle and drive off the grain, &c. from the neck; grease the neck with tallow every time the stone is up.

Lay the stone down and turn off the back smooth,* 2.280 and grind more sand. Stop the mill; raise the stone a little, and balance it truly with weight laid on the lightest side. Take 〈◊〉〈◊〉 equal to this weight, melt it, and run it into a hole made in the same place in the plaister, largest at bottom to keep it in, fill the 〈◊〉〈◊〉 with plaister: take up the runner again, by the staff over them, and if in good face give them a nice dressing, and lay them down to grind wheat.

Art. 27. Directions for making a Hopper, Shoe and Feeder.

THE dimension of the hopper of a com∣mon mill is 4 feet at the top, and 2 feet deep, 〈◊〉〈◊〉 hole in the bottom 3 inches square, with a 〈◊〉〈◊〉 gate in the bottom of the front, to les∣•••• it at pleasure: the shoe 10 inches long, and 5 wide in the bottom, of good sound oak. The side 7 or 8 inches deep at the hinder end, 〈◊〉〈◊〉 inches at the foremost end, 6 inches longer 〈◊〉〈◊〉 the bottom at the fore end, slanting more than the hopper behind, so that it may have li∣berty to hang down 3 or 4 inches at the fore end, which is hung by a strap, called the feeding-string, passing over the fore end of the hop∣per-frame, and lapping round a pin in front of the meal-beam, that will turn by the hand, called the feeding-screw.

The feeder is a piece of wood turned in a 〈◊〉〈◊〉, about 20 inches long, 3 inches diameter in the middle against the shoe, tapered off to 1 1-2 inches at the top; the lower end is handed and a forked iron drove in it, that

spans over the ryne fitting into notches made on each side,* 2.281 to receive it right above the spindle, and turns with it; the upper end run∣ning in a hole in a piece across the hopper-frame. In the large part next the shoe are set 6 iron knockers, 7 inches long, half an inch diameter, with a tang at each end, turned square to drive into the wood, th••se knock against, and shake the shoe, and there by shake in the grain regularly.

Then put grain into the hopper, draw wa∣ter on the mill, regulate the feed by turning the feed-screw, until the stream falling into the eye of the stone, is proportioned to the size thereof, or the power of the mill. Here ends the mill-wrights work, with respect to grinding, and the miller takes charge thereof.

Art. 28. Of Bolting-chests and Reels.

BOLTING chests and reels are of dif∣ferent lengths, according to the use they are for. Common country chests (a top view of one of which is shewn pl. VII. fig. 9.) are commonly about 10 feet long, 3 feet wide, and 7 feet 4 inches high, with a post in each corner, the bottom 2 feet from the floor, with a board 18 inches wide, set slanting in the back side, to cast the meal forward in the chest, to make it easily taken up; the door of the whole length of the chest, and two feet wide, the bottom side board below the door 16 inches wide.

The shaft of the reel equal in length with the chest,* 2.282 4 inches diameter, 6 square, two bands 〈◊〉〈◊〉 each end, 3 1-4 and 3 3-4 diameter, gud∣geons 13 inches long, 7-8 of an inch diameter; 〈◊〉〈◊〉 inches in the shaft, round 2 1-2 inches at the neck, with a tenon for a socket or handle, 〈◊〉〈◊〉 ribs 1 1-2 inch deep, 1 1-8 inch thick, half 〈◊〉〈◊〉 inch shorter at the tail, and 1 1-2 inch at the head, than the shaft, to leave room for the meal to be spouted in at the head, and the 〈◊〉〈◊〉 to fall at the tail; four ••ets of arms, that 〈◊〉〈◊〉 12 of them, 1 1-2 inch wide, and 5-8 thick. The diameter of the reel from out to out of 〈◊〉〈◊〉 ribs, is one third part of the double width 〈◊〉〈◊〉 the cloth. A round wheel of inch boards, 〈◊〉〈◊〉 diameter equal to the outside of the ribs, 〈◊〉〈◊〉 1-2 inches wide, measuring from the outside towards the centre, (which is taken out) is to 〈◊〉〈◊〉 framed to the head of the reel, to keep the 〈◊〉〈◊〉 from falling out at the head unbolted. But a hoop 4 1-2 inches wide, and 1-4 thick, 〈◊〉〈◊〉 the tail, to fasten the cloth to. The 〈◊〉〈◊〉 is sewed two widths of it together, to each round the reel; putting a strip of strong then 7 inches wide at the head, and 5 inches 〈◊〉〈◊〉 the tail of the cloth, to fasten it to the reel 〈◊〉〈◊〉. Paste a strip of linen, soft paper, or sham∣••y leather (which is the best) 1 1-2 inch wide 〈◊〉〈◊〉 each rib, to keep the cloth from freting. Then put the cloth on the reel tight, and sew a nail it to the tail and stretch it length ways 〈◊〉〈◊〉 hard as it will bear, nailing it to the head. N. B. 6 yards of cloth covers a 10 feet reel. Bolting reels for merchant are generally ••••ger than for country work, every part should be stronger in proportion as necessary. They

are best when made to suit the wide cloths.* 2.283 The socket gudgeons at the head should be much stronger, they being apt to wear out and troublesome to repair.

The bolting hopper is made through the floor above the chest, 12 inches square at the upper and 10 inches at the lower end; the foremost side 5 inches and the back side 7 inches from the top of the chest.

The shoe 2 feet long at the bottom of the side pieces, slanting to suit the hopper at the hinder end, set 4 inches higher at the hinder than the fore end, the bottom 17 inches long and 10 inches wide. There should be a bow of iron riveted to the fore end to rest on the top of the knocking wheel, fixed on the socket gud∣geon at the head of the chest, which is 10 inch∣es diameter, 2 inches thick, with 6 half rounds cut out of its circumference by way of knock∣ers, to strike against the bow, and lift the shoe 3-4 of an inch every stroke to shake in the meal.

Art. 29. Of setting Bolts to go by Water.

THE bolting reels are set to go by water as follows:

Make a bridge 6 by 4 inches, and 4 inches longer than the distance of the tomkin posts, described art. 20; set it between them on rests fastened into them, 10 inches below the cogs of the cog-wheel, and the centre of it half the di∣ameter of the spur-wheel in front of them; on this bridge is set the step gudgeon, of an up∣right

shaft,* 2.284 with a spur-wheel of 16 or 18 cogs to gear into the cog-wheel. Fix a head-block to the joists of the 3rd floor for the upper and of this shaft, put the wheel 28, plate VII on 〈◊〉〈◊〉 hang another head-block to the joists of the 2nd floor near the corner of the mill at 6, for the step of the short upright shaft that is to 〈◊〉〈◊〉 fixed there, to turn the reels 1 and 9. Hang another head-block to the joists of the 3rd 〈◊〉〈◊〉 for the upper end of the said short upright, 〈◊〉〈◊〉 fix also head-blocks for the short shaft at the head of the reels, so that the centres of all those shafts will meet. Then fix a hanging left in the corner 5, for the gudgeon of the 〈◊〉〈◊〉 horizontal shaft 27—5 to run in. After the head-blocks are all fixed, then measure the length of each shaft, and make them as fol∣lows, viz.

The upright shaft 5 1-2 inches for common 〈◊〉〈◊〉, but if for merchant work, with Evans's elevators; &c. added, make it larger 6 or 7 inches: the horizontal shaft 27—5 and all the others 5 inches diameter. Put a socket-gud∣geon in the middle of the long shafts to keep them steady; make them 8 or 16 square, expect at the end where the wheels are hung, where they must be 4 square. Band their ends, put in the gudgeons, put them in their proper plac∣es in the head-blocks, to mark where the wheels are to be put on them.

Art. 30. Of making Bolting Wheels.

MAKE the spur-wheel for the first upright with a 4 1-2 inch plank, the pitch of the cogs

the same as the cog-wheel,* 2.285 into which it is to work, put two bands 3-4 of an inch wide, one on each side of the cogs, and a rivet between each cog to keep the wheel from spliting.

To proportion the cogs in the wheels to give the bolts the right motion, the common way is—

Hang the spur-wheel and set the stones to grind with a proper motion, and count the re∣volutions of the upright shaft in a minute, and compare its revolutions with the revolutions that a bolt should have, which is about 36 revo∣lutions a minute. If the upright goes 1-6 more, put 1-6 less in the first driving-wheel than in the leader, suppose 15 in the driver the 18 in the leader: but if their difference be more (fast one half) there must be a difference in the next two wheels; observing, that if the motion of the upright shaft be greater than the bolt should be, then the driving-wheel must be proportion∣ably less than the leader; but if it be slower, then the driver must be greater in proportion. The common size of bolting wheels is from 14 to 20 cogs; if less than 14 the head-blocks will be too near the shafts.

Common bolting wheels should be made of plank at least 3 inches thick, well seasoned, and are best to be as wide as the diameter of the wheel, and banded with bands near as wide as the thickness of the wheel, made ge∣nerally of rolled iron, about 1-8 of an inch thick. Some make them of 2 inch plank, cros∣sed and no bands: but this proves no saving, as they are apt to go to pieces in a few years. For hooping wheels see art. 19, and for find∣ing the diameter of the pitch circle see art. 9.

The wheels are generally 2 inches more in di∣ameter than the pitch circle if banded;* 2.286 but if 〈◊〉〈◊〉, they should be more. The pitch or dis∣tance of the cogs are different, if to turn 1 or 〈◊〉〈◊〉 bolts 2 1-2 inches, but if more, 2 3-4: but if ••••ch heavy work, they should be not less than 3 inches. Their cogs are half the pitch in thickness, the shank to drive tight in an inch 〈◊〉〈◊〉 hole.

When the mortises are made for the shafts 〈◊〉〈◊〉 the head, and notches for the keys to hang 〈◊〉〈◊〉, drive the cogs in and pin their shanks at 〈◊〉〈◊〉 side, and cut them off half an inch from 〈◊〉〈◊〉 wheel.

Hang the wheels on the shafts so that they will gear a proper depth, about 2-3 the thick∣ness of the cogs; dress all the cogs to equal distance by a gauge; then put the shafts in their places, the wheels gearing properly, and 〈◊〉〈◊〉 head-blocks all secure, set them in moti∣on by water. Bolting reels should turn to drop 〈◊〉〈◊〉 meal on the back side of the chest, as it 〈◊〉〈◊〉 then hold more, and will not cast out the 〈◊〉〈◊〉 when the door is opened.

Art. 31. Of Rolling-screens.

THESE are circular sieves moved by water, and are particularly useful in cleaning wheat 〈◊〉〈◊〉 merchant work. They are of different constructions.

1st. Those of one coat of wire with a screw 〈◊〉〈◊〉 them.

2nd. Those of two coats, the inner one nail∣•••• to 6 ribs, the outer one having a screw be∣tween it and the inner one.

3rd.* 2.287 Those of a single coat and no screw.

The first kind answers well in some, but not in all cases, because they must turn a certain number of times before the wheat can get out, and the grain has not so good an opportunity of separating, there being nothing to change its position, it floats a considerable way with the same grains uppermost.

The double kind are better because they may be shorter and take up less room; and worse, for being more difficult to be kept clean.

The 3rd kind has this advantage; we can keep the grain in it a longer or shorter time at pleasure, by raising or lowering the tail end, and is also tossed about more; but they must be longer. They are generally 9 or 10 feet, long, 2 feet 4 inches diameter, if to clean for 2 or 3 pair of stones, but if for more, they should be larger accordingly: will clean for from 1 to 6 pair of stones. They are made 6 square, with 6 ribs, which lie flatwise, the outer cor∣ners taken off to leave the edge 1-4 of an inch thick; the inner corners so as to bring it near∣ly to sharp edges, the wire work nailed 〈◊〉〈◊〉 with 14 ounce tacks.

They are generally moved by the same up∣right shaft that moves the bolts, by a wheel on its upper end with two sets of cogs: those that strike downwards gearing into a wheel striking upwards that turns a laying shaft, with two pulleys on the other end, one of 24 inches diameter, to turn a fan with quick mo∣tion, the other 8 inches, over which passes a strap to a pulley 24 inches diameter, on the gudgeon of the rolling screen, to reduce its motion to about 15 revolutions in a minute. See pl. VII. fig. 23. This may do for mills in the small

way,* 2.288 but where they are in perfection for mer∣chant-work, with elevators, &c. and have to clean wheat for 2,3 or 4 pair of stones, they should be moved by cogs.

Art. 32. Of Fans.

THE Dutch fan is a machine of great use 〈◊〉〈◊〉 blowing the dust and other light stuff from 〈◊〉〈◊〉 the wheat; there are various sorts of 〈◊〉〈◊〉; those that are only for blowing the 〈◊〉〈◊〉, as it falls from the rolling-screen, are generally about 15 inches long, and 14 inches 〈◊〉〈◊〉 in the wings, and have no riddle or then in them.

To give it motion, put a pulley 7 inches ••••eter on its axle for a band to run on, from the pulley on the shaft that moves the screen 24 inches diameter, to give it a swift 〈◊〉〈◊〉, when the band is slack it slips a little the small pulley, and the motion is slow; but 〈◊〉〈◊〉 tight, the motion is quicker; by this the 〈◊〉〈◊〉 is regulated.

Some use Dutch fans complete, with riddle 〈◊〉〈◊〉 screen under the rolling screen for mer∣chant-work, and again use the fan alone for ••••••try-work.

The wings of those, which are the common ••••••ers wind-mills or fans, are 18 inches long, 〈◊〉〈◊〉 20 inches wide, but are set in motion with pulley instead of a cog-wheel and wallower.

Art. 33. Of the Shaking Sieve

THEY are of considerable use in country mills, to sift indian meal, separating it into se∣veral degrees of fineness if required, and take the hulls out of buckwheat meal, that are apt to ••ut the bolting-cloth, and the dust out of the grain, if rubbed before ground; and are sometimes used to clean wheat or screenings instead of rolling screens.

If they are for sifting meal they are 3 feet 6 inches long, 9 inches wide, 3 1-2 inches deep; see it pl. VI. fig. 16. The wire work is 3 feet long, 8 inches wide; across the bottom of the tail end is a board 6 inches wide to the top of which the wire is tacked, and then this board and wire tacked to the bottom of the frame, leaving an opening at the tai••∣end for the bran to fall into the box 17, the meal falling into the meal-trough 15, the head-piece should be strong to hold the iron bow at 15, through which passes the lever that shakes the sieve, in the following manner. Take two pieces of hard wood 15 inches long and as wide as the spindle, and so thick that when one is put on each side just above the trundle, it will make it 1 1-2 inch thicker tha•• the spindle is wide. The corners of these and taken off to a half round, and they are tied to the spindle with a small strong cord. The•••• are for to strike against the lever that worse on a pin neat its centre, which is fastened 〈◊〉〈◊〉 the sieve, and shakes it as the trundle good round; see it represented pl. VI. This lever must always be put to the contrary side of the

spindle,* 2.289 that it is of the meal-spout, else it will draw the meal to the upper end of the 〈◊〉〈◊〉: there must be a spring fixed to the sieve 〈◊〉〈◊〉 draw it forward as often as it is driven 〈◊〉〈◊〉. It must hang on straps and be fixed so 〈◊〉〈◊〉 to be easily set to any descent required, by 〈◊〉〈◊〉 of a roller in form of the feeding screw, only longer, round which the strap winds.

Having now given directions for making and putting to work, all the machinery of one 〈◊〉〈◊〉 the completest of the old fashioned grist∣••••, that may do merchant-work in the small 〈◊〉〈◊〉, as represented by plates VI. VII. VIII. 〈◊〉〈◊〉 but not to near so much advantage as 〈◊〉〈◊〉 the late and new improvements, which 〈◊〉〈◊〉 shewn by plate X.

Art. 34. Of the Use of draughting Mills, &c.

PERHAPS some are of opinion that ••aughts are useless pictures of things, serving 〈◊〉〈◊〉 to please the fancy. This is not what ••••tend by them; but to give the reader true 〈◊〉〈◊〉 of the machines, &c. described, or to be 〈◊〉〈◊〉. They are all drawn on a small scale of 〈◊〉〈◊〉 of an inch for a foot, in order to suit the 〈◊〉〈◊〉 of the book, except plate V. which is 1-4 〈◊〉〈◊〉 an inch for a foot, and this scale I recom∣mend, as most buildings will come on the size 〈◊〉〈◊〉 a common sheet of paper.

N. B. Plate XII. was made after the above directions, and has its explanations to suit it. The great use of draughting mills, &c. to add by, is by conveying our ideas more

plain,* 2.290 than is possible to be done by writing or words, which may be misconstrued or forgot∣ten; but a draught, well drawn, speaks for it∣self, when once understood by the artist; who, by applying his dividers to the draught and to the scale, finds the length, breadth and height of the building, or the dimensions of any piece of timber, and its place in the building, &c.

By the draught, the bills of scantling, boards, rafters, laths, shingles, &c. &c. are known and made out; it should shew every wheel, shaft, and machine, and their places. By it we can find whether the house is suffici∣ent to contain all the works that are necessary to carry on the business; the builder or own∣er understands what he is about, and carries on cheerfully without error; it directs the mason where to put the windows, doors, navel-holes, the inner walls, &c. whereas, if there be no draught every thing goes on, as it were, in the dark; much time is lost and errors are committed to the loss of many pounds. I have heard a man say, he believed his mill was 500l. better, by having employed an experi∣enced artist, to draw him a draught to build it by. And I know by experience the great util∣ity of them. Every master builder ought at least, to understand them.

Art. 35. Directions for planning and draughting Mills.

1st. If it be a new seat, view the ground where the dam is to be, and where the mill house is to stand, and determine on the height

of the top of the water in the head-race where it is taken out of the stream;* 2.291 and level from it for the lower side of the race down to the seat of the mill-house, and mark the level of the water in the dam there.

2nd. Begin where the tail-race is to empty into the stream, and level from the top of the water up to the mill-seat, noticing the depth thereof in places as you pass along, which will be of use in digging it out.

Then find the total fall, allowing 1 inch to a rod for fall in the races, but if they are very wide less will do. Then, supposing the fall to be 21 feet 9 inches, which is sufficient for an overshot, mill, and the stream too light for an undershot, consider well what size stone will suit, for I do not recommend a large stone to a weak, nor a small one to a strong stream. I have proposed stones 4 feet diameter for light, and 4,6 for middling, and 5 or 5 feet 6 inches diameter for heavy streams. Suppose you determine on stones 4 feet, then look in table I, (which is for stones of that size) column 2, for the fall that is nearest 21 feet 9 inches, your fall, and you find it in the 7th example. Column 3 contains the head of water over the wheel 3 feet; 4th, the diameter of the wheel 18 feet; 5th, its width, 2 feet 2 inches, &c. for all the proportions to make the stone re∣volve 106 times in a minute.

Having determined on the size of the wheels and size of the house, heights of the stories to suit the wheels, and machinery it is to contain, and business to be carried on therein, proceed to draw a ground plan of the house, such as plate VI, which is 32 by 55 feet. See the de∣scription

of the plate.* 2.292 And for the second story, as plate VII, &c. for the 3rd, 4th and 5th floors, if required, taking care to plan eve∣ry thing for the best, and so as not to clash one with another.

Draw an end view, as plate VIII, and a side view, as plate IX. Take the draught to the ground and stake out the seat of the house. It is commonly best to set that corner of an overshot mill that the water comes in at far∣thest in the bank: but take great care to re∣consider and examine every thing more than once whether it be planned for the best; be∣cause, much labour is often lost for want of due consideration, and by setting buildings in, and laying foundations on wrong places. This done, you may from the draughts make out the bills of scantling and iron work.

Art. 36. Bill of Scantling for a Mill, 32 by 55 Feet, 3 Stories high, such as described Plate VI. VII. VIII. & IX. The Walls of Mason-work.

For the first Floor.

2 sills, 29 feet long, 8 by 12 inches, to lay on the walls for the joists to lay on.

48 joists, 10 feet long, 4 by 9 inches; all of timber that will last well in damp places.

For the second Floor.* 2.293

2 posts, 9 feet long, 12 by 12 inches.

2 girders, 30 feet long, 14 by 16 inches.

48 joists, 10 feet long, 4 by 9 inches.

For the Floor over the Water-house.

1 cross girder, 30 feet long, 12 by 14 inches, for one end of the joists to lay on.

2 posts to support the girder, 12 feet long, 12 by 12 inches.

16 joists, 13 feet long, 4 by 9 inches; all of good whiteoak or other timber that will last in damp places.

For the third Floor.

4 posts, 9 feet long, 12 by 12 inches, to sup∣port the girders.

2 girder-posts, 7 feet long, 12 by 12 inches, to stand on the water-house.

2 girders, 53 feet long, 14 by 16 inches.

90 joists, 10 feet long, 4 by 9 inches.

For the fourth Floor.

6 posts, 8 feet long, 10 by 10 inches, to support the girders.

2 girders, 53 feet long, 13 by 15 inches.

30 joists, 10 feet long, 4 by 8 inches for the mid∣dle tier of the floor.

60 joists, 12 feet long, 4 by 8, for the outside tiers, which extends 12 inches over the walls, for the rafters to stand on.

2 plates, 54 feet long, 3 by 10 inches: these lay on the top of the walls, and the joists on them.

2 raising pieces,* 2.294 55 feet long, 3 by 5 inches: these lay on the ends of the joists for the raf∣ters to stand on.

For the Roof.

54 rafters, 22 feet long, 3 inches thick, 6½ wide at bottom; and 4½ at top end.

25 colar beams, 17 feet long, 3 by 7 inches.

2760 feet of laths, running measure.

7000 shingles.

For Doors and Window-cases.

12 pieces, 12 feet long, 6 by 6 inches, for door-cases.

36 pieces. 8 feet long, 5 by 5 inches, for window-cases.

For the Water-house.

2 sills, 27 feet long, 12 by 12 inches.

1 sills. 14 feet long, 12 by 12 inches.

2 spur-blocks, 4 feet 6 inches long, 7 by 7 inches.

2 head-blocks, 5 feet long, 12 by 14 inches.

4 posts, 10 feet long, 8 by 8, to bear up the penstock.

2 capsills, 9 feet long, 8 by 10, for the penstock to stand on.

4 corner posts, 5 feet long, 4 by 6 inches, for the corners of the penstock.

For the Husk of a Mill of one Water-wheel and two Pair of Stones.

2 sills, 24 feet long, 12 by 12 inches.

4 corner posts, 7 feet long, 12 by 14 inches.

2 front posts, 8 feet long, 8 by 12 inches.

2 back posts, 8 feet long. 10 by 12 inches, to sup∣port the back ends of the bridge-trees.

2 other back posts,* 2.295 8 feet long, 8 by 8 inches.

2 tomkin posts, 12 feet long, 12 by 14 inches.

2 interties, 9 feet long, 12 by 12 inches, for the outer ends of the little cog-wheel shafts to rest on.

2 top pieces, 10 feet 6 inches long, 10 by 10 inches.

2 beams, 24 feet long, 16 by 16 inches.

2 bray-trees, 8½ feet long, 6 by 12 inches.

2 bridge-trees, 9 feet long, 10 by 10 inches.

4 plank, 8 feet long, 6 by 14 inches, for the stone bearers.

20 plank. 9 feet long, 4 by about 15 inches, for the top of the husk.

1 head-blocks, 7 feet long, 12 by 15 inches, for the wallower shafts to run on. They serve as spurs also for the head-block for the wa∣ter-wheel shaft.

For the Water and big Cog-wheel.

1 shaft, 18 feet long, 2 feet diameter.

8 arms for the water-wheel, 18 feet long, 3 by 9 inches.

••6 shrouds, 8½ feet long, 2 inches thick, and 8 deep.

••6 face boards, 8 feet long, 1 inch thick, and 9 deep.

••6 bucket boards, 2 feet 4 inches long, and 17 inches wide.

40 feet of boards, for foaling the wheel.

〈◊〉〈◊〉 arms for the cog-wheel, 9 feet long, 4 by 14 inches.

••6 cants, 6 feet long, 4 by 17 inches.

For little Cog-wheels.* 2.296

2 shafts, 9 feet long, 14 inches diameter.

4 arms, 7 feet long, 3½ by 10 inches.

16 cants, 5 feet long, 4 by 18 inches.

For Wallowers and Trundles.

60 feet of plank, 3½ inches thick.

40 feet of plank, 3 inches thick, for bolting gears.

Cogs and Rounds.

200 cogs, to be split, 3 by 3, 14 inches long.

80 rounds, to be split, 3 by 3, 20 inches long.

160 cogs, for bolting works, 7 inches long, and 1¾ square: but if they be for a mill with machinery complete, there must be more ac∣cordingly.

Bolting-shafts.

1 upright shaft, 14 feet long, 5½ by 5½ inches.

2 horizontal shafts, 17 feet long, 5 by 5 inches.

1 upright shafts, 12 feet long, 5 by 5 inches.

6 shafts, 10 feet long, 4 by 4 inches.

Art. 37. Bill of the large Irons for a Mill of two Pair of Stones.

2 gudgeons, 2 feet 2 inches long in the shaft; neck 4½ inches long, 3 inches diameter, well steeled and turned. See plate XII, fig. 16.

2 bands, 19 inches diameter inside, ¾ thick, and 3 inches wide, for the ends of the shaft.

2 bands, 20½ inches inside, ½ an inch thick, and 2½ in∣ches wide, for shaft.

2 bands, 23 inches inside. ½ an inch thick, and 2½ inches wide, for shaft.

4 gudgeons, 16 inches in the shaft, 3½ inches long,* 2.297 and 2½ inches diameter in the neck for wallower shafts: See fig. 15, plate XII.

4 bands, 10 inches diameter inside, ½ an inch thick, and 2 wide, for do.

4 bands. 12 inches diameter inside, ½ an inch thick and 2 wide, for plate.

4 wallower bands, 3 feet 2 inches diameter inside, 3 inches wide and ¼ of an inch thick.

4 trundle bands, 2 feet diameter inside, 3 inches wide, and ¼ of an inch thick.

2 spindles and rynes; spindles 5 feet 3 inches long from the foot to the top of the necks; cock-heads 7 or 8 inches long above the necks; the body of the spindles 3¼ by 2 inches; the neck 3 inch∣es long and 3 inches diameter; the balance rynes proportional to the spindles, to suit the eye of the stone, which is 9 inches diameter. See plate XII, fig. 1,2,3.

〈◊〉〈◊〉 steps for the spindles, fig. 4

2 sets of damsel-irons, 6 knockers to each set.

2 bray-irons, 3 feet long, 1¾ inch wide, ½ an inch thick; being a plain bar, one hole at the lower, and 5 or 6 at the upper end.

Bill of Iron for the Bolting and Hoisting-works in the common Way.

2 spur-wheel bands, 20 inches diameter from out∣sides, for the bolting spur-wheel, ¾ of an inch wide, and ¼ thick.

2 spur-wheel 12 inches diameter from outsides, for the hoisting spur-wheel.

2 step-gudgeons and steps, 10 inches long, 1½ inch thick in the tang, or square part; neck 3 inch∣es long, for the upright shafts. See plate XII, fig. 5 and 6.

2 bands, for steps, 5 inches diameter inside, 1¼ wide, and ¼ thick.

2 gudgeons, 9 inches tang; neck 3 inches long, 1½ square, for the top of the uprights.

8 bands,* 2.298 4½ inches diameter inside.

1 socket-gudgeon, 1½ of an inch thick; tang 12 inches long; neck 4 inches; tenon to go into the socket 1½ inch, with a key-hole at the end. See fig. 8 and 9.

14 gudgeons, necks 2½ inches, tangs 8 inches long, and 1 inch square, for small shafts and one end of the bolting-reels.

10 bands, for necks 4 inches diameter inside, and 1 inch wide.

4 socket-gudgeons, for the 4 bolting-reels, 1¼ square; tangs 8 inches; necks 3 inches, and te∣nons 1½ inch, with holes in the end of the tangs for rivets, to keep them from turning: the sock∣ets 1 inch thick at the mortise, and 3 inches be∣tween the prongs. See fig. 8 and 9. Prongs 8 inches long and 1 wide.

8 bands 3½ inches, and 8 bolting-reels. 4 inches diameter, for the bolting-reel shafts.

For the Hoisting-wheels.

2 gudgeons, for the jack wheel, neck 3½ inches, and tang 9 inches long, 1½ square.

2 bands, for the jack wheel, neck 4½ inches diameter.

2 gudgeons, for the hoisting-wheel, neck 3½ inch∣es, tang 9 inches long, and 1¼ inch square.

2 bands, for the hoisting-wheel, neck 7 inches diameter.

6 bands, for bolting-heads, 16 inches diameter in∣side, 2¼ wide, and ⅙ of an inch thick.

6 bands, for bolting-heads, 15 inches diameter in∣side, 2¼ wide, and 1/6 of an inch thick.

N. B. All the gudgeons should taper a little, as the sizes given is their largest part. The bands for shafts should be a little widest at the foremost side to make them drive well; but those for heads should be both sides equal.—6 picks for the stones, 8 inches long, and 1¼ wide, will be wanted.

Explanation of the Plates.

PLATE V,* 2.299

Drawn from a scale of ¼ of an inch for a foot.

Fig. 1 a big cog-wheel, 8 feet 2⅓ inches the dia∣meter of its pitch circle; 8 feet 10⅓ inches from out to out; 69 cogs, 4½ inch pitch.

2 a little cog-wheel, 5 feet 10⅓ inclies the diame∣ter of its pitch circle, and 6 feet 6 inches from out to out, to have 52 cogs 4¼ pitch.

3 a wallower, 3 feet 1¼ inches the diameter of its pitch circle, and 3 feet 4¼ inches from out to out; 26 rounds 4½ pitch.

4 a trundle, 1 foot 8⅓ inches the diameter of its pitch circle, and 1 foot 11⅓ inches from out to out; 15 rounds 4¼ inch pitch.

5 the back part of the big cog-wheel.

6 a model of locking 3 arms together.

7 the plan of a forebay, shewing the sills, caps, and where the mortises are made for the posts, with a rack at the upper end to keep off the trash.

PLATE VI.—The Ground-plan of a Mill.

Fig. 1 and 8 bolting-chests and reels, top view.

2 and 4 cog-wheels that turn the reels.

3 cog-wheel on the lower end of a short upright shaft.

〈◊〉〈◊〉 and 7 places for the bran to fall into.

〈◊〉〈◊〉, 6, 6, three garners on the lower floor for bran.

〈◊〉〈◊〉 and 10 posts to support the girders.

11 the lower door to load waggons, horses &c. at.

12 the step-ladder, from the lower floor to the husk.

13 the place where the hoisting casks stand when filling.

14 and 15 the two meal-troughs and meal-spouts.

16 meal shaking sieve for indian and buckwheat.

17 a box for the bran to fall into from the sieve.

18 and 19 the head-block, and long spur-blocks, for the big shaft.

Fig. 20 four posts in front of the husk,* 2.300 called bray posts.

21 the water and cog-wheel shaft.

22 the little cog-wheel and shaft, for the lower stones.

23 the trundle for the bur stones.

24 the wallower for do.

25 the spur-wheel that turns the bolts.

26 the cog-wheel.

27 the trundle, head wallower and bridge-tree, for country stones.

28 the four back posts of the husk.

29 the two posts that support the cross girder.

30 the two posts that bear up the penstocks at one side.

31 the water-wheel, 18 feet diameter.

32 the two posts that bear up the other side of the penstock.

33 the head-blocks and spur-blocks, at water end.

34 a sill to keep up the outer ends.

35 the water-house door.

36 a hole in the wall for the trunk to go thro',

37 the four windows of the lower story.

PLATE VII.—Second Floor.

Fig. 1 and 9 a top view of bolting-chests and reels,

2 and 10 places for bran to fall into.

3 and 8 the shafts that turn the reels.

4 and 7 wheels that turn the reels.

5 a wheel on the long shafts between the uprights.

6 a wheel on the upper end of the upright shaft.

11 and 12 two posts that bear up the girders of the 3rd floor.

13 the long shaft between two uprights.

14 five garners to hold tole, &c.

15 a door in the upper side of the mill-house.

16 a step-ladder from 2nd to 3rd floor.

Fig. 17 the running bur mill-stone laid off to be dressed.* 2.301

18 the hatchway.

19 stair way.

20 the running country stone turned up to be dres∣sed.

21 a small step-ladder from the husk to and floor.

22 the places where the cranes stand.

24 the pulley-wheel that turns the rolling-screen.

25 and 26, the shaft and wheel that turns the rol∣ling-screen and fan.

27 the wheel on the horizontal shaft to turn the bolting-reels.

28 the wheel on the upper end of the first upright shaft.

29 a large pulley that turns the fan.

30 the pulley at the end of the rolling-screen.

31 the fan.

32 the rolling-screen.

33 a step-ladder from the husk to the floor over the water-house.

34 and 35 two ports that support the girders of the 3rd floor.

36 a small room for the tailings of the rolling-screen.

37 a room for the fannings.

38 do. for the screenings.

39 a small room for the dust.

40 the penstock of water.

41 a room for the miller to keep his books in.

42 a fire-place.

43 the upper end door.

44 ten windows in the 2nd story, 12 lights each.

PLATE VIII

Represents a view of the lower side of a stone mill-house 3 stories high, which plan will suit tolera∣bly well for a two story house, if the third story be not wanted. Part of the wall supposed to be open, so that we have a view of the stones, running gears, &c.

Line 1 represents the lower floor,* 2.302 and is nearly level with the top of the sills, of the husk and water-house.

2, 3 and 4 the second, third, and fourth floors.

5 and 6 are windows for admitting air under the lower floor.

7 the lower door, with steps to ascend to it, which commonly suits best to load from.

8 the arch over the tail-race for the water to run from the wheel.

9 the water-house door, which sometimes suits better to be at the end of the house, where it makes room to wedge the gudgeon.

10 the end of the water-wheel shaft.

11 the big cog-wheel.

12 the little cog-wheel and wallower, the trundle being seen through the window.

13 the stones, with the hopper, shoe and feeder, as fixed for grinding.

14 the meal-trough.

We have an end view of the husk frame—there are thirteen windows with 12 lights each.

PLATE IX

Represents an outside view of the water end of a mill-house, and is to shew the builders, both ma∣sons, carpenters and mill-wrights, the height of the walls, floors, and timbers; places of the doors and windows, with a view of the position of the stones and husk-timbers, supposing the wall open so that we could see them.

Fig. 1, 2, 3 and 4 shews the joists of the floors.

5 represents a fish turning with the wind on an iron rod, which does as well as a weather-cock.

6 the end of the shaft for hoisting outside of the house, which is fixed above the colar-beams above the doors, to suit to hoist into either of them, or either story, at either end of the house, as may best suit.

Fig. 7 the dark squares,* 2.303 shewing the ends of the girders.

8 the joists over the water-house.

9 the mill-stones, with the spindles they run on, and the ends of the bridge-trees as they rest on the brays aa. bb shews the end of the brays, that are raised and lowered by the levers cc, called the lighter-staffs, thereby raising and lowering the running stone.

10 the water-wheel and big cog-wheel.

11 the wall between the water and cog-wheel.

12 the end view of the two side-walls of the house.

Plate X is explained in the Preface.

Art. 39. Of Saw-mills.—Their Utility.

THEY are for sawing timber into all kinds of scantling, boards, laths, &c. &c. are used to great advantage where labour is dear. One mill, attended by one man, if in good order, will saw more than 20 men with whip-saws, and much more exactly.

Construction of their Water-wheels.

They have been variously constructed; the most simple and useful of which, where wa∣ter is plenty, and above six feet fall, is the flutter-wheel; but where water is scarce, in some cases, and for want of sufficient head in others, to give flutter-wheels sufficient mo∣tion, high wheels, double geared, have been found necessary. Flutter-wheels may be made suitable for any head above six feet, by making

them low and wide,* 2.304 for low heads; and high and narrow for high ones, so as to make about 120 revolutions, or strokes of the saw, in a minute: but rather than double gear I would be satisfied with 100.

A TABLE of the Diameter of Flutter-wheels from out to Outsides, and their Width in the clear, suitable to all Heads from 6 to 30 feet.

Head of water.	Diameter.	Width.
ft.	f. in.	f. in.
6	2:8	5:6
7	2:10	5:0
8	2:11	4:8
9	3:0	4:3
10	3:1	4:0
11	3:2	3:9
12	3:3	3: 6
13	3:4	3:3
14	3:5	3:0
15	3:6	2:9
16	3:7	2:6
17	3:8	2:4
18	3:9	2:2

Head of water.	Diameter.	Width
ft.	f. in.	ft. in.
19	3:10	2:0
20	3:11	1:10
21	4:0	1:9
22	4:1	1:8
23	4:2	1:7
24	4:3	1:6
25	4:4	1:5
26	4:5	1:4
27	4:6	1:3
28	4:7	1:2
29	4:8	1:1
30	4:9	1:0

N. B. The above wheels are proposed as narrow as will well do on account of saving water; but if there is very plenty of it, the wheels may be made wider than directed in the table, and the mill will be more power∣ful.

Of Gearing Saw-mills.* 2.305

Of this I shall say but little they being ex∣pensive and but little used.—They should be geared so as to give the saw about 120 strokes in a minute, when at work in a common log. The water-wheel is like that of another mill, whether of the undershot, overshot, or breast kind; the cog-wheel of the spur kind, and as large as will clear the water. The wal∣lower commonly has 14 or 15 rounds, but so as to produce the right motion. On the wal∣lower shaft is a balance-wheel, which may be of stone or wood: this is to regulate the motion. There should be a good head above the wa∣ter-wheel to give it a lively motion, else the mill will run heavily.

The mechanism of a complete saw-mill is such as to produce the following effects, viz.

1. To move the saw up and down, with a sufficient motion and power.

2. To move the log to meet the saw with an uniform motion.

3. To stop of itself when within 3 inches of being through the log.

4. To draw the carriage with the log back by the power of water ready to enter again.

The mill is stopped as follows, viz. When the gate is drawn the lever is held by a catch, and there is a trigger, one end of which is within half an inch of the side of the carriage, on which is a piece of wood an inch and a half thick nailed, so that it will catch against the trigger as the carriage moves, which throws the catch off of the lever of the gate, and it ••uts down at a proper time.

Description of a Saw-mill.* 2.306

Plate XI. Is an elevation and perspective view of a saw-mill, shewing the foundation, walls, frame, &c. &c.

Fig. 0,1, The frame uncovered, 52 feet long, and 12 feet wide.

Fig. 2, The lever for communicating the motion from the saw-gate to the carriage, to move the log. It is 8 feet long, 3 inches square, tenoned into a roller 6 inches diameter, reach∣ing from plate to plate, and working on gud∣geons in them; in its lower side is framed a block 10 inches long, with a mortise in it 2 inches wide its whole length to receive the up∣per end of the hand-pole, having in it seve∣ral holes for an iron pin, to join the hand-pole to it to regulate the feed, by setting the hand∣pole nearer the centre of the roller to give less, and farther off, to give more feed.

Fig. 3, The hand-pole or feeder, 12 feet long, and 3 inches square where it joins the block

Fig. 4, tapering to 2 inches at the lower end, on which is the iron hand 1 foot long, with a socket, the end of which is flattened steel∣ed and hardened, and turned down at each side half an inch to keep it on the rag-wheel.

Fig. 5, the rag-wheel. This has four cants 4½ feet long, 17 by 3 inches in the middle, lapped together to make the wheel 5 feet di∣ameter, is faced between the arms with 2 inch plank, to strengthen the laps. The cramp or ratchet-iron is put on as a hoop near 1 inch square, with ratchet-notches cut on its outer edge, about 3 to an inch. On one side of the

wheel are put 12 strong pins,* 2.307 9 inches long, to tread the carriage back, when the backing works are out of order. On the other side are the cogs, about 56 in number, 3 inch pitch to gear into the cog-wheel on the top of the tub-wheel shaft, with 15 or 16 cogs. In the shaft of the rag-wheel are 6 or 7 rounds, 11 inches long in the round part, let in near their whole thickness, so as to be of a pitch equal to the pitch of the cogs of the carriage, and gear into them easily: the ends are tapered off outside and a band drove on them at each end, to keep them in their places.

Fig. 6 the carriage. Is a frame 4 feet wide from outsides, one side 29 feet long, 7 by 7 inches; the other 32 feet long, 8 by 7 inches, very straight and true, the interties at each end 15 by 4 inches, strongly tenoned and braced into the sides to keep the frame from racking. In the under side of the largest piece are set two rows of cogs, 2 inches between the rows, and 9 inches from the fore side of one cog to that of another; the cogs of one row between those of the other, so as to make 4½ inch pitch, to gear into the rounds of the rag-wheel. The cogs are about 66 in number; shank 7 inches long, 1¾ inch square; head 2¾ long, 2 inches thick at the points, and 2¼ inches at the shoul∣der.

Fig. 7 the ways for the carriage to run on. These are strips of plank 4½ inches wide, 2 inch∣es thick, set on edge, let 1½ inch into the top of the cross sills, of the whole length of the mill, keyed fast on one side, made very straight both side and edge, so that one of them will pass easily between the rows of cogs in the car∣riage,

and leave no room for it to move side ways.* 2.308 They should be of hard wood well seasoned, and hollowed out between the sills to keep the dust from lodging on them.

Fig. 8, the fender posts. The gate with the saw plays in rabbits, 2½ deep and 4 inches wide, in the fender posts, which are 12 feet long, and 12 inches square, hung by hooked tenons, the front side of the two large cross beams in the middle of the frame, in mortises in their upper sides, so that they can be moved by keys to set them plum. There are 3 mor∣tises two inches square through each post, within half an inch of the rabbits, through which pass hooks with large heads, to keep the frame in the rabbits: they are keyed at the back of the posts.

Fig. 9, the saw, which is 6 feet long, 7 or 8 inches wide when new, hung in a frame 6 feet wide from the outsides, 6 feet 3 inches long between the end pieces, the lowermost of which is 14 by 3 inches, the upper one 12 by 3, the side pieces 5 by 3 inches, 10 feet long, all of the best, dry, hard wood. The saw is fastened in the frame by two irons in form of staples, the lower one with two screw pins passing through the lower end, screwing one leg to each side of the end piece; the legs of the upper one are made into screws, one at each side of the end piece, passing thro' a broad flat bar that rests on the top of the end piece, with strong burs 1¾ inches square, to be turned by an iron span made to fit them. These straps are made of flat bars, 3 feet 9 inches long, 3 inches wide, ¾ thick before turned; at the turn they are 5 inches wide,

square,* 2.309 and split, to receive the saw, and tug-pins, then brought nearer together, so as to fit the gate. The saw is stretched tight in this frame, by the screws at the top, exactly in the middle at each end, measuring from the outside; the top end standing about half an inch more forward than the bottom.

Fig. 10, the forebay of water, projecting through the upper foundation wall.

Fig. 11, the flutter-wheel. Its diameter and length according to the head of water, as shewn in the table. The floats are fastened in with keys, so that they will drive inward when any thing gets under them, and not break. These wheels should be very heavy, that they may act as a fly or balance to regulate the mo∣tion, and work more powerfully.

Fig. 12, the crank—see it represented by a draught from a scale of 1 foot to an inch—〈◊〉〈◊〉 XII. fig. 17. The part in the shaft 2 feet 〈◊〉〈◊〉 inches long, 3¾ by 2 inches, neck 8 inches long thick, and 12 inches from the centre of the neck 〈◊〉〈◊〉 the centre of the wrist or handle, which is 〈◊〉〈◊〉 inches long to the key-hole, and 2 inches thick.

The gudgeon at the other end of the shaft 〈◊〉〈◊〉 18 inches in the shaft, neck 3½ long, 2¾ dia∣meter.

The crank is fastened in the same way as gudgeons. See art. 13.

Fig. 12—13, the pitman; which is 3½ inch∣es square at the upper end, 4½ in the middle, and 4 near the lower end, but 20 inches of the lower end is 4½ by 5½, to hold the boxes and key, to keep the handle of the crank light.

Pitman Irons of an improved Construction.* 2.310

See Plate XII. fig. 10,11,12,13,14.18. Fig. 10 is a plate or bar, with a hole in each end, through which the upper ends of the lug pins 11—11 pass, with a strong bur screwed on each, they are 17 inches long, 1⅓ inches square, turned at the lower end to make a round hole 1½ diameter, made strong round the hole.

Fig. 12 is a large flat link, passing thro' a mortise near the lower side of the end of the saw-frame. The lug pins pass one through each end of this link, which keeps them close to the gate sides.

14. Is a bar of iron 2 feet long 3½ inches wide, ½ inch thick, at the lower end, and 1⅓ at the upper end. It is split at the top and turn∣ed as the fig. to pass through the lug pins. At fig. 13 there is a notch set in the head of the pitman bar 14, 1½ inch long, nearly as deep as to be in a straight line with the lower side of the side pins made a little hollow, steel∣ed and made very hard.

Fig. 18, is an iron plate 1½ inch wide, half an inch thick in the middle, with 2 large nail-holes in each end, and a round piece of steel welded across the middle and hardened, made to fit the notch in the upper end of the pitman, pl. XIV. and drawn close by the lug pins, to the under side of the saw-frame and nailed fast. Now, if the bearing part of this joint be in a straight line, the lower end of the pitman may play without friction in the joint, because both the upper and lower parts will roll with∣out

sliding,* 2.311 like the centre of a scale-beam, and will not wear.

This is by far the best plan for pitman irons. The first set I ever seen or heard of has been in my saw-mill 8 years, doing much hard work, and has not cost 3 minutes to adjust them; whereas others are frequently very troublesome.

Fig. 14, the tub-wheel for running the car∣riage back. This is a very light wheel, 4 feet diameter, and put in motion by a motion of the foot or hand, at once throwing it in gear with the rag-wheel, lifting off the hand and clicks from the ratchet, and hoisting a little gate to let water on the wheel. The moment the saw stops, the carriage with the log begins to move gently back again.

Fig. 15, the cog-wheel on the top of the tub-wheel shaft, wit 15 or 16 cogs.

Fig. 16, the log on the carriage, sawed part through.

Fig. 17, a crank and windlass to increase power, by which one man can draw heavy logs on the mill, and turn them by a rope round the log and windlass.

Fig. 18, a cant hook for rolling logs.

Fig. 19, a double dog, fixed into the hind∣most head-block, used by some to hold the log.

Fig. 20, are smaller dogs to use occasionally at either end.

Fig. 21—22, represents the manner of shooting water on a flutter-wheel by a long open shute, which should not be more perpen∣dicular than an angle of 45 degrees, left the water should rise from the shute and take air, which would be a great loss of the power.

Fig. 23,* 2.312 represents a long, perpendicular, tight shute; the gate 23 is always drawn ful∣ly, and the quantity of water regulated at the bottom by a little gate r for the purpose. There must be air let into this shute by a tube entering at a.* 2.313 These shutes are for saving expence where the head is great, and should be much larger at the upper than lower end, else there will be a loss of power.† 2.314 The per∣pendicular ones suit best where a race passes within 12 feet of the upper side of the mill.

OPERATION.

The sluice drawn from the penstock 10, puts the wheel 11 in motion—the crank 12 moves the saw-gate and saw 9 up and down, and as they rise they lift up the lever 2, which pushes forward the hand-pole 3, which moves the rag-wheel 5, which gears in the cogs of the carriage 6, and draws forward the log 16 to meet the saw, as much as is proper to cut at a stroke. When it is within 3 inches of being through the log, the cleet C, on the side of the carriage, arrives at a trigger and lets it fly, and the sluice-gate shuts down: the miller in∣stantly draws water or the wheel 14, which runs the log gently back, &c. &c.

Art. 40. Description of a Fulling-mill.

FIG. 19 plate XII, is the penstock, water-gate and spout of an overshot fulling-mill, the whole laid down from a scale of 4 feet to an inch.

Fig. 20 one of the 3 interties,* 2.315 that are framed one end into the front side of the top of the stock-block; the other ends into the tops of the 3 circular pieces that guide the mallets: they are 6 feet long, 5 inches wide, and 6 deep.

Fig. 21 are the 2 mallets; they are 4 feet 3 inches long, 21 inches wide, and 8 thick, shap∣ed as in the figure.

Fig. 22 their handles, 8 feet long, 10 inches wide, and 〈◊〉〈◊〉 thick. There is a roller passes through them, 8 inches from the upper ends, and hang in the hindermost corner of the stock-post. The other ends go through the mallets, and have each on their under side a plate of iron faced with steel and hardened, 2 feet long, 3 inches wide, fastened by screw-bolts, for the tappet-blocks to rub against while lifting the mallets.

Fig. 23 the stock-post, 7 feet long, 2 feet square at the bottom, 15 inches thick at top, and shaped as in the figure.

Fig. 24 the stock where the cloth is beaten, shaped inside as in the figure, planked each side as high as the dotted line, which planks are put in rabits in the post, the inside of the stock, being 18 inches wide at bottom, 19 at top, and 2 feet deep.

Fig. 25 one of the 3 circular guides for the mallets; they are 6 feet long, 7 inches deep, and 5 thick; are framed into a cross sill at bot∣tom that joins its lower edge to the stock-post. This sill forms part of the bottom of the stock, and is 4 feet long, 20 inches wide, and 10 thick.

The sill under the stock-post is 6 feet long, 20 inches wide, and 18 thick. The sill before the stock is 6 feet long and 14 inches square.

Fig. 26 the tappet-arms,* 2.316 5 feet 6 inches long, 21 inches each side the shaft, 12 inches wide, and 4 thick. There is a mortise through each of them 4 inches wide, the length from shaft to tappet, for the ends of the mallet handles to pass through. The tappets are 4 pieces of hard wood, 12 inches long, 5 wide, and 4 thick, made in the form of half circles pined to the ends of the arms.

Fig. 27 the overshot water-wheel, similar to other mills.

Fig. 28 one of the 3 sills, 16 feet long, and 12 inches square, with walls under them as in the figure.

OPERATION.

The cloth is put in a loose heap into the stock 24; the water being drawn on the wheel the tappet-arms lift the mallets alternately, which strike the under part of the heap of cloth, and the upper part is continually falling over, and thereby turning and changing its position under the mallets, which are of the shape in the fi∣gure, to produce this effect.

Description of the Drawings of the Iron-works, Plate XII.

Fig. 1 is a spindle, 2 the balance-ryne, and 3 the driver, for a mill-stone. The length of the spin∣dle from the foot to the top of the neck is about 5 feet 3 inches; cock-head 8 or 9 inches from the top of the neck, which is 3 inches long, and 3 dia∣meter; blade or body 3½ by 2 inches thick; foot 1¼ inch diameter; both neck, foot, and top of the cock-head steeled, turned and hardened.

Fig. 2. The balance-ryne is sometimes made with 3 horns,* 2.317 one of which is so short as only to reach to the top of the driver, which is let into the stone right under it; the other to reach near as low as the bottom of the driver: but of late are mostly made with 2 horns only, which may be made sufficiently fast by making it a little wider than the eye, and let into the stone a little on each side to keep it steady and from moving sideways. Some choose them with 4 horns, which fills the eye too much.

Fig. 3 is the driver, about 15 inches long.

Fig. 4 the step for the spindle-foot to run in. It is a square box 6 inches long, 4 inches wide at top, but less at bottom, and 4 inches deep outsides, the sides and bottom half an inch thick. A piece of iron 1 inch thick is fitted to lay tight in the bot∣tom of this box, but not welded; in the middle of which is welded a plug of steel 1½ inch square, through which is punched a hole to fit the spin∣dle-foot ¼ of an inch deep. It must be tight to hold oil.

Fig. 5 a step-gudgeon for large upright-shafts, 16 inches long and 2 square, steeled and turned at the toe.

Fig. 6 the step for it, similar to 4 but less pro∣portionable.

Fig. 7 a gudgeon for large bolting-shafts, 13 inches long and 1½ square.

Fig. 8 a large joint-gudgeon, tang 14 inches, neck 5, and tenon 2 inches long, 1½ inch square.

Fig. 9 the socket part to fit the shaft, with 3 ri∣vet holes in each.

Fig. 10—14—18 pitman-irons, described art. 39.

Fig. 15 the wallower-gudgeon, tang 16 inches, neck 3½ inches long, and 2½ diameter.

Fig. 16 the water-wheel gudgeon, tang 2 feet 2 inches long, neck 4½ inches ditto, 3¼ square.

Fig. 17 a saw-mill crank, described art 39.

N. B. The spindle-ryne,* 2.318 &c. is drawn from a scale of 2 feet to an inch, and all the other irons 1 foot to an inch.

In addition to what is said of saw-mills, by Thomas Ellicott, I add the following.

Of hanging the Saw.

First, set the fender-posts as near plum every way as possible, and the head-blocks on which the log is to lay, level. Put the saw right in the middle of the gate, measuring from the outsides, with the upper teeth about half an inch farther forward than the lower ones; set it by the gate and not by a plumline—this is to give the saw liberty to rise without cut∣ting, and the log room to push forward as it rises. Run the carriage forward, so that the saw strike the block—stick up a nail, &c. there—run it back again its full length, and, standing behind the saw, set it to direct exactly to the mark. Stretch the saw in the frame rather most at the edge, that it may be stiffest there. Set it to go, and hold a tool close to one side, and observe whether it touch equally the whole length of the stroke—try if it be square with the top of the head-blocks, else it will not make the scantling square.

Of whetting the Saw.

The edge of the teeth ought to be kept straight, and not suffered to wear hollowing—the teeth set a little out, equal at each side, and the outer corners a little longest—they will clear their way the better. Some whet the under side of the teeth nearly level, and others a little drooping down; but then it will never saw steady—will be apt to wood too much;—they should slope a little up, but very little, to make it work steady. Try a cut through the log, and if it comes out at the mark made to set it by, shews it to be right hung.

Of Springing Logs Straight.

Some long small logs will spring so much in sawing as to spoil the scantling, unless it can be held straight: to do which make a clamp to bear with one end against the side of the car∣riage, the other end under the log with a post up the side thereof—drive a wedge between the post and log, and spring it straight; this will bend the carriage side—but no matter—it is no injury.

Of moving the Logs, to the Size of Scantling, &c.

Make a sliding-block to slide in a rabbet in front of the main head-block: fasten the log to this with a little dog on each side, one end of which being round, is drove into a round hole, in the front side of the sliding block, the other flatted to drive in the log, cutting across the grain, f••anting a little out—it will draw the log tight, and stick in the better. Set a post of hard wood in the middle of the main block close to the sliding one, and to ex∣tend with a shoulder over the sliding one, for a wedge to be drove under this shoulder to keep the block tight. Make a mark on each block to measure from—when the log is mov∣ed the key is driven out. The other end next the saw is best held by a sliding dog, part on each side of the saw pointed like a gauge, with two single joint dogs, one on each side of the saw.

Remedy for a long Pitman.

Make it in two parts by a joint 10 feet from the crank, and a mortise through a fix∣ed beam, for the lower end of the upper part to play in, the gate will work more steady, and all may be made lighter.

The feed of a saw-mill ought to be regulated by a screw fixed to move the hand-pole nearer or farther from the centre of the roller that moves it, which may be done as the saw arrives at a knot without stopping the mill.

END OF PART FIFTH.

Notes

• * 1.1

  This sluggish, inactive principle, or force, by which a body inclines to a state of rest, is called Inertia.
• † 1.2

  The same principle of inertia, which inclines a body to remain at rest, also inclines it to continue in motion for ever, if once put in motion, and that in a right-lined direction, unless changed by some force; therefore no body, moving in a strait line, can be turned into a curve line, but by some force; the consideration of which may lead us to the knowledge of the true principles of some mills. See the latter part of art. 73.
• * 1.3

  Art. 1.
• * 1.4

  In the course of this work, I shall shew, that a quadruple impulse pro∣duces only double velocity: See art. 7 and 46. We should follow philoso∣phers only in the paths of truth; because, if all men are subject to err▪ even the most eminent philosophers may have erred.

  If a theory will not agree with practice, we may suspect it is not true; and the theory of the momentum or force of bodies in motion, being as their velocities simply, does not agree with practice, with respect to the effects they produce, either in circular motion, art. 30, falling bodies, art. 9, spouting fluids, art. 45, wind on mill-sails, art. 69, therefore we have reason to suspect that this theory may not be true, in every respect.
• * 1.5

  Art. 2.
• * 1.6

  It is this attraction of gravity between the heavenly bodies, that keeps up the order of their motion, in their revolutions round each other. See Ferguson's Lectures, page 23.
• † 1.7

  The centre of gravity of a body, is that point on which, if the body be suspended, it will remain at rest in any position; or it is the centre of the whole weight or matter of the body. Art. 14.
• ‡ 1.8

  The diameter of the earth is allowed to be about 8000 miles; there∣fore we may suppose the centre of gravity of the earth to be about 4000 miles from its surface; and any small distance from its surface, such as 1 mile high, will make no sensible difference in gravity. But when the dis∣tance is so great as to bear a considerable proportion to the distance of the centre of gravity of the earth, then the power of gravity will decrease sensibly. Thus, at the distance of the moon, which, at a mean, is about 60 semi-diameters of the earth, the power of gravity is to that on the sur∣face of the earth, as 1 to 3600. See Martin's Philosophy.
• * 1.9

  Art. 2.
• * 1.10

  This resistance will be as the surfaces of the bodies; therefore the smaller the body of equal matter, the greater will be the velocity of its fall. But it has been proved, by experiment, that a feather will fall with the same velocity as a guinea, in vacuo. See Ferguson's Lectures, page 183.
• † 1.11

  A worthy and ingeuius young man, having prepared a vessel of wrought iron, about 3 inches diameter, and 9 inches long, partly filled with water, had put it into a smith's fire, and was trying some experiments, when the aperture. by which the steam was meant to issue, got stopped by some means (as is supposed) and the vessel burst with noise like a cannon, carried off his right arm, and left it laying across one of the upper beams of the shop, and otherwise desperately wounded him. This prodigious power is applied to raise water out of coal-mines, &c. from great depths, in sur∣prising quantities, and to turn mills; it may (in my opinion) be applied to many other useful purposes, which it is not yet applied to.

  On this subject much might be said; but as it does not immediately con∣cern this work, perhaps I have said enough to excite the reader to peruse the several 〈◊〉〈◊〉 authors on philosophy, who have treated largely and well 〈◊〉〈◊〉 and to them I must refer.
• * 1.12

  Art. 3.
• * 1.13

  Motion,
• * 1.14

  Absolute.
• * 1.15

  Relative.
• * 1.16

  If two ships, A and B, move with the same velocity, in the same di∣rection, then their absolute motion is the same, and they have no relative motion, and neither of them will appear, to a person on board of the other, 〈◊〉〈◊〉 move at all. Hence it is, that although the earth is continually revolving about its axis, with a velocity, at the equator, of about 1042 miles in an hour, and round the sun, in continual absolute motion, with a velocity of about 58000 miles an hour—yet, as all objects on its surface have the same absolute motion, they appear to be at rest, and not to move at all: therefore all motion of bodies on the earth, appears to us to be absolute motion, when compared with objects fixed on the earth; yet, if we take into consideration 〈◊〉〈◊〉 absolute motion of the earth, all motion on it will appear to be merely re∣••••tive.

  If two ships, A and B, moving with equal velocities, pass each other then they will appear, to a spectator on board of either, to move with 〈◊〉〈◊〉 their respective real velocities.

  Hence the reason, why a person, riding against the wind, finds its 〈◊〉〈◊〉 greater, and with it, its force less, than it really is.
• * 1.17

  Motion,
• * 1.18

  Equable.
• * 1.19

  Accelerated.
• * 1.20

  A falling body is constantly acted upon by all the power of its own gra∣vity; therefore its motion is continually increased.
• * 1.21

  Retarded.
• † 1.22

  A cannon-ball, projected perpendicular upwards, is constantly resis•••••• by the whole power of its own gravity; therefore its motion will be conti∣nually decreased, and totally stopped as soon as the sum of this resistance amounts to the first impulse, by axiom 3d, art. 1, when it will begin to de∣scend, and its motion will be continually increased by the same power of 〈◊〉〈◊〉 own gravity: its motion downwards will be equal to its motion upwards, 〈◊〉〈◊〉 every part of its path, and it will return to the mouth of the cannon 〈◊〉〈◊〉 the velocity and force that it left it; and the time of its ascent and descent will be equal, supposing there was no resistance from the air—but this resist∣ance will make a considerable difference.

  From this principle of accelerated motion in falling bodies, may app•••••• the reason, why water poured from the spout of a tea-kettle, will not con∣tinue in a stream farther than about two feet, and this stream become smaller as it approaches the place where it breaks into drops; because 〈◊〉〈◊〉 attraction of cohesion keeps the water together, until the accelerated mo∣tion of its fall, which stretches the stream smaller and smaller, overcome the cohesion, and then it breaks into drops, and these drops become further asunder while they continue to fall: therefore, if the clouds were to 〈◊〉〈◊〉 themselves in torrents, the water would fall on the earth in drops. 〈◊〉〈◊〉 may serve to shew the disadvantage of drawing the gate of a water-mill at 〈◊〉〈◊〉 great distance from the float-board: but more of this hereafter. 〈◊〉〈◊〉 art. 59.
• * 1.23

  Art. 6.
• * 1.24

  Momentum of bodies in mo∣tion.
• * 1.25

  Laws of mo∣tion.
• * 1.26

  By the first law, a body at rest, inclines to continue so for ever, by its ••sinertia or inactive power, and a body in motion inclines to continue so 〈◊〉〈◊〉 ever, passing over equal distances in equal times, if it meets with no re∣sistance, and will move on in a right line. For want of resistance the planets and comets continue their motions undiminished, while moving bowles or wheels are reduced to a state of rest by the resistance of the air, and th•••• friction of the parts on which they move. See Ferguson's Lectures on Me∣chanics.

  It is this friction of the parts, and resistance of the air, which renders it impossible for us to make a perpetual motion; because this friction and re∣sistance are to be overcome, and although it may be reduced to be very small, yet man cannot, with all his art, by mechanical combinations, 〈◊〉〈◊〉 as much power as will overcome it. Philosophers have demonstrated the impossibility of making it; but I think none ought to assert that it will never be found; for there are many perpetual motions in the heavens. If any man would spend his time in this way, it should be to seek for a created power that he might apply to this purpose, and not to create one.
• * 1.27

  Art. 7.
• * 1.28

  New position.
• * 1.29

  This is evident, when we consider that a body must fall a quadruple distance to obtain double velocity, by art. 9; and a quadruple head or pres∣sure of fluid produces a double velocity to the spout, by art. 46. The velo∣city, in both these cases, is as the square root of the impulse, and the im∣pulse as the squares of the velocity, therefore the change of effective mo∣tion or velocity will always be as the square root of the impulse or force impressed, and the force impressed as the squares of the velocity or effective motion.
• † 1.30

  Action and re-action are equal; that is, if a hammer strikes an anvil▪ the anvil will re-act against the hammer with an equal force to the action of the hammer.

  The action of our feet against the ground, and the re-action of the ground against our feet, are equal.

  The action of the hand to project a stone, and the re-action of the stone against the hand, are equal.

  If a cannon, weighing 6400lbs. gives a 24lb. ball a velocity of 640 〈◊〉〈◊〉 per second, the action of the powder on the ball, and its re-action against the cannon, are equal; and if the cannon has liberty to move, it will have a velocity, which multiplied into its weight, will be equal to the velocity of the ball multiplied by its weight: their instant momentums are always equal. See Martin's Philosophy.
• * 1.31

  Fig. 1.
• * 1.32

  Of instantane∣ous momen∣tums of bodies in motion.
• * 1.33

  This shews that non-elastic bodies communicate only half their original force; because the force required to cause the bodies to recede from each other, is equal to the force that gave them velocity to meet; and the force that caused the body to recede with velocity 10, is equal to the force that stopped velocity. 10.
• * 1.34

  Fig. 2.
• * 1.35

  Art. 8.
• * 1.36

  Because elastic bodies impinging, recede, after the stroke, with the same velocity with which they meet; therefore, a heavy body in motion, impinging on a lighter body at rest, will give it a greater velocity than that with which it was struck; for if the heavy body be not stopped, but move forward after the stroke, with a certain velocity, that velocity, added to the velocity before the stroke, will be the velocity of the lighter body.
• † 1.37

  This also shews evidently, that non-elastic bodies communicate only half their force. A knowledge of this is of great use in establishing a true theory of water-mills.
• * 1.38

  Fig. 4.
• * 1.39

  Compound motion.
• ‡ 1.40

  This doctrine of the momentum of bodies in motion, and communi∣cation of motion, being as their velocities simply, was taught by Sir Isaac Newton, and has been received by his followers to this day; which appears to be true, where the whole force is instantaneously spent or communicated; therefore I have changed the term to instant momentum. I have tried the experiment, by causing different weights to strike each other with different velocities, both on the principle of pendulums, and by causing them to move in horizontal circles; and, in both cases, 4lbs. with velocity 1, ba∣lanced 2lbs. with velocity 2; their momentums each were 4: so that the theory appears to be proved to be true. Yet I think we have reason to doubt its being true in any other sense; because it does not agree with prac∣tice. All the bodies we put in motion, to produce effects, produce them in proportion to the squares of their velocities, or nearly, as will appear in the course of this work: But I fear I shall draw on me the ridicule of some, if I should doubt a theory long established; but I think we should follow others only in the paths of truth. Doubtless Sir Isaac meant the force to be instantly spent: and I have understood that the Dutch and Italian philoso∣phers have held and taught, these 100 years past, that the momentum of bo∣dies in motion, is as the squares of their velocities; and I must confess it appears to be really the case, with respect to the effects they produce; which is generally as their quantity or weight multiplied into the squares of their velocities. I found it impossible to reconcile the theory of the force of bodies in motion, being as their simple velocities, to the laws of circular motion, art. 13, where a double velocity produces a quadruple central force; of falling bodies, art. 9, where the velocity is as the square root of the impulse or dis∣tance fallen, and the effects as the squares of the velocities; of projectiles, where a double velocity produces a quadruple random, art. 12; of bodies descending on inclined plains, art. 10, where the velocities are as the square roots of the perpendicular descents, and the effects as the squares of their velocities; of spouting fluids, art. 45, where their velocities are as the square roots of their perpendicular heights or pressures, and their effects as the squares of their velocities, with equal quantities; of wind on mill-falls, art. 69, where the effects are as the cube of the velocity of the wind; because here the quantity is as the velocity, and the effect of equal quantities being as the squares of the velocity, amounts the effects to be as the cubes.

  But when I discovered that a quadruple impulse was requisite to give double velocity, both in falling bodies and spouting fluids, and, by axiom 3, the power that produced a motion in a body, and the power that destroyed said motion, were equal, I concluded that the effects produced by bodies in motion, were as the squares of their velocities; and then I found the whole theory to agree with practice. Hereafter I shall say, that the effective mo∣mentum, or force of bodies in motion, is as the squares of their velo∣cities.
• * 1.41

  Art. 8.
• * 1.42

  A double velo∣city produces a quadruple effect.
• * 1.43

  We should pay no regard to time, in calculating the effective force of bodies in motion. Because, if 1lb of matter move with 1 degree of velo∣city, it will produce a certain effect (before it ceases moving) in an unknown time. Every other pound of matter, moving with equal velocity, will produce an equal effect in equal time. But if each pound of matter move with double velocity, it will produce 4 times the effect, but requires a dou∣ble time; which difference in time no way affects the sum total of the ef∣fects of the matter put in motion to move any practical machine. There∣fore we should totally leave time out of this calculation, seeing it tends to lead us into errors.
• * 1.44

  Art. 8.
• * 1.45

  Fig. 3.
• * 1.46

  Art. 8.
• * 1.47

  6-10ths of power lost by non-elasticity.
• * 1.48

  Art. 8.
• * 1.49

  Greatest effect of striking fluids not more than half their moving power
• * 1.50

  It is evident, that in every equal part of time, the body receives an impulse from gravity, that will propel it an equal distance, and give it an equal additional velocity; therefore it will produce equal effects in equal times, and their velocity will be proportional to the time.
• † 1.51

  If the velocity, at the end of one second, be 32,4 feet, at the end of two seconds it will be 64,8, at the end of three seconds 97,2 feet per second, and so on.
• ‡ 1.52

  That is, as the square of 1 second is to the space passed through 16,2, so is the square of 2 seconds, which is 4, to 64,8 feet, passed through at the end of 2 seconds, and so on, for any number of seconds. Therefore the spaces passed through at the end of every second, will be as the square num∣bers 1,4,9,16,25,36, &c. and the spaces passed through, in each second separately, will be as the odd numbers 1,3,5,7,9,11,13,15, &c.
• * 1.53

  Art. 9,
• * 1.54

  That is, as the square root of 4, which is 2, is to 16,2, the velocity ac∣quired in falling 4 feet: so is the square root of any other distance, to the velocity acquired, in falling that distance.
• † 1.55

  That is, suppose the body as it arrives at the lowest point of its fall, and has acquired its greatest velocity, was to be turned in a horizontal di∣rection, and the velocity to continue uniform, it would pass over double the distance, in that direction that it had descended through in the same time.
• ‡ 1.56

  This is evident from the consideration, that in every equal part of dis∣tance it descends through, it receives an equal effective impulse from gra∣vity. Therefore 4 times the distance, gives 4 times the effective (but not instant) impulse.
• ‖ 1.57

  This is evident, when we consider, that a quadruple distance or impulse, produces only double velocity, and by axiom 3 a quadruple resistance will be required, to stop double velocity; consequently their force is as the squares of their velocities, which brings them to be directly as their dis∣tances descended through: and this agrees with the second law of spouting ••••uids. Art. 45.
• § 1.58

  That is, if a body fall 16 feet, and strike a non-elastic body, such as hot iron, soft lead, clay, &c. it will strike with velocity 32, and produce a certain effect in a certain time. Again if it fall 64 Feet, it will strike with velocity 64, and produce a quadruple effect, in a double time; because, if a perfectly elastic body fall 16 feet in one second of time, and strike a per∣fectly elastic plain, with velocity 32 feet, it will rise 16 feet in one second of time. Again, if the body fall two seconds of time, it will fall 64 feet, and strike with velocity 64, and rise 64 feet in two seconds of time. Now, if we call the rising of the body the effect of the striking velocity (which it really is) then all will appear clearly. But any thing here advanc∣ed, if contrary to the opinion of many learned and ingenious authors, ought to be doubted, unless known to agree with practice.
• * 1.59

  Art. 9.
• * 1.60

  This is evident when we consider,

  1. That it is a proportion of the surfaces, that meets the resistance; and,

  2. That a double velocity strikes a double quantity of resisting particles in the same time.

  3. That a double velocity strikes each particle with double the instant, and four times the effective force, by art. 6.

  Therefore, the instant resistance is as the squares of their velocities, and will soon amount to the whole force of gravity, and reduce the motion to be uniform. This is the reason why hail and rain falls with such mode∣rate force; whereas if it was not for the resistance of the air, they would prove fatal to those they fall upon. Compare this with the effect of wind on mill-sails, proved by experiment, to be as the cubes of the velocity, Art. 69, and with the effects of spouting fluids, proved to be as the cubes of their velocities, with equal apertures. Art. 67, and 7th law of spout∣ing fluids.

  Again, consider that the solid content of bodies decreases, as the cubes of their diameters, while their surfaces decrease only as the squares of their diameters; Consequently the smaller the body, the greater the resist∣ance, in proportion to its weight: and this is the reason why heavy bodies, reduced to dust, will float in the air; as, likewise, feathers, and many other bodies of great surface and little matter. This seems to show, that air is, perhaps, as heavy as any other matter whatever, of an equal degree of fineness or smallness of particles.

  These are the laws of falling bodies supposing them to fall in vacuo, or in an unresisting medium; and without considering that gravity increases, as the square of the distance from the center of gravity of the attracting power decreases (4. law of gravity, art. 2;) because any small distance, such as comes in our practice, will make no sensible difference. But as they fall in the air, which is a medium of great resistance, the instant resistance is as the opposing surfaces of the falling body, and as the squares of their ve∣locities, their motion will greatly differ from these laws, in falling great distances, or with light bodies; but in small distances, such as 30 feet or less, and heavy bodies, the difference will be imperceptable in common practice.
• * 1.61

  In this table, the first column contains the total space fallen through, which is as the squares of the times or velocities, by law 3. The second column contains the velocity acquired, which is as the square root of the distance fallen, and as the time of the fall, by laws 〈◊〉〈◊〉 and 4. The third column contains the space fallen through each second, which is as the odd numbers.
• * 1.62

  Art. 8.
• * 1.63

  Fig. 5.
• * 1.64

  Art. 10.
• * 1.65

  Fig. 6.
• * 1.66

  Of projectiles.
• * 1.67

  Art. 12.
• * 1.68

  Fig, 7.
• * 1.69

  Central for∣ces.
• * 1.70

  It may be well to observe here, that this central force is no real power but only an effect of the power that gives the body the motion. Its iner•••••• causes it to recede from the centre, and fly off in a direct tangent line, 〈◊〉〈◊〉 the circle it moves in. Therefore this central force can neither add to, 〈◊〉〈◊〉 diminish from the power of any mechanical or hydraulic engine, unless it be by friction.
• * 1.71

  Art. 13.
• * 1.72

  Laws of ••en∣tral forces.
• * 1.73

  This shews, that when mill-stones are of unequal diameters, and re∣volve in equal times, the largest should have the draught of their furrows ••ess, in proportion as their central force is more, which is inverse propor∣tion; also that the draught of a stone should vary, and be in inverse pro∣portion to the distance from the centre. That is, the greater the distance 〈◊〉〈◊〉 less the draught.

  Hence we conclude, that if stones revolve in equal times, their draught must be equal next the centre: that is, so much of the large stones, as is equal to the size of the small ones, must be of equal draught. But that ••••art which is greater, must have less draught in inverse proportion, as the distance from the centre is greater, the furrows must cross at so much less ••••gle; which will be nearly the case (if their furrows lead to an equal dis∣tance from their centres) at any considerable distance from the centre of 〈◊〉〈◊〉 stone; but near the centre the angles become greater than the propor∣tion, if the furrows be straight, as appears by the lines g 1, h 1, g 2, h 2, g 3, 〈◊〉〈◊〉 3, in fig. 1, pl. XI. the angles near the centre are too great, which seems to ••••dicate, that the furrows of mill-stones should not be straight, but a little curved; but what this curve should be is very difficult to determine exact∣ed by theory. By theory it should be such as to cause the angle of furrows ••••ossing, to change in inverse proportion with the distance from the centre, which will require the furrows to curve more, as they approach the cen∣tre.
• * 1.74

  Laws of cen∣tral forces, to be considered in draughting mill-stones.
• † 1.75

  This shows that mill-stones of equal diameters, having their veloci∣ties unequal, should have the draught of their furrows, as the square roots 〈◊〉〈◊〉 their number of revolutions per minute. Thus, suppose the revolu∣tions of one stone to be 81 per minute, and the mean draught of the fur∣rows 5 inches, and found to be right; the revolutions of the other to be 〈◊〉〈◊〉; then to find the draught, say, As the square root of 81, which is 9, is 〈◊〉〈◊〉 the 5 inches draught: so is the square root of 100, which is 10, to 4, 5 inches, the draught required (by inverse proportion) because the 〈◊〉〈◊〉 must decrease as the central force increases.
• * 1.76

  Art. 13.
• * 1.77

  That is the greater the distance the less the central force. This 〈◊〉〈◊〉 that mill-stones of different diameters, having their peripheries revolvi•••• with equal velocities, should have the angle of draught, with which 〈◊〉〈◊〉 furrows cross each other, in inverse proportion to their diameters, beca•••••• their central forces are as their diameters, by inverse proportion, 〈◊〉〈◊〉 and the angle of draught should increase, as the central force 〈◊〉〈◊〉 and decrease, as it increases.

  But here we must consider, that, to give stones of different diameter equal-draughts, the distance of their furrows from the centre, must be direct proportion to their diameters. Thus, as 4 feet diameter, is 〈◊〉〈◊〉 inches draught: so is five feet diameter to 5 inches draught. To 〈◊〉〈◊〉 the furrows of each pair of stones cross each other at equal angles, 〈◊〉〈◊〉 proportional distances from the centre, see fig. 1, plate XI. where 〈◊〉〈◊〉 g d, g f, h a, h c, and h e, show the direction of the furrows of the 4, 5•• 6 feet stones, with their proportional draughts; now it is obvious 〈◊〉〈◊〉 they cross each other at equal angles, because the respective lines are ••••∣rallel, and cross in each stone, near the middle of the radius, which 〈◊〉〈◊〉 that in all proportional distances, they cross at equal angles, consequent∣ly their draughts are equal.

  But the draught must-be further increased, with the diameter of stone, in order to increase the angle of draught in the inverse ratio, 〈◊〉〈◊〉 central force decreases.

  To do which say: If the 4 feet stone has central force equal 1, what ••••••∣tral force will the 5 feet stone have? Answer: ,8 by the 7th law.

  Then say) If central force I requires 5 inches draught, for a 5th stone, what will central force, 8 require? Answer: 6,25 inches dra••••••. This is, supposing the verge of each stone, to move with equal velo••••••. This rule may bring out the draught nearly true, provided there be 〈◊〉〈◊〉 much difference between the diameter of the stones. But it appears me, that neither the angles with which the furrows cross, nor the dis∣tance of the point from the centre, to which they direct, is a true 〈◊〉〈◊〉 of the draught.
• * 1.78

  Art. 13.
• * 1.79

  These are the laws of circular motion and central forces. For expe∣rimental demonstrations of them, see Ferguson's Lectures on Mechanics, page 27 to 47.

  I may here observe that the whole planetary system is governed by these laws of circular motion and central forces. Gravity acting as the string, and is the centripetal force; and as the power of gravity decreases, as the square of the distance increases, by the 4th law of gravity, art 2; and as the centripetal and centrifugal forces must always be equal, in order to keep the body in a circle. Hence apears the reason why the planets most remote from the sun have their motion so slow, while those near him have their motions swift; because their celerities must be such as to create a centrifugal force equal to the attraction of gravity.

  I may here observe, that modern philosophers begin to doubt the exi∣stence of inertia, as defined by Newton, to be different and independent from gravity, but seem to conclude that they are both one thing; but when we consider that the whole force of gravity is exerted as centripetal force, to keep the heavenly bodies in a circle. It cannot be that same power, cause or principle, that causes the bodies to continue their motion, unless one cause can produce two effects each equal to itself, contrary to axiom 4. Again we may consider, that gravity decreases, as the squares of the distance of the body from the attracting power increases, but inertia is the same every where; and if we suppose the body to be removed out of the sphere of at∣traction of gravity, there will be no gravity at all, yet inertia will act in its full power, to continue the motion or rest of a body, by axiom 1 and 2. Hence in this light gravity and inertia appear to be two very different principles and ought to be distinguished by different names: but here we may dispute about words, for in other light•• they appear to be the very same thing.
• * 1.80

  Attempt to prove the ex∣istence of in∣ertia.
• * 1.81

  Art. 14.
• * 1.82

  Art. 14.
• * 1.83

  Fig. 12. Reasons why wheel carri∣ages over∣turn.
• * 1.84

  But one prin∣ciple in me∣chanical pow∣ers.
• * 1.85

  General laws of mechanical powers.
• * 1.86

  Art. 15.
• * 1.87

  Laws of the lever.
• * 1.88

  That is, the power P, fig. 8, which is 1 multiplied into its distance B C, from the centre 12, is equal to the weight 12 multiplied into its dis∣tance A B I, each product being 12.
• * 1.88.1

  Fig. 8.
• † 1.89

  That is, the power multiplied into its distance moved, is equal to the weight multiplied into its distance moved.
• ‡ 1.90

  That is, the power multiplied into its perpendicular descent, is equal to the weight multiplied into its perpendicular ascent.
• * 1.91

  Laws of the lever hold uni∣versally true in all mecha∣nical powers or engines.
• * 1.92

  Fig. 8.
• * 1.93

  Art. 17,
• * 1.94

  Different kinds of le∣vers.
• * 1.95

  Great power exerted by the muscles of the human frame.
• * 1.96

  Art. 18.
• * 1.97

  Fig.9 Compound Lever.
• * 1.98

  General rule.
• * 1.99

  Fundamental principle of all rules for cal∣culating the power or ve∣locity of any combination of wheels or levers.
• * 1.100

  Art. 19.
• * 1.101

  Fig. 9.
• * 1.102

  In order to abreviate the work, I shall hereafter use the following Algebraic signs, viz.

  • The sign + more, for addition.
  • − less, for subtraction.
  • × multiplied, for multiplication.
  • ÷ divided, for division.
  • = equal, for equality.

  Then, instead of 8 more 4 equal 12, I shall write 8+4=12. Instead of 12 less 4 equal 8, 12−4=8. Instead of 6 multi∣plied by 4 equal 24, 6×4=24. And instead of 24 divided by 3 equal 8, 24|3=8.
• * 1.103

  Art. 19.
• * 1.104

  Fig. 11.
• * 1.105

  Art. 20.
• * 1.106

  The power on the water-wheel given, to find the power exerted on the mill-stone.
• * 1.107

  Rule to find the velocity of the mean cir∣cle of a mill∣stone.
• * 1.108

  Art. 21.
• * 1.109

  Rule to find the force ex∣erted to move a mill-stone.
• * 1.110

  Philosophers have hitherto attributed this loss of power to friction, which is owing to the vis••nertia of matter.
• * 1.111

  No power gained by in∣creasing the diameter of undershot wa∣ter-wheels, on the principle of lengthening the lever.
• * 1.112

  Fig. 11.
• * 1.113

  Art. 22.
• * 1.114

  The true ad∣vantages that large wheels have over small ones.
• * 1.115

  Art. 22.
• * 1.116

  No power gained by dou∣ble gears, but some loft.
• * 1.117

  Many and great have been the losses sustained by mill-builders, on ac∣count of their not properly understanding these principles. I have often 〈◊〉〈◊〉 with great high wheels built, where those of half the size and expence would do better; and double gears, where single would do better, &c. &c.
• * 1.117.2

  Losses sustain∣ed by errors.
• * 1.118

  Fig. 10.
• * 1.119

  Art. 24.
• * 1.120

  Of the pulley, an easy way to compute its power.
• * 1.121

  In this engine there is great loss of original power, by the great friction of the pullies and ropes in bending, &c. But there is a very great improve∣ment lately discovered, on the pulley, which is as follows: Make a system of pullies of such construction, that when those of the upper block all fixed together on one pin will revolve in equal time, and the same in the lower block, which effectually evades all the friction of the sides of the pullies and ropes passing through the blocks. But as it is almost impossible to pro∣portion the diameters of the pullies to the motion of the ropes so exactly, it will be best to let them have liberty to turn on the pin, so as to stretch all the ropes equally.
• * 1.121.3

  Great im∣provement on a system of pullies.
• † 1.122

  There is but little loss of original power in this engine, because it has but little friction.
• * 1.123

  Inclined plain its use.
• * 1.124

  Art. 26.
• * 1.125

  The wedge equal to an in∣clined plain.
• * 1.126

  Rule to com∣pute the po∣wer of the wedge.
• * 1.127

  Now if we consider that ••he one 12 acting on one side of the wedge 〈◊〉〈◊〉 presents the re-action of the ground on the underside of the inclined pl••i•••• will then plainly see that the wedge and inclined plain are both one 〈◊〉〈◊〉 for if this wedge be applied to raise a weight of 12, it will require 2 〈◊〉〈◊〉 of 1 to drive it under the weight. But if the ground would give way 〈◊〉〈◊〉 the wedge as easily, and move the same distance that the weight raises, 〈◊〉〈◊〉 the weight would be raised only half the height; consequently, I would 〈◊〉〈◊〉 the wedge under the weight, and this yielding of the ground equal to 〈◊〉〈◊〉 raising of the weight, will truly represent the yielding of the cleft on 〈◊〉〈◊〉 side of the wedge. And this is the true principle of the wedge notwithstand∣ing so much has been said to prove it to be equal to 〈◊〉〈◊〉 inclined planes. 〈◊〉〈◊〉 Ferguson's lectures.
• * 1.128

  Art. 27.
• * 1.129

  Principles and power of the screw.
• * 1.130

  Art. 28.
• * 1.131

  Art. 29.
• * 1.132

  But I think it is evident, that this loss of 1-3 of the original power producing effects by machines, arises from the visinertia of the matter 〈◊〉〈◊〉 to be moved. For suppose the machine be an elevator, applied to 〈◊〉〈◊〉 wheat, fig. 17, art. 34, it is evident, that if we apply only as much power will hold the weight of the wheat in the buckets in equilibrio, we will 〈◊〉〈◊〉 no motion: then in order to obtain a lively motion, we will be obliged ••••••••∣ply a further power, which I expect we will find will be nearly 1-3 of whole, art. 41; and this 1-3 part of the power will be continually emp•••••••• in changing the state of the wheat from rest to a lively motion. Besides, is shewn in art. 31, that the friction of most machines is not more than 〈◊〉〈◊〉 part of the weight upon a plain; and by the difference between the diame∣ters of the wheels and gudgeons, is reduced to 1-1000 part of the 〈◊〉〈◊〉 or the moving power.
• * 1.132.4

  One third of the original power lost, to overcome in∣ertia, in many machines.
• * 1.133

  Art. 30. Fly-wheel no increaser of power.
• * 1.134

  Its use.
• * 1.135

  Friction.
• * 1.136

  Philosophers, treating of friction, seem to agree in telling us, that 〈◊〉〈◊〉 perfectly hard body of any weight could be made perfectly smooth and 〈◊〉〈◊〉 and laid on a horizontal plain perfectly hard, smooth and even, that then 〈◊〉〈◊〉 least force would move the said weight in any horizontal direction; and 〈◊〉〈◊〉 it is the roughness of the best polished and smoothed bodies, that is the 〈◊〉〈◊〉 cause of friction; because the body in being moved, has first to be 〈◊〉〈◊〉 ••ver the prominent parts, which is of the nature of an inclined plain. 〈◊〉〈◊〉 also say, in treating of the attraction of c••hesion, that if two bodies of 〈◊〉〈◊〉 same kind of matter could be made perfectly smooth and even, so that 〈◊〉〈◊〉 parts would meet exactly, they would strongly cohere or stick together attraction; by which it appears that the doctrine of friction is not yet 〈◊〉〈◊〉 explained.
• * 1.136.5

  Philosophers opinions about it.
• * 1.137

  Its laws.
• † 1.138

  They also say, that it is proved by experiment, that if a square 〈◊〉〈◊〉 wood or brass, as F, fig.13, four inches wide, and 1 inch thick, be made 〈◊〉〈◊〉 and laid on a smooth plain, A B C D, and the weight P hung over a 〈◊〉〈◊〉 that it will require the weight P to be nearly 1-3 part of the weight of 〈◊〉〈◊〉 body F, to draw it along; and that the same, whether it be on its 〈◊〉〈◊〉 or edge. This proves law 1st, that friction is not increased by incre•••••• the surface of contact.
• * 1.138.6

  Fig. 13.
• ‡ 1.139

  It has also been proved by experiment, that if we fix the lever L, to 〈◊〉〈◊〉 the weight F, making o its centre of motion, and by a cord make F 〈◊〉〈◊〉 the lever at the point 1, and hang the weight Q at the end of the lever 〈◊〉〈◊〉 pullie, and make Q just sufficient to move F; Q will then be found to be 〈◊〉〈◊〉 of P, because it will have to move F but 1-7 of the distance. Then move the cord from 1 to 2, and we find the weight Q must now be doubled equal to 2-7 of P to move F; (the reason is evident from the laws of the lever) because F is double the distance from the centre of motion that it was at 1, and it will have to move double the distance if the lever, or power Q move the same distance. This shews that friction is as the distance from the centre of mo∣tion; that is, it is as the diameter of the gudgeons, double diameter, double friction; therefore gudgeons ought to be as small as possible, so as to be suf∣ficiently strong to endure the stress of the weight.
• * 1.139.7

  Increased by velocity.
• * 1.139.8

  Is directly as the distance of the rub∣bing surfa∣ces from the centre of motion.
• * 1.140

  Art. 31.
• * 1.141

  They have also proved by experiment, that if F be a brass plate of 6 ounces, and A B C D a brass plate, both well polished and oiled, then it will require the weight P to be nearly 2 ounces to move F. But if F be loaded with 6, 8 or 10lb. then a sixth part of that weight will be sufficient to draw it along. This proves that the ratio of the friction to the weight decreases, as the weight increases: the reason of which decrease of proportion I take to be as follows, viz. Great part of the friction arises from the cohesion of the parts, even the grease put on to destroy the cohesion, has a cohesion of its own; and this cohesion of parts or of the grease, will not increase with the weight or velocity.—Again, if we allow the friction to be occasioned by the weight of the body having to be raised over the prominent parts of the rub∣bing surface, it is evident, that when it is raised by being started, that it has not to be raised again; therefore the greater the velocity, the less proporti∣on will this resistance (occasioned by the raising of the body) bear to the ve∣locity.

  I have made an experiment similar to that of fig. 13, with a flat sided glass bottle, on a smooth poplar plank, oiled; also on a well polished steel plate oiled, and when loaded with 10lb. it was drawn by 1lb. and when load∣ed with 22lb. it was drawn by 2lb. and when loaded with 60lb. it was drawn by 4 1-2 lbs. which is about 1-13 part: and the motion was greatly accele∣rated, which gives reason to conclude, that less weight would have continu∣ed the motion, after once begun.

  We may reasonably suppose, that the gudgeons of mills, &c. well polished, running on good stones or brass boxes, &c. and well oiled, have as little fric∣tion as the bottle and plank; and as we find that the proportion of friction decreases as the weight increases, we may suppose that in great weights it will not amount to more than 1-20 part of the weight, supposing the gudge∣ons to be the full size or diameter of the wheels, for so they must be in order to be on the same principles of plains rubbing together. Upon these princi∣ples I compute the friction of the gudgeons of a well hung water-wheel, as follows: viz. As the diameter of the wheel is to the diameter of the gud∣geons, so is 1-20 part of the weight of the wheel, to the weight that will ba∣lance the friction.

  EXAMPLE.

  Suppose a wheel 15 feet diameter, with gudgeons 3 inches diameter, and weighing 4000lb. by supposition; then, say as 15 feet is to 3 inches, so is 4000|20 to 3,3lb. the weight on the periphery of the wheel that will ba∣lance the friction of 4000lb.: which is less than 1-1000 part of the weight. But note that for the same reasons, that friction does not increase with the velocity in direct proportion, neither will it decrease in direct proportion with the velocity of the rubbing surface of the gudgeon: hence we must con∣clude again that the friction is more than 1-1000 part. By which it ap∣pears, that the friction of the gudgeons, well set on good stones or 〈◊〉〈◊〉 boxes, is not in mills worthy of the expence of evading. It bears but a 〈◊〉〈◊〉 proportion to the friction or resistance of the air, especially where the velo∣city is great. See art. 9, and 9th law of falling bodies.
• * 1.142

  It is not in∣creased in direct pro∣portion with the weight.
• * 1.143

  The ratio decreases as the weight and velocity increases.
• * 1.144

  Experiment made.
• * 1.145

  Ratio of friction to the weight.
• * 1.146

  Not more than 1-20 part on a plain in great weight.
• * 1.147

  Not more than 1-1000 part in great machines and great weights.
• * 1.148

  Art. 31.
• * 1.149

  To reduce friction.
• * 1.150

  By friction wheels. Fig. 14.
• * 1.151

  Rollers appli∣ed to reduce friction.
• * 1.152

  Fig. 15.
• * 1.153

  No friction in rollers.
• * 1.154

  Fig.16.
• * 1.155

  To explain this, let us suppose the rollers aaaaaa to have cogs, and the shaft A, and box to have cogs also, the rollers gearing into the shaft and into the inside of the box. Now it is evident, that if the box will turn round the axle, it must be without any sliding of parts; (and in fact, the prominent 〈◊〉〈◊〉 of the rollers, axle and box, will act as cogs) then, if the rollers and axle 〈◊〉〈◊〉 all of one diameter, they will have an equal number of cogs; and as the dia∣meter of the box will be 3 times the diameter of the rollers, it will 〈◊〉〈◊〉 3 times a•• many cogs. Now it is evident, that the axle must turn 1 〈◊〉〈◊〉 times round, before the same cogs of the rollers and shaft will meet, 〈◊〉〈◊〉 were together when it started; because, in that time the rollers will 〈◊〉〈◊〉 moved over 1-3 of the box: therefore the axle must turn 3 3-3 times equal 〈◊〉〈◊〉 4 times round, by the time the box is once measured by the rollers. 〈◊〉〈◊〉 suppose we hold the axle at rest, and turn the box round like a carriage 〈◊〉〈◊〉 then, while the box turns 1 1-3 times round the axle, it will cause the 〈◊〉〈◊〉 to move once round; and while the box or wheel turns round the 〈◊〉〈◊〉 times, the rollers will run round it three times. For suppose we divide 〈◊〉〈◊〉 box into 3 parts, B C and D, then beginning to turn the box from B to 〈◊〉〈◊〉, is evident, that while the roller a b measures once round the axle and 〈◊〉〈◊〉 to the same place, it will also measure the box from B to C, and C will 〈◊〉〈◊〉 taken the place of 〈◊〉〈◊〉, and the next revolution of the roller, D will take 〈◊〉〈◊〉 place of C, and the third revolution B returns to where it was at first, 〈◊〉〈◊〉 the box has made 4 revolutions, while the rollers have made 3 round 〈◊〉〈◊〉 axle, and without any sliding of parts, therefore without friction. I 〈◊〉〈◊〉 go on to shew, that if the axle be much larger than the rollers, they will 〈◊〉〈◊〉 work without sliding.
• * 1.155.9

  The princi∣ples of the ap∣plication of rollers ex∣plained.
• * 1.156

  Effect of a machine, what.
• * 1.157

  Old theory of maximum, motion, and load of en∣gines.
• * 1.158

  Art. 34.
• * 1.159

  Fig. 17.
• * 1.160

  Theory of maximums explained by application of an elevator. Fig. 17.
• * 1.161

  Art. 34.
• * 1.162

  Investigation of the old theory.
• * 1.163

  Art. 35.
• * 1.164

  Old theory doubted.
• * 1.165

  New theory.
• * 1.166

  Art. 35.
• * 1.167

  Art. 36.
• * 1.168

  Art. 36.
• * 1.169

  Theory for the motion and load of en∣gines moved by a power whose motion is equably ac∣celerated.
• * 1.170

  Art. 37.
• * 1.171

  Since writing the above, I have seen Atwood's Treatise on Motion, wherein he gives a set of accurate experiments, to prove (beyond doubt) that the conclusion I have drawn is right, viz. That the charge occupies its proportional part of the whole velocity. See the American Encyclope∣dia, Vol. X. p. 786.
• * 1.172

  William war∣ing's theory.
• * 1.173

  Art. 38.
• * 1.174

  Definition.
• * 1.175

  Demonstra∣tion.
• * 1.176

  Art. 38.
• * 1.177

  Part omitted.
• * 1.178

  Further ex∣tracts from W. Waring's pub∣lication con∣cerning his new theory.
• * 1.179

  The effect of under shot wheels as the squares of the velocities of the water.
• * 1.180

  Art. 39.
• * 1.181

  W. Waring's theory doubt∣ed.
• * 1.182

  It not agree∣ing fully with practice.
• * 1.183

  Art. 40.
• * 1.184

  Because the distance it will recede after the stroke through any 〈◊〉〈◊〉 medium, will be as the squares of its impinging velocities.
• * 1.185

  Art. 40.
• * 1.186

  Art. 41.
• * 1.187

  Fig. 19.
• * 1.188

  Art. 41.
• * 1.189

  Power and ef∣fect as 3 to 2 on overshot wheels.
• * 1.190

  Art. 41.
• * 1.191

  Art. 41.
• * 1.192

  The reason why the wheel hears so great a load at a maximum, 〈◊〉〈◊〉 pears to be as follows, viz.

  A 16 feet head of water over a gate of 1 foot, issues 32,4 cubic 〈◊〉〈◊〉 water in a second, to strike the wheel in the same time, that a heavy 〈◊〉〈◊〉 will take up in falling through the height of the head. Now if 16 〈◊〉〈◊〉 feet of elastic matter, was to fall 16 feet, and strike an elastic 〈◊〉〈◊〉 would rise by the force of the stroke, to the height from whence it 〈◊〉〈◊〉 or, in other words, it will have force sufficient, to bear a load of 16 ••••∣bic feet.

  Again, if 32 cubic feet of non-elastic matter, moving with the same ve∣locity, (with which the 16 feet of elastic matter struck the plain) strike a 〈◊〉〈◊〉 in the same time, although it communicate only half the force, that 〈◊〉〈◊〉 it motion; yet, because there is a double quantity striking in the 〈◊〉〈◊〉 time, the effects will be equal, that is, it will bear a load of 16 cubic 〈◊〉〈◊〉 or the whole column to hold it in equilibrio.

  Again, to check the whole velocity, requires the whole column, 〈◊〉〈◊〉 produces the velocity, consequently, to check any part of the velocity will require such a part of the column that produces the part 〈◊〉〈◊〉 and we find by art. 41, that, to check the velocity of the wheel, 〈◊〉〈◊〉 ,577 of the velocity of the water, it requires 2-3 of the whole 〈◊〉〈◊〉 and this is the maximum load. When the velocity of the wheel, is 〈◊〉〈◊〉 plied by 2-3 of the column, it produces the effect, which will be to 〈◊〉〈◊〉 power, as 38 to 100; or as 3,8 to 10, somewhat more than 1-3, and 〈◊〉〈◊〉 friction and resistance of the air may reduce it to 1-3.
• * 1.193

  Art. 41.
• * 1.194

  Maximum charge of overshot wheels, sup∣posing the same quantity to be always in the buck∣ets.
• * 1.195

  Art. 41. 〈◊〉〈◊〉
• * 1.196

  A true theory deduced.
• * 1.197

  Art. 42.
• * 1.198

  Art. 42.
• * 1.199

  Art. 43.
• * 1.200

  Smeaton's opinion of the proper veloci∣ty for the cir∣cumference of overshot wheels, does not agree with practice.
• * 1.201

  The principle of the power that moves overshot wheels is that of a fall∣ing body.
• * 1.202

  Their veloci∣ties vary, and will be as the square root of their diame∣ters.
• * 1.203

  This rule found to agree with practice.
• * 1.204

  Their veloci∣ties will be a mean be∣tween the least and greatest of a body falling through its diameter.
• * 1.205

  Art. 43.
• * 1.206

  Water presses harder on the lower than upper quarter of the whele.
• * 1.207

  The whole descent must be nicely di∣vided be∣tween head and fall.
• * 1.208

  It makes no difference whether the water stands perpendicular above the aperture, or incliningly (see plate III, fig. 22.) providing the perpendicular height be the same; or whether the quantity be great or small, providing 〈◊〉〈◊〉 be sufficient to keep up the fluid to the same height.
• * 1.209

  Art. 45.
• * 1.210

  This law is similar to the 4th law of falling bodies, their velocities be∣ing as the square root of their spaces passed through; and by experiment it is known, that water will spout from under a 4 feet head 16,2 feet per se∣cond, and from under a 16 feet head, 32,4 feet per second, which is only double to that of a 4 feet head, although there be a quadruple pressure. Therefore by this law we can find the velocity of water spouting from un∣der any given head; for as the square root of 4 equal 2 is to 16,2 its veloci∣ty, so is the square root of 16 equal 4, to 32,4 its velocity. And again, as 16,2 squared, is to 4 its head, so is 32,4 squared, to 16 its head; by which ratio we can find the head that will produce any velocity.
• * 1.210.10

  Foundation of the rule for finding the ve∣locity of wa∣ter under any head.
• † 1.211

  It is evident that a double velocity will vent a double quantity.
• ‡ 1.212

  If the pressure be equal, the velocity must be equal; and it is evident, that double quantity with equal velocity will produce a double effect.
• ‖ 1.213

  That is, if we suppose 16 cubic feet of water to issue from under a 4 feet head in a second, and an equal quantity to issue in the same time from under 16 feet head, then their effects will be as 4 to 16. But we must note, that the aperture in the last case must be only half of that in the first, as the velocity will be double.
• sect 1.214

  This is evident from this consideration, viz. that a quadruple impulse is required to produce a double velocity, by law 2nd, where the velocities are as the square roots of their heads; therefore their effects must be as the squares of their velocities.

  DEMONSTRATION.

  LET A F, (plate III, fig. 26) represent a head of water 16 feet high, and suppose it divided into 4 different heads of 4 feet each, as B C D E; then sup∣pose we draw a gate of 1 foot square at each head successively, always sinking the water in the head, so that it will be but 4 feet above the centre of the gate in each case.

  Now it is known that the velocity under a 4 feet head, is 16,2 feet per second; say 16 feet to avoid fractions, which will issue 16 cubic feet of wa∣ter per second, and for sake of round numbers, let unity or 1 represent the quantity of a cubic foot of water; then, by the 7th law the effect will be as the quantity multiplied by the square of the velocity; that is, 16 multipli∣ed by 16 is equal to 256, which 1 multiplied by 16, the quantity, is equal to 4096, the effect of each 4 feet head; and 4096 multiplied by 4 is equal to 16384, for the sum of effects, of all the 4 feet heads.

  Then as the velocity under a 16 feet head is 32,4 feet, say 32 to 〈◊〉〈◊〉 fractions: the gate must be drawn to only half the size, to vend the 〈◊〉〈◊〉 feet of water per second as before, (because the velocity is double) 〈◊〉〈◊〉 find the effect, 32 multiplied by 32, is equal to 1024; which multiplied 16 the quantity, gives the effect, 16384, equal the sum of all the 4 feet 〈◊〉〈◊〉 which agrees with practice and experience, the best teachers. But 〈◊〉〈◊〉 effects were as their velocities simply, then the effect of each 〈◊〉〈◊〉 head would be, 16 multiplied by 16, equal to 256; which, multiplied is equal to 1024, for the sum of the effects of all the 4 feet heads: and mul∣tiplied by 32 equal to 512, for the effect of the 16 feet head, which 〈◊〉〈◊〉 half of the effect of the same head when divided into 4 parts; which is con∣trary to both experiment and reason.

  Again, let us suppose the body A of quantity 16, to be perfectly 〈◊〉〈◊〉 fall 16 feet and strike F, a perfect elastic plain, it will (by laws of 〈◊〉〈◊〉) strike with a velocity of 3•• feet per second, and rise 16 feet to 〈◊〉〈◊〉

  But if it fall only to B, 4 feet, it will strike with 16 feet per 〈◊〉〈◊〉 rise 4 feet to A again. Here the effect of the 16 feet fall is 4 times the 〈◊〉〈◊〉 of the 4 feet fall, because the body rises 4 times the height.

  But if we count the effective momentum of their strokes to be as ve∣locities simply, th••n 16 multiplied by 32 is equal to 512, the momen•••• 〈◊〉〈◊〉 the 16 feet fall; and 16 multiplied by 16 is equal to 256; which, 〈◊〉〈◊〉 by 4, is equal to 1024, for the sum of the momentums of the str•••• 〈◊〉〈◊〉 feet divided into 4 equal falls, which is absurd. But if we count 〈◊〉〈◊〉 mo∣mentums to be as the squares of their velocities, the effects will be equal.

  Again, it is evident that whatever impulse or force is required to 〈◊〉〈◊〉 body a velocity, the same force or resistance will be required to 〈◊〉〈◊〉 therefore, if the impulse be as the square of the velocity produced, 〈◊〉〈◊〉 or resistance will be as the squares of the velocity also. But the 〈◊〉〈◊〉 as the squares of the velocity produced, which is evident from this 〈◊〉〈◊〉 ration, Suppose we place a light body at the gate B, of 4 feet head, and ••••sed with 4 feet of water; when the gate is drawn it will fly off with 〈◊〉〈◊〉 ••••••∣city of 16 feet per second; and if we increase the head to 16 feet, it 〈◊〉〈◊〉 off with 32 feet per second. Then, as the squares of 16 equal to 2•••• the square of 32 equal to 1024, so is 4 to 16. Q. E. D.

  To compare this 7th law with the theory of undershot mills, 〈◊〉〈◊〉 art. 42, where it is shewn that the power is to the effect as 3 to 1; 〈◊〉〈◊〉 by the 7th law, the quantity shewn by the scale, plate II, to be 32,4 multi∣plied by 1049,76 the square of the velocity, which is equal to 3401, 212 〈◊〉〈◊〉 effect of the 16 feet head: then, for the effect of a 4 feet head, with 〈◊〉〈◊〉 aperture quantity, by scale, 16,2 multiplied by 262,44, the velocity ••∣ed, is equal to 425,1528, the effect of a 4 feet head; here the ratio of effects are as 8 to 1.

  Then, by the theory, which shews that an undershot wheel will 〈◊〉〈◊〉 of the water that turns it, to the whole height from which it descended 1-3 of 32,4 the quantity, being equal to 10,8 multiplied by 16, perpendicu∣lar ascent; which is equal to 172,8, effect of a 16 feet head; and 〈◊〉〈◊〉 16,2 quantity, which is equal to 5,4 multiplied by 4, perpendicular 〈◊〉〈◊〉 is equal to 21,6 effect of 4 feet head, by the theory: and here again ••••∣tio of the effects are as 8 to 〈◊〉〈◊〉; and,

  by 7th law,

  • as 3401,2124, the effect of 16 feet head,
  • is to 425,1528, the effect of 4 feet head,

  by the theory.

  • to is 172,8 the effect of 16 feet head,
  • to 21,6 the effect of 4 feet head,

  The quantities being equal, their effects are as the height of their head ••••rectly, as by 5th law, and as the squares of their velocities as by 7th 〈◊〉〈◊〉 Hence it appears, that the theory agrees with the established laws, 〈◊〉〈◊〉 take to be a confirmation that it is well founded.
• * 1.215

  Art. 46. Fig. 26.
• * 1.216

  Fig. 26.
• * 1.217

  Art. 47
• * 1.218

  Theory that is established compared with the esta∣blished laws. And found to agree.
• * 1.219

  Art. 46.
• * 1.220

  Art. 47.
• * 1.221

  The effects of striking fluids with equal apertures are as the cubes of their velocities, for the following reasons, viz. 1st, If an equal quantity strike with double velocity, the effect is quadruple on that account by the 7th law; and a double velocity expends a double quantity by 3d law; there∣fore, the effect is amounted to the cube of the velocity.—The theory for un∣dershot wheels agrees with this law also.
• † 1.222

  The falling body is acted on by the whole force of its own gravity, in the whole of its descent through any space; and the whole sum of this action that is acquired as it arrives at the lowest point of its fall, is equal to the pressure of the whole head or perpendicular height above the issue; there∣fore their velocities are equal.
• ‡ 1.223

  That is, they re-act back against the penstock with the same force that it issues against the obstacle it strikes: this is the principle by which Bar∣ker's mill, and all those that are improvements thereon, moves.
• * 1.224

  Art. 47.
• * 1.225

  When non-elastic bodies strike an obstacle, one half of their force is spent in a lateral direction, in changing their figure, or in splashing about See art. 8.

  For want of due consideration or knowledge of this principle, many have been the errors committed by applying water to act by impulse, when it would have produced a double effect by its gravity.
• * 1.226

  Laws of moti∣on and spout∣ing fluids app∣lied in prac∣tice.
• * 1.227

  Art. 47.
• * 1.228

  Art. 47.
• * 1.229

  Art. 47.
• * 1.230

  To explain which, let A B C D, plate III, fig. 22, be a vessel of water of a cubical form, with a small tube as H, fixed therein; let a hole of the same size of the tube be made at o, and covered with a piece of pliant leather, nailed thereon, so as to hold the water. Then fill the vessel with water by the tube H, and it will press upwards against the leather, and raise it in a convex form, requiring just as much weight to press it down, as will be equal to the weight of water in the tube H. Or if we set a glass tube over the hole at o, and pour water therein, we will find that the water in the tube o, must be of the same height of that in tube H, before the leather will subside, even if the tube O be much larger than H; which shews, that the pressure upwards is equal to the pressure downwards; because, the water pressed up against the leather with the whole weight of the water in the tube H. Again, If we fill the vessel by the tube I, it will rise to the same height in H that it is in I; the pressure being the same in every part of the vessel as if it had been filled by H; and the pressure on the bottom of the vessel will be the same, whether the tube H be of the whole size of the ves∣sel, or only one quarter of an inch diameter. For suppose H to be 1-4 of an inch diameter, and the whole top of the vessel of leather as at o, and we pour water down H, it will press the leather up with such force, that it will require a column of water of the whole size of the vessel, and height of H, to cause the leather to subside. Q. E. D.

  And again, Suppose we make two holes in the vessel, one close to the bot∣tom, and the other in the bottom, both of one size, the water will issue with equal velocity out of each; which may be proved by holding equal vessels under each, which will be filled in equal time; which shews, that the pres∣sure on the sides and bottom are equal under equal distances from the sur∣face. And this velocity will be the same whether the tube be filled by pipe I, or H, or by a tube the whole size of the vessel, provided the perpendicu∣lar height be equal in all cases.

  From what has been said, it appears, that it makes no difference in the power of water on mill-wheels, whether it be brought on in an open forebay and perpendicular penstock, 〈◊〉〈◊〉 down an inclining one, as I C; or under ground in a close ••••••nk, in any 〈◊〉〈◊〉 that may best suit the situation and cir∣cumstances, provided that the 〈◊〉〈◊〉 be large enough to supply the water fast enough to 〈…〉〈…〉 from sinking.

  This pric•••••• 〈…〉〈…〉 has sometimes taken place in undershot mills. 〈…〉〈…〉 against the bottom of the buckets, thereby destroying or 〈…〉〈…〉. See art. 54.
• * 1.231

  Hydrostatic paradox ex∣plained.
• * 1.232

  Art. 49.
• * 1.233

  Water may be conveyed to the wheel of a mill any way most conveni∣ent.
• * 1.234

  Art. 48.
• * 1.235

  For demonstration 〈…〉〈…〉 Brita••.
• * 1.236

  Theorem for finding the pressure of the water on the gate, &c.
• * 1.237

  Art. 50.
• * 1.238

  Great strength required to hold water under high heads.
• * 1.239

  Art. 51.
• * 1.240

  Rule for find∣ing the velo∣city of spout∣ing water.
• * 1.241

  Art. 52.
• * 1.242

  Rule for find∣ing the effect of any gate, drawn under any head on an undershot wheel.
• * 1.243

  Art. 53.
• * 1.244

  Fig. 19.
• * 1.245

  Demonstra∣tion that the power of wa∣ter on over∣shot wheels, is as the quantity, multiplied in∣to their dia∣meters or per∣pendicular descent.
• * 1.246

  Art. 53.
• * 1.247

  Rule for mea∣suring the power of the mill-seat.
• * 1.248

  Art. 54
• * 1.249

  Water acts with as much power on an overshot, as if it was all to act fairly on the breast bucket, in the whole of its perpendicular descent.
• * 1.250

  This error has been the cause of many expensive errors in the applica∣tion of water.
• * 1.251

  Fig. 20, pl. III.
• * 1.252

  Demonstra∣tion.
• * 1.253

  Fig. 21.
• * 1.254

  Demonstrated by a chain and buckets.
• * 1.255

  Art. 54
• * 1.256

  Proved by ex∣periment.
• * 1.257

  Of the fric∣tion of the apertures of spouting fluids.
• * 1.258

  Art. 55.
• * 1.259

  Need not be regarded in undershot mills; But must be noted in overshots.
• † 1.260

  This seems to be proved by Smeaton, in his experiments; (see 〈◊〉〈◊〉 art. 67) where, when the head was 33 inches, the sluice small, draw••, 〈◊〉〈◊〉 to the 1st hole, the velocity of the water was only such as is assigned theory, to a head of 15,85 inches, which he calls virtual head. But 〈◊〉〈◊〉 the sluice was larger, drawn to the 6th hole, and head 6 inches, the 〈◊〉〈◊〉 head was 5,03 inches. But seeing there is no theorem yet discovered which we can truly determine the quantity or effect of their friction, acc••••ing to the size of the aperture, and height of the head; therefore 〈◊〉〈◊〉 not, by the established laws of hydrostatics, determine exactly, the 〈◊〉〈◊〉 or quantity expended through any small aperture; which renders the 〈◊〉〈◊〉 but little better than conjecture in these cases.
• * 1.261

  Pressure of the air the cause of the rise of fluids.
• * 1.262

  This will appear, if we consider and suppose, that the friction does ••••∣••••bly retard the velocity of the fluid to a certain distance. Say half as 〈◊〉〈◊〉 from the side or edge of the aperture, towards its centre; and we may ••••∣sonably conclude, that this distance will be nearly the same in a 2 and 〈◊〉〈◊〉 aperture; so that in the 2 inch aperture, a ring on the outside, half a•• 〈◊〉〈◊〉 wide, is sensibly retarded, which is about 3-4 of the whole; while, 〈◊〉〈◊〉 12 inch aperture, there is a ring on the outside half an inch wide, 〈◊〉〈◊〉 about 1-6 of its whole area.
• * 1.263

  Art. 56.
• * 1.264

  This seems to be the principle of whirl winds at sea, called water spouts; the wind meeting from different points, forms a quick circular mo∣tion; and by the centrifugal force forms a partial vacuum in the centre, which gives liberty to the water to rise a little, which is by the rapidity of the motion of the air, rent into very small particles: which so increases the surface, that the air takes sufficient hold of it to carry it up. And as the wind meeting has no way to vent itself but in a perpendicular direction, therefore, a brisk current is formed upwards, carrying the water with it, at sea; but on the land, it raises leaves of trees and other light bodies. See Franklin's Letters.
• * 1.264.11

  Principles of water-spo•• at sea.
• * 1.265

  Fig. 23. pl. III.
• * 1.266

  Principles of syphons for decanting li∣quors.
• * 1.267

  Art. 56.
• * 1.268

  Fig. 24, pl. III.
• * 1.269

  principles of Pumps for raising water.
• * 1.270

  Fig. 20.
• * 1.271

  To convey water under valleys and over hills.
• * 1.272

  Art. 59.
• * 1.273

  Of the force of definite & indefinite quantities of water.
• * 1.274

  Indefinite quantity of water ap∣plied
• * 1.275

  Definite quan∣tity applied.
• * 1.276

  Art. 59.
• * 1.277

  A perfectly definite quan∣tity applied, but cannot be applied to a wheel in prac∣tice.
• * 1.278

  But this difficulty is now overcome by the valve wheel: See annota∣tion, art. 73.
• * 1.279

  Paradoxical mill that will not move empty.
• * 1.280

  Fig. 25.
• * 1.281

  Art. 60.
• * 1.282

  Breast and pitch-back wheels does not run before the gravity of the water.
• * 1.283

  If gravity could be either decreased by velocity downwards, or increas∣ed by velocity upwards, then a virtical wheel without friction, either of gud∣geons or air, would require a great force to continue its motion; because, its velocity would decrease the gravity of its descending side, and increase it on its ascending side, which would immediately stop it: whereas it is known, that it requires no power to continue its motion, but what is necessary to overcome the friction of the gudgeons, &c.
• * 1.284

  Direct the wa∣ter down∣wards when there is too much head, on overshot, pitch-back, or breast wheels.
• * 1.285

  Art. 60.
• * 1.286

  Art. 61.
• * 1.287

  Simple rule for calculat∣ing the power of any mili∣seat.
• * 1.288

  Art. 61.
• * 1.289

  Water by percussion spends its force on the wheel in the following time, which is in proportion to the distance of the float-board, and differ∣ence of the velocity of the water and wheel.

  If the water runs with double the velocity of the wheel, it will spend all its force on the floats, while the water runs the distance of two float∣boards, and while the wheel runs the distance of one; therefore the wa∣ter need not be kept to act on the wheel from the point of impact further than the distance of about two float-boards.

  But if the wheel runs with two thirds of the velocity of the water, then, while the wheel runs the distance of two floats, and while the water would have ran the distance of three floats, it spends all its force; therefore the water need be kept to act on the wheel only the distance of three floats past the point of impact.

  If it be continued in much longer it will fall back, and re-act against the following bucket and retard the wheel.
• * 1.290

  Power of 16 cubic feet of water per se∣cond, calcu∣lated on five different ap∣plications.
• * 1.291

  Art. 62.
• * 1.292

  Rule for find∣ing the cir∣cumference and diameter.
• * 1.293

  Rule for find∣ing the area of stone,
• * 1.294

  And surface passed.
• * 1.295

  Art. 62.
• * 1.296

  Art. 62.
• * 1.297

  Experiments.
• * 1.298

  Art. 63.
• * 1.299

  Rule for pro∣portioning the size of the stones to suit the power of the seat.
• * 1.300

  And power to the size of the stone.
• * 1.301

  Art. 63.
• * 1.302

  Proper velo∣city of the stone deduced from experi∣ments in practice.
• * 1.303

  The diameter of a 4 feet stone squared, multiplied by ,7854 equal 12,56 its area; which squared is 157,75 feet, the surface passed at one re∣volution: and 8 multiplied by 8 equal 64, which multiplied by ,7854 equal 50,24 being the area of an 8 feet stone; which squared is 2524,04 the the surface passed, which surfaces are as 1 to 16.
• * 1.304

  Art. 63.
• † 1.305

  Because the 8 feet stone will revolve only half as often as the 4 〈◊〉〈◊〉 therefore their quantity of surface passed, &c. can be only half as 〈◊〉〈◊〉 more as it was in the last case; that is as 8 to 1.
• ‡ 1.306

  A French author (M. Fabre) says, that by experiments he has ••ound that to produce the best flour, a stone 5 feet diameter should revolve be∣tween 48 and and 61 times in a minute. This is much slower than prac∣tice in America, but we may conclude that it is best to err on the 〈◊〉〈◊〉 slower than faster than common practice; especially when the power is 〈◊〉〈◊〉 small for the size of the stone.
• * 1.307

  Art. 63.
• * 1.308

  Art. 64.
• * 1.309

  Directions for digging canals through rocky ground.
• * 1.310

  Fig. 36.
• * 1.311

  They need not be of equal width nor depth in all places;
• * 1.312

  But the area of their section must be the same or not less than the given size.
• * 1.313

  Rule for find∣ing the right size to convey any quantity required.
• * 1.314

  Art. 65.
• * 1.315

  An acre of a mill-pond contains 43560 cubic feet of water, for every foot of its depth.

  Suppose your pond contains 3 acres and is 3 feet deep, then 43560, mul∣tiplied by 3, is equal 130680, which multiplied by 3, is equal 392040 cubic feet, its contents, which divided by the cubic feet your mill uses per se∣cond (say 10) is equal 39204 seconds, or 10 hours, the time the pond will keep the mill going.
• * 1.316

  Of the proper fall in canals.
• * 1.317

  Art. 65.
• * 1.318

  Air-pipes ne∣cessary to pre∣vent tight trunks from bursting.
• * 1.319

  If they are too small they are worse than none.
• * 1.320

  Art. 66.
• * 1.321

  Air prevents trunks from bursting.
• * 1.322

  To prevent ice from gathering on overshot wheels when standing, the water is shut out of the trunk by a gate at the canal, and what leaks thro' it is let thro' a hole in the bottom of the trunk: the water is let in again with full force.
• * 1.323

  Art. 67.
• * 1.324

  Art. 67.
• * 1.325

  Art. 67.
• * 1.326

  Art. 67.
• * 1.327

  Art. 67.
• * 1.328

  The weight of the scale makes part of the weight both ways, viz. both of the weight and counter-weight.
• * 1.329

  Art.67.
• * 1.330

  When the wheel moved so slow as not to rid the water so fast as 〈◊〉〈◊〉 by the sluice, the accumulated water falls back upon the 〈…〉〈…〉 the wheel immediately ceases moving.

  Note—This note of the author argues in favour of drawing the 〈◊〉〈◊〉 the floats.
• * 1.331

  Art. 67.
• * 1.332

  This is determined by the common maxim of hydrostatics; that the velocity of spouting waters is equal to the velocity that a heavy body would 〈◊〉〈◊〉 in falling from the height of the reservoir; and is proved by the 〈◊〉〈◊〉 of jets, to the height of their reservoirs nearly.
• * 1.333

  Art. 67.
• * 1.334

  The resistance of the air in this ••ase ceases, and the friction is ••••••••∣ded, as 12lb. in the scale was sufficient to stop the wheel after it 〈◊〉〈◊〉 in full motion, and therefore somewhat more than a counter-balance 〈◊〉〈◊〉 impulse of the water.
• † 1.335

  I may here observe, that it is probable, that if the gate of the sluice 〈◊〉〈◊〉 been drawn as near the float-boards as possible, (as is the practice in Ame∣rica, where water is applied to act by impulse alone) that the wheel would have continued to move until loaded with 1 1-2 times the weight of the max∣imum load, viz. 9lb.6 oz. multiplied by 1 1-2 is equal to 14lb.1 oz. Then it would have agreed with the theory established art 41. This perhaps es∣caped the notice of our author.
• * 1.336

  Art. 67.
• * 1.337

  This observation of the author I think a strong confirmation of the truths of the theory established art. 41; where the maximum velocity is made to be, 577 parts of the velocity of the water, and the load to be 2-3 the greatest load: For if the gate had been drawn near the floats, the greatest load would probably have been 14lb. 1 oz. or as 3 to 2, of the maximum load.
• * 1.338

  Art. 67.
• * 1.339

  If the true maximum velocity of the wheel be, 577 of the velocity of the water, and the true maximum load be 2-3 of the whole column, as shewn in art.42; then the effect will be to the power in the ratio, of 100 to 38, or as 10 to 3,8, a little more than appears by this table of experiments, in column 9 and 10: the difference is owing to the disadvantageous application of the water on the wheel in the model.
• * 1.340

  Art. 67.
• * 1.341

  Art. 67.
• * 1.342

  Art. 67.
• * 1.343

  Art. 67.
• * 1.344

  I may here observe, that our friend Smeaton may be wrong in his ••••∣c••asion, that the best general ratio of the velocity of the water to that of the wheel will be as 5 to 2; because, we may observe, that in the first ••••••••∣ment, where the virtual head was 15,85 inches, and the gate drawn to 〈◊〉〈◊〉 1st hole, the ratio is as 10:3,4. But in the last experiment, where 〈◊〉〈◊〉 is as 5,03 inches, and gate drawn to the 6th hole, the ratio is as 10:〈◊〉〈◊〉 and that the 2nd term of the ratio increases gradually, as the head 〈◊〉〈◊〉, and quantity of water increases: therefore we may conclude, that the large openings of mills, that the ratio may approach to 3 to 2; which 〈◊〉〈◊〉 agree with the practice and experiments of many able mill-wrights of ••••••∣rica, and many experiments I have made on mills. And as it is better 〈◊〉〈◊〉 give the wheel a velocity too great than too slow, I conclude, the 〈◊〉〈◊〉 an undershot mill must have nearly 2-3 of the velocity of the water, to 〈◊〉〈◊〉 a maximum effect.
• † 1.345

  Perhaps the author is here again deceived by the imperfection of 〈◊〉〈◊〉 model; for had the water been drawn close to the float, the load that 〈◊〉〈◊〉 totally stop the wheel would always be equal to the column of water 〈◊〉〈◊〉 on the wheel. See the note page 70. The friction of the shute and air 〈◊〉〈◊〉 ••••∣stroyed great part of the force of his small quantity of water.
• * 1.346

  Art. 67.
• * 1.347

  Art. 68.
• * 1.348

  Art. 68.
• * 1.349

  The small difference in the value of 12 strokes of the pump from the former experiments, was owing to a small difference in the length of the stroke, occasioned by the warping of the wood.
• * 1.350

  Art. 68.
• * 1.351

  These observations of the author agree with the theory art. 41—42. In add that non-elastic bodies, when acting by impulse or collision ••••••cate only half of their original power, by the laws of motion.
• * 1.352

  Art. 68.
• * 1.353

  Art. 68.
• * 1.354

  Art. 68.
• * 1.355

  Art. 68.
• * 1.356

  Probably this wheel was working forge of furnace bellows, which have deceived many by their slow regular motion.
• † 1.357

  Read May 31st and June 14th, 1759, in the Philosophical society of London.
• * 1.358

  Art.69.
• * 1.359

  I decline giving any description or draught of this machine, as I have not room; but I may say, that it was constructed so as to wind up a weight, (as did the other model) in order to find the effect of the power. I may al∣so insert a specimen of a set of experiments, which I scar will not be well understood, for want of a full explanation of the machine.
• ‡ 1.360

  In the following experiments the angle of the sail is accounted from the plain of their motion; that is, when they stand at right angles to the axis, their angle is denoted 0 deg.; this notation being agreeable to the language of practitioners, who call the angle so denoted the weather of the sail; which they denominate greater or less, according to the quantity of the angle.
• * 1.361

  Art. 69.
• I 1.362

  Plain sails at an angle of 55 degrees.
• II 1.363

  Plain sails weathered according to common practice.
• III 1.364

  Weathered according to Maclaurin's theorem.
• IV 1.365

  Weatherd in the Dutch manner, tried in various positions.
• V 1.366

  Weathered in the Dutch manner, but enlarged towards the extremities.
• VI 1.367

  8 Sails, being factors of elipses in their best positions.
• * 1.368

  Art. 69.
• * 1.369

  This confirms the 7th law of spouting fluids.
• * 1.370

  Art. 69.
• * 1.371

  Principles on which is founded the undershot table.
• * 1.372

  Principles on which is founded the undershot table.
• * 1.373

  Principles on which is founded the undershot table.
• * 1.374

  CHAP.1.
• * 1.375

  One advantage large wheels has over small ones is, they cast off the back-water much better. The buckets of the low wheel will lift the water much more than those of the high wheel; because, the nearer the water rises to the centre of the wheel, the nearer the buckets approach the horizontal or lifting position.

  Fig. 28 is an undershot wheel. Some prefer to slant the forebay under the wheel, as in the figure, that the gate may be drawn near the floats; because (say they) the water acts with more power near the gate, than at a distance; which appears to be the case, when we consider, that the nearer we approach the gate, the nearer the column of water ap∣proaches to be what is called a perfect definite quantity. See art. 59.

  Others again say, that it acquires equal power in descend∣ing the shute (it will certainly acquire equal velocity, abating only for the friction of the shute and air). When the shute has a considerable descent, the greater the distance from the gate, the greater the velocity and power of the water; but where the descent of the shute is not sufficient to overcome the friction of the air, &c. then the nearer the gate, the greater the velocity and power of the water; which argues in favour of drawing the gate near the floats. Yet, where the fall is great, or water plenty, and the expence of a deep penstock considerable, the small difference of power is not worth the expence of obtaining. In these cases, it is best to have a shallow penstock, and a long shute to convey the water down to the wheel, drawing the gate at the top of the 〈◊〉〈◊〉 which is frequently done, to save expence, in building 〈◊〉〈◊〉 mills, with flutter-wheels, which are small undershot 〈◊〉〈◊〉 fixed on the crank, so small as to obtain a sufficient 〈◊〉〈◊〉 of strokes of the saw in a minute, say about 120. 〈◊〉〈◊〉 wheel is to be calculated of such size as to suit the velocity 〈◊〉〈◊〉 the water at the point of impact, so as to make that 〈◊〉〈◊〉 of revolutions in a minute.

  For the method of shooting the water on an 〈◊〉〈◊〉 wheel, where the fall is great, see Thomas Ellicott's 〈◊〉〈◊〉 part 5, plate 1, fig. 6.
• * 1.376

  Best to car∣ry the water down a long shute to the wheel, in high heads.
• * 1.377

  Observations.
• * 1.378

  CHAP.1.
• * 1.379

  Tub Mills described.
• * 1.380

  CHAP.1.
• * 1.381

  Note, that in fig. 30, I have allowed the gate to be drawn inside of the penstock, and not in the shute near the wheel, as is the common practice; because the water will leak out much along side of the gate, if drawn in the shute. But here we must consider, that the gate must always be full drawn, and the quantity of water regulated by a regulate in the shute near the wheel; so that the shute will be per∣fectly full, and pressed with the whole weight of the head, else a great part of the power may be lost.

  To shew this more plain, suppose the long shute A, from the high head (shewn by dotted lines) of the undershot mill, fig. 28, be made tight by being covered at top, then, if we draw the gate A, but not fully, if the shute at bottom be large enough to vent all the water that issues through the gate, when the shute is full to A, then it cannot fill higher than A; therefore, all that part of the head above A is lost, it being of no other service than to supply the shute, and keep it full to A, and the head from A to the wheel is all that acts on the wheel.

  Again, when we shut the gate, the shute cannot run emp∣ty, because it would leave a vacuum in the head of the shute at A; therefore the pressure of the atmosphere resists the water from running out of the shute, and whatever head of water is in the shute, when the gate is shut, will balance its weight of the pressure of the atmosphere, and prevent it from acting on the lower side of the gate, which will cause it to be very hard to draw—For, suppose 11 feet head of water to be in the shute when the gate was shut, its pressure is equal to about 5lb. per square inch; then, if the gate be 48 by 6 inches, which is equal to 288 inches, this multiplies by 5, is equal to 1440 lb. the additional pressure on the gate.

  Again, if the gate be full drawn, and the shute be not much larger at the upper than lower end, all these evils 〈◊〉〈◊〉 take place to cause the loss of power. To remedy all this, put the gate H at the bottom of the shute to regulate the quantity of water by, and make a valve at A to shut on the inside of the shute, like the valve of a pair of bellows, which will shut when the gate A is drawn, and open when the gate shuts, to let air into the shute; this plan will do better tha•• long open shutes, for saw-mills with flutter-wheels or tub mills, as by it we evade the friction of the shute and resistance of the air.

  The reader will with difficulty understand what is here said, unless he be acquainted with the theory of the pressure of the atmosphere, vacuums, &c. See these subjects, touched on in art. 56.
• * 1.382

  CHAP.1.
• * 1.383

  Tub mills act with less power than undershots.
• * 1.384

  They are preferable to others, with plenty of water.
• * 1.385

  Should move 2-3 the velocity of the water
• * 1.386

  Rules To find the velocity of the water.
• * 1.387

  Its diameter
• * 1.388

  The quanti∣ty of water required.
• * 1.389

  The size of the aper∣ture.
• * 1.390

  And size of the canal.
• * 1.391

  On Breast Mills the water acts both by per∣cussion and gravity.
• * 1.392

  CHAP. I.
• * 1.393

  Plate IV. Fig. 31.
• * 1.394

  Pitchback wheels have their mo∣tion equal to overshots
• * 1.395

  CHAP. I.
• * 1.396

  Fig. 31,
• * 1.397

  Wheel of new con∣struction.
• * 1.398

  Fig. 32.
• * 1.399

  Principles on which the breast mill table is founded.
• * 1.400

  CHAP. I.
• * 1.401

  Rules
• * 1.402

  To find the velocity of a breast wheel
• * 1.403

  Its number of revolu∣tions.
• * 1.404

  Revolutions of the stone.
• * 1.405

  CHAP. I.
• * 1.406

  Power re∣quired.
• * 1.407

  Area of the canal.
• * 1.408

  Fig. 33. Overshot Wheel de∣scribed.
• * 1.409

  Of shooting on the water
• * 1.410

  Proper ve∣locity of the water spouting on the wheel.
• * 1.411

  Rule for proportion∣ing the head to the wheel
• * 1.412

  Rules
• * 1.413

  For finding the number of revolu∣tions of the wheel.
• * 1.414

  Ditto of the stone.
• * 1.415

  To find the quantity of water re∣quired.
• * 1.416

  Rule to find the size of the canal.
• * 1.417

  Single gear does not suit overshot wheels, high or low.
• * 1.418

  In the year 1786, I invented and made a model of 〈◊〉〈◊〉 wheel of this structure, intending thereby to apply steam 〈◊〉〈◊〉 propel land-carriages, and exhibited a drawing thereof to the legislature of Maryland, and obtained a patent (for my im∣provements in mills, and also) for applying steam to land-carriages, in that state; but could not attend to put it in prac∣tice. Since which time, the late ingenious James Rumsey has applied steam to a wheel of this structure, I hear, with great success, and obtained a patent, in Europe, for the in∣vention; which, probably, was original with him also, as it frequently happens, that two persons, reasoning right on a mechanical subject, think alike, and invent the same thing, without any communication with each other. He has also applied this wheel to water-mills, which I did not intend to do. This may properly be called the Valve Wheel.
• * 1.419

  Rules for calculating motion, &c.
• * 1.420

  Principles on which they are founded.
• * 1.421

  Art. 74.
• * 1.422

  To find the revolutions of the stone.
• * 1.423

  To find the proper num∣ber of cogs, &c.
• * 1.424

  Art. 74.
• * 1.425

  Circle of motion.
• * 1.426

  Art. 74.
• * 1.427

  Art. 74.
• * 1.428

  Art. 74.
• * 1.429

  Rules
• * 1.430

  To find the diameter & circumfe∣rence of cir∣cles.
• * 1.431

  To find the pitch circle of wheels.
• * 1.432

  Art. 75.
• * 1.433

  New rule for finding the pitch circle.
• * 1.434

  Art. 76.
• * 1.435

  Fig. 35.
• * 1.436

  Art. 76.
• * 1.437

  Common rule not true
• * 1.438

  Art. 76.
• * 1.439

  Fig. 34.
• * 1.440

  A triangle constructed to shew the radius of the pitch circle of many wheels.
• * 1.441

  Rule for measuring the contents of garners.
• * 1.442

  To measure the contents of a hopper.
• * 1.443

  Art. 77.
• * 1.444

  To make a garner to hold a given quantity.
• * 1.445

  Ditto, 〈◊〉〈◊〉 hopper.
• * 1.446

  Art. 78.
• * 1.447

  Of the fi∣gures de∣scribed by the cogs of wheels in motion.
• * 1.448

  Fig. 37.
• * 1.449

  Which di∣rects to the proper for∣mation of their cogs.
• * 1.450

  Art. 79.
• * 1.451

  Principles of Spur Gears.
• * 1.452

  The pitch of the driver should be the largest.
• * 1.453

  Art. 79.
• * 1.454

  Their ad∣vantage.
• * 1.455

  Their disad∣vantages.
• * 1.456

  Fig. 38.
• * 1.457

  Fig. 39.
• * 1.458

  Rule for de∣scribing the sides of the cogs to the epicycloid.
• * 1.459

  Art. 79.
• * 1.460

  Principle of Face Gears.
• * 1.461

  They have much fric∣tion
• * 1.462

  Their ad∣vantages
• * 1.463

  Their disad∣vantages.
• * 1.464

  For if the bearing of the cogs be small, and the stress so great that they cut one another, they will wear exceed∣ing fast; but if it be so large, and the stress so light, the they only polish one another, they will last very long.
• * 1.465

  Art. 80.
• * 1.466

  Directions for forming the cogs.
• * 1.467

  Art. 80.
• * 1.468

  Principles of Bevel Gear.
• * 1.469

  Art. 81.
• * 1.470

  Have but little fric∣tion.
• * 1.471

  Rule for proportion∣ing the wheels.
• * 1.472

  Art. 8.
• * 1.473

  Their ad∣vantages.
• * 1.474

  Disadvan∣tages.
• * 1.475

  Fig. 43.
• * 1.476

  Universal joint.
• * 1.477

  Its use.
• * 1.478

  Principles of Rolling Screens and Fans.
• * 1.479

  Art. 83.
• * 1.480

  Art. 84.
• * 1.481

  This I have from Timothy Kink, being one principle of his improved fan.
• * 1.482

  Art. 8••.
• * 1.483

  Art. 84.
• * 1.484

  To understand this subject better, let us consider, that when we strike a flint with steel, we choose the sharpest part of the flint; then the surface of contact is so small, that the force of the stroke creates friction enough to strike or gene∣rate fire: But if we strike a thick smooth part of the flint, the force will not be sufficient to strike fire, the surface being too large. Hence we may conclude, that the smaller the r••••••ing surface, the greater the heat; and if the surface was so small as to strike fire continually, it would be very difficult to keep the gudgeon cool. If a gudgeon heats at 3 inches bearing on the stone, lengthen it to 6 or 8 inches. I have seen them in use from 2 1-2 to 10 inches bearing on the stone; and those who had the longest (being men of the greatest ex∣perience in the milling business) accounted their length to be a good remedy against the heating.
• † 1.485

  Water is a great conductor of heat, and wonderful is the effect of the principle of evaporation, in carrying off the heat from bodies; every particle of water that evaporates, car∣ries off a quantity of heat with it. Dr. Franklin asserts, that by evaporation a man could be froze to death the warmest day ••••n summer.
• * 1.486

  Art. ••4.
• * 1.487

  The grease operates in lessening friction, perhaps, in three ways. 1st. The particles of the grease, by filling 〈◊〉〈◊〉 the pores of the stone and gudgeon, makes the sliding sur∣faces more perfectly smooth. 2d. The particles of great act as rollers between the sliding surfaces. 3d. It destroy the co-hesion that might otherwise take place between the surfaces. See Art. 31. and 33.

  Oil is said to answer best for spindle feet and step gudgeons tallow for common gudgeons, and black lead mixt with ••l∣low for cogs, which forms a glossy polish on them that will wear a long time.
• * 1.488

  Art. 84.
• * 1.489

  If you have not a foundation of solid rocks, or so heavy, that the water tumbling over, will never move them, there should be such a foundation made with great stones, not lighter than millstones (if the stream is heavy, and the tumble great) well laid, as low and close as possible, with their upstrea•• end lowest, to prevent any thing from catching under the••. But if the bottom is sand or clay, make a foundation of the trunks of long trees, laid close together on the bottom of the creek, with their but ends down stream, as low and close 〈◊〉〈◊〉 possible, across the whole tumbling space. On these may 〈◊〉〈◊〉 built the dam, either of stone or wood, leaving 12 or 15 〈◊〉〈◊〉 below the breast or fall, for the water to fall upon. See 〈◊〉〈◊〉 3, plate X, which is a front view of log dam, shewing 〈◊〉〈◊〉 position of the logs, also of the stones in the abutments.
• † 1.490

  If the dam is built of timber and small stones, &c. 〈◊〉〈◊〉 the breast perpendicular of strait logs, laid close one 〈◊〉〈◊〉 another, putting the largest, longest, and best logs on 〈◊〉〈◊〉 top; make another wall of logs 12 or 15 feet upstream, lay∣ing them close together, to prevent lamprey eels from work∣ing through them, not so high as the other, by 3 feet; tie these walls together, at every 6 feet, with cross logs, with the buts down stream, dovetailed and bolted strongly to the logs of the lower wall, especially the upper log, which should be strongly bolted down to them. The spaces between these log walls, are to be filled up with stones, gravel, &c. Chuse a dry season for this work; then the water will run through the lower part, while you build the upper part tight.

  To prevent any thing from catching against the top log, flag the top of the dam with broad or long stones, laying the downstream end on the upstream side of the log, to extend a little above it, the other end lowest, so that the next tier of stones will lap a little over the first; still getting lower as you advance upstream. This will glance logs, &c. over the dam, without catching against any thing.&If suitable stones cannot be had, I would recommend strong plank, or small logs, laid close together, with both ends pinned to the top logs of the wall, the upstream end being 3 feet lower than the other: But if plank is to be used, there need only be a strong frame raised on the foundation logs, to support the plank, or the timber it is pinned to. See a side view of this frame, fig. 45. plate IV. Some plank the breast to the front posts, and fill the hollow space with stone and gravel; but this may be omitted, if the foundation logs are sufficiently long upstream, under the dam, to prevent the whole from floating away. Stone first, and then gravel, sand and clay, are to be filled in above this frame, so as to stop the water. If the abutments are well secured, the dam will stand well.
• * 1.491

  Art. 85.
• * 1.492

  If the dam is built of stone, make it in the form of an arch or semicircle, standing upstream and endeavour to fix strong abutments on each side, to support the arch; then, in laying the stones, put the widest end upstream, and the more they are drove downstream, the tighter they will press together. All the stones of a dam should be laid with their upstream ends lowest, and the other end lapped over the pre∣ceding, in manner of the shingles or tiles of a house, to glance every thing smoothly over, as at the side 3, of fig. 3, plate X. The breast may be built up with stone, either on a good rock or log foundation putting the best in front, leaning a little upstream, and on the top lay one good log, and another 15 feet upstream on the bottom, to tie the top log to, by se∣veral logs, with good buts, downstream, dovetailed and bolted strongly, both at bottom and top of the top and upstream logs; ••ill in between them with stone and gravel, laying large stones slanting next the top log, to glance any thing over it. This will be much better than to build all of stone; because if one at top give way, the breach will probably increase rapidly, and the whole go down to the bottom.
• * 1.493

  Art. 87.
• * 1.494

  If the tumbling space is not long enough, the water will be apt to overflow the abutments, and if they are earth or loose stones, they will be broken down, and perhaps a very, great breach made. If the dam is of logs, the abutments had best be made of stone, laid as at the side 3, in fig. 3; but 〈◊〉〈◊〉 stone is not to be had, they must be made of wood, although subject to rot soon, being above water.
• † 1.495

  I have, in many instances, seen the mill set so close in the dam, that the pierhead or forebay was in the breast; so that in case of a leak or breach about the forebay or 〈◊〉〈◊〉, there is no chance of shutting off the water, or conveying it another way; but all must be left to its fate. The mill in frequently broken down, and carried away; even the mill-stones are carried a considerable distance down the stream and sometimes buried under the sand, and never found.

  The great danger of this error will appear more plain, 〈◊〉〈◊〉 we suppose si•• mills on one stream, one above the other, each at the breast of the dam; and a great flood to break the 〈◊〉〈◊〉 or uppermost dam, say through the pierhead, carrying with it the mill, stones and all; this so increases the flood, that i•• overflows the next dam, which throws the water against the mill, and it is taken away; the water of these two dams 〈◊〉〈◊〉 now so augmented the flood, that it carries every mill before it, until it comes to the dam of the sixth, which it sweep away also; but suppose this dam to be a quarter of a 〈◊〉〈◊〉 above the mill, which is set well into the bank, the extra wa∣ter that is thrown into the canal, runs over at the waste left in its banks for the purpose; and the water having a free pas∣sage by the mill, does not injure it; whereas, had it been at the breast of the dam, it must have went away with the rest. A case, similar to this, actually happened in Virginia in 1794; all the mills and dams on Falling creek, in Chesterfield county, were carried away at once, except the lowest, (Mr. Ward∣••••••e's); whose dam, having broke the year before, was rebuilt a quarter of a mile higher up; by which means his mill was saved.
• * 1.496

  If the foundation is not good, but abounding with quick∣s••••ds the wall cannot be expected to stand, unless it be made good by driving down piles until they meet the solid ground; on the top of which may be laid large flat pieces of timber, for the walls to be built on; they will not rot under water, totally excluded from the air.
• † 1.497

  It is a common practice to build walls plumb outside, and better them all from the inside; which throws the centre of their gravity to one side of their base. See art.14. There∣fore if it settles any, it will incline to fall outwards. Mill-walls should be battered as much outside, as to be equal to the offsets inside, to cause the whole weight to stand on the centre of the foundation, unless it stand against a bank, as the wall next the waggon, in plate VIII. The bank is very apt to press the wall inwards, unless it stands battering. In this case, build the side against the bank plumb, even with the ground, and then begin to batter it inwards. The plumb rules should be made a little widest at the upper end, so as to give the wall the right inclination, according to its height; to do which, take a line, the length equal to the height of the wall, set one end, by a compass point, in the lower end of the plumb rule, and strike the plumb line; then move the other end just as much as the wall is to be battered in the whole height; and it will shew the inclination of the side of the rule that will batter the wall exactly right. This error of building walls plumb outside, is frequently committed in building the abutments of bridges; the consequence is, they fall down in a short time; because the earth between the walls is expanded a little by every hard frost, and tumbles the walls over.
• * 1.498

  Art. 86.
• * 1.499

  I have but little experience in this; but will quote an experienced author (George Sample, on Free Trade.) He says,

  Concerning Lime, Mortar and Grout.

  I have, from my childhood, been well acquainted with the nature of lime and sand made into mortar, of all sorts that have been used in buildings in these countries, and tried nu∣merous experiments with them. On which, together with what I have observed and learned from old experienced workmen, during the course of upwards of sixty years, I think I can safely affirm, that good mortar, that is made of pure and well burnt limestone, properly made up with sharp clean sand, free from any sort of earth, loam or mud, will, within some considerable time, actually petrify, and, as it were, turn to the consistency of a stone. I remember I had one of my remarks from an old Scotch mason; which I shall give you in his own identical words: that is,

  When a hundred years are past and gane, Then gude mortar is grown to a stain (or stone.)

  I need not explain what I mean by sharp clean sand; but I shall give you this one caution, that it is better to put too much sand in your mortar, than too little. I know workmen choose to have their mortar rich, because it works pleasanter; but rich mortar will not stand the weather so well, nor grow so hard, as poor mortar will do. If it was all lime, it would have no more strength, in comparison, than clay.
• * 2.1

  Description of the Ele∣vator.
• * 2.2

  Plate VI. Fig. 1.
• * 2.3

  Fig. 2.
• * 2.4

  Art. 88.
• * 2.5

  Conveyer.
• * 2.6

  Fig. 3.
• * 2.7

  Meal Con∣veyer.
• * 2.8

  Fig. 12. Of the Hopper-boy
• * 2.9

  Sweepers, their use.
• * 2.10

  Art. 88.
• * 2.11

  Drill.
• * 2.12

  Descender.
• * 2.13

  Fig. 1.
• * 2.14

  Art. 88.
• * 2.15

  Art. 89.
• * 2.16

  Of receiv∣ing the wheat.
• * 2.17

  Art. 89.
• * 2.18

  Tail flour & middlings hoisted and bolted over.
• * 2.19

  Middlings ground over with the wheat.
• * 2.20

  Which saves labour and time.
• * 2.21

  Screenings cleaned.
• * 2.22

  Art. 89.
• * 2.23

  Of elevating grain from ships, if measured at the mill.
• * 2.24

  Art. 90.
• * 2.25

  If the gain is not be measured at the mill, it is elevated out of the vessel's hole immediately by an eleva∣tor that raises and lowers with the tide.
• * 2.26

  By the strength of one man.
• * 2.27

  Art. 90.
• * 2.28

  Lifting the wheat up it∣self.
• * 2.29

  ••00 bushels per hour.
• * 2.30

  Into a con∣veyer that conveys it into any garner, and at the same time rubs off the dust.
• * 2.31

  Art. 90.
• * 2.32

  Application to a mill for grinding merchant work in par∣cels; the grain eleva∣ted from the waggon into any garner, and from them again, into the roll∣ing screen, &c. by draw∣ing gates; and kept se∣parate.
• * 2.33

  Art. 91.
• * 2.34

  Meal kept separate.
• * 2.35

  Art. 91.
• * 2.36

  Advantages gained.
• * 2.37

  Application to a grist-mill.
• * 2.38

  Way to keep the grists sepa∣rate.
• * 2.39

  Art. 92.
• * 2.40

  Advantages.
• * 2.41

  Form of the chest.
• * 2.42

  Art. 92.
• * 2.43

  Art. 93.
• * 2.44

  Quantity a horse can hoist.
• * 2.45

  Elevator to be wrought by a man.
• * 2.46

  Applying his weight to turn the machine.
• * 2.47

  Art. 94.
• * 2.48

  Quantity he can hoist, at the rate of 200 bushels per hour.
• * 2.49

  The advanta∣ges of this ap∣plication of man's strength.
• * 2.50

  Art. 74.
• * 2.51

  Art. 94.
• * 2.52

  Art. 94.
• * 2.53

  Construction of the wheat-elevator.
• * 2.54

  Strap.
• * 2.55

  Art. 95.
• * 2.56

  To make Buckets for wheat of wood.
• * 2.57

  Fig. 9.
• * 2.58

  Art. 95.
• * 2.59

  Fig. 2
• * 2.60

  Meal-buckets of wood.
• * 2.61

  Fig. 9
• * 2.62

  Sheet-iron buckets.
• * 2.63

  Art. 95.
• * 2.64

  Meal Buckets of sheet iron.
• * 2.65

  Size and mo∣tion of pul∣leys,
• * 2.66

  To hoist 300 bush. an hour.
• * 2.67

  Art. 95.
• * 2.68

  590 bushels.
• * 2.69

  200 bushels.
• * 2.70

  Make the lower case crooked to suit the swag of the strap.
• * 2.71

  Art. 95.
• * 2.72

  Dimensions of the ease-boards.
• * 2.73

  Fig. 1.
• * 2.74

  Of casing the pulleys.
• * 2.75

  Art. 95.
• * 2.76

  Common way of casing them.
• * 2.77

  Fig. 1. pl. VI.
• * 2.78

  Art. 95.
• * 2.79

  Let the wheat in at the bot∣tom to prevent its choaking.
• * 2.80

  Give the up∣per pulley mo∣tion, and it will carry most.
• * 2.81

  Art. 95.
• * 2.82

  Construction of crane-spouts.
• * 2.83

  Art. 95.
• * 2.84

  See the description of this Elevator in art. 90.
• * 2.85

  Construction of an elevator for taking the wheat out of a ship's hold.
• * 2.86

  Art. 95.
• * 2.87

  Construction of a meal ele∣vator.
• * 2.88

  Art. 96.
• * 2.89

  Meal must be let in some distance up.
• * 2.90

  Frame for the lower pulley.
• * 2.91

  Art. 96.
• * 2.92

  There must be barges on the lower pulley.
• * 2.93

  Plate 6, fig. 3.
• * 2.94

  To lay out a meal convey∣er.
• * 2.95

  Art. 97.
• * 2.96

  To make the flights.
• * 2.97

  Lifting flights.
• * 2.98

  Art. 97.
• * 2.99

  Conveyer ap∣plied to cool the meal.
• * 2.100

  Construction of a grain con∣veyer.
• * 2.101

  Art. 98.
• * 2.102

  With a sheet-iron spite
• * 2.103

  With a wood∣en spire.
• * 2.104

  Construction of the hopper-boy.
• * 2.105

  Fig. 12.
• * 2.106

  Fig. 13.
• * 2.107

  To distance the flights.
• * 2.108

  To make them tract truly
• * 2.109

  To give them the right incli∣nation.
• * 2.110

  Art. 99.
• * 2.111

  To put them in.
• * 2.112

  Sweepers.
• * 2.113

  Upright shaft
• * 2.114

  Art. 99.
• * 2.115

  For attending one boulting-hopper.
• * 2.116

  Two hoppers.
• * 2.117

  Three hop∣pers.
• * 2.118

  Art. 99.
• * 2.119

  Should be moved by a strap.
• * 2.120

  Art. 100.
• * 2.121

  Art. 100.
• * 2.122

  Late philoso∣phical disco∣veries, shew∣ing why meal is so soon made fit for boulting by the ma∣chines.
• * 2.123

  Art. 121.
• * 2.124

  Meal should be spread thin while hot, and it will cast out the moisture, and will not breed worms.
• * 2.125

  Boults better,
• * 2.126

  And does the work to geeater per∣fection.
• * 2.127

  Art. 101.
• * 2.128

  With less waste.
• * 2.129

  Afford more room.
• * 2.130

  Dispatch more work.
• * 2.131

  Art. 101.
• * 2.132

  Will last a long time.
• * 2.133

  Require less power.
• * 2.134

  Save a great expence.
• * 2.135

  289 dollors a year in board and wages, in a double mill.
• * 2.136

  Art. 101.
• * 2.137

  Certificates confirming the above.
• * 2.138

  Art. 101.
• * 2.139

  Art. 101.
• * 2.140

  Bill of materials for the wheat-elevator.
• * 2.141

  Art. 102.
• * 2.142

  Bill of iron.
• * 2.143

  For a Meal elevator.
• * 2.144

  Art. 102.
• * 2.145

  Bill of iron.
• * 2.146

  Art. 102.
• * 2.147

  For a hopper-boy.
• * 2.148

  Art. 1••2.
• * 2.149

  Art. 102.
• * 2.150

  Art. 103.
• * 2.151

  By trying many experiments, and with much labour, striving to invent a new machine for rubbing the dust off the grains of wheat, and breaking the ••eaps of dust mixed with wheat that is tread on the ground; and for shelling of the white caps, breaking the rotten, fly-eaten, and smut grains, and to break the garlick, &c. I discovered this principle; which I afterwards used with a common pair of bur mill-stones, properly dressed for grinding wheat, and always found it to succeed well, without breaking any good grains, 〈◊〉〈◊〉 the white caps to fine dust.
• * 2.152

  Art. 103.
• * 2.153

  Art. 104.
• * 2.154

  The best way of facing and sharpening stones.
• * 2.155

  Art. 104.
• * 2.156

  There must be furrows in the stone.
• * 2.157

  Their use.
• * 2.158

  Should be very hard near the eye.
• * 2.159

  Art. 104.
• * 2.160

  Their faces should touch only 10 inches from the skirts.
• * 2.161

  It is asserted by some (and I believe, not without reason) that it is ••••••∣lute••y necessary to have a bridge-tree that shall have a degree of elastic 〈◊〉〈◊〉 which gives the stone a tremulous motion up and down, and therefore 〈◊〉〈◊〉 a trituration more completely, making more lively flour than it would 〈◊〉〈◊〉 supposing the bridge-tree to be a solid immoveable rock. But what is 〈◊〉〈◊〉 proper degree of elasticity, or size of a bridge-tree, suitable to the weight 〈◊〉〈◊〉 the stone, I know not; not having experienced this matter sufficiently, to give an opinion on it: but I am inclined to think that this is an error.

  One disadvantage in having a very elastic bridge-tree, is, when the 〈◊〉〈◊〉 run empty, they come together with more force, and heat quicker; and if once made red hot, it totally destroys the good sharp quality of the 〈…〉〈…〉 far as the heat penetrates.
• * 2.162

  The bridge should be elastic.
• * 2.163

  Of the draught of the furrows.
• * 2.164

  Too much draught makes much coarse meal.
• * 2.165

  Art. 105.
• * 2.166

  Art. 105.
• * 2.167

  Art. 105.
• * 2.168

  Art. 105.
• * 2.169

  Small stones should have less draught in proportion than large ones.
• * 2.170

  Art. 105.
• * 2.171

  Quarter dress with many quarters to be prefered.
• * 2.172

  Of facing new stones with sand & picks.
• * 2.173

  〈◊〉〈◊〉 red staff is longer than the diameter of the stones, and three inches 〈◊〉〈◊〉 the edge, which is made perfectly straight, on which is rubbed red 〈◊◊〉〈◊◊〉 with water; which shews the highest parts of the faces of the 〈◊〉〈◊〉, when rubbed over them, by leaving the red on those high parts.
• * 2.174

  Art 106.
• * 2.175

  Of laying out the furrows, to suit the quality of the stone
• * 2.176

  Depth of the furrows.
• * 2.177

  For the form of the bottom of the furrow, see plate XI, fig. 5. The curve line e b shews the bottom, b the feather edge, and e the back 〈◊〉〈◊〉 If the bottom had been made square at the back as at e, the grain would 〈◊〉〈◊〉 in the corner, and by the centrifugal force, would work out along the furrows without passing over the lands, and part would escape unground. The back edge must be sloped for two reasons: 1st, that the meal may be pushed 〈…〉〈…〉 the feather edge: 2nd, that the furrow may grow narrower, as the face of the stones wears away, to give liberty to sharpen the feather edge, without making the furrows too wide. Fig. 5 represents the face of two 〈◊〉〈◊〉, working together, the runner moving from a to d. When the furrows 〈◊〉〈◊〉 right over one another as at a, there is room for a grain of wheat; 〈◊〉〈◊〉 they move to the position of b, it is flattened, and at c, is clipped in two by the feather edges, and the lands or plains operate on it as at d.
• * 2.178

  Art. 106.
• * 2.179

  Of opening the stones near the cen∣tre.
• * 2.180

  Stones in the best order.
• * 2.181

  Of hanging the stone with a balance-ryne.
• * 2.182

  Art. 107.
• * 2.183

  But here we must observe, whether the stone be of a true balance, 〈◊〉〈◊〉 hangs on the cock head, and if not, it must be truly balanced, by running lead into the lightest side. This ought to be carefully attended to by the maker, because the stone may be made to balance truly when at rest; yet, if every opposite part does not balance each other truly, the stone may be greatly out of balance when in motion, although truly balanced at rest: and this is the reason why the bush of some stones cannot be kept tight but a few hours, while others will keep tight several months, the spindles being good, and stones balanced when at rest. The reason why a stone that is ba∣lanced at rest, will sometimes not be balanced in motion, is, that if 〈◊〉〈◊〉 up∣per side be heaviest on one side, and the lowest side be heaviest on the other side of the centre, the stone may balance at rest, yet, when set in motion the heaviest parts draw outwards more by the centrifugal force, which will put the stone out of balance while in motion: and this argues in favour of a stiff ryne. The best method that I have heard of for hanging stones with stiff horned rynes, appears to be as follows: Fix a screw to each 〈…〉〈…〉 regulate by, which is done thus—after the horns are beded, sink under 〈◊〉〈◊〉 horn a strong bur, through which the screw is to pass from the back of the stone, and fasten them in with lead; then, after the stone is laid down, 〈◊〉〈◊〉 the screws from the top of the stone, screwing them till the points bear 〈◊〉〈◊〉 on the horn: then proceed to hang the stone, which is very easily done, by turning the screws.
• * 2.183.1

  Of balancing the stone.
• * 2.184

  Stiff ryne.
• * 2.185

  Directions for hanging a stone with a stiff ryne.
• * 2.186

  Art. 107.
• * 2.187

  Directions for regulating the grinding.
• * 2.188

  The miller should by many experiments, find the quantity of water that best suits his mill, and have a mark made on the staff by which he draws the gate, that he may draw a suitable quantity at once.
• * 2.189

  Art. 108.
• * 2.190

  If the stones be over-fed, it is not possible that the bran should be well 〈◊〉〈◊〉, because the sharp edges on the face of the stone, that is made for the purpose of scraping the bran clean, is kept from it by the quantity of 〈◊〉〈◊〉 that is between the stones.
• * 2.191

  Directions for judging of the grinding by feeling the Meal.
• * 2.192

  Art. 109.
• * 2.193

  Instead of a sieve, you may take a shovel and hold the point 〈◊〉〈◊〉 stream of meal, and it will catch part of the bran, with but little meal 〈◊〉〈◊〉 with it; which may be separated by tossing it from one hand to the 〈◊〉〈◊〉 wiping the hand at each toss.
• * 2.194

  Directions for sharpening the the stones with picks.
• * 2.195

  For keeping them in good face.
• * 2.196

  To prevent the steel from striking your fingers, take a piece of leather but 5 by 6 inches square, make a hole through the middle, and put the 〈◊〉〈◊〉 of the pick through it, keeping it between your hands and the pick, 〈◊〉〈◊〉 a loop in the lower edge, through which put one of your fingers, 〈…〉〈…〉 the lower part from the stone.
• * 2.196.2

  To guard the fingers from the steel.
• * 2.197

  Art. 110.
• * 2.198

  〈◊〉〈◊〉 sharpen 〈◊〉〈◊〉 without stopping them.
• * 2.199

  But care should be taken to prevent the sand from getting mixed 〈◊〉〈◊〉 the meal: it should be catched in some vessel, the ston•••• being suffered 〈◊〉〈◊〉 quite empty, the small quantity that will remain in the stone will 〈◊◊〉〈◊◊〉 the flour. But I do not wish to encourage a lazy miller, to neglec∣ting up the stone.

  When stones are first set to grind, they incline to raise, and grind 〈◊〉〈◊〉 for a considerable time, the true reason of which is difficult to assign. 〈◊〉〈◊〉 attribute it to the expansion of the metal in the spindle: it has been 〈◊〉〈◊〉 to me, that it is the steam, or the rarifaction of the air, by the heat pro∣duced by the action of the stones, which, not having a perfectly free 〈◊〉〈◊〉 to escape, bears up a part of the weight of the stone; and this cause 〈◊〉〈◊〉 ••••∣crease, until the stones are heated to the greatest degree.
• * 2.200

  Of the most 〈◊〉〈◊〉 fine∣ness of flour.
• * 2.201

  Art. III.
• * 2.202

  Experiment made thereon.
• * 2.203

  〈◊〉〈◊〉 might be difficult to assign the true reason why pressure or heat has 〈◊〉〈◊〉 an effect on flour, as to destroy that life or principle, that causes it to 〈◊〉〈◊〉 and raise in the baking—But we may form a few conjectures.

  〈◊〉〈◊〉, May not this life be that vegetative quality that causes the grain 〈◊〉〈◊〉, seeing it is a fact known by experience, that if the grain be damaged, either by wet or heating in a heap so as to destroy its vegetation, that 〈◊〉〈◊〉 that is made thereof will not bake well? And I presume, that if 〈◊〉〈◊〉 heated by any means, so as to destroy its vegetative quality, it will 〈◊〉〈◊〉 flour that will have an easy fermentation; and it is probable, that 〈◊〉〈◊〉 of heat is generated by the act of grinding when great pressure 〈◊〉〈◊〉, which cannot be avoided if the stones be dull.

  〈◊〉〈◊〉, If we consider that most bodies are in part composed of air, which 〈◊〉〈◊〉 solid and fixed state, and constitutes a proportional part of their 〈◊〉〈◊〉, and this proportion is different in different species of matter, from 〈◊〉〈◊〉 to 1-2, and in one species of wheat has been found, by experiments, to 〈◊〉〈◊〉 of its whole weight; that is, 12lb. of fixed air in 60lb. or one bushel 〈◊〉〈◊〉. Now this air is roused into action two ways, viz. by fermentati∣on and by heat, and as fast as it is roused, it instantly leaves the body, 〈◊〉〈◊〉 expands itself into about a million times more space than it filled 〈◊〉〈◊〉 in the form of a dense body. See Martin's Philosophy. New cyder 〈◊〉〈◊〉 a large portion of this fixed air, which flys off by fermentation, leaving 〈◊〉〈◊〉 cask considerably emptied; and as soon as the fixed air is all gone, the fer∣mentation ceases.

  Query, Is not this fixed air the very soul of vegetation and fermentation and may not the degree of heat generated by grinding with great 〈◊〉〈◊〉 set it in motion and cause it to leave the flour, thereby not only destroying its life, but greatly lessening its weight, to the great loss of the miller; 〈◊〉〈◊〉 although he expects by hard squeezing to reap profit, reaps loss? As a ••••••∣firmation of this hypothesis, we may observe, that many experiments have been made, by weighing a quantity of wheat carefully, before it was 〈◊〉〈◊〉 and then weighing every thing that it made in manufacturing, and 〈◊〉〈◊〉 found it to be lacking in weight from 1 to 5lb. per bushel; which could 〈◊〉〈◊〉 be accounted for any way better, than supposing the loss to be 〈◊〉〈◊〉 the escape of the fixed air. Therefore, I conclude, that stones 〈◊〉〈◊〉 revolve slow and be kept sharp; and the larger they are, the slower will 〈◊〉〈◊〉 require to go, and the lighter may they press the grain, and yet grind a 〈◊〉〈◊〉 suf∣ficient quantity, and make the best flour.
• * 2.204

  The vegeta∣tive quality must not be destroyed.
• * 2.205

  Of Garlic.
• * 2.206

  The complete separation of this garlic from the wheat, is so 〈◊〉〈◊〉 that it has hitherto ba••fled all our art. Those grains that are 〈…〉〈…〉 those that are smaller, can be separated by screens; and those that are 〈◊〉〈◊〉 lighter, may be blown out by fans: but those that are of the same size, 〈◊〉〈◊〉 nearly of the same weight, cannot be separated without putting the 〈◊〉〈◊〉 water, where the wheat will sink, and the garlic swim. But this method 〈◊〉〈◊〉 too tedious for the miller to practise, except it be once a year, to clean up 〈◊〉〈◊〉 headings, or the like, rather than loose the wheat that is mixed with 〈…〉〈…〉 cannot be otherwise sufficiently separated. Great care should 〈◊〉〈◊〉 farmers to prevent this troublesome thing from getting root 〈◊〉〈◊〉, which, if it does, it will be almost impossible ever to root it 〈◊〉〈◊〉 because it propagates by both seed and root, and is very hardy.
• * 2.206.3

  Of separating it from the wheat.
• * 2.207

  Art. 112.
• * 2.208

  Of dressing stones to suit the garlic.
• * 2.209

  The best me∣thod of mana∣ging garlicky wheat.
• * 2.210

  Art. 112.
• * 2.211

  Of chopping wheat to dry the garlic.
• * 2.212

  Must not be chopped too fine.
• * 2.213

  Timothy Kirk of York-Town (Pennsylvania) has communicated by an invention of his, an improved fan, for cleaning wheat, the 〈◊〉〈◊〉 which, is, to blow the grain twice with one blast of wind; which, 〈◊〉〈◊〉 further improvements, appears to offer fair to effect a complete 〈◊〉〈◊〉 of the garlic from the wheat, and every other substance that is 〈◊〉〈◊〉 the grain.
• * 2.214

  Of preparing middlings to be ground over.
• * 2.215

  Art. 113
• * 2.216

  Of grinding middlings.
• * 2.217

  Art. 113.
• * 2.218

  〈◊〉〈◊〉 all this trouble and loss of time may be saved by a little simple 〈◊〉〈◊〉 of late invention, that will cost but a few dollars, viz. As the 〈…〉〈…〉 by the first bolting, let them be conveyed into the eye of the stone, 〈◊〉〈◊〉 with the whea••, as directed a••••. 89, plate 8: by which means, the 〈◊〉〈◊〉 thereof may be made into superfine flour, without any loss of time or 〈◊〉〈◊〉, of being too hard pressed for wa••t of the bran to keep the stones 〈◊〉〈◊〉. This mode I first introduced, and several others has 〈…〉〈…〉 it 〈◊〉〈◊〉 approbation.
• * 2.219

  Of bolting and grinding over ship-stuff, &c.
• * 2.220

  Art. 113.
• * 2.221

  Of grinding shorts or bran over.
• * 2.222

  But the merchant miller is to consider, that there is a certain degree 〈◊〉〈◊〉 closeness or perfection that he is to aim at, in manufacturing which wi•••• yield him the maximum, or greatest profit possible, in a given time. And this degree of care and perfection will vary with the prices of wheat a•••• flour, so that what would yield the greatest profit at one time, would 〈◊〉〈◊〉 money at another; because, if the difference of the prices of wheat and 〈◊〉〈◊〉 be but little, then we must make the grain yield the most possible, to obtain any profit. But if the price of flour be much above that of the wheat, the•• we had best make the greater dispatch, even if we should not do it so well, 〈◊〉〈◊〉 order that the greater quantity may be done while those prices lasts: wher••∣as, if we were to make such dispatch when the price of flour was but little above that of wheat, we would sink money.
• * 2.222.4

  Of the degree of perfection most possible.
• * 2.223

  Of the differ∣ent qualities of wheat.
• * 2.224

  Art. 114.
• * 2.225

  Of the quali∣ty of stones to suit hard dry wheat.
• * 2.226

  Such wheat as is produced by the mountainous and clay lands, of the 〈◊〉〈◊〉 distant from the sea and tide waters, is generally of a brownish co∣••••••, the grain appearing flinty, and sometimes the inside a little transparent, 〈◊〉〈◊〉 cut by a sharp knife. This transparent kind of wheat is generally 〈◊〉〈◊〉, and of a thin skin, and will make as white flour, and as much of it, as the whitest grain.
• * 2.227

  And damp soft wheat.
• † 2.228

  Such is the wheat that is raised in all the low, level, and sandy lands, of countries near the sea and tide waters of America, where it is customary to 〈◊〉〈◊〉 out their wheat on the ground by horses, and it sometimes gets wet by 〈◊〉〈◊〉 and dew, and the dampness of the ground. This grain is naturally of 〈◊〉〈◊〉 fairer colour, and softer; and when broken, the inside is white, which shews it to be nearer a state of pulverization, and is more easily reduc∣ed to flour, and will not bear as much pressure as the grain that is raised on 〈◊〉〈◊〉 and clay lands, or such, that when broken, appear solid and transparent.
• * 2.229

  Art. 114.
• * 2.230

  Also garlicky wheat.
• * 2.231

  It is very difficult to convey my ideas of the quality of the stones to the reader, for want of something to measure or compare their degree of p••rosi∣ty or closeness, hardness or softness with. The knowledge of these different qualities is only to be attained by practice and experience; but I may ob∣serve, that there is no need of any pores in the stone to be larger in diameter than the length of a grain of wheat, for whatever they are larger, is so much loss of the face, because it is the edges that does the grinding; therefore all large pores in stones are a disadvantage. The greater the number of pores in the stone, (so as to leave a sufficient quantity of touching surfaces, to reduce the flour to a sufficient degree of fineness) the better.

  Mill-stone makers ought to be acquainted with the true principles 〈◊〉〈◊〉 which grinding is performed, and with the art of manufacturing grain into flour, that they may be judges of the quality of the stones suitable to the quality of the wheat, of different parts of the country; also, of the best manner of disposing of the different pieces of stone, of different qualities, in the same mill-stone, according to the office of the several parts, from the centre to the verge of the stone. See art. 104.

  Mill-stones are generally but very carelessly and slightly made, where••••, they should be made with the greatest care and to the greatest nicety. The runner must be balanced exactly on its centre, and every corresponding op∣posite part of it should be of equal weight, or else the spindle will not keep tight in the bush: (see art. 107.) and if it is to be hung on a balance ryne, it should be put in at the formation of the stone, which should be nicely ba∣lanced thereon.

  But above all, the quality of the stone should be most attended to, that 〈◊〉〈◊〉 piece of an unsuitable quality for the rest, be put in; it being known to most experienced millers, that they had better give a high price for an extraordi∣nary good pair, than to have an indifferent pair for nothing.
• * 2.232

  Of making Mill-stones.
• * 2.233

  Principles of bolting.
• * 2.234

  Art. 115.
• * 2.235

  This method I have been informed is practised in England: they several bolting cloths of different degrees of fineness for the same reel. 〈◊〉〈◊〉 first put on the fine one, and pass the meal through, which takes out 〈◊〉〈◊〉 su∣perfine flour; they then take off the superfine cloth, and put on the 〈◊〉〈◊〉 ••••∣gree of fineness, which takes out the common fine flour; and so on 〈◊〉〈◊〉 the different degrees, the cloths having drawing strings at each 〈◊〉〈◊〉 drawing the ends close.
• * 2.235.5

  English mode of bolting.
• * 2.236

  Art. 115.
• * 2.237

  Late improve∣ments made in bolting.
• * 2.238

  Of bolting over.
• * 2.239

  Art. 115.
• * 2.240

  This appears reasonable, when we consider, that many dark 〈◊〉〈◊〉 and transparent substances (while in a solid state) when 〈◊〉〈◊〉, 〈◊〉〈◊〉 white, and their whiteness is proportionate to their degree of pulver•••••• 〈◊〉〈◊〉 for instance, salt, allum, and many kinds of stone, and particularly 〈◊〉〈◊〉—Ice pulverized is as white as snow—transparent wheat 〈…〉〈…〉 flour.
• * 2.241

  Art. 115.
• * 2.242

  Art. 116.
• * 2.243

  Art. 116.
• * 2.244

  Art. 117.
• * 2.245

  Art. 118.
• * 2.246

  Art. 117.
• * 2.247

  Art. 118.
• * 2.248

  Art. 118.
• * 2.249

  Art. 118.
• * 2.250

  〈…〉〈…〉 of 8 feet to an inch, except pl. V. which is 4 feet
• * 2.251

  Art. 1.
• * 2.252

  Art. 2.
• * 2.253

  Art. 3.
• * 2.254

  Art. 3.
• * 2.255

  Art. 3.
• * 2.256

  Art. 4.
• * 2.257

  Art. 6.
• * 2.258

  Art. 7.
• * 2.259

  Art. 8.
• * 2.260

  Art. 9.
• * 2.261

  The following tables are calculated to give the stones the revolutions per minute mentioned in them, a•• near as any suitable number of cogs and rounds would permit, which motion I find is 8 or 10 revolutions per minute slower than proposed by Evans in his table;—his motion may do best i•• cases where there is plenty of power and steady work on one kind of grain: but in country mills, where they are continually changing from one kind to another, and often starting and stopping, I presume a slow motion will work most regular. His table being calculated for only one size of mill-stones, and mine for four, if any choose his motion, look for the width of the wa∣ter-wheel, number of cogs, and rounds and size of the wheels to suit them, in the next example following, keeping to my table in other respects, and you will have his motion nearly.
• * 2.262

  Art. 10.
• * 2.263

  Art. 10.
• * 2.264

  Art. 11.
• * 2.265

  Art. 12.
• * 2.266

  Art. 12.
• * 2.267

  Art. 13.
• * 2.268

  Art. 14.
• * 2.269

  Art. 14.
• * 2.270

  Art. 15.
• * 2.271

  Art. 16.
• * 2.272

  Art. 17.
• * 2.273

  Art. 18.
• * 2.274

  Art. 19.
• * 2.275

  Art. 20.
• * 2.276

  Art. 21.
• * 2.277

  Art. 21.
• * 2.278

  Art. 23.
• * 2.279

  Art. 26.
• * 2.280

  Art. 26.
• * 2.281

  Art. 27.
• * 2.282

  Art. 28.
• * 2.283

  Art. 28.
• * 2.284

  Art. 29.
• * 2.285

  Art. 30.
• * 2.286

  Art. 30.
• * 2.287

  Art. 31
• * 2.288

  Art. 31.
• * 2.289

  Art. 33.
• * 2.290

  Art. 34.
• * 2.291

  Art. 35.
• * 2.292

  Art. 35.
• * 2.293

  Art. 36.
• * 2.294

  Art. 36.
• * 2.295

  Art. 30.
• * 2.296

  Art. 36.
• * 2.297

  Art. 37.
• * 2.298

  Art. 37.
• * 2.299

  Art. 38.
• * 2.300

  Art. 38.
• * 2.301

  Art. 38.
• * 2.302

  Art. 38.
• * 2.303

  Art. 38.
• * 2.304

  Art. 39.
• * 2.305

  Art. 39.
• * 2.306

  Art. 39.
• * 2.307

  Art. 39.
• * 2.308

  Art. 39.
• * 2.309

  Art. 39.
• * 2.310

  Art. 39.
• * 2.311

  Art. 39.
• * 2.312

  Art. 39.
• * 2.313

  The use of this air-tube is shewn art. 71, page 12, of part II
• † 2.314

  Must be very strong else they will burst.
• * 2.315

  Art. 40.
• * 2.316

  Art. 40.
• * 2.317

  Art. 40.
• * 2.318

  Art. 40.