A light to the art of gunnery wherein is laid down the true weight of powder, both for proof and action, of all sorts of great ordnance : also the true ball and allowance for wind, with the most necessary conclusions for the practice of gunnery, either in sea or land-service : likewise the ingredients and making of most necessary fire-works, as also many compositions for the gunner's practice, both at sea and land / by Capt. Thomas Binning ...

Decimal Arithmetick.

CHAP. I. Definitions.

A Fraction or broken Number, is a Number less than an Unite, or One; and according to the common way of Fractions, is expressed by two Numbers set one over the other with a small line, thus, ¾; the upper Number is called the Numerator, and the lower the De∣nominator.

The Denominator sheweth into how many parts the Unite or Whole of any thing is to be divided.

The Numerator sheweth how many of these parts are signi∣fied by the Fraction.

A Decimal Number is that which is expressed by an Unite, with a Cipher, or Ciphers, as 10: 100: 1000: 10000: 100000: &c.

A Decimal Fraction is that whose Denominator is a Deci∣mal Number, as 3/10: 46/100: 728/1000: 2342/10000: 57689/100000: &c.

Decimal Fractions, whether they stand alone, or be joined with Integers, have always a Comma, or a small Rectangular Line before them, to distinguish them from Integers, which is therefore called a Separating Line, as ⌊4, ⌊36, ⌊348, 4⌊2, 490⌊086, &c.

As in Integers the Value or Denomination of Places do in∣crease by Tens, from the Unite place towards the left hand: So in Decimals the Value or Denomination of places do de∣crease

by Tens, from the Unite place towards the right hand: As in the Table following.

The Table.

9.	8.	7.	6.	5.	4.	3.	2.	1.	0.	1.	2.	3.	4.	5.	6.	7.	8.	9.
Thousand Millions.	Hundred Millions.	Ten Millions.	Millions.	Hundred Thousands.	Ten Thousands.	Thousands.	Hundreds.	Tens.	Ʋnits.	Tenths.	Hundredths.	Thousandths.	Ten Thousandths.	Hundred Thousandths.	Millionths.	Ten Millionths.	Hundred Millionths.	Thousand Millionths.

In Decimal Fractions, the Numerators are only set down, without the Denominators; but the Denominators are easily known, for they are the same with the Denomination of the last Figure of the Numerator. As in the Examples following.

Examples.⌊6 is

Six.	Numerator.
Tenths.	Denominator.

The common way 6/100

⌊42 is

Forty two.	Numerator.
Hundredths.	Denominator.

The common way 42/100

⌊364 is

Threee Hundred sixty four..	Numerator.
Thousandths.	Denominator.

The common way 364/1000

CHAP. II. Addition and Subduction in Decimals.

ADdition and Subduction in Decimals, whether in pure Decimals, or in Integers mixt with Decimals, differ not from Addition and Subduction in Integers, only care must be had to place the separating Lines of the Numbers under one another; as also the places of like denomination under one another; and the separating Lines of the Sum or Difference, must be placed under the separating Lines of the Numbers added, or subducted. See the Examples.

Examples in Addition.

⌊347

⌊268

⌊149

⌊764

⌊8972

⌊643

⌊8

⌊79

3⌊1302

346⌊98

74⌊2

6⌊934

⌊8

⌊07

428⌊984

In Addition and Subduction, let the place of the Fraction remain so many places as they were, and no more.

Example.

Addition.

35⌊72

78⌊05

113⌊77

Subduction.

78⌊25

35⌊75

42⌊50

Examples in Subduction.

⌊724

⌊482

⌊242

⌊89

⌊5796

⌊3104

⌊6427

⌊36

⌊2827

64⌊279

48⌊384

15⌊895

46⌊2

9⌊746

36⌊454

59⌊872

6⌊9

52⌊972

74⌊0

65⌊98

8⌊02

34⌊2

⌊642

33⌊558

CHAP. III. Multiplication in Decimals.

THe Numbers to be multiplied together, are called Fa∣ctors; and the Number found out by Multiplication, is called Product.

Multiplication, whether in pure Decimals, or in Integers mixt with Decimals, is the same in Operation with Multipli∣cation in Integers: The last Numbers of the Factors must be set one under the other, as if they were Integers, not regar∣ding the placing of the separating Lines under one another, as in Addition and Subduction: And from the Product must be cut off with a separating Line so many of the last Figures, as there are places of Decimals in both the Factors.

Examples. 〈 math 〉〈 math 〉

If it happen, when the Multiplication is ended, that there be fewer Figures in the Product, than there are places of De∣cimals in both Factors (which may often occur when the Pro∣duct is a Fraction) in such case, as many places as are wan∣ting, so many Ciphers must be prefixed to the Product on the left hand thereof, and then a separating Line must be prefixt to sign the Product so increased for a Decimal.

Examples. 〈 math 〉〈 math 〉

In Multiplication with Fractions, cut off so many places as there are Figures of the Fractions, in the Multiplicand and Multiplier.

Examples. 〈 math 〉〈 math 〉

CHAP. IV. Division in Decimals.

DIvision, whether in pure Decimals, or Integers mixt with Decimals, is the same in Operation with Division in Integers. But care must be had to give a true denomination to the first Figure of the Quotient; (according to this Rule).

The Rule.The first Figure of the Quotient is always of the same de∣nomination with that place of the Dividend, which stands, or is supposed to stand over the Unite of the Divisor.

It will happen sometimes, that the Unite place of the Divi∣sor will stand beyond all the significant Figures of the Divi∣dend, towards the right hand, or towards the left. In this case you must put Ciphers to the right or left of the Dividend, until you come over the Unite place of the Divisor.

As for Example.If 3⌊47 is to be divided by 0⌊000462, they must stand thus; 0⌊000462) 0003⌊47 (And the denomination of the first Figure of the Quotient will be thousands of Integers.

Another Example.If 34 is to be divided by 642⌊79, they must stand thus; 642⌊79) 34⌊0000 (And the denomination of the first Figure of the Quotient will be hundreds of Decimals.

Note, That what Ciphers are added to the right hand of the Dividend, immediately next the Integers must have a separa∣ting Line (or a Comma) before them.

In Division, the Fractions being equal, the Work is as whole Numbers are.

If unequal, add so many Ciphers to the Dividend, as the Fraction of the Divisor exceedeth the Fraction of the Divi∣dend in places, that you may find your Fraction in the Quoti∣ent.

Examples. 〈 math 〉〈 math 〉

Other Examples. 〈 math 〉〈 math 〉 Because the Fraction is two Fi∣gures in the Divisor; Therefore I add two Ciphers to the Dividend. As in this third Example.

If in Division I be to divide by a great many Figures, I may make a Table for them.

Example. Which is done, first doubling of it, then adding it until nine times, if I will ten, which proves it. 〈 math 〉〈 math 〉

1	52678
2	105356
3	158034
4	210712
5	263390
6	316068
7	368746
8	421424
9	474102
10	526780

Because the Fraction is three Figures in the Divisor, there∣fore I add three Ciphers to the Dividend. As in this last Ex∣ample.

CHAP. V. Of the Square Root.

A Square Number is that which is made and produced of two equal Numbers multiplied together, or else of one Number multiplied by it self; as 16 is a Square Number, be∣cause

it is produced of 4 by 4, (which are Numbers equal, or one Number multiplied by it self) likewise 25, 36, 49, are three Square Numbers, for they are Products of the Multiplica∣tion of two equal Numbers, or of one Number multiplied by it self, as 5 by 5, 6 by 6, and 7 by 7. For the Products may be understood by their Unites in a Plane, of such kind as shall represent the form and figure of a Geometrical Plane, as you see here under.

[illustration]

The Superfice.

4, the side of the Square.

[illustration]

The Superfice.

5, the side of the Square.

It is evident by the generation of Squares, that you may make a Square of all Numbers given, and that you may ex∣tract the Root of all Squares proposed; and that likewise all Numbers proposed may be the side of some Square or ano∣ther.

There is a Double Root and a Double Square, viz. Simple and Compound; The Simple Root is that which hath but one Number, as are 1, 2, 3, 4, 5, 6, 7, 8, and 9; the Squares of which are called Simple Squares. The Compound Root, is that which hath more than one Number, as are 10, 11, 12, 20, 30, &c. the Squares of such are called Compound Squares. And before you will extract the Compound Root, you must know by heart the nine Simple Roots with their Squares, by means of the following Table.

A Table of the Simple Roots with their Squares.

Simple Roots.	1	2	3	4	5	6	7	8	9
Simple Squares.	1	4	9	16	25	36	49	64	81

To extract all Roots or Sides of Compound Squares. You must well understand and imprint in your memories the fol∣lowing Chapter.

CHAP. VI. Extraction of the Square Root in Decimals.

IN extracting the Root or Side of a Compound Square, you must first mark the Square Number given, with Points or Pricks from the right hand to the left, beginning with the first Figure towards the right hand, marking over that Figure one Prick or Point, then set another over the third Figure, and another over the fifth; and so proceeding continually from the right hand to the left, marking still with a Prick over every third Figure, leaving the other Figures unmarked, until you come to the last Square towards the left hand.

〈 math 〉〈 math 〉 First find the Simple Root of the Figure or Figures that remain towards the left hand, multiply that Root in it self subtract it out of the Figures towards the left hand: Then draw down the next two Figures to that Re∣mainder, and say 2 times 5 the Quotient is 10; set 10 under 72, and see how often it may be found in 72, say 6 times; then set 6 under 6, and set 6 also in the Quotient; then multiply 106 by 6, cometh 636, sub∣tract it from 726, there remaineth 90: Then draw down the next two Figures to that Re∣mainder, and say, 2 times 56 in the Quoti∣ent is 112; set 112 under 902, and see how often it may be found in 902, say 8 times; then set 8 under 4, and set 8 also in the Quo∣tient, then multiply 1128 by 8 cometh 9024, subtract it from 9024 there remaineth nothing; so that 568 the Quoti∣ent is the just Root of the Square Number 322624, &c.

Another Example. 〈 math 〉〈 math 〉 &c.

CHAP. VII. Of the Cube Root.

A Cube is a Solid Body, comprehended of six equal Square Superficies, and is like unto the Dye of a Table-board.

Definition. * 1.1Every Number multiplied in it self maketh a Square Num∣ber, of which the Root or Side is the Number multiplied; and every Square multiplied by its Root, maketh a Cube Num∣ber, (by the 20th Definition of the 7th Book of Euclide): As 4 times 4 makes 16, (a Square Number, of which the Root is 4) the which 16 being multiplied by the Root 4, the Product giveth 64, a Cube Number, of which the Root is 4.

Likewise 5 times 5 maketh 25, a Square Number, which being multiplied by its Root 5, the Product giveth 125, a Cube Number, of which the Root is 5, and so of others. And before you can extract the Compound Cube Roots, you must first know the nine Simple Cube Roots, with their Squares and Cubes. As appeareth in the following Table, which is divided in three Lines, whereof the first (which is the uppermost) containeth the nine Simple Roots; and the second Line (which is the middle Line) containeth the nine Squares; and the third Line, which is the lowest, contain∣eth the Cube Numbers.

A Table of the Simple Roots, with their Squares and Cubes.

Simples.
Sides.	1	2	3	4	5	6	7	8	9
Squares.	1	4	9	16	25	36	49	64	81
Cubes.	1	8	27	64	125	216	343	512	729

CHAP. VIII. Extraction of the Cube Root in Decimals.

TO prepare a Cube Number for Extraction, put a Point over the first place thereof towards the right hand, (to wit, the place of Unites); then passing over the second and third places, put another point over the fourth; and passing over the fifth and sixth, put another over the seventh, and in

that order, (to wit, two places being intermitted between every two adjacent Points) place as many Points as the Num∣ber will permit: So 157464 being given, you are to place the Points as here followeth; and so many Points as are in that manner placed, of so many Figures the Root demanded will consist.

〈 math 〉〈 math 〉 Having thus prepared your Number, you may see it distributed by the Points into several Cubes: So in the same Ex∣ample 157 is the first Cube, and 464 the second.

First, Find the Simple Cube Root by the preceding Table of 157, which is 5; subscribe the Cube of that Root under the first Cube of the Number given; so 125 being the Cube of 5 the Root, I write it under 157 the first Cube of the Number given, and subtract this Cube from the first Cube of the Number pro∣pounded, placing the remainder orderly underneath the Line: So 125 the Cube of 5 being subtracted from 157, the remainder is 32: to the said remainder, bring down the next Cube of the Number pro∣pounded, (to wit, the Figures or Ciphers which stand in the three next places) placing the said Cube next after, to wit, on the right hand of the remainder; so the next Cube 464 being placed after the remainder 32, there will be found the Number 32464, which may be called the Resolvend. Having drawn a Line under the Resolvend, square the Root in the Quotient, that is, multiply it by it self, and subscribe the tri∣ple of the said Square or Product, under the Resolvend, in such manner, that the first place (to wit, the place of Unites) of the said triple Square, may stand directly under the third place (or place of hundreds) in the Resolvend: So the Square of the Root 5 is 25, the Triple whereof is 75, which I subscribe under the Resolvend in such manner, that the Figure 5, which is in the first place, (to wit, the place of Unites) in the Tri∣ple Product 75, may stand under 4, which is seated in the third place of the Resolvend. Triple the Root or Number in the Quotient, and subscribe this Triple Number in such man∣ner

that the first place thereof, (to wit, the place of Unites) may stand directly under the second place (to wit, the place of Tens) in the Resolvend: So the triple of the Root 5 is 15, which I subscribe in such manner, that the Figure 5, which is in the first place (to wit, the place of Unites) in the said triple Number, doth stand directly under 6, which is seated in the second place of the Resolvend: The triple Square of the Root, and the triple of the Root being placed one under the other as is directed, draw a Line underneath, and add them together in such order as they are seated, and let the Sum be esteemed as a Divisor: So the Triple Square 75, and the triple Number 15 being added together, as they are ranked in the Work, the Sum will be 765 for a Divisor: Let the whole Resolvend, except the first place thereof towards the right hand, (to wit, the place of Unites) be esteemed as a Dividend; then demanding how often the first Figure (to∣wards the left hand) of the Divisor is contained in the corre∣spondent part of the Dividend, and observing in that behalf the Rules before taught in Division, write the Answer in the Quotient: So I ask how often 7 (the first Figure of the Di∣visor towards the left hand) is contained in 32, (the corre∣spondent part of the Dividend placed above) the Answer will be 4, wherefore I write 4 in the Quotient: Having drawn another Line under the Work, multiply the triple Square be∣fore subscribed by the Figure last placed in the Quotient, and subscribe this Product under the said triple Square, (to wit, Unites under Unites, Tens under Tens, &c.) So 75 being multiplyed by 4, the Product is 300, which I subscribe under 75 (the triple Square). Multiply the Figure last placed in the Quotient, first by it self, and then the Product by the triple Number before subscribed; this done, subscribe the last Pro∣duct under the said triple Number, (to wit, Unites under Unites, Tens under Tens, &c.) So 4 being squared or multi∣plied by it self, the Product is 16, which being multiplyed by the triple Number 15, the Product is 240, this therefore I sub∣scribe under the aforesaid triple Number 15. Subscribe the Cube of the Figure last placed in the Quotient, under the Re∣solvend, in such manner that the first place of this Cube, (to wit, the place of Unites) may stand under the place of Unites in the Resolvend: So 64 being the Cube of 4, I write it under the Re∣solvend

32464, in such manner, that the Figure 4, which is in the place of Unites in the Cube 64, may stand under the Figure 4, which is seated in the place of Unites of the Resol∣vend: Drawing yet another Line under the Work, add the three last Numbers together in the same order as they are sea∣ted, and subtract the Sum of them from the Resolvend, pla∣cing the Remainder orderly underneath: So the Sum of the three last Numbers, as they are ranked in the Work, is 32464, which if you subtract out of the Resolvend 32464, the Re∣mainder is 0. Thus the whole Work being finished, the Cube Root of 157464, (the Number propounded) is found to be 54.

Note 1. When the Sum of the three last Numbers before mentioned is greater than the Resolvend, the Work is errone∣ous, and then you are to reform it by placing a lesser Figure in the Quotient.

Note 2. For every one of the particular Cubes (distin∣gushed by the Points) except the first Cube on the left hand, a Resolvend is to be set apart, by bringing down to the Remain∣der the next Cube. And as often as a Resolvend is set apart, so often is a new Divisor to be found, by adding the triple of all the Root in the Quotient (consisting of what number of pla∣ces soever) to the triple of the Square of such Root, after they are orderly placed, according as is above-mentioned.

Note 3. The Work of the Table of Simple Cubes in Folio 9, for finding the first Figure of the Root, (as before declared) is but once used in the Extraction of the Root of any Num∣ber whatsoever; but the Work of all the following Rules, is to be used for the finding of every place in the Root except the first.

The practice of these three Notes will be seen, when we describe how to extract the Cube Root of Numbers not Cu∣bical.

CHAP. IX. Another Example wrought by the Genitures.

SUppose a Number given to be 16387064, of which the Cube Root is required: First, You must cut the Cube gi∣ven into Ternaries from the right hand to the left, (as was de∣clared in Chap. 8.) Then find the Root of the first Cube from the left hand 16. Wherof the greatest Root is 2, for 2 being multiplied cubically, giveth 8, the which 8 being deducted from 16, the first Cube of the Number propounded, there remaineth 8, then set the Root found 2, with the Square thereof above it, and by the same the Geniture, and then find a second Figure for the Root of the second Cube, and you shall have 5, which ye shall set down with its Square and Cube under it, right against the Geniture towards the right hand; then multiply each one by another, and add the Pro∣ducts together, there cometh 7625, which being subtracted from 8387, there doth remain 762; In the same manner find a Root for the Numbers remaining to be extracted, and it shall be the Root of your third Cube; And the Example will stand thus.

〈 math 〉〈 math 〉

And seeing there remaineth nothing, it is manifest that the Number propounded 16387064 is a Cube Number, and

the Root thereof is 254. By the 4th Proposition of the second, and 20th Definition of the seventh Book of Euclide.

When we come to calculate the Table of Cubes, by which you may make an Inch Rule for height, or Line of Diameters, the way shall be described how to extract the Cube Root of Numbers not Cubical, or as they are termed Irrational Num∣bers, from which no true Root can be obtained, yet many times the Error will not be ••/100000 part of an Unite.

CHAP. X. Principles of Geometry.

THere are divers Reasons which make me to give these few Principles of Geometry, because the whole Work of this Book, is either to be done by Arithmetick or Geome∣try; and besides that a Gunner cannot obtain to know the truth of a Diameter of a Ball, except he can Geometrically extract the Wind of the Bore of the Peece, and thereby find the Ball fitting such a Peece: And in general will be most useful for any Gunner.

Definitions.

• 1. A Point or Prick, is that which is the least of all Mate∣rials, and it is the beginning of Things, as being void of Length, Breadth, and Depth, having neither Part nor Quan∣tity (expressible in Numbers), and therefore it admits of no Division, but that which is mental only. This Point or Prick is represented unto you by the Letter A. Thus A.
• 2. A Line is a Magnitude extending it self in length, with∣out breath or thickness, (whether it be a straight line or crook∣ed) and (in respect of its length) may be divided into Parts, but will admit of no other division, but in length only. As is set forth to you by the Line BC; the extremities whereof be∣ing Points as B and C.
  [illustration]
• ...

• 3. A Right or Straight Line, is the nearest Distance that can be betwixt two Points; As is the former Line BC.
• 4. Circular or Crooked Lines are longer, though they be extended no further than Right Lines, as are the Lines DE and FG.
  [illustration]
• 5. Right-lined Parallels, are two straight Lines, so drawn, as they are equi-distant in all places one from the other; so that although they were infinitely extended, yet could they never meet; as may be seen by the Lines HI and KL.
  [illustration]
• 6. A Circular Parallel, is a Circle drawn either within or without another Circle, upon one and the same Centre, as is
  [illustration]

• seen by the two Circles, viz. NOPQ and RSTV, being both drawn upon the same Centre W, and therefore are pa∣rallel one to another.
• 7. A Superficies is the second kind of Quantity, and to it are attributed two Dimensions, Length and Breadth, but not Thickness, for a Superficies is the term or end of a Body, as a Line is the end and term of a Superficies. As WXYZ is a Superficies.
  [illustration]
• 8. The Extreams of a Superficies are Lines, as the Ends, Limits, or Bounds of a Line, are Points confining the Line; so are Lines the Limits, Bounds and Ends inclosing a Superfi∣cies; As in the foregoing Figure you may see the Superficies inclosed with four Lines, viz. YW, WX, XZ, and YZ, which are the Extreams or Limits thereof.
• 9. A plain Superficies, is that which lyeth equally between his Lines, like as a Right Line is the shortest extention or draught from one Point to another; so a plain Superficies is the shortest extention or draught from one Line to another: As in the preceding Figure WXYZ.
• 10. A Figure is that Magnitude comprehended by one Line, or more Lines than one: Under one Line is a Circle; Under more Lines is a Triangle, Quadrangle, Pentagon, Hex∣agon; and so forth.
• ...

• 11. A Circle is that Figure which is comprehended under one Line, called the Circumference, as ABCD; in the mid∣dle whereof there is a Point called the Centre, as E; from which, to the Circumference, all Lines being drawn are equal; As in the said Circle the Lines EA, EB, EC, and ED are equal.
  [illustration]
• 12. The Diameter of a Circle, is a Right Line drawn through the Centre thereof, and ending at the Circumference on either side, dividing the Circle into two equal parts: As the Line AEC in this Circle is the Diameter thereof, because it passeth from the Point A to the Point C, and so likewise through the Centre E, and divideth the whole Circle into two equal parts.
• 13. The Semi-diameter being the half thereof; as AE and EC, the one Term whereof being the Centre, and the other the Circumference: It followeth by the 11th Definition hereof, that all Lines drawn from the Centre to the Circumference are equal; Therefore is BE and ED likewise Semi-diameters.
• ...

• 14. A Semi-circle is a Figure which is contained under the Diameter, and under that part of the Circumference which is cut off by the Diameter, as the Semi-circle ABC, is con∣tained under the Diameter AC, and also under the part of the Circumference ABC, which is cut off by the Diameter AC.
• 15. A Quadrant is the fourth part of a Circle, or is con∣tained under two Semi-diameters, and the fourth part of the Circumference, as in the preceding Circle AEB or BEC.
• 16. A Segment of a Circle, is a part of the Circle contain∣ed under a Chord-Line, (not being the Diameter) and a part of the Circumference, as FBG being the lesser Segment; and the Remainer to the whole Circle being the greater.
• 17. A right-lined Angle, is the Inclination, or bowing of one Line to another, which being extended, do concur or meet in a Point, as in the preceding Circle AEB or AEH, &c. the middle Letter signifying always the Angle, as E.
• 18. Of Right-lined Angles there be three kinds, viz. A Right-Angle, an Obtuse or Blunt-Angle, and an Acute or Sharp-Angle.
• 19. A Right-Angle is that, when one Line falling upon another maketh the Angles on both sides equal, then either of those Angles is a Right-Angle: and the Right Line which standeth erected, is called a Perpendicular-Line to that upon which it standeth. As upon the Right-Line AC, suppose there do stand another Line BE, (as in the preceding Circle) in such sort, that it maketh the Angles on either side thereof equal, namely the Angle AEB on the one side, equal to the Angle BEC on the other side, then are each of those Angles Right Angles, and the Line BE, which standeth erected on the Line AC, is a Perpendicular to the said Line AC.
• 20. An Obtuse-Angle is that which is greater than a Right-Angle, as the Angle HEB (in the preceding Circle) is greater than the Angle AEB, by the Angle AEH, and therefore is an Obtuse-Angle.
• 21. An Acute or Sharp-Angle, is that which is less than a Right-Angle, as the Angle AEH is an Acute-Angle, because it is less than the Right-Angle AED, by the other Acute-Angle DEH.

[Obs. 1] Here you are to observe, That the Circumference of every Circle doth differ from the Circle, as that which is contained, doth differ from that which containeth.

[Obs. 2] The Circumference of every Circle, is understood to be divided into 360 Parts, called Degrees; and every one of these into 60 other Parts, called Minutes; or into 100 Parts, called Centesms: But the reason of this Division may be demanded, Wherefore into 360, & into no other Number, did the first Ar∣tists divide every Circumference? I Answer, That only Magni∣tude being to be divided into certain parts, the same ought to be divided into the least and best, for dividing as in equal parts: But so it was, that no Number under 360 could be had, as be∣ing divisible into more equal parts; and likewise being a Num∣ber not very troublesom to the Memory. Therefore not with∣out Cause or Reason they made choice of that Number before any greater or lesser.

[Obs. 3] From an Arch of the Circumference is taken the Measure or Quantity of all Angles; for the Quantity of an Angle, is an Arch or Ark of the Circumference, described from the An∣gular Point, and contained betwixt the two Lines forming the Angle. As the Arches FG, DE, AC, described from the Angular Point B: So that so many Degrees as are con∣tained in these Arches, such is the quantity of the Angle ABC,

[illustration]

I say all these Arches being equal; not according to quantity of extension: for certain it is that FG will be lesser than AC;

but I say that they are equal according to the number of Parts, for there are more Parts in the Arch AC than in FG, al∣though the quantity of the one be greater than the quantity of the other; because all Circles described from the same Centre are equal, all being divided into 360 Degrees.

From hence it follows that every Angle may be measured by an Arch of a Circle actually divided; whether it be Semi-circle, Quadrant, or Line of Chords, (the construction of which hereafter followeth); And first by a Semi-circle divided into 180 Degrees: First, Lay the Centre of the same upon the Angular Point, and the Diameter upon one of the Lines for∣ming the Angle, the Degrees contained between these two Lines upon your Instrument is the measure of your Angle. As in this Example, The Centre of your Semi-circle placed upon the Angular Point A, and the Diameter upon AC, the Arch contained between AB and AC, such is DE, which is the measure of the Angle DAE 36 Degrees.

[illustration]

22. The measure of any Right-lined Angle, may be had by a Line of Chords, which is described upon a Ruler; which Line is virtually the Arch of a Circle; The Projection whereof is as followeth. Let there be a Quadrant, or fourth part of a Circle, as BAC, divided into 90 Degrees; First, Into three parts, each containing 30 Degrees, by taking the Semi-diameter, as AB, with your Compasses; place one foot

in C, and with the same wideness set the other foot in F; set again the one foot of your Compasses in B, (the Compasses not being altered) and with the other take the extent BG: So your Quadrant shall be divided into three equal parts, viz. CG 30 Degrees, CF 60, and the rest unto B 90 degrees: Every one of these being again subdivided into three equal parts; so shall you have the Quadrant divided into nine parts, or 90 degrees, each part containing ten degrees: and so into small parts according to the largeness of your Quadrant.

[illustration]

The Quadrant being performed and truly divided: you shall draw a Line from B to C, which shall be the Chord of 90 degrees; again you shall place the one foot of your Com∣passes at C, and extend the other to 10 degrees; the same ex∣tention you shall lay off from C to D, upon the Line of Chords; still keeping the one foot of your Compasses at C, again extend your Compasses to 20 degrees, and lay them off from C to E; and so accordingly to all the rest, till you have finished the division of your Line. Which being performed, shall serve you to measure the quantity of all Right-lined An∣gles, as well as by any Circular Arch; being more portable, and more ready for use, than any Circular Instrument, as Semi-circle, Quadrant, &c. as by the following practice is evident.

The Use of the Line of Chords. 23. Let there be an Angle, as ABC, whose quantity is de∣sired: The same is performed by a Line of Chords; if you place the one foot of your Compasses at the end of your Line, and the other upon 60 degrees; then the Compasses remaining at the same wideness, place the one foot at B, and draw an Arch as DE; whose wideness you shall take by your Com∣passes, and apply the same to your Scale upon the Line of Chords, you shall have the Quantity of the Angle 36 degrees.

[illustration]

But if the Angle be Obtuse or Blunt, as FBC, extend the Compasses upon your Scale to 60 degrees, drawing an Arch from the Angular Point; then first take off 90 degrees from your Line of Chords, and place the same from E to G, the remainer being taken from G to F, the distance whereof is 54 degrees; which two Arches being added together, shall give the quantity of the Angle FBC, reckoned 144 degrees. And thus much for finding the quantity of all Right-lined Angles, by the Line of Chords upon your Scale.

CHAP. XI. Geometrical Problems.

Prob. 1.

To divide a Line given into two equal Parts, at Right-Angles.

[Prob. 1] LEt the Line given be AB; having placed the one foot of your Compasses at A or B; extend the other at pleasure, above the half of the Line by estimation, and draw two Ar∣ches, the one above the Line, and the other beneath; then keeping the Compasses at the same wideness, place the one foot at the other end of the Line, cutting the former Arches in C and D with the other foot, lay a Ruler at the points C and D; and where the same doth cut the Line AB, as in E, so shall the Line AB be cut into two equal halves at E, which was required; and the Lines CE and ED, shall be both per∣pendicular to the Line AB, by the 19th Definition of this.

[illustration]

Prob. 2.

An Angle being given, to divide the same into two halves.

Let the Angle be ABC, to be divided into two equal halves: Place the one foot of your Compasses at B, and extend the other at your pleasure to D and E; describe two Arches cut∣ting each other in the point F: So shall you divide the Angle ABC into two equal halves, if you draw a Line from B to F, with two Angles ABF, and FBC, as equal to the whole Angle ABC, being divided into two halves.

[illustration]

Prob. 3.

From any Point, or from the end of a Line, to erect or raise a Perpendicular.

Let there be given the Line AB, and the Point in the same given C, from which a Perpendicular is to be raised.

Place the one foot of your Compasses at C, and with the other take at pleasure above the Line, as D; then from the point D, describe the Arch of a Circle, as ECF, cutting the Line AB in F; then lay your Ruler at F and D, and where it cutteth the Arch as in E, draw a Line from C to E, which shall be perpendicular to AB, from the point C.

[illustration]

Again from the point A, a Perpendicular is raised the same manner of way; placing one foot of your Compasses at A, extend the other above the Line to the point G; and draw from G the Arch IAH, cutting the Line at H; then laying your Ruler by G and H, and where it cutteth the Arch as in I; from A to I draw a Line, so shall AI be a perpendicular from the end of the Line AB, or from the point A.

The same may be performed by the Line of Chords, as by the practice is evident.

The same another way. A Perpendicular may be raised after this manner; As let the Line be AB; and a Point in the same Line given, let be C: place the one foot of the Compasses at C, and with the other draw an Arch above a Quadrant, as GED; then place the distance of CD from D to E; then placing the one foot at E, draw the Arch GF: then removing your Compasses, place the one foot at G, and with the other cut the Arch in F: Lastly, From F to C, draw a Line FC; so shall FC be a Perpendicular from the point C.

[illustration]

Prob. 4.

From a Point without a Line, to let fall a Perpendicular to a Line given.

[illustration]

Let the Line given be AB, and the Point without the same at C: Draw a Line to AB at Oblique Angles, as CD; which

you shall cut (by the first Problem) in two halves at E; then place the one foot of your Compasses at E, extend the other unto C, drawing the Arch CF: and where the same cutteth the Line AB, as in F, from C to F draw a Line, as CF; so shall CF be a Perpendicular let fall from the Point C, upon the Line AB, as was required.

Prob. 5.

A Line being given, to draw a Parallel to the same, at any Distance required.

[illustration]

Let the Line given be AB, and the Distance from C: Ex∣tend your Compasses to the length of C, and placing one foot of your Compasses in any Point of the Line, draw two Ar∣ches; and by the Com∣passe of these Arches, draw a Line as DE; which shall be parallel to AB required; as CE.

The same another way. Let the Line given be AB, and the Point at C: From the Point C, draw a Line at pleasure unto AB, which shall touch in F, which you shall cut (by the first Problem) into two halves at E: take then a Point betwixt F and A at pleasure, which is here G: draw then a right Line from the Point G, through E, and set the Distance DE, equal to the Line EG: draw then a Line through the Points CD; so shall the same Line be pa∣rallel to the Line AB.

[illustration]

Prob. 6.

Two Lines being given, to find a third proportional Line.

Let A and B be two Lines given, and let it be required to find a third Line in proportion to them.

First, Make any Angle as CDH; then set the Line A from D to E, and the Line B from D to F, and also from D to G; then draw EF: that done, by the Point G draw a parallel to EF, as GH: So shall DH, be the third proportional Line required.

[illustration]

A. 4.

B. 6.

DE. 4.

DF. 6.

DG. 6.

DH. 9.

Prob. 7.

Three Lines being given, to find a fourth in proportion, that is to perform the Rule of Three in Lines.

Let AB and C be three Lines given, and it is required to find a fourth proportional Line.

First (as in the last Problem) make any Angle at Pleasure, as the Angle EFG; Then take with your Compasses the Line A, and set it from F to H; take also the Line B, and set it from F to I, and draw the Line HI: That done, take the third Line C, and set it upon the Line FG, viz. (always up∣on the same Line where the first Line A was placed) from F to K; then by K draw a Parallel to HI, as KL, to cut FE in L: So shall FL be the fourth Proportional Line required.

[illustration]

FH. 12.

FI. 14.

FK. 18.

FL. 21.

Prob. 8.

To divide a Line given into two parts, in proportion one to the other, according to two Lines given.

Let AB be a Line given, to be divided into two such parts, that the lesser may be in proportion to the greater: As the Line C, to the Line D.

From the end A draw the Line AE, making the Angle BAE: then set the Line C from A to F, and the Line D from F to E, and draw the Line EB: Lastly, By the Point F draw a Parallel to EB, as FG, to cut AB in G: So shall AB be divided in G, as C to D, which was required.

[illustration]

AF. 20.

FE. 30.

AG. 16.

GB. 24.

Prob. 9.

To cut off from a Line given any part or parts required.

Let in the last Diagram AB be a Line given, and let it be required to cut off from it ⅖ parts.

First, From the end A, draw the Line AE, making any Angle as BAE; then set on any five equal parts from A to E, and also two of the same parts from A to F: That done, draw the Line EB; then by F draw a Parallel thereunto, to cut AB in G: So shall AG be the ⅖ parts of AB, which was required.

Prob. 10.

To divide a Line in such sort, as another Line is before divided.

This Problem differeth not much from the two last Problems. Draw a Right Line at pleasure, as the Line OB, which Line you shall divide into 100 equal parts as exactly as you can; then extend your Compasses to the Distance OB, and describe an Arch; in which arch you are to include the desired Line A; then draw the Line OC, and you have the Angle COB: which we shall hold for a ground-Rule; because the Legs OB and OC, contain each of them 100 or 1000 parts, which is in the Line A.

[illustration]

For Example.I would have 35 parts of the Line A, (whose whole length making 100 parts, as the Line OB doth): I number on the Line OB 35 parts from O to F; with this distance I draw the Arch FG; then is the nearest Distance from F to G a Right Line, which is the 35 parts of the Line A.

Likewise if it were desired to have 15 parts of the Line A: Then draw from O the Arch ED; which Distance is the de∣sired 15 parts of the Line A; as the Learned Adriani Meti

doth teach. And also how to find the Parts of a longer Line, than the Line of Measure it self is; it is done after the same manner; and is of great use to a Gunner.

Ʋse.This may be of great use, if the Gunner be to find the first Round Ball in a strange place, and the Weight unequal to Ours.

Prob. 11.

Between two Lines given, to find a mean Proportion.

Let A and B be two Lines given, between the which it is re∣quired to find a mean Proportion.

Join the Lines A and B so together, that they make one Right Line as CD, being joined together in the Point E: and upon the Line CD describe the Semi-circle, viz. CFD: Then upon the Point E, where the Lines A and B being joined together meet, erect a Perpendicular to cut the Limb in F, as EF, which shall be a mean Proportion between the Lines A and B required.

[illustration]

The same another way.

Again in the same Diagram, let the Lines A and G be given, between the which it is required to find a mean Proportion.

Take the Line G, and lay it down from C to D, and draw CD; whereupon describe the Semi-circle CFD: Then take the Line A, and set it from D to E; Then upon the Point E, erect a Perpendicular to cut the Limb in F; Lastly, Draw DF, which shall be a mean Proportion between DE and DC, or between the Lines A and G required. And if you draw CF, it shall be a mean between B and G, that is between CE, and CD.

Prob. 12.

To divide a Line given by Extream and Mean Proportion.

Let AB be a Line given to be divided by Extream and Mean Proportion. Increase AB at length to C; then upon the Point A erect a Perpendicular as AD, of the length of AB: That done, take half AD, or AB, and set it from A to E, then with the distance ED make the Arch DG: So shall AB be divided by Extream and Mean Proportion in G, and AG is the greater Segment, and GB the lesser.

[illustration]

The same another way.

[illustration]

Let HI be a Line given, to be divided by Extream and Mean Proportion. Upon the end I, erect a Perpendicular, as I K, of the length of half the given Line HI; then draw the subtendant side HK: That done, set KI from K to L; again, set HL from H to M; so shall HI be divided by Extream and Mean Pro∣portion in M: And HM shall be the greater Segment, and MI the lesser.

Prob. 13.

The greater Segment of a Line divided by Extream and Mean Proportion, to find the whole Line.

Let AB be the greater Segment given, and the whole Line is required. Increase BA to C; then upon the end B erect a Perpendicular of half the length of AB, as BD; and draw the subtendant side AD; from which subtract DB, rests AF: That done, set AF from A to C; so shall CB be the whole Line required.

[illustration]

Prob. 14.

To describe a Circle upon any three Points given, not being in a Right Line.

Let ABC be three [Prob. 14]

[illustration]

Points given. Set one foot of the Compasses in the middle Point at B, and open your Com∣passes to any extention that is above one half of the distance between B, and the farthest of the other two Points, and with that distance draw the blind Arches DE and FH: with the same extent set one foot in C, draw the Arch FH: A∣gain with the same ex∣tent, setting one foot in the Point A, draw the Arch DE: then laying a Ruler to the Intersection of these Arches, draw the Lines DG and HG;

which will cross each other in the Point G: and there is the Centre of the Circle inquired. Where setting one foot of your Compasses, and extending the other to any of the three Points, you describe the Arch of a Circle, which shall pass through the three Points given, and give the whole Circum∣ference required: which having, you may find the Diameter by the 12th Definition of Chap. 10. of this Book.

Observation.* 1.2Here is to be observed, That if any Town, Fort or Place be Besieged or Blocked up by an Enemy, and the Enemy shoot∣ing continually, there are divers Segments or Pieces of their Ball found in the Place; and it is desired to know what Ord∣nance they do Batter with. The Gunner shall take the Seg∣ment or piece of the Ball, and lay it on a piece of Paper, and set there down by the Circumference three Pricks or Points, as ABC in the Figure following, and thereby, and by the pre∣ceding Problem, shall find the Diameter, Centre, and Cir∣cumference of the Ball, whereby you may know the weight of that Ball; as is described in pag. 54.

[illustration]

Prob. 15.

How to Reduce a Right Line into the Circumference of a Circle.

The Line given being AB, to be reduced into a Circum∣ference.

[illustration]

The which Line AB, you shall first divide into three equal parts, and of these three Parts you shall make an Equilateral

Triangle, as CDE;

[illustration]

the half of CD is F, and the half of the side DE is G; and where they cut one another as in H, that is the Centre of the Triangle CDE: fur∣ther divide DF into halves with the point I; draw then a right Line from the Cen∣tre H, to I, which is HK; and divide the Line HI into four e∣qual parts, of which you shall add one part unto HI, which shall be HK, (which is the same fourth part five times set); set then one foot of your Compasses in the point H, and the other in the point K; and draw with the same distance a round Circle, whose Cir∣cumference shall be equal to the Line given, viz. the Line AB, which was required.

Prob. 16.

How to reduce the Circumference of a Circle given, into a Right Line.

[illustration]

Let the Circle given be ABCD. Divide the same Circle in four equal parts with the two Diameters BC, and DL, which cut∣teth one another at Right Angles in A; divide AC in the middle in E, through the which draw DI, and from I draw a Perpendicular upon DL, and divide AB in Extream and Mean Proportion at F, (by Problem 12 of this) draw FH, and

parallel to the same from B draw BG, which cutteth the pro∣longed Line DL in G; so is AG a fourth part of the Cir∣cumference BDCL.

The Mean Proportion betwixt DL and AG, the fourth part of the Circumference, giveth the side of a Square equal to the Circle.

From DE subtract the half of AC, there remaineth DK, (which is equal to BF) and is the side of a Decagon inscribed in the Circle.

Prob. 17.

The Diameter of a Circle being given, to find its Proportion to the Circumference, or the Reverse.

* 1.3Whensoever the Circumference of a Circle is divided into 10000 equal parts, then doth the Diameter thereof contain 3183 of the said parts, saith Adriani Meti. But Archimedes sheweth us the easiest and fittest for our purpose; to wit, That if the Circumference be divided into 22 equal parts, then the Diameter doth contain seven of the like parts: as is demon∣strated in this Figure, where you may see, that in the Circle ABC, the Circumference is divided into 22 equal parts, and the Diameter AB doth contain seven of the same parts.

[illustration]

A Light to the Art of Gunnery.

CHAP. XII. How to know the Proportion of a true Fortified Iron Gun.

BY the Demonstration of the last Problem, you have the proportion of a true Fortified Iron Piece, for a true For∣tified Peece of Ordnance being of Iron, hath 11 Diameters of the Bore about the Breech, measuring at the Touch-hole be∣twixt the Rings; which to describe is thus.

In the Diagram of the 17th Problem, the Diameter being divided into 7 equal parts, as is the Diameter AB; then take with your Compasses one of the same parts, and set one foot in the Centre, and with the other draw the Circle EGF, then shall the Line EF be the Diameter of the Bore of that Peece of Ordnance, and the Circle ACB, the Circumference of the Breech of the same Peece at the Touch-hole: where it followeth that one 22 part of a well proportioned Peece of Ordnance made of Iron, measured about the Breech, is half the Diameter of the Bore of the same Peece; the which is 11 Diameters of the Bore, as aforesaid: And therefore one side Metal, or the thickness of Metal at the Touch-hole is 1 ¼ Di∣ameter of the Bore, as appeareth from G to C, which is com∣pleatly demonstrated by the said Diagram of the 17th Pro∣blem: Also by the Neck, near the Musle of the Gun, are se∣ven Diameters of the Bore about; which is near ⅗ parts of the Diameter in Metal.

* 1.4If you should take the Diameter of the Breech of this Peece seven times to be the length of the Peece, and allow three of those parts betwixt the Breech and the Meeks, or Tru∣nions, and four of these parts betwixt the Meeks and the Musle of the said Peece, then that Peece hath her true proportion.

The Reason why one Gun must have more, and another less Powder. Thô there are many Guns that are some shorter, and some longer, yet they ought not to be thinner of Metal; for if they be thinner, then they are not able to have their true proportion of Powder, either for Proof or Action: Likewise know that true Fortified Guns, and true Bored Brass Ordnance, be their Denomination what it will, ought to have at the least 9 Dia∣meters of the Bore about the Breech, measuring at the Touch∣hole, and at the Meeks 7 Diameters of the Bore, and 5 Dia∣meters about the Musle at the Neck: if they have less than is above-said, they cannot suffer their true proportion of Pow∣der, either for Proof or Action: but this you must help, by what shall be fully described in its proper place.

CHAP. XIII. How to Extract the Wind from the Bore of a Peece Geometrically, and thereby to know a fit Ball for the same.

* 1.5FIrst, You are to draw the Diameter of the Bore BD, and that Line you are to divide into two equal halves, as EB and ED; then you have the Centre E, by which you draw the Circle ADCB: Which being done, with your Compasses at the same extent draw an Arch from the point D, extended to AEC; then draw the Chord-Line ALC; keep∣ing still your Compasses at the same extent, measure from A to D, then to C, and so to O: then extend your Compasses from D to O, and draw the Arch ON, which cutteth the Diameter in F: then divide the Line FB into three equal parts, and take one of these parts and place under the Centre E in H, extend your Compasses from H to D, and draw the Circle, whose Diameter is DG, and is the Ball fitting for

such a Peece, where you are to observe that GB is the Height of the Wind of the Peece.

[illustration]

Observation.

And though this former Demonstration be approved by ma∣ny Gunners, yet I find it by my Observation, better to demon∣strate the Wind of a Peece, as in the Figure following.

First, Draw the Diameter BA, which being divided into two equal parts at C, extend your Compasses from C to A or B, and draw the Circle 1.2.3.4.5, which here repre∣sents the Bore of the Peece: Keeping your Compasses at the same extention, place one foot in A, and draw the Arch

2,* 1.6 C, X; then drawing the Chord-Line 2, X, it divides the Semi-diameter of the Bore into two equal parts; then you are to extend your Compasses to the distance AD, or DC: So fixing one foot of your Compasses in A, you are to mea∣sure five of these Dimensions about the Circle, as you see them described, 1.2.3.4.5; then you must extend your Compasses from A to 5, and draw the Arch 5, Q, whereof A is the Centre; then you must divide the distance OB into two equal parts, and take one of these parts, and set it upon the Diame∣ter below C in the point E; then you are to extend your Compasses from E to A, keeping one foot in E, draw the Circle, whose Diameter is AEO: and is a Ball fit for such a Peece as hath for Diameter ACB.

[illustration]

The same by Calculation.

In the following Diagram AB, the height of the Bore of a Peece being given, to find the Diameter of the Ball AO.

First, Take the Semi-Radius AL, and set it off in the Cir∣cumference from A towards B five times, as you see here mar∣ked with 1.2.3.4. G; or 1.2.3.4. Q: then extend your Compasses from A to G, and draw the Arch GOQ, so is AO the Diameter of the Ball, and BO the Wind.

[illustration]

Now to find this by Calculation, First consider that AG or AQ is equal to AO, and A 1 equal to AL; then AL being the Semi-Radius 50000, is equal to the Chord A 1, withal considering that the Chord of an Arch is equal to dou∣ble the Sine of half that Arch; Now then 25000 the half of AL is the Sine AE, which in the Table of Natural Sines, giveth 14° 29′, for the Arch AE, the double whereof giveth 28° 58′, for the quantity of the Arch A 1, which being quin∣tupled, or multiplied by 5, giveth 144° 50′ for the Arch AG or AQ, so that the Arch GBQ is 70° 20′: The Angle ACG may be measured with a Line of Chords from the Plane Scale to be 144° 50′. The Chord whereof AG, is equal to twice the Sine of 72° 25′, viz. 95327; the double whereof is 190654, which is equal to the height of the Ball, in comparison to the Bore AB, 200000, twice the Radius, or the whole Diameter.

In Proportion, as Double is to Double, so is Single to Sin∣gle: Therefore as 190654 is unto the Diameter 200000, so is the half thereof 95327, the Sine of 72° 25′ unto the Radius: I say then, if the height of the Bore of any Peece of Ord∣nance be divided into 100000 parts, then the Diameter of the Ball is for the same Peece 95327 of the same parts; and the Wind is the Difference, which is 4673 parts, so that the Bore will be about 21 ⅖ times the height of the Wind.

If the Height of the Bore be given, to find the Diameter of the Ball.

The Proportion is: As the Radius is to the Height of the Bore given: So is the Sine of 72° 25′, unto the Diameter of the Ball required.

Or, if the Diameter of the Ball be given to find the Bore: Say then,

As the Sine of 72° 25′ is in Proportion to the Diameter of the Ball: So is the Radius to the Height of the Bore.

Example 1.I have an Iron Ball whose Diameter is four Inches, and weigheth 9 lb English Weight, and I desire to know what height the Bore of the Peece will be, which this Ball shall fit, the Wind duly extracted.

Sine of

72° 25′

95327

Inches

4

Radius

100000

4

400000

〈 math 〉〈 math 〉

I Answer, The Height of the Bore of such a Peece of Ord∣nance is 4 Inches and ⅕ part fere.

Example 2.I have a Gun whose Bore is 6 Inches Diameter, and I would know what Diameter must the Ball have, that will fit such a Peece, the Wind duly extracted.

Radius

••⌊00000

Inches

6

Sine of

72° 25′

95327

6

5⌊71962

I Answer, The Diameter of the Ball that will fit such a Peece, must be 5 Inches, and 7/10 parts of an Inch. And so of others.

Another way to Extract the Wind of a Gun, as well Geometrically as by Calculation.

[illustration]

The Height of the Bore of any Peece of Ordnance being given, as the Bore AK or GM (in the preceding Diagram) to find the Diameter of the Ball: First, With 60° of the Line of Chords, I draw the Circle DEF; then with 72° of the same Line, I draw the Arches EO and OF, which doth meet in the Point O: From O through the Centre P, I draw the Diameter KA: then from the Centre P, I draw Right Lines through the Points E and F, which doth cut the Circle AK in B and C, and the Circle GM in H and I: So that BC is 72° of the Circle KA, and HI is 72° of the Circle GM, as well as EF is of the Circle DEF: then extend the Com∣passes from A to B, setting one foot in A, with the other draw the Arch BLC; so is AL the Diameter of a Ball for the Bore AK: Or from G to H, setting one foot in G, with the other draw the Arch HNI; so is GN the Diameter of a Ball for the Bore GM: Or otherwise, not having a Line of Chords to measure 72°, upon the Circumference of the Bore given: As here in the Bore AK, divide the Circumference of the Bore into five equal parts, as BCSAR, and every one of these parts shall be 72 Degrees.

Now to Calculate this Arithmetically; the Chord AB be∣ing equal to AL containeth 144°, or twice 72°; the Sine of 72°, is 95105, the double whereof is 190210, for the Chord AB or AL, which hath such proportion to the height of the Bore AK 200000, as the Diameter of the Ball is to the Bore. I say then, the Bore being 200000, and the Diameter of the Ball 190210, the one being subtracted from the other, the Difference is 9790, which is the height of the Wind: And if you divide the Diameter of the Bore 200000, by the height of the Wind 9790, the Quotient will give the Wind to be somewhat less than the 20 ½ part of the Bore.

• The Diameter of the Bore 200000
• The Diameter of the Ball 190210
• The Difference is the Wind 9790

〈 math 〉〈 math 〉 The Quotient giveth 20 42/100 Times, so that it is less than 20 ½ Times.

As the Chord of 144°, viz. 190210, is in Proportion to the Diameter 200000; So is the half thereof the Sine of 72°, viz. 95105, unto the Radius 10000.

The Diameter of a Bore being given, to find the Ball.Hence it followeth, That as the Radius is in Proportion to the Diameter of the Bore; So is the Sine of 72° 00′ to the Diameter of the Ball.

Or if the Diameter of a Ball were given to find the Bore.Then should the Proportion be, as the Sine of 72° 00′, viz. 95105 is unto the Diameter of the Ball: So is the Radi∣us 100000 unto the Height of the Bore.

Example 1. There is a Gun whose Bore is 7 Inches Diameter, I would know what Diameter must the Ball have, that will fit such a Peece, the Wind duly extracted. 〈 math 〉〈 math 〉

I Answer, The Diameter of the Ball that will fit such a Peece, must be 6 Inches and 65/100 parts of an Inch.

Example 2. There is an Iron Ball whose Diameter is 6 Inches, and weigheth 30 lb 6 Ounces, English Weight: I desire to know what height the Bore of a Peece will be, which this Ball shall fit, the Wind duly extracted.

Sine of

72° 00′

95105

Inches

6

Radius

100000

6

600000

〈 math 〉〈 math 〉

I Answer, The Height of the Bore of such a Peece of Ord∣nance will be 6 Inches and 3/10 parts of an Inch. And so of others.

Observation.

The Diameter of the Peece ACB is 4 ⅕ Inches very near, which is the Diameter of a Ball of 9 ¼ lb Scots weight.

And the Diameter of the Ball which is AEO 4 Inches, is 8 lb Scots weight. Now the aforesaid Diameter ACB of 4 ⅕ Inches, is the Diameter of a Ball of 10 ⅜ lb English weight.

And likewise the Diameter AEO; of 4 Inches, is the Dia∣meter of a Ball of 9 lb English weight.

* 1.7 That 8 lb Scots maketh 9 lb English.

For the first Demonstration, the Diameter DB is 3 ⅘ In∣ches, which is near the Diameter of a Ball of 6 17/20 lb Scots weight, And near the Diameter of a Ball of 7 11/16 lb English weight. And the Diameter DHG is 3 ½ Inches, which is the Diameter of a Ball of 5 lb 6 ⅛ Ounces very near of Scots weight. And the Diameter of 3 ½ Inches, is near 6 lb Eng∣lish weight, not following the Tables of Mr. Smith, nor any other that I have seen as yet set forth; As I intend to De∣monstrate in its due place.

Objection. This Geometrical Description may be said by some, That they know better; for Mr. Hexham hath deciphered the Bore

[illustration]

of the Peece, and the Ball in another manner: Therefore I will Demonstrate the Way that Mr. Hexam takes to extract the Wind of a Peece, and thereby to find the true Ball.

Examples. Take the just Diameter of the Bore of your Peece, which you divide into two equal parts, and draw the Circle ABE; then the Compasses at the same station, you place one foot in A, and another in B, and draw the Cross Arches ACB: From C draw a Line through the Centre D to E, and then draw the Line AE: then place one foot of your Compasses in E, and draw the Arch AB: then place one foot of your Compasses in the Centre D, and extend the other to the Arch F, so draw the Circle FG: which he saith is the way to find a true Ball.

Answer to the Objection. Here you have the Demonstration of Mr. Henry Hexham, where you see a gross mistake; For as he supposeth FG, or EK to be the true Ball: And I find IE is the true Ball for that Peece, and have wrought this as you have it in Folio 28. Wherefore I leave the Ingenious Gunner to judg, which of these Experiments are the best and truest.

CHAP. XIV. The Demonstration of the Cannon-Bore, and of all other Peeces of Ordnance to the Rabinet, by Letters: As also the Geometrical Extracting or Deducing of the Wind or Vent of those Peeces, whereby you may know the exact Diameter of the true Ball fitting those Peeces.

	Weight of Ball.
	lb	lb
WA is the Bore of the Cannon-Royal; the distance betwixt A and B, is the true Vent or Wind, that ought to be betwixt the Ball B, and the Bore A—	64	72
WC is the Bore of the Cannon-Ordinary; the Distance CD is the Wind; and D the Height of the Ball—	48	54
WE is the Bore of the French-Cannon; EF the Wind; F the Diameter of the Ball —	36	40 ½
WG is the Bore of the Demi-Cannon Royal; GH the Wind; H the Diameter of the Ball —	30	33 ¾
WI is the Bore of the Demi-Cannon Ordinary; IK the Wind; K the Diameter of the Ball —	24	27
WL is the Bore of the Culvering, or Demi-French Cannon; LM the Wind; and M the Diameter of the Bore —	18	20 ¼
WN is the Bore of the Quarter-Cannon Ordina∣ry; NO the Wind; and O the Diameter of the Ball —	12	13 ½
WP is the Bore of the Demi-culvering; PQ the Wind; and Q the Diameter of the Ball —	8	9
WR is the Bore of a large Sacker; RS the Wind; and S the Diameter of the Ball —	6	6 ¾

WT is the Bore of a Sacker; VT the Wind; and V the Height of the Ball —	5	5 ⅝
WX is the Bore of a Minion; XY the Wind; and Y the Height of the Ball—	3	3 ⅜
WZ is the Bore of a Faucon; ZX the Wind; and X the Height of the Ball —	2	2 ¼
W = is the Bore of a Rabinet; = ⊙ the Wind; and ⊙ the Height of the Ball —	1	1 ⅛

Note: In the Column next your left hand you have the Scots Weight of the Ball; and in the Column next your right hand you have the English Weight of the same.

The Ancient and Later Rules given for Gunners, to give Powder to great Ordnance of all sorts, that are drawn on Carriages.

* 1.8In Ancient times it is said, That the great Chamber'd-Guns, that shot Stone-Ball, had for their ordinary one pound of Powder to three pound and half, or at most four pound weight of their Ball. This was certainly the first Invention of Guns; and in regard they could not cast Iron, they made their Guns, as Coopers do Cask, with Staves of Iron and Hoopes. Like∣wise that those Guns that shot Iron-Ball, most have to every three pound of Iron-Ball, one pound of Powder; and this they held for a general Rule, not examining the Fortification of their Peeces. Now at this time Powder was made of all the three Ingredients equal, and therefore could not be strong. But afterward it was found, that all sort of Field-Ordnance, not being Chamber'd, but true Bored, should be loaded in this manner, (to wit) The Gunner shall take the Diameter of the Ball, or the Diameter of the Bore of the Peece with a pair of Compasses; and this Diameter three times the Gunner must set off upon his Gun from the Touch-hole toward the Mussel; which distance being fil'd with Powder, then, said they, One pound of Powder was allowed to two pound of Ball: this was the Rule of the Primitive Gunners. But now in our time Powder is so variously made, and the difference is such, that it is hardly possible to the best Judgment, to give a true Rule what Powder is sufficient either for Proof or Action;

and therefore the Gunner ought to try his Powder before he load his Peece; for it is beyond all question, that if the Pow∣der be decayed, there must be more of it used than of fresh dry Powder: but if Powder be of his Majesties Tower-Proof, as I am informed, that then the Gunner need not take near so much Powder to shoot among a party of Men, not being at a great distance, as the Peece would crave to batter a Fortificati∣on, or Wall, or Gate, or Ship.

But because the young Gunner, that is not yet experimen∣ted in his Practice, may be taught how he shall load all man∣ner of Guns; and that it is to be understood, that ordinarily those that will be called Gunners, though not known in the Art, use to load their Guns with half the weight of the Ball of Powder; this they hold for a general Rule to all Guns, which Rule is not to be slighted on some occasions, with true-Bored, true-Fortified Ordnance, (yet it may be said, they have this by Tradition) to hold this Rule, without adding to reinforc'd Ordnance, or deducting from those that are lessened of Metal; so that by this they not having any other Rule, disco∣ver their own nakedness or emptiness of Art, for I am per∣swaded that no experienced Gunner, but will hold that the Gunner ought to search, try, and find the Nature and Fortifi∣cation of a Gun or Guns, before he do hold himself obliged to give a Gun Powder, and thereby to prove a true Charge of Powder for the same.

CHAP. XV. The Reasons why I give Guns Powder according to their Fortifications.

THese first Rules were derived from the weight of Ball; but since the Rules were made from the weight of the Peece: for they held generally that four ounces of Pouder was suffici∣ent for the Gunner to give a Brass Gun, to every hundred weight for Service; and three ounces to every hundred weight of Iron Guns. Neither this nor the other being right, for I have seen Trumpet-bored Iron Guns of 1200 weight, that

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could not have half the alowed Powder that either of these Rules did allow of. And likewise I read the Cause of the death of King James the second of Scotland, was by the breaking of a great Gun at the Siege of Rosbrugh.

For these and the following Reasons, I do not hold with that common received Rule, than which many Gunners know no better, but to give Ordnance Powder by the weight of the Gun. For if there be a Peece of Ordnance of Iron weighing 1600 pound weight, likewise there is another Peece of the same Bore, and of the same weight: Now by the Rule of weight it must have the like Powder.

* 1.9But will you consider, for your Instruction, this Peece is longer, and having no more Metal in her than the other, of necessity she must be thinner of Metal; for what she hath of the length, she must want of her thickness, the Bore being both of one denomination; and since she is thinner, it fol∣loweth she must not have so much Powder as the other.

* 1.10Likewise if by the Weight of Guns they should have their Powder, why then do not Founders, where they now make them eight foot long, do not make them ten foot? for it is known to the World, that a Peece of ten foot long will shoot farther than a Peece of eight foot long, but not without equal Powder: Wherefore it is to be considered, they must be both of one Fortification; and being alike in strength, the longest of the two ought to shoot farthest, because more of her Pow∣der is spent in Fire before she deliver her Ball.

Question. But some may demand what I mean by Fortified Ordnance?

Answer. * 1.11For their Fortification, know that there are Ordnance of several Fortifications, as is before shown in pag. 41. where it is sufficient to be understood: and therefore I set the Tables of their Powder here, by their proportions and shape, and shew how to understand the Fortifications of Guns, and also what Powder ought to be given to Guns according to their Fortifications: As first you see the Geometrical Demon∣stration

[illustration]

This is the true Geometricall Demonstration of the Bores of Ordinance, with the heigth of their Ball from 1^lib to 64^lib Scots weight, And the true Wind which ought to be betwixt the Diameter of the Bore and the Diameter of the Ball. Likewayes of the English weight of the Ball from 1.2^lib. to 72^lib And their Wind betwixt the Diameter of the Ball, and the Diameter of the Bore. This doth not hold with the Generall Rule that a 1/20 part of the Diameter of the Ball is the Wind for all Guns But if all Ball were Cast or Turned to a true Roundness, then though they did only fitt to goe home, the less wind the better.

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of Archimedes's Proportion in pag. 40. how fitly that doth give the true Proportion of all true Bored and true Forti∣fied Iron Ordnance.

Now to be capable of the same Proportion Arithmetically, the Proportion is, as 22 the Circumference is unto 7 the Dia∣meter: So must 11 the number of times which the Diameter of the Bore measured about her Breech be, to a number sought for; which by the Work I find to be 3 ½ Diameters of the Bore, which this Peece is of Diameter at the Touch-hole.

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Cometh 3 and ½ ½ which is equal to ½.

Rules to find the thickness of a True Bored Gun in one side Metal, by all the Diameter.

Whilst the Bore it self is one of the Diameters, that being deduced from 3 ½, rests 2 ½, whereby 1 ¼ is the thickness of that Peece in one side Metal; and because these be the Ord∣nance of Iron, by which the Ground-Rule may be and ordi∣narily is laid down, to give Guns their Powder of other For∣tifications; for you must know that there are some lessened, as thinner Fortified, and so cannot have the same proportion of Powder, though they shoot one and the same Ball: Likewise there are reinforc'd or thicker Ordnance at the charged Cyllin∣der, which shoot the same Ball, and must have more Powder: So you may see that the Iron Peece is 11 Diameters of the Bore about the Breech, 9 Diameters at the Trunions, and 7 at the Neck.

* 1.12Likewise the Brass Peece is no thicker at the Charged Cy∣linder, than the Iron Peece is at the Trunions, yet shoots the same Ball, and must have the same Powder; her Proportion is 9 Diameters of the Bore about the Breech, 7 about the Ears, and 5 about the Neck.

Seeing you have the Proportion of these true Fortified Ord∣nance; now it followeth of necessity that the Powder of all such Ordnance should be known: And as writing at length would be tedious, therefore I have Calculated Tables both for Proof and Action, not denominating the Names or Weight of these Ordnance.

But thus fortified with 11 Diameters of the Bore about the Breeech, if Iron, Ordnance shooting from one pound Ball to 48 pound.

Also the same Tables will serve for Brass Ordnance, being Fortified with 9 Diameters of the Bore about the Breech, by what name soever you define them, shooting from one pound Ball, to 48 pound Ball.

The Weight of the Ball and Fortification of Ordnance, are true Rules to give Guns their Powder.

Hereby it is clear, That we are not to examine the Weight of Ordnance, and thereby to give them Powder; but inspe∣ction is to be had to the Fortification of all sorts of Ordnance, as also to their Weight of Ball: To find the Ball fitting a Peece, by extracting the Wind Geometrically, whereby you may have the true Diameter of the Peece, and by the Diameter you may find the Weight of the Ball, as shall be shown at large in its place, in Tables, Scale, or Height-Rule, and also Arithmetically.

But in regard there hath never any pains been taken for re∣gulating the true Powder for Ordnance, I have therefore set down these Tables following for Powder, for Proof and Acti∣on of true-Bored and true Fortified Ordnance.

Table for Proof-Powder, for True-Bored and True-Fortified Ord∣nance, either of Brass or Iron.

B	P	B	P	B	P
1	1      00	17	11      12	33	22      00
2	2      00	18	12      00	34	22      10
3	3      00	19	12      11	35	23      05
4	4      00	20	13      06	36	24      00
5	5      00	21	14      00	37	24      10
6	6      00	22	14      11	38	25      05
7	7      00	23	15      05	39	26      00
8	8      00	24	16      00	40	26      10
9	8      12	25	16      11	41	27      05
10	9      08	26	17      05	42	28      00
11	10      00	27	18      00	43	28      10
12	10      08	28	18      11	44	29      05
13	10      14	29	19      05	45	30      00
14	11      02	30	20      00	46	30      10
15	11      05	31	20      10	47	31      05
16	11      08	32	21      05	48	32      00

In this Table you have the weight of Ball, in the first, third, and fifth Columns, and is marked with the Letter B; and in the second, fourth, and sixth Columns, the Powder to prove these Guns, which is marked with the Letter P, being true-Bored and Fortified, Brass 9, and Iron 11 Diameters of the Bore about the Breech.

Table for Action, of True-Bored and True-Fortified Ordnance, either of Brass or Iron.

B	P	B	P	B	P
1	0      10	17	7      11	33	14      10
2	1      02	18	8      00	34	15      02
3	1      12	19	8      07	35	15      09
4	2      05	20	8      14	36	16      00
5	3      00	21	9      05	37	16      07
6	3      09	22	9      12	38	16      14
7	4      03	23	10      03	39	17      05
8	4      12	24	10      10	40	17      12
9	5      02	25	11      01	41	18      03
10	5      06	26	11      08	42	18      10
11	5      10	27	12      00	43	19      01
12	6      00	28	12      07	44	19      09
13	6      06	29	12      14	45	20      00
14	6      12	30	13      05	46	20      07
15	7      02	31	13      12	47	20      14
16	7      07	32	14      03	48	21      05

In this Table you have the weight of Ball, in the first, third, and fifth Columns, marked with the Letter B; and in the second, fourth, and sixth Columns, being marked with the Letter P, the Powder for Acti∣on, for the Guns being Fortified as before-said, either Brass or Iron. The Proportion you find in the Copper print, N′ 1 and N° 2.

A Scale you have for Powder, both for English and Scots true-Bored true-Fortified Ordnance, Brass or Iron, for Service, on the Quadrant-Rule.

Having shown the Proportion of these Ordnance, and their due Powder, both for Proof and Action, it is now necessary to know the Proportion of their Ladles, Rammers, and Spong-heads.

First, Know that all true-Fortified Ordnance have not one Proportion of Powder, as you may see by the foregoing Ta∣bles; neither must their Ladles be of equal length or breadth according to their Bore.

* 1.13To make this the more clear, know that the Powder doth not lie in one proportioned length in every true-Bored, true-Fortified Peece; For those that shoot from one pound Ball to eight pound, the Powder lieth three Diameters of the Ball in length in a Cartradge, made on a Mold of the Diameter of the Ball.

* 1.14The names of these Ordnance are these; a Base, a Fauco∣net, a Faucon, a Minion, a Saker, and a Demi-culvering.

* 1.15Likewise for these Ordnance that shoot from eight pound Ball to eighteen pound, the Powder lyeth about two Diame∣ters and a half long in a Cartradge, made on the Diameter of the Ball; their names are Demi-Culvering, Quarter-Cannon, Culvering, or French Demi-Cannon.

* 1.16And for these true-Bored, true-Fortified Ordnance, that shoot from 18 lb Ball to 48 lb, the Powder lyeth two Diame∣ters and a quarter long in a Cartradge, made on a Mold of the Diameter of the Ball: The names of these Ordnance, are Culvering, or French Demi-Cannon, Demi-Cannon Ordi∣nary, Demi-Cannon Royal, French-Cannon, and Cannon-Ordinary; and other names they have, as Bazalisks, &c.

By what is before taught, you may know that the Ladles of Ordinance, though of one Fortification, ought not to be of one Proportion.

* 1.17You must make the Ladles for small Ordnance, viz. from one pound to eight, of three Diameters of the Ball in length, with as much as will nail it on the Ladle-head, and the breadth of those Ladles ought to be of 1 ⅚ one Diameter and five sixth parts of the Ball; this Ladle nailed on a wooden head made of purpose, three fills thereof of Powder will serve for Proof, and 2 fills of Powder will serve for Action to these Guns.

And the Ladles for true-Bored, true-Fortified Ordnance, shooting from 8 lb Ball to 18, ought to be two Diameters

and a half of the Ball long, with as much as will nail it on the Rammer-head; and the Breadth of these Ladles, one and five sixth parts of the Diameter of the Ball: Three of these Ladles full of Powder will serve for Proof, and two full of Powder will serve for Action.

Also those Ladles for true-Bored, true-Fortified Ordnance, that shoot from 18 lb Ball to 48 lb, or 64 lb, ought to be two Diameters of the Ball long, and one and five sixth parts of the Diameter of the Ball broad: Three of these Ladles full of Powder will serve for Proof, and two full of Powder will serve for Action.

CHAP. XVI.

AS there are true-Bored, true-Fortified Ordnance both of Brass and Iron; that is to say, 11 Iron, and 9 Brass: So there are true-Bored Iron Ordnance of 10 Diameters of the Bore in the Breech, and Brass of 8 Diameters of the Bore about the Breech.

And because I know that some Gunners are not acquainted with Arithmetick, (for I have been at Sea with a Gunner that could not read) and so such Men not being able to Calculate the Powder of any Guns: Therefore for the publick good of all, I have taken the pains to Calculate Tables for their help; these Tables serve for Iron of 10 Diameters of the Breech, and may well serve for Brass of 8 of the Breech, as the Figures hereby sheweth; For the Iron Gun is 10 Diameters of the Bore about the Breech, 8 2/11 at the Ears, and 6 4/11 at the Neck.

The Brass Peece is 8 2/11 Diameters of the Bore about the Breech, 6 4/11 at the Ears, and 4 6/11 at the Musle: And their Diameters are wrought by the Rule of Archimedes; that is to say, As 22 is to 7, so is 10, 8 2/11, 6 4/11, or 8 2/11, 6 4/11, 4 6/11, to their Diameters: As you have it clearly demonstrated in its proper place; For by their Fortifications they are to have their Powder, as the Tables following sheweth.

This Table sheweth Proof-Powder for Iron Ordnance of 10 Diame∣ters of the Bore, and for Brass of 8 2/11 Diameters of the Bore about the Breech.

B	P	B	P	B	P
1	0      12	17	8      13	33	16      08
2	1      08	18	9      00	34	17      00
3	2      04	19	9      08	35	17      08
4	3      00	20	10      00	36	18      00
5	3      12	21	10      08	37	18      08
6	4      04	22	11      00	38	19      00
7	5      03	23	11      08	39	19      08
8	6      00	24	12      00	40	20      00
9	6      09	25	12      08	41	20      08
10	7      02	26	13      00	42	21      00
11	7      08	27	13      08	43	21      08
12	7      14	28	14      00	44	22      00
13	8      02	29	14      08	45	22      08
14	8      06	30	15      00	46	23      00
15	8      08	31	15      08	47	23      08
16	8      10	32	16      00	48	24      00

This Table sheweth Powder for Acti∣on for Iron Ordnance of 10 Dia∣meters of the Bore about the Breech, and for Brass of 8 Diameters about the Breech.

B	P	B	P	B	P
1	0      7 ½	17	5      12 ½	33	11      02
2	0      12	18	6      00	34	11      07
3	1      04	19	6      5 ½	35	11      12
4	1      12	20	6      10 ⅔	36	12      01
5	2      04	21	6      15 ⅚	37	12      06
6	2      10 ¾	22	7      05	38	12      11
7	3      02	23	7      10 ½	39	13      02
8	3      07	24	7      15 ¼	40	13      07
9	3      12	25	8      05	41	13      12
10	4      1 ½	26	8      10	42	14      01
11	4      3 ½	27	9      00	43	14      06
12	4      8 ½	28	9      05	44	14      11
13	4      12 ½	29	9      10 ½	45	15      00
14	5      1 ¾	30	10      01	46	15      05
15	5      5 ¾	31	10      06	47	15      10
16	5      8 ½	32	10      10	48	16      00

The Proportion you have in the Copper Plates, N° 3 and 4.

In the last preceding Tables, the first Table or the Table next your left hand, sheweth the weight of the Ball, in the first, third, and fifth Columns, and is marked with the Let∣ter B; in the second, fourth, and sixth Columns, you have the Powder to prove these Guns, which are marked with the Letter P; being true-Bored and Fortified as before-said.

In the right hand Table you have the Weight of the Ball in the first, third, and fifth Columns, marked with the Let∣ter B; and in the second, fourth, and sixth Columns, being marked with the Letter P, the Powder for Action for the Guns, being Fortified as before-said, either of Brass or Iron.

Now there are Ordnance of Iron Fortified with 9 Diame∣ters of the Bore about the Breech, and Brass of 7 about; And in regard I have seen divers mistakes about giving them Powder, even of Men professing great Knowledg without Reason; Therefore I will here describe these Tables following, to give them their due Powder. Lower Fortified than 9 of Iron, and 7 of Brass, you shall hardly find a true-Bored Peece of Ordance; The Iron Ordnance being 9 Diameters of the Bore about the Breech, 7 at the Trunions, and 5 8/11 at the Musle or Neck; The Brass Ordnance of 7 Diameters of the Bore at the Breech, 5 8/11 about the Trunions, and 4 1/11 at the Neck.

This Table is the Proof for Iron Ord∣nance of 9 Diamet. in the Breech, and Brass of 7.

B	P	B	P	B	P
1	0      8 ½	17	6      06	33	12      00
2	1      1 ½	18	6      09	34	12      06
3	1      10 ⅓	19	6      12	35	12      12
4	2      03	20	7      02	36	13      01
5	2      12	21	7      09	37	13      07
6	3      4 ½	22	8      00	38	13      13
7	3      13 ½	23	8      6 ½	39	14      03
8	4      04	24	8      12	40	14      09
9	4      13	25	9      02	41	14      15
10	5      3 ¼	26	9      6 ½	42	15      05
11	5      08	27	9      13	43	15      11
12	5      12	28	10      03	44	16      01
13	5      15 ¼	29	10      09	45	16      07
14	6      1 ½	30	10      15	46	16      13
15	6      2 ¾	31	11      05	47	17      03
16	6      04	32	11      10 ½	48	17      08

This Table is the Powder for Action, for Iron of 9, and Brass of 7 Di∣meters of the Bore about the Breech.

B	P	B	P	B	P
1	0      5 ½	17	4      3 ½	33	8      00
2	0      10	18	4      06	34	8      4 ½
3	0      15	19	4      9 ¾	35	8      8 ½
4	1      04	20	4      13	36	8      13
5	1      10	21	5      00	37	9      01
6	1      15 ½	22	5      05	38	9      04
7	2      05	23	5      09	39	9      08
8	2      09	24	5      13	40	9      11
9	2      12	25	6      0 ¾	41	9      14
10	2      15 ½	26	6      4 ¾	42	10      00
11	3      1 ½	27	6      09	43	10      03
12	3      4 ½	28	6      13	44	10      5 ½
13	3      7 ¾	29	7      0 ¾	45	10      08
14	3      11	30	7      4 ½	46	10      12 ½
15	3      14 ¼	31	7      09	47	11      00
16	4      01	32	7      13 ½	48	11      03

The Proportions you have in the Copper Plate, N° 5 and 6.

Now as these are the Tables for true-Fortified, and lessened in Metal, I hold convenient to give Tables for Reinforc'd Ordnance; these have commonly, being Brass, 10 Diameters of the Bore about the Breech, and Iron 12 about the Breech. And though to some these Tables may seem foolish, I have seen those who have been esteemed Able Gunners, that knew not how to give such Guns Powder; yea, they have in my presence wagered, and not one of them knew what they wagered concerning two such Guns lying at the Head of Ferveer confer; where amongst six Gunners one only understood to give these two Guns their true Powder; as at the Discus∣sion, a Gentleman of the Ordnance to the States did manifest in favour of the one Man.* 1.18

I also have been in contest with one professing great Art, and was a rare Person in Art: Yet in the Castle of Edenburgh, there was a Gally-Gun of Brass that did shoot 28 lb Ball; and thereby he did conclude that Peece to have 13 or 14 lb of Powder for Action: In hearing this Expression I did laugh:* 1.19 The Gentleman was offended, and asked if I could teach him, (it was but in disdain); I answered, Sir, if you know not bet∣ter than you express, I am sure I am able to teach you in this point: Whereupon he went out at the Castle-Gate, and was ever mine Enemy from that time forth. And to satisfie the Reader, I will give the Dimensions of that Peece: She was but 7 Diameters of the Bore about the Breech, and 5 ½ about the Musle, for she was plain without Rings, except the Base and Musle-Rings, or Cornish-Rings; so that by her Fortifi∣cation she could suffer but 6 lb and 13 ounces of Powder; and with so much I have caused her to be discharged divers times, and could do Service with this Peece,* 1.20 which could not be done with a true-Fortified Peece; for with this Peece I have shot over the Steeple of Edinburgh, and the Ball hath fallen at the next Lodging where Cromwel did lie. And this I did for three times together, till our Governour discharged me to shoot any more for troubling his Friend. Therefore I say, An able Man may be mistaken of a Gun, when he neither knoweth the Fortification nor Proportion how to Work to give a Peece Powder.

So to avoid trouble to Artists for Calculating, and to instruct those Gunners that are not capable of Calculation, I have here

set down the Demonstration of 〈◊〉〈◊〉 Guns of Iron, having 12 about the Breech, and Brass having near 10 Diameters about the Breech, and are called Reinforc'd Ordnance. The Figures following Demonstrate the true Proportion of these Reinforc'd Ordnance, which require more Powder than true-Bored, true-Fortified Ordnance, as you may see by the Tables following; which Tables might have been first of all: but I observe that the Ground-Rule must be put in the first place; And those that do take their Demensions from it do follow, whether they be Reinforc'd or lessened of Metal, such as are formerly described.

These following Tables, are Tables for Reinforc'd Ord∣nance, which are such as have more strength of Fortification, and are more able to endure firing: Such as be the Baza∣lisk, Serpents, or Slings, &c. and are good to shoot with at a great distance. Having, as I suppose, given a full account of the true allowance of Powder for all sorts of true-Bored Ord∣nance, both for Proof and Action, whether they be Brass or Iron Guns, it followeth that the Gunner ought to know how to go to work with his Peece, when he is to apply these Ta∣bles, by which he is to give fire.

* 1.21First, He shall take a piece of Twine, which is to be well waxed, as the Shoemakers do their Thread, that it do not stretch nor shrink; then measure the Peece about at the Touch-hole betwixt the Rings, and taking with a pair of Compasses the Diameter of the Bore at the Musle, measure the Twine how many Diameters of the Bore is contained about the Breech of the Peece, that keep in memory. Now you are to know what Ball fits that Peece, as is plainly set down pag. 42. Geometrically; but may be exactly found in the Tables of Height and Weight of Shot, and in the Tables of Diameters of Bores, either Scots or English. When you have found the Diameter of the Ball, if you cannot Arithmetically find the Weight by the Diameter of the Ball, then you may resort to the Tables for such Fortifications, and next the weight of Ball you have the weight of Powder for that Peece: but you must be sure your Peece must be true-bored, as is mentioned in pag. 58. For if the Peece be either Taper'd, Chamber'd, or Trumpet-bored, these Tables will do no service.

Proof-Powder for Reinforc'd Ord∣nance, or Iron Guns of 12 Dia∣meters of the Bore about the Breech, and Brass Guns near 10 Diame∣ters.

B	P	B	P	B	P
1	1      05	17	15      01	33	28      08
2	2      09	18	15      05	34	29      10
3	3      10	19	16      07	35	30      08
4	5      01	20	17      05	36	31      08
5	6      08	21	18      02	37	32      04
6	8      05	22	18      15	38	33      01
7	9      01	23	20      00	39	34      02
8	10      06	24	20      12	40	35      00
9	11      06	25	21      09	41	35      12
10	12      05	26	22      08	42	36      08
11	12      15	27	23      07	43	37      08
12	13      10	28	24      12	44	38      05
13	14      01	29	25      01	45	39      04
14	14      07	30	26      00	46	40      02
15	14      10	31	26      14	47	41      00
16	14      14	32	27      10	48	41      12

In this Table you have the weight of Ball, in the first, third, and fifth Columns, and is marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Powder to prove these Guns, which is marked with the Letter P; being true-Bored and Fortified, as above written.

Powder for Action of Reinforc'd Ordnance, or Iron Guns of 12 Di∣ameters of the Bore about the Breech; and Brass near 10 Dia∣meters about the Breech.

B	P	B	P	B	P
1	0      13	17	10      02	33	19      04
2	1      7 ½	18	10      05	34	19      14
3	2      4 ½	19	11      01	35	20      08
4	3      00	20	11      10	36	21      01
5	3      15	21	12      03	37	21      09
6	4      14	22	12      15	38	22      01
7	5      08	23	13      08	39	22      10
8	6      02	24	14      00	40	23      03
9	6      10	25	14      08	41	23      12
10	7      02	26	15      00	42	24      06
11	7      09	27	15      12	43	24      14
12	7      15	28	16      03	44	25      08
13	8      05	29	16      12	45	26      03
14	8      14	30	17      04	46	26      13
15	9      06	31	18      01	47	27      04
16	9      12	32	18      10	48	28      14

In this Table you have the weight of Ball, in the first, third, and fifth Columns, marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Pow∣der for Action, which is marked with the Letter P; being true-Bo∣red and Fortified, as above written.

These Proportions you have in the Copper Plate, N° 7 and 8.

CHAP. XVII. To find the Weight of an Iron Ball in English Inches Arithmetically for Scots Weight.

FOr those that cannot find the Weight of the Ball by Arith∣metick, I will here shew them a Rule, and also Tables which I have Calculated, as well Decimally, as in Pounds, Ounces, and Drams, from eight parts to eight of an Inch of the Diameter of a Ball, unto 10 Inches Diameter, both in Scots and English Weight, and also in Scots and English In∣ches, for the Artificial Gunner his more ease.

It falls out many times that the Gunner cannot find Weights and Scales to weigh his Shot; it is therefore necessary the Gunner should know how to find the Weight of his Shot Arithmetically; as thus, If you desire to know the weight of a Ball, whose Diameter is just Inches, without any Fraction or parts of an Inch, then you are to multiply the Diameter Cubically; then double that Product, and divide the Total by 16, you have in the Quotient the Pounds that the Ball weigheth; and what Remainer you have over, you shall know that Remainer is Ounces.

Example. There is a Ball of 4 Inches Diameter given, to find his Weight: The Cube of 4 is 64, which being doubled maketh 128; this 128 being divided by 16, (the ounces in a pound) the Quotient giveth 8, which is 8 lb of Scots Weight which that Ball doth weigh.

Behold the Work.

4

4

16

4

64

64

128

〈 math 〉〈 math 〉

Eight pound of Scots weight is the true weight of that Ball.

An because every Gunner hath not Arithmetick at his fin∣gers ends, and also to ease the Artificial Gunner, I have taken the pains to Calculate these following Tables, both of Scots and English Weight and Measure, &c. as before-said. I do not take them on trust as others do, but have Calculated them my self from the Ground-Rules, and have given credit to none, because I never found any yet truly set forth.

Tables for Iron Ball, whose Diameters being measured with English Inches, are exactly Calculated for Scots Weight, from eight parts to eight parts of English Inches, unto ten Inches: Decimally.

B	Li.       Parts.	B	Li.       Parts.	B	Li.       Parts.	B	Li.       Parts.
⅛	00       00024	2 ⅝	02       26099	5 ⅛	16       82642	7 ⅝	55       41528
¼	00       00195	2 ¾	02       59961	5 ¼	18       08789	7 ¾	58       18555
⅜	00       00659	2 ⅞	02       97046	5 ⅜	19       41089	7 ⅞	61       04663
½	00       01562	3	03       37500	5 ½	20       79687	8	64       00000
⅝	00       03052	3 ⅛	03       81470	5 ⅝	22       24731	8 ⅛	67       04712
¾	00       05273	3 ¼	04       29102	5 ¾	23       76367	8 ¼	70       18945
⅞	00       08374	3 ⅜	04       80542	5 ⅞	25       34741	8 ⅜	73       42847
1	00       12500	3 ½	05       35937	6	27       00000	8 ½	76       76562
1 ⅛	00       17798	3 ⅝	05       95435	6 ⅛	28       72290	8 ⅝	80       20240
1 ¼	00       24414	3 ¾	06       59180	6 ¼	30       51758	8 ¾	83       74023
1 ⅜	00       32495	3 ⅞	07       27319	6 ⅜	32       38550	8 ⅞	87       38062
1 ½	00       42187	4	08       00000	6 ½	34       32812	9	91       12500
1 ⅝	00       53638	4 ⅛	08       77368	6 ⅝	36       34692	9 ⅛	94       97485
1 ¾	00       66992	4 ¼	09       59570	6 ¾	38       44336	9 ¼	98       93164
1 ⅞	00       82397	4 ⅜	10       46753	6 ⅞	40       61890	9 ⅜	102       99683
2	01       00000	4 ½	11       39062	7	42       87500	9 ½	107       17187
2 ⅛	01       19946	4 ⅝	12       36645	7 ⅛	45       21313	9 ⅝	111       45825
2 ¼	01       42383	4 ¾	13       39648	7 ¼	47       63476	9 ¾	115       85742
2 ⅜	01       67456	4 ⅞	14       48218	7 ⅜	50       14136	9 ⅞	120       37085
2 ½	01       95312	5	15       62500	7 ½	52       73437	10	125       00000

In this Table you have eight Columns; in the first, third, fifth, and seventh Columns, there are the Inches, and eight parts of Inches that the Diameter of the Ball doth contain, and are marked with the Letter B: And in the second, fourth, sixth, and eight Columns, you have the weight of these Diameters of Iron Ball in Scots Weight; under Li. you have Pounds; and under Parts, you have the Deci∣mal parts of Pounds.

Tables for Iron Ball, whose Diameters being measured with English In∣ches, are exactly Calculated for Scots Weight, in Pounds, Ounces and Drams, from eight parts to eights part of English Inches, unto 10 Inches.

B	Li.       On.       Dr.	B	Li.       On.       Dr.	B	Li.       On.       Dr.
1	00      02      00	4	08      00      00	7	42      14      00
1 ⅛	00      02      14	4 ⅛	08      12      06	7 ⅛	45      03      07
1 ¼	00      03      14	4 ¼	09      09      08	7 ¼	47      10      01
1 ⅜	00      05      03	4 ⅜	10      07      08	7 ⅜	50      02      04
1 ½	00      06      12	4 ½	11      06      04	7 ½	52      11      12
1 ⅝	00      08      09	4 ⅝	12      05      14	7 ⅝	55      06      10
1 ¾	00      10      11	4 ¾	13      06      05	7 ¾	58      02      15
1 ⅞	00      13      03	4 ⅞	14      07      11	7 ⅞	61      00      12
2	01      00      00	5	15      10      00	8	64      00      00
2 ⅛	01      03      03	5 ⅛	16      13      04	8 ⅛	67      00      12
2 ¼	01      06      12	5 ¼	18      01      06	8 ¼	70      03      00
2 ⅜	01      10      13	5 ⅜	19      06      09	8 ⅜	73      06      14
2 ½	01      15      04	5 ½	20      12      12	8 ½	76      12      04
2 ⅝	02      04      03	5 ⅝	22      03      15	8 ⅝	80      03      04
2 ¾	02      09      09	5 ¾	23      12      03	8 ¾	83      11      13
2 ⅞	02      15      08	5 ⅞	25      05      09	8 ⅞	87      06      01
3	03      06      00	6	27      00      00	9	91      02      00
3 ⅛	03      13      00	6 ⅛	28      11      09	9 ⅛	94      15      10
3 ¼	04      04      10	6 ¼	30      08      04	9 ¼	98      14      14
3 ⅜	04      12      14	6 ⅜	32      06      03	9 ⅜	102      15      15
3 ½	05      05      12	6 ½	34      05      04	9 ½	107      02      11
3 ⅝	05      15      04	6 ⅝	36      05      09	9 ⅝	111      07      05
3 ¾	06      09      07	6 ¾	38      07      01	9 ¾	115      13      11
3 ⅞	07      04      06	6 ⅞	40      09      14	9 ⅞	120      05      15

In this Table you have six Columns; in the first, third, an fifth Columns, there are the Inches, and eight parts of Inches, that the Dia∣meter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Weight of these Diameters of Iron Ball in Scots Weight; under Li. you have Pounds, under On. Ounces, and under Dr. Drams.

The Height-Rule you have on the side of the Quadrant, which proves this Table.

This Table be Admirable to some Gunners, and especially English, because their Weight and the Scots Weight doth not hold alike; have perused the Tables of Weight by most of the Authors of Gunnery, and I find them all to agree, and hold firm, as Mr. Nye writeth. But indeed I find nothing of ingenuity, for a Man to copy a Table from anothers Works, and never examine the Truth of the Work; But I have made use of their own Ground-Rule, and find not one of them to have wrought it, or set the Table down truly.

I will here set down the Ground-Rule by which they are to make their Table, that the Ingenious Gunner may Correct it himself at his pleasure.

* 1.22Thus they set it down, 2 Inches Diameter give 1 pound 1 ounce.

Now having this for a Rule, you may, if you please, make a Table.

Behold the Work.〈 math 〉〈 math 〉

Where you see, if 2 Inches give one pound one ounce, 2 ¼ Inches giveth 1 pound, 8 ounces, and 3 drams, whereof 16 make an ounce. And by their Tables, because they would

be near the Right, they set down 4 Inches to give 8 pound 15 ounces; where by this Work it will be but 8 pound 8 oun∣ces.

* 1.23But there is another more sure way, by this Work follow∣ing: Say, As 2 Inches is to one pound two ounces: So is the Diameter given, unto the Weight required.

Behold the Work.〈 math 〉〈 math 〉* 1.24

Tables for Iron Ball, whose Diameters being measured with English Inches, are exactly Calculated Decimally for English Weight; from eight parts to eight parts of English Inches, unto 10 Inches.

B	Li.       Parts.	B	Li.       Parts.	B	Li.       Parts.	B	Li.       Parts.
⅛	00      00027	2 ⅝	02      54361	5 ⅛	18      92972	7 ⅝	62      34219
¼	00      00220	2 ¾	02      92456	5 ¼	20      34888	7 ¾	65      45874
⅜	00      00742	2 ⅞	03      34177	5 ⅜	21      83725	7 ⅞	68      67746
½	00      01758	3	03      79687	5 ½	23      39648	8	72      00000
⅝	00      03433	3 ⅛	04      29153	5 ⅝	25      02823	8 ⅛	75      42801
¾	00      05933	3 ¼	04      82739	5 ¾	26      73413	8 ¼	78      96313
⅞	00      09421	3 ⅜	05      40610	5 ⅞	28      51584	8 ⅜	82      60703
1	00      14062	3 ½	06      02930	6	30      37500	8 ½	86      36133
1 ⅛	00      20023	3 ⅝	06      69864	6 ⅛	32      31336	8 ⅝	90      22769
1 ¼	00      27466	3 ¾	07      41577	6 ¼	34      33228	8 ¾	94      20776
1 ⅜	00      36557	3 ⅞	08      18234	6 ⅜	36      43369	8 ⅞	98      30319
1 ½	00      47461	4	09      00000	6 ½	38      61914	9	102      51562
1 ⅝	00      60342	4 ⅛	09      87039	6 ⅝	40      89029	9 ⅛	106      84671
1 ¾	00      75366	4 ¼	10      79517	6 ¾	43      24878	9 ¼	111      29810
1 ⅞	00      92697	4 ⅜	11      77597	6 ⅞	45      69626	9 ⅜	115      87143
2	01      12500	4 ½	12      81445	7	48      23437	9 ½	120      56836
2 ¼	01      34940	4 ⅝	13      91226	7 ⅛	50      86478	9 ⅝	125      39053
2 ¼	01      60181	4 ¾	15      07104	7 ¼	53      58911	9 ¾	130      33960
2 ⅜	01      88388	4 ⅞	16      29245	7 ⅜	56      40903	9 ⅞	135      41721
2 ½	02      19727	5	17      57812	7 ½	59      32617	10	140      62500

In this Table you have eight Columns, in the first, third, fifth, and seventh Columns, are the Inches and eight parts of Inches that the Diameter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, sixth, and eighth Columns, you have the Weight of these Diameters of Iron Ball in English Weight: under Li. you have Pounds, and under Parts, you have the Decimal Parts of of Pounds.

Tables for Iron Ball, whose Diameters being measured with English In∣ches, are exactly Calculated for English Weight, in Pounds, Ounces, and Drams, from eight parts to eight parts of English Inches, unto 10 Inches.

B	Li.       On.        Dr.	B	Li.       On.       Dr.	B	Li.       On.       Dr.
1	00      02      04	4	09      00      00	7	48      03      12
1 ⅛	00      03      03	4 ⅛	09      13      15	7 ⅛	50      13      13
1 ¼	00      04      06	4 ¼	10      12      12	7 ¼	53      09      07
1 ⅜	00      05      14	4 ⅜	11      12      07	7 ⅜	56      06      09
1 ½	00      07      10	4 ½	12      13      00	7 ½	59      05      03
1 ⅝	00      09      10	4 ⅝	13      14      10	7 ⅝	62      05      08
1 ¾	00      12      01	4 ¾	15      01      02	7 ¾	65      07      05
1 ⅞	00      14      13	4 ⅞	16      04      11	7 ⅞	68      10      13
2	01      02      00	5	17      09      04	8	72      00      00
2 ⅛	01      05      09	5 ⅛	18      14      14	8 ⅛	75      06      14
2 ¼	01      09      10	5 ¼	20      05      09	8 ¼	78      15      07
2 ⅜	01      14      02	5 ⅜	21      13      06	8 ⅜	82      09      11
2 ½	02      03      03	5 ½	23      06      05	8 ½	86      05      13
2 ⅝	02      08      11	5 ⅝	25      00      07	8 ⅝	90      03      10
2 ¾	02      14      13	5 ¾	26      11      12	8 ¾	94      03      05
2 ⅞	03      05      07	5 ⅞	28      08      04	8 ⅞	98      04      14
3	03      12      12	6	30      06      00	9	102      08      04
3 ⅛	04      04      11	6 ⅛	32      05      00	9 ⅛	106      13      09
3 ¼	04      13      04	6 ¼	34      05      05	9 ¼	111      04      12
3 ⅜	05      06      08	6 ⅜	36      06      15	9 ⅜	115      13      15
3 ½	06      00      08	6 ½	38      09      14	9 ½	120      09      02
3 ⅝	06      11      03	6 ⅝	40      14      04	9 ⅝	125      05      04
3 ¾	07      06      10	6 ¾	43      04      00	9 ¾	130      05      07
3 ⅞	08      02      15	6 ⅞	45      11      02	9 ⅞	135      06      11

In this Table you have six Columns, in the first, third, and fifth Columns, there are the Inches and eight parts of Inches, that the Dia∣meter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Weight of these Diameters of Iron Ball in English weight; under Li. you have Pounds, under On. Ounces, and under Dr. you have Drams.

This Height-Rule you have on the side of the Quadrant.

By which Work and Tables you may examine any other Weight, if you will compare.

Example. As in the preceding Example, 3 Inches Diameter giveth 3 pound 12 ounces and 12 drams, as you may see by the Work.

Also I demand what giveth 4 Inches of Diameter. 〈 math 〉〈 math 〉

Another Example. If 4 Inches of Diameter give 9 pound weight, what shall 8 Inches give? Answer, 72 pound.〈 math 〉〈 math 〉

Another Example with a Fraction. If 4 Inches of Diameter give 9 pound, what shall 6 ¾ In∣ches give. 〈 math 〉〈 math 〉

I Answer, This Ball of 6 ¾ Inches Diameter, weigheth 43 pound 4 ounces fere; which proves both the Work and Tables to be true and just.

Observation.* 1.25 It is to be observed, That as there is a difference betwixt Scots and English Weight, viz. as 8 to 9, which was menti∣oned in pag. 54. so is there likewise a difference between Scots and English Inches, which is as 9 to 10; that is to say, 9 Eng∣lish Inches make 10 Scots Inches; as it appeareth in the Ta∣bles following.

Tables for Iron Ball, whose Diameters being measured with Scots Inches, are exactly Calculated Decimally for Scots Weight; from eight parts to eight parts of Scots Inches, unto 10 Inches.

B	Li.      Parts.	B	Li.      Parts.	B	Li.      Parts.	B	Li.      Parts.
½	00      00018	2 ⅝	01      64826	5 ⅛	12      26646	7 ⅝	40      39774
¼	00      00142	2 ¾	01      89512	5 ¼	13      18607	7 ¾	42      41726
⅜	00      00481	2 ⅞	02      16546	5 ⅜	14      15054	7 ⅞	44      50299
½	00      01139	3	02      46037	5 ½	15      16092	8	46      65600
⅝	00      02225	3 ⅛	02      78091	5 ⅝	16      21829	8 ⅛	48      48877
¾	00      03844	3 ¼	03      12815	5 ¾	17      32372	8 ¼	51      16811
⅞	00      06105	3 ⅜	03      50315	5 ⅞	18      47826	8 ⅜	53      52935
1	00      09112	3 ½	03      90698	6	19      68300	8 ½	55      96214
1 ⅛	00      12975	3 ⅝	04      34072	6 ⅛	20      93899	8 ⅝	58      46754
1 ¼	00      17798	3 ¾	04      80542	6 ¼	22      24731	8 ¾	61      04663
1 ⅜	00      23689	3 ⅞	05      30216	6 ⅜	23      60903	8 ⅞	63      70047
1 ½	00      30755	4	05      83200	6 ½	25      02520	9	66      43012
1 ⅝	00      39102	4 ⅛	06      39601	6 ⅝	26      49691	9 ⅛	69      23667
1 ¾	00      48837	4 ¼	06      99527	6 ¾	28      02521	9 ¼	72      12117
1 ⅞	00      60068	4 ⅜	07      63083	6 ⅞	29      61118	9 ⅜	75      08469
2	00      72900	4 ½	08      30377	7	31      25587	9 ½	78      12830
2 ⅛	00      87441	4 ⅝	09      01515	7 ⅛	32      96038	9 ⅝	81      25307
2 ¼	01      03797	4 ¾	09      76604	7 ¼	34      72574	9 ¾	84      46006
2 ⅜	01      22075	4 ⅞	10      55751	7 ⅜	36      55305	9 ⅞	87      75035
2 ½	01      42383	5	11      39062	7 ½	38      44336	10	91      12500

In this Table you have eight Columns, in the first, third, fifth, and seventh Columns, are the Inches and eight parts of Inches that the Diameter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, sixth, and eighth Columns, you have the Weight of these Diameters of Iron Ball in Scots Weight: under Li. you have Pounds, and under Parts you have the Decimal Parts of of Pounds.

Tables for Iron Ball, whose Diameters being measured with Scots In∣ches, are exactly Calculated for Scots Weight; in Pounds, Ounces and Drams, from eight parts to eight parts of Scots Inches, unto 10 Inches.

B	Li.      On.      Dr.	B	Li.      On.      Dr.	B	Li.      On.      Dr.
1	00      01      07	4	05      13      05	7	31      04      02
1 ⅛	00      02      01	4 ⅛	06      06      05	7 ⅛	32      15      06
1 ¼	00      02      14	4 ¼	06      15      06	7 ¼	34      11      10
1 ⅜	00      03      13	4 ⅜	07      10      01	7 ⅜	36      08      14
1 ½	00      04      15	4 ½	08      04      14	7 ½	38      07      02
1 ⅝	00      06      04	4 ⅝	09      00      04	7 ⅝	40      06      06
1 ¾	00      07      13	4 ¾	09      12      04	7 ¾	42      06      11
1 ⅞	00      09      10	4 ⅞	10      08      15	7 ⅞	44      08      01
2	00      11      11	5	11      06      04	8	46      10      08
2 ⅛	00      14      00	5 ⅛	12      04      05	8 ⅛	48      07      13
2 ¼	01      00      10	5 ¾	13      02      15	8 ¼	51      02      11
2 ⅜	01      03      09	5 ⅜	14      02      07	8 ⅜	53      08      08
2 ½	01      06      13	5 ½	15      02      09	8 ½	55      15      06
2 ⅝	01      10      06	5 ⅝	16      03      08	8 ⅝	58      07      08
2 ¾	01      14      05	5 ¾	17      05      03	8 ¾	61      00      12
2 ⅞	02      02      10	5 ⅞	18      07      10	8 ⅞	63      11      03
3	02      07      06	6	19      10      15	9	66      06      14
3 ⅛	02      12      08	6 ⅛	20      15      00	9 ⅛	69      03      13
3 ¼	03      02      01	6 ¼	22      03      15	9 ¼	72      01      15
3 ⅜	03      08      01	6 ⅜	23      09      12	9 ⅜	75      01      06
3 ½	03      14      08	6 ½	25      00      06	9 ½	78      02      01
3 ⅝	04      05      07	6 ⅝	26      07      15	9 ⅝	81      04      01
3 ¾	04      12      14	6 ¾	28      00      06	9 ¾	84      07      06
3 ⅞	05      04      13	6 ⅞	29      09      12	9 ⅞	87      12      00

In this Table you have six Columns; in the first, third, and fifth Columns, there are the Inches, and eight parts of Inches, that the Dia∣meter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Weight of these Diameters of Iron Ball in Scots Weight; under Li. you have Pounds, under On. Ounces, and under Dr. Drams.

Tables for Iron Ball, whose Diameters being measured with Scots Inches, are exactly Calculated for English Weight, from eight parts to eight parts of Scots Inches, unto ten Inches: Decimally.

B	Li.       Parts.	B	Li.       Parts.	B	Li.       Parts.	B	Li.       Parts.
⅛	00      00020	2 ⅝	01      85429	5 ⅛	13      79976	7 ⅝	45      44746
¼	00      00160	2 ¾	02      13200	5 ¼	14      83433	7 ¾	47      71942
⅜	00      00541	2 ⅞	02      43615	5 ⅜	15      91936	7 ⅞	50      06587
½	00      01281	3	02      76792	5 ½	17      05604	8	52      48800
⅝	00      02503	3 ⅛	03      12853	5 ⅝	18      24558	8 ⅛	54      98702
¾	00      04325	3 ¼	03      51917	5 ¾	19      48918	8 ¼	57      56413
⅞	00      06868	3 ⅜	03      94105	5 ⅞	20      78805	8 ⅜	60      22052
1	00      10252	3 ½	04      39536	6	22      14337	8 ½	62      95741
1 ⅛	00      14596	3 ⅝	04      88331	6 ⅛	23      55637	8 ⅝	65      77600
1 ¼	00      20023	3 ¾	05      40610	6 ¼	25      02823	8 ¾	68      67746
1 ⅜	00      26650	3 ⅞	05      96493	6 ⅜	26      56016	8 ⅞	71      66303
1 ½	00      34599	4	06      56100	6 ½	28      15335	9	74      73389
1 ⅝	00      43990	4 ⅛	07      19552	6 ⅝	29      80902	9 ⅛	77      89125
1 ¾	00      54942	4 ¼	07      86968	6 ¾	31      52836	9 ¼	81      13631
1 ⅞	00      67576	4 ⅜	08      58468	6 ⅞	33      31257	9 ⅜	84      47027
2	00      82012	4 ½	09      34174	7	35      16286	9 ½	87      89433
2 ⅛	00      98371	4 ⅝	10      14204	7 ⅛	37      08042	9 ⅝	91      40970
2 ¼	01      16772	4 ¾	10      98680	7 ¼	39      06646	9 ¾	95      01757
2 ⅜	01      37335	4 ⅞	11      87720	7 ⅜	41      12218	9 ⅞	98      71914
2 ½	01      60181	5	12      81445	7 ½	43      24878	10	102      51562

In this Table you have eight Columns; in the first, third, fifth, and seventh Columns, there are the Inches, and eight parts of Inches that the Diameter of the Ball doth contain, and are marked with the Letter B: And in the second, fourth, sixth, and eight columns, you have the weight of these Diameters of Iron Ball in English Weight; under Li. you have Pounds; and under Parts, you have the Deci∣mal parts of Pounds.

Tables for Iron Ball, whose Diameters being measured with Scots In∣ches, are exactly Calculated for English Weight, in Pounds, Ounces, and Drams, from eight parts to eight parts of Scots Inches, unto 10 Inches.

B	Li.       On.       Dr.	B	Li.       On.        Dr.	B	Li.       On.       Dr.
1	00      01      10	4	06      09      00	7	35      02      10
1 ⅛	00      02      05	4 ⅛	07      03      02	7 ⅛	37      01      05
1 ¼	00      03      03	4 ¼	07      13      15	7 ¼	39      01      01
1 ⅜	00      04      04	4 ⅜	08      09      06	7 ⅜	41      01      15
1 ½	00      05      09	4 ½	09      05      07	7 ½	43      04      00
1 ⅝	00      07      01	4 ⅝	10      02      04	7 ⅝	45      07      03
1 ¾	00      08      13	4 ¾	10      15      13	7 ¾	47      11      08
1 ⅞	00      10      13	4 ⅞	11      14      01	7 ⅞	50      10      01
2	00      13      02	5	12      13      00	8	52      07      13
2 ⅛	00      15      12	5 ⅛	13      12      13	8 ⅛	54      15      13
2 ¼	01      02      11	5 ¼	14      13      06	8 ¼	57      09      00
2 ⅜	01      06      00	5 ⅜	15      14      11	8 ⅜	60      03      08
2 ½	01      09      10	5 ½	17      00      14	8 ½	62      15      05
2 ⅝	01      13      11	5 ⅝	18      03      15	8 ⅝	65      12      07
2 ¾	02      02      02	5 ¾	19      07      13	8 ¾	68      10      13
2 ⅞	02      07      00	5 ⅞	20      12      10	8 ⅞	71      10      10
3	02      12      05	6	22      02      05	9	74      11      12
3 ⅛	03      02      01	6 ⅛	23      08      14	9 ⅛	77      14      04
3 ¼	03      08      05	6 ¼	25      00      07	9 ¼	81      02      03
3 ⅜	03      15      01	6 ⅜	26      08      15	9 ⅜	84      07      08
3 ½	04      06      05	6 ½	28      02      07	9 ½	87      14      05
3 ⅝	04      14      02	6 ⅝	29      12      15	9 ⅝	91      06      09
3 ¾	05      06      08	6 ¾	31      08      07	9 ¾	95      00      04
3 ⅞	05      15      07	6 ⅞	33      05      00	9 ⅞	98      11      08

In this Table you have six Columns, in the first, third, and fifth Columns, there are the Inches and eight parts of Inches, that the Dia∣meter of the Ball doth contain, and are marked with the Letter B; and in the second, fourth, and sixth Columns, you have the Weight of these Diameters of Iron Ball in English weight; under Li. you have Pounds, under On. Ounces, and under Dr. you have Drams.

CHAP. XVII. The Use of the preceding Tables.

* 1.26IF the Diameter of an Iron Ball be measured with Scots In∣ches, I would know what the same Ball weigheth in Eng∣lish Weight.

Example. There is an Iron Ball, whose Diameter is 5 ½ Scots Inches; I demand what the same Ball weighs in English Weight.

Look in the Table in pag. 80. under B in the fifth Column, where you find 5 ½ Inches; and right against it, in the sixth Column, you have 17 pound and 056/1000 pounds, which is the just weight of the same Ball.

Or otherwise, Look in the Table in pag. 81. under B, in the third Column, where you find 5 ½ Inches; and right against it, in the fourth Column, you have 17 poound, 00 oun∣ces, and 14 drams, which is also the just Weight of the same Ball.

Or if the Diameter of an Iron Ball be measured with Scots Inches; I desire to know what the same Ball weigheth in Scots Weight.

Example. There is an Iron Ball whose Diameter is 6 ⅛ Scots Inches; I demand what doth the same Ball weigh in Scots Weight.

Look in the Table in pag. 78. under B, in the fifth Co∣lumn, where you find 6 ⅛ Inches; and right against it, in the sixth Column, you have 20 pound and 938/1000 parts of a pound, which is the just weight of the same Ball in Scots Weight.

Or otherwise, Look in the Table in pag. 79. under B, in the third Column, where you find 6 ⅛ Inches; and right against it, in the fourth Column, you have 20 pounds and

15 ounces, which is also the just weight of the same Ball in Scots Weight. And this I will assure you to be truth, be∣cause I have calculated all these Tables with my own hand, and they are since revised and truly done, by the laborious pains of Mr. Robert Webster.

CHAP. XVIII. To Extract the Cube Root of a Number not Cubical.

* 1.27I Doubt not but Men of Reason will think, that in Calculating all these Tables, I have taken great pains, so that you need to take the less: And because there are many Gunners that cannot use their Pen, and some that can∣not understand the use of Tables, I therefore for their help will here set down an Height-Rule for Ball, from one pound to an hundred pound, both in Scots and English Weight. But before this Height-Rule be made, it is needful to set down a Cubical Table, for except you have this Table, the Height-Rule can∣not be truly made.

To Calculate this Table, it is necessary that you can Ex∣tract the Cube Root of Irrational Numbers; which Numbers are so termed, because that from such Numbers you cannot extract a true Cube-Root, and therefore to the Number pro∣pounded you must add 3, 6, or 9 Cyphers; by which you may Extract the Cube-Root without sensible error, as it doth appear in the Examples following.

Example. Let it be required to extract the Cube-Root of 8302348.

〈 math 〉〈 math 〉Having distributed the Number given into several Cubes by Points, as is directed in Chap. 8. of this. I demand the Cube-Root of 8, (the first Cube on the left hand) which I find to be 2; wherefore placing 2 in the Quotient, and 8 the Cube thereof, under 8 the first Cube, I draw a Line, subtracting 8 out of 8, the Remainder is 0, which I subscribe under the Line. This is always the first Work, and is no more repeated in the whole Extraction, (as was intimated in the third Note of chap. 8.); then bringing down the next Cube, (to wit, the Figures standing in the three following places of the Number propounded) which is 302, I place it after the Remainder 0, so is 302 the Resolvend; this done, ha∣ving drawn a Line underneath the Resolvend, I seek for the triple of the Square of the Root, viz. The Root in the Quotient is 2, which multi∣plied by it self produceth the Square 4, the triple whereof is 12; this I subscribe under the Resolvend, in such manner, that the Figure 2 in the Unites place of this triple Square 12, may stand directly under the Figure 3, which is seated in the third place of the Resolvend, (to wit, the place of Hundreds): Again, I triple the Root 2, which produceth 6, and subscribe this tri∣ple Number 6 under the second place (or place of Tens) in the Resolvend, to wit, under 0; then drawing a Line under the Work, and adding together the said two Numbers last sub∣scribed, as they are ranked, the Sum of them is 126 for a Di∣visor: That done, esteeming 30, to wit, all the places except the first or place of Unites in the Resolvend, as a Dividend, I demand how often the Divisor 126 is contained in 30, and not finding it once contained therein, I write 0 in the Quotient; and now because the sum of the three Numbers which ought

to have been produced (according as was mentioned in Chap. 8.) by the multiplication of 0, (which was last placed in the Quotient) amounts to 0, the Resolvend 302, out of which the said Sum should have been subtracted, remains the same without alteration; wherefore having drawn a Line un∣der the Work, I write down anew the old Resolvend 302, and bringing down the next Cube 348, I annex it to the said 302, so there will be a new Resolvend, to wit, 302348. Then squaring the Root 20, (that is, multiplying of it by it self) the Product is 400; which I triple or multiply by 3, and subscribe the Product 1200 under the new Resolvend in such manner, that the place of Unites in this triple Quadrate 1200 may stand under the place of Hundreds, or third place of the Resolvend 302348, to wit, under 3: Again, I sub∣scribe the triple of the Root 20, which is 60, in such manner, that the place of Unites in this triple Root 60 may stand un∣der the place of Tens or second place of the Resolved; then adding together the two Numbers last subscribed, to wit, 1200 and 60, in such order as they are ranked in the Work, the Sum is 12060 for a Divisor. Again, esteeming the whole Resol∣vend, except the first place, (or place of Unites) as a Divi∣dend, to wit, 30234, I demand how often 1 (the first Figure of the Divisor towards the left hand) is contained in 3, the corespondent part of the Dividend; and though it be three times contained in it, yet (according to the first Note in Chap. 8.) I dare take but 2; (for if I should take 3, and pro∣ceed according as was declared in Chap. 8. a Number would arise greater than the Resolvend, from which such Numbers arising ought to be subtracted) wherefore I write 2 in the Quotient. Then multiplying the triple Square 1200 before subscribed by 2, (the Figure last placed in the Quotient) the Product is 2400, which I subscribe under the said 1200, (to wit, Unites under Unites, and Tens under Tens, &c.) Also multiplying the triple Root 60, before subscribed by 4, (the Quadrate of 2, the Figure last placed in the Quotient) the Product is 240, which I subscribe under the said triple Root 60; last of all I subscribe 8 the Cube of the said new Root 2, under the place of Unites, or first place of the Resolvend, to wit, under 8; and having added together those three Num∣bers last subscribed, to wit, 2400, 240, and 8, as they stand

in Ranks in the Work, the sum of them is 242408, which be∣ing deducted from the Resolvend 302348, there will remain 59940. Wherefore the Work being finished, I find 202 to be the number of Unites contained in the Cube-Root of 8302348 the Number propounded: and because, after the Extraction is ended, there happens to be a Remainder, to wit, 59940, I conclude that the Cube-Root sought is greater than the said 202, but less than 203; yet how much it is greater than 202, no Rules of Art hitherto known will exactly discover, although we may proceed infinitely near, as by the following Rule will be manifest.

To find the Fractional part of the Root very near. Ternaries of Ciphers, to wit, 000,000000, or 000000000, &c. are to be annexed to the Number first propounded; then esteeming the Number propounded with the Ciphers annexed to be but one entire Number, the Extraction is to be made according as hath been prescribed in this Chapter; and look how many Points were placed over the Number first given, so many of the foremost places in the Quotient are the Integers or Unites contained in the Cube-Root sought, and the rest of the places in the Quotient are to be esteemed as the Numerator of a Decimal Fraction; which Numerator consists of so many places as there were Points over the Ciphers first annexed: so if 8302348 were given as before to find the Cube-Root thereof, (according to this Rule) annex Ciphers as you here see in the Work. And then if you prosecute the Extraction according to the Rules foregoing, you shall find the Cube-Root sought to be 202⌊48, &c. that is, 202 48/100 and more; where∣fore you may conclude that 202 48/100 is less than the true Root, but 202 49/100 is greater than it; So that by annexing two Ter∣naries of Ciphers, to wit, six Ciphers to the number pro∣pounded, you will not miss 1/100 part of an Unite of the true Root; as also by annexing three Ternaries of Ciphers, to wit, 9 Ciphers, you will not miss 1/1000 part of an Unite of the true Root; and in that order you may proceed infinitely near, when you cannot obtain the true Root. The whole Operati∣on of the said Example you have in the next page, where you may observe, that for the more certain and easie placing, as well of the Numbers, which constitute the several Divisors, as of those which constitute the Ablatitious Numbers to be sub∣tracted

from the several and respective Resolvends, down right Lines are drawn between the particular Cubes of the Number propounded, first distinguished by Points as below. 〈 math 〉〈 math 〉

Another Example wrought by the Genitures. In like manner the Cube-Root of 2, will be found to be near equal to 1⌊25992, &c. that is, 1 25992/100000 parts and more. And the Work will stand thus. 〈 math 〉〈 math 〉

The Proof of the Cube-Root. The Extraction of the Cube-Root is proved by multiply∣ing the Root Cubically; to wit, the Root being first multiplied by it self, the Product shall give a Square Number, the which Square being multiplied again by the said Root, the Number arising, or last Product (in case there be no Remainder after the Extraction is finished) will be equal to the Number pro∣pounded:

〈 math 〉〈 math 〉So in the Example of Chap. 8. the Cube-Root 54 being multiplyed first by it self, produceth 2916, which is a Square Number, then the said Square 2916, being multiplyed by the Root 54, pro∣duceth 157464, which is a Cube Num∣ber equal to the number propounded, whose Cube-Root was required. So that the Extraction is right, and the same Root found is the true Cube-Root of the Number proposed. But when after the Extraction is finished, there happens to be a Remainder, and that the Root is found as near as you please in Integers and Decimal parts, (by annexing Ciphers as in this Chapter) then such mixt Number expressing the Root, being multiplyed Cubically, must produce a mixt Number less than the Number first propounded; yet so near unto it, that if the Figure standing in the last place of the Decimal Fraction in the Root be made greater by 1, and the mixt number so in∣creased be multiplied Cubically, the Product must be greater than the Number first propounded: so in the first Example of this Chapter, if 202⌊48 be multiplied Cubically, it produceth 8301305⌊49, &c. which is less than the propounded Num∣ber 8302348; but if 202⌊49 be multiplied Cubically, there∣will arise 8302535⌊49, &c. which is greater than the said gi∣ven Number.

Behold the Work. 〈 math 〉〈 math 〉

The Table of Cubes, whereby the Height-Rule is made. This Height-Rule you have on the side of the Quadrant Rule, both for Scots and English Ball.

A	B	A	B	A	B	A	B	A	B
1	1000	26	2962	51	3708	76	4235	101	4657
2	1259	27	3000	52	3732	77	4254	102	4672
3	1442	28	3036	53	3756	78	4272	103	4687
4	1587	29	3072	54	3779	79	4290	104	4702
5	1709	30	3107	55	3802	80	4308	105	4717
6	1817	31	3141	56	3825	81	4326	106	4732
7	1912	32	3174	57	3848	82	4344	107	4747
8	2000	33	3207	58	3870	83	4362	108	4762
9	2080	34	3239	59	3892	84	4379	109	4776
10	2154	35	3271	60	3914	85	4396	110	4791
11	2223	36	3301	61	3936	86	4413	111	4805
12	2289	37	3332	62	3957	87	4430	112	4820
13	2351	38	3361	63	3979	88	4447	113	4834
14	2410	39	3391	64	4000	89	4464	114	4847
15	2466	40	3419	65	4020	90	4485	115	4862
16	2519	41	3448	66	4041	91	4497	116	4877
17	2571	42	3476	67	4061	92	4514	117	4890
18	2620	43	3503	68	4081	93	4530	118	4904
19	2668	44	3530	69	4101	94	4546	119	4918
20	2714	45	3556	70	4121	95	4562	120	4931
21	2758	46	3583	71	4140	96	4578	121	4946
22	2802	47	3608	72	4160	97	4594	122	4959
23	2843	48	3634	73	4179	98	4610	123	4973
24	2884	49	3659	74	4198	99	4626	124	4986
25	2924	50	3689	75	4217	100	4642	125	5000

In this Table you have ten Columns, in the 1st, 3d, 5th, 7th, and 9th Columns, you have the Weight of the Ball, from 1 lb to 125 lb, and are marked with the Letter A; and in the 2d, 4th, 6th, 8th, and 10th Columns, you have the Cube-Roots and Parts correspondent to the Weight of Ball, which are marked with the Letter B; as shall ap∣pear in the Examples following.

CHAP. XIX. The way to find the Diameter of the first pound Ball.

NOw if any Artificial Gunner desire to make a Height-Rule or Scale to know the Weight of his Shot, by measuring the Diameter of the Ball, and by this Cubical Table: First he must know the exact Diameter of a Ball of one pound weight, of what sort of Metal or Stone he desires his Height-Rule or Scale for; the which to do, observe these Rules follow∣ing.

First, Search until you find a Ball of that Metal very smooth, of any size or weight, and take the Diameter ex∣actly of that Ball, with a pair of Callabassero Compasses. Then draw that Diameter on a peece of Paper, or plain Board, and divide it in as many equal parts as you please; then weigh that Ball exactly well, which being done, multiply the Divi∣sions of the Diameter of the Ball Cubically, and divide that Product by the weight of the Ball; so from that Quotient of your Division, you are to extract the Cube-Root, and the Quotient is the parts of that Ball which weigheth one pound weight of that Metal.

Example. The Ball given is a Ball of Iron, whose weight is 12 lb; and his Diameter is divided into 300 equal part; which done, work as followeth.

〈 math 〉〈 math 〉

By which I find 131 parts of the Ball given to be the just Diameter of a Ball of one pound weight, of that Country-Weight. As you may see by the Diameters herewith annex∣ed; the Line AB the Diameter of the Ball given, and the Line CD the Ball found for one pound.

After you have found the true Diameter of one pound Ball, you must divide the same into 1000 equal parts; or make a Diagonal Scale of the same Diameter of the one pound Ball, and so resort to the Table of Cubical Numbers; and having a Scale of Paper or Wood ready, you may set the Diameter of the Ball on it, from one pound as far as the Table doth run.

* 1.28And that I may make it the more plain, be∣hold the Diameter of a Ball of 12 pound; and from that, by working as is before taught, you may have the Diameter of one pound Ball, which is here found, and true in every Condi∣tion. Thus having the Table of Cubical Numbers, wherein you find the first pound is 1000 in its Root, and the second 1259 of the parts of one pound Ball, which is 259 parts more than the Ball of one

pound; which added to the Diameter of one pound, gives the Diameter of a Ball of 2 pound; which place on your Ruler, then the Table gives 1442, for the Diameter of a Ball of 3 pound; and if you take 442, and add to the Diameter of one pound Ball, you have the Diameter of a Ball of 3 pound: And thus you may encrease and go upward till you have a compleat Height-Rule of what height you please.

So making it, as you are taught, you may answer any Question demanded of the Weight of Ball, of the Metal and Weights of the place it is made for. For all places have not one Weight, as you see by the Table following.

The Proof of the Height-Rule. Now every Height-Rule for Ball, of what Metal soever it be made for, is proved in manner following: That when you extend your Compasses to the height of one pound, and with the same extention turn your Compasses, you shall reach 8 pound; and if you take the Diameter of a 2 pound Ball, and turn the Compasses about, must fall in 16 pound Ball; and of 3 pound to 24 pound: So that all Ball being twice the Diameter of the other, must carry 8 times the weight of the other.

Further-more, By the Cubical Table, with the Diagonal Scale of the height of one pound Ball, you may give an ac∣count to make Height-Rules, shewing the Weight of Iron Ball in any Place or Country, knowing the proportion it beareth with our own Scots or English Weight: So that here it will be very requisite, in regard ordinarily every Countrey have their own dinstinct Weights and Measures, to give a Ca∣talogue of some several Places and their Weights compared with ours as you see, and as shall be further demonstrated for the Gunner's more ease.

Table of the Weights of several Places being compared with ours of Edinburgh.

100 pounds at Edinburgh maketh at	lb.
London	112
Antwerp	108
Bollogne, betwixt 139 and	140
Catalogne	160
Cullen	102
Cureland	98
Dantzick	122
Florence	142
Lubeck	110
Lyons	120
Genua, betwixt 152 and	153
Amsterdam	100
Venetia, great Weight	106
Prague	62
Lublin	128

* 1.29〈 math 〉〈 math 〉I set here for Example; There is a Gun in Edinburgh, measured by the Height-Rule, and is found to shoot 36 lb Ball; Now the Question is, What weight of Ball the same Peece doth shoot at London: And comparing the Weights together, you will find it stand thus.

And that Peece which shooteth 36 lb Ball at Edinburgh, will require at London a Ball of 40 lb 5 ounces English weight.

Another Example. Likewise if there were a Peece at Edinburgh, which shoots 9 lb Ball; I would know what the Weight of a Ball fit for that Peece shall be of Dantzick Weight.

Behold the Work. 〈 math 〉〈 math 〉 You see that of that Weight it will be 10 pound 15 ounces, and 68/100 parts of an ounce.

And so generally the Gunner may fit himself with Ball in all Places.

And as there is a diversity in the Weights of several Places, so is there likewise a diversity in the Foot: And that here it will be necessary to give a Catalogue of some several places, and their Feet compared with our Foot.

A Catalogue of the Feet of several Places compared with ours of Edinburgh.

100 foot of Edin∣burgh maketh	Foot.
Of the Ancient Romans	87⌊19
Of the Ancient Greeks	83⌊14
Of the Ancient Babylonians	74⌊38
Of Alexandria	72⌊73
Of the Isle Samos	72⌊73
Of Arabia	81⌊82
Of London	90⌊00
Of Paris	82⌊64
Of Leyden	87⌊19
Of Antwerp	95⌊87
Of Copenhagen	90⌊00
Of Venice	77⌊60
Of Toledo	100⌊00
Of Stratsburg	94⌊22

Example. There is a Gun in Edinburgh, whose Diameter of the Bore is measured by the Height-Rule to be 6 ¼ Inches; I demand how many Inches of London shall the Diameter of the Bore of the same Peece be. 〈 math 〉〈 math 〉

I Answer, That Peece whose Diameter of the Bore is 6 ¾ Inches at Edinburgh, is but 5 ⅝ Inches of Diameter at London.

Another Example. There is a Gun at London which shooteth a Ball of 6 ¾ In∣ches Diameter; I demand of how many Inches Diameter shall a Ball be at Edinburgh which shall fit the same Peece. 〈 math 〉〈 math 〉

I Answer, That Peece which shooteth a Ball of 6 ¾ Inches Diameter at London, shall certainly require a Ball to fit her at Edinburgh of 7 ½ Inches.

Any Ingenious Gunner observing all the Rules that hath been described in this Chapter, may make an Height-Rule for any Metal of Ball.

For more clearing of this, I shall set here a Table of equal Diameters and different Weight.

The Diameters of Ball of one Country Weight to be found by equal and several Divisions of several Metals and Stones, as they are compared with Iron.

Iron is in Proportion to	The Proportion of Iron Ball compared with other Metals and Stones.
Copper—	as 8 is to 09
Silver—	as 24 is to 31
Lead—as	16 is to 23
Quicksilver—	as 56 is to 95
Gold—	as 8 is to 19
Tin —	as 120 is to 111
Marble—	as 96 is to 43
Sclate —	as 48 is to 13
Stone —	as 144 is to 35
Brick —	as 288 is to 65

Example. There is a Gun which shooteth a Ball of Iron weighing 24 pounds; I demand what shall a Ball of Lead of the same Diameter weigh. 〈 math 〉〈 math 〉

I Answer, This Peece shall require a Ball of Lead which weigheth 34 lb and 8 ounces, which shall be of the same Dia∣meter as was the Iron Ball of 24 pounds.

Another Example. There is a Gun which shooteth a Ball of Iron weighing 36 pounds; I demand what shall a Ball of Stone of the same Diameter weigh. 〈 math 〉〈 math 〉

I Answer, This Peece shall require a Ball of Stone which weigheth but 8 lb and 12 ounces, which shall be of the same Diameter as was the Iron Ball of 36 lb.

CHAP. XX.

FOr the Gunners further ease, I have set down Tables both of Scots and English Weight of Iron Ball, from 1 lb to 100 lb; with the Diameters of the Ball both in Scots and English Inches, and parts of Inches; together with the Height of the Bores of the Ordnance that the same Ball shall fit in the like Inches: So that he may take the Diameter of a Ball, (only knowing the Weight); as also the Height of the Bore of the Peece, which the same Ball shall fit, from any Diagonal Scale of Inches, divided into Decimal parts.

Tables for Iron Ball, wherein you have the Weight of every Ball given in Scots Weight, from 1 lb to 100 lb; together with the Diameters or Height of every Ball in Scots Inches and parts of Inches; exactly Cal∣culated to each pound Weight above-mentioned.

A	B	A	B	A	B	A	B
1	2.2222	26	6.5833	51	8.2410	76	9.4129
2	2.7998	27	6.6667	52	8.2944	77	9.4540
3	3.2049	28	6.7480	53	8.3473	78	9.4948
4	3.5276	29	6.8273	54	8.3994	79	9.5351
5	3.8000	30	6.9050	55	8.4510	80	9.5752
6	4.0380	31	6.9808	56	8.5019	81	9.6150
7	4.2509	32	7.0551	57	8.5522	82	9.6544
8	4.4444	33	7.1279	58	8.6019	83	9.6934
9	4.6223	34	7.1991	59	8.6511	84	9.7322
10	4.7876	35	7.2694	60	8.6997	85	9.7708
11	4 9421	36	7.3377	61	8.7478	86	9.8089
12	5.0877	37	7.4050	62	8.7953	87	9.8468
13	5.2251	38	7.4709	63	8.8423	88	9.8843
14	5.3559	39	7.5360	64	8.8889	89	9.9217
15	5.4804	40	7.5999	65	8.9349	90	9 9587
16	5.5997	41	7.6627	66	8.9806	91	9.9954
17	5.7140	42	7.7246	67	9.0257	92	10.0319
18	5.8238	43	7.7853	68	9.0703	93	10.0681
19	5.9298	44	7.8452	69	9.1146	94	10.1041
20	6.0320	45	7.9042	70	9.1584	95	10.1398
21	6.1310	46	7.9623	71	9.2018	96	10.1752
22	6.2268	47	8.0196	72	9.2448	97	10.2104
23	6.3197	48	8.0761	73	9 2874	98	10.2454
24	6.4100	49	8.1318	74	9.3297	99	10.2801
25	6.4978	50	8.1868	75	9.3714	100	10.3147

In this Table you have eight Columns, in the 1st, 3d, 5th, and 7th Columns, marked with the Letter A, is the Weight of the Ball in Scots Weight; and in the 2d, 4th, 6th, and 8th Columns, marked with the Letter B, you have the Diameter of the Ball in Scots Inches, and De∣cimal parts of Inches. The Geometrical Demonstration of these two Tables is in pag. 54.

Tables for Iron Ball, wherein you have the Weight of every Ball given in Scots Weight, from 1 lb to 100 lb; together with the Height of the Bore of each Peece answering to those Balls, given in Scots Inches and parts of Inches, Exactly Calculated to each pound weight of Ball above mentioned, the Wind being truly extracted.

A	B	A	B	A	B	A	B
1	2.3529	26	6 8695	51	8.5993	70	9.8223
2	2.9645	27	6.9566	52	8.6550	77	9.8650
3	3.3934	28	7.0414	53	8.7102	78	9.9076
4	3.7351	29	7.1241	54	8.7645	79	9 9497
5	4.0235	30	7.2052	55	8 8184	80	9.9915
6	4.2754	31	7.2843	56	8.8715	81	10.0330
7	4.5010	32	7.3618	57	8.9240	82	10.0742
8	4.7058	33	7.4378	58	8.9759	83	10.1149
9	4.8424	34	7.5121	59	9.0272	84	10.1553
10	5.0156	35	7.5855	60	9.0779	85	10.1956
11	5.1774	36	7.6567	61	9.1281	86	10.2354
12	5.3300	37	7.7270	62	9.1777	87	10.2749
13	5.4739	38	7.7957	63	9.2267	88	10.3141
14	5.6109	39	7.8637	64	9.2754	89	10.3531
15	5.7414	40	7.9303	65	9.3234	90	10.3917
16	5.8664	41	7.9959	66	9.3711	91	10.4300
17	5 9861	42	8.0605	67	9 4181	92	10.4681
18	6.1011	43	8.1238	68	9.4647	93	10.5058
19	6.1876	44	8.1863	69	9.5109	94	10.5434
20	6.2943	45	8.2479	70	9.5566	95	10.5807
21	6.3976	46	8.3085	71	9.6016	96	10.6176
22	6.4975	47	8.3683	72	9.6467	97	10.6543
23	6.5945	48	8.4272	73	9.6912	98	10.6909
24	6.6887	49	8.4854	74	9.7353	99	10.7271
25	6.7803	50	8.5427	75	9.7788	100	10.7632

In this Table you have eight Columns, in the 1st, 3d, 5th, and 7th Columns, mar∣ked with the Letter A, is the weight of Ball in Scots Weight; and in the 2d, 4th, 6th, and 8th Columns, marked with the Letter B, you have the Height of the Bore of each Peece, which those Balls shall fit, the Wind truly Extracted, in Scots Inches, and De∣cimal parts of Inches: Which you have in the Copper Plate, pag. 56, 57.

Tables for Iron Ball, wherein you have the Weight of every Ball given in English Weight, from 1 lb to 100 lb; together with the Diameter or Height of every Ball in English Inches and parts of Inches; exactly Calculated to each pound Weight of Ball above-mentioned.

A	B	A	B	A	B	A	B
1	1.9230	26	5.6969	51	7.1313	76	8.1455
2	2.4228	27	5.7690	52	7 1776	77	8.1811
3	2.7735	28	5.8394	53	7.2233	78	8.2163
4	3.0526	29	5.9081	54	7.2685	79	8.2513
5	3.2883	30	5.9752	55	7.3131	80	8.2860
6	3.4943	31	6.0409	56	7.3571	81	8.3203
7	3 6786	32	6.1051	57	7.4007	82	8.3544
8	3.8460	33	6.1681	58	7.4437	83	8.3883
9	4.0000	34	6.2298	59	7.4862	84	8.4218
10	4.1430	35	6.2903	60	7.5283	85	8.4551
11	4.2767	36	6.3496	61	7.5699	86	8.4881
12	4.4026	37	6.4079	62	7.6110	87	8.5209
13	4.5216	38	6.4651	63	7.6517	88	8.5534
14	4.6347	39	6.5223	64	7.6920	89	8.5857
15	4.7425	40	6.5766	65	7.7318	90	8.6177
16	4.8457	41	6.6309	66	7.7712	91	8.6495
17	4 9446	42	6.6844	67	7.8104	92	8.6811
18	5.0397	43	6.7370	68	7.8490	93	8.7124
19	5.1313	44	6.7888	69	7.8873	94	8.7436
20	5.2198	45	6.8399	70	7.9252	95	8.7744
21	5.3054	46	6.8902	71	7.9628	96	8.8051
22	5.3883	47	6.9398	72	8.0000	97	8.8356
23	5.4688	48	6.9886	73	8.0369	98	8.8658
24	5 5469	49	7.0368	74	8.0734	99	8.8959
25	5.6229	50	7.0844	75	8.1096	100	8.9258

In this Table you have eight Columns, in the 1st, 3d, 5th, and 7th Columns, marked with the letter A, is the Weight of the Ball in English Weight; and in the 2d, 4th, 6th, and 8th Columns, marked with the Letter B, you have the Diameter of the Ball in English Inches, and Decimal parts of Inches.

Tables for Iron Ball, wherein you have the Weight of every Ball given in English Weight, from 1 lb to 100 lb; together with the Height of the Bore of each Peece answering to those Balls, given in English Inches and parts of Inches; Exactly Calculated to each pound weight of Ball above-mentioned, the Wind being truly extracted.

A	B	A	B	A	B	A	B
1	2.0362	26	5.9446	51	7.4414	76	8.4997
2	2.5653	27	6.0198	52	7.4897	77	8.5368
3	2.9371	28	6.0933	53	7.5374	78	8.5735
4	3.2322	29	6.1650	54	7.5845	79	8.6101
5	3.4817	30	6.2350	55	7.6311	80	8.6463
6	3.6998	31	6.3035	56	7.6770	81	8.6821
7	3.8950	32	6.3705	57	7.7225	82	8.7176
8	4.0722	33	6.4363	58	7.7673	83	8.7530
9	4.2353	34	6.5007	59	7.8117	84	8.7880
10	4 3403	35	6.5638	60	7.8556	85	8.8227
11	4.4804	36	6.6257	61	7.8990	86	8.8571
12	4.6123	37	6.6865	62	7.9419	87	8.8914
13	4.7369	38	6.7462	63	7.9844	88	8.9253
14	4.8554	39	6.8059	64	8.0264	89	8.9590
15	4.9683	40	6.8625	65	8.0680	90	8.9924
16	5.0764	41	6.9192	66	8.1091	91	9.0256
17	5.1801	42	6.9750	67	8.1500	92	9.0585
18	5.2797	43	7.0299	68	8.1903	93	9.0912
19	5.3544	44	7.0840	69	8 2302	94	9.1238
20	5.4467	45	7.1373	70	8.2698	95	9.1559
21	5.5361	46	7.1898	71	8.3090	96	9.1879
22	5.6226	47	7.2415	72	8.3478	97	9.2198
23	5.7066	48	7.2925	73	8.3863	98	9.2513
24	5.7881	49	7.3427	74	8.4244	99	9.2827
25	5.8630	50	7.3924	75	8.4622	100	9.3139

In this Table you have eight Columns, in the 1st, 3d, 5th, and 7th Columns, mar∣ked with the Letter A, is the weight of Ball in English Weight; and in the 2d, 4th, 6th, and 8th Columns, marked with the Letter B, you have the Height of the Bore of each Peece, which those Balls shall sit, the Wind truly Extracted, in English Inches, and Decimal parts of Inches: Which you have in the Copper Piece herewith.

〈1 page duplicate〉〈1 page duplicate〉

〈1 page duplicate〉〈1 page duplicate〉

Thus having both Arithmetically, and by Tables, given Instructions how to make an Height or Diameter-Rule for Ball; and likewise having shown both Arithmetically, Geo∣metrically, and by Tables, how to deduct the Wind from the Bore of a Peece, thereby to know her true Diameter of Ball; and having given Tables of the Weight of Ball by their Dia∣meters: Therefore it follows, by the Weight of the Ball and Fortification of the Peece, that all Ordnance have their Pow∣der either for Proof or Action.

And, as I have shown by the Tables, all Brass or Iron Ordnance ought to have their Powder to their Proof; for True-Bored Ordnance, and True-Fortified, the Weight of their Ball from 1 lb to 8 lb, and from 8 to 18 three quarters of their Balls Weight; and from 18 to 48, two third parts of the Weight of the Ball, and so infinitely.

For their Ordinary, follow the Tables where you may serve sufficiently, and save Powder.

For Powder in Service or Action, it is to be referred to the Gunners discretion; and here I will give you Tables, whereby the Gunner may give Powder to Taper-Bored Ordnance, ei∣ther for Proof or Action, or any hot Service, from 1 lb Ball to 36 lb Ball.

CHAP. XXI.

AS formerly I have shown, all Ordnance are not true-bored; therefore I suppose it will be necessary for the Young Gunner to know how to give Taper-Bored Guns their Pow∣der; and though they are not ordinarily in these Countries, yet it may happen sometime the Gunner may be ordered to make use of such. In my Judgment there are no Guns more fit to go in the Head of Regiments in an Army than Taper-Bored Guns are: I mean not Leather Guns, by which the King and Country hath been cheated, but such as they make in Holland of Brass, Cast Ordnance. Neither do I mean those Taper'd Guns, with which the Hollanders cheat the World, being Plates of Brass within and without, betwixt the Skins there are Bars and Hoops of Iron.

A Table of Powder for Taper-Bored Ordnance, both for Proof, Action, and Storm; from one pound Iron Ball, to 36 pound.

Iron Ball	Proof.	Action.	Storm.
lb	lb      on.      dr.	lb      on.      dr.	lb      on.      dr.
1	00      05      05	00      04      00	00      03      00
2	00      10      11	00      08      00	00      06      00
3	01      00      00	00      12      00	00      09      00
4	01      05      05	01      00      00	00      12      00
5	01      10      11	01      04      00	00      15      00
6	02      00      00	01      08      00	01      02      00
7	02      05      05	01      12      00	01      05      00
8	02      10      11	02      00      00	01      08      00
9	03      00      00	02      04      00	01      11      00
10	03      05      05	02      08      00	01      14      00
11	03      10      11	02      12      00	02      01      00
12	04      00      00	03      00      00	02      04      00
13	04      05      05	03      04      00	02      07      00
14	04      10      11	03      08      00	02      10      00
15	05      00      00	03      12      00	02      13      00
16	05      05      05	04      00      00	03      00      00
17	05      10      11	04      04      00	03      03      00
18	06      00      00	04      08      00	03      06      00
19	06      05      05	04      12      00	03      09      00
20	06      10      11	05      00      00	03      12      00
21	07      00      00	05      04      00	03      15      00
22	07      05      05	05      08      00	04      02      00
23	07      10      11	05      12      00	04      05      00
24	08      00      00	06      00      00	04      08      00
25	08      05      05	06      04      00	04      11      00
26	08      10      11	06      08      00	04      14      00
27	09      00      00	06      12      00	05      01      00
28	09      05      05	07      00      00	05      04      00
29	09      10      11	07      04      00	05      07      00
30	10      00      00	07      08      00	05      10      00
31	10      05      05	07      12      00	05      13      00
32	10      10      11	08      00      00	06      00      00
33	11      00      00	08      04      00	06      03      00
34	11      05      05	08      08      00	06      06      00
35	11      10      11	08      12      00	06      09      00
36	12      00      00	09      00      00	06      12      00

In this Table is four Columns, in the first, under Iron Ball, is the Weight of the Ball that these Guns ordinarily shoot; in the second, under Proof, is the Weight of Powder for Proof; in the third, un∣der Action, is the Weight of Powder for Action; and in the fourth Column, under Storm, is the Powder for Service. The right order of all Gun-Founders is, That for every 6 lb Ball the Peece shoots, they allow 1 lb for the Wind.

〈1 page duplicate〉〈1 page duplicate〉

[illustration]

This is the Ge〈…〉〈…〉stration of the Diameter of Ball, And the Diameter of the Bores of Ordinance From one 〈…〉〈…〉 weight: And as I am informed, commonly used in England by which Demon〈…〉〈…〉 of the Diameter of the Bore is Sufficient wind for all Guns.

CHAP. XXII. To find the Diameter and Length of the Taper'd Chamber of a Peece.

* 1.30PRovide a Tamken to the Bore or Height of the Ball; put it on the end of an Half-Pike, and put it up till it stop at the Chamber or top; take that out again, having before mar∣ked the Half Pike; then put up the Half-Pike in the Gun to the Breech, and mark the Half-Pike again; then take a Peece of bowed Wire, and put it in at the Touch-hole to the lower part of the Chamber, and mark the Wire above the Gun; then hale it up till it hack at the upper part of the Chamber, and mark the Wire there again; so measuring betwixt these two Marks of the Wire, you have the small end of the Taper-bore; then measuring the Diameter of the Tamken, and so you have the great End: Then taking the Distance between the marks of the Half-Pike, so having both Diameters and Length, (if you will) you may draw the form of a Taper'd Chamber on Paper, and extract the Wind from it, for the Cartrage go∣ing up with more ease.

CHAP. XXIII. For Chamber-Bored Guns.

THese Guns are tryed with ¼ part of their Balls weight of Powder; So that a Peece shooting 24 lb Ball, is proved with 6 lb Powder: For Ordinary, there is allowed for every pound of Ball 3 ounces of Powder, so that there needs no Table to those Ordnance, for there is not many of those to be found but Mortar-Peeces.

* 1.31But certainly those Peeces must be ancient since their Foun∣dation; That Josephus in his Antiquities of the Jews doth say, That there were Stones shot into Jerusalem at the Siege of great weight; that at one time one of these Stones shot off the Head of a Man, and carried it several furlongs from the Body.

As I am here to speak of Chamber-Bored Ordnance, so I do remember that in Holland they use to bore their Guns of 6 lb Ball to 8 lb, and that there may come of these Guns to be made use of.

* 1.32Now know that of Chamber-Bored Guns, there are three sorts; to wit, first, Those that shoot Iron Ball; Secondly, Those that shoot Stone Ball; and thirdly, Those that shoot Granadoes and Fire-Works.

First, Know that it is a Chamber-Bored Peece which hath two right and true Bores; the one is the vacant Cylinder, all from the Musle till you come to the Charged Cylinder; the Charged Cylinder is from the Touch-hole to the great Bore, called the Chamber, because it is not so great a Bore as the other.

But if this Chamber be too long and narrow, or small to continue Powder for this sort of Peeces, then the Ball may be delivered before all the Powder be fired, and do little Execu∣tion; For it is without controversie, that the vehemency of any Ball struck from a Peece, is by vertue of the Powder fired in the Peece before it come out, and is rather hindred than fur∣thered by any Powder that is fired after it is out. Likewise there be Chambers short and wide, which may be harmful; for the Powder all firing suddenly, before it loose the Ball, the strength thereof many times doth burst the Peece; Therefore it is best in this, as in all other cases, a true Proportion be kept.* 1.33

CHAP. XXIV. To know the true Proportion of the Chambers of Ordnance.

* 1.34ANd first of them which shoot Iron Ball; a well propor∣tioned Chamber for a Peece that shooteth Iron Ball, ought to be three Diameters of the great Bore long in the Chamber, and three quarters of the Diameter of the Ball, the Diameter of the Chamber: Having this Proportion, they ought to have one pound Pouder for every three pound of Ball for Proof; and for Action three quarters of a pound; this being so plain it needs no Tables.

The true Proportion of a Chamber in a Chamber-Bored Peece that shooteth Stone, is once and a half the Diameter of the Ball long, and the Diameter of the Chamber is two third parts of the Diameter of the Ball; having this Proportion, one pound of Powder will serve to prove a Peece that shooteth 4 pound of Ball, and three quarters of a Pound for Action, the Ball being Stone.

Now I suppose, and I hope that I need not doubt, but hi∣therto there is enough written and declared to the use of great Ordnance of most sorts that are used, and how with caution they ought to be handled.

* 1.35And because I in my Youth have served for a Gunner both by Sea and Land, not doubting that any need Instruction that are undertakers to be Gunners, (but as aforesaid) it may be some Friends may prefer some Young Men before they be ca∣pable, even to be Gunners of good Ships, who never knew how to shoot a Gun in anger.

CHAP. XXV. Therefore I will here give some needful Obser∣vations for Gunners of Ships.

1. THe first is, That the careful Gunner coming into a new Ship, diligently and carefully measure his Guns, to know whether they, or any of them, be full Fortified, Re∣inforced, or lessened in Metal.

2. Then he shall with a Ladle and Sponge draw and make clean all his Guns within, that there remain not any old Pow∣der, Stones, Iron, or any other thing that may do harm.

3. That he shall search all his Guns within, to know if they be Taper'd, Chamberd, or true-Bored, or whether they be crackt, flawed, or Hony-comb'd within: And finding what Ball she shoots, to make the Weight of the Ball above the Port; that thereby he may set the same Mark or Number upon the Cartrage and Case, that in time of Service, those who bring the Powder may not go wrong.

4. The Guns being dimensioned and clean as aforesaid, the Gunner shall take half a Ladle of Powder for every Gun, and blow them off, Sponge them well; and finding them clean, Load then the Peece or Guns with their respective Cartrages and Powder; which being rammed home, with a strait Wad after it, then let the Ball roll home to the Wad, and set a Wad close home to the Ball, that the Ball roll not out with the tum∣bling of the Ship; then must he Tamken that Peece at the Musle or Bore, with a Wooden Tampken, which he must Tallow with hard Tallow round about for preserving the Powder from Water; Likewise make a little Tapon of Ockam for the Touch hole, which must be tallowed also for Water, before the Leaden Apron be put over; then make your Peece fast as occasion best presents.

5. The Peece loaded and fast, then the Gunner is to have to every Peece 24 Cartrages at least ready made; to wit, 12 filled, and 12 empty in sort: Likewise he must be careful, so

long as the Gunner's Crew are busie with the Powder, that there be no burning Match or other fire in the Ship; also to lay his Cartrages in Barrels or Chests in sort, that when there is occasion to be brought, it be without abuse.

* 1.366. The Gunner must see that he sort his Ball very well, and lay every sort by themselves in several Cases, and upon every Case set the weight of one of the Shot which is in them. Also he ought to make the Bags for H••il, for the Guns above, ready betime, and fill them with Stones, Small Shot, or pieces of old Iron, which may do great dammage to the Ene∣mies Men.

7. If it fall out that any new Ports must be cut out in the Ship, the Gunner must be careful that they be above a Beam, or close by if possible; also that they be not higher or lower than the Ports before; Likewise that there be room for the Guns to play, because if one Gun should be dismounted, there might be another brought to her place: And observe, that the Carriage standing on her Truckes, the uppermost part of the Carriage must come to stand in the middle of the Port up and down, that a Man may lay his Piece as he pleaseth.

8. The Gunner must be careful that the Powder in the Room be well covered with Hides; also that the Axtrees of the Truckes be well smear'd with Sope; * 1.37also that his Ropes, Ram∣mers, and Sponges be ready at hand; and he must not let the Powder lie unturned above one month, otherwise the Salt-Peter will descend to the lower part of the Barrel, which is to be feared if Men should make use of that Powder: And he must every Month draw the Ordnance, if he fear they have got any Wet or Moist to the Powder, also for fear of the Salt-Peter dissolving, which may prejudice the Peece. And he must be careful of the Candle and Fire about the Gun-Room and Powder-Room, that there come no disaster. Likewise he must keep a good Account of all Materials that belong to the Guns, as Ball, Match, and Powder, what part thereof he spends, and also what now remains, that he may give a good account what is become of them.

9. A Gunner must use all diligence before he Rencounter with his Enemy, to set a Balley of Water betwixt every two Guns, that when they see conveniency, they may dip the Sponges for cooling of the Peeces, and fear of Fire remaining,

which may do hurt: And that he be careful not to shoot ex∣cept he hit, for it is sure, when the Enemy sees that he is not hurt, it gives him more courage: But to encourage Young Gunners, I will counsel them at Sea, not to use a Lont-Staff in Service, but first observing the way of both Ships, whe∣ther the one heave and the other set, or both heave and set to∣gether; and also the sailing of the Ships, if both one way, or on several Tacks, whereby he shoot not in vain: Now if the Gunner have a small piece of light Match, he standing at the left side of the Peece, shall set his right foot in the Carriage, look∣ing over the Peece, and according as he sees occasion give fire, and at the fire giving, retire his right foot, and before the Peece be recoiling the Gunner is free; and by trying his Dexterity, will make a good Experiment, and that he will do good Ser∣vice: But if the Ball have not done to your expectation, you may help the next; for when you see from the Breech of your Peece to the Musle, and so to the Mark, you have a sight of three things; so Euclide avers, that seeing over any three things, you have a right Line from the first to the third, through the second; for there is no Man dare promise to make a good Shot at Sea, if he have no experience of the Peece, and observation of the Ships motion.

10. Also the Gunner must be sure that there be no melted Stuff for Fire-Works done in the Ship but on Shore, for it is dangerous for a Gunner, and great hazard for Ship and Goods, yea and Mens lives: Likewise there may no Fire-Work be brought above in the Round-house or Cabin to stand, for fear of shot, but must be kept below till time of need, either in the Powder-Room, or Steward-Room: By the hazard of such things there hath been many and cruel Examples.

Of Necessaries that a Sea-Gunner ought to have for his Ordnance. Necessaries that a Gunner ought to have for his Ordnance are many, and the quantity is according to the quantity and quality of his Guns; and also if he be in a Man of War, or a Merchant-Man, then there is difference of Provisions, only I will here name them, let every Gunner take what he thinks

will fit, and at the Voyage end give an account what is spent, and what he hath, and how he spent that which is gone.

• * 1.38Powder.
• Round Shot in sort.
• Double-heads in sort.
• Cut Iron of foot or foot and half long.
• Wooden Tampkens in sort.
• Cartrage-Paper.
• Threed, Needles, Twine, and Starch.
• Match.
• Mallets, Hand-Spoaks, Rammer-heads, Worms, Ladles.
• Sponge-heads, and Staves to place them on.
• Beds and Coins in sort.
• Old Strouds for Breeching, and twice laid Stuff for Tackles.
• Lashers, double and single Blocks, new Rope for Double Tackles, some old Strouds for Sponges, some Lines.
• Marline, tarred Twine, Port-Ropes.
• Moulds for Cartrages in sort, Axel-Trees and Truckes.
• Budg-Barrels, and Lint-Spindles, Crows, Splice-Irons.
• Primes, Staples and Rings, Tackle-Hooks, Nails.
• Thimbles, Port-Bands, Sheet-Lead, and Lead-Shot.
• Old Canvas, Seales and Weights in sort.
• Lanthorns, Dark-Lanthorns, Powder-Measures.
• Sope, Horns, and Prime-Irons, Height-board.
• Height-Ruler and Compasses.

With what other Instruments he finds needful.

CHAP. XXVI. How to Dispart a Peece of Ordnance.

[illustration]

AN easie way to Dispart a Peece of Ordnance. First, Take the Diameter of the Peece upon the thickest part at the Breech with a pair of Callabasser Compasses, and likewise at the Musle at the thickest part thereof; then draw upon a Paper or Board both Diameters: So laying a Ruler through

the Centre, draw the Diameter, and then you may the easier take the Difference betwixt them.

Example.* 1.39The Diameter of the Breech (in the preceding Figure) is EF, the Diameter at the Musle CD, and the Diameter of the Bore AB; so you see the Difference betwixt the two Cir∣cles is DF or EC, which is the true Dispart of that Peece. If you take a piece of Wax, or Straw, or Stick, of the length DF, and set on the Muslle at D, you have a true Dispart: I have made them of Iron and screwed them on.

CHAP. XXVII. How to level a Peece of Ordnance to shoot at Blank.

* 1.40SHooting Point-Blank is a term very much misconstrued amongst our Gunners, for I have heard some say, they have shot a mile and more Point-Blank; the which is contrary to the nature of Great Ordnance, for it is observed, that it is much to shoot 350 Paces Blank, accounting 5 foot to a Pace, which is little over the ⅓ part of a mile.

But to shoot Point-Blank, is to be understood, that then the hollow Cylinder of the Peece lieth upon a level Line, so that the Ruler of the Quadrant being put into the Mouth of the Peece, the Plumb-Line hangeth perpendicular, then that Peece lieth to shoot Point-Blank.

To know how to make a good Shot at a Mark, within Point-Blank-reach of the Peece.

The Peece lying as is before shown, set the Dispart of the Peece at the place required on the Musle, then a Ruler from the Dispart to the Breech of the Peece; so turning your Peece to the Mark, you looking from the Breech alongst the Ru∣ler to the Mark desired; fire your Peece, and if there be

nothing defective in the Peece, or Carriage, or Platform, you make a good Shot: But if the Peece lie so, that the Ruler of the Quadrant being in her Concavity, and the Plumb-Line cut any of the Quadrant, then is that Peece said to be cleva∣ted, and will shoot further than when she lieth level, except there be some Object which lieth higher than the Peece to stop it. And if that Peece lie so, that when the Ruler of the Qua∣drant is in her, the Plumb-Line hang without the Line of Level, then that Peece is said to lie under Metal, and will not shoot so far as if the Peece were lying level, except there be a very great descent under the Peece.

Moreover it is certain, if Men have time, and the Object lying within Point-Blank-reach of the Peece, that the industri∣ous Gunner observing these Rules, may do good Service at the first or second Shot: for it is certain, that if a Man look along any three things or marks on one Line, then betwixt the first and third there is a right Line over the second; so that if a Man look from the Breech of a Peece, over the end of his Dispart on the Musle of the Peece, and to the Mark he is to shoot at, then the Breech of that Peece and that Mark li∣eth on a right Line through the Dispart: Therefore it is ima∣gined, the Mark being within Blank-Reach of the Peece, if the Peece be loaded and fired she will make a good shoot, all impediments being removed.

CHAP. XXVIII.

IF the Ball err, contrary to your expectation, either above the Mark or below, or on either side, follow the Rules follow∣ing to help the next.

Rule 1. If the Shot err too high or too low, help it thus,

When you have done as is described, and that the Shot hath carried too high as in D, or too low as in E, the Mark you shoot at being in C; having loaded your Peece, you are to find

the middle of the Bore of the Peece, and the places on the Base-Ring and Musle-Ring corresponding, then you are to set the Dispart, so you cause traverse your Peece till you bring the Breech of the Peece A to the top of the Dispart at the Musle B, and the Mark C in a Line; after Fire given, you hold this for a Rule.

But the Gunner may lay his Peece very artificially, and yet the Shot may carry contrary to expectation several ways; if it be too high as in D, help it thus; having laid your Peece as at first, in the Line ABC, and found the Ball in D; then lengthen your Dispart on the Musle-Ring, till looking over the Peece you find ABD; this done, you are to cause lift the Breech of your Peece, till over your Peece and Dispart you find the appointed Mark C; then fire, and you will hit your desired Mark.

* 1.41Likewise if your Shot at first had been below the Mark, as in E; you are to Load her and bring her to her first station, and then you are to take from your Dispart so much, till you have the Line ABE; this done, you are to lower the Metal of your Peece, till you find your desired Mark ABC; fire your Peece and you do good service.

Now if the Ball should come to light on either side of the Mark, as (in the second Figure of the Copper Peece) in E to the right hand; to help the next, lay your Peece in all points as before, with her Dispart; then you are to go to the Breech of your Peece, and find at your conveniency a place on the Base-Ring, looking over the Dispart, you see the mark of the shot at E; mark narrowly that place of the Base-Ring, (with Chalk or what you please) keeping that mark to look over your Peece, then you cause traverse your Peece till look∣ing over your mark on the Breech, your Dispart, and behold C your desired Mark in a Line; fire that Peece and you have your desire. And if to the left hand, you may help in the same manner.

* 1.42But if you were to shoot at any known distance, without the Blank-reach of the Peece, upon any degree of Random, first measure the distance to the Object, and as you find it in proportion to the Blank-reach of the Peece, the same quantity you may take from the Dispart. For if your distance be ¼ farther than the Blank-reach of the Peece, then take from the

Dispart ¼ part of its length; by holding this proportion, if the Object be on a right Line from you, you will do good service. Many times it falls out, that when a Gunner enters a Battery, Castle, or other Fortification; before he can have time to observe Rules, orders are given to fire some Ordnance; it may be in all his Life he hath not seen the like before that time, therefore he must lay his Peece by the discretion of his Eye and former experience; if then his Ball strike the Mark, his experience and discretion is a good Rule; but if the Ball go besides expectation, you may help as is before taught. For if the Gunner observe these Rules cautiously, he shall find both pleasure and profit, and have praise of the Spectators.

CHAP. XXIX. The way to Shoot a Ball from a Hill to a Valley, or from a Valley to a Hill.

* 1.43MAny and divers Opinions are there of shooting from Height to Valleys, as Nicholas Tartaglia in his first Book of Colloquies, and 26th Colloquie, affirmeth, That though the Mark be within Blank-reach of a Peece, the Ball shot under Metal will strike above the Mark aimed at. Likewise one William Claes, in his Book called the Practick Busketrie, pag 94. affirmeth the same by many Instances, That a Ball shot from a Height will over-shoot the Mark, though there be no impe∣diment. But I cannot blame the Hollander, in regard his Country is very plain, and no remarkable Height, whereby he might have confirmed what he saith by practice. But I ra∣ther adhere to Luigui Callado; for in his Practick manual de Arteyleria, Chap. 8. he informs, That a Ball being shot from a Height, will strike below the Mark; as I my self by pra∣ctice have found divers times.

* 1.44For in the year 1650, I was in the Castle of Edinburgh, when that Army of Rebels to our King did beleaguer that Castle, so that many times I had occasion to shoot so far under Metal, or below the Level-Range, that I have been forced to

cut the Brest-band of the Carriage quite out, and so to elevate the Breech of the Peece, that it hath been supposed she would fall over the Wall; and though in this case I durst not coin my Peece with fast Bed and Coin, yet always I found the Ball to hit below the Mark till I helped it.

* 1.45One remarkable instance I had of this, in shooting at that Mirror of his time for loyalty and gallantry, James Mar∣quess of Montr••ss his Head, standing on the Pinacle of the Tolbooth of Edinburgh, with which the Enemy reproach us, as counting loyalty a sin worthy of death. Now at this time I was by the Governor commanded, that there should not a Gun be shot in the Castle; which I took as an ill Omen of what followed; I demanded a reason for it: he told me I had too much Blood on my Head already: I being somewhat troubled, lest his Majesty, and those that loved him, both a∣broad and in the Castle, should suppose me a helper to the Treachery, desired the Governor to give me Orders in pre∣sence of all the Souldiers, otherwise I would not desist. * 1.46So he sent for me, and on the Head of the Parado, commanded me that no Ordnance should be shot in the Castle; for if any Gunner should do it, I should suffer a Counsel of War. Ne∣vertheless, being curious to have down the Head, which de∣served Honour above what I can write, I laid a Peece of 24 lb Ball; and because I durst not be accessary to any Acting, far less to that, I desired Thomas Kniblo, who was Keeper of the Magazine, that he should fire that Peece, after he saw the Go∣vernor and I gone to walk; which he did. The Governor hearing a Shot, and I in his company, inquired who had shot that Gun: I answered, I knew not; so that one returned to the Wall to know who it was, and whereat he shot; the young Man answered, Sir, I thought that it was sin in you and the Master Gunner to suffer these Men to fortifie themselves, and raise Batteries before your Nose, and you not stop them, where∣fore I shot at this, meaning the Battery.

But that Providence had ordered that Head to be taken down with more Honour, I admired of its abiding, for the Ball took the Stone joining to the Stone whereon it stood; which Stone fell down, and killed a Drummer, and a Souldier or two, on their march betwixt the Lucken-Booths and the Church, and the Head remained, till by his Majesty it was

caused to be taken down, and buried with such honour as was due to it.

* 1.47Now any that knows the Place, knoweth that betwixt the Fore-wall of the Castle and the Tolbooth is not a quarter of a mile; so that it was in Blank-reach of a Demi-Cannon: Yet the Peece lying higher than the Mark shot at, shot lower than the Mark: And I am of Opinion, that Reason must give it to be so, in regard that the Parallel Line made betwixt the Breech and the Dispart, lay 8 Inches near above the Bore of the Peece; and if it carried about so far below the Mark, I am sure she perfected the Line, the Bore made parallel to the Imaginary Line above: * 1.48So much for shooting from a Height to a Valley, which may be helped, by laying your Peece so as your Imaginary Line parallel to the Bore, direct you half a foot above the Mark, then you shall do good Service.

It is also to be observed, that shooting from a Valley to a Height, that a Ball will over-shoot the Mark, if it lie within point-Blank-reach of the Peece: Reason should give it so: for the Peece being elevated to a great Height, the Ball with the force and exaltation of the Powder, doth elevate above the true Line, which the Bore maketh to the Mark, in regard of the Wind or Vacancy that is betwixt the Ball and the Peece: As was found by shooting at the Castle of Edinburgh, where the Gunners shooting to dismount our Ordnance, most of their Shot flew over the whole Castle, till observed by the Gunners and helped. But when we come to treat of Obser∣vations of Heights, Depths, and Distances, by the Quadrant, you will have further satisfaction.

CHAP. XXX. To know how to make as good a Shot by Night as by Day.

* 1.49AS there is none will deny, that among the many Terrifi∣cations which may be put upon an Enemy, to shoot amongst them by Night is not one of the least of them: But

[illustration]

if you will shoot by Night, you must provide by Day, and observe as followeth.

First, You are to lay your Peece by day, as is formerly taught, being loaded with Powder and Shot, as if you were to make presently your execution at the place. * 1.50Then take a Mariners Compass, and set that on the Breech of the Peece, and looking over the Peece you see the Mark, and observe how the place bears off you, so that in the Night you may know how, and on what Point of the Compass the Place bears off you, when you are to give Fire; then take a Line and plum∣met at the Musle of the Peece, and right over the middle of the Musle let the Plummet hang to the Platform; so you shall remark, or make a mark on the Line where it cutteth with the lower edg of the Bore of the Peece at the Musle; and like∣wise remark where the Plummet toucheth the Platform: And for your more assurance, you may let the Peece be fired in the day time at the same Mark; and as you find that Shot to prosecute, you may proceed as is before-taught, and in the Night you may do good Service.

* 1.51First, Set your Peece as is before shown by the Compasse, causing your Matross or Pioneer to traverse the Peece to your desire; then go to the Musle with your Plumb-Line, causing them to elevate or abase the Metal, till you find the Plumb-Line and Plumb fall in their former stations: So in firing that Peece you may do good Service by Night or by Day.

But withal you must observe the distance to the Mark, if you be to shoot beyond Blank-reach of the Peece, also how the Wind is, whether with or against you, or on which side; for by these means the Ball may change her Course; and so if you have a Dark Lanthorn, that you may see your Compasse and Plumb-Line, observing all these things, you may shoot by Night as well as by day.

But to know whether you shoot right in the Night or not.* 1.52It shall be requisite to take some Butter, or Tallow, and melt them in some Kettle, wherein you shall dip your Ball that is to be shot, and roll the same Ball in fine Powder, that the Powder may stick fast to it; and when you have done, put

home the Powder in your Peece; and observe you put no Wad betwixt the Powder and the Ball; so when you give fire, the Ball will flame as a Candle; and where the Ball doth light, the mixture will fly on the Object, by the light whereof you will see whether you have hit the Object or not.

CHAP. XXXI. To know how far any Peece will shoot at any degree of Random.

* 1.53THis task is so difficult as there are Proportions of Ord∣nance, yea it will alter by the alteration of Weather; likewise if the place lie higher, the Peece shall shoot farther over a Valley at the same Random, than she shall from a Valley to a Height; for these Reasons, I have found none that ever made Tables for great Ordnance, that would or could make them good on all Accounts and all Degrees.

Now the only Rule by which a Gunner may know how many Paces his Peece will shoot, in elevating from Degree to Degree, is to take good notice how far she shoots Point-Blank, as also Horizontal with the Metal; which Distance being mar∣ked to be ⅓ part, or a half, or ⅔ parts farther than Point-Blank, then hath he a convenient Proportion to work by, and to find his desire reasonably near.

Example.There is a Demi-Cannon shoots Point-Blank 200 Geome∣trical Paces, and Horizontal with the Metal 400 Paces, this holds proprtion as 2 to 1, the one half less: Therefore say by the Rule of Three, As 2 is to 1, so is 200 to 100 Paces, that this Peece shoots farther at every Degrees elevation. Yet not wholly through the Table, for there is a rebating in every Degrees elevation: Now to find this, you shall yet di∣vide 100 by 44, and you have 2 3/11: So as 3 times 11 is 33, and 11 is 44; therefore when you desire to make this Table,

[illustration]

take 2 from 100 there remains 98, which added to 200 makes 298; then take 2 from 98, and there remains 96, which be∣ing added to 298, giveth 394: This is the first and second De∣gree elevated; this continues till 35 Degrees elevation, where you have 44; and you have for 35 Degrees elevation 2400 Paces; then the addition is 28, and the rebate of every De∣gree 3; by which you may make this Table following: and in doing so with all others you have your desire.

* 1.54 A Random-Table for a Demi-Cannon to 45 Degrees.

1	298	16	1528	31	2308
2	394	17	1594	32	2344
3	488	18	1658	33	2378
4	580	19	1720	34	2410
5	670	20	1780	35	2440
6	758	21	1838	36	2468
7	844	22	1894	37	2493
8	928	23	1948	38	2515
9	1010	24	2000	39	2534
10	1090	25	2050	40	2550
11	1168	26	2098	41	2563
12	1244	27	2144	42	2573
13	1318	28	2188	43	2580
14	1390	29	2230	44	2584
15	1460	30	2270	45	2585

This is now a brief way of making a Table of Randoms for a Demi-Cannon, which may be done in like manner for any Peece of Ordnance whatsoever; first knowing the true Distance she shoots at Point-Blank, and the Distance she shoots lying Horizontal by the Metal, compute Difference, and work as before, you have your desire.

As this Table is for a Demi-Cannon, so there must be one for every sort of Ordnance the Gunner makes use of; And he shall hardly find truth.

CHAP. XXXII. The Geometrical Quadrant, with the Uses in Measu∣ring Distances, Heights, and Depths, and Distan∣ces most useful for a Gunner.

First, To measure the Height of any Tower, Wall, or Castle, or any other Body, standing on a Plane, if you have access to it, by the Gunter's Quadrant.

SEt the Ruler of the Quadrant so to your Eye, that you see through the Sights, from the place where you stand, the mark you desire to observe; then note what part of Ʋmbra Recta, or Versa, your Thread cuts, and you shall find the Height in this manner.

1. If the Thread of the Plummet fall on 100, then is the Height desired equal to the Distance betwixt the Observers foot, and the Ground or Root of the thing observed.

* 1.552. Otherways, if the Thread fall on the parts of Ʋmbra Recta, or Right Shadow, then is the distance betwixt the Ob∣servers foot and the ground of the thing observed, less than the Height of the Body observed, according as the parts cut off Right Shadow by the Thread is to 100; Therefore use the Rule of Proportion, otherwise called the Rule of Three, and set the parts of Right Shadow in the first place, cut by the Thread or Plummet-Line, and the 100 in the second, and the Distance you are from the Root, or foot of the Mark, in the third, and the fourth place will shew the desired Height; as you may see in the Example following.

Example. Suppose the Thread to fall on 25 parts of Ʋmbra Recta, and the distance betwixt your Foot and the Wall be 30 foot: Then say, as 25 parts of Right Shadow is to 100; so is

[illustration]

[illustration]

30 foot the distance given, to 120 foot the Height required: to which you must add the length betwixt the Observers Eye and the Ground.

3. But if the Gunner cannot Cipher, then do this; go so far back or fore, till you see the Mark desired, and that the Plummet-Line of your Quadrant (being still observing) fall on the parts of Right Shadow: And know that if the Line fall on 100, the Distance is equal to the Height: If the Line fall on 75 parts, then the Distance is three-quarters of the Height; if it fall on 66 ¾ parts, then is the Distance ⅔ parts of the Height; if on 50 parts, the half of the Height: if on 33 ⅓ parts, one third part of the Height; and if on 25 parts, one, quarter of the Height; by which you may con∣clude the Height of what you observe.

4. But in observing, if the Thread fall in parts of Ʋmbra Versa, or Contrary Shadow, then know that the Distance of the Ground to the Place observed, is more than the Height of the same: And the Proportion is, as 100 parts is more than the parts cut off the Contrary Shadow; so is the Distance from the Mark, unto the Height of the thing observed.

Example. Suppose the Thread to fall on 25 parts of Ʋmbra Versa, and the Distance betwixt your Foot and the Wall be 300 foot: Then say, As 100 parts is to 25 parts of Contrary shadow; so is 300 foot the Distance given, to 75 foot the Height re∣quired. To which if you add the Distance betwixt the Ob∣servers Eye and the Ground, you shall have the true Height.

5. And if you cannot Cipher, then go so far backward or forward, always seeing the Mark desired, till the Thread fall on what parts of Contrary Shadow you would have it; and if it be 100, then is the Distance and Height equal; if it fall on 75 parts, then is the Distance one quarter more than the Height; if it fall on 66 ⅔ parts, then is the Distance one third part more than the Height; if the Thread fall on 50, then is the Distance one half more than the Height; if it fall on 33 ⅓, then is the Distance ⅔ more than the Height; if on 25, then is the Distance three quarters more than the Height:

Ever adding the length from your eye to your foot, then you shall certainly have the true Height.

6. This manner is used to measure the Height of any thing, whereto you may have access: If it were that you must mea∣sure the Height of a Wall, or any other thing standing on the side of a River, then you must have two Observations; in manner following: First, Measure the distance from your station to the side of the River; being come to the brim of the Water, stand perpendicularly upright, draw down the brim of your Hat before your face, till you looking by the brim of your Hat, see the Foot or Root of the place you would mea∣sure; then turn your self about, observing in all things your gesture, till you see on that side of the River where you stand, some Hill, Down, House, or any other Mark; thus you shall measure with your foot the distance to it, and then Work as is before shown.

Secondly; To measure the Height of any thing standing on a Plane from you, when you can have no access to it, or were hindred by the Enemy to come near it.

1. To this Work you must have two several Observations, as followeth: Put the Ruler of the Quadrant to your eye, in such manner, that through the Sights you see the Mark desired;* 1.56 take notice then what parts of Contrary, or Right Shadow is cut by the Thread or Plummer-Line, and then where you stand set up a Staff; then you are to go a remarkable distance backward or forward, and take there your second station; and observe your Mark as before, then note well what parts of Contrary or Right Shadow your Line cutteth; note that also down: Now if it be so, that in both your stations the Plummet-Line hath fallen on parts of Right Shadow, then deduce the lesser from the grea∣ter, and keep the Difference: Then say by the Rule of Three, As the Difference in the parts of Ʋmbra Recta, is to 100 parts in the Quadrant; So is the Distance between the two Sta∣tions to the desired Height of that Body: But it is to be

understood, that you must not forget to add the Height of your Eye from the Ground.

Example. In the first place, when you find the Thread fall in 25 parts of the Right Shadow, and in the second on 50; then let the distance betwixt the stations be 30 foot.

Say then by the Rule of Three; As 25, the difference of the parts of Observation, is to 100 parts in the Quadrant; So is 30 foot the distance of the Stations, to 120 foot the Height required; to which add the Height of your Eye.

2. But if at one Station (or possibly at both Stations) the Thread falls on parts of Contrary Shadow, then the parts must be converted to parts of Right Shadow, as shall be shown in the following Example.

Example. * 1.57Suppose there were placed some Guns on the top of a Hill, as in the Figure by A; by which the Gunners in the Valley B have a great deal of loss and trouble; wherefore order is gi∣ven to one of them, to do his endeavour to dismount these Peeces at A: Now to do this with understanding, and what hast convenient; First, He must know the height of the Hill AD, with the distance BD: Then he may by Prop. 47. of the first Book of Euclide, find the length of the Hypothenu∣sal Line AB; to be assured how many degrees of the Qua∣drant his Peece must be elevated to the Mark.

Take for Example. We say that the first Station observed, the Thread fell on 25 parts of Contrary Shadow, and at the second on 90 parts of Right Shadow; then you cannot take 90 parts from 25 parts; therefore you must alter the 25 parts of Contrary Shadow to parts of Right Shadow, in manner following: Multiply 100, the one side of the Quadrat by it self, and you have 10000; this you divide by 25 the parts of Contrary Shadow, and you have in the Quotient 400 parts of Right Sha∣dow,

which is equal to 25 parts of Contrary Shadow; then take 90 parts from 400 parts, there remain 310 for the Diffe∣rence: Also let the Distance betwixt the two Stations, from B to C, be 200 foot: Then say by the Rule of Three; As 310 is to 100 parts in the Quadrant; So is 200 foot the Di∣stance of the Stations, to 64 16/31, which is very near 64 ½ foot, the Height of the Hill AD: We should now shew the way to find the Distance AB and BD; that those who cannot Cipher, may understand this.

Thirdly; Therefore we will give one Example or two, that they may do such without Arithmetick.

These must search out their Stations, in which the Thread may fall on all such parts of the Right and Contrary Shadow as they desire, which is easie to be done, if they go discretly for∣ward or backward, and measure the Distance betwixt the Sta∣tions, till the Thread fall where they desire.

1. If the Thread fall at the first Station upon 100, and at the second on 50 parts of Right Shadow, then is the Distance half the Height.

2. Or if the Thread fall at the first Station upon 100, and at the second on 66 ⅔ of Right Shadow, then is the Distance betwixt your Stations one third part of the desired Height.

3. And if the Thread fall at the first Station on 100, and at the second on 75 of Right Shadow, then is your Distance just one quarter of the desired Height.

4. Likewise if at the first Station the Thread fall on 100, and at the second on 66 ⅔ parts of Contrary Shadow, then is the Distance half the Height.

5. Or if the Thread fall at the first Station on 100, and at the second on 50 parts of Contrary Shadow, then is the Di∣stance equal to the Height desired.

6. The same it shall be, if at the first Station the Thread fall on 50 parts of Right Shadow, and the second on 66 ⅔ of Contrary Shadow: But still remember to add the Height of your Eye above the Ground.

Fourthly; To measure the Distance to any place, or the Breadth and Length of any Plane or Water.

By what hath been said before, it appears plainly that in the measuring the Height of any thing, there must be once a known Distance, to wit, some length of the Plane whereon the Height is erected: Likewise in measuring any Distances, as the length of a Field, it is very necessary to know the Height of something thereby; which may be easily done: for if you were to measure the Distance to a Fort, Battery, Trinal, or Bulwark, which you desire to know; if the Distance be not great, in that case you need know no Height but your Eye from the Ground where you stand; But if the Distance you would measure be great, then it is needful to have a known Height to stand upon, which Height you must add to the Height of your Eye, which may be done with a Plumb-Line, whose Marks you know: Then Work as followeth.

Example. Take for Example, that you desire to measure the Distance from B to D; then turn the Centre of your Quadrant to your Eye, and observe through both your Sights the Point D; re∣mark well what part of Right or Contrary Shadow the Thread cutteth; If it happen to fall on 100 parts, then ought the Di∣stance to be equal to your Height: But if the Thread fall on parts of Contrary Shadow, which in such Cases is ordinary, then is your desired Length more than your known Height, so much in proportion as 100 is more than the parts cut of Con∣trary Shadow, which the Line sheweth. Therefore say by the Rule of Three; As the parts of Contrary Shadow, which the Plumb-Line sheweth, is to 100; So is the known Height unto the Distance required.

Example. The Thread cutteth 1 ⅓ parts of Contrary Shadow, and the Height from the Eye to the Ground is 5 foot: Then work as followeth, and you will find the length BD to be 375 foot. 〈 math 〉〈 math 〉

Now having the Perpendicular AD, and the Base BD, you may easily find the Hypothenusal AB, to be near 380 foot: But here you are to extract the Square Root, for Eu∣clide in the 47 Prop. of the first Book of his Elements, hath proved by Demonstration, That in Right-Angled Triangles, the Square which is made of the side subtending the Right Angle, is equal to the Squares which are made of the sides containing the Right Angle. Where if two sides be given, we may find the third side thus; in the Right-Angled Trian∣gle ADB, you have AD 64 ½ foot, and you have the Base BD 375 foot; whose Squares being added, and the Square-Root extracted, you shall have the Square-Root near to be 380 ½ foot for the Hypothenusal AB: For Extracting the Square Root, it is described in Chap. 6, and 7.

This I have done for the use of Young Gunners, that when occasion may present, they may lay their Peeces at a reasona∣ble Degree, thereby to come near the Mark at the first Shot; And always may observe a greater distance from a Height to a Valley.

Example. There is a Castle, as the Figure sheweth, and in the Bat∣tery

there lies a Peece of Ordnance; If it were desired of the Gunner to know if this Peece might be of service to dismount the Peece in the Battery C: Now the Gunner must desire time to measure the Distance from him to the Battery C; whereby he may the more assuredly Answer.

Then shall he take a Line and measure the Height AB; then standing at A, shall take the Quadrant with the Centre to his Eye, and beholding through the Sights the Mark C, Remark narrowly the parts cut by the Plumb-Line, which is without fail parts of the Contrary Shadow: Then say, As the parts of Contrary Shadow are to 100; So is my Height from the low Battery to the Distance required. Let the Height AB be 95 foot, and the parts of Contrary Shadow 5 ¼ and you will find the Facit to be 1809 ½ foot, or 362 Geometrical Paces very near.

〈 math 〉〈 math 〉

But if you please to reduce the Distance to Paces, divide the Quotient by 5, for 5 foot make a Pace, and you have as aforesaid.

This is so clear, that I think any Gunner may perceive, that if he in the Battery C, elevate his Peece two Degrees above the Level, that then he might do good Service, and by once firing, if the Ball go beyond expectation, you may help the second.

* 1.58The like may the Gunner in the Battery B do, and also the Gunner in the Battery A to C: and so each to other, for they have double Advantages of the Gunner at Sea, except he be lying in a River; and let his Ship lie never so still, so long as she is a-float, she hath ever a Motion, nevertheless the Obser∣vant Gunner in a Ship may do good Service.

For I my self in the year 1652, or 53, being forced from Scotland, when the War began betwixt the States of Holland,

and the (then) State of England; and as many better than I were in necessity, I put my self in a Frigot of Terveer, one Jacques Wolfes Captain, I served there for a Gunner, and in our Voyage to Shetland to bring home the Hollands East-India Fleet, we met with a Storm, where we lost above 20 Sail of our Fleet, our Ship was called Prince Rupert; but with this Ship we were forced to come to Anchor betwixt Fulla and Shetland, and by providence road the Storm out; when we had fair Weather, we went to Brasa Sound in Shetland, and there riding at Anchor with three Ships of our Fleet: the Commander or Corporal of the Souldiers and I fell at Dispute concerning his Men, that they could not shoot at a Mark; whereupon he told me, That I could not shoot so well with a great Gun, as any of them did with their Musquet; at last I wa∣gered with him that I would shoot as near with a great Gun, as he himself with a Musquet; whereupon we agreed, (the Wager was two Rix Dollars): I sent the Quarter-Master to our Captain, who was aboard one of his Consorts at Din∣ner, for liberty to shoot; which was granted: The Mark we were to shoot at, was the Buoy of the Anchor of the same Ship our Captain was aboard of; so that we had the four Cap∣tains for Judges: I brought a Sacker-Cut, from the breast of the Steerage to the Main-Mast; I disparted and loaded her, and set her to the Port, I set her to the middle-Port of the Ship; then we were at a contest who should shoot first; I gave him that priviledg: So after he shot, he found he came not near by three yards, as it was alledged; and that he might be better pleased, I gave him liberty to shoot again,* 1.59 where he made lit∣tle mends: Then I laid my Gun to the Port, and observing the ranging of the Ship, I gave fire at my conveniency, and strook the Buoy, which lay about 150 paces from us; there are Men here in London that did see it. I say, good Service may be done aboard a Ship, if the Gunner be cautious. And by this I would have you know, that I would have Gunners to consider, that the middle of a Ship is the only place for to make a good shot, though by accident there may be some made either afore or after; as I will give an Example.

Example. * 1.60Suppose there is a Ship in a River or smooth Road a pretty distance off, as this Ship E F: The Gunner is demanded if he could do any good Service with his Guns at the Battery on the Shore G, which only could wrong them.

* 1.61This you must consider, could not be answered, till he knew what distance he lay off; threfore he must observe as followeth: First, With a Lead-Line measure the length from your Topmast-Head to the Water, as from E to F; then go to the Topmast-Head in F, and observe with the Centre of your Quadrant to the Eye, that through the Sights you see the Battery G, and in all things doing as in the Battery A for clearing.

Example. Let the Height from the Water to the Topmast-Head be 90 foot, the parts cut of Contrary Shadow 5; so set it on the the Rule as followeth.

〈 math 〉〈 math 〉 which is 360 Geometrical Paces.

* 1.62Suppose the Gunner in the Ship had a Demi-Cannon, which shooteth Point-Blank 200 Paces; Therefore may the Gunner conclude to elevate his Peece 2 Degrees, and thereby at the first shot be pretty near the Mark; by which he may help the se∣cond: Even so may the Gunner in the Valley at the Battery G, observe to do good service on the Ship E F: Likewise the Gunner in the Battery A, may do good Service every where round about, if he observe what is before set down: Never∣theless my desire is to set down another Example of observing by the Cross-Staff.

Example. It is desired to know the Breadth of the Bulwork ABC: First, You are to observe the Distance to the same, as from D to B, which we suppose to be 750 foot: Take the Cross-Staff as EFG, having thus on the end of your Staff a Cross, as FG, at such distance as you may see by the Transom F in C, and G in A;* 1.63 then divide the length of your Staff in as many equal parts as you please: As here let be 15 parts, and the Cross FG, we make 7 of the same parts: Then say by the Rule of Three, As 15 parts the length of the Staff, is to 750 foot E B; So is 7 parts the length of the Cross, to 350 foot for the Bulwork ABC: Do the like with all others, and give good heed to the following Questions and Answers, which are useful for all Commanders, Captains, or practised Gunners, as well in Offensive as Defensive Service by Sea or Land.

If a Man were on the top of a Rock or Hill, on the side of a River, and on the other side saw a Tree, and would know the distance over to that Tree, as the Figure CAB: To do this you have two Observations, the one is the Line of Level; then go∣ing on a Right Line from A to C, you observe, and find the Thread cut 54 parts of Right Shadow; then measuring your distance AC, and finding it 68 foot, you follow the Ground-Rules, 54 gives 100, what 63 foot Difference of Stations. 〈 math 〉〈 math 〉

CHAP. XXXIII. Questions for the Practice of what hath been formerly taught.

Quest. 1. WHen a General with his Army hath besieged a strong Fort, Castle, or Town, and hath secured his Army by Intrenchments, and hath taken notice of the most fitting places for Approaches: Now the Question is to the Gunner, How near they may approach the place with Batteries, and at what Distance the Cannon will do best service, that there they may be planted and made.

Answer. If I were to answer, I would desire to approach as near as it were possible to come, and to plant the Batteries about 100, and some 50 foot from one another; and if it were possible, even to the Counterscarp; not only thereby to give the place most dammage by the Guns, but also to frustrate the Enemy from sallying out, as likewise to do them most prejudice at their Casements, to Guns and Gunners, by which they might be forced not to dare to shew a Head above the Wall.

Question 2. This Resolution is good, but very dangerous to perform; for as the Proverb is, It is dangerous to chase a Dog out of his Nest; for if there be a brave Enemy within, how could you approach so near, but it should cost many a brave Souldier his life?

Answer. As it is without controversie, where Carpenters work there must fall Chips; but that will never cool the courage of a brave generous Spirit, ever considering, where-ever we are, we are in the Hand of God; yea, the danger is not in all pla∣ces alike, for if you be where there is Earth enough to work, there you begin to cast up Trenches and Mounts against the Town to save your selves from harm; for the higher the Earth

is, the deeper is the Trench to be made, to save you from the sight of the Enemy.

Question 3. When you are approacht so near the Enemies strength, that the Cannon is to do service, Whether should you chuse a Bulwork or a Curtain, for your storm-place to play upon?

Answer. That must be according to the greatness of the place; if the Bulworks be of great distance one from another, in that case I would rather chuse a Bulwork than a Curtain, there to make my Breach, thinking that I should come sooner to my advancement there, because the Bulwork is better fortified than the Curtain, and is a principal Strength: And if you make your Breach for Men to enter, you find them sometimes cut off, so that you may begin to fortifie there anew, where you are as it were in the Enemies Bosom; this occasion you have not in a Curtain. See Capt. Hexham.

Question 4. If you did storm this Bulwork, and found there some Guns that before you had not seen the like, and that you must pre∣sently use them against the Enemy, and know not what Ball they shoot; What is the quickest way to find their true Pow∣der and Ball?

Answer. If the Peece be left loaded, she must be drawn; for the Ene∣my in policy might so leave a Peece, on purpose to split about their ears that take her: When drawn, a piece of bowed Wire being put in at the Touch-hole down to the bottom of the Concave, upon the Metal mark that Wire with a Knife; hale the Wire up till it hack on the upper part of the Metal in the Chamber, and mark as before your Wire; take the di∣stance betwixt the two marks, and that is the Diameter of the Bore: And see if it be the Diameter of the Bore at the Musle: if you find her a true-bored Peece, then take your Compasses, and extend them to the length betwixt the lower mark and the hack of the Wire; this Extention being taken on the Scale of Powder gives you her Powder; and extend∣ing your Compasses betwixt the marks, lay that to the Height-Rule, and you will have the Height of the Ball: Otherwise finding the Weight of the Ball, resort to the Table of Pow∣der

for that Fortification, and where you find her Weight of Ball, you will find the Weight of Powder for that Peece, for having the Diameter of the Bore and one side Metal, double the one side Metal, and add the Bore to it, you have the Dia∣meter of the whole Peece: Then say, As 7 is to 22; So is the Diameter of the Peece to her Circumference: And having one side Metal at the Breech and Musle, you have a Dispart: So presently you may do good Service.

Question 5. When you have the Diameter of the Bore of a Peece, How do you know what Ball will serve that Peece to shoot, and neither be too high, thereby to hurt the Peece; neither too low, to miscarry by reason of the too much Wind?

Answer. As it is convenient the Ball be something lower than the Bore of the Gun that it serves for; and some have thought fit to declare one quarter of an Inch to be a sufficient Wind to all Balls; and others have declared, that a twentieth part of the Diameter of the Ball, is a sufficient Wind for all Guns: I hold that quarter of an Inch to be altogether absurd; because except a Man can give the true Demonstration, as you are taught, and is set forth in pag. 42, to 52. he shall never know how to extract the Wind betwixt the Bore of a Peece and her Ball. For if you please to try for fancy; A Cannon of 8 Inches in the Bore, shall have the Wind for her Ball 1/•••• ⅛ part of the Diameter; as also a Base of two Inches in the Diame∣ter of the Bore, hath but ••/1•• part of the Diameter of the Bore; for if a Peece of 1 lb Ball shall have proportionable to 9 lb Ball, she would have no Wind at all; and if a Gun of 63 lb Ball had proportionable Wind as a Gun of 9 lb Ball, she would have too much by ••/1•• part; behold the Demonstra∣tion, Folio 102. and a Peece of 4 ¼ Inches in the Bore, hath just 1/20 part of the Diameter of her Bore, for the Wind to her Ball: which will never stand as a general Rule, except it be Geometrically demonstrated, where you will find the Height of the Cannon-Ball just 2••/1•• parts of her Bore, the small Ball ••••/1•• parts, and the other 20/19 parts: Wherefore I aver, all that hath been writ to this purpose, is but Supposition and no real Rule; but Geometrically you have your desire, and need not to follow any other Rule for extracting the Wind to find the True Ball.

Question 6. When you have obtained Geometrically the True Diameter of a Ball to fit a Peece, the Question is, How shall you know the Weight of that Ball it being Iron?

Answer. Some receive this by a common Opinion, that 4 Inches Dia∣meter of a Cast Iron Ball is 9 lb Averdupoise Weight, as you may see by Dr. Weybard's Tactimetria; wherefore I say that is the most certain Rule. Now if 4 Inches Diameter weighs 9 lb; What shall two Inches weigh? you will find the work stand thus. 〈 math 〉〈 math 〉

And it is a general Rule; behold you see a Ball of 2 Inches Diameter weigheth 1 lb 2 ounces: If you hold this for a Rule, you may Work and Correct all Tables of this kind that are made in England: Likewise, I say, you may find the Weight of any Iron Ball thus; Say, 〈 math 〉〈 math 〉

It hath been ever observed for good, that the Tables of Mr.

Norton, Smith, and Nye; and therefore Capt. Sturmy in his Ma∣gazine for Mariners, doth follow the same Rule, and gives us the same Tables of Mr. Nye, as he supposeth refined: for he sayeth, Two Inches and a quarter of a Ball, weigheth 1 lb 5 ounces: I will let you see the Error. 〈 math 〉〈 math 〉

Now here a Ball of 4 Inches Diameter by his Tables, weighs but 7 lb 6 ounces: But I praise Mr. Norton, who says, We must not expect truth from his Tables. But Capt. Stur∣my affirms his translation of Nye to be truly Calculated; if they be true, I must be quite wrong.

Mr. Nye saith. 〈 math 〉〈 math 〉

Now you may perceive, that they err only by neglecting to Calculate their Tables; But as the Blind lead the Blind, so they both fall in the Ditch; for he gives 8 ½ lb, or 8 lb 8 oun∣ces.

And by Capt. Sturmy his Tables, I find a Ball of 8 Inches Diameter to be 58 lb 14 ounces; and yet he hath set down in his Tables a Ball of 7 ¼ Inches for 58 lb. And by the Tables of Mr. Nye, though he hath placed 71 lb, I can find by his working but 68 lb for the weight of a Ball of 8 Inches Dia∣meter.

So this will be proved by the Line of Numbers, for if you say 4 Inches gives 9 lb, what shall 2 Inches give; place one foot of your Compasses in four Inches, and the other in 2 In∣ches, keeping the Compasses at the same extent, set one foot in 9, and measure downwards 3 of these Extents, which will reach to 1 lb 2 ounces; likewise say, if 2 Inches give 1 lb 2 ounces, what shall 8 Inches weigh; extend your Compasses from 2 to 8 Inches; the Compasses at the same extent, place one foot in 1 ⅛ part, and three of these Extents will strike at 72 lb: But if the Weight of a Ball should be demanded in Scotland, you shall find a Ball of 1 lb is 2 Inches; and one of 4 Inches 8 lb; and 8 Inches Diameter (if you observe the

Work of the Table) 64 lb; you will find the same by using the Line of Numbers; in saying, a Inches Diameter gives 1 lb, what 4 Inches; and by laying one foot of your Com∣passes in 2, the other in 4 Inches Diameter, and with the same extent set one foot in 1, and with three of these extents you shall find 8 lb weight: thus you may do in finding the Weight of Ball, knowing their Diameter to what Height you will; and find the true Weight either Scots or English, without being beholden to Tables; though you have in pag. 100, ex∣act Tables Calculated Arithmetically, from eight parts to eight parts of Inches unto 10 Inches Scots Weight; And in pag. 102 you have the like number of Inches Calculated for Ball in English Weight: This is the quickest way, and reasonable true; if there be not holes in the Ball, or, as I have seen some, a great Ring about them, which might have taken up the Wind of the Peece.

Question 6. Pray you what Cautions or Circumspections would you use in order to your Approaches making, that thereby the Ar∣my might have the least hazard, and greatest speed to come to the Places where the Batteries are to be made for the Cannon, thereby to be more certain of a hopeful and good success over the Enemy?

Answer. * 1.64To Answer this, you must know you may have many hin∣derances, if there be a resolute Enemy in the Strength; Ne∣vertheless observe;

• 1. You must be careful of your Leaguer, that it be well trenched and secure from fear of the Enemy, in all Quarters, by Trenches and Flank-works; then chuse to set your Batte∣ries most conveniently in the opposition of their Strengths, and observe that there be no Hill, nor deep Ditch to hinder the Souldiers, if occasion offer to an Assault.
• 2. That your Approaches be intrenched to open or shut, and to make such a way to come to the Batteries, and be sure it be well covered and guarded with Men to keep it.
• 3. That the Platforms be large enough for the Guns to Re∣verse, and also to command the Place they shoot at.
• 4. If there be Earth enough, that you make the Trenches deep and wide enough, and well flanked.
• ...

• 5. That with advice and deliberation, you Batter all the high Flankers, the while you are making your Approach-Trenches.
• 6. When you have brought your Trenches to the Counter∣scarp, then make your Platform and Beds for your Peeces by the Point of the Counterscarp, by which you may hurt their Low-Flankers, and take them away; and so continuing your Battery that you bring down their Counterscarp, and the body or face of their Work.

Question 8. When you are approached so near as you can, how shall you then Storm and Breach a Bulwark at the Point, that is both Offensive and Defensive?

Answer. If you use thereto 18 or 20 Peeces, all Whole or Half-Cannon, and plant them so as they may shoot Right Angular, and cross one the other; and if the Approach be so near as ought to be, I would have 4 of my Guns only play to dis∣mount the Enemies Ordnance in their Places, where-ever I could perceive they lay, and by this means make my Storm more free.

Question 9. If you were to shoot at a distance, what Gun would you chuse, a Reinforc'd-Gun, or a True-Fortified?

Answer. It is true, that if you elevate a Reinforc'd-Gun to 45 Degrees, and the True-Fortified to the same, shooting both one Ball, that then the Reinforc'd Peece will drive his Ball more violently, and shall fly farther than the Ball of the True-For∣tified Peece: And great reason for it, the Reinforc'd is long and well Fortified; they of Brass are 10 Diameters of the Bore about the Breech, and his Proof of Powder is ⅚ parts of his Balls weight, and some the whole Balls weight; and the True-Fortified but 9 Diameters of the Bore, which gives a great difference in Powder, for she is proved with ⅔ parts of her Balls weight of Powder; besides the one is longer by half as long again as is the other; for the one being 18, and some 20 foot long, the other is but 10 or 12 foot long: by these Reasons, being better Fortified, hath more Powder, more length, and but equal Ball; she must burn more of the Pow∣der

before the Ball be delivered, which must of necessity more violently drive the Ball farther than the True-Fortified Gun.

Question 10. Thus it followeth, that the longer a Peece is, the more strength she hath, and doth violently carry her Ball farther.

Answer. This is so to appearance; for as we say any thing conveyed through a Pipe or Bore, hath his Course more violent accor∣ding as the Bore is long, and hath been found so to do by some: But I say experience teacheth otherwise now, for I have seen a Demi-Cannon tryed, being of a reasonable length, and broke a foot and a half at the Musle; yet when the Peece was tryed again and again, did carry her Ball as far as she did before.

Question 11. How is this, that a Sling doth shoot farther than a True-Fortied Peece, or other such-like Peece, which is shorter than a Sling?

Answer. I hold that which Reason and Experience both sheweth: Namely, that the strength of any Peece is so much more as the Peece is longer; but being fortified accordingly, and with this restriction, that it is done with an indifferent length; for from 8 to 12 foot long, being of the same Bore and Fortification, the Peece shall add to the flight of her Ball: But from 12 to 20 foot long, you shall see them abate of the Balls flight; the reason is, in all those too long Guns, the Powder is burned before she deliver her Ball, whereby the flame and strength of the Balls flight is abated. This is strange, and opposeth the thoughts of many Gunners; but by my Experience here in England by Saltwich. I found it so, and therefore not to be con∣troverted.

Question 12. But if you load a long Peece with so much more Powder, and being thereto Fortified, should not that give strength to the fire, that thereby the Ball should more vehemently be far∣ther driven?

Answer. It is without all question, that a Peece doth most harm ha∣ving its greatest Loading; yet it is found ordinarily, that in

all Guns having Powder above half the Balls weight, all taketh not fire; yea, I my self at Saltash in Cornwal, gave a Quar∣ter-Cannon, shooting 12 lb Ball, more than her ordinary al∣lowance, and laying 6 pair of Sheets on the Ground, on the descent of the Ground; and after fire given, I found two ounces of the Powder whole, by which you may guess what more was burnt after it came out of the Peece by the flame; and so I suppose the Balls flight is not increased but diminish∣ed: Whereby you may understand that too much Powder is disadvantageous for Ordnance, and that there ought inspecti∣on to be had to their Loading: And for these reasons I have Calculated these Tables, which I am sure is the nearest Truth to give Ordnance their Powder, of any yet given out by any other. But I know some Gunners will be offended to think that by these Tables, the Fortification of their Guns consi∣dered, they should be drawn to an Account of what Powder they have spent.

Question 13. If you were to shoot from the Battery G, in the Figure 133, to the Ship E; if you had your choise, whether would you use a Demi-Cannon or a Bazilisk?

Answer. If it were a calm day, and the Skie clear, and the distance betwixt both about 300 or 400 Paces, then I would hold little or no difference which of the two to chuse; but if it were a little Wind, the Skie thick, and the Air damp and moist, I would rather chuse a Demi-Cannon than a Sling, or rather a Whole-Cannon than a Demi-Cannon. My Reason is this, That the Wind, and Mist, or Rain, hath not so much strength to divert a great Ball as a small, which is found Experimen∣tally: for divers times I have shot from the Castle of Edin∣burgh to the Links of Leith, when the Enemy was exercising; but when there was a gale of Wind on either side, or against, I found the small Ball to err; but the Demi-Cannon came much nearer my expectation.

Question 14. If you were to shoot from a Valley, as at the Point B, against the Hill A, or from the top of the Hill A to the Valley B; is there any difference in laying of the Ordnance?

Answer. There are divers Opinions about shooting of this nature, for most do say, that shooting against the Hill from a Valley, the Ball will be below the Mark; and likewise shooting from the Hill to the Valley, that the Ball will strike below the Mark; but as I have shewn by my own Experience, these Authors are not to be owned: for I doubt it is with divers that have writ of Gunnery, as that the Proverb will hold good, viz. Many Men speak of Robin Hood, that never shot in his Bow. So I doubt some have writ they know not what themselves, never being experimented.

Question 15. By this I perceive there is no Rule, or Fundamental Ground can be made, by which you can make a Table of Randoms, whereby the Gunner may lay his Peece to shoot such Distance by such Degrees of the Quadrant being thereto elevated.

Answer. This I affirm, and my Reasons you have in pag. 122, which if any Man will truly consider, he will either not think to aver Random-Tables, or otherwise to make Tables for every Gun that is made, and also for every Wind and Weather that is, when they are to make use of the Guns; and he must not for∣get to make Tables for every Ground he is to shoot over: Which will keep them at work all their lives, and never con∣clude to any good purpose.

Question 16. Is it possible to give a general Rule, that instantly you may plant your Ordnance on a March against the Enemy in the Field, when the General intends to give Battel?

Answer. I believe not, because of the many hinderances and impedi∣ments that do many times follow; for the Rule of Discretion is that which must then be observed, and the Order of the Ge∣neral, and therefore is carried a competency of Field-Pieces, which are to be planted at the Head of the Battel, and some be∣twixt the Vant and the Middleward, by 2 or 3 together on the Flanks and Wings of the Musqueteers, being covered with the Wings of Horsmen, or as occasion presents and suffers them; some of these on the Front of the Army, playing with diligence on the Enemies Brigades; and if the Fields be plain

and even, then as the Army hath by them Cannon, Demi-Cannon, Field-Peeces and Slings, which may be planted for the greater annoyance of the Enemy at a greater distance; for every Regiment ought to have 2 or 3 Field-Peeces, which must be planted at the Head of the Leaguer, and must stand a little elevated with Earth, (if possible); all these will cool the Enemy before the Battels draw near; and some of these Field-Peeces may be removed as occasion will serve, where they may gaul the Enemy so, that Gunners being Men expert, and ha∣ving good Attendants, may be very advantagious to an Army.

CHAP. XXXIV. The Order and Necessaries for Guns to March by Land, they having six Demi-Cannons, six Sakers or De∣miculverings, with two Whole-Cannons, besides their Field-Ordnance.

BEfore the Train doth march, there goeth out Pioneers, each of which is furnished with either a Shovel, Scoop, Pickax, Crow or Handspike; having for their Commanders, a Cap∣tain, Lievtenant, and two Corporals, with a Drum to every Company; who are to make plain the way for the Cannon.

After them first follow the 6 Sackers or Demiculverings, drawn with their respective Horses, with their Provision of Ball in Wagons, and their Powder in Wagons, besides there must be at the Rear of the Cannon, if any whelm, help suffi∣cient to mount them again.

Next follow them six Demi-Cannon, with their Shot and Powder conform; Then 2 Whole Cannon, with their Powder and Ball accordingly.

Then the Carriage of Ladles, Sponges, and Rammers, Match, Crowes, and Handspiks, and Budg-barrels: These be∣sides the Field-Peeces for the respective Regiments, take a great many Horses, Wagons, and Men, for their Attendants.

Now when the Cannons are on their March, every Gunner to his respective place, must march at the right side of his

Peece, and by them their Harbingers, who take notice of all the Ropes, and other Provisions for Draught, and help them if defective: and also to see that the Axtrees be well soped or tallow'd, that thereby the Train may march without stop: The Wagon-Master must have spare Horses by his Draught, if any fail either in Wagons, or in Draughts of the Ordnance. Several have given Rules for so many Horses to a Peece of such a Weight; as thus, every 500 lb of Metal for a Horse-Draught; where the Guns alone, besides the Car∣riages, must have 120 Horses: So I reckon for Guns, Carri∣ages, and spare Horses, there will be 180 Horses: Now for Powder, Ball, and other Provisions, 100 Horses more with Wagons, besides Wagons for the Officers.

This is supposed to be for so many Cannon in fine plain Way; but the Horses in every Country are not all alike, for I have been drawing Cannon, and allowed but to every Horse 350 lb, and hardly able to perform; but sure it is, where Horses are to be prest, there need no halt to be made for Draught, if the Conductors be provident. But if there should fortune Cannon to be drawn in places where Horses or Oxen (for if you order a Yoke of Oxen for a Horse-Draught it will be equal) are not to be found; Therefore I will set down a general Rule, how these Guns may be drawn by the strength of Men. And the Calculation shall be made for the forenamed 14 Guns; by which may be reckoned any other Draught having the Weight.

First, It is conceived an indifferent Man will draw 100 lb for his part, (but on a plain way); therefore for ordinary, I do allow a Man to draw 80 lb weight: And you will find, counting the weight of these 14 Peeces thus; The Cannon 7000 lb, a peece, is 14000 lb for them two; then the Demi-Cannon 4500 lb, and these 6 are 27000 lb; for the 6 Demi∣culverings 3200 lb a peece, and these will weigh 19200 lb; which in all is 60200 lb: which sum being divided by 80, (the pounds of draught for one Man) will make 752 Men to draw the 14 Peeces of Cannon. Now these 752 Men to em∣ploy with discretion and good order, that every Man may do his endeavour, you are to make fast your Ropes in this man∣ner, on either side of the Carriage; before on the Hackes one Rope, and on the middle of the Bolt or Brestband one; And

upon every Rope, shall be so many Ropes so made fast, as every Man may have 2 ½ foot distance one from another; so that the Draught-Ropes for a Demiculvering must be 17 fathom long: Now for the Demi-Cannon and Cannon, they may be reckoned by their proportion; so the Men are set to Work, as the Figure hereby doth shew.

This will be thought a new Invention, but I used the same in my Lord Middleton his Service from Aberdene to Fyvie, where I caused them to make these Sled-feet, as you see fast to the Carriage, in this manner; near to the Breech of the Peece there is a Bolt, whereon the end of the Sled-foot is; and under it, at the foot-end of the Carriage, a Square-hack to lay over the Sled-foot, and then a Rope through the Sled-foot: And a Man or two thereby shall steer a Gun by a Height or Hole, in the way where she is to be drawn, so that many times it saves the Guns from falling over.

And when you are to meet your Enemy, or make use of your Guns, you may lift up your Sled-feet, and lay them all along the side of the Carriage in manner as you see, on a Hack where they do not trouble, and unhacking the Ropes from the Hacks before, you may use your Gun at your pleasure.

CHAP. XXXI. By knowing the Weight of one Peece of Ordnance true-bored, to find the Weight of another true-bored Peece, being of the same Metal.

BEcause it falleth out sometimes, that in a Fort or Ship are Guns, not having their Weight described upon them; Therefore in such occasions, not to let the Gunner be to seek, but that he may give her Weight without great trouble, I shall here set down some Examples, whereby the Gunner may with ease find the Weight of any great Ordnance whereby he may be able to shew, what store of Horses or Men are compe∣tent to draw these Ordnance, if occasion require.

These Examples and Rules I intended to have given by a Gauge-Rule; and because these ways are more easie to do,

and quicker dispatched, I shall only take by the way to let you know, that I will admit there is a Brass Saker weighing 1900 lb Weight; and as it is given out in other Questions, she is 3 ¾ Inches in the Diameter of the Bore: Now it is commonly found, these Guns are about the Breech, measuring at the Touch-hole, 9 Diameters of the Bore: I say then, if I bring 3 ¾ Inches all into Quarters, then I have 15 Quarters; with which I multiply the 9 Diameters of her Breech, and I find them 135 Quarters; which dividing by 4, I bring again to whole Inches, and find 33 ¾, which we will here call 34 In∣ches, for the Circumference of her Breech: Then I say by the Rule of Three; As 22 is to 7, So is 34 to 10 9/11 Inches.

The Work. 〈 math 〉〈 math 〉

This 10 9/11 of Inches, is the Diameter of that Saker; if she be true-Bored, she is true-Fortified: And such are the only Guns to make choice of for finding by their Weight, the Weight of any other Brass Peece: Therefore, I say,

Example. If a Gun of 11 Inches Diameter at the Chamber weighs 1900 lb; What shall a Peece of 18 Inches Diameter weigh?

Thus by the Table of Logarithms.

The Logarithm of 11 Inches, is—	1,041393
The Logarithm of the greater, 18 Inches is—	1,255272
Difference Increasing—	213879
	3
The Triple whereof is—	641637
The Weight of the known Peece is 1900 lb—	3,278754
Sum is—	3,920391

Which is the Logarithm of 8325 lb, for the Weight of the great Gun.

Here you see that this operateth well by the Table of Lo∣garithms, and the Weight of the Peece is found to be 8325 lb. Now to find the same by the Line of Numbers on the Scale, you are to place one foot of your Compasses in 11, and the other in 18; keeping the Compasses at the same extent, set one foot in 1900, and then triple turning the Compasses, the last foot will touch at 8325, as before.

Another Example. Also there is a Peece, I know not what her Weight is; but I find the Diameter of this Peece to be 8 ¾ Inches: And I place the Work to find her Weight as before.

Behold the Work.

The Diameter of the known Peece is 11 Inches—	1,041393
The Logarithm of the Diameter of the other 8 ¼—	0,942008
Difference decreasing—	99385
	3
Triple of the Difference is—	298155
Which Subtracted from the Logarithm of 1900—	3,278754
Rests—	2,980599

Which is the Logarithm of 956 ⅓ lb, for the Weight of the lesser Peece, which was required.

The Weight thus found by Logarithms, you will find the like by the Line of Numbers, if you extend your Com∣passes from 11, the known Diameter, to 8 ¾, the Diameter of the Peece whose Weight you would have; the same extent three times from 1900 down the Scale, will reach to 956 ⅓.

This former Work you may find on the Line of Numbers, if you place one foot in 9, the Diameter of the Bore that be∣girts the Peece at the Touch-hole, and the other foot in 7, which is most near the Diameter that begirts the other Peece, and the Compasses at the same Extent, place one foot in 1900 the Weight of the known Peece, and three times turned downward, will light on 956 ⅓, as before.

CHAP. XXXVI. By knowing the Weight of one Peece of Iron Ordnance, to find the Weight of another Peece of Iron Ord∣nance.

Suppose an Iron Saker of 3 ¾ Inches Diameter of the Bore, this Peece weigheth 1600 lb; I find all such Peeces to have 11 Diameters of the Bore about the Breech; for which cause I work as before, and bring 3 ¾ into quarters, which I multiply by 11 the Diameters of the Bore about the Breech, and I find 165, which I divide by 4, to bring again into In∣ches, and the Quotient is 41: Then I say, by the Rule of Archimedes; As 22 is to 7, so is 41 to 13 1/22 Inches.

〈 math 〉〈 math 〉

The Fraction is so small not to be valued.

So that I find 13 Inches to be the Diameter of an Iron Sa∣ker, whose Weight is 1600 lb, and that the same is a true-Bored, true-Fortified Peece: Now there is an Iron Peece whose Weight I know not, but I find the Diameter of that Peece at the Touch-hole or Charged Cylinder to be 21 Inches: To find the Weight of this Peece Logarithmically.

Example. I say, a Peece of Ordnance of Iron, of 13 Inches Diame∣ter, weighing 1600 lb; What shall an Iron Peece of 21 In∣ches Diameter weigh?

The Work will stand thus.

The Logarithm of 13 Inches, is—	1,113943
The Logarithm of 21 Inches, is—	1,322219
Difference increasing—	208276
	3
Triple of the Difference is—	624828
The Weight of the known Peece 1600, is—	3,204119
Sum is—	3,828947

Which is the Logarithm of 6744 lb, for the Weight of the Peece inquired.

If you will Work by the Line of Numbers on the Scale, you will find it near the same; for if you place one foot of your Compasses in 13 inches the Diameter of the known Peece, and the other in 21 inches the Diameter of the Peece whose Weight you desire to know; keeping your Compasses at the same extent, set one foot in 1600, the Weight of the known Peece, turning your Compasses three times up the Scale, and you will find the third extent will reach 6744, which is the weight of the Peece required.

Another Example. There is also a Peece of Iron Ordnance, whose Diameter I find in the charged Cylinder to be 8 ¼ inches; the Question is, to find her Weight.

The Log. of the known Peece, 13 inches is—	1,113943
The Log. of the other Peece, 8 ¼ inches is—	0,916454
Difference decreasing—	0,197489
	3
Triple of the Difference is—	0,592467
Which subtracted from the Log. of 1600—	3,204119
Rests—	2,611652

Which is the Logarithm of 409 lb, for the weight of the Peece inquired.

Finding here the weight of this Peece to be 409 lb, you see it followeth, that great or small Ordnance their Weight may be found; yet for variety we will have another Example.

Example. I will admit there is a Peece sound, whose Diameter is 10 ½ inches; and the Weight of this Peece I demand.

The Log. of the known Peece, 13 inches is—	1,113943
The Log. of the other Peece, 10 ½ inches is—	1,021189
Difference decreasing—	0,092754
	3
Triple of the Difference is—	0,278262
Which being subtracted from the Log. of 1600—	3,204119
Rests—	2,925857

Which is the Logarithm of 843 lb, for the weight of the Peece inquired.

This and the former is found on the Line of Numbers, if you extend your Compasses from 13, to 8 ¼; and with the same extention turned three times down the Scale, you have 409 lb. If you extend from 13 to 10 ½, and with the same extent from 1600, three times turned down finds 843 lb for the weight of the Peece inquired. And so much for the finding the Weight of Ordnance, thereby to provide what Horses, Oxen, or Men are able to draw them. As the Figure here demonstrates.

Having, as I suppose, satisfied the Gunner for what is in∣cumbent for him to act both by Sea and Land, with all sort of great Ordnance, either true-Bored, Taper'd, or Chamber-Bored: Now it remains that I satisfie my Friends, who expect to hear something of those Peeces that shoot Granado's, or other Fire-Works; as likewise of the Pattard; and of their Ingredients, Compositions, and the manner of using them.

CHAP. XXXVII. Of Powder and its Ingredients.

IT is a Paradox to many, to think that Salt-peter, Brimstone, and Coal, being incorporated, should be the only Compo∣sitions for Powder: But know this, That whosoever desires to learn to shoot in great Ordnance, or to make Fire-Balls, or any kind of Fire-Works, should learn to know the nature and sympathy of these three.

Salt-peter that is pure and of a Christal Colour is best; the refining whereof is set down by divers Authors, as Mr. Nye, and others; yet the nature of it is to burn downward, but if pure and well refined, will burn upward, with a great deal less noise.

Brimstone is hot and loves the fire, and the fire loves it; it is of a sharp nature; when you kindle it, it fireth upward; its colour is of a bright Yellow if it be good.

The Coal neither augmenteth nor diminisheth any strength or force of it self, only it soon taketh fire, by which the Salt-peter and Brimstone receiveth the fire, and perfecteth their Work: The best Coal is made of the lightest Wood, and the lighter the Wood is, the Coal shall be the better. And it is obvious to all, that when these two opposites, viz. Salt-peter and Brimstone are incorporate, and fired together, the Coal nourishing the fire, there is nothing can resist the force there∣of, until the fire dissolve the whole in the Air.

Example. If you load a Gun with Powder, (which is nothing but these Ingredients incorporate) or any other narrow Pipe, so soon as the fire comes to the Body, and the Composition is se∣parate by the fire; then doth it force it self out to the Air so vehemently that nothing can withstand it.

Powder is made of divers sorts, as Cannon-Powder, Pistol-Powder,

Musquet-Powder, and Powder for Fire-Works.

Powder may be tryed three manner of ways; First, Put your hand in a quantity of Powder, and gripe it hard, if it crack and make a noise in your hand, you may judg it is good; but if it crack not in your hand, it is either not well wrought, or it is spoiled.

The second way, is by taking a little Powder, and put it on a smooth plain Board, or a piece of flat Stone; put fire to it, if it go up quickly to smoak, and leave no marks behind it, you may judg it good; but if it burn slowly, and leave white Corns behind it, then you may suppose it is not well incorpo∣rated, and hath too much Salt-peter in it, or that there is too much Dust and Coal therein.

The third is by the Taste; if it be too sharp in the taste, it is like to come moist; but if it taste a little Niterish and sweet, and hard-corned, it is good: There are several other ways to try the goodness of Powder, that for brevity I here omit.

Of Fire Works. There are several Sorts of Fire-Works, some for Offensive Service, some for Defensive Service, and some for Recreations and Sport: I intend only to speak of those which are to be used in earnest, not minding to meddle with those for Recrea∣tion at this time, in regard they are so learnedly treated by di∣vers Authors.

Of Fire-Works, and those Ingredients used for Compositions. As there are sundry and numerous Ingredients that may be used in Fire-Works; so Fire-Works are so to be mixed as they may work several effects, according to the several occasions may be produced in War; therefore it is impossible for any Man to lay down Rules, which only must be observed; but that the Gunner may have a taste of every Dish, that are neces∣sary to be used in bringing Enemies to Ruine, and Rebels to the Obedience of their Lawful Princes, observe these following.

The Loading and Ʋse of the Mortar-Peece. These Peeces are not to be used as great Ordnance, in shoot∣ing at great Distances; but, as it were, to throw a Granade, or Fire-Ball, or Stones, over Walls, or into Garisons, being seated high or low; or from a Garison to Cast a Ball into the Enemies Works or Batteries, thereby to frustrate them of their intents, by taking a way those Men most active in the same.

The Mortar-Peece may be elevated to any degree of the Quadrant; but the contrary you may observe in great Ord∣nance, for they cannot be elevated above 45 degrees; and the nearer you approach to any place to shoot at it, you must de∣ball your Peece under 45 degrees; so that if Tables were to be made for Great Ordnance, they may not exceed 45; and Tables for Mortar-Peeces may be made from 1 to 45 degrees, and from 45 to 90 degrees.

Now he that would Load a Mortar-Peece, may elevate her Musse to what degree he will for his own conveniency, the Peece made clean, you put the Powder in the Chamber, and upon the Powder a Wad of Rope-yarn, Hay, or what you can provide; then you put a Turf of Earth cut on purpose, that is large wider than the vacant Cylinder upon the Wad, which fills the Chamber, and then you put the Granade or other Fire-Work above that Turf, and putting Grass or Hay about your Granade, that it may lie as you would in the Mor∣tar, and also to keep the Powder in the Mortar from the fire of the Feusey.

The Mortar Peece being thus Loaded, you cannot give fire, with any hope of success, before you observe and know, how far the Distance is betwixt you and the place where you would have your Ball to light, and also know, how far that Mortar-Peece can cast her Ball from Degree to Degree; likewise you must observe the Weather, whether it be calm, or blows hard, or if the Wind be with or against you, or if it be to the right or left of you: Having duly considered these things, the Gun∣ner may do well the first shot; but if he erre, he must amend the next.

So that it stands to reason, that when you have found the

Distance to the place you would lay your Ball at, that you may know by this Table near what Degree of the Quadrant the Peece must be laid to reach thither.

90	0	75	403	60	661
89	80	74	425	59	673
88	124	73	448	58	693
87	148	72	450	57	708
86	171	71	473	56	723
85	195	70	496	55	737
84	219	69	500	54	751
83	243	68	521	53	765
82	267	67	540	52	779
81	289	66	562	51	792
80	291	65	580	50	804
79	313	64	599	49	816
78	335	63	608	48	827
77	359	62	626	47	838
76	381	61	644	46	848

Now if you were with a Mortar-Peece at the back of a Wall near a beleaguered place, and there were a remarkable place, as Magazine, or Store-House, or Corn-Barn, and it is desired to lay the Granade or Fire-Ball in that place, the distance be∣twixt you and this place being found to be 243 paces, as in the Figure from A to M; Then look in the Table, and see what Degree is opposite to 243, and you will find 83 De∣grees, and so the Mortar-Peece A must be elevated to 83 De∣grees to cast her Ball or Granade into the House M. Do so with all other.

When you would discharge a Mortar-Peece, first you must set fire to the Feusie of the Granade or Fire-Work, and you must see it burn well before you give fire at the Touch-hole, and mark narrowly where the fall is, thereby to help the next if need require, in form as aforesaid.

The Feusies for Granades or Fire-Balls, may be filled with this Receipt; 1 part Powder, ½ part Salt-peter, ¼ Brimstone, and ¼ part Rosin, being all well beat to Meal, and moistned with Linseed-Oil.

Now follows the Proportion of the Pattard, and Ʋse thereof with all things belonging thereto. The best Pattards are made of Copper, to wit, 1/10 part of Brass: they are made of Iron also, some more some less, as the Figures sheweth: The Pattard A is 12 Inches long, the Diameter at the Breech is 7 ½ Inches, and the Diameter of the Concave is 5 Inches; then the one side Metal must be 1 ¼ In∣ches thick; she is at the Musle ½ inch thick, and the Diameter of the Bore at the Mouth is 10 inches, and weigheth 76 ½ lb.

There is another Pattard as B, which is 9 inches long; the Metal at the Musle is ½ inch thick, and by the Touch-hole 1 inch thick; the Diameter of the Bore at the Mouth is 7 inches, and the Bore at the Breech 4 inches.

To fix your Pattard to do good Service at a Gate, or Castle, or other Fort, or Garison; you must have before the Mouth of the Pattard a good Oaken Plank of about 2 foot in square; this Plank may be banded with Iron, both on the one side and on the other, as the 2 Planks D D, both being but one Plank, but the Bands of Iron are on the one side cross the other; the Plank may be 3 or 4 inches thick; the Powder to the Pattard B may be 4 lb, and the Powder to the Pattard A about 6 ½ lb; when you have loaded the Pattards, and rammed the Powder home, you shall put in the Musle of the Pattard a Wooden Tamken, which you shall beat home with a Wooden Mallet, till it be fast enough; then you may fill the Chinks with hard Tallow, and melt Pitch or Wax and run round about the Tamken, that the Powder in the Pattard may be preserved from Water. When you are to apply the Pattard, and make it fast to a Gate, you must first bore the Touch-hole thereof, and fill the same with some Powder mixed with Linseed-Oil; but a Feusie may be better, filled with the Composition for Granade Feusies, that it may take time to burn before the Pattard fire, that the Man may remove that made it fast. To make it fast, you must have two Hack-Bolts, as E, with Scrues at the ends, which are to scrue into the Gate, where you have the Plank D, to which the Pattard G is fast with a Chain by the Ears in the middle, or by a Staple drove in the Gate, to which the Chain is fast, as you see by the Figure G and D, to the Gate F: To

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carry this Pattard, you must have a Wagon with Wheels, as the Figure H: This Wagon must be as broad as the Plank be∣fore the Pattard, having in the fore-part three sharp-pointed Iron Pikes, that when it is run at the Gate it may hold fast, that the Man or Men may stand thereon, and fix their Scrues, to which they must make fast the Plank with the Pattard: Then giving fire to the Feusie, and removing back the Pattard, having done Execution to expectation, the Parties may enter according to the Commands given.

While this Work was intended for the Young Gunners In∣struction, I hold it my duty to shew you that there is no Fire-Work that can be invented or made for Offensive Service, but the same will and may be made use of for Defensive Service; but some may be made for Defensive Service, which can hard∣ly be useful in Offensive Service, as Barrels for smoaking out of a Mine, or Balls, or Bags to burn the Wood, or Rubbish cast in to fill up a Ditch, Powder-pots, and such like.

Granades to shoot out of a Mortar-Peece. The Mortar-Peece shoots all sorts of Fire-Works; First, Granades, the Shells made of Iron; Secondly, Balls or Bags made of Canvas, in form of Granades; Thirdly, A Mortar-Peece may shoot Stones coated with Fire-Works, or Stones in the Night to fall among the Enemy, as if it rained Stones.

1. For the first the Iron Shell of a Granade must be filled with good Powder, and some well-powdered Brimstone mixt with it, that thereby the Powder may throughly fire the more suddenly. In your Granade you may put some little Balls of unquenchable Composition, that when the Shell breaks and brings down the Rubbish of a House, those little Balls may raise Fire afterward; which is fearful in a Garison, and is one of the greatest terrors can come among them.

Canvas-Balls for Granades. 2. These Balls must be made of strong Canvas; when you have made your Canvas-Ball, you may fill it with Sand, and then take two Iron Rings, and mould your Ball strongly in form as you see the Ball in the Copper Plate N° 3. But if your

Ball be of great weight, single Line will not serve to mould your Ball, and therefore you must make it a great deal less than the Bore of your Mortar-Peece, both in regard of the moul∣ding and coating of your Ball.

The Ingredients or Composition to fill this Ball. Take Powder, Salt-peter, and Brimstone, of each a like quantity, these you shall beat small, and incorporate them to∣gether; moisten them with Linseed-Oil, and work them with your hands till you make a Paste, that it may stick together in small Balls if need be; This is a Slow Composition.

Another for the same. To this Composition you must take 4 parts of Powder, 3 of Salt-peter, and 3 of Brimstone; these being severally beat to Meal, moistned with Linseed-Oil, and wrought as aforesaid; This is a good Composition.

Another for the same. Take 12 parts of Salt-peter, bray it not very small, and 12 parts of Brimstone not small beat, work them well together, and moisten them with 2 parts of Linseed-Oil; then take 6 parts of good Salt-peter, bray it as small as Currants; incor∣porate these Ingredients, and make a Ball thereof as big as a Walnut; and if it burn as long as you may tell 30 soberly, then is the Composition both good and strong.

When you have found your Composition good, you may fill your Bag at discretion.

In moulding, you must have 2 Iron Rings of the thickness of ¼ of an inch each of them; the one 4 inches Diameter, and the other 3; and as you mould the Ball, rive the Line through the Rings; to which you must have a Splice-Iron, or Marlin-Spike of Horn; a tack of Harts-Horn is good to do it with: In the largest of your Rings you may set your Feusie; the Feusie may be made of Wood, the Pipe bored; you may bore 3 or 4 small holes near the lower end; it is the custom of Feusies to reach the middle of the Granade or Ball; you may

pierce this Ball when filled with Fire-Work, and put therein Iron Pipes, loaded with Powder and Shot; but be sure the Touch-hole be wide enough, that Rust doth not stop them from firing; these Pipes must be beat in, till their Musles be equal to the Line.

Then you must coat this Bag with these Ingredients follow∣ing; Take Pitch, melt it, and put therein Oil till it be tough and pliable; then put some Powder in it; and if you take Hurds or Tow, and spread on a Table, run this Stuff upon it; then wrap your Ball therein, and open your great Ring for your Feusie-Hole, and stop it with a Plug.

When you are to use this Ball, take out the Plug, and put therein your Feusie filled; then Load your Mortar-Peece, and set your Ball in the Mortar in the same manner you do your Granade; having laid your Peece as she ought to be, then fire the Feusie, and so your Peece: If this Ball fall near any thing that will take fire, it will burn, and do the Enemy great harm.

For those Stones, that may be shot from a Mortar-Peece, if you dip them in Composition made for Water-Balls, with Pitch, Rosin, and Wax, When they are coming down (as it were from Heaven) into a Garison, it puts them in great fear, and makes them gather about the fire.

Then you may have a Mortar-Peece loaded, and put therein stones as big as a Mans head; and laying her as the other, these stones falling amongst the people, put them quite out of heart.

Another Granade for a Mortar-Peece. If you make a Ball of Canvas, as is before shown, well moulded and filled with Sand, then melt Pitch and Rosin, and dip the Canvas Bag in it; but you may have Musquet-Shot cut in two, and clap them on this Coat as full as the Bag can stand, as you see in the Copper-Peece N° 2; then Coat it again, put in the Feusie; and if you fire it among Men, it will do great harm, the Sand being put out, and the Bag fill'd with Powder.

Another for the same. If you let a Pully-maker or Turner turn of hard Wood two half Balls to join each in other, as the Figure 2 demon∣strates; they two being joyned make a Spheral Body, as you

see, then mould them strongly together with Wire, and with a Goudg cut out little slices of the Wood, as may help lodg half Musquet-Ball; then dip it in melted Pitch and Rosin one dip over, and set shot; then Coat it again; this Ball being filled with fine Powder, and a Feusie put into it, it will serve either to be shot as a Granade, or heaved as a Hand-Granade, and will do good Service.

To make a Composition for Fire-Arrows. Take 2 parts of Salt-peter, 2 of Powder, 1 of Rosin, 1 of Brimstone; pound these Ingredients very small, and mix them together; then moisten them with Brandy-Wine and Lin∣seed-Oil, or Oleum Benedictum; then fill your Bag of Can∣vas made for the purpose, very hard and full, then stick an Ar∣row-head through the Bag, and make it fast with Twine, Rope-Yarn, or such like; and put a Plug for the Feusie-Hole, where you mind to fire it; then coat it over with Pitch, rub Powder in the Touch-hole, give fire to it, and shoot it where you will, and it will burn very well.

But if you would not have it burn, till it light at the place appointed, in regard you would not have it seen, you shall take a little good Tinder of a Fingers length, and put it in at the part you mind it shall take fire; put that Tinder in fire, and shoot it where you please.

There are Gunners, that when they have moistned their Composition, clap it about the Arrow, and then lay Canvas about it, and few it fast, bore holes, prime it, fire it, and shoot it, where they have a mind; but it must be coated first: The form of an Arrow you have in the Copper plate N 5. You may fill the Hedghog N° 4, in the Copper peece with this Composition.

To make Fire-Trunks. Amongst Fire-Works a Trunk is one, for they may be made with easie charge; First, Cause the Block-maker to make a Trunk of hard Wood, and reasonable thick, (though you make the Ball small) you may put two Hoops of Iron about it, and at the great end leave Wood enough to make a Socket for the end of a Pike or Pole.

The Compositions for Trunks. Take Brimstone, Pitch, and Wax, alike quantity, melt them over a slow fire, and put thereto 2 parts of Salt-peter mealed, with ¼ part of Verdigrease, and 1/•• part of Camphire; all these being mixed together, add ⅛ part of Linseed-Oil, stir it well about, and take Hurds, Tow, or Hemp, and make wet with this Composition, which you shall roll up in form of Balls; these Balls you tie together with Twine, and when they are cold, you bore them cross through, which Holes you prime with Powder-dust; you may make of these Balls as many as you please; you may coat these Balls with melted Pitch, and roll them in Powder-dust.

To Load the Trunk. First, Load her with a quantity of Powder, as the Gun∣ner thinks fit to carry out his Ball and not break the Trunk; then put home to the Powder one of those cross-bored Balls, and for his Wad to keep him to the Powder, take a little Meal-Powder moistned with Linseed-Oil and made into Dow; and upon that load Powder and Ball again; then put upon the Ball of this slow Composition; then load Powder, and then Ball, and then of slow Composition again, till your Trunk be full; Then take the Lance and make fast in the Trunk, and set him to your shoulder in form of a Musquet; let one fire at the Mouth of the Trunk, and you may shoot these Balls round about where you please, and they will burn. These Balls may be used in Iron-Shell Granades, or in Wooden-shell Granades, if they be so big as to contain them; for when the Granade breaks they will burn furiously.

To make Balls to show Light in the Night. Take Antimony 1 lb, Rosin 1 lb, Brimstone 3 lb, Salt-peter 1 lb, Coal 1 lb; make many Balls thereof, bind them up with Tow: If the Enemy lie near your Walls, Ditches, or Tren∣ches, for your own satisfaction, you may fire one or more of these Balls, and throw them over, where you have any suspici∣on; These Balls will give you light to see, if any be near your Fortification. And if you find the Enemy, you may fire your great Guns of what sort you will for their annoyance, still throwing of these Balls to give light to know the Enemies pro∣ceedings.

To make an Extraordinary Fire-Work, which being put into a Mine, or on a Breach for Storm; shall suffocate or kill those who come in the Smoke of it. Take of Horse Litter, that hath been sufficiently spoiled by the Horses, dry it in the Sun; likewise take some of the dirt that Hogs have lain upon, and dry it also; dried Cow-Gall, old wollen Clouts, chop all these small; then take 1 part of Wax, 1 part of Hogs-Lard, 3 parts of Powder meal'd, ¼ part of Ratsbane, ¼ part Orpiment brayed to Meal, ¼ part Verdi∣greese; mix all these things together, and fill a Bag therewith being well coated, put a Feusie into it, and give fire; heave it among the Enemy, or shoot it to them, it will do excellent Service.

But if you fill a Barrel of this Composition, and set it in a Breach where the Enemy is to storm; if the Wind carry the Smoak from you, the more it burns, the more it will smoak; and I am sure no Man can be able to act in that Smoak, so that you may have great advantage of your Enemy in contriving this Smoak; as Figure 8 in the Copper peece sheweth.

To make a Fire-Work that shall stink fearfully. Take Brimstone 2 lb, Rosin 1 lb, Kitchin-stuff 1 lb, Assa Foetida 1 lb; melt these together, then take shavings of Horn, or the parings of Horse-Hoofs that are dry, mix a good quantity with the former melted stuff; then take Hemp, Tow, or Rags of Linnen, or Wollen, or Okam, as much as will drink up the Composition, and make thereof a Fire-Ball; this being roll'd in a little Powder meal'd, and Mans Dung; set fire to it, and it will stink so, as who comes in the Smoak will rather fly, than abide the Smoak, (if they be able); you may put this in Bags, and make Balls or Hedg-Hogs thereof at your pleasure.

To make by Fire, in time of Storm, a Smoak among the Stormers. Take a large strong Barrel and pitch it close, half full of Quick-Lime; then set in the middle of the Barrel such a quan∣tity of Powder in a close Cask, that, when fire is given, may

blow the great Barrel, and all that is in it to pieces; and be sure you put in this little Barrel a Pipe or Feusie filled with Composition, that may reach through the great Barrel; Then fill the great Barrel full with the aforesaid Lime, and lay it at the Breach, where the Enemy is to storm; and when you see your best advantage, having a Train laid of purpose, you may give fire, and if fire come to the Powder, it will so spoil those about it, that they, by filling their Eys, Throats, and Noses, shall not be able to see, or walk: by this means the Besieged may have advantage against the Enemy. If Lime were used for cleansing the Decks, instead of Stones, I believe it would give much satisfaction at some times; but Quick-Lime is dangerous, if Water come to it unawares. This Lime is no∣thing but Lime-stone burn'd, that no Water hath been near; then it must be very well bray'd, and made as fine (if possible) as flower; the finer you make it, the greater harm it shall do to the Enemy; and being dry and light, will continue the lon∣ger ere the Smoak dissolve.

Another Barrel in time of a Storm. But if you would play with your Enemy, you may fill your great Barrel with fine pibble Stones, Musquet-Shot, and pieces of old Iron, in form of our Powder-Chests at Sea; this being fired, while they are thick about it, will make rare sport for the Defendant, and make them afraid of worse to follow; and then if you can ply them with Hail-shot from your Guns, and small shot, Hand Granades may give them cause to re∣tire, if they can, with the greater safety, as the Figure in the Copper peece 10, doth shew.

The Proportion of Compositions for Offensive Fire-Works.

• 1. Take one part of good Powder, one part of Salt-peter, and half a part of Brimstone, and a quantity of Saw-dust, or old rotten Wood, which will make a great Smoak: These being well mixed with Linseed Oil, and wrought under your hands, until you make the Composition to a Paste, that it may hold together to make Balls.
• 2. Take gross Cannon-Powder 1 lb, Salt-peter 1 lb, Brim∣stone ¼ of a lb; pound these very well in a Mortar, or a Powder-Mill, and mix them together; moisten them with

• Linseed-Oil, and work them well with your hands to a strong Dow or Paste, as is beforesaid.
• 3. If you take very good Powder, beat it very small, searce it through a Sieve, and moisten it with Linseed-Oil, work it to a Dow or Paste; it is good if you make use of it presently; for this Composition is too strong to be kept, and therefore you may add to it half so much Salt-peter, and a little Brimstone, then it may be kept.
• 4. If you take of the best Pistol-Powder you can get, beat it very small, searce it through a narrow Sieve, moisten it with Linseed-Oil, work it well as is before taught, and you have the best and strongest Composition without doubt amongst all the others; but it is likewise too strong to be kept long, and fearful, if dry, to be fired.
• 5. If you take gross Gun-Powder, as much as you please, and as much Salt-peter, being moistned with Linseed-Oil, and wrought as the rest, with a little Brimstone.
• 6. If you take two pound and a half of gross Gun-powder, and 4 lb of Salt-peter, and 1 lb of Brimstone, all well beat, and searced through a Sieve; then being moistned with Lin∣seed-Oil and wrought as before.
• 7. Take 1 lb and a quarter of Powder, 1 lb of Salt-peter, three quarters of a lb of Brimstone, half a lb of Sponk, the Heart of Willow, or old rotten Wood rubbed small; all these being moistned with Linseed-Oil, work them well with your hands as the other Compositions are.
• 8. To 4 lb of Powder, take half a lb of Brimstone, and half as much Salt-peter as both the other; all these being well pounded and searced through a Sieve, (as aforesaid) and being moistened with Linseed-Oil, work as the rest.
• 9. If to 2 lb of Powder you take 1 lb of Salt-peter, half a lb of Brimstone, and half a lb of Coal or rotten Wood, these all being well moistned with Linseed-Oil, and wrought, this will make a good ordinary Composition.
• 10. Take to 1 lb of gross Powder, 2 lb of Salt-peter, and the quarter part of these two of Brimstone; these being all pounded and searced, and moistned with Linseed-Oil, and wrought as formerly instructed.
• 11. If you take 1 lb of good Powder, a quarter of a lb of Brimstone, and 6 ounces of Salt-peter; these being all moist∣ned

• with Linseed-Oil, and well wrought; then you take one fourth part of Spunk, or Saw-dust well rubbed, mix this Composition with it, and you have your desire.
• 12. Take 4 lb of Powder, 1 lb of Salt-peter, ½ a lb of Brimstone; these being moistned with Linseed-Oil, and well wrought; Lastly, Take half a lb of Rosin, and as much Pitch small pounded, and searced through a small Sieve, and then a little Saw-dust mixed therewith, with rotten Wood rub∣bed small in your hands; this is for the flame or smoak: If you would have it to spread abroad, put some brayed Glass therein. This Composition may be used amongst your Recre∣ations, but it is not to be long kept.
• 13. Take of Musquet Powder 12 ounces, Coal 4 ounces, Brimstone 3 ounces, moistned with a little Linseed-Oil; this being well wrought may be likewise used.

These following Compositions should not be moistned at all, but made altogether dry, and so used.

• 1. Take what quantity of Salt-peter you will, and the fourth part of that of Brimstone, with a little Powder, and a little Coal; all these being fiuely pounded, and searced through a small Sieve; mix therewith some rotten Wood to increase the flame.
• 2. If you take 1 lb of Salt-peter, ½ a lb of Brimstone, a lit∣tle Coal, and a little rotten Wood, the best you can have, to make a Smoak; the first two pounded and searced, and the rest mixed therewith.
• 3. Take 2 ounces of Powder, 1 lb of Salt-peter, 2 ounces of Mercury; these 3 well pounded and searced; then 2 oun∣ces of rotten Wood rubbed between your hands, and 2 ounces of Pitch; these two beaten small not searced, mix them to the other Ingredients.
• 4. You may take 1 lb of Salt-peter, pounded and searced, a little Spunk, with a little Rosin; work the same as afore∣said, then mix them all together.
• 5. If you take Salt-peeer and Brimstone, each alike, and a little rotten Wood; this is also a good Composition in Balls or Bags, and will keep long unspoiled, and hath likewise no danger in the firing: It is esteemed to be the best of all Com∣positions,

• and gives no strong fire, as the moistned Balls do.
• 6. Take 3 lb of Salt-peter, 1 lb of Brimstone, mix them with Coal, or rotten Wood which is light; if you use to these Balls Feusies it will not be amiss, or some of the slow Compo∣sition moistned with Oil.

All these may be made in Cloth-Balls, coated as aforesaid, and made use of as the Gunner pleaseth, for offending of an Enemy.

As there is nothing now unlawful, (though never so base) that can be acted against an Enemy; so it is very common for Persons to take upon them to be Spies and Intelligencers, who void of fear will enter with the Enemy in their Army, Lea∣guer or Garison, on purpose to betray them. Those Men who will give themselves to be Spies, they must certainly be of an idle and base disposition, void of the fear of God or Man, and subtil, secret, and Masters of all Villany; yet there are many simple Men, that for love of Mony do put themselves out for this use; these Men, although they be instructed in what they are to go about, and how they may carry themselves in the same; nevertheless, either before or after they have done their Business, by some instinct of fear, otherwise by the Ju∣stice of Heaven, they are cast down, and by their own simpli∣city divulge something, which brings them to be apprehended, and through torture confess the Matter, and according to the Law of Arms receive Justice beyond other Malefactors, in regard the Offence of Treachery, under the colour of Friend∣ship, is a Treason, and Treason is as the sin of Witchcraft, which will certainly be punished both by God and Man.

But if the Gunner should have occasion to use one of these for his secret Business, he should chuse one of those, who had been employed in such business before, and of such a nature, that though he be threatned, and asked questions seeming as though he might have been betrayed; nevertheless he must stand unalterably to his own innocency, without fear to change his colour, or coldness of heart to tremble; but with a merry countenance, dexterity in speech, knowing subtilty to answer what is demanded.

I do remember, at the Line at Leith, when his Majesties Army lay there; one day there came a pretty subtil young Man from Cromwel's Army, making his pretence that he had

left his Service of purpose to serve the King; he was brought before General Alexander Leslie, who put the Matter sleightly by, and gave the young Man leave and freedom to take Ser∣vice where he pleased; whereupon he took occasion to go down the Line, see all our Army, and continued two dayes: I sent for the young Man, and in company I did alledg he was a Spie; he put it off with the finest jokes that could be; assu∣ring me, There was not a faithfuller Subject than he in the Army, swearing effectually to the point; but that afternoon he went to the Enemy to receive his Reward; he was a spright∣ly young Man, but of a solid and discreet behaviour, that in∣deed I did admire his audacity and impudency; this Fellow was fit for a Spie.

Another; when I was in the Castle of Edinburgh, a Soul∣dier came running right up from the Enemies Works, that if he had been a Runaway, they might have killed him; but this fellow came running into our Moat, and when he was there, feigned himself mad, and would be up; the Governor Don∣dass desired to have him up; so I caused hale him up by a Rope about his middle, (I am sure the Wall rubbed the Skin off his hand); yet when he came in, he was slabbering, as it is said David did before the King of Gath, 1 Sam. 21. but hear what he would, and see what he would, he answered nothing to that purpose; but after he had been that day and night in the House with the Governor, he found the way back to the Enemy without help: Such as these are worthy to be Spies.

Now though I will not encourage any Person to any Action so far below a good ingenious Spirit; nevertheless I will shew you what Fire-Balls they use, and the subtilty they use in the perusing those Fire-Works in laying of them: And therefore for Examples-sake, I will here shew the use of them, that thereby you may the better guard your selves from the trea∣chery of Spies.

They use these following Fire-Works, when they intend to burn the Barns of Corn, or Store-houses where the Corn of the place lieth, or Powder-Magazines, in regard it is impossi∣ble for them to come into them, but that it is useful and neces∣sary they have some Windows or Slits in the Walls, wherein they heave their Fire-Work, which is made in this manner.

Take one part of Colophony, or Rosin, two parts of quick-Brimstone,

one part of Salt-peter, these three pounded very small and mixed together; put to them so much Linseed-Oil as will make the Composition like a Conserve; then make Balls of the same, and if you will, you may make it for Ar∣rows to shoot out of a Bow, or Cros-bow, or by observing what is said of Fire-Trunks, they may be used in the same manner, or they may be heaved by a Mans hand.

There are other Fire-Works that they use, as this strong Composition.

Take 3 parts of Powder, one part of Brimstone, which be∣ing pounded small to Meal, mix them very well in a Bowl, put into them the bigness of a Walnut of Greek Pitch, or Co∣lophony, which must also be small stamped, and in the mixing you shall let some drops of Turpentine fall, as also a spoonful of Linseed-Oil, and then make it to Paste with Brandy-Wine, that if occasion be you may make Balls of it.

But if you fill Bags with this Stuff, well packed together, and make therein a Hole, and put a stopper into it; then dip these Bags in the following Composition.

Take one part of Brimstone, let it melt, and put into it one quarter part of Wax; when that is melted, put in one part of Pitch, and let that melt, and stir them together, take it from the fire, and mix into it one quarter-part of Powder.

Or Coat these Balls with this Composition; Take 3 parts of Brimstone, melt it, and put into it 1 part of Wax, and 1 and a half of Grease, one quarter-part of Turpentine, and as much Vernice; when all is melted, set the Kettle a distance from the Fire, and put therein 3 parts of fine Powder; mix them, or stir them well together: when this is to be used, you shall take the stopper out of the Prime-hole, and in the place thereof, put in a piece of Match as long or short as you please, according as you would have them to do execution. The making of this Match you are taught in pag. 172. To such Actions as these, the Match must be chosen that smokes not, for they use to lie till a certain time, and smoaking Match will discover them.

Example. I desire a Fire to begin within 3 hours time, therefore I take a long piece of Match, which I intend to use; and I measure the same exactly; I light that Match, and mark how much of

it burns ¼ of an hour; I measure my Match again, by which I know how much is burned in the quarters time, and 12 times so much must be the measure of Match for the time appoin∣ted; it must be laid Serpent-like about the Ball, that the parts touch not other, neither the Bag, as the Figure in the Cop∣per Peece, N° 7.

There are some may make use of the Fire-Arrow, which may be made sundry ways; some make them thus.

Take Powder ¼ part, 2 parts Brimstone, and 1 part Salt-peter, each well pounded to Meal, and searced; mix these three Materials together, moisten them either with Brandy or Linseed-Oil, and then melt Rosin, and pour it into Water, which makes it hard; then pulverize it, and take one part of it and mix with the former Ingredients; then pound them to∣gether very well till they are fit to make Balls of; then may you take of this Composition, and lay about an Arrow-Head, and wrap it about with Fustian or Canvas, and seiz it about the shank of the Arrow-Head; this Arrow-Head so armed, you Coat it as other Fire-Works; then make a Priming-hole towards the point of the Arrow; stop it, and when you make use of it, fire and shoot it where you desire: As the Fi∣gure in the Copper Peece, N° 5.

Here follows Compositions for Fire-Works for Storm, divers manner of wayes.

• 1. Take Powder 4 lb, Salt-peter 3 lb, Brimstone 1 ½ lb, Rosin 1 ½ lb; these being all well beat and mixed together, and moistned with Linseed-Oil. This is a good Composition for Fire-Balls, and burn in the Water.

To make Fire-Balls to burn on the Water.

• 2. Take Powder 15 lb, Salt-peter 10 lb, Brimstone 4 lb, Rosin 2 lb; moistned with Linseed-Oil.
• 3. Take Powder 10 lb, Salt-peter 8 lb, Brimstone 2 lb, Rosin 1 lb; moistned with Linseed-Oil.
• 4. Take Powder 4 lb, Salt-peter 6 lb, Brimstone 2 lb, Ro∣sin 1 lb; moistned with Linseed-Oil.
• 5. Take Salt-peter 8 lb, Brimstone 8 lb, Coal 1 ½ lb, An∣timony

• ... 〈1 page duplicate〉〈1 page duplicate〉

• 1 lb, Amber 1 lb, Camphire 2 lb, Turpentine 1 lb, Rosin 1 ½ lb; all beat small and moistned with Linseed-Oil.

Another for Water-Balls.

• 6. Take Powder 9 lb, Salt-peter 7 lb, Brimstone 2 lb, dry Tanners Lee 1 lb; moistned with Linseed-Oil.
• 7. Take Powder 3 lb, Salt-peter 2 lb, Brimstone 1 lb, Co∣lophony 1 ½ lb, Amber 1 ½; moistned with Linseed-Oil.
• 8. Take Powder 6 lb, Salt-peter 6 lb, Brimstone 4 lb, Co∣lophony 3 lb; all small beaten, and moistned in Linseed-Oil.
• 9. Take Powder 1 lb, Salt-peter 1 lb, Brimstone 2 lb; moistned with Linseed-Oil.
• 10. Take Powder 2 lb, Salt-peter 1 lb, Brimstone 2 lb; moistned with Linseed-Oil.
• 11. Take Powder 2 lb, Salt-peter 2 lb, Brimstone 2 lb; all beat small, and moistned with Linseed-Oil: These Balls may be used to Fire-Works and Fire-Balls.
• 12. Take Powder 2 lb, Salt-peter 5 lb, Rotten Wood, or Tanners Lee 1 lb, good Brimstone 1 lb, Salt 1 lb; these all beat small and mixed together, moistned with Linseed-Oil.

To make a long burning Composition for Fire-Balls.

• 13. Take Powder 10 lb, Salt-peter 4 lb, Brimstone 6 lb, Filings of Steel 4 lb, Sawdust 4 lb; and after you have moist∣ned the Composition, mix the filings of Steel and Sawdust amongst it; then make Balls of this Composition, and tie them as other Balls.

Another that is soften.

• 14. Take Salt-peter 5 lb, Brimstone 2 lb, Coals 1 lb, Saw∣dust 1 lb, mixed amongst it.
• 15. Take Salt-peter 2 lb, Brimstone 1 ½ lb, Powder 1 ½ lb; these being beat small and mixed together; take Turpentine, melt it, and moisten these Ingredients in it.

Another Composition for Fire-Arrows.

• 16. Take Salt 8 lb, Brimstone 3 lb, Coals 1 lb, Sawdust 1 lb.
• 17. Take Salt-peter 2 lb, Powder 2 lb, Brimstone 1 ½ lb; you may use it to what you please.

[illustration]

For Powder-Pots, or Stink-Pots. Take fine Powder, mixt with some Brimstone small beat; put therein some Assa Foetida, some pieces of Verdigreese, and some Camphire: This heaved in a Ships Round-House, Fore-Castle, or betwixt Decks, will make a fearful stink and smoak.

To make Match that shall not Smoak. Take a glazed Earthen Pot, and put therein clean red Sand till it be ⅔ full; coil therein Match, so that no part thereof touch other; then cover it well with the foresaid Sand, and coil Match thereon as before, and then put Sand above it till the Pot be full; which done, you are to put the Cover on the Pot, and lute it close, that no Smoak come forth of it; put this Pot into a Sinder or Charcoal-Fire, and cover it all over; let the Pot stand there till the Fire extinguish of it self; then take it out, shake the Sand off, and your Match is ready.

I could infinitely have added, but being straitned, do con∣clude, That as yet to the Art of Gunnery there is

NO END.

Notes

• * 1.1

  Definition of the Cube Root.
• * 1.2

  By a Seg∣ment, or a piece of a Ball being found, to know the weight of the whole Ball.
• * 1.3

  The true knowledg of this Problem is of great use for Gunnders, both by Sea and Land.
• * 1.4

  The true proportion of a Gun.
• * 1.5

  A good way to find the Wind of a Peece of Ordnance under four pound Ball.
• * 1.6

  A true way to Extract the Wind of a Peece of Ord∣nance, and thereby to find her true Ball.
• * 1.7

  There is a Difference between Scots and English Weight, as So that the Difference between Scots and English weight is as 8 is to 9; that is to say,8 is to 9.
• * 1.8

  According to the cu∣stom in former times, the loading of Powder.
• * 1.9

  Great Cautions to be ob∣served in giving Guns Pow∣der.
• * 1.10

  That Guns ought to be proporti∣oned in length to their For∣tification.
• * 1.11

  Curiosity is good, if a man be not taught he cannot be perfect.
• * 1.12

  The true Proportion of a true Bored, and true For∣tified Peece of Ordnance.
• * 1.13

  The Pro∣portion of Powder as supposed.
• * 1.14

  Names of Guns.
• * 1.15

  Proportion of Powder, and names of Guns.
• * 1.16

  Proportion of Powder and names of Ord∣nance.
• * 1.17

  Proportion of Ladles.
• * 1.18

  How many Gunners at the Wager, and but one capa∣ble.
• * 1.19

  This Di∣spute was between a general Person and a Gunner.
• * 1.20

  What may be done with a les∣sened peece, as if it were a Morter-Peece.
• * 1.21

  These Rules are to be ob∣served.
• * 1.22

  Mr. Nye says, That two Inches Diameter, is 1 pound 1 ounce.
• * 1.23

  The truest Rule.
• * 1.24

  For by this Rule I have Cal∣culated the Table fol∣lowing.
• * 1.25

  The diffe∣rence be∣twixt Scots and English Weight.
• * 1.26

  Ʋse of the Tables of Iron Ball, measured with Scots Inches.
• * 1.27

  You have the Diameter and Weight of Scots and English Ball, on the Scale, on the side of the Qua∣drant: Also the Dimension of one side Metal, both Brass and Iron Ordnance, by which you may give Powder for Action.
• * 1.28

  The Demonstration and Diameter of a Ball of 12 pound being given, the Diameter of one pound Ball is also given, as in pag. 92.
• * 1.29

  A Rule to rectifie the Weights of divers Pla∣ces with ours.
• * 1.30

  Most ne∣cessary.
• * 1.31

  Chamber-Bored Guns were of old as is supposed.
• * 1.32

  Three sorts of Cham∣ber'd Ord∣nance.
• * 1.33

  Things incident ought to be with di∣ligence ob∣served for fear of danger.
• * 1.34

  The true Proportion of Right Chambers in Peeces.
• * 1.35

  I was a Gunner when the Spanish ships came to the Downs, in the year 1639.
• * 1.36

  Most need∣ful, for great hurt may come by a Ball too high.
• * 1.37

  These not to be neg∣lected.
• * 1.38

  I leave to the Gun∣ners own discretion the quan∣tity of ne∣cessaries.
• * 1.39

  The only way to Dispart a Peece of Ordnance.
• * 1.40

  What Point-Blank Distance is.
• * 1.41

  Observe the Cop∣per Peece, Numb. 1.
• * 1.42

  Observe the figure in the Cop∣per Peece, Numb. 2.
• * 1.43

  I suppose mistakes, or trusting to other Mens Works, makes one beget ano∣ther.
• * 1.44

  By Expe∣rience.
• * 1.45

  A Remar∣kable In∣stance.
• * 1.46

  When a Sheep is General of an Army of Lions they may be beat.
• * 1.47

  The Rea∣sons of their for∣mer mi∣stakes.
• * 1.48

  Behold the Figure AC.
• * 1.49

  Fire in the Night is terror to an Enemy.
• * 1.50

  Good Ob∣servations if follow∣ed.
• * 1.51

  In the Night as by Day.
• * 1.52

  To be sure you will see where your Ball Lights.
• * 1.53

  Ʋncertain to find ex∣act truth in Random Tables.
• * 1.54

  This Ta∣ble I had from Wil∣liam Class in his Pra∣ctice of Gunnery.
• * 1.55

  Conclusi∣ons and Observati∣ons done by the Quadrant
• * 1.56

  To know how far, or what Distance you are from the Ene∣mies Forts, or Strengths, is most necessary for a Gun∣ner.
• * 1.57

  Experience is the best School∣master.
• * 1.58

  Necessary Observa∣tions for Gunners either by Sea or Land.
• * 1.59

  This is true, and can be witnessed.
• * 1.60

  In the Fi∣gure, Num. 133.
• * 1.61

  The Peece he is to use here, is a Demi-Cannon, which shoots Point-blank 200 Paces.
• * 1.62

  At a De∣grees the Demi-Cannon shoots 394 Paces.
• * 1.63

  The Breadth or Length of a Courtain or Bulwork is all to be done in one manner.
• * 1.64

  But not Dundass Governor.