The making of rockets in two parts, the first containing the making of rockets for the meanest capacity, the other to make rockets by a duplicate proposition, to 1000 pound weight or higher / experimentally and mathematically demonstrated, by Robert Anderson.

PART II. TO OUR PYROBOLISTES.

A duplicate Proposition.

HAving one Rocket well proved in all its Parts, viz. a three Inch Rocket. Then,

To decrease the Velocity of the Com∣position of the aforesaid Rocket, to make it fit for a 4 Inch 4½ and 5 Inch Rocket.

And to increase the Velocity of the aforesaid Composition, to adapt it to a 2 Inch 1½ and 1 Inch Rocket, keeping the same kind of Boring.

Secondly, From the exposed Rocket of 3 Inches, to increase the Diameter of the Orifice of the Rockets of 4: 4½ and 5

Inches Diameter; and to decrease the Diameter of the Orifice of the Rockets of 2: 1½ and 1 Inch Diameter, to a∣dapt them to the exposed Rocket, keeping the Composition of the same Velocity.

From Experimental and Mathematical Demonstration.

The Resolution of this Problem will manifestly shew, the invalidity of the Doctrine of Shooting by the increase and decrease of Powder; and that weak and narrow Scantling it pinfolds in, too mean for this lofty Engine. It also tells the Gun-Founder how to give his Guns their due Fortification; otherwise they may be∣come useless Instruments of War. It teacheth our Pyrobolistes to direct their Work so that it may rise well, and not break nor fall. It teacheth Artificers to increase and decrease the force or strength of their Materials in any possible Propor∣tion assigned.

This Proposition was publickly proposed three Months before the publication of this Book, but no Resolution given by any.

PROPOSITION XIV.

The Complication of Rockets in Rela∣tion to their Borers.

FRom a 2 Inch and half Rocket, we Complicate other Rockets, viz. a four Inch Rocket thus, we take the Cube of 4, which is 64, also we take the Cube of 2½, which is 15.625, with which we divide 64, the Quotient is 4▪ and so many times the lesser Rocket is contained in the greater, that is as 4 is to 1. Then I look into the Tables of Ranges for the year 1691. Iune 1, and in the second Column I find the requisite of Powder 1 and 4, and against the 4 in the third Column I find the Range 3377; and in the third Column against 1 I find the Range 652, which I multiply by 4, the Ratio of the Rockets, and it is 2608: Now if this last Number had been equal to 3377, the Range with the Quadruple of Powder, it would have confirmed the shooting by the increase and decrease of

Powder; but as it is short, it is a visible Demonstration of the error of that Do∣ctrine: and if the Doctrine of shooting by the increase and decrease of Powder were true, there would be no need for our Pyrobolistes to give different Velo∣cities of Compositions to different sizes of Rockets, but one Composition would have served all sizes; which every Youth knows the Contrary.

[illustration]

In the Parabola A H Z let A G be 2608, and A H 3377; then G Z and H Z are the Velocities of the equal and unequal Ranges. Toricellius 22. Prop. de motu projec. lib secund.

Then as G Z the Velocity of the e∣qual Range; is to one third of the Dia∣meter of the four Inch Rocket 1. 333; so is H Z the Velocity of the unequal

Range, to a larger Diameter of the 4 Inch Rocket, to keep the same Composi∣tion.

Or as the equal Range 2608, is to the unequal Range 3377; so is the square of the Diameter of the Orifice of the 4 Inch Rocket, to the square of the Diameter of the Orifice of the Rocket inlarged, keep∣ing the same Composition.

Or as the equal Range 2608, is to the unequal Range 3377; so is the Area of the Orifice of the Rocket of 4 Diameter, when taking ⅓ of the Diameter; to the Area of the Orifice of the same Rocket when enlarged, to bare the Composition that would serve a Rocket of two Inches and a half, taking ⅓ of the Diameter of the Rocket for the Diameter of its Orifice.

Example.

• 2608 The equal Range 3.4′6308
• 3377 The unequal Range 3.028531
• The square of 1.333, &c. the Diam. of the equal Oriffice .249660
• Take the half .361883
• The Diam. of the new Orifice 1.516 one Inch and half .180941

Take another Example.

August 24. 1691. I look in Column 2, and find the Requisites of Powder half an Ounce, and 2 Ounces, and against those Requisites in Column 3 I find 1482 the unequal Range, and 236 the equal Range; which I multiply by 4, and it makes 944.

• 944 The equal Range 2.974972
• 1482 The unequal Range 3.170848
• The Square of 1.333, &c. the equal Orifice .249660
• .445536
• The Diameter of the new Ori∣fice 1.67 .222768

Here may be seen the concurrence of Experiments made upon another account, not then thinking to apply it to the Com∣plication of Rockets. I made 2 Rockets of 4 Inches Diameter, and a Taper bit ac∣cording to this method, and bored three Diameters, and left 2 Inch••s Solid, and they rose well.

An example of a Rocket of 6 Inches Diameter, keeping the same Compositi∣on. Take the Cube of 6, which is 216,

divide that Cube by the Cube of 4, which is 64, the Quotient is 3, that is the Com∣position in the Rocket of 4 Inches, is to the Composition in the Rocket of 6 Inches, is as 1 to 3; then I look in the Table of Aug. 24. and find in the second Column the Requisites of Powder half an Ounce, and an Ounce and a half; and against these Requisites in Column three 800, the unequal Range, and 236 the equal Range, which I multiply by 3, and it makes 708: then as 4 is to 6, so is twelve half quarters of an Inch, the Diameter of the new Orifice of the four Inch Rocket, to eigh∣teen half quarters of Inches; that is 2 Inches and 1 quarter: or as 4 is to 6, so is 1½, that is 3 halfs, to 4½ half Inches, that is 2¼. Then I had no such Ranges, that their Requisites of Powder were in Proportion as the Cube of 6 is to the Cube of 2½; therefore was I forced to help my self by Proportion, which is the same in Substance.

• 708 The equal Range 2.850033
• 800 The unequal Range 2.903089
• The Square of 2¼, or 18 half quarters 2.510544
• The half of this Logarithm 2.563600
• Half quarters of Inches 19.13 that is 2.2 is 1.281800

A second Example, April 21▪ 1692.

I look in Column 2, and find the Re∣quisites of Powder 12 Drams, and 36 Drams; and against these Requisites in the third Column I find 1176 the unequal Range, and 303 the equal Range, which I multiply by 3, and it makes 909.

• 909 The equal Range 2.958564
• 1176 The unequal Range 3.070407
• The Square of 18 half quarters 2.510544
• 2.622387
• 20.47, that is 2 Inches and a half, and 47/100 1.311193

Here may be seen one Example makes the Diameter a little more than two Inches and a half, and in the other a little less, therefore we make the Taper Bores just two Inches and a half for a 6 Inch Rocket. To work from a two Inch and a half Rocket to an Inch, put the unequal Range in the first place, and the Work is done. The Composition these 4 and 6 Inch Rockets were made of, were 1 Sulphur, 1½ Coal, and 4 Saltpetre; but I believe 1 Sulphur, 1 Coal, and 4 Salt∣petre would do better, there being no

great danger of the Rocket breaking, by Reason of the large Diameter of the Bore, and Tapering to a point; and by the same Reason, a lesser solid Head is required, that is about 2 Inches in a 4 Inch, and 1¼ in a 6 or 8 Inch Rocket, will suffice.

PROPOSITION XV.

The Complication of Rockets in Rela∣tion to their Composition, with some Cautions and Limitations.

TO decrease the Velocity of the Com∣position of 1, 1½, and 4, which served to a 2½ Inch Rocket, to make it fit for a 4 Inch Rocket: remember the Ratio of the Rockets are as 1 to 4. Look in the Table of Ranges, and find the Requisites of Powder in the second Column, as 1 to 4, and against them in the third Column the Ranges, viz. 3377 and 652, then multiply the equal Range by 4, and it is 2608, (in fig. 1.) In the Parabola Z A H, let A H be equal to 3377, and A G equal to 2608; then H Z, and G Z will be

the Velocity of the Powder, which pro∣jected those Ranges, and we increase or decrease the Velocity of the Salpetre by the Ratio of G Z to H Z: then let A C in fig. 2, be equal to H Z in fig. 1, and A B in fig. 2, be equal to G Z in fig 1; then draw the Ordinate C H and B G in fig. 2, and by these two Lines, viz. C H and B G we increase or decrease the Ve∣locity of the Coal. Further, let D F in fig. 3, be equal to C H in fig. 2; and D E in fig. 3. be equal to B G in fig. 2: draw the Ordinates F K and E I, and by these 3 Lines we increase or decrease the Ve∣locity of the Sulphur.

Then if we take the Logarit••m of (0) (1) (••) (4) (8) 3377 3.518531 1.759265 0.879632 0.439816

And is 26••8 3.416308 1.708154 0.854077 0.427038 that is, the Ranges under (0), their Lo∣garithm under (1) the half of the Log. under (2), the numbers answering those Logarithms are the Lines H Z and G Z in fig. 1. The Logarithm under (4) is the fourth part of the Logarithm under (1): The Numbers answering these Lo∣garithms, are the Lines C H, and B G in

fig. 2. Further, the Logarithm under (8) is the eighth part of the Logarithm under (1); the Numbers answering those Lo∣garithms, are the Ordinates F K and E I in the Parabola F D K.

• Or you may take the difference of the Logarithms under (1) viz. 102223
• Half 51111
• Quarter 25555
• Eighth 12777

By Adding or Subtracting these Log. to or from the Logarithm of the Salt∣petre, Coal, and Sulphur, you have your desire, viz. their Velocities either in∣creased or decreased: or thus, take the difference of the Logarithm of the two Ranges 102223, and Subtract it from the Logarithm of the Square of the Number of Drams, Ounces, or Pounds of Salt∣petre, or from the Logarithm of the fourth power of the Numbers of Drams, Ounces, or Pounds of Coal. And Lastly, that difference being Subtracted from the Lo∣garithms of the eighth power of the Num∣ber of the Drams, Ounces, or Pounds of Sulphur, there will remain three Lo∣garithms, the first being divided by 2, the

second by 4, and the third by 8; there will remain three Logarithms, the Num∣bers answering to which, will be the Num∣ber of Drams, and Tenths of the Salt∣petre, Coal, and Sulphur desired.

• To Weaken the Velocity of the Com∣position of 1, 1½, and 4.
• 3377 The unequal Range 3.518531
• 2608 The equal Range 3.416308
• The Square of 64 Drams of Saltpetre 3.612360
• Take the half 3.510137
• Drams 56.9 nine Tenths of Saltpetre 1.755068

• The fourth power of twenty four Drams of Coal 5.520844
• The difference of the Lo∣garithm of unequal, and equal Ranges Subtract .102223
• Is the Logarithm of the fourth power, which being divided by fourth 5.418621
• 22 Drams 63/100 of Coal 1.354655
• ...

• The eighth power of fix〈…〉〈…〉 Drams of Sulphur 9632960
• The difference of the Loga∣rithm .102223 Subtract .102223
• Is the Logarithm of the eighth power which being divi∣ded by 8 9.530737
• 15 Drams 54/100 of Sulphur 1.191342

The Composition will be Sulphur 15½, Coal 22½, and Saltpetre 57; but if you quicken the Velocity, the equal Range will be in the first place of the Propor∣tion.

PROPOSITION XVI.

Tables of Ranges made with Mortar-pieces.

JUne 1. 1691. On Wimbleton-Heath at 15 deg. of Elevation, with a four Inch Mortar-piece, and a turned Iron Ball.

1	2	3
Experi∣ments.	Powder.	Chain.
1	½	213
2	1	652
3	2	1640
4	4	3377

August 24. 1691: At 15 deg. of Elevati∣on, with a 3½ Inches Mortar-piece, and a turn'd Iron Ball.

1	2	3	4	5
	The Chamber of this Mortar-piece a Frustum of a Cone.	The Chamber of this Mortar piece a Frustum of a Sphere.
	Powder	Chain.	Powder	Chain.
1	½	236	½	144
2	1	496	1	304
3	1½	800	1½	1258
4	2	1482	2	3394

•• April 21. 162. At 15 deg. of Elevati∣on, with a 3½ Inch Mortar-piece, and a turn'd Iron Ball.

1	2	3
Experiment.	Powder.	Chain.
1	12	303
2	24	746
3	36	1176
4	48	1820
5	60	2698

Thus have I given plain and easie Rules to the Young Pyrobolistes for the making of small Rockets; and also for the making of great Rockets, to them of a greater Knowledge and Purse, even such as was reputed impossible; for a 4 Inch Rocket was given in by our ablest Pyrobolistes to be out of size, and there∣fore impossible to rise. Now, if that 4 Inch Rocket was thought so, what will they say to them of 6, 8, 10 or 12 Inches Diameter; for certainly this Rule takes in all sizes to 500 or 1000 weight, or higher.

Necessary Tables for Rockets.

Inches and half Inches.	Pounds of Rockets. Ounces	Ounces of Compos. for Rockets.	Pounds of the Mall. Ounces
1	2 3	4	5 6
1	02	0••01	12
1½	08	0004	0002 08
2	001 02	0010	0006 0••
2½	002 04	0018	0011 11
3	003 12	0032	0020 04
3½	006 00	0051	0032 04
4	009 00	0076	0048 00
4½	012 13	0108	0068 08
5	017 09	0148	0093 12
5½	023 06	0197	0120 12
6	030 06	0256	0162 00
6½	038 10	0326	0206 06
7	048 04	0407	0251 00
7½	059 05	0500	0316 06
8	072 00	0607	0384 00
8½	086 06	0728	0460 09
9	102 08	0864	0546 12
9½	120 09	1016	0643 00
10	140 10	1285	0748 04
10½	162 13	1372	0868 03
11	187 02	1578	0998 04
11½	213 14	1805	••40 10
12	423 00	2048	1296 ••0

The Use of these Necessary Tables.

IN the first Column you have the Inches and half Inches, to 12 Inches. In the second and third Columns you have the weight of Pounds and Ounces of the Rockets, when six Diameters in length. In the fourth Column you have the Ounces of Composition to fill those Rockets 4 Diameters. In the fifth and sixth Columns you have the weight of the Mallets to drive those Rockets in Pounds and Ounces.

An Example in the whole, for a three Inch Rocket. I find 3 in the first Co∣lumn under Inches and half Inches; in the second and third Column, under Pounds and Ounces of Rockets. I find three Pounds and 12 Ounces the weight of the Rocket when finished, being 6 Diameters. In the fourth Column I find 32 Ounces of Composition to fill 4 Dia∣meters. In the fifth and sixth Columns I find 20 Pounds 4 Ounces for the Mallet to drive that Rocket.

When Rockets are of a great weight, the Mallet will be too heavy to manage, therefore do thus. The Mallet of a three Inch Rocket, viz. 20 Pounds weight is

of a good size; and we will make an Example of a 3 Inch and 7½ Rockets, and we will take it as useful that all Rockets to 3 Inches Diameter, may be filled with eight Charges, but further not, then a∣gainst 7½ in the first Column. In Co∣lum 4 I find 500 Ounces of Composition for that Rocket, which I divide by 8, and the Quotient will be 62.5. In the Para∣bola A H Z, let A H be the Number of Ounces 5062 5 in the Mallet for the 7½ Rocket, and A G the Number of Ounces 324 in the Mallet for a 3 Inch Rocket; then the Ordinates H Z and G Z will be the Forces of those Mallets; then as H Z is to G Z, so is 62.5 to 15.811, that is 15 Ounces and ^••• ₁₀₀₀ shall be your Charge of Composition. Further, divide 62.5 by 15.811, the Quotient will be 3. ^2•22/10000 the Number of Charges in the eight part of the Composition; then multiply 39529 by 8, there will be 31. ^••3 ₁₀₀₀ Charges in that Rocket. Lastly, give about eighteen blows to every Charge, with that Mallet for the 3 Inch Rocket, so your Work will be done, by two Men, in two hours.

• 324 2.510545
• 62.5 Squared 3.591760
• 5062.5 Sub. 6.102305
• 3.704364
• ½ 2.397941
• 15.811 is Sub. 1.198970
• 62.5 is from 1.795880
• 3.9529 Rest 0.596910
• 8. Log. 0.903090
• 31.623 Sum of 2 Logarithm 1.500000
• 15811 Add 1.198970
• 500. the Sum of Logarithm 2.698970

Iune 26. 1696. Then was fired a 4 and 6 Inch Rocket, Mr. Ayres Junior fired them both off a hand, Mr. Dandridge, Mr. Rodway, my self, and several other being present: the 6 Inch Rocket had 3 Inches solid Head, that is about the double of what it ought to have had, the Reason of that was to hold Fire; it moved off the Nails at about 78 deg. of Elevation, and the Horizontal Range was just 15 Chains, that is 330 Yards, by which we may find the Altitude of that Parabola it moved in, and the greatest Range, and Conse∣quently the greatest Perpendicular Alti∣tude it could have reached.

[illustration]

In the Parabola A B C, Let A C be equal to 330 Yards, A D equal to 165 the Angle D A E 78 degrees, then in the right Angled Triangle E D A.

• Radius 90 10.000000
• Tangent 78 10.672525
• A D 165 2.217484
• D E 776.22 2.889989
• D B 388.11
• As the Sine of the double of the Elevation 407 2.609594
• Is to Radius 1000 3.000000
• So is the Horizontal distance at 78 deg. 330 2.518514
• To the greatest Range in the Parabola 810.8 2.908920
• Half of the greatest Range is the Perpend▪ hight desired 405.4

So then the greatest height of that 6 Inches Rocket in its flight was three hundred eighty and eight Yards, had it been put Perpendicular, its height would have been four hundred and five Yards.

The flight of Rockets does sufficiently well agree with that of the Parabola at each end of the Quadrant; but towards 45 degrees it differs more.

A Rocket of an Inch and half Diame∣ter, filled 5 Diameters, and bored two and a half, and a little more, with this Composition, viz. 8 Powder-dust, 6 Salt∣petre, 2½ Coal, and 1 Sulphur, and layed to 30 degrees of Elevation; Ranged the Rocket 880 Yards, that is half a Mile.

To make Rockets to Swim upon the Water, Dive into the Water, and keep above the Water.

An Example of an Inch Rocket.

MAke the Case 12 Diameters, which will be in this Example 12 Inches, fill it with two Compositions, viz a Weaker and a Stronger; fill 2 Inches with the Weaker Compsition, then 1½ with the Strong, then 2 with the Weak, 1½ with the Strong. Lastly, 2 Inches with the Weak, then there will remain 3 Inches for Corn Powder, for the Report.

The Weak Composition to Swim above Water; take 3 of meal Powder, 1 of Coal.

The Strong Composition to Dive under the Water, and leap above the Water; take 8 of mealed Powder, 1 of Saltpetre, and 1 of Coal.

To divide the Driver.

FRom the lower end of your Driver set off 3 Inches, then 2 Inches, then 1 ••, then 2 Inches, then 1½▪ Lastly, 2 Inches; make the Rockets of a just length, and so you may see the Divisions of the Driver appear above the Case as you fill.

The Use.

FIre the Rocket in your Hand with with your Port-fire, through it into a deep Water, (otherwise it will stick in the Mud) it will Swim a little while; but when the Strong Composition takes fire it will Dive, and when the Strong Compo∣sition is spent it will jump up, &c. The Weak Composition being the last, the Rocket for some time will Swim upon the Water, and then give a Report. This Rocket is all Solid.

To make a Rocket Charger.

LET the length of the Charger E G, be one Diameter and half, the breadth of the Charger H Z, one Dia∣meter and one third, the length of the

Neck of the Charger that slippeth upon the Handle B C, two Diameters; the breadth of that Ferril A B, one third of the Diameter of the Rocket: betwixt eight or nine of these Charges will fill a Rocket 4 Diameters.

[illustration]

You may cut the Charger A B C D H G Z A in Paper, then it may be made in Copper, Close A to D, and B to C, Sod∣der both ends together; bring H G Z into more than half a round, and A B and C D in a round, put it then upon a Handle, then it is fit for use.

To make good Coal for Rockets.

TAke pieces of a light dry Deal Board about 12 Inches in length, and a∣bout the thickness of 2 Fingers or less; put them into an Oven, put fire to the Wood; when they are burned enough take them out, and put them into an Iron, Brass, or Eathern Pot, close it well with a Cover, that it takes no Air, the Fire be∣ing extinguished, beat it and pass it through a fine Sieve, then it is fit for use. If the Wood be not well burnt, put it in∣to the Oven again, and so repeat your Work: such Coal will make a Rocket fly very lively, if not with two much Life.

Compositions for Reports.

	A	B	C	D
〈…〉〈…〉 Saltpetre	9.	4.	3.	2.
Salt of Tartar	3.	3.	2.	1.
Sulphur	1.	2.	1.	1.

Take Sulphur 1, Tartar 3, and Salt∣petre 9, grind these well together, and dry them. A few Grains of this Powder being fired, will give as great a Clap as a Musket when it is discharged. Dr. French, pag. 171. Take any of these Ingredients

under A B C or D, mix them well toge∣ther, put a little quantity of that mixture into a Fire-Pan, set it upon the Fire, and in a little time it will give a great Report.

A further use of the Tables.

WHat is done in the 14 and 15 Pro∣positions, by taking the Cubes of the Diameter of the Bores of the Rockets, may be done by the Tables in 2 and 3, or Tab 4. Thus, look in the first Column for the Diameters of the Rockets, viz. 2½ and 4, and against them, in Column 2 and 3, I find 2 Pounds and 4 Ounces, and 9 Pounds, divide the greater Number by the lesser, the Quotient will be 4, near enough, so the Ratio of these two Rockets are as 4 to 1, and this is by the weight of the Rockets.

In the other Example I find 4 and 6 in the first Column, and against them 〈…〉〈…〉 Column 4, I find 76 and 256 Ounces of Composition for these two Rockets; then divide the greater by the lesser, the Quoti∣ent will be 3 and more, which is the same thing as if you made use of the Cubes of their Diameters; for indeed these Tables are made by the Cubes of the respective Diameters.