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.

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.