To cut the rigging and proposals for the improvement of great artillery / by Robert Anderson.

To Cut the Rigging.

LET A be one Ship, and B the other, and B C the Rigging to be Cut in the Point E.

PROPOSITION I.

The greatest Range of the Piece in the Parabola, the Line of Impulse, the Ascent, or Height of the Rigging to be Cut, and the Angle of Elevation being given. To find the Horizontal Distance, or the Distance from one Ship to the other.

[illustration]

Then, In the Right Angled Tri∣angle ABC, the Angle BAC, the double of the greatest Range in the Parabola G, of the Culverin; the Line of Impulse AD, and the Per∣pendicular Ascent BE, or the Height of the Rigging to be cut with this Qualification, as G:DC::DC:CE being given. To find AB the Distance of the two Ships.

Then R:r + Z::S:BC, that is rS + Zs / R = BC in Diag. and Z²/G = CE in Diag. then Z² + PG / G = BC in Diag. that is Z² + PG / G = ZS + rS / R that is Z²R=ZGS + GrS − GPR.

G= 9374 the double of the greatest Range of the Culverin.

BE=P= 5 Paces, 5 foot to a Pace.

AD=r= 106

Sine of 8^d=S= 13917

Rad. =R= 100000

DC=Z= 1371.31

The Equation in Numb. Z²=Z1304.57958 + 91415.43548

A Method to extract the Roots of square Equations.

Take half the Number of the Coeficient. To the square of that half, add or subtract the absolute Number, according to the Sign + or −, then extract the square Root of that Sum or Difference, which Root added to or subtracted from the half Coe∣ficient, the Sum or Difference will be the Root of the Equation.

Example. Half the Coeficient is 652.28979, its square is 425481.9701382441, to which add the absolute Number 91415.43548, the Sum is 516897.4056182441, whose square Root is 718.95, which added to the half Coeficient makes 1371.24 the desired =Z. Geometrically thus,

[illustration]

In Fig. Z, If OD be made the As∣cent, and DE the double of the great∣est Range in the Parabola, DC will be a mean Propor∣tion. In Fig. Y, If AC be made Ra∣dius, and CB the Sine of the Angle of Elevation, and AD the Line of Impulse, then DE will be a fourth Proportion. In Fig. Z, If RC be made equal to DE in Fig. Y, and CD in Fig. Z, be made equal to the double of the greatest Range, then CA will be a mean Proportion. Further in Fig. Y, if AC be Radius, and CB the Sine of the Angle of Elevation, and AD be made equal to the greatest Range in the Parabola, then DE will be a fourth Pro∣portion. Let DF in Fig. Z, be made equal to DE in Fig. Y, then AL will be the Line desired.

GP = square of DC, and GrS / R = square of AC, also because the sine of GP is −, and GrS / R is +, therefore the square of AD is the difference of those Squares, 47. I. Euclid. and GS / 2R = the Line DF, therefore the Square of DE + the square of AD is = the square of AF, which Line AF + DF = AL the Line desired.

By Logarithms.

G 9374	3.971925	G 9374	3.971925	G 9374	3.971925
r 106	2.025306	8 deg. S	4.143555	P 5	0.698970
8 deg. 8.13917	4.143555	GS	8.115480	GP	4.670895
Sum Log.	10.140786	2R subst.	5.301030	DC	2.335447
R 100000 sub.	5.000000	DF 652.31	2.814450	CA subst.	2.570393
½	5.140786			Sine of DAC	9.765054
CA 371.87 is	2.570393			tang. of DCA	10.145085
				DC	2.335447
r= 106	AD from	12.480532
Z= 1371.24	DF subst.	2.814450from
r + Z=AC 1477.24 3.169468	tang. of AFD	9.666082
Sine 82. 9.995753	sine of FAD	9.957736 sub.
AB 1462.9 3.165221	AF 719.	2.856714
				FD 652.31
				AL 1371.31

A	B
Deg.	Hor. Dist.
3	606.01
4	790.66
5	965.35
6	1134.6
7	1300.2
8	1462.9

In the Column A the Deg. of Eleva∣tion, to hit an Object at the Horizontal Distances in the Column B, at the As∣cent of 5 Paces with a Culverin.

Two Ships lying at the distance of 1135 Paces, the Culverin requires 6 deg. of Elevation, charged with 10 Pound of Powder, to hit the other Ship at 5 Paces above the plain Parallel to the Horizon where the Gun is mounted.

Here note, The Distance between the two Ships is to be taken by Instrument, or by good Estimation.

Of a MUSQUET. PROP. II.

A Musquet-Barrel made a little wider towards the Britch than forward, the Britch-pin easily to screw in and out, to take aim at the Mark by the in∣side of the Piece, fixed fast with Timber and Screws, with a Ball fitting the Muzzle of the Piece, charged with half an Ounce of Powder, put to a Mark, Ranged the Ball in a right Line 200 Yards, or 120 Paces (won∣derful exactly) if not farther. Wimbleton-Heath in the Year 1690.

By this we find the greatest Range of the Musquet thus,

The Line of Impulse of the Saker	124	2.093422
The greatest Range of the Saker	5654	3.752356
The Line of Impulse of the Musquet	120	2.079181
The great. Range of the Musq. proxime that is, more than 5 English Miles.	5472	3.738115

By this, and what is said at Prop. VIII. To Hit a Mark, the Futura of a Musquet is known.

There are Fowling-Pieces whose Length of their Chases are 8 Foot, the Diameter of their Bores Bastard-Musquet, that is 7/10 of an Inch; such a Piece (cer∣tainly) will Range its Ball 10 Miles (the Air excepted). What Use may be made of this, I leave to ingenious Persons that delight in these Matters.

Here some cry aloud against these great Ranges, but what my Hands act, and my Feet measure, and my Eyes see, I shall freely assert, and endeavour to main∣tain.

Of GRANADOES commonly call'd blind. PROP. III.

SUch are those Granadoes which have no Fusce burning in the flight, but has a Steel and Flint or Firestone placed within the Granado, to fire the Powder when it ar∣rives to the Earth; the Description of which is set down in Casimire in his great Art of Artillery, Part I. Book IV. Chap. 3. in Plate marked M, Fig. K, Numb. 121; as also the Cy∣lindrical Fireshot, the Spheriode with a Dovetail to be screwed in, to direct it in its flight, Boxes to be fill'd with small Granadoes and other things of consequence, to be shot either out of the Mortar-piece or Long-Gun, are treated on in the fore-cited place, and therefore saves the labour here.

These, with many other things belonging to great Ar∣tillery lie fair from Improvement.

PROP. IV.

IN the Year 1673. I published my Genuine Use of the Gun, upon the Principles of Galileus without any accidental Impediment, that is, that the Transit of the Bullet to be in the Curve of a Parabola, and from that to Hit a Mark at demand within the reach of the Piece Analitically, as well upon Ascents as Descents, as upon the Plain of the Hori∣zon. In the Year 75, Mons. Blundell in his de jeter les Bombes, pag. 283. propounded that Problem to the Royal Academy of Sciences of France, to be resolved Geometrically, Mons. Buot, Romer the Sweed, and Mons. de la Hire set upon the Mathematical Part, from Page 285. to Page 312. of the said de jeter les Bombes; whilst Mons. Marriott and Perault made many Experiments several times repeated be∣fore the Royal Academy, Mons. the Dauphin being present,

viz. with Water, with a Bow, with a Cross-Bow, a Stone-Bow, an Engin in imitation of the ancient Balistes, with a Pistol, and with Quicksilver, all agreeing precisely with that of Galileus de jeter les Bombes, pag. 490. For which Service the French King made Mons. Blondell Master de Camp and gave him about 200l. sterl. a Year, as I am cre∣dibly informed. Whilst the French Mathematicians and Philosophers were a trying the Truth of this noble Inven∣tion of the famous Galileus, for the carrying on of their Warlike Designs; here in England some Persons made Ex∣periments upon Black-Heath, and near Newington-Butts, but what they amounted to I know not.

By these means the French Engineers sling their Shot as exa∣ctly as the Benjamites, and ours in England remain as at first.

But as I have been at some Pains and Charge to bring the Use of Great Artillery to a greater perfection than formerly, in my Genuine Use of the Gun, and in a Treatise To Hit a Mark, so now, I move forward, that ingenious Persons may be instructed in that Art, so they may be capable to serve, and to be an Honour to their King and Country.

In order to which: For the Improvement and Practice of the MORTAR.

LET there be a firm Platform, and a Mortar-piece about 6 Inches diameter, with a fit Ball, mounted in a Carriage to move from an Horizontal to a Vertical Line, and to be firmly fixt to any degree and Minute at demand, and even ground for two Mile in length; such a Platform, Mortar-piece, and level Ground, is fit for extraordinary Service, and to instruct the Gunners, that so they may see

and understand the Ranges of their Piece, and learn to strike any Mark at demand within the reach of the said Piece.

The Gunners to be instructed one day in a Week through∣out the Year, and upon publick days to shoot for a Piece of Plate given by the King, tho to the value of 5 s. in doing which, His Majesty will be no Loser if Wars continue.

For the Improvement and Practice of LONG-GUNS.

LET there be a firm Platform to mount the Guns upon, and 2 or 3 Mile of Ground to Range the Shot, and a moveable Butt to be set up perpendicular to the Horizon, the Gunners to be practised one day in a Week, and to shoot for a Piece of Plate on general days; such a Method will make them expert Gunners, and that Prince that will not use some such Method to exercise his Gunners, will lose a great deal more than that Charge comes to when he puts them to Service.

If any make Objections, and say, That the Gunners cannot practice that of the Parabola.

To which I Answer.

I'll take a Gunner of the Capacity of a Youth of 14 years of Age, and teach him Arithmetick, and so much of Geome∣try that is requisite for Practice, and learn him the Use of the Mortar, that he shall be capable to strike any Mark at de∣mand within the reach of the Piece when it is demanded of him, and to teach the rest of the Gunners to do the like.

But,

If the Gunners say they can strike any Mark at demand within the reach of the Piece according to that of the Parab.

Then, To conclude my Endeavours.

Concerning the Improvement of Great Artillery, I freely offer to be at the Charge of Platform, Mortar-piece mounted, Powder, Ball, and all things necessary for extraordinary Ser∣vice, and a Medal of Silver, if they whom it chiefly concerns will command the Gunners to endeavour to strike a Mark at any place within the reach of the Piece, and he that comes nearest the Mark with the most rational Rules of Art, shall have the Medal of Silver.

Not to omit the Example of two eminent Soldiers.

When the Lord Fairfax besieged Worcester, he had a Scotch Man for his Engineer; Nathaniel Nye, a very young Man, went to the L. Fairfax, and desired that he and the Scotch Engineer might have a fair Tryal with their Mortar-piece against the Town, and he that did the best Service, should be the L. Fairfax's Engineer; to which the L. Fairfax readily answered, All the reason in the world. The said Nat. Nye blew up the Magazine, which forced them to surrender, for which he was made the L. Fairfax's Engineer, and Master Gunner of Worcester. From an eminent Person now living that was an Eye and Ear Witness.

Oliver Cromwell sent for Mr. Wright, a Joyner by Profession, and took care of his Family, sent him to the Siege of Dunkirk, with 2 Eighteen Inch Mortar-pieces, which were so well managed by the said Wright and one Stint, that the first Gra∣nado they threw into the Town fell near the Town-House, and made such a prodigious Breach, that the Governur of the Town set up the white Flag immediately, and capitu∣lated.

But, when unworthy Persons and Relations were preferr'd the Government dwindled to

FINIS.