Page:History of the Royal Society.djvu/264

 ''then must the Axis of that Cylinder in which the Bullet moves cross the Axis of the Mark, beyond which interjection the mark being placed, the Bullet must be carried necessarily wide of the Mark on the contrary side to the recoil of the Piece. ''

Let $$ad=a. $$

and $$d c = r. $$

and therefore $$a b = r - \surd : r^2 a^2 $$

Therefore $$a b. a d:: r - \surd : r^2 a^2 a : : I. x$$ (x being any given quantity.)

Wherefore $$a= x r-x\surd: r^2a^2: $$

and $$x \surd. : r^2a^2 : = xr - a. $$

Therefore $$x^2 r^2 x^2 a^2 xr^2 - 2xra + a.$$

Therefore $$2 x ra = x^2 a^2 + a^2 $$

Therefore $$axr = a x^2 + I$$

Quod &c.

f e k = f l p = p h m = the Angle of Recoil p h n ''the Angle of Reflexion made at the parting of the Bullet from the Piece. When p h n > p h m (m h being always parallel to f g) then must h n intersect f g if continued.''

''Some other Experiments I have also made with another Piece (about the same length, but of a bore near two tenths of an Inch less) and ordered in the same manner; and do find, that with a small charge the Bullet is shot (thence too) wide of the mark on the same side on which the Recoil is made, and with a full Charge wide the contrary side. ''