4 ON RIFLED GUNS. 



we have 



dW jr 2 TT . / , y\ 



Differentiating again, and dividing b} r (//, we find 



>--0*9 + &*0^ 



dl 2 2n.l r ' ■"""" V a " lj^n.l"""\ 2 "' I J dt 2 ' ^ G) 



(5) — Dividing equation (5) by 2 -, and denoting the number of turns of the missile in a 

 unit of time by v, we find 



At the mouth of the piece, y = l, and 



" = ST/ V < 7) 



(6) — Denoting the distance passed over by the projectile while turning once on its axis 

 by d, we have 



7 V 2 n. I 

 *=.-_=-—. (S) 



(7) — The passage of the missile from its place of rest to the mouth of the piece is a caso 

 of constrained motion, and the conditions of constraint are given by Eq. (4.) 

 Make the following notation, viz: 



P = intensity of the force on back of the projectile in direction of axis. 

 M — mass of the projectile. 



I = moment of inertia of the projectile with reference to axis of piece. 

 N z= normal pressure on edge of land. 

 /= Coefficient of friction. 



6 = Angle of inclination of an element of the twist to axis of piece. 

 s= Any indefinite arc of the helix. 

 Then will 



(P-M.^).^-I.^.^-/. N ., g= o. ) (A) 



3 j — j). sin 3. '1'' -\- cos 0. 3 y; j 



which latter substituted above gives 



(P. - M. ?— f . -/. N cos o\ Sy — (l. '-— +f. N. p. sin o\ 3 W= 0. 



From Eq. (4) we have 



M r+ [r- ^(l-cos(i ,.?))] ,, _■* ,. sin (i ,f). ^=0. 



or, Eq. (4), 



p- * r- £^. ,>. sin (i *. ^ Vy = o. 



(5/1 = 0. 

 (316) 



