ON RIFLED GUNS. 



dt 2 dt 2 



d 2 ¥ 



Substituting the value of — -g-, as given by Eq. (G), we find 



, 2 P - A 1 . 1. -^- cos (\ -. ? \ X 2 . 



M + Ai.L^rinA*.?) ' 



n.l 



Multiplying both numbers by M, and subtracting from P= P, 



P-M. 



d 2 y 

 dt 2 



^• L ^0«-i) 



P + H.V 2 . ^.cotA-. 



(14) 



d 2 y 



Again, substituting the value of -j: f , as given in Eq. (G), we find 



di 2 



d 1 '/-• - 2 . 



-TV = ,• SHI 



dt 2 n. I 



I d 2 <F _ I X 3 



/< di? j> n. I 





(15) 



Before the value of A 1 can be employed, it will be necessary to find cos 8, and sin 6, in 

 functions of y. For this purpose we have 



sin : 



V^-hv Vi + ^ V 1 ^-— (H)' 



<fy 1 1 



V 



COS : 



>-* ,/ 1+ ^ 7i + ^^(*.o'i 



(16) 



which substituted in the value for A 1 , a will disappear, and give 



i , ,*,.m & . 



f+P- 



7:2 ■ ( x y 



,. Sill I + 7T. - 



, ( l-/,.^. S in(^.0) 

 and making A=A'/), the formula will stand 



!-/.„.£. sin (**?) 



(17) 



(318) 



