produce Translation and Rotation in the Bores of Rifled Guns. 199 

 tions of motion, 



M -S= G -vfei^ +1 ^ • • (10 > 



<P<t> _ Br *-/» . n i v 



^ 2 ~ */l+P ' Mp 2 ' (L1 > 



and hence the normal pressure on the rib of the projectile, 



IV VTT¥ d?± 



r ' k-^ 'dfi ' 



But if -cr be the angular velocity of the projectile, and h be the 

 pitch of the rifling, we have the following relation between the 

 velocities of translation and rotation, 



_d(f> _ 2-7T _ 2tt dz 

 ~~ dt~~ h ~ h dt 



Hence 

 and 



d*$_2w d*z 

 dt 2 ~~ h ' dt*' 



r k-fi x h df* ' 



d*z 

 Now substituting in this equation the value of -^ derived from 



(10), we have 



(13) 



or 



B_ 27T/QVTTI 2 



And this equation gives the ratio between the pressures produ- 

 cing translation and rotation. 



We now proceed to determine the increment of the gaseous 

 pressure due to the resistance, &c. offered by the rifling to the 

 forward motion of the shot. We shall imagine a smooth-bored 

 gun to fire a shot of the same weight as that of the rifled gun. 

 We shall further suppose that the two projectiles are delivered 

 with the same velocity ; and we wish to know, the same ballistic 

 effect being produced by the two guns, what is the increased 

 pressure which the rifled gun has had to sustain. Now the 

 equation of motion in the case of the smooth-bored gun is 



m S= g > • • • < i4 > 



