202 Captain Noble on the Ratio between the Forces tending to 



t iv * 2 +( sm J J 



U.cos^ *. sin (-£--g-l I 



in F 



Ar 



>. (25) 



Rr 



Mp 2 



r 1 ■ «• 



A; . sin — 



Hence 



R = 



£ . sin 



7T 



dt 2 ' 



h.i 



But 



v* 2+ ( sm J J 



d^_7JT ^ 

 dt*~ h' dt 2 \ 



and making the necessary substitutions, we obtain for the ratio 

 between the forces producing rotation and translation, 



R 2V 



sin 



7T 



(26 





(27rp 2 sin— + rhk) 



In precisely the same manner as in the former case, and on the 

 same hypotheses, we may show that if G" denote the gaseous 

 pressure in a bore rifled on the system we are now considering, 

 and G denote the gaseous pressure in a similar smooth-bored 

 gun, we shall have 



G"=G + R 



fi x h 



. IT 



sin— 

 n 



l^+'V?^!? 



• (27) 



J 



Hence if we have three guns of the, same diameter of bore, viz. 

 a smooth-bore gun, a rifled gun, the grooves of which are similar 



