Motion of a Spinning Projectile. 371 



Since r contains the factor /, and t does not contain /, it 

 follows that the expression on the right of this last equation 

 does not involve I at all, and is therefore continuous as u 

 pusses through the value u x . Integrating (103) we get 



-» = (/-»? (0}CH-t3-(2+/)(3+/)P+. . . . } . (104 ) 



If Z 2 denotes the linear deviation of the shot correspond- 

 ing to this angular deflexion of the line of: flight, then 



dZ 2 . 



——=77 approximately 



Therefore, 



Z 2 = I77^X, 



= I77WC/T, 



j dr 



7)1-, 



-J- 



=</- 1 ^(£) 2 { D+cl °g« T+ i T3 



-(2+/)(8+/5y,T» + }. . (105) 



The constants C and D have to be determined so as to 

 make Z 2 and its rate of increase both zero when u = u . The 

 constants so determined will, however, only be applicable 

 when u is greater than 1060 feet per second. The new 

 values of the constants that must be used when u has fallen 

 below 1060 have to be determined so as to make Z 2 and its 

 rate of increase continuous when i< = 1060. 



74. In the case of the rifle-bullets, which are the worst 

 cases of all spinning shot, we have shown that the value of t 



probably does not become much greater than — at effective 



«v 

 ranges. Consequently, the ratio of the magnitude of the 

 term containing t 5 in (105) to the term containing t 3 pro- 

 bably does not become greater than 



1 (2+/)(3+/ )3 2 



9 a p 5 2> 



