Motion of a Spinning Projectile. 367 



justifies us in assuming that a good value of <j> is obtained 

 by carrying the series only as far as the point where the 

 terms are small. 



65. As we are only going to use a few terms of the series, 

 we may make use of the relation (90) between the coeffi- 

 cients. Then the result is 



*=(/-l)f {-^T + ^T- (f)W)T3 + . . . .} 



=(/-*) ?f:{-.r-^ 



+ (2+/)t3-;(2+/)(3+/)t4.../J, . (93) 



where 



_2mT_lB(ol gA 

 fr ~ f A uWcl 



/ Wcu Q u 



(94) 



Using equation (76) to eliminate co from this, we get 

 1 2?rB£ u _ 1 2?rK 2 w 



T ~fmvcdu " / n^ M ' " • ■ (95;) 



where K is written for the radius of gyration of the shot 



about its axis. The coefficient of — in the last expression 



for r is the same for all similar shot, provided N is the same 

 for all, for c is proportional to the linear dimensions of the 

 shot. For the rifle-bullets, for which N is 33, 



d 44 

 T ~ /c7x33: 



U 



< 8 u 



d 1 u 

 = fc 42 u' 



. . . 



(96) 



4 

 If we assume that c= ~d, 



then 









1 u 

 T ~ 56/ u "' 



1 

 "56/ 



when w = w . 



• • 



(97) 



When u has dropped down 



to ~ M , about 480 



feet pei 



r sec. 



r the Mark VII. bullet, the 



m 









T = 



3 



= 28/' 





2C2 



(98) 



