Motion of a Spinning Projectile. 373 



Also, when u=Ui 



J i-'-r » {!-$}• • • <™> 



76. When u has fallen below w„ the factor / 2 in (106) must 

 be replaced by l x 2 . Then it is convenient to write the 

 equation in the form 



Z 2 -Z 2 '=t^ CB l *{D» + 0"log.jS +(^- ) 3 }. (Ill) 

 To make Z 2 = Z 2 / when w = w n we get 



Again, from equation (111), when u — u lf 



S-¥ G '-{-?-¥}.-- "«> 



and to make the rate of increase of Z 2 continuous we must 

 make the right-hand sides of (110) and (112) equal. Hence 



Thus, when u < w l5 



Z 2 _Z/ = /=- 1 G© 3 {^g) 3 -V 



-3(^+4 -*) log. S} 



_3^^ 1 (^ + P^-^)}.(113) 



Equations (108) and (113) give the amount of drift at all 

 effective ranges. 



77. In the expressions for the drift of a shot we have the 

 very uncertain number/, as well as the quantity c, involved 

 in G, which we can only guess at. But since these quan- 

 tities occur as factors in our expressions, we can at least 

 give the ratio of the drift at any one range to the drift at 



