Motion of a Spinning Projectile. 369 



below ui, at which the law 'of resistance changes, and these 

 new constants are determined by making a, y, and their 

 rates of increase continuous at the critical point where 



69. Deviation due to Wind. — In equation (47) we have 

 found the angular deflexion, 77, of the line of flight due to a 

 wind perpendicular to the trajectory. But the useful form 

 of the result will give the linear deviation of the shot from 

 the plane in which it started its motion. If Z x denotes this 

 linear deviation, then 



-~ = tan 7} = rj approximately, 



u u 

 Therefore, 



Y*X 



id A. w Y 

 Zji = w\ ■ —A, 



J u u 



= w 1 



*udt w ^ 



J u u ' 



=H'-|> (100J 



a result attributed to Colonel Younghusband in GreenhilPs 

 4 Notes on Dynamics.' 



70. The values of t and X can be obtained from Bash- 

 forth's tables giving T v and S u , and thence the wind devia- 

 tion can be calculated for any range X. We may also 

 calculate the deviation in terms of X by using the expressions 

 for t given in equations (3) and (15) . By means of these 

 equations we find 



Z 1 = — Ale 1 -1-X\, . . . (101) 

 u L J 



when X<X X , 



and 



^-S+fp" 1 - 1 )' 



(102) 



when X>Xj. 



In the following table for wind deviation the first two 

 columns of values are calculated by means of Bashforth's 

 tables for T v and S v , and the last column by means of 

 equations (101) and (102). The good agreement between 



