Motion of a Spinning Projectile. 345 



28. 1 he constants for the trajectory when w<1063. — 

 Another portion of the table given in section 24, for larger 

 ranges however, is given below. 



Xfeet 



3000 

 60'-l 



1803 



3600 

 85''7 



3085-2 



4200 

 118'-4 

 4972-8 



4800 

 159 N 5 

 7656 



5400 

 210'-1 

 11345-4 



6000 

 271 '-8 

 16308 



SX10- 2 ... 



PuttiDg X = 3000, X'=4800, 8 = 600 in an equation 

 differing from (28) only in having k' for &, we get 



^ ggo 1630800 _ 2269080 + 765600 _ 12732 

 497280-617040 + 180300 ~ 6054' 



whence Z 2 = 4840 approximately. 



To get r' it is better to take 8 as large as we conveniently 

 can. Putting, therefore, 8 = 1200 and X = 3600 in an equa- 

 tion similar to (26), we get 



7200 2400 



1630800 - 1 531200 + 308520 = r'e\ mo (e 484( ' - 1) 2 , 



180 j60_ 



or 408120 = r'e l2l (e 121 -l) 2 , 



whence r' = 223800. 



180 60 



Also 765600-308520 = 1200 q ' + r 'e™(e 121 -l), 

 and therefore q' = - 148*93. 



Lastly, p' is obtained from the equation 



180 



308520 =p' + 3600^ + r'e isi, 



which gives p' = 145900. 



The equation for y when u < 1063, that is, when the range is 

 greater than 700 yards, is 



X 7 = 223800£ 2420 -145900-148-9;X, . 



(34) 



the angle 7 being expressed in minutes. 



29. 1 he constants for the Mark VI. bullet. — By applying 

 similar methods to the results given in the range table for 



