Motion of a Spinning Projectile. 359 



liberty to assume one relation between these variables. 

 Suppose, then, that 



p dT* +Z dTdT'"' ' ' • ' ^ 0) 

 Then (57) and (60) give 



%-p&h"-° < 61) 



Multiplying (60) by p the equation becomes 



dT\ p dT/ ' 

 whence 



dfL _ E 2 



dT~ p 2 > ' 



where E is some constant. Again, from (61), 



(62) 



1 ,-72 



Now, there is no reason why - -^& should be a large 



quantity, and we know that a is large. Let us suppose, for 

 the moment, that the latter is much larger than the former. 

 Then 



I -j£ j = a approximately, .... (64) 



and consequently 



E 4 

 P 



(f-l)im rf. 



m rp rp2 



(65) 



55. We can now show that the approximation in (64) is 

 justified, for we get from (65) 



log # p=log # E-±log,<r. 



Therefore, 



p dT' ~ 4 a dT 2 + 16 V d£) ' ' ' [ } 



Now the largest term in a is m 2 , and this term disappears 

 from the differential coefficient of cr. Consequently both 



