€6 



Mr. G. F. (J. Searle on the Impulsive 



velocity is zero, the small change of velocity being the same 



in either case. ___ 



W 



Table IV. — Values of 



w - 



n. 



J/=0. 



■1=180°. 



•4,= 30°. 

 ^=150°. 



4/= 60°. 

 ^=120°. 



^=90°. 



'• 01 



1020 



1-018 



1-013 



1-010 



02 



1-085 



1-074 



1.053 



1042 



03 



1-208 



1-180 



1126 



1-099 



0-4 



1-417 



1361 



1-247 



1-190 



05 



1-778 



1-667 



1-444 



1-333 



06 



2-441 



2-222 



1-782 



1-562 



07 



3-845 



3-374 



2-432 



1-961 



i 0-8 



■ 



7716 



6481 



4-012 



2-778 



0-85 



12-986 



10-640 



5 949 



3-604 



0*9 



27-701 



22-091 



10-873 



5-263 



«-/§ 17. In § 32 of my previous paper I obtained approximate 

 expressions for the components of the radiated momentum, in 

 directions parallel and perpendicular to u, by treating w as 

 small from the beginning. It will be convenient to express 

 these results in terms of m Q =2/j,Q 2 /3a, the electromagnetic 

 mass of the sphere for infinitesimal speeds. 



If P M * be the component in the direction of u, then 



p _ m o™ 2 JL Ti 1 + w _ 2n(3-5?i 2 ') 

 u ~ v 'Sn* |_ g l-»i 3(l-?i 2 ) 2 " 



. . . /3 + w* l+n n(9-12n 2 -n 4 )\n 

 - Bm - + IT- l0g I^ " 3(l-n 2 ) 2 JJ 



= ?^(A-Bsin^) 3 



where A and B are functions of n. 



I For numerical calculations it is convenient to express P« in 



the form of a series, which we may use when n is small. Thus 



p m^r [1,2 , 2.3 ,., 3.4 B , 1 



. . a . f 3 34 , 117 , 276 . i"l 



* In the previous paper (Phil. Mag. Jan. 1907) the momentum in the 

 direction of u was denoted by P a and the momentum perpendicular 

 to u by P 2 . 



