6$ 



Mr. Gr. F. C. Searle on the Impulsive 

 Table VI.— Values of --^- =-C sin 2iK 



7?'. 



C. 



i 

 | 



1 



vPtj 



m w 2 . 





; <j/= o°. 



i//=75°. 



1 ^=30°. 

 ^ = 60°. 



^=45°- 



o-i 



0-0051 







0025 



00044 



0-0051 



0-2 



0-0106 







0053 



00092 



0-0106 



03 



00172 







0-0086 



0-0149 



0-0172 



0'4 



0-0256 







0-0128 



0-0222 



0256 



05 



00375 







0-0187 



00325 



0-0375 



06 



0-0560 







00280 



0-0485 



0-0560 



07 



0-0888 







00444 



00769 



0-0888 



0-8 



0-1606 







0-0803 



0-1391 



0-1606 



0-85 



0-2382 







01191 



0-2063 



0-2382 



09 



0-4039 







0-2020 



0-3498 



0-4039 



§ 18. I shall now consider the energy and the momentum 



which are radiated when the impulsive change of velocity 



affects the direction but not the magnitude of the velocity. If 



the direction of the velocity is changed by the angle a, we have 



u 2 = u 1 = n 1 v, 



w 2 = 2?/ 1 2 (l — cos ol) = 4721V sin 2 \ol, 

 t»V — UiU 2 2 sin 2 a)*= 2n^v 2 sin Ja(l — n* cos 2 i<x)^. 

 Hence, by § 11, we have 



W 1 , 1+Z 



u -z lo si^z- 2 ' 



where 



y _ 2ni sin -J a(l — n 2 cos 2 -J a)* 

 1 — ft! 2 cos a 

 When n x is small, the numerical calculation of W/Uo is best 

 made by the series 



U 13 + 5 + 7 + -J' 



which, by § 11, is always valid when n x is less than unity. 



If the denominator of each term of the last series be ex- 

 panded in powders of n 2 , we obtain a double series in n 2 . This 

 can be rearranged in the form of a single power series in n 2 y . 



