Motion of an Electrified Sphere. 61 



the resultant momentum in the pulse formed on stopping the 

 sphere 



*-*{(*>#;-£} • • <«» 



_U f4n 1 3 8n t 5 12m 7 1 



This result agrees with that given in § 19 of my earlier 

 paper. In Table III. the numerical values of Piv/U are given 

 as well as the ratio of F 1 to M 1? i. e. the ratio of the momen- 

 tum carried off in the pulse to the momentum of the field 

 before the velocity is destroyed. It will be easily seen from 

 (39) and (44) that, when n y is very small, P 1 /M 1 = n 1 2 5. On 

 the other hand, when n x approaches unity, only the logarithmic 

 parts of the expressions for P x and M x need be considered, and 

 we find that although both P x and M 2 tend to infinity, their 

 ratio Pi/Mj tends to UDity. 



p t , p 



Table III. — Values of Tt - and of ^- . 

 b iVi! 



n 1 . 



p 1? VU . 



P./M,. 



0-6 



PWUo- 



Px/Mv'J i 















0-08308 



0-08728 



o-i 



0-00027 



0-00201 



0-7 



0-15699 



0-12988 



0-2 



0-00221 



0-00816 



0-8 



0-30113 



019239 



0-3 



000780 



0-01878 



085 



0-43029 



023664 



0-4 



001977 



003459 



0-9 



0-61711 



029702 



05 



004237 



005676 



10 



OO 



1-00000 



If the " impulse " of the force which stops the motion of 

 the sphere be I l5 then 



M 1 -I 1 =P 1) 



and hence, by (39) and (44), 



Ii-Mx-P, 



v IV nfj n l-"i nj 



Since (1 — -«i)log(l — ?2]) tends to zero as n x tends to unity, 

 it follows that the limiting value of I is 2Uq/v. 



Thus it appears that if a charged sphere moving at the 



