246 Mr. J. J. Thomson on the Electric and Magnetic 



1 c 



■ . For values of r<H we may, as before, substitute 

 o 



W If (^Q*) for Jf 7 in the inte 8' ral - Now 



df {lili) - 8~~ ""' 



. - . the integral 



o- rrr»- 2 (3w 2 -r 2 )(36w 2 + 122 2 -48^ 2 ) , , , 

 = RsJJ J — 8? '-dlfydz. 



uTTCT 



By transforming to polars, this may be shown to be -rrr- 



Adding this to the part of the integral due to values of r > It, 

 we get for the coefficient of vv f 9 



hair 



As before, the coefficients of uv' 9 vu' 9 uw r , &c. disappear by 

 inspection. 



The coefficient of ww f 



= <r{((r 2 d " * - 1 dxd dz- 

 ' JJJ ty dz r dy dz r' ^ ' 



d? 1 d? 1 



substituting, for values of r > K, as before -j— ^ — for 



in the integral, it becomes ^ dz T ** dz T ' 



J J J ~l^ dxdydz > 



1 2r77T 



which, by transforming to polars, may be shown to be ,-p . 



1 d 2 ^ 

 For values of r < It we may, as before, substitute ~& -t — r-C^Qi) 



^2 ^ J Wdydz K ^ 4/ 



for ~ — r— - r in the integral. Now 

 dydz r' & 



On making this substitution, the integral 

 <r fff V«> , , , 3<7„- 



Adding this to the part obtained before, we get for the coeffi- 

 cient of ww' ', 



12<T7T , 3<77r 



__ + _ )0r3 „r. 



From the part of j I 1 H — dxdydz which arises from that 

 part of H due to e and that part of -=- due to e f , we can see, 



