﻿460 Mr. Gr. B. JefYery on the Tiro-Dimensional 



From (4) d I J /I d / d<r\\\ n 



and hence ylr=Ar 2 logr + ~Br 2 + G \ogr. . . . (V.) 



Next seek a solution for which i/r is a function of 6 only- 

 Let 



then 1 



V*^ = ^0" 



V ^= J (4©" + ©'"'). 



Substituting in (4) 



20'6 // = 4^®'' + ^0" // . 

 Integrating 0'- = 4^0' + v%" f + a, 



or „ /^f <Z®' 



'3v f d®' 



2 J v /0 7s -Gv© /2 -3rt0 7 ^-3/> 

 This may be written 



-#-f 



j9 ' 



J V{%' — X.)(®' — ^(S'-fo + x + n)' 



where \, ^ are constants. 

 Write 



0' = A, sin 2 <j) + fju cos 2 (/>,, 



and the integral becomes 



Finally introduce new constants, /j, »i 





\ — 



P ^2_^~ X —' 2 ^ 



in 



and we have 



^t=S' = 2z/(l - »r - Pm 2 ) + 6i/& 2 mV{™(<9 - <9 ) } (VI.) 

 where &, ?«, # are arbitrary constants. 



