11G Prof. H. Lamb on the Uniform 



TVe thus obtain the solution 



2k a. 



-x< 



(22) 



2k o,j ' 



W ~ 2k §i ' 



which is easily verified. 



The equation (20) may be written 



the solution of which is well-known, the simplest type being 



(23) 



-Kx 



%=C<? ~ h '\r. Adopting this, we have, finally, 

 "~ fa + 2k fa x ' 



__M , JL <& 

 e_ by + 2k fa > 



u -~fa +2*3.- ' 



• (24) 



w lie re 



% = 



Q e -Hr-x) 



(25) 



Since ^ must obviously involve only zonal harmonics of 

 negative degree, we write 



A 



+ A 1 |-i. + A J 



For small values of Zr we have 



ki 



>m 



+ 



ri /l . £i« \ 



(2(5) 



(27) 



which leads to 



2/c^ * 2k\'6r ~dx r + 3 ^ 2 r ""/ ' 



.},1(28) 



2/c\ 3yr + 3 



2«y ■ 



h*2L = -£/ _ B - X ■ Az 2 B 2 l 



3 2 1 



2 A- 3. 



2A L 





■}• 



