184 . . PROFESSOR A. F, H. LOVE ON THE 



The right-hand members of these equations can be simplified by introducing the 

 functions # and r~ l dEJdr. We have 



1 d6 n r d /Id 



2n+l dr ~ r dr 2n+l dr \r dr 



1 (#0* , 2n dflA 

 ~2n-t-lVdr 2 r dr/' 

 and 



d6, 

 r-r-! 



2 + 



and thus the equation for P B becomes 

 d'P 2ndP p p 



T > r A- J: 



. , , 3 



"" 



2n+l\dr 2 r dr/ 2+lA 2 \dr a r 



I 



2n+ 

 by the equation (36). Hence we have 



where P' H satisfies the equation 



r dr 

 Again, we have 



1 df n = 1 d Jd*E. 2(n+ 

 r cZ? 1 ? dr 1 d?- 8 r 



+ 



r dr / J r dr J 



r dr V? 1 dr / ' 

 and 



,3 dE. _ d'E. 2(n + l) dE B 3 dE B 



/ ~T 1~5 1 7 ' J 



r r ar* ? dr r dr 



_ r d . 



dr \r c// % / ? dr 



