40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



Q = /dV _dF\d<p /dV _dF\l-fi 2 d<p /dV _dF\ 1 d<p 



~\dr Br)~dr \djt ty / ~r*~" dp dX dXj (1 - ft^'dX 



1 J \dr J \dr J r \b\ J (1 -p 2 )r 2 J d<p 



+ 2 * dr ' dr 



f^y + /a^i-^ + /a^y i \ 



1 I \drj \dfi/ r \dl/ (l-/( ! )rj 1 - /r dp 



2 dp t dp 



1 I Vdr/ Vfy/ r 2 Vd/l/ (1 - ,« 2 ) rf (I - p 2 ) 6? 



+ 2 3/1 r 2 ~&l 



faj(i-„ 2 V^ f 3 V\ 

 + i 7 j IV / ajtc J + \ap/ + r a 2 (,^) 



L a// l — p 2 dr 



where, finally, V, F, and <p are each to be replaced by a converging 

 series of the form 



aP°+ pP' . . . . + vP (n) 



and where the series for V and F will contain known functions of 

 r and known constants, but the series for <p will contain similar 

 terms whose functions and constants are to be determined. 



In order to obtain an approximate idea of the practical solution 

 we may take the above given value of V, 



V= ( r R 2 ) i + /jLW( Ur.y-1), 

 r \ZRj \2RJ 



which agrees with the form of the converging series when we put 



$ - d = £ = . . =0 



and further take for the function of F the following. 

 F = a + br + c (p. 2 - $) 



