PAPER BY PROF. OBERBECK. 163 



If we multiply the first by x the second by y and add we obtain 



dj\ = dW 

 dr dr 



or if we introduce the value of /i 



sr~*£+<i+o^ w 



If on the other hand the first of the above equations is multiplied 

 by y the second by x aud subtracted there results 



or 



Since furthermore 



df 2 _ c- dq> 

 dr ' dr 



'•''"+(* + O^=0 (25) 



r dr \ dr J 



aud 



d<p_ c 

 ~dr~ 2 r ' 



therefore we have in equation (25) an ordinary differential equation for 

 the determination of W im 

 If furthermore we put 



™=» (26) 



then equation (25) becomes 



d , dW\ , , .. rdW 



a f aw \ y o / ,a u \ 



This gives the following integral where A is the constant of inte- 

 gration : 



dW , A , 



dr /x—2 



This may finally be written — 



dr jx—2 



