PAPER BY PROF. OBERBECK. 163 



If we multiply the first by x the secoutl by y aud add we obtain 



dr " dr 

 or if we introduce the value of /i 



'Lf=_fc'^+(A+r)'^ (24) 



dr dr dr ^ 



If ou the other haud the first of the above equations is multiplied 

 by y the second by x aud subtracted there results 



dfi _ _ f- dq) 

 dr ^ dr 



or 



fc^+(A+r)^=0 ...... (25) 



dr dr 



Since furthermore 



r dr \ dr 



and 



dcp__c 

 dr~ 2*' 



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

 the determination of Wt. 

 If furthermore we put 



~ = ^^ (26) 



then equation (25) becomes 



d / dW\ , , ., / dW . 



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

 gration : 



dW , . A , 



dr j^—2 



\ This may finally be written — 



d\V , 1 . A 



dr ^ /x—2 



