and on Co-resolvents. 



183 



16. From (6), that is to say from 



cl}x 



If. dt ~ clx 

 ~dt 

 we deduce by integration 



iog.(..»)=iog.{cr|f) } 



(8) 



or 



dt 



and by differentiation 



2_ dHi 

 u' df^ 



w 



r d It ^ 

 [-dt.) 



d'x 

 d t' 



d'x 

 dt^ 





d X 

 dt 



dx 



and (8) enables us to write (7) in the form 



1 ^1:!^ 



It ' df 



2f- 



d^ 

 dt 



+ r 



dx 

 dt 



= 



from which if we eliminate u by means of (8) and 

 obtain 



d'x 



dt' 



J dx ^ 



dt 



17. Now assume 



/ d^ 

 ' df 

 dx 

 dt 



dx 

 dt 





p 



whence 



d^x 

 dJ' 



dp 



cTt 



dp 



d^ X d^ p 



P> and ^^3 = ;,- 



dx^ ^''-^ &X}'P 



d X -^ ' dj P ax^ '■ ^a X) 

 and eliminate t from (12). That equation becomes 



d^p 1 



dp 



dx 



3 (dp\'' , 2 



4 Kdx ) 







(9) 

 (10) 



-(11) 

 (10) we 



(12) 



-(13) 

 (lilo) 



- (16) 



