154 



To reduce (89) substitute 



t = (a -r (1 4R'(a)) (pu— (1 24)R''ia)) (-10) 



Where a is a root of R(t). In this case take a = 1 d. Then equation (40) 

 may be written, 



t -= ((1 d) + ((— d 2),(pn. — pv)) (-H ) 



where pv = d^ * 



Since (p'v) ^ = ip^v — g,pv — g, — m2) V ''■) 2)d3 and (— p'v) pu — pv) 

 = ((7'/rT)(u + V) — (n' r:){\i. — V) — :^^c' <7) IV) (Note 1) we have, remem- 

 bering the relation (dt du) ;= (R(t))^ ^ _^ v = (—1 ((2)' -) |'((2) ' ^d + 



a' 



— (u + v)(ct' cr)(u — V) — 2(^7' ^)v)du 4- (K + V = (— (d— (2)' -(^''^^)(v )u) 



— ((2)\ 2) 2 log (r7(u — v),,ff^u + v ) + y 

 ( The above is equation 42. ) 



Note: Schwarz. Formeln der elliptscheu Functionen, p. 13. 



