|9(i •>' FU.HSAWA. 



/r]-\-rPV fZ-c (TV dV 



\(hi / fh- (In- d: dk 



Since 



er|iiation (97) rnkes the form 



+ '-^"'/'''-^ + ''\'''- 1 )--' V-^ 



This eqnatic^ii is also satisfied by T',, I .,, and 13. 



With J'K'oln, we in:iy ])iit /,■ + -^- = a and then equation (Î)S) 

 heeonies 



^ r/ç- r/ç (la 



in wliicli forni, tlie p-irtial differential equation was o-iven for tlie first 

 time hy Jaeohi. 



The al)ove demonstration ofJaeobi's partial differential equation 

 is substantially the same as the one given by lU'iot and lîouquet* in 

 their Avell-known treatise on elliptic functions, the only difference 

 being that, in their demonstration, tlie intermediary steps are conducted 

 bv means of Weierstrass' function .//. 



lîciot and lîonqiiet «jive also the following- forms of the pai'tial 

 differential e(juati()n : — 



* JjOO. cit. p. 529. 



