ON ELLIPTIC AND HYPERELLIPTIC FUNCTIONS, 111 



By putting z + w,z + ui' for (z), and making use of equations (6), section 5, 

 we have 



C is easily determined from this, and we have 

 It, men,———, ^=ir, \ro have from A, 



n, 01,1 1 





fjtv^fji'v'^o, mod. 2. 



Betti then shows that vr^ = ^Uil^ -^yrith the same « + l values which 



are used in the ' Fundamenta I^ova,' will give us aU the generality we re- 

 quire ; and consequently if we transform om- expressions in a manner similar 

 to that we employed last section, and remember that 



and multiply the conjugate factors by means of the last four equations of 

 section 6, we shall have the following four ei^uations : — 



/, r~ ^'<^'\-. ^''"'''fl -n/'fl^ - 7..«'i,i(!<>«2 ,.^ 



v^i^o- A / 1 V 0'j, o(^'cr<^) y 



- 1 



p-i 



