ON ELLIPTIC AND HYPERELLIPTIC FUNCTIONS. 351 



But 2A2A^Jc.M^.^'c= 



= 2eKJc, l + "^A S + '^'sJc. 3+ • • )«„- ^2,0-7',, . + n/; a + '-^J'c, 3+ • • K 



= 1, € u —i'Sie'u -\- t:% '>' 1^ • 



^c^c e ^c CO ' '^ V V V 



Again, 



-iS^Sv^'v'-pS A2,G,, /,, ,K;, ^K,, V- 2p2,Vp'2A2,G., A .K'. pK'., p- 

 = 2 A''»A''V2.2,(2.G,, ,K,, J J,, ,K,_ ,, - a,2,,m,r^,S,(2,2,G,, /,, ,K; ^,)K.. ^ 

 - ^-Sp^.m^.r^S/S^S^G,, ,J,, ,K;, ^)K,, ,,- 2,2,.y-^,S,(2,2,G,, /,, ,K;, ^)K',, ^, 



-^•2p2. Vp2,(j', p- ^ G,, ,)k,, ,, - 2,S, Vp.2.(j', , - ^ G,, ^)k; 



-aKK,_, + m,K,_2+ . . . .)(r,J',., + rJ',,2+ . .. .) 



-2(r/,, , + r,J;, + r,j;3+ . . . . )(r,K; ,+nK; 2 + ^3^',, 3+ • • ■ •) 



<•• p 



