354 REPORT — 1873. 



1 p^; dr; , 1 P< „ 



2 o • ~; — - I — r = *<o5 2 o • ~ = ait .... , 



1 Pa;^") f?.r("'^ 



also let M(.r) be a rational and entire function of the |-^ jtli, N(.r) one of 



the (-^—l|th order ; also let 



P(.r)M2(a;)— Q(.i;)NX«)=n(.r)0(.T), where 



Tl{x) = {x-x\) , {x-x^), {x-x^) , (.^'-a•p), 



....(.^•-.^f))..(.^-.r('">), 



we consequently have for fici^), where a^ is one of the roots of P(.r)=0, 



ct>(a ) = — —• Weierstrass has shown that it is possible to deter- 



mine x\, x'[, X2, xl, &c. from the hyperelliptic differential equations by 

 reversion of series, and that conseqiiently in terms of Mj, ?(o, nj. . . , . 



— " may be expressed by a series fiu[..Uj"^, ^4..•i4'"^ "p--'^'p"^)- 



whence the expression for — Xt-^ will become F (— , —...., — ), or, 

 other words, the arguments may be taken as small as we i)lease. 



