304 ON THE THIRD ELLIPTIC INTEGRAL AND THE ELLIPSOTOMIC PROBLEM. 

 To connect up the 





= i 



are equal, so that 



and thus, with 20 = a, 



'Math. Ann 

 bisection formulas for p 



We arrive at the ( 

 6u and 6 (u v), with 

 application, the functio 

 but the separate theta f 



This quotient, qualifi 

 of u when v is a half-pe 

 quotient is the fi th roo 

 when v is an aliquot //, th 

 pseudo -elliptic integral. 



The formation of this 

 chief object, and in the 

 out of the determinatioi 



The Transformation f 

 of symmetric function! 

 dynamical utility, it hat 



>r(J 1o riyio' 

 t*-r.()6 .qq 



qq , 



qq 



.4ua xacwi 



V**/i 



(23), 



nO . 



.oiA liilo'ii 



,8()S JOT ,A ..".ami' .HA 



.lo traa 

 ,808 .IoT ,A ,.aniT .ti 



.77 . 



(25), 



i(>(irf HBUIP. illiw ,lo 

 ,80S .Io7 ,A ,. 



i-twol 



results are thus merely 



i"ti<-nl of tw<> theta functions, 



.bioli is required in dynamical 



: up]- >yed by KLKIN in top-motion; 



Mid Mr, is an elliptic function 



t.-n >' i.s the half-period K, and the 



'it of the elliptic functions of u 



: we express the result of ABEL'S 



i simplest values of p. has been >ur 

 lii|*H>toniic problem has l>een carried 

 >f the Elliptic Function. 



solved at the same time by m- 

 but as Transformation has no 

 >ir. 



