534 
ON THE TRANSFORMATION OF ELLIPTIC FUNCTIONS. 
[869 
50 - re = 5 ’ B -7pJ^v (r’-Zp + V(p'-*p-n 
64a 2 p = (p 2 — 4p — l) 2 (p 2 — 2 p + 5), 
or say 
8a V/3 = (p 2 — 4p — 1) Vp 2 — 2p + 5: 
64 (a 2 — 1) p = (p — l) 5 (p — 5), 
a 
5 
J 
P 
64^S 2 (T = (cr 2 — 4 er — l) 2 (<r 2 — 2cr + 5), 
— 8/3 V er == (c 2 — 4cr — 1) Ver 2 — 2cr + 5, 
64 (/3 2 — 1) er = (o- — l) 5 (a- — 5), 
/3 _ p 2 + 20p — 5 
a p 2 (p 2 — 4p — 1) ’ 
a/3-equation, see No. 3. 
The pa-equations for the cases in question, n — 3 and n = 5, are the so-called 
Jacobian equations of the fourth and the sixth degrees, studied by Brioschi (in the third 
appendix above referred to) and by others: the foregoing a/3-equations have not (so 
far as I am aware) been previously obtained; as rationally connected with the 
pa-equations, they must belong to the same class of equations. 
Cambridge, England, December 18, 1886.