32 
A TRANSFORMATION IN ELLIPTIC FUNCTIONS. 
[896 
to in my “ Note sur les Covariants, &c.,” Crelle, t. L. (1855), pp. 285—287, [135], 
and is given with a demonstration in my paper “ Sur quelques fornmies pour la trans 
formation des integrates elliptiques,” Crelle, t. lv. (1858), pp. 15—24, [235], see No. iv.; 
viz. from the identical relation JU 3 — IU°H + 4<H 3 = — <E> 2 , which connects the covariants 
of a quartic function, it at once follows that if 
U = (cl, b, c, d, e\x, l) 4 , 
and H is the Hessian hereof, 
H = (ac — b 2 , (ad —be), ae + 2bd — Sc 2 , 2 (be — cd), ce — d 2 \x, l) 4 ; 
then writing 
we have 
dz _ 2 dx 
V(- 4z 3 + zl — J) \/{(a, b, c, d, e'^x, l) 4 ] ’ 
which is the transformation in question.