C. XIII. 
60 
[949 
950] 
473 
,nd higher 
3S of the 
s they lie 
t lines on 
t cone can 
.s appears 
a quartic 
such lines 
lines lie 
ever that, 
ly (as in 
her orders 
that the 
nes of the 
950. 
ON THE SEXTIC RESOLVENT EQUATIONS OF JACOBI 
AND KRONECKER. 
[From Grelle’s Journal d. Mathematik, t. cxm. (1894), pp. 42—49.] 
:h are the 
of inter 
ne special 
>ut having 
h, n it is 
tot in the 
the order 
or further 
jessary for 
The equations referred to are : the first of them, that given by Jacobi in the 
paper “ Observatiunculae ad theoriam aequationum pertinentes,” Crelle, t. xm. (1835), 
pp. 340—352, [Ges. Werke, t. ill., pp. 269—284], under the heading “ Observatio de 
aequatione sexti gradus ad quam aequationes sexti gradus revocari possunt,” and the 
second, that of Kronecker in the note “ Sur la resolution de l’équation du cinquième 
degré,” Comptes Rendus, t. xlyi. (1858), pp. 1150—1152. Jacobi’s equation is closely 
connected with that obtained by Malfatti in 1771, see Brioschi’s paper “Sulla resol- 
vente di Malfatti per l’equazione del quinto grado,” Mem. R. 1st. Lomb., t. ix. (1863) ; 
but the characteristic property first presents itself in Jacobi’s form, and I think the 
equation is properly described as Jacobi’s resolvent equation. The other equation has 
been always known as Kronecker’s resolvent equation ; it belongs to the class of 
equations for the multiplier of an elliptic function considered by Jacobi in the paper 
“ Suite des notices sur les fonctions elliptiques,” Crelle, t. III. (1828), pp. 303—310, see 
p. 308, [Ges. Werke, t. I., pp. 255—263, see p. 261]: say Kronecker’s equation belongs 
to the class of Jacobi’s Multiplier Equations. We have in regard to it the paper by 
Brioschi, “ Sul metodo di Kronecker per la resoluzione delle equazioni di quinto grado,” 
Atti 1st. Lomb., t. i. (1858), pp. 275—282, and see also the “Appendice terza” to 
his translation of my Elliptic Functions (Milan, 1880) : it seems to me however that 
the theory of Kronecker’s equation has not hitherto been exhibited in the clearest 
form. 
I consider the forms 
12345 
13524 
13254 
12435 
24315 
23541 
35421 
34152 
41532 
45213 
52143 
51324