144] 
A THIRD MEMOIR UPON QUANTICS. 
335 
Also if the discriminant be written 
K(U)=. 
a k 
h b 
j i 
a n 
№ 33 
a ï 
9 1 
i f 
c i 
<& % 
ï § 
© $ 
j h 
l k 
9 1 
3 m 
% m 
© u 
then the values of 23, jp, î, 33t> If (equations (20) of 35) are 
= akg + 2hjl — 
23 = bih + 2fid — 
(& = cjf + 2gil — 
3-jp = bch + bij — 
3 © = caf + cjk — 
3p) = ab g + aki — 
aP — gin.? — fk, 
bP — hf 2 — kH, 
cP - fg 2 ~ Pj, 
ck 2 + 2gfk - 2 bgl +fP -f-j - fih, 
aP + 2 ligi — 2 chi + gP — g-k — gjf 
bj 2 + 2fhj — 2afl + hP — hH — hkg, 
3 1 = bej + cfli — bg 2 4- 2 kig — 2 ckl +jP — Ph — fij, 
3\$ = cak + agf— clP + 2 ijh — 2 ail + kP —j 2 f — gjk, 
33Bt = abi + biig — af 2 + 2jkf — 2bj l + iP — k-g — hid, 
6% = abc 4- 3fgh + 3 ijk + 21 3 — afi — bgj — chk — 21 gk — 2 Ihi — 2 Ifj. 
The equation K (U) = R = 64<S 3 — T 2 would however afford a perhaps easier formula for 
the calculation of the discriminant.]