126 
MR. A. CAYLEY’S SECOND MEMOIR UPON QUANTICS. 
No. 26. 
+ 
] 
aT 
— 
20 
PbeY 
— 
120 
Pcdf 
+ 
160 
PceY 
+ 
360 
Pd”eY 
— 
640 
PdPf 
+ 
256 
d*e' 
+ 
160 
a-Pdf 
— 
10 
PPPY 
+ 
360 
a~bPY 
— 
1640 
Pbcdef" 
+ 
320 
PbcPf 
— 
1440 
PbdY 
+ 
4080 
Pbd^ef 
— 
1920 
a~bde* 

1440 
PPeY 
+ 
2640 
PPdY 
+ 
4480 
PPdPf 
— 
2560 
a~Pe* 
— 10080 arcd^ef 
+ 5760 aWV 
+ 3456 a^(Pf 
— 2160 
— 640 ab^cf^ 
+ 320 ab^def^ 
— 180 aPe^f 
+ 4080 aPPef"" 
+ 4480 aPcdrf 
-14920 aPcdPf 
+ 7200 aPcd^ 
+ 960 aPd^ef 
— 600 aPd-p 
— 10080 ahPdf 
+ 960 abPPf 
+ 28480 abPd^ef 
— 16000 abPdP 
— 11520 abcd^f 
+ 7200 abcdh^ 
abd^e 
+ 3456 aPf^ 
-11520 aPdef 
+ 6400 aPe^ 
+ 5120 aPdy 
— 3200 aPd'^P 
aPd^e 
acd^ 
+ 256 Pf 
— 1920 Pcef- 
— 2560 PdY- 
+ 7200 PdPf 
— 3375 Pe'^ 
+ 5760 PPdf 
— 600 PcPf 
— 16000 Pcd‘ef 
+ 9000 Pcde^ 
+ 6400 pdy 
-4000 Pd^e‘ 
-2160 PcY- 
+ 7200 PPdef 
— 4000 PPP 
-3200 PPdy 
+ 2000 PPd‘P 
Pcd^e 
^ Pd^ 
bpef 
bPd~f 
bPde‘ 
bPd^e 
bPd^ 
Pdf 
Pe^ 
Pd'^e 
Pd* 
The tables Nos. 13 to 24 are the irreducible covariants of the degrees 1, 2, 3, 4 
and 5 of a quintic. No. 13 is the quintic itself ; No. 15 is the Hessian ; No. 19 is the 
qiiartinvariant ; No. 22 is the linear covariant ; the other covariants can be referred 
to by their degree and order, or simply by the number of the table. The foregoing 
covariants are connected by the equation of the degree 5 and order 1 1, 
(No. 13)(No. 21) + (No. 14)(No. 18)-(No. 15)(No. 17)=0. 
The table No. 25 is the simplest octinvariant, and the table No. 26 is the discrimi- 
nant ; we have 
(No. 26) = (No. 19)"-1152(No. 25). 
