24 PROFESSOR CAYLEY’S NINTH MEMOIR ON QUANTICS. 
Table No. 87. — Identification of the 23 irreducible covariants of the binary quintic 
Table No. 
A (a, h, c , d, e,f X#, y ) 5 / 13 
B — 28 80o(A, Aj 4 ( 
c = 8 ^o(A, A ) 2 ( 
D=-i(A,B ) 2 ( 
E =}(A, B) ( 
F =*(A, C) ( 
G=-i ( B ? B ) 2 ( 
C) 2 + fB 2 ( 
I =-i(B, C) ( 
J=-i(B,D) 2 ( 
K =— (B, D) ( 
E = — 2“o{A, H)-f--jBE { 
M=-^(B,H) 2 -iBG ( 
N =i(B, H) ( 
O — — (B, J) ( 
P=-i(A, M)-BK ( 
Q =}(B, M) 2 ( 
B=-i(B, M) ( 
S = -96(D, M)+16BO-7GK { 
T = -(J, M) ( 
U 0)+*GQ { 
y=-(B,T) ( 
W=-1(0,T) ( 
) 2 ( 
) 2 
* =c f/y 
14 
) 2 ( 
) 6 
<z=(.ffy 
15 
) 3 ( 
) 3 
i=(/0 2 
16 
) 3 ( 
) 5 
c/o 
17 
) 3 ( 
) 9 
(/» 
18 
) 4 ( 
)° 
(' 0 2 
19 
) 4 ( 
) 4 
20 
) 4 ( 
) 6 
(M 
21 
) 5 ( 
) 4 
a =U i Y 
22 
) 5 ( 
) 3 
Cg) 
23 
n 
) 7 
(/» 
24 
) e ( 
) 2 
t=(pY 
S3 
) 6 ( 
) 4 
O ) 
84 
) 7 ( 
) 4 
M 
*90 
) 7 ( 
) 5 
if*) 
*91 
) 8 ( 
)° 
W 
25 
) 8 ( 
) 2 
H 
*92 
) 9 ( 
) 3 
O ) 
*93 
) n ( 
)‘ 
7=(r«) 
*94 
) i2 ( 
)° 
«) 
29 
) ,3 ( 
)‘ 
M 
*95 
H 
)° 
(('«)> 7) 
29a 
338. The Table exhibits the generation of the several covariants; viz. (A, B) denotes 
chA . c^B — c^A . JB, (A, B) 2 denotes d 2 A . b 2 B — 2<Tch,A . bp^B + d 2 A . b 2 B, &c. (s ee post. 
No. 348). The column f, i = (ff)\ Sic. shows Gokdan’s notation, and the generation 
of his 23 forms ((//) 4 written as with him iox{f,f)*, Sic.): it will be observed that 
the forms are not identical ; if the calculations had been made de novo, I should have 
adopted his values, simply omitting numerical factors of the several forms (thus every 
term of i, =(ffy contains the factor 2 . (120) 2 , =28800): of course the presence of 
these numerical factors renders the f, i, <p, Sic. as they stand inconvenient for the 
expression of results ; and the numerical fixation of the values was no part of Gokdan’s 
object. But by reason of the existing Tables the change of notation is in fact more 
