606 
PROFESSOR CAYLEY’S TENTH MEMOIR ON QUANTICS. 
367. Sylvester obtained an expression for the N.G.F. of the quintic : this is 
a 0 . 
1 
-fa 3 • 
# 3 -f x 5 -f X 9 
-fa 4 . 
X^-\- X 6 
-fa 5 . 
zy» . 1 zy»3 1 ry*l __ /y»l i 
tu j tAz | it' tAz 
-f-ct 6 . 
cc 3 -f ad 
-fa 7 . 
ry* 1 ry>- > __ />*• ' 
tAz I it/ tAz 
-fa 8 . 
xZ-j-X 4 
-fa 9 . 
CC 3 -f X h — X 7 
+ a 10 . 
1 /yid _ zy»10 
tAz I tAZ tAZ 
-fa 11 . 
ry* 1 zy»3 __ __ zy»9 
tAz I tAZ tAZ 
-fa 13 . 
n. 
i 
^00 
1 
o 
-fa 13 . 
ry* __ rv* 1 __ zy» 9 
tAZ tAZ tAZ 
-fa 14 
. V* 1‘ / v -f __ zy»8 
tAZ tAZ tAZ 
+ a 15 . 
- __ /^>9 
-fa 10 . 
, | • - ___ » 1 zy»10 
tAZ tAZ tAZ 
-fa 17 . 
_ t 7_ 7 .9 
tAZ tAZ 
-fa 18 . 
l—l 
1 
r 
00 
1 
o 
-fa 10 . 
__ ry*0 ___ zy»7 
tAZ tAZ 
-fa 20 . 
0 Q 
— v * - __ . . •' > /y» - 
tAZ tAZ tAZ 
-fa 33 . 
— a; 11 
— a 3 x 3 . 
1— a 3 # 6 . 1 — a 4 . 1 — 
viz., expanding this function in ascending powers of a, x, then if a term is Ncdaf, this 
means that there are precisely N asyzygetic covariants of the cleg-order O.jx. 
368. It is known that the number of the irreducible covariants of the binary quintic 
is =23 ; representing these by the letters a, b, c, d, e,f, g, li, i, j, k, l, m, n, o, p, q, r, 
s, t, u, v, w ( a the quintic itself), the deg-orders of these, and the references to the 
tables which give them are 
