774] 
TABLES FOR THE BINARY SEXTIC. 
373 
Or, using the capital letters A, B,..., Z to denote the 26 covariants in the same 
order, the table is 
0 
2 
4 
6 
8 
10 
12 
] 
A 
2 
B 
G 
D 
3 
E 
F 
G,=(A, Cf 
H 
4 
I 
J> = (A, E) 2 
E, = (A, Ef 
¿,=(2), Cf 
5 
M, = ( C, Ef 
X, = (C, Ef 
O, = (A Ef 
6 
p 
Il II 
7 
S, = (A, E 2 ) 4 
T,=\A, E 2 ) 3 
8 
U, = (C, EJ 
9 
V, =(G, FA) 4 
10 
X,=(A,EJ 
12 
Y, = (G, E 3 ) s 
15 
Z, = (G, E 4 f 
A is the sextic. P is Salmon’s C, p. 204. 
B is Salmon’s A, p. 202. TV ,, ,, D, p. 207. 
I „ „ B, p. 203. ¿T „ „ E, p. 253. 
The references are to Salmon’s Higher Algebra, 2nd Ed., 1866. 
In the present short paper I give the leading coefficients of the first 18 covariants, 
A to R (some of these are of course known values, but it is convenient to include 
them) : for the next four covariants S, T, U, V, the leading coefficients depend upon 
the coefficients of A, C, G and E-, viz. writing 
A = (a, b, c, d, e, f y\x, yf, 
E 2 = («, }0, H i$, y) 4 , 
o =(«', 4$'> W> i g/ ’ € '$. x > yy> 
G = (a", i/3", j%y"> *8", tïï e "’ 2/) 8 > 
we have 
S, Coeff. x 2 = ae — b8 + cy — <2/3 + ea, 
T, „ x 4 = a8 — 2by + 3 c/3 — 4 da, 
U, „ x 2 = 2d8 — /3'y + y & — 28'a, 
V, „ = 280a"e - 35/3"3 + 10 7 " 7 - 208"/3 + 24e"a. 
Similarly the invariant W and the leading coefficients of X, Y depend on the coefficients 
of ri, G and E 3 ] and the invariant Z depends on the coefficients of G and E 4 .