314 
[458 
458. 
ON THE ANHAHMONIC-RATIO SEXTIC. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. x. (1870), 
pp. 56, 57.] 
Mr Walker’s equation is A (X 2 — X + l) 3 + P (X 2 — X) 2 = 0 ; changing the sign of X, 
and also the numerical multipliers of I, A (so as to convert the discriminant equation 
into its standard form A = / 3 — 27 J 2 ), the equation is 
4A (X 2 + X + l) 3 - 27P (X 2 + X) 2 = 0. 
I remark that this is most readily obtained as follows; writing 
A = (a — d)(h — c), 
B — (b — d) (c — a), 
G = (c — d) (a — b), 
then we have A + B + C = 0, 
/ = * (M 2 + £ 2 + C 2 ) = - (BG + GA + AB), 
J=jh(Z-G)(C-A)(A-B), 
V(A ) = ^ABG, 
see my Fifth Memoir on Quantics, Phil. Trans., vol. cxlviii. (1858), pp. 429—460, [156]. 
And observe also, that in virtue of the relation A + B + G = 0, we have 
Hence writing 
12/ = M 2 + AB+B* = As + AC+C* = B° + BC+C n -. 
4 \/(A) 
31 
x + — + 1 
Aj