664] 
ON THE 16-NODAL QUARTIC SURFACE. 
183 
Writing successively 9 — b and 9 = c, we obtain 
(a-d) (e -/) 
1, e + f ef 
1, b + c, be 
1, a + d, ad 
= (a —f) (b — d)(b — e) [ac] - (a — b) (b — f) (d — e) [ab\ 
+ (a — b)(b — e) (d —f) [ce?] 
(a — d)(e—f) 
1, e + f, ef 
1, b + c, be 
1, a + d, ad 
( a —e)(b — d) (b —f) [bd]; 
= — (a — c) (c —f) (d — e) [ac] +{a—f)(c — d) (c — e) [ab] 
- (a - e) (c - d) (c -f) [cd] + (a - c) (c - e) (d -/) [bd]; 
which values of [&] and [c], combined with the foregoing equation 
(a - d) (e -/) f[b\ V[c] = - V[ac] Vp] + f[cd] \/[bd], 
give the required quartic equation between '/[ac], '/[ab], '/[cd], V[6d]. 
Cambridge, 2 August, 1877.