C. XII. 
13 
[817 
817] 
ON THE SIXTEEN-NODAL QUARTIC SURFACE. 
97 
But substituting for a, b, c, l, m, n their values 
111111 
f’ 9’ h* p’ q’ r 
, we have in 
all 8 equations for the determination of qr, rp, pq, git, lif fg; viz. if for greater con 
venience we introduce the new symbols 21, 23, (S = qraa", rp/3'{3", pqy'y", then the 
8 equations are 
Proc. Lond. 
assume 
But in virtue of the equation a + ¡3 + y = 0 the first four equations are equivalent to 
three equations only, and they determine 21, 23, 6, that is, p, q, r, which give at once 
l, m, n; and similarly the second four equations are equivalent to three equations 
only, and 21, 25, (£ being known they determine gh, hf, fg, that is, f, g, h, which give 
at once a, b, c: the identification of the two forms is thus completed. 
Cambridge, 11 th January, 1883. 
2. these are