PEOFESSOE CAYLEY ON EECIPEOCAL STJEFACES. 
217 
The general surface of the Order n without Singularities. Article No. 50. 
50. In the general surface of the order n without singularities, we have 
n =n, 
a =n 2 — n, 
l =±n(n-l)(n-2)(n-3), 
z = n(n— l)(n— 2), 
h =0, 
k =0, 
t =0, 
q =0, 
% = 0 , 
j = 
c =0, 
h =0, 
r =0, 
a =0, 
6 = 0 , 
36=0, 
c =0, 
B=0, 
P =o, 
7=0, 
i =0, 
n' = n{n—Vf, 
a! ~ n{n— 1), 
d =%n(n—2)(n 2 —9), 
z =3n(n—2), 
V V)(n— 2){n 2 — n 2 -\-n— 12), 
k' =^(w-2)^ lo -6w 9 +16w 8 -54^+164ri 6 -288w 5 +547w 4 -1058?i 3 +1008^-1214w+1464), 
t 1 = %n(n — 2 ){n 7 — 4 n 6 + 7 n h — 45 n 4 + 1 1 4n z — 1 1 1 n 2 + 5 4 Sn — 9 6 0) , 
q 1 = n(n— 2){n— 3)(n 2 -\-2n— 4), 
§’ = n(n-2)(n z —n 2 -\-n—\2), 
/ = 0 , 
c' =4n(n— l)(n— 2), 
MDCCCLXIX. 
2 II 
