590 
ON THE THEORY OF RECIPROCAL SURFACES. 
[416 
Taking then further as given the 5 quantities j', &>', C\ B\ 
equations (18) and (21) give p, a, 
equation (19) gives 2/3'+ 37'+ St\ 
(20) 
(28) 
so that taking also t' as given, these last three equations determine /3', 7', 0'; and 
finally 
equation (22) 
(23) 
(24) 
(25) 
viz. taking as given in all 20 quantities, the remaining 26 will be determined. 
634. In the case of the general surface of the order n, without singularities, we 
have as follows: 
ft = ft, 
a = n (n — 1), 
8 = f ?? (n — 1) (n — 2) (11 — 3), 
k — ft (ft — 1) (n— 2), 
11 = 11 (n— l) 2 , 
a' = n (n — 1), 
8' = \n (ft — 2) (ft 2 — 9), 
k = 3ft (ft — 2), 
b' = \n (ft — 1) (ft — 2) (ft 3 — ft 2 + ft — 12), 
k' = ift (ft - 2) (ft 10 - 6ft 9 + 16ft 8 - 54ft 7 + 164ft 6 - 288ft 5 + 547ft 4 -1058ft 3 +1068ft 2 -1214« + 1464), 
if = (ft - 2) (ft 7 - 4ft 6 + 7ft 5 - 45ft 4 + 114?i 3 - 111ft 2 + 548ft - 960), 
q' = n(n — 2) (ft — 3) (ft 2 + 2ft — 4), 
p = ft (ft — 2) (ft 3 — ft 2 + ft — 12), 
c' — 4ft (ft — 1) (11 — 2), 
b! = ift (ft - 2) (16ft 4 - 64ft 3 + 80ft 2 - 108ft + 156), 
r' — 2ft (ft — 2) (3ft — 4), 
= 4ft (11 — 2), 
/3'= 2ft (ft-2) (lift-24), 
7' = 4?i (ft — 2) (ft — 3) (?i 3 — 3ft + 16), 
the remaining quantities vanishing.