PROFESSOR CAYLEY ON THE THEORY OF RECIPROCAL SURFACES. 
87 
From the several cases of a cubic surface we obtain as in the memoir ; but applying 
to the same surfaces the reciprocal equation for (3 , instead of the results of the memoir, 
we find 
h! = - 4, 
y-l_16„= — 198, 
g' 2 (a= 45, 
g+g 1 = is, 
x =5 
(so that now 2, as is also given by the cubic scroll). And combining the two 
sets of results, we have 
h = 
24, 
X = 
5, 
P = 
¥+l<7, 
v = — 
¥+i hg. 
h' — — 
4, 
g'= 
1 
CO 
pH 
x'=- 
7, 
+=6- 
■\g. 
v' = f — 
~bsg > 
but the coefficients g , x, x',f,f are still undetermined. To make the result agree with 
that of the Addition, I assume x= — 86, x' = —1, g— -h 28 ; whence we have 
$=2n(n— 2)(llw— 24) 
-(110^ — 272)6 + 442 
_(4|7 w _ 315 ) c + ^ r 
+ J^0 + JJJPy + 198* 
-24C-28B +86i-5j-^ x +±i0-fu 
+ 4 C' + 1 OB' + -f 7/ + 8^' — —foJ ; 
and if we substitute herein the foregoing value of 442 + ¥ r ? we obtain 
(3'=2n(n— 2)(llw— 24) 
+ (-66^+184)6 
+ ( — 93^+252 )c 
+ 153/3+93y+66£ 
— 24C — 28B -i -27 j -38% 6- fa, 
+ 4C' + 10B'+? V + 7/+ 8 
which, except as to the terms in a,, aJ , the coefficients of which are not determined, 
agrees with the value given in the Addition. 
Dr. Zeuthen considers that in general i'=i ; I presume this is so, but have not 
verified it. 
