415] 
ON THE THEORY OF RECIPROCAL SURFACES. 
581 
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, 
g' + 16v =-198, 
g'+ 2/a = 45, 
g +g' = 18, 
A =5 
(so that now A + A' = — 2, as is also given by the cubic scroll). And combining the 
two sets of results, we have 
h = 24, 
A =5, 
P = 2 r+h> 
v =-^ + ^<7, 
b! = - 4, 
<j = 18 —g, 
A' = - 7, 
n’ = 6 - ^/7, 
7/ — 9 1_ n • 
v 4 16 V » 
but the coefficients g, x, x', f f are still undetermined. To make the result agree 
with that of the Addition, I assume « = — 86, x = — 1, g = + 28 ; whence we have 
/3' = 2ft (n — 2) (1 l?i — 24) 
-(110«- 272)6 + 44^ 
- 315) c + ^r 
+ ¿^£ + ^7+198* 
- 24G - 28B + 86i -oj -*£x + 6 ~ f 03 
+ 4(7' + 105' 4- i + 7/ 4- 8*'- £0'-/V; 
and if we substitute herein the foregoing value of 44q + r, we obtain 
/0' = 2?i («-2) (11?? -24) 
+ (- 66« + 184) 5 
4* (— 93« 2o2) c 
+ 153/3 4- 93y + 66£ 
- 24(7 - 28B - i - 27j - 38* + ™ 6 -fo> 
4- 4<7' + 10 J B' + i'+ 7/ + 8£0'-/V, 
which, except as to the terms in &>, &>', 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.