26 



On the Theory of Reciprocal Surfaces. [Nov. 16, 



but I have not as yet any means of determining the coefficients /,/' of 

 the terms in w, 



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'+l6i, = — 198, 



g' + Zfx = 45, 



9+9 = 18, 



X m 5 



(so that now X + \'=— 2, as is also given by the cubic scroll). And 

 combining the two sets of results, we have 



h= 24, 



X= 5, 



= - 4, 



= IS-,?, 



__9_ l 



but the coefficients a?, #',/,/' are still undetermined. To make the 

 result agree with that of the Addition, I assume a?=— 86, «*5r~*J. 

 ^= + 28 ; whence we have 



/3 , = 2w(w-2)(llw-24) 

 -(110^-2/2)5 + 44^ 

 - ( f»-315)c + «ir 

 4-^/3 + ^7+ 198* 

 - 24C- 28B + 86 2 -5/-f x + 4 {d -f<o 

 + 4C+ 10B' + 1 + 7/ + 8x'-^' -/'">'; 

 and if we substitute herein the foregoing value of 44j + ^r, we obtain 



j3'=2»(»— 2)(llw-24) 

 + (-66rc+184)5 

 + (--93rc + 252)c 

 + 153/3 + 937+66* 

 - 24C - 28B-z- 27i-38x+f 3— > 

 +4C'+lOB'+i'+7/+8 x '-i0 , -/V J 



which, except as to the terms in w, a/, 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. 



