224 
PROFESSOR CAYLEY OX RECIPROCAL SURFACES. 
y = 18— </, 
at =x l , 
x' = -7, 
p'=e-to, 
»' =1 
and the formula thus is 
j3'= 2n(n-2)(lln-24) 
-(110^-272)5+44^ 
— (116w— 303)c+- 2 % 
+£f+3+248y+1985 
-24C+y-10^+^— 50— 18B'— 6tf- |5' 
— xi—tfi! + T$g ( — 1 6B — 8% — 0 + 1 6B' — 8y,' — 5'), 
where x, x', g are constants which remain to be determined. The cubic surfaces fail 
to determine them, for the reason that in all of them we have i= 0, i’ = 0 ; and 
16B+8%+$ — 16B' + 8%' + ^: this last is a very remarkable relation, for the existence 
of which I do not perceive any a 'priori reason. 
Substituting herein for q, r their values from No. 11, this may be written in the form 
/3'=2w^—2)(ll«— 24) +5(— 66^+184) +c(—^f%+240) 
+141/3+^y+665 
-x’ i’ + 7/_ 6^- f^- 5C'— 18B' 
-(a?+87)t-21/-V% +¥? -24C 
+ iV(-16B— 8*;— 4+16B' + 8 % '+(3'). 
64. We have of course by interchanging the unaccented and accented letters, the 
reciprocal equation giving the value of /3. 
Recapitulation. Article Nos. 65 to 68. 
65. In recapitulation, I say that we have between the 42 quantities 
n, a, &, * ; 5, 7c, t, q, %,j ; c, Ti , r, <r, 5, %; /3, y, i ; B, C, 
v!, a i, 5', yJ ; 5', +, t\ q', c', h', r\ u ', Q', /3', y', i ! ; B', 0, 
in all 25 equations, viz. these are 
a = a', 
«'= ^-l)_25-3c, 
jc'=3w(m— 2)— 65— 8c, 
5' =Aw(«_2)(rc s -9)-(w s w— 6)(25 + 3c) + 25(5 — l) + 65c+-fc(c— 1), 
