228 
PROFESSOR CAYLEY ON RECIPROCAL SURFACES, 
and adding to the last preceding equation we have 
26w-12c+/3-«-7/-8%+i0-4C-lOB=2. 
Substituting for % its value in terms of the accented letters, we obtain for /3' the value 
We have 
and thence 
{3'=f3+26n -12c +a'+7/+8%'— |0'+4C'+1OB' 
-2Qn'+12J-i-7j-8x+±Q -4C-10B. 
c ,== — 3 cl-\-/c-\- 3 
12c' — 26w'= — 36#+12 /k+10%'; 
writing herein 
n!=a-\-K— <r— 2C— 4B— 2j— 3%— <r, 
the value is 
= _26a+22*-20C-40B-20;-30x-10<r. 
Or substituting for z its value —a(n— 2)+B— g— 2<r, we have 
12c' — 26w'=a(22ra— 70) — 20C— 18B — 20/— 30%— 22g> — 44<r ; 
or substituting for a, g, a their values, this is 
= {?*(>— 1) — 25— 3c}(22%— 70) — 20C — 18B— 20/— 30*; 
— 225(w— 2) + 44/3+66 7 +66£ 
-27c(rc-2)+108j3+27 7 +27 Q, 
and adding hereto the remaining terms, 
|3 + 2 6 w — 12 c + £' + 7/ + 8%' — 10' + 4C'+ 1€B' 
-i-7j - 8% +^9 - 4C - 10B, 
we have 
/3'=2n(»-2)(llra-24)+5(--66»+184)+c(-93n+252)+153|3+93 7 +66$ 
+»' + 7 /' + 8%'- ^'+ 4C' + 10B' 
-z-27/-38% +-^9 — 24C — 28B. 
Comparing this with the value of /3', No, 63 of the foregoing Memoir, we should have 
0=^cn- 12c— 12/3— 
-(#'+ 1 )i' -14%-'10'-9C'-28B' 
-(* + 86>- + 6/+%- 29 +28B 
++ 6 -£(-16B-8%-5+16B' + 8%'+5'), 
or, what is the same thing, 
0 = 13cm — 48c — 48/3 — 1 3 7 + <P, 
if for shortness 
0>=-(4o/+ 4 )i' — 56%'— 75'— 36C'— 112B' 
-(4.r+344>'+24/+70%-85 +112B 
+M-16B-8%-5+16B'+8 x '+5'). 
