PROFESSOR CAYLEY ON RECIPROCAL SURFACES. 
229 
I do not attempt to verify this equation, but I will partially verify a result deducible 
from it ; viz. if <£' is the like function of the accented letters, then we have 
$-$'=n-rr, 
where 
n=(4tf'— 4#— 340>>24y+126x+224B+36C— 0 
-fc(16B+8x+0); 
and IT is the like function of the accented letters. And this being so, we should have 
13cw-48c-48B-13y+n=13cW-48c'-48/3'-13y'+IT, 
or, as this may be written, 
13crc— 48c— 48/3 — 13y-t-ri=2. 
We have 
26»-12e+j3-i-7y-8*+$fl-4C-10B=2; 
and multiplying by —4 and adding, the equation to be verified is 
13w(c-8)-13(4/3+y)+n+4z+28; , +32 % -2T+16C+40B=2. 
But we have from the Memoir 
— 1 3w(c — 8) + 1 3(4/3 + y) -52/-78 x +130-52C-lO4B=2, 
which reduces the equation to 
n+4f— 24/-46 X +110— 36C— 64B=2; 
or substituting for IT its value, this is 
(4^_4 r _336>-+8O x + lO0+16OB-2A(16B+8 x +0)=^, 
that is 
4(^-^_84>-(^-1O)(16B+8 x + 0) = 2, 
an equation which is satisfied if 
and 
<7=20, or else 16B + 8 X +0 = 16B'-f-8 X ' + 4. 
