A MEMOIR ON THE THEORY OF RECIPROCAL SURFACES. 
358 
[411 
and IT is the like function of the accented letters. And this being so, we should have 
13 cn — 48c — 485 — 137 + n = 13cV — 48c' — 48/3' — 187' + IT, 
or, as this may be written, 
13cn - 48c - 48)8 - 13 7 + II = 2. 
We have 
2 6n- 12c + /3 — i — 7j — 8* +£0-4(7-105 = 2; 
and multiplying by —4 and adding, the equation to be verified is 
ISn (c - 8) - 13 (4/8 + 7) + n + 4t + 28j + 32 x - 20 +16(7+ 405 = 2. 
But we have from the Memoir 
- 13n (c - 8) + 13 (4/3 + 7) - 52j - 78 % + 130 - 52(7 - 1045 = 2, 
which reduces the equation to 
n + 4i- 24j - 46% + 110 - 36(7 - 645 = t; 
or substituting for II its value, this is 
(4«' - 4x - 336) i + 80% +100 + 1605 - 2A (165 + 8 % + 0) = 2, 
that is 
4 (x' - x - 84) i - (£$r - 10) (165 + 8 X + 0) = 2, 
an equation which is satisfied if 
i! = i, x — x, 
and 
g = 20, or else 165 + 8* + 0 = 165' + 8* + 0'.