329 
411 
411. 
A MEMOIR ON THE THEORY OF RECIPROCAL SURFACES. 
[From the Philosophical Transactions of the Royal Society of London, vol. clix. (for the 
year 1869), pp. 201—229. Received November 12, 1868,—Read January 14, 1869.] 
The present Memoir contains some extensions of Dr Salmon’s theory of Reciprocal 
Surfaces. I wish to put the formulae on record, in order to be able to refer to them 
in a “Memoir on Cubic Surfaces,” [412], but without at present attempting to com 
pletely develope the theory. 
Article Nos. 1 to 5. Extension of Salmon’s Fundamental Equations. 
1. The notation made use of is that of Salmon’s Geometry, [2nd Ed.] pp. 450—459, 
[but reproduced in the later editions, see Ed. 4. (1882), pp. 580—592], with the 
additions presently referred to; the significations of all the symbols are explained by 
way of recapitulation at the end of the Memoir. I remark that my chief addition to 
Salmon s theory consists in a modification of his fundamental formulas (A) and (B); 
these in their original form are 
a (?i — 2) = k -(- p -I- 2<r, 
b (n — 2) = p + 2/3 -t- S'y + St, 
c (n — 2) = 2a- + 4/3 + 7, 
a (n - 2) (n - 3) = 28 + 3 [ac] + 2 [ah], 
h {n - 2) (n - 3) = 4k+ [ah] 4- 3 [6c], 
c (n — 2) (to — 3) — 6h+ [ac] + 2 [6c], 
where 
[a6] = ah — 2 p, 
[ac] = ac — 3 a, 
[6c] = he — 3/8 — 27 - i. 
c. VI. 42