415] 
577 
415. 
CORRECTIONS AND ADDITIONS TO THE MEMOIR ON THE 
THEORY OF RECIPROCAL SURFACES {Phil. Trans, vol. clix. 
1869, [411]). 
[From the Philosophical Transactions of the Royal Society of London, vol. clxii. (for the 
year 1872), pp. 83—87. Received July 22,—Read November 16, 1871.] 
1. I AM indebted to Dr Zeuthen for the remark that although the “off-points” 
and “off-planes,” as explained in the memoir, are real singularities, they are not the 
singularities to which the в, в' of the formulae refer. The most convenient way of 
correcting this is to retain all the formulae with в, в' as they stand, but to write 
to' for the number of “off-points” and “off-planes” respectively; viz. we thus have 
<w, off-points, 
в, unexplained singular points, 
and 
со', off-planes, 
в', unexplained singular planes, 
the formulae as they stand, taking account of the unexplained singularities в and в', 
but not taking any account at all of the off-points and off-planes <u, &/. The extended 
formulae in which these are taken into account are: 
a (n — 2) = к — В + p + 2<x + 3со, 
h (n — 2) = p + 2/3 -f- З'у + St, 
c (n — 2) = 2cr + 4/3 4- 7 + в + со, 
a (n — 2) (n — 3) = 2 (S — C — 3ft)) + 3 (ac — Scr — % — 3<u) -t- 2 (ab — 2p —j), 
b (n — 2) (n — 3) = 4k + (ab — 2p — j) + 3 (be — 3/3 — 2y — г), 
c (n — 2) (n — 3) = 6h + (ас — 3<т — ^ — Зга) + 2 (be — 3/3 — — г), 
which replace Salmon’s original formulae (A) and (B). 
C. VI. 
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