580 CORRECTIONS AND ADDITIONS TO THE MEMOIR [415 
5. It was also pointed out to me by Dr Zeuthen that in the value of 24i given 
in No. 10 the term involving % should be — 6% instead oi + 6%, and that in consequence 
the coefficients of % are erroneous in several others of the formulae. Correcting these, 
and at the same time introducing the terms in co, and writing down also the terms 
in 0 as they stand, we have 
4 i = ... — 2% + 30 — 3o), 
24i = ... — 6% + 90 — 9<w, 
2cr = ... — 0 — ft), 
8p = ... + 6% — .90+ 9a), 
8 /£=...— 6% + 170 — 25ft), 
23=...+ 6% — 90 + 15®, 
8 n' = ... — 30% + 210 — 45ct), 
c' = ...- 12% + 100 - 20«. 
The equations of No. 11, used afterwards, No. 53, should thus be 
41+ 6r = ( on — 12)c —18/3 — 5y — 2%+ 30 — 3ft), 
— 24i —8q + 18r = (— 8n + 16) b + (15n — 36) c — 34/3 + 9^ + 4j — 6% + 90 — 9co ; 
and from these I deduce 
44q + ^-r = (44n - 88) b + n - 63) c - ^ /3 - a§a 7 - 1321 - 87i - 22j - ^ 0. 
6. In No. 32 we have (without alteration) 0=16; but in the application (Nos. 40 
and 41) to the surface FP 2 + GR 2 Q 3 = 0 we have 0 = 0, and there are o)=fpq off-points, 
F =0, P = 0, Q = 0, and x = 9P f I close-points, G = 0, P = 0, Q = 0. The new equations 
involving co are thus satisfied. 
7. I have ascertained that the value of /3' obtained, Nos. 51 to 64 of the memoir, 
is inconsistent with that obtained in the “ Addition ” by consideration of the deficiency, 
and that it is in fact incorrect. The reason is that, although, as stated No. 53, the 
values of two of the coefficients D, E may be assumed at pleasure, they cannot, in 
conjunction with a given system of values of A, B, C, be thus assumed at pleasure; 
viz. A, B, C being = 110, 272, 44 respectively, the values of D, E are really deter 
minate. I have no direct investigation, but by working back from the formula in the 
Addition I find that we must have D = ^-, E — 315; the values of the remaining 
coefficients then are 
F=™, G = - 7 -^, H = - uloa, / = -198; 
or the formula is 
/3' = 2n (n — 2) (lift — 24) 
-(110/1 — 272)0+ 44 ? 
- (±p- n - 315) c + ^-r 
+ i|5/3 + i(^5 7+ 198i 
- hC — gB — xi — Xj — /¿% — v0 —fco 
- h'C' - g'B' - x'i - \'j' - fj,'x - v 0' -fco' ; 
but I have not as yet any means of determining the coefficients f f of the terms 
in ft), CO .