276 
[142 
142. 
NUMERICAL TABLES SUPPLEMENTARY TO SECOND MEMOIR 
ON QUANTICS. 
[Now first published (1889).] 
In the present paper I arrange in a more compendious form and continue to 
a much greater extent the tables (first of each pair) given Nos. 35—39 of my 
Second Memoir on Quantics, 141, pp. 260—264, which relate to the cubic, the quartic 
and the quintic functions; and I give the like tables for the sextic, the septimic and 
the octavic functions respectively. The cubic table exhibits the coefficients of the several 
xz terms of the function 1 (1 — z . 1 — xz. 1 — x*z. 1 — x z z), or, what is the same thing, 
it gives the number of partitions of a given number into a given number of parts, 
the parts being 0, L 2, 3, (repetitions admissible): or again, regarding the letters 
а, b, c, d, as having the weights 0, 1, 2, 3 respectively, it shows the number of literal 
terms of a given degree and given weight. And similarly for the quartic, quintic, sextic, 
septimic and octavic tables respectively, the parts of course being 0, 1,... up to 4, 5, 
б, 7 or 8, and the letters being a, b, ... up to e, f, g, h or i. The extent of the 
tables is as follows: 
cubic table 
extends to deg-weight 
18—27 
quartic „ 
y> 
18—36 
quintic „ 
)> » 
18—45 
sextic „ 
)> 
15—45 
septimic „ 
y> 
12—42 
octavic „ 
)) )f 
10—40 
viz. for the quintic, the sextic and the octavic functions these are the deg-weights 
of the highest invariants respectively. I designate the Tables as the ad-, ae-, af-, ag-, 
ah- and cw-tables respectively. 
It is to be noticed that in the several tables the lower part of each column is 
for shortness omitted; the column has to be completed by taking into it the series