mbda]2 = 2, [lambda]1 = 1, p1 = 2,
P2 = 2, p3 = 1, p4 = 1, the reader will have no difficulty in
constructing the diagrams of the eighteen solutions.

The next and last example of a multitude that might be given shows the
extraordinary power of the method by solving the famous problem of the
"Latin Square," which for hundreds of years had proved beyond the
powers of mathematicians. The problem consists in placing n letters a,
b, c, ... n in the compartments of a square lattice of n^2
compartments, no compartment being empty, so that no letter occurs
twice either in the same row or in the same column. The function is
here

{[Sigma][a]1^(2^n-1).[a]2^(2^n-2)...([a]_n-1)^2.[a]n}^n,

and the operator D_n^{2^(n-1)}, the enumeration being given by

D_n^{2^(n-1)}.{[Sigma][a]1^(2^n-1).[a]2^(2^n-2)...([a]_n-1)^2.[a]n}^n,
([a] = [alpha])

See _Trans. Camb. Phil. Soc._ vol. xvi. pt. iv. pp. 262-290.

AUTHORITIES.--P. A. MacMahon, "Combinatory Analysis: A Review of the
Present State of Knowledge," _Proc. Lond. Math. Soc._ vol. xxviii.
(London, 1897). Here will be found a bibliography of the Theory of
Partitions. Whitworth, _Choice and Chance_; Edouard Lucas, _Theorie
des nombres_ (Paris, 1891); Arthur Cayley, _Collected Mathematical
Papers_ (Cambridge, 1898), ii. 419; iii. 36, 37; iv. 166-170; v.
62-65, 617; vii. 575; ix. 480-483; x. 16, 38, 611; xi. 61, 62,
357-364, 589-591; xii. 217-219, 273-274; xiii. 47, 93-113, 269;
Sylvester, _Amer. Jour, of Math._ v. 119 251; MacMahon, _Proc. Lond.
Math. Soc._ xix. 228 et seq.; _Phil. Trans._ clxxxiv. 835-901; clxxxv.
111-160; clxxxvii. 619-673; cxcii. 351-401; _Trans. Camb. Phil. Soc._
xvi. 262-290. (P. A. M.)

COMBUSTION (from the Lat. _comburere_, to burn up), in chemistry, the
process of burning or, more scientifically, the oxidation of a
substance, generally with the production of flame and the evolution of
heat. The term is more customarily given to productions of flame such as
we have in the burning of oils, gas, fuel, &c., but it is conveniently
extended to other cases of oxidation, such as are met with when metals
are heated for a long time in air or oxygen. The term "spontaneous
combustion" is used when a substance smoulders or inflames apparently
without the intervention of any external heat or light; in such cases,
as, for example, in heaps of cotton-waste soaked in oi