COM 
number of combinations of each quantity 
with itself 4; and therefore the miiuber of 
changes 16 ; if with the same exponent the 
given quantities were 5, the number of 
changes would be 25 ; and in general, if tlie 
Dumber of the quantities were n, the num- 
ber of changes would be n^. 
Suppose the quantities 3, and the expo- 
nent of variation 3, the number of clianges 
is found 27 =: 3^, eiz. a a a, aab, aba, baa, 
a a c, aca, caa, abb, bab, bba, ah c, hoc, 
bca, acb, cab, cba, acc, cac, cca, bbb, 
bbc, ebb, beb, bcc, ebe, ceb, ccc. In 
like manner it will appear, if the quantities 
were 4, and the exponent 3, that the num- 
ber of changes would be 64 = 4’ ; and in 
general, if the number of quantities was = 
n, and the exponent 3, the number of 
changes would be 
proceeding in this manner it will be 
found, if the number of quantities be n, and 
the exponent n, that the number of changes 
would be m'. Wherefore, if all the antece- 
dents be added, where the exponent is less, 
the number of all tlie possible changes will 
befoiind ^ -j- 
&c. till the number subtracted from n leaves 
1, because the beginning is from single 
quantities taken once. 
Since, then, the number of all possible 
changes is in a geometrical progression, the 
first or smallest term of which is n', the 
largest n”, and the denominator n ; it will 
be equal (nP + ‘ — n) -J- (ri — 1). Suppose 
n = 4, the number of all possible variations 
will be (4 — 4) - 7 - (1 — 4) = — ^ = 340. 
Suppose again n = 24, the number of all 
the possible variations will be (24^^ — • 24) 
(24 — 1) = 32009658644406818986777 
955348250600 divided by 23 = 139172428 
8887252999425128493402200. In so many 
various methods may the 24 letters of the 
alphabet be varied and combined among 
themselves. 
Combination, in chemistry, is the inti- 
mate union of two bodies, by chemical at- 
traction, into one substance, so that neither 
of them can be recognized, nor can they be 
separated from each other by any mecha- 
nical force. Of this principle are the fol- 
lowing instances. Salt will unite with wa- 
ter, from which it cannot be separated 
again but by chemical agency. Sulphur 
and lime may by heat be united and form 
a compound, the properties of wl^iich are 
totally dissimilar to those of either the sub- 
stances used. In both cases an affinity 
has been exerted between the substances, 
COM 
and they have combined. Combination is 
to be distinguished from mixture, in which 
dissimilar particles are blended togcflier, 
without being united by attraction, in 
which no new. qualities are acquired, in 
which the difference of parts is easily dis- 
covered, and these parts are capable of 
being separated by mechanical means. It 
is distinguished from aggregation, which is 
merely th i union of particles of the same 
kind of matter, forming an aggregate, uni- 
form in composition, but possessing all tlie 
properties of tlie particles of which it is 
coniposed. 
Combination, in militaiy science. One 
ought to regard combination as forming a 
part of military science. A general who 
has an enterprize in contemplation, should, 
before he risks the execution of it, combine 
well in his mind all the ideas that can lead 
to its success ; and he ought not always to 
rely on his own solution of the case. But 
when his ideas on the subject are pretty 
well fixed, he should lay them before the 
general officers, who are under his orders 
or command, for their opinion and concur- 
rence. 
Combinations, in law. Combinations 
to do unlawful acts, are punishable before 
the unlawful acts are executed ; this is to 
prevent the consequences of combination 
and con.spiracies, See. 
COMBRETUM, in botany, a genus of 
the Octandria Monogynia class and order. 
Natural order of Calycanthemse. OnagrEe, 
Jussieu. Essential character : calyx four 
or five-toothed, bell-shaped, superior; co- 
rolla four or five-petalled, inserted into the 
calyx; stamina very long; seed one, four 
or five-angled, thg angles membranaceous. 
There are four species. Tliis genus is very 
imperfectly known, and being a very fine 
one, deserves the attention of the ciiitiva- 
tors of exotic plants. 
COMBUSTION. The temperature of 
bodies may be raised by various means, ' 
which are generally such as produce an agi- 
tation among the particles. The sun’s 
light, and also the chemical or mechanical 
actions of bodies upon each other, if suffi- 
ciently intense or rapid, produce tliis effect. 
One of the most generally known methods 
of producing a liigh teuiperature consists in 
striking or rubbing bodies together; and 
there is no action more familiar to ns, for 
this purpose, than tlie striking of a fiint 
against a piece of steel. Whenever an ele- 
vated temperature is thus produced iii a 
body communicating with the open air, it 
