COM 



COM 



in all the manners possible, can under- 

 go. Let there be two quantities a and b, 

 their variations will be two ; consequent- 

 ly, as each of them may be combined 

 with itself, to these there" must be added 

 two variations more. Therefore the num- 

 ber of the whole will be 2 4- 2 = 4. If 

 there were three quantities, and the ex- 

 ponent of the variation 2, the combina- 

 tions will be 3, and the changes 3 ; to 

 wit, a b, a c, b c, and b a, c a, c b ; to 

 which if we add the three combinations 

 of each quantity with itself tt a, b b, c c, 

 we shall have the number of changes 

 3 + 3 + 3 = 9. 

 In like manner, it is evident, if the 



fiven quantities were 4, and the exponent 

 , that the number of combinations will 

 be 6, and the number of changes like- 

 wise 6, and the number of combinations 

 of each quantity with itself 4 ; and there- 

 fore the number of changes 16 ; if with 

 the same exponent the given quantities 

 were 5, the number of changes would be 

 25 ; and in general, if the number of the 

 quantities were n, the number of changes 

 would be Tj*. 



Suppose the quantities 3, and the ex- 

 ponent of variation 3, the number of 

 changes is found 27 = 33,^3. a a a, a a b, 

 a b a, b a a, a a c, a c a, c a a, a b b, b a b, 

 b b a, a b c, b a c, b c a, a c b t c a b t c b a, 

 a c c, c a c, c c a, b b b, b b c, c b A, b c b, 

 b c c, c b c, c c b, c c c. In like man- 

 ner it will appear, if the quantities were 

 4, and the exponent 3, that the number 

 of changes would be 64 = 43 ; and in 

 general, if the number of quantities was = 

 n, and the exponent 3, the number of 

 changes would be rtf. 



By proceeding in this manner it will 

 be found, if the number of quantities 

 be n, and the exponent ??, that the num- 

 ber of changes would be n n . Where- 

 fore, if all the antecedents be added, 

 where the exponent is less, the number 

 of all the possible changes will be found 

 nn .|_ n n-i + n n-* + n n-3 + n n-4, &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 1 ; 

 it will be equal (n^i n} -f- (n 1). 

 Suppose n = 4, the number of all possi- 

 ble variations will be (45 4)-r-(l 4) = 

 1020 . 

 -o =340. 



Suppose again n = 24, the number 

 f all the possible variations will be 



(24 1 * 24) + (24 1) = 32009658644- 

 406318986777955348250600 divided by 

 23 = 139172428888725299942512849340- 

 2200. 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 

 attraction, into one substance, so that 

 neither of them can be recognized, nor 

 can they be separated from each other by 

 any mechanical force. Of this principle 

 are the following instances. Salt will 

 unite with water, from which it cannot 

 be separated again but by chemical agen- 

 cy. Sulphur and lime may by heat bfc 

 united, and form a compound, the pro- 

 perties of which are totally dissimilar to 

 those of either the substances used. In 

 both cases an affinity has been exerted 

 between the substances, and they have 

 combined. Combination is to be distin- 

 guished from mixture, in which dissimi- 

 lar particles are blended together, with- 

 out being united by attraction, in which 

 no new qualities are acquired, in which 

 the difference of parts is easily discover- 

 ed, and these parts are capable of being 

 separated by mechanical means. It is 

 distinguished from aggregation, which is 

 merely the union of particles of the same 

 kind of matter, forming an aggregate, 

 uniform in composition, but possessing all 

 the properties of the particles of which 

 it is composed. 



COMBINATION, in military 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 solu- 

 tion of the case. But when his ideas on 

 the subject are pretty well fixed, he 

 should lay them before the general offi- 

 cers, who are under his orders or com- 

 mand, for their opinion and concur- 

 rence. 



COMBINATION, in law. Combinations 

 to do unlawful acts are punishable before 

 the unlawful acts are executed ; this is to 

 prevent the consequences of combination 

 and conspiracies, &c. 



COMBRETUM, in botany, a genus of 

 the Octandria Monogynia class and or- 

 der. Natural order of Calycanthemx. 

 Onagrse, Jussieu. Essential character : 

 calyx four or five toothed, bell-shaped, 

 superior ; corolla four or five-petalled, 

 inserted into the calyx ; stamina very 

 long ; seed one, four or five-angled, the 

 angles membranaceous. There are four 



