COM 
C O M 
C O M 
393 
II. To find the number of changes and alterations 
•which any number of quantities can undergo , when com- 
bined in all possible varieties of mays, with themselves 
and each other , loth as tjse things themselves , and the 
order or position of them. 
One thing- admits but of one order or position. 
T'vo things may be varied four ways ; thus> 
aa, ab, la, lb. 
Three quantities, taken by twos, may be 
varied nine ways ; thus aa, ab, ac, ba, ca , bb , be, 
cb , cc. 
In like mann,er four things, taken by twos, 
may be varied 4 2 or 16' ways; and 5 things, by 
twos, 5“ or 25 ways ; and, in general, n tilings, 
taken by twos, may be changed or varied n l 
different ways. 
For the same reason, when taken by threes, 
the changes will be id ; and when taken by 
fours, they will be n ' ; and so generally, when 
taken by «s, the changes will be id. 
Hence then, adding all these together, the 
whole number of changes or combinations in n 
things, taken both by 2s, by 3s, by 4s, & c. to 
ns, will be the sum of the geometrical series 
» -j- / 2 2 -j- id -j~ id - - - - which sum is — 
— 1 
r X «• 
71 1 
For example, if the number of tilings n be 4 ; 
4 4 — t l 255 
this giveS y 4 — X 4 340. 
4 — 1 * 3 
And if n be 24, the number of letters in the 
alphabet, the theorem gives 
041 * 1 04 
X 24 = 24 i+ — 1 X -- - - = 
24—1 23 
1391724288887252999425128493402200. In so 
many different ways, therefore, may the 24 let- 
ters of the alphabet be varied or combined 
among themselves, or so many different words 
may be made out of them. 
COMBRETUM, a genus of the class and 
order octandria monogynia. The calyx is 
five-toothed, bell-shaped, superior corolla 
four-petalled, stam. very long, seed one, four 
or live angled, angles membranaceous. There 
are four species, natives of South America 
and the West Indies. 
COMBUSTION. There is perhaps no 
phenomenon more wonderful in itself, more 
interesting on account of Us utility, or which 
has more closely occupied the attention of 
chemists, than combustion. When a stone 
or a brick is heated, it undergoes no change 
except an augmentation of temperature ; and 
when left to itself, it soon cools again, and 
becomes as at tirst. But with combustible 
bodies the case is very different. When 
heated to a certain degiee in the open air, 
they suddenly become much hotter of them- 
selves ; continue for a considerable time in- 
tensely hot, sending out a copious stream of 
caloric and light to the surrounding bodies. 
This emission, after a certain period, begins 
to diminish, and at last ceases altogether. The 
combustible has now undergone a most com- 
plete change; it is" converted into a sub- 
stance possessing very different properties, 
and no longer capable of combustion. Thus 
when charcoal is kept for some time at the 
temp-.-; attire of about 800°, it kindles, be- 
comes intensely hot, and continues to emit 
light and caloric for a long time. When the 
emission ceases, the- charcoal has all disap- 
peared, except an inconsiderable residuum 
of ashes; being almost entirely converted 
into carbonic -acid gas, which makes its es- 
cape, unless the experiment is conducted in 
proper vessels. If it is collected, it is found 
to exceed greatly in weight the whole of the 
charcoal consumed. 
The first attempt to explain combustion 
was crude and unsatisfactory. A certain 
elementary body, called fire, was supposed 
to exist, possessed of the property of devour- 
ing certain other bodies, and converting 
them into itself. When we set fire to a 
grate full of charcoal, we bring, according to 
this hypothesis, a small portion of the ele- 
ment of fire, which immediately begins to 
devour the charcoal, and to convert it into 
fire. Whatever part of the charcoal is not 
fit for being the food of lire is left behind in 
the form of a lies. 
A much more ingenious and satisfactory 
hypothesis' was proposed in 1665 by Dr. 
Hooke. According to this extraordinary 
man, there exists in common air a certain 
substance, which is like, it not the very 
same with, that which is fixed in saltpetre. 
This substance has the property of dissolving 
all combustibles ; but only when their tem- 
perature is considerably raised. The solu- 
tion takes place with such rapidity, that it 
occasions both heat and light, which in his 
opinion are mere motions. 
About ten years after the publication of 
Hooke’s Micrographia, his theory was adopt- 
ed by Mayow, without acknowledgment, in 
a tract which he published at Oxford on 
saltpetre. We are indebted to him for a 
number of very ingenious and important 
experiments, in which lie anticipated several 
modern chemical philosophers; but his rea- 
soning is for the most part absurd, and the 
additions which he made to the theory of 
Hooke are exceedingly extravagant. To 
the solvent of Hooke he gives the name of 
spiritus nitro-aereus. It consists, he sup- 
poses, of very minute particles, which are 
constantly at variance with the particles of 
combustibles, and from their quarrels all the 
changes of things proceed. Fire consists in 
the rapid motion of these particles, heat in 
their less rapid motion. The sun is merely 
nitro-aerial particles moving with great rapi- 
dity. They fill space. Their motion be- - 
comes more languid according to their dis- 
tance from the sun ; and when they approach 
near the earth, they become pointed, and 
constitute- cold. 
The attention of chemical philosophers 
was soon drawn away from the theory ot 
Hooke and Mayow to one of a very different 
kind, first proposed by Beecher, but new-mo- 
delled by his disciple Stahl with so much 
skill, arranged in such an elegant systematic 
form, and furnished with such numerous ap- 
propriate and convincing illustrations, that 
it almost instantly caught the tancy, raised 
Stahl to the highest rank among philoso- 
phers, and constituted him the founder of 
the Stahlian theory of combustion. 
According to Stahl, all combustible sub- 
stances contain in them a certain body, 
known by the name of phlogiston, to which 
they owe their combustibility. This sub- 
stance is precisely the same in all combus- 
tibles. These bodies of course owe their 
diversity to other ingredients which they 
contain, and with which the phlogiston is 
combined. Combustion, and all its attendant 
phenomena, depend upon the separation and 
dissipation of this principle; and when it ;s 
once separated, the remainder ot the body is 
incombustible. Phlogiston, according toStahl, 
is peculiarly disposed to he affected by a 
violent whirling motion. The heat and the 
light, which make their appearance during* 
combustion, are merely two properties of 
phlogiston when in this state of violent agita-l 
tion. Ingenious as this theory was, it want! 
’ed the support ot demonstration. Thdj 
existence of phlogiston was gratuitously ad-1 
milled, and every one was at liberty to at-l 
tach his own idea to the term, 'i he theory! 
accordingly under ..cnt many changes in th$ 
hands of Macquer, Priestley, Craw lord, ancl 
Kirwan, but difficulties multiplied in proporl 
tion to the progress of discovery in othel 
departments 01 the science. The last o 
these philosopher* took much pains to provi 
t hat hydrogen performed the office which tin 
Stahlian theory assigned to phlogiston. Thi: 
he attempted in a treatise published on pur 
pose, entitled, ‘ An Essay on Phlogiston, anc 
the Constitution of Acids.’ 
In 1777 the celebrated Swedish chemist 
Scheele, published a treatise, entitled, 1 Che 
rnical Experiments on Air and Fire,’ wliicl 
perhaps exhibits a more striking display o 
the extent of his genius than all his othe: 
publications. After a vast number of expe 
riments, conducted with astonishing inge 
nuity, he concluded, that caloric is com 
posed of a certain quantity of oxygen com 
billed with phlogiston ; that radiant heat, ; 
1 substance which lie supposed capable o 
being propagated in straight lines like light 
and not capable of combining with air, i 
composed of oxygen united with a greate 
quantity of phlogiston, and light of oxygei 
united with a still greater quantity. He sup 
posed too, that the difference between Iff 
rays depends upon the quantity of phlogis 
ton. The red, according to him, contain 
the least; the violet, the most phlogiston. lSj 
phlogiston Mr. Scheele seems to have mean 
hydrogen. It is needless therefore to exa 
mine his theory, as it is now known that tff 
combination of hydrogen and oxygen form 
not caloric but water. The whole fabric 
therefore, lias fallen to the ground; but th 
importance of the materials will always 1> 
admired, and the ruins of the structure mm 
remain eternal monuments of the genius 0 
the builder. 
During these different modifications of tff 
Stahlian theory, the illustrious Lavoisier wa 
assiduously occupied in studying the phono 
mena of combustion, lie seems to hav 
attached himself to this subject, amd to hav 
seen the defects of the prevailing theory, a 
early as 1770. The first precise notion^ 
however, of whatever might be the reaj iff 
ture of combustion, were suggested to hir 
by Bayen’s paper 011 the oxydes of mercury 
which he heard read before the Academy 'c 
Sciences In 1774. These tirst notions, o 
rather conjectures, he pursued with unwej 
ried industry, assisted by the numerous dis 
coveries which were pouring in from a 
quarters; and by a long series of the md 
laborious and accurate experiments and da 
quisitions ever exhibited in chemistry, h 
fully established the existence of this generl 
law: “ In every case of combustion, oxygj 
combines with the burning body.” Th 
noble discovery, the fruit of genius, indu 
try, and penetration, has reflected new lig] 
oii every branch of chemistry, has connec 
ed and- explained a vast number of facts fo 
merly insulated and inexplicable, and Iff 
new-modelled the whole, and moulded it ini 
the form of a science. 
