D I V 
543 
T) ! y 
lines will evidently cut the proposed exten- 
sion AB in a different point. Now as the 
line BD may be produced towards D with- 
out limitation, and straight lines may be 
drawn from L to an infinite number of points 
in the extended line BD ; therefore the ex- 
tension AB may be divided without end, or 
beyond any assignable number of parts. 
Or thus: suppose a line, AD, Plate Mis- 
cel. fig. 5 G, perpendicular to BF ; with the 
centres C, C, C, ike. and distances CA, CA, 
<kc. describe circles cutting the line GH in 
the points e, e, & c. Now the greater the 
radius AC is, the less is the part e G ; but 
the radius may be augmented in infinitum, 
and therefore the part cG may be diminished 
in the same manner; and yet it can never 
be reduced to nothing, because the circles 
can never coincide with the right line BF. 
Consequently the parts of any magnitude 
may be diminished in infinitum. 
Thus far we have shewn that extension 
may be divided into an unlimited number of 
parts; but with respect to the limits of the 
divisibility of matter itself we are perfectly in 
the dark. W c can indeed divide certain bo- 
dies into surprisingly fine and numerous par- 
ticles, and the works of nature offer many 
fluids and solids of wonderful tenuity ; but 
both our efforts, and those naturally small ob- 
jects, advance a very short way towards infi- 
nity. Ignorant of the intimate nature of 
matter, we cannot assert whether it may be 
capable of infinite division, or whether it ul- 
timately consists of particles of a certain 
size, and of perfect hardness. We shall now 
add some instances of the wonderful tenuity 
of certain bodies, which have been produced 
either by art, or discovered by means of mi- 
croscopical observations amongst the stupen- 
dous works of nature. 
The spinning of wool, silk, cotton, and 
such-like substances, affords no bad speci- 
mens of this sort; since the thread which has 
been produced by this means has often been 
so very fine as almost to exceed the bounds of 
credibility, had it not been sufficiently well 
authenticated. Mr. Boyle mentions that two 
grains and a half of silk was spun into a 
thread 300 yards long. A few years ago a 
lady of Lincolnshire spun a single pound of 
woollen yarn into a thread of 168,000 yards 
long, which is equal to 95 English miles. 
Also a single pound-weight of line cotton- 
yarn was lately spun, in the neighbourhood 
of Manchester, into a thread 134,400 yards 
long. 
The ductility of gold likewise furnishes a 
striking example of the great tenuity of mat- 
ter amongst the productions of human inge- 
nuity. A single grain-weight of gold lias 
been often extended into a surface equal to 
50 square inches. If every square inch of it 
is divided into square particles of the hun- 
dredth part of an inch, which will be plainly 
visible to the naked eye, the number of those 
particles in one inch square will be 10,000; 
and multiplying this number by the 50 
inches, the product is 500,000 ; that is, the 
grain of gold may be actually divided into 
at least half a million of particles, each of 
which is perfectly apparent to. the naked eye. 
Yet if those particles are viewed in a good 
microscope, they will appear like a large sur- 
foce, the ten-thousandth part of which might 
by this means be easily discerned. 
Ao ingenious artist in London has been 
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able to draw parallel lines upon a glass plate, 
as also upon silver, so near one another, that 
10,000 of them occupy the space of one 
inch. Those lines can be seen only by the 
assistance ot a very good microscope. * An- 
other workman has drawn a silver wire, the 
diameter of which does not exceed the 750th 
part of ah inch. But those prodigies of hu- 
man ingenuity will appear extremely gross 
and rude, if they are compared with the im- 
mense subtilty of matter which may every 
where be observed amongst the works of na- 
ture. The animal, the vegetable, and even 
the mineral kingdom, furnish numerous ex- 
amples of this sort. 
What must be the tenuity of the odorifer- 
ous parts of musk, when we find, that a piece 
ot it will scent a whole room in a short time, 
and yet it will hardly lose any sensible part 
of its weight ! But supposing it to have lost 
one-hundredth part of a grain weight, when 
this small quantity is divided and dispersed 
through the whole room, it must so expand 
itself as net to leave an inch square of space 
where the sense of smell may not be affected 
by some of its particles. Flow small must 
then be the weight and size of one of those 
particles ! 
The human eye, unassisted by glasses, can 
frequently perceive insects so small as to be 
barely discernible. The least reflection 
must shew that the limbs, the vessels, and 
other parts of such animals, must infinite- 
ly exceed in fineness every endeavour of 
human art. But the microscope has disco- 
vered wonders that are vastly superior, and 
such indeed as were utterly unknown to our 
forefathers, before the invention of that no- 
ble instrument. 
Insects have been discovered so small as 
not to exceed the 10,000th part of an inch: 
so that 1,000,000,000,000 of them might be 
contained within the space of one cubic inch ; 
yet each animalcule must consist of parts 
connected with each other ; with vessels, 
with fluids, and with organs necessary for its 
1 motions, for its increase, for its propagation, 
&c. How inconceivably small must those 
organs be ! and yet they are unquestionably 
composed of other parts still smaller, and still 
farther removed from the perception of our 
senses. 
Several writers, when treating of the di- 
visibility of matter, have mentioned two cu- 
rious theorems, which are established on the 
supposition that matter is divisible without 
end. 
Theorem I. A quantity of matter, how- 
ever small, and any finite space, however 
large, being given ; it is possible that that 
matter may be diffused through all that 
space, and so fill it, as not to leave in it a 
pore, whose diameter will exceed a given 
right line. 
Let the given space be a cube, whose side 
is AB, so that the cube be equal to ABj ! 
and let the quantity of matter be represent- 
ed by b 3 ; also let a line D be the limit of 
the diameter of the pores. 
The side AB being a finite quantity, may 
be conceived to be divisible into parts equal 
to the line D. Let the number of those parts 
be repres ented by n, so that nV> — AB, and 
ra 3 D 3 = A hi 3 . Conceive the given space 
to be divided into cubes, each of whose sides 
be equal to the right line D, and the num- 
ber of those cubes will be n\ which cubes 
may be represented by E, F, G, H. 
Again, let the particle *5 3 be supposed 
to be divided into parts whose number 
is « 3 ; and in each cubic space let there 
be placed one of those particles, by 
which means the matter b z will be diffused 
through all the given space. Besides, each 
particle being placed in its cell, may lie 
formed into a concave sphere, whose dia- 
meter may be equal to the given line D ; 
whence it will follow, that each sphere will 
touch that which is next to it ; and thus the 
quantity of matter b\ be it ever so small, will- 
fill the given finite space, however large, in 
such a manner as not to leave in it a pore, 
larger in diameter than the given line D. 
Corollary. There may be a given body, 
whose matter if it he reduced into a space 
absolutely full, that space may be any given- 
part of the former magnitude. 
Theorem II. There may be two bodies 
equal in bulk, whose quantities of matter 
may be very unequal, and though they have 
any given ratio to each other, yet the sums 
of the pores or empty spaces in those bodies- 
may almost approach the ratio of equality. 
The demonstration of this theorem is* ea- 
sily derived from the foregoing : for since the 
matter of a body may be conceived to be 
condensable into any part of the original 
hulk ; therefore supposing two bodies, A and 
B, of equal bulk, to be such that the matter 
of A be 100 times the matter of B; the 
matter of B may be conceived to be con- 
densed into 1,000,000th part of its origi- 
nal bulk, and of course the matter of A will 
be condensed into one hundred 1,000,000th 
parts of the same bulk ; in which case the 
spaces left in the original bulk of B will be to 
the spaces left in the original bulk of A, as 
999,999 to 999,900, which numbers are 
nearly equal to each other. 
Instead of the above-mentioned numbers, 
the proportions of the quantities or matter 
may be increased at pleasure, and so may. 
the proportion of the original bulks of the 
bodies to the spaces into which they may be 
conceived to be condensable. 
DIVISION, in arithmetic, one of the four 
fundamental rules, by which we find how 
often a less number, called the divisor, is 
contained in a greater, called the dividend ; 
the number of times which the divisor is 
contained in the dividend being termed the 
quotient. See Arithmetic, and Algebra. 
Division, in natural philosophy, is the 
taking a thing to pieces, in order to have a 
more complete conception of the whole: 
this is frequently necessary in examining very- 
complex beings, the several parts of which, 
cannot be surveyed at one view. Thus to . 
learn the nature of a watch the workman 
takes it to pieces, and shews us the spring, 
wheels, axles, pinions, balances, dial- plate, 
pointer, case, &c. and after describing the 
uses and figures of each of them apart, ex- 
plains how they contribute to form the whole 
machine. See Clockwork. 
Division, in music. This word bears 
two constructions. With theoretical musi- 
cians it implies the division of the intervals of 
the octave; but taken in a practical sense;-, 
signifies a long series of notes so running into 
each other as to form one connected chain of 
sounds; and which, in vocal music, is- al- 
ways applied to a single syllable. The sing- 
