DIVISIBILITY

, a property in quantity, body, or extension, by which it becomes separable into parts; either actually, or at least mentally.

Such divisibility is infinite, if not actually, at least potentially; for no part can be conceived so small, but another may be conceived still smaller; for every part of matter must have some finite extension, and that extension may be bisected, or otherwise divided; for the | same reason, these parts may be divided again, and so on without end.

We are not here contending for the possibility of an actual division in infinitum: it is only asserted that however small a body is, it may be still farther divided; which it is presumed may be called a division in infinitum, because what has no limits, is called infinite.

The infinite, or indefinite divisibility of mathematical quantity is thus proved, and illustrated by mathematicians: Suppose a line AD perpendicular to BF; and another as GH also perpendicular to the same BF; with the centres C, C, C, &c, and distances CA, CA, &c, describe circles cutting the line GH in the points e, e, &c. Now, the greater the radius AC is, the lefs is the part eG; but the radius may be augmented in infinitum, and therefore the part eG may be diminished in the same manner; and yet it can never be reduced to nothing, because the circle can never coincide with the right line BF. Consequently the parts of any magnitude may be diminished in infinitum.

All that is supposed, in strict geometry, concerning the divisibility of magnitude, amounts to no more, than that a given magnitude may be conceived as divided into a number of parts, equal to any given or proposed number.

It is true that there are no such things as parts infinitely small; yet the subtilty of the particles of several bodies is such, that they far surpass our conception; and there are innumerable instances in nature of such parts actually separated from one another.

Several instances of this are given by Mr. Boyle. He speaks of a silken thread 300 yards long, that weighed but two grains and a half. He measured leaf-gold, and found by weighing it, that 50 square inches weighed but one grain: if the length of an inch be divided into 200 parts, the eye may distinguish them all; therefore in one square inch there are 40,000 visible parts; and in one grain of it there are two millions of such parts; which visible parts no one will deny are still farther divisible.

Again, an ounce weight of silver may be gilt over with 8 grains of gold, which may be afterwards drawn into a wire 13,000 feet long, and still be all covered with the same gilding.

In odoriferous bodies a still greater subtilty of parts is perceived, and even such as are actually separated from one another: several bodies scarce lose any sensible part of their weight in a long time, and yet continually fill a very large space with odoriferous particles. Dr. Keil, in his Vera Physica, Lect. 5, has calculated the magnitude of a particle of Assafœtida, which will be the (57/10000000000000000)th part of a cubic inch. And in the same Lecture he shews that the particles of the blood in animalculæ, observed in fluids by means of microscopes, must be less than that part of a cubic inch which is expressed by a fraction whose numerator is 8, and denominator unity with 30 ciphers after it.

The particles of light, if light consist of real particles, furnish another surprising instance of the minuteness of some parts of matter. A small lighted candle placed on a plain, will be visible two miles, and consequently its light fills a sphere of 4 miles diameter, before it has lost any sensible part of its weight. Now, as the force of any body is directly in proportion to its quantity of matter multiplied by its velocity; and since it is demonstrated that the velocity of the particles of light is at least a million of times greater than the velocity of a cannon-ball, it is plain, that if a million of these particles were round, and of the size of a small grain of sand, we durst no more open our eyes to the light, than expose them to sand shot point-blank from a cannon.

By help of microscopes, such objects as would otherwise escape our sight, appear very large: there are some small animals scarce visible with the best microscopes; and yet these have all the parts necessary for life, as blood, and other fluids. How wonderful then must the subtilty of the parts be, which make up such fluids!

Whence is deducible the following theorem:

Any particle of matter, how small soever, and any finite space, how large soever, being given; it is possible for that small sand, or particle of matter, to be diffused through all that great space, and to fill it in such manner, as that there shall be no pore in it, whose diameter shall exceed any given line; as is demonstrated by Dr. Keil. Introduct. ad Ver. Phys.

, the faculty or quality of being capable of being divided.