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to be that which has length, breadth, and thicknefs, or is divifible in three refpects, namely, of length, breadth, and thickness.

No finite or imaginable divifion of a line can ever produce a point or indivisible part. A line is therefore divifible into an infinite number of other lines, or fimilar parts, and confequently much more is a fuperficies, and yet more a folid. A mathematical folid, that is to fay, pure extenfion, is divisible to infinity and if the elements of matter be of the fame nature as the aggregates they compofe, matter is likewife infinitely divifible. A variety of remarkable confequences follow from these plain deductions; of which we fhall proceed to mention a few inftances both theoretical and practical. Thus,

Any quantity of matter, how fmall foever, and any finite space, how great foever, being given (as for example, a cube circumfcribed about the orb of Saturn) it is poffible for the fmall quantity. of matter to be diffused throughout all that space, and to fill it, fo that there fhall be no pore or interstice in it, whofe diameter shall exceed a given finite line.

To prove this, fuppofe the cube to be divided. into fall cubes, whofe fides shall each be equal to half the given line. It will be easily seen, that the number of small cubes will not be infinite. Imagine the quantity of matter to be then divided into a number of parts equal to that of the small cubes, and a particle to be placed in the center of each cube. The whole fpace will thus be filled, and

the

the greatest distance between two adjacent particles, or, in other words, the diameter of any pore or interstice, will be lefs than the given line.

Hence there may be given a body, whofe matter, if it could be reduced or compreffed into a fpace abfolutely full, that space may be any given part of its former magnitude.

Again; there may be two bodies of equal bulk, a and their quantities of matter may be unequal in any proportion; yet the fum of their pores, or quantity of void space in each of the two bodies, fhall be nearly in the proportion of equality to each other.

This is not fo obvious as the former inftance, but an example will render it clear.

Suppose one thousand cubic inches of gold to contain one cubic inch of matter, or, in other words, when reduced into a space absolutely full, to be equal to one cubic inch: then one thousand cubic inches of water will contain one nineteenth part of an inch of matter when reduced. Confequently, the void fpaces in the gold will be nine hundred and ninety-nine cubic inches, and those in the water nine hundred and ninety-nine cubic inches, and eighteen nineteenth parts of an inch; that is, they will be nearly in the ratio of equality.

Yet, the actual divifibility of matter can proba- R bly be carried but to a certain degree. The ultimate particles of bodies, it is most likely, are not to be altered by any force in nature. But there are nevertheless, many inftances which fhew to

Gold is nineteen times as heavy as water.

what

what inconceivably minute parts bodies may be actually divided.

S A grain of leaf-gold will cover fifty square

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υ

inches, and contains two millions of vifible parts; but the gold which covers the filver wire, used in making gold lace, is fpread over a furface twelve times as great.

In making this wire, it is usual to gild a cylindrical bar of filver ftrongly, and afterwards draw it into wire, by paffing it fucceffively through holes of various magnitudes in plates of fteel. By this means the surface is prodigiously augmented; notwithstanding which, it ftill remains gilded fo as to preserve an uniform appearance even when examined with the microscope. The quantities of gold and filver, and the dimensions of the wire, are known. With thefe data it is eafy to calculate, and from calculation it is proved, that fixteen ounces of gold, which, if in the form of a cube, would not measure one inch and a quarter in its fide, will completely gild a quantity of filverwire fufficient to circumfcribe the whole globe of the earth.

The animalculæ obferved in the milt of a codfish are so small, that many thousands of them might ftand on the point of a needle.

Suppofing the globules of the blood in thefe animalcula to be in the fame proportion to their bulk as the globules of a man's blood bear to his body, it appears, that the fmalleft vifible grain of fand would contain more of thefe globules than 10,256

3

10,256 of the largest mountains in the world would contain grains of fand.

Thefe inftances may ferve to fhew the amazing v fineness of the parts of bodies, which are nevertheless ftill compounded. Gold, when reduced to the thinneft leaf, ftill retains those properties which arise from the modification of its parts. Microscopic animalculæ are without doubt organized bodies, and the particles of their circulating fluids must be poffeffed of specific qualities. Even the rays of light are compounded of an almost infinite variety of particles, which, when separated from each other, exhibit the powers of exciting ideas of colours. None of these are the ultimate particles of which all buddies are formed, for they all bear evident marks of compofition. How inconceivably small then must thofe particles be!

To these ultimate particles alone it is, that im- w penetrability can be attributed. Penetration takes place in all compounded bodies. Water exifts in the pores of wood. Air in the pores of water. Quick filver in the pores of gold, &c. &c.

Some philofophers have questioned whether im- x penetrability be really a property of matter; and it must be confeffed, that, notwithstanding this idea is fo closely connected in the formation of our compound idea of matter, yet, if we examine from whence the notion is originally obtained, we shall find that our knowledge is much less certain than we may have fufpected.

To make this clearer, we must confider that our y notion of impenetrability is derived from the sense

of

of feeling. We move the hand towards a body, and, in fituations where motion is not generated, it is prevented by that 'body from going forward; from which we conclude, that the body poffeffes a part of space to the exclusion of every other body; that fay, that it is impenetrable.

Z But, in order to justify this conclufion, it is neceffary that we fhould be certain that it is the body itself, actually occupying space, which refifts the preffure; and of this we cannot be affured, fince we, obferve many inftances in which bodies afford refiftance to other bodies which move in fpaces at fome diftance from the refifting body. Thus, the loadstone, in certain circumstances, refifts the motion of iron which approaches towards it; and there is no doubt but this refiftance or repulfion, if exerted on any part of a man, would afford a fenfation fimilar to that which arifes from contact. If the man had not fight, or fome other fense to perceive that the refifting body was really distant, he would, from the fense of touch, conclude that the body was in contact with the part perceiving; and if any force he could produce were infufficient to overcome that refiftance, he would conclude the body to be impenetrable.

A

Now, by feveral experiments, which we shall have occafion to mention in the course of this work, there is the highest reafon to conclude that all bodies exert a repulfive force on each other, and that the common effects which are attributed to contact and collifion are produced by this repul