AN

ELEMENTARY TREATISE

ON

MECHANICS.

Preliminary Remarks and Definitions.

1. MATTER has been variously defined by philosophers, and some have even doubted whether we can be morally certain of its existence. It is not our intention, nor does it belong to the nature of our subject, to enter into discussions of this kind. Relying solely upon experiment, we give the name of matter or body, to whatever is capable of producing, through our organs, certain determinate sensations; and the power of exciting in us these sensations, constitutes for us so many properties, by which we recognise the presence of bodies. But among these properties, two only are absolutely essential in order to our having a perception of matter. These are extension and impenetrability, of which the sight and touch are the first judges.

2. The character derived from extension is self-evident; when we see or touch a body, this body, or, if you please, the power which it has of affecting us, resides in a certain portion of space. The place which it occupies is therefore determinate; and by this very circumstance it is extended.

3. When we pass our hands over the surface of a body, we perceive that the matter of which it is composed, is without us; moreover, two distinct portions of matter can never be made to coincide, or identify themselves, the one with the other, in such a manner that the same absolute points of space shall at the same time give us the sensation of both. In this consists the property of impenetrability.

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To show how this property, together with that of extension, is necessary to constitute a body, I will refer to familiar phenomena in which these properties are observed separately.

If an object be placed before a concave mirror, there will be formed, at a certain distance from the mirror, an image of the object. This image, distinct from the parts of the space that surround it, is extended but not impenetrable. The hand may be thrust through it without experiencing the smallest resistance, and the parts that come in contact with the hand, vanish instead of being displaced. A piece of wood or stone does not admit of being thus penetrated. Moreover, by means of a second mirror properly disposed, an image of another object may be made to occupy the same place with that of the first, without the latter being displaced, or in any way deranged. Indeed the same coincidence may be effected with a third, a fourth, or any number of images. These images are extended, but not impenetrable; they are forms, but not sensible matter. I say sensible matter, for we shall see hereafter that light which constitutes these images, is itself probably composed of material particles of an insensible tenuity, which move with amazing velocity, and only pass by each other in this case at immense intervals, by which they are separated from each other.

4. It is here proper to speak of certain phenomena which seem, at first sight, to be opposed to what we have laid down with regard to the impenetrability of matter, but which, examined more attentively, only tend to confirm it.

When a solid body is suffered to fall into any fluid, as water for example, it sinks and seems to penetrate the fluid; but it in fact only separates and displaces the parts that compose it, for if the vessel containing the fluid be formed with a narrow neck toward the top, like a bottle, the fluid will be seen to rise as the body enters, and to a greater or less height, exactly in proportion to the size of the immersed body. What has taken place therefore, is only a division and separation of parts, and not strictly a penetration. The same may be said when an edged tool is forced into a block of wood, only the parts of the wood are separated with more difficulty than those of water. The same may be said also when a nail is driven into clay, lead, or gold, in which cases it only makes an opening sufficient for its admission. Indeed the mass thus pierced is not entirely separated,

but the parts are nevertheless pressed and crouded together; and if we examine those which surround the opening, caused by the nail, we shall find sensible marks of this pressure. The nail in its turn may likewise be pierced by steel, and this again by other bodies.

We hence infer that bodies, even the most hard and compact, are not composed of matter absolutely continuous, but of parts aggregated together, and placed at distances, which, under the influence of external causes, may become greater or less. It is on this account that the dimensions of any given mass of matter are capable of being increased by heat, or diminished by cold, that the particles of salt admit of being separated and distributed, and as it were, lost among the particles of water; that mercury attaches itself to a piece of gold immersed in it, and insinuates itself into the interior of this compact substance. These mixtures and dissolutions sometimes take place without any apparent augmentation of bulk, this bulk being estimated according to the exterior surface of the bodies in question, without regard being had to the void spaces, sensible or insensible to us, which may be found to exist among their parts. In all this there is only separation and mixture without any actual penetration of material particles.

This want of material continuity in bodies is known under the general name of porosity, and we call pores the interstices or empty spaces by which these particles are separated from each other. Porosity seems to be a property common to all bodies, although it does not belong to the essence of matter, since we can conceive of sensible bodies which are entirely destitute of void space.

5. Thus admitting that bodies may be considered as composed of smaller parts which constitute their essence, we may be asked, what is the form and magnitude of these parts. As to the magnitude, it should seem that it is extremely minute; for to whatever extent we carry the division, in the case of gold, for example, by the processes of wire-drawing, filing, and beating, the smallest particles preserve invariably all the properties that belong to the entire mass. Crystallized bodies reduced to an almost impalpable powder, upon being examined with a microscope, are found to exhibit the same forms and the same angles which characterize the whole mass of the crystal. We have

examples of a division carried to a still greater extent in odours, the sense being affected in this case by particles proceeding from the odoriferous body that are absolutely invisible and impalpable. From these few instances, and a thousand others that might be mentioned, it is evident that a body without changing its character, without ceasing to be of the same identical nature with the largest masses that surround us, may be divided into parts, the smallness of which eludes the power of the senses, and almost that of the imagination.

6. The question has been much discussed, whether matter by infinitely divisible; but it is now pretty generally agreed that the dispute is about words. If the point in question relate to abstract geometrical divisibility, there can be no doubt of the truth of the affirmative; for however infinitely small we suppose a particle, from the very circumstance of its being extended, we can always conceive this extent divided into two halves, and each of these into two others, and so on without end (Calc. 4). But if we mean by the question an actual physical divisibility, nothing can be decided absolutely one way or the other. It seems however by all we can learn, that we should at some stage of the division arrive at material particles which would not admit of being broken, or altered, or transmuted the one into the other; for to whatever chemical operation they are subjected, into whatever combinations they are made to enter, however they may be brought to constitute a part of living beings, they always return to their former state, with their original properties unchanged. The infinite variety of processes of this kind through which the same material particles have been made to pass since the world was created, does not appear to have produced the smallest alteration.

7. But how can such a system of particles exist collected together in the form of solid and resisting masses, as we see they are in a great number of bodies, in all indeed when they are properly examined? This state, as we shall see hereafter, is produced and maintained by the natural powers with which all parts of matter are endued, and which cause them to tend toward each other, as it were by an attraction. But if there existed only forces of this kind, the particles would continue to approach till they came into actual contact with each other, that is, until they were arrested by the impenetrability of their parts, which would not admit of the contraction and dilatation which are con

stantly observed in bodies. We accordingly infer that there is a general cause of interior repulsion in bodies, by which the attractive forces are continually balanced. This cause which resides in all bodies, seems to be referrible to the principle of heat. The particles of each body, actuated at the same time by these two opposite forces, naturally put themselves in a state of equilibrium, resulting from a compensation of energies, and they approach and recede, according as the forces to which they are exposed from without favor the attractive or repulsive principle. It is with these minute bodies as it is with the planets of our system, which are found to move and oscillate, as it were, in orbits of variable forms and dimensions, without the system being destroyed, or the general equilibrium being disturbed. From these different conditions of equilibrium arise, as we shall see hereafter, all the secondary and changeable forms of bodies, such, for example, as are denominated æriform, liquid, and solid, crystallized, hard, elastic, &c.

8. In all the phenomena which present themselves, the particles of matter act, or rather are acted upon, as if they were perfectly inert, that is, deprived of all power of self-direction. They can be moved, displaced, stopped, by causes foreign to themselves, but we never have been able to discover the least trace of any thing like choice or will proper to the particles themselves. If the ball which rolls upon a billiard table in consequence of the impulse that is given to it, loses by little and little its velocity, and at length comes to a state of rest, it is entirely the effect of the continual resistance that it meets with from the roughness of the cloth with which it comes in contact, and from the particles of the air through which it passes. Make the cloth more smooth, or the air more rare, and the same impulse would keep it longer in motion; substitute for the cloth a marble slab highly polished, or a band of stretched wire, the elasticity of which is still more perfect, and the ball would continue its motion for a much longer time; from all which it is to be inferred, that if the obstacles were completely removed, there would be no diminution of the velocity first communicated, and the motion would never cease. A stone thrown from the top of a tower, and urged at the same time by the impulse of the hand and by gravity, will come to the ground after proceeding a certain distance, losing at the same time its horizontal velocity, by imparting it to the particles of air against which it impinges.