Читать книгу A Treatise on Mechanics - Henry Kater - Страница 3

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(1.) Placed in the material world, Man is continually exposed to the action of an infinite variety of objects by which he is surrounded. The body, to which the thinking and living principles have been united, is an apparatus exquisitely contrived to receive and to transmit impressions. Its various parts are organised with obvious reference to the several external agents by which it is to be effected. Each organ is designed to convey to the mind immediate notice of some peculiar action, and is accordingly endued with a corresponding susceptibility. This adaptation of such organs to the particular influences of material agents, is rendered still more conspicuous when we consider that, however delicate its structure, each organ is wholly insensible to every influence except that to which it appears to be specially appropriated. The eye, so intensely susceptible of impressions from light, is not at all affected by those of sound; while the fine mechanism of the ear, so sensitively alive to every effect of the latter class, is altogether insensible to the former. The splendour of excessive light may occasion blindness, and deafness may result from the roar of a cannonade; but neither the sight nor the hearing can be injured by the most extreme action of that principle which is designed to affect the other.

Thus the organs of sense are instruments by which the mind is enabled to determine the existence and the qualities of external things. The effects which these objects produce upon the mind through the organs, are called sensations, and these sensations are the immediate elements of all human knowledge. Matter is the general name which has been given to that substance, which, under forms infinitely various, affects the senses. Metaphysicians have differed in defining this principle. Some have even doubted of its existence. But these discussions are beyond the sphere of mechanical philosophy, the conclusions of which are in nowise affected by them. Our investigations here relate, not to matter as an abstract existence, but to those qualities which we discover in it by the senses, and of the existence of which we are sure, however the question as to matter itself may be decided. When we speak of “bodies,” we mean those things, whatever they be, which excite in our minds certain sensations; and the powers to excite those sensations are called “properties,” or “qualities.”

(2.) To ascertain by observation the properties of bodies, is the first step towards obtaining a knowledge of nature. Hence man becomes a natural philosopher the moment he begins to feel and to perceive. The first stage of life is a state of constant and curious excitement. Observation and attention, ever awake, are engaged upon a succession of objects new and wonderful. The large repository of the memory is opened, and every hour pours into it unbounded stores of natural facts and appearances, the rich materials of future knowledge. The keen appetite for discovery implanted in the mind for the highest ends, continually stimulated by the presence of what is novel, renders torpid every other faculty, and the powers of reflection and comparison are lost in the incessant activity and unexhausted vigour of observation. After a season, however, the more ordinary classes of phenomena cease to excite by their novelty. Attention is drawn from the discovery of what is new, to the examination of what is familiar. From the external world the mind turns in upon itself, and the feverish astonishment of childhood gives place to the more calm contemplation of incipient maturity. The vast and heterogeneous mass of phenomena collected by past experience is brought under review. The great work of comparison begins. Memory produces her stores, and reason arranges them. Then succeed those first attempts at generalisation which mark the dawn of science in the mind.

To compare, to classify, to generalise, seem to be instinctive propensities peculiar to man. They separate him from inferior animals by a wide chasm. It is to these powers that all the higher mental attributes may be traced, and it is from their right application that all progress in science must arise. Without these powers, the phenomena of nature would continue a confused heap of crude facts, with which the memory might be loaded, but from which the intellect would derive no advantage. Comparison and generalisation are the great digestive organs of the mind, by which only nutrition can be extracted from this mass of intellectual food, and without which, observation the most extensive, and attention the most unremitting, can be productive of no real or useful advancement in knowledge.

(3.) Upon reviewing those properties of bodies which the senses most frequently present to us, we observe that very few of them are essential to, and inseparable from, matter. The greater number may be called particular or peculiar qualities, being found in some bodies but not in others. Thus the property of attracting iron is peculiar to the loadstone, and not observable in other substances. One body excites the sensation of green, another of red, and a third is deprived of all colour. A few characteristic and essential qualities are, however, inseparable from matter in whatever state, or under whatever form it exist. Such properties alone can be considered as tests of materiality. Where their presence is neither manifest to sense, nor demonstrable by reason, there matter is not. The principal of these qualities are magnitude and impenetrability.

(4.) Magnitude.—Every body occupies space, that is, it has magnitude. This is a property observable by the senses in all bodies which are not so minute as to elude them, and which the understanding can trace to the smallest particle of matter. It is impossible, by any stretch of imagination, even to conceive a portion of matter so minute as to have no magnitude.

The quantity of space which a body occupies is sometimes called its magnitude. In colloquial phraseology, the word size is used to express this notion; but the most correct term, and that which we shall generally adopt is volume. Thus we say, the volume of the earth is so many cubic miles, the volume of this room is so many cubic feet.

The external limits of the magnitude of a body are lines and surfaces, lines being the limits which separate the several surfaces of the same body. The linear limits of a body are also called edges. Thus the line which separates the top of a chest from one of its sides is called an edge.

The quantity of a surface is called its area, and the quantity of a line is called its length. Thus we say, the area of a field is so many acres, the length of a rope is so many yards. The word “magnitude” is, however, often used indifferently for volume, area, and length. If the objects of investigation were of a more complex and subtle character, as in metaphysics, this unsteady application of terms might be productive of confusion, and even of error; but in this science the meaning of the term is evident, from the way in which it is applied, and no inconvenience is found to arise.

(5.) Impenetrability.—This property will be most clearly explained by defining the positive quality from which it takes its name, and of which it merely signifies the absence. A substance would be penetrable if it were such as to allow another to pass through the space which it occupies, without disturbing its component parts. Thus, if a comet striking the earth could enter it at one side, and, passing through it, emerge from the other without separating or deranging any bodies on or within the earth, then the earth would be penetrable by the comet. When bodies are said to be impenetrable, it is therefore meant that one cannot pass through another without displacing some or all of the component parts of that other. There are many instances of apparent penetration; but in all these, the parts of the body which seem to be penetrated are displaced. Thus, if the point of a needle be plunged in a vessel of water, all the water which previously filled the space into which the needle enters will be displaced, and the level of the water will rise in the vessel to the same height as it would by pouring in so much more water as would fill the space occupied by the needle.

(6.) Figure.—If the hand be placed upon a solid body, we become sensible of its impenetrability, by the obstruction which it opposes to the entrance of the hand within its dimensions. We are also sensible that this obstruction commences at certain places; that it has certain determinate limits; that these limitations are placed in certain directions relatively to each other. The mutual relation which is found to subsist between these boundaries of a body, gives us the notion of its figure. The figure and volume of a body should be carefully distinguished. Each is entirely independent of the other. Bodies having very different volumes may have the same figure; and in like manner bodies differing in figure may have the same volume. The figure of a body is what in popular language is called its shape or form. The volume of a body is that which is commonly called its size. It will hence be easily understood, that one body (a globe, for example) may have ten times the volume of another (globe), and yet have the same figure; and that two bodies (as a die and a globe) may have figures altogether different, and yet have equal volumes. What we have here observed of volumes will also be applicable to lengths and areas. The arc of a circle and a straight line may have the same length, although they have different figures; and, on the other hand, two arcs of different circles may have the same figure, but very unequal lengths. The surface of a ball is curved, that of the table plane; and yet the area of the surface of the ball may be equal to that of the table.

(7.) Atoms—Molecules.—Impenetrability must not be confounded with inseparability. Every body which has been brought under human observation is separable into parts; and these parts, however small, are separable into others, still more minute. To this process of division no practical limit has ever been found. Nevertheless, many of the phenomena which the researches of those who have successfully examined the laws of nature have developed, render it highly probable that all bodies are composed of elementary parts which are indivisible and unalterable. The component parts, which may be called atoms, are so minute, as altogether to elude the senses, even when aided by the most powerful scientific instruments. The word molecule is often used to signify component parts of a body so small as to escape sensible observation, but not ultimate atoms, each molecule being supposed to be formed of several atoms, arranged according to some determinate figure. Particle is used also to express small component parts, but more generally is applied to those which are not too minute to be discoverable by observation.

(8.) Force.—If the particles of matter were endued with no property in relation to one another, except their mutual impenetrability, the universe would be like a mass of sand, without variety of state or form. Atoms, when placed in juxtaposition, would neither cohere, as in solid bodies, nor repel each other, as in aeriform substances. On the contrary, we find that in some cases the atoms which compose bodies are not simply placed together, but a certain effect is manifested in their strong coherence. If they were merely placed in juxtaposition, their separation would be effected as easily as any one of them could be removed from one place to another. Take a piece of iron, and attempt to separate its parts: the effort will be strongly resisted, and it will be a matter of much greater facility to move the whole mass. It appears, therefore, that in such cases the parts which are in juxtaposition cohere and resist their mutual separation. This effect is denominated force; and the constituent atoms are said to cohere with a greater or less degree of force, according as they oppose a greater or less resistance to their mutual separation.

The coherence of particles in juxtaposition is an effect of the same class as the mutual approach of particles placed at a distance from each other. It is not difficult to perceive that the same influence which causes the bodies A and B to approach each other, when placed at some distance asunder, will, when they unite, retain them together, and oppose a resistance to their separation. Hence this effect of the mutual approximation of bodies towards each other is also called force.

Force is generally defined to be “whatever produces or opposes the production of motion in matter.” In this sense, it is a name for the unknown cause of a known effect. It would, however, be more philosophical to give the name, not to the cause, of which we are ignorant, but to the effect, of which we have sensible evidence. To observe and to classify is the whole business of the natural philosopher. When causes are referred to, it is implied, that effects of the same class arise from the agency of the same cause. However probable this assumption may be, it is altogether unnecessary. All the objects of science, the enlargement of mind, the extension and improvement of knowledge, the facility of its acquisition, are obtained by generalisation alone, and no good can arise from tainting our conclusions with the possible errors of hypotheses.

It may be here, once for all, observed, that the phraseology of causation and hypotheses has become so interwoven with the language of science, that it is impossible to avoid the frequent use of it. Thus, we say, “the magnet attracts iron;” the expression attract intimating the cause of the observed effect. In such cases, however, we must be understood to mean the effect itself, finding it less inconvenient to continue the use of the received phrases, modifying their signification, than to introduce new ones.

Force, when manifested by the mutual approach or cohesion of bodies, is also called attraction, and it is variously denominated, according to the circumstances under which it is observed to act. Thus, the force which holds together the atoms of solid bodies is called cohesive attraction. The force which draws bodies to the surface of the earth, when placed above it, is called the attraction of gravitation. The force which is exhibited by the mutual approach, or adhesion, of the loadstone and iron, is called magnetic attraction, and so on.

When force is manifested by the motion of bodies from each other, it is called repulsion. Thus, if a piece of glass, having been briskly rubbed with a silk handkerchief, touch successively two feathers, these feathers, if brought near each other, will move asunder. This effect is called repulsion, and the feathers are said to repel each other.

(9.) The influence which forces have upon the form, state, arrangement, and motions of material substances is the principal object of physical science. In its strict sense, Mechanics is a term of very extensive signification. According to the more popular usage, however, it has been generally applied to that part of physical science which includes the investigation of the phenomena of motion and rest, pressure and other effects developed by the mutual action of solid masses. The consideration of similar phenomena, exhibited in bodies of the liquid form, is consigned to Hydrostatics, and that of aeriform fluids to Pneumatics.