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(252.) Liquids differ from aëriform fluids by their _cohesion_, which may be regarded as a kind of approach to a solid state, and was so regarded by Bacon (193.). Indeed, there can be little doubt that the solid, liquid, and aëriform states of bodies are merely stages in a progress of gradual transition from one extreme to the other; and that, however strongly marked the distinctions between them may appear, they will ultimately turn out to be separated by no sudden or violent line of demarcation, but shade into each other by insensible gradations. The late experiments of Baron Cagnard de la Tour may be regarded as a first step towards the full demonstration of this (199.). But the cohesion of liquids is not, like that of solids, so modified by their structure in other respects as to destroy the mobility of their parts one among another (unless in those cases of nearer approach to the solid state which obtain in viscid or gummy liquids). On the contrary, the two qualities co-exist, and give rise to a number of curious and intricate phenomena.

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(253.) One of the most remarkable of these is capillary attraction, or capillarity as it is sometimes called. Every body has remarked the adhesion of water to glass. The elevation of the general surface of the liquid where it is in contact with the containing vessel; the form of a drop suspended at the under side of a solid: these are instances of capillary attraction. If a small glass tube with a bore as fine as a hair be immersed in water, the water will be observed to rise in it to a certain height, and to assume a concave surface at its upper extremity. The attraction of the glass on the water, and the cohesion of the parts of the water to each other, are no doubt the joint causes of this curious effect; but the mode of action is at once obscure and complex; and although the researches of Laplace and Young have thrown great light on it, further investigation seems necessary before we can be said distinctly to understand it.

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(254.) As the capillarity and cohesion of the parts of liquids shows them to possess the power of mutual attraction, so their elasticity demonstrates that they also possess that of repulsion when forcibly brought nearer than their natural state. From the extremely small extent to which the compression of liquids can be carried by any force we can employ, compared with that of air, we must conclude that this repulsion is much more violent in the former than in the latter, but counteracted also by a more powerful force of attraction. So much more powerful, indeed, is the resistance of liquids to compression, that they were usually regarded as incompressible; an opinion corroborated by a celebrated experiment made at Florence, in which water was forced through the pores (as it was said) of a golden ball. More recent experiments by Canton, and since by Perkins, Oërsted, and others, have demonstrated however the contrary, and assigned the amount of compression.

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(255.) The consideration of the motions of fluids, whether liquid or expansible, is infinitely more complicated than that of their equilibrium. When their motions are slow, it is reasonable to suppose that the law of the equable distribution of pressure obtains; but in very rapid displacements of their parts one among the other, it is not easy to see how such an equable distribution can be accomplished, and some phenomena exist which seem to indicate a contrary conclusion.

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(256.) Independent of this, there are difficulties of an almost insuperable nature to the regular deductive application of the general principles of mechanics to this subject, which arise from the excessive intricacy of the pure mathematical enquiries to which its investigation leads. It was Newton who set the example of a first attempt to draw any conclusions respecting the motion of fluid masses by direct reasoning from dynamical principles, and thus laid the foundation of HYDRODYNAMICS; but it was not till the time of D’Alembert that the method of reducing any question respecting the motions of fluids under the action of forces to strict mathematical investigation could be said to be completely understood. But the cases even now in which this mode of treating such questions can be applied with full satisfaction are few in comparison of those in which the experimental method of enquiry as already observed (189.) is preferable. Such, for example, is that of the resistance of fluids to bodies moving through them; a knowledge of which is of great importance in naval architecture and in gunnery, where the resistance of the air acts to an enormous extent. Such, too, among the practical subjects which depend mainly on this branch of science, are the use of sails in navigation; the construction of windmills, and water-wheels; the transmission of water through pipes and channels; the construction of docks and harbours, &c.

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_Nature of Solids in general._

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(257.) The intimate constitution of solids is, in all probability, very complicated, and we cannot be said to know much of it. By some recent delicate experiments on the dimensions of wires violently strained, it has been shown that they are to a certain small extent capable of being dilated by tension, as they are also of being compressed by pressure, but within limits even narrower than those of liquids. Usually, when strained too far, they break, and refuse to re-unite; or, if compressed too forcibly, take a permanent contraction of dimension. Thus, wood may be indented by a blow, and metals rendered denser and heavier by hammering or rolling. There is a certain degree of confusion prevalent in ordinary language about the hardness, elasticity, and other similar qualities, of solids, which it may be well to remove. Hardness is that disposition of a solid which renders it difficult to displace its parts among themselves. Thus, steel is harder than iron; and diamond almost infinitely harder than any other substance in nature: but the compressibility of steel, or the extent to which it will yield to a given pressure and recover itself, is not much less than that of soft iron, and that of ice is very nearly the same with that of water.

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(258.) Again, we call Indian rubber a very elastic body, and so it is; but in a different sense from steel. Its parts admit of great mutual displacement without permanent dislocation; however distorted, it recovers its figure readily, but with a small force. Yet, if Indian rubber were to be enclosed in a space that it just filled, so as not to permit its parts to yield laterally, doubtless it would resist actual compression with great violence. Here, then, we have an instance of two kinds of elasticity in one substance; a feebler effort of recovery from distorted figure, and a more violent one from a state of altered dimension. Both, however, originate in the same causes, and are referable to the same principles; the former being in fact only a modified case of the latter, as the effort of a steel spring, when bent, to recover its former shape, is referable to the same forces which give to steel its hardness and strength to resist actual compression and fracture.

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(259.) The toughness of a solid, or that quality by which it will endure heavy blows without breaking, is again distinct from hardness though often confounded with it. It consists in a certain yielding of parts with a powerful general cohesion, and is compatible with various degrees of elasticity. Malleability is again another quality of solids, especially metals, quite distinct from toughness, and depends on their capability of being deprived of their figure without an effort to recover it and without fracture.

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(260.) Tenacity, again, is a property of solids more directly depending on the cohesion of their parts than toughness. It consists in their power of resisting separation by a strain steadily applied, while the quality of toughness is materially influenced by their disposition to communicate through their substance the jarring effect of a blow. Accordingly, the tenacity of a solid is a direct measure of the cohesive attraction of its parts, and is the best proof of the existence of such a power.

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_Crystallography._

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(261.) It cannot be supposed that these and many other tangible qualities, as they may be called, should subsist in solids without a corresponding mechanism in their internal structure. That they have such a mechanism, and that a very curious and intricate one, the phenomena of crystallography sufficiently show. This interesting and beautiful department of natural science is of comparatively very modern date. That many natural substances affected certain forms must have been known from the earliest times. Pliny appears to have been acquainted with this fact, at least in some instances, as he describes the forms of quartz and diamond. But till the time of Linnæus no material attention seems to have been bestowed on the subject. He, however, observed, and described with care, the crystalline forms of a variety of substances, and even regarded them as so definite a character of the solids which assumed them, that he supposed every particular form to be generated by a particular salt. Romé de l’Isle pursued the study of the crystalline forms of bodies yet farther. He first ascertained the important fact of the constancy of the angles at which their faces meet; and observing further that many of them appear in several different shapes, first conceived the idea that these shapes might be reducible to one, appropriated in a peculiar manner to each _substance_, and modified by strict geometrical laws. Bergmann, reasoning on a fact imparted to him by his pupil Gahn, made a yet greater step, and showed how at least one species of crystal might be built up of thin laminæ ranged in a certain order, and following certain rules of superposition. He failed, however, in deducing just and general conclusions from this remark, which, correctly viewed, is the foundation of the most important law of crystallography, that which connects the primitive form with other forms capable of being exhibited by the same substance, by a certain fixed relation. An idea may be formed of what is meant by this sort of connection of one form with another, by considering a pointed pyramid built up of cubic stones, disposed in layers, each of which separately is a square plate of the thickness of a single stone. These layers, laid horizontally one on the other, and decreasing regularly in size from the bottom to the top, produce a pyramidal form with a rough or channeled surface; and if the layers are so extremely thin that the channels cease to be visible to the eye, the pyramid will seem smooth and perfect.

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(262.) Very shortly after this, and without knowledge of what had been done by Gahn and Bergmann, the Abbé Haüy, instructed by the accidental fracture of a fine group of crystals, made the remark noticed already (in 67.), and reasoning on it with more caution and success, and pursuing it into all its detail, developed the general laws which regulate the superposition of the layers of particles of which he supposes all crystals to be built up, and which enable us, from knowing their primitive forms, to discover, previous to trial, what other forms they are capable of assuming; and which, according to this idea, are called derivative or secondary forms. Mohs and others have since imagined processes and systems by which the derivation of forms from each other is facilitated, and have corrected some errors of over-hasty generalization into which their predecessors had fallen, as well as advanced, by an extraordinary diligence of research, our knowledge of the forms which the various substances which occur in nature and art actually do assume.

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(263.) In what manner a variety in point of external form may originate in a variety of figures in the ultimate particles of which a solid is composed, may very readily be imagined by considering what would happen if the bricks of which an edifice is constructed had all a certain _leaning_ or bias in one direction out of the perpendicular. Suppose every brick, for instance, when laid flat on its face, with its longer edges north and south, had its eastern and western faces upright, but its northern and southern ones leaning southwards at a certain inclination the same for each brick; a house built of such bricks would lean the same way, if the bricks fitted well together. If, _besides this_, the eastern and western faces of the bricks, instead of being truly upright, had an inclination eastward, the house would have a similar one, and all its four corners, instead of being upright, would lean to the south-east. Suppose, instead of a house, a pyramid were built of such oblique bricks, with the sides of its base directed to the four points of the compass; then its point, instead of being situated vertically over the centre of its base, would stand perpendicularly over some point to the south-east of that centre, and the pyramid itself would have its sides facing the south and the east, more highly inclined to the horizon than those towards the north and west.

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(264.) Whatever conception we may form of the manner in which the particles of a crystal cohere and form masses, it is next to impossible to divest ourselves of the idea of a determinate figure common to them all. Any other supposition, indeed, would be incompatible with that exact similarity in all other respects which the phenomena of chemistry may be considered as having demonstrated. However, it must be borne in mind that this idea, plausible as it may appear, is yet in some degree hypothetical, and that the laws of crystallography, as determined from inductive observation, are quite independent of any supposition of the kind, or even of the existence of such things as ultimate particles or atoms at all.

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(265.) Still, that peculiar internal constitution of solid bodies, whatever it be, which is indicated by the assumption of determinate figures, by their splitting easier in some directions than in others, and by their presenting glittering plane surfaces when broken into fragments, cannot but have an important influence on all their relations to external agents, as well as to their internal movements and the mutual actions of their parts on one another. Accordingly, the division of bodies into crystallized and uncrystallized, or imperfectly crystallized, is one of the most universal importance; and almost all the phenomena produced by those more intimate natural causes which act within small limits, and as it were on the immediate mechanism of solid substances, are remarkably modified by their crystalline structure. Thus, in transparent solids, the course taken by the rays of light, in traversing them, as well as the properties impressed upon them in so doing, are intimately connected with this structure. The recent experiments of M. Savart, too, have proved that this is also the case with their power of resistance to external force, on which depends their elasticity. Crystallized substances, according to the results of these experiments, resist compression with different degrees of elastic force, according to the direction in which it is attempted to compress them; and all the phenomena dependent on their elasticity are affected by this cause, especially those which relate to their vibratory movements and their conveyance of sound.

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(266.) There can be little doubt that modifications, similarly depending on the internal structure of crystals, will be traced through every department of physics. In that interesting one which relates to the action of heat in expanding the dimensions of substances, a beginning has already been made by Professor Mitscherlich. It had long been known that all substances are dilated by heat, and no exception to this law has been found, so long as we regard the _bulk_ of the heated body. Thus, an iron rod when hot is both longer and thicker than when cold; and the difference of dimension, though but trifling in itself, is yet capable of being made sensible, and is of considerable consequence in engineering. Thus, too, the quicksilver in a common thermometer occupies a larger space when hot than when cold; and being confined by the glass ball, (which also expands, but _not so much in proportion_,) it is forced to rise in the tube. These and similar facts had long been known; and accurate measures of the total amount of dilatation of a variety of different bodies, under similar accessions of heat, had been obtained and registered in tables. But no one had suspected the important fact, that this expansion in crystallized bodies takes place under totally different circumstances from what obtains in uncrystallized ones. M. Mitscherlich has lately shown that such substances expand differently in different directions, and has even produced a case in which expansion in one direction is actually accompanied with contraction in another. This step, the most important beyond a doubt which has yet been made in pyrometry, can however only be regarded as the first in a series of researches which will occupy the next generation, and which promises to afford an abundant harvest of new facts, as well as the elucidation of some of the most obscure and interesting points in the doctrine of heat.

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(267.) From what has been said, it is clear that if we look upon solid bodies as collections of particles or atoms, held together and kept in their places by the perpetual action of attractive and repulsive forces, we cannot suppose these forces, at least in crystallized substances, to act alike in all directions. Hence arises the conception of _polarity_, of which we see an instance, on a great scale, in the magnetic needle, but which, under modified forms, there is nothing to prevent us from conceiving to act among the ultimate atoms of solid or even fluid bodies, and to produce all the phenomena which they exhibit in their crystallized state, either when acting on each other, or on light, heat, &c. It is not difficult, if we give the reins to imagination, to conceive how attractive and repulsive atoms, bound together by some unknown tie, may form little machines or compound particles, which shall have many of the properties which we refer to polarity; and accordingly many ingenious suppositions have been made to that effect: but in the actual state of science it is certainly safest to wave these hypotheses, without however absolutely rejecting them, and regard the _polarity of matter_ as one of the ultimate phenomena to which the analysis of nature leads us, and of which it is our business fully to investigate the laws, before we endeavour to ascertain its causes, or trace the mechanism by which it is produced.

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(268.) The mutual attractions and repulsions of the particles of matter, then, and their polarity, whether regarded as an original or a derivative property, are the forces which, acting with great energy, and within very confined limits, we must look to as the principles on which the intimate constitution of all bodies and many of their mutual actions depend. These are what are understood by the general term of _molecular forces_. Molecular attraction has been attempted to be confounded by some with the general attraction of gravity, which all matter exerts on all other matter; but this idea is refuted by the plainest facts.

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CHAP. II.

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OF THE COMMUNICATION OF MOTION THROUGH BODIES.--OF SOUND AND LIGHT.

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(269.) The propagation of motion through all substances, whether of a single impulse, as a blow or thrust, or of one frequently and regularly repeated, such as a jarring or vibratory movement, depends wholly on these molecular forces; and it is on such propagation that sound and very probably light depend. To conceive the manner in which a motion may be conveyed from one part of a substance to another, whether solid or fluid, we may attend to what takes place when a wave is made to run along a stretched string, or the surface of still water. Every part of the string, or water, is in succession moved from its place, and agitated with a motion similar to that of the original impulse, leaving its place and returning to it, and when one part ceases to move the next receives as it were the impression, and forwards it onward. This may seem a slow and circuitous process in description; but when sound, for example, is conveyed through the air, we are to consider, 1st, that the air, the substance actually in motion, is extremely light and acted upon by a very powerful elasticity, so that the force which propagates the motion, or by which the particles adjacent act on, and urge forward, each other, is very great, compared with the quantity of materials set in motion by it: and the same is true, even in a greater degree, in liquids and solids; for in these the elastic forces are even greater, in proportion to the weight, than in air.

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(270.) A general notion of the mode in which sounds are conveyed through the air was not altogether deficient among the ancients; but it is to Newton that we owe the first attempt to analyze the process, and show correctly what takes place in the communication of motion from particle to particle. Reasoning on the properties of the air as an elastic body, he showed the effect of an impulse on any portion of it to consist in a condensation of the air immediately adjacent in the direction of the impulse, which then, re-acting by its spring, drives back the portion which had advanced to its original place, and at the same time urges forward the portion before it, in the direction of the impulse, so that every particle alternately advances and retreats. But, in pursuing this idea into its details, Newton fell into some errors which were pointed out by Cramer, though their origin was not traced, nor the reasoning corrected, till the subject was resumed by Lagrange and Euler; nor is this any impeachment of the penetration of our immortal countryman. The mathematical theory of the propagation of sound, and of vibratory and undulatory motions in general, is one of the utmost intricacy; and, in spite of every exertion on the part of the most expert geometers, continues to this day to give continual occasion for fresh researches; while phenomena are constantly presenting themselves, which show how far we are from being able to deduce all the particulars, even of cases comparatively simple, by any direct reasoning from first principles.

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(271.) Whenever an impulse of any kind is conveyed by the air, to our ears, it produces the impression of sound; but when such an impulse is regularly and uniformly repeated in extremely rapid succession, it gives us that of a musical note, the pitch of the note depending on the rapidity of the succession (see art. 153.). The sense of harmony, too, depends on the periodical recurrence of coincident impulses on the ear, and affords, perhaps, the only instance of a sensation for whose pleasing impression a distinct and intelligible reason can be assigned.

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(272.) Acoustics, then, or the science of sound, is a very considerable branch of physics, and one which has been cultivated from the earliest ages. Even Pythagoras and Aristotle were not ignorant of the general mode of its transmission through the air, and of the nature of harmony; but as a branch of science, independent of its delightful application in the art of music, it could be hardly said to exist, till its nature and laws became a matter of experimental enquiry to Bacon and Galileo, Mersenne and Wallis; and of mathematical investigation to Newton, and his illustrious successors, Lagrange and Euler. From that time its progress, as a branch both of mathematical and experimental science, has been constant and accelerated. A curious and beautiful method of observation, due to Chladni, consists in the happy device of strewing sand over the surfaces of bodies in a state of sonorous vibration, and marking the figures it assumes. This has made their motions susceptible of ocular examination, and has been lately much improved on, and varied in its application, by M. Savart, to whom we also owe a succession of instructive researches on every point connected with the subject of sound, which may rank among the finest specimens of modern experimental enquiry. But the subject is far from being exhausted; and, indeed, there are few branches of physics which promise at once so much amusing interest, and such important consequences, in its bearings on other subjects, and especially, through the medium of strong analogies, on that of light.

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_Light and Vision._

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(273.) The nature of light has always been involved in considerable doubt and mystery. The ancients could scarcely be said to have any opinion on the subject, unless, indeed, it could be considered such to affirm that distant bodies could not be put into communication without an intermedium; and that, therefore, there must be _something_ between the eye and the thing seen. What that something is, however, they could only form crude and vague conjectures. One supposed that the eyes themselves emit rays or emanations of some unknown kind, by which distant objects are as it were felt; a singularly unfortunate idea, since it gives no reason why objects should not be equally well seen in the dark--no account, in short, of the part performed by _light_ in vision. Others imagined that all visible objects are constantly throwing out from them, in all directions, some sort of resemblances or spectral forms of themselves, which, when received by the eyes, produce an impression of the objects. Vague and clumsy as this hypothesis obviously is, it assigns to the object a power, and to light a diffusive propagation in all directions, which are, the one and the other, independent of our eyes, and therefore goes to separate the phenomena of _light_ from those of _vision_.
