Preliminary Discourse on the Study of Natural Philosophy

by John F. W. Herschel

(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.

(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.

Crystallography.

(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.

(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.

(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.

(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.

(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.

(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.