Very little is known about the molecular constitution of solid bodies. The most obvious property of a solid is, that it preserves its shape so long as it is not acted upon by external forces. Moreover, when such forces are applied, the solid indeed becomes deformed, but it even tually regains its original shape after the forces have been removed, provided they did not ex ceed a certain magnitude called the °elastic limit" which is peculiar to the solid under ex amination, and to the way in which the forces were applied. We are obliged to conclude, from these facts, that the molecules of a solid are not free to roam about, but that some or all of them have determinate mean positions about which they may oscillate and rotate, but from which they never permanently depart except when constrained to do so by an external force great enough to overcome the internal forces (whatever they may be) which normally deter mine the mean positions of the molecules. Some solids are brittle toward forces that are sud denly applied to them, although they yield slowly, and after the manner of a viscous fluid, to smaller forces that are applied continuously for a long time. A mass of cold pitch, for example, may be easily shattered by a blow, and yet when allowed to rest for a sufficient time upon an inclined plane, it yields gradually to the relatively insignificant force of gravity, loses its shape and slowly flows down the plane. It is evident that solids of this character must have exceedingly complicated structures. Max well suggested that they consist of two kinds of molecular groups, of which one is more stable than the other, and he supported his argument with considerable ingenuity. His views were purely speculative, however, and it appears to be fairly evident that the first advances that we make toward a good understanding of the molecular structure of solids must be based upon a study of bodies of crystalline nature, like quartz and iron.
It is certain that in crystals there is some definite regularity of orientation, either in the molecules themselves, or in their motions ; and it may be fair to assume that this regularity is of such nature that any given molecule, in its vibratory excursions, never passes outside of a certain imaginary ellipsoid, which may be con ceived to be described about the mean position of the molecule. Crystals may then be regarded as aggregates of such ellipsoids, piled up in such a way that the corresponding axes of all of them are either parallel throughout the mass, or at least arranged in accordance with some definite geometrical scheme. When a substance crystallizes, either from solution or from a state of fusion, the ellipsoids that bound the crystal molecules must necessarily arrange themselves so that the potential energy of the resulting solid is as small as it can be, consistently with the conditions under which the solidification takes place. For the sake of illustrating the applica tion of the molecular theory to the explanation of crystal structure, we may assume the ellip soids to be simple spheres, and we may also assume that the potential energy of the system is least when the spheres are grouped together as closely as possible. The problem of crystal structure is then reduced, in its geometrical aspect, to the simple one of finding out how to pack the greatest number of equal spherical balls into a given space; and in order to properly comprehend the principles that are involved, a little patient experimentation with a liberal sup ply of buckshot or spherical bullets is desirable. It will be found that pyramids can be built with them, apparently in several ways; though the internal structure of the pile is really the same in all cases. The slant faces of these pyramids correspond to the plane faces of the actual crystal. When a crystal is forming (say by deposition from a solution) we are to conceive that a continuous series of exchanges is going on, all over its surface. Molecules of the dis
solved substance are caught by the attraction of the growing crystals, but, on the other hand, molecules of the solidified crystal are con tinually passing into solution again; and the gradual increase in size of the crystal is due to the fact that in a unit time more molecules are caught by it than are lost again. Suppose, now, that the surface of a partially formed crystal is injured slightly, and let us represent the injury, in our shot pile, by removing a few of the shot from one of the faces of a pyramid. A molecule that happens to lodge in the injured place will be in contact with more of the other attracting spheres than it would touch if it were to collide with one of the uninjured parts of the crystal, and it will, therefore, be held more firmly in place. In the exchange of molecules between the crystal and the solution, a molecule thus embedded will be less likely to be torn away again; and this action tends to preserve the flatness of the faces of the growing crystals, and to cause the repair of damaged places to proceed with greater rapidity than the growth along normal, uninjured parts.
In the mathematical investigation of crystal line structure it is usual to speak of crystals as possessing a "lattice-likeD structure in space,— a space-lattice being defined as a numerous set of fixed points, arranged in such a way that the point-distribution is identically the same in every region. The points may be considered to be the mean positions about which the re spective molecules oscillate. From the point of view of the investigator this conception has proved to be exceeding useful, but for the pur pose of giving a general conception of crystal structure the idea of piled spheres or ellipsoids is perhaps simpler and clearer.
It has been said, above, that the molecules of bodies attract one another. We do not know much, however, about the mechanism by which the attraction makes itself felt, nor even about the law in accordance with which the attraction falls off with increasing distance. It would be natural to assume it to vary as the inverse square of the distance, but it is usually held that there is good evidence that it falls off more rapidly than this, as the distance increases. Maxwell assumed, in certain of his writ-incl, that the attraction varies as the inverse fifth power of the distance, but he apparently chose this law merely because it rendered certain of his equations more manageable. William Suth erland has advanced reasons for believing that the inverse fourth power is more nearly cor rect for the distances that are commonest between the molecules of gases under ordinary conditions of density. We do not even know that the forces between molecules are "central," — that is, we do know that the attractive force exerted by a molecule tends toward definite points within the substance of the mole cules. Helmholtz showed, in a paper published in 1847, that if the universe consists of smooth spherical molecules, which attract one another only by forces that are directed toward their centres, the great fact of the conservation of energy is a necessary consequence (see ENERGETICS) ; but as we now have good rea son for believing that molecules are not bodies of this sort, the principle of the conservation of energy must be regarded as a mere fact of observation. The distance at which the at tractive force exerted by a molecule is still sensible is of course indefinite, depending as it does upon the delicacy of the means that are employed for the detection of the force. Maxwell showed that a soap-bubble would be come unstable when its thickness is reduced until it is only equal to the radius of sensible molecular attractive power; and as Reinold and Rucker have shown that soap-films become un stable at a thickness of about one two-millionth of an inch, we may take this as a rough esti mate of the limiting distance at which molec ular attractive power ceases to be sensible.