To my mind, some of the most interesting truths in the whole range of science are those which have not been, and in many cases probably never can be, verified by trial. Thus the chemist assigns, with a very high degree of probability, the vapour densities of such elements as carbon and silicon, which have never been observed separately in a state of vapour. The chemist is also familiar with the vapour densities of elements at temperatures at which the elements in question never have been, and probably never can be, submitted to experiment in the form of vapour.
Joule and others have calculated the actual velocity of the molecules of a gas, and even the number of collisions which must take place per second during their constant circulation. Physicists have not yet given us the exact magnitudes of the particles of matter, but they have ascertained by several methods the limits within which their magnitudes must lie. Such scientific results must be for ever beyond the power of verification by the senses. I have elsewhere had occasion to remark that waves of light, the intimate processes of electrical changes, the properties of the ether which is the base of all phenomena, are necessarily determined in a hypothetical, but not therefore a less certain manner.
Though only two of the metals, gold and silver, have ever been observed to be transparent, we know on the grounds of theory that they are all more or less so; we can even estimate by theory their refractive indices, and prove that they are exceedingly high. The phenomena of elliptic polarisation, and perhaps also those of internal radiation,[463] depend upon the refractive index, and thus, even when we cannot observe any refracted rays, we can indirectly learn how they would be refracted.
In many cases large quantities of electricity must be produced, which we cannot observe because it is instantly discharged. In the common electric machine the cylinder and rubber are made of non-conductors, so that we can separate and accumulate the electricity. But a little damp, by serving as a conductor, prevents this separation from enduring any sensible time. Hence there is no doubt that when we rub two good conductors against each other, for instance two pieces of metals, much electricity is produced, but instantaneously converted into some other form of energy. Joule believes that all the heat of friction is transmuted electricity.
As regards phenomena of insensible amount, nature is absolutely full of them. We must regard those changes which we can observe as the comparatively rare aggregates of minuter changes. On a little reflection we must allow that no object known to us remains for two instants of exactly the same temperature. If so, the dimensions of objects must be in a perpetual state of variation. The minor planetary and lunar perturbations are infinitely numerous, but usually too small to be detected by observation, although their amounts may be assigned by theory. There is every reason to believe that chemical and electric actions of small amount are constantly in progress. The hardest substances, if reduced to extremely small particles, and diffused in pure water, manifest oscillatory movements which must be due to chemical and electric changes, so slight that they go on for years without affecting appreciably the weight of the particles.[464] The earth’s magnetism must more or less affect every object which we handle. As Tyndall remarks, “An upright iron stone influenced by the earth’s magnetism becomes a magnet, with its bottom a north and its top a south pole. Doubtless, though in an immensely feebler degree, every erect marble statue is a true diamagnet, with its head a north pole and its feet a south pole. The same is certainly true of man as he stands upon the earth’s surface, for all the tissues of the human body are diamagnetic.”[465] The sun’s light produces a very quick and perceptible effect upon the photographic plate; in all probability it has a less effect upon a great variety of substances. We may regard every phenomenon as an exaggerated and conspicuous case of a process which is, in infinitely numerous cases, beyond the means of observation.
CHAPTER XXV. ACCORDANCE OF QUANTITATIVE THEORIES.
In the preceding chapter we found that facts may be classed under four heads as regards their connection with theory, and our powers of explanation or prediction. The facts hitherto considered were generally of a qualitative rather than a quantitative nature; but when we look exclusively to the quantity of a phenomenon, and the various modes in which we may determine its amount, nearly the same system of classification will hold good. There will, however, be five possible cases:—
(1) We may directly and empirically measure a phenomenon, without being able to explain why it should have any particular quantity, or to connect it by theory with other quantities.
(2) In a considerable number of cases we can theoretically predict the existence of a phenomenon, but are unable to assign its amount, except by direct measurement, or to explain the amount theoretically when thus ascertained.
(3) We may measure a quantity, and afterwards explain it as related to other quantities, or as governed by known quantitative laws.