solidifies and rises in temperature to 32° Fahr. A like effect is still more beautifully displayed in the well known lecture-room experiment, of the suspended crystallization of a solution of sodium sulphate, in which a sudden rise of temperature of 30° or even 40° Fahr. is often manifested.

The science of electricity is full of the most varied and interesting cases of inversion. As Professor Tyndall has remarked, Faraday had a profound belief in the reciprocal relations of the physical forces. The great starting-point of his researches, the discovery of electro-magnetism, was clearly an inversion.

Oersted and Ampère had proved that with an electric current and a magnet in a particular position as antecedents, motion is the consequent. If then a magnet, a wire and motion be the antecedents, an opposite electric current will be the consequent. It would be an endless task to trace out the results of this fertile relationship when once fully understood. No small part of Faraday's researches was occupied in ascertaining the direct and inverse relations of magnetic and diamagnetic, amorphous and crystalline substances in various circumstances. In all other relations of electricity the principle of inversion holds. The voltameter or the electro-plating cell is the inverse of the galvanic battery. As heat applied to a junction of antimony and bismuth bars produces electricity, it necessarily follows that an electric current passed through such a junction will produce cold. Thus it is apparent that inversion of cause and effect is a most fertile ground of prediction and discovery.

The reader should carefully notice, however, that the inversion of natural phenomena is exactly true only of the character of the effect, not the amount. There is always a waste of energy in every work, because a certain part of it is dissipated in the form of conducted or radiated heat, and escapes beyond our use. Theoretically speaking,

we might imagine a train of magnetic engines and electromagnetic machines, which should alternately convert the same energy into motion and electricity. Similarly, by a proper arrangement of bars of antimony and bismuth, the same current of electricity might be converted into heat and reconverted into electricity an indefinite number of times. But, practically speaking, there would be an enormous loss of energy at each conversion, so that the ultimate effect would dwindle down to an inconsiderable fraction of the original amount of energy.

Facts known only by Theory.

Of the four classes of facts enumerated in p. 157 the last remains unconsidered. It includes the unverified predictions of science. Scientific prophecy arrests the attention of the world when it refers to such striking events as an eclipse, the appearance of a great comet, or any other phenomenon which every one can verify with his own eyes. But it is surely a greater matter for wonder that in many cases a physicist may describe and measure phenomena which eye cannot see, nor sense of any kind appreciate. In most cases this arises from the effect being too small in amount to affect our organs of sense, or come within the powers of our instruments as at present constructed. There is another class of yet more remarkable cases, where a phenomenon cannot possibly be observed, and yet we can say what it would be if it were observed. In astronomy, systematic aberration is an effect of the sun's proper motion almost certainly known to exist, but which we have no hope of detecting by observation in the present age of the world. As the earth's motion round the sun combined with the motion of light causes the stars to deviate apparently from their true positions to the extent of about 18" at the most, so the motion of the

whole planetary system through space must occasion a similar displacement of at most 5". The ordinary aberration can be readily detected with modern astronomical instruments, because it goes through a yearly change in direction or amount, but the systematic aberration is constant and permanent so long as the planetary system moves uniformly in a sensibly straight line. Only then in the course of ages, when the curvature of the sun's path becomes apparent, can we hope to verify the existence of this kind of aberration. A curious effect also must be

produced by the sun's proper motion upon the apparent periods of revolution of the binary stars.

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 can never 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 also is 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. Sir W. Thomson has not yet given us the exact absolute magnitudes of the particles of matter, but he has ascertained by several distinct methods the limits within which their magnitudes must lie. Many of such scientific results must for ever be 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 polarization, and perhaps also the theory of internal radiation", 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 even a little damp, by serving as a conductor, prevents this separation from enduring any sensible time. Hence there is little or 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. Dr. Joule, indeed, believes that all the heat of friction is but transmuted electricity.

As regards phenomena of insensible amount, Nature is absolutely full of them. We must, in fact, regard those considerable changes which we can observe as the comparatively speaking infinitely 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 indefinitely, or rather infinitely numerous, but usually too small to be detected by h Balfour Stewart, Elementary Treatise on Heat,' 1st edit. p. 198.

observation, although their amounts may be confidently assigned by theory. There is every reason to believe that chemical and electric actions of almost indefinitely small amount, are constantly in progress. The hardest and most fixed substances, if reduced to sufficiently small particles, and diffused in pure water, manifest oscillatory movements which must be due to chemical and electric changes, so slight that they may go on for years without affecting appreciably the weight of the particles. The earth's magnetism must affect more or less every object which we handle. As Professor 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 diamagnetici.' The sun's light produces a very quick and perceptible effect upon the photographic plate; in all probability it has a much less effect upon a great variety of substances. We may regard every apparent phenomenon as but an exaggerated and conspicuous case of a process which is, in indefinitely more numerous cases, beyond the means of observation. Yet in a great proportion of these cases exact calculation will enable us to estimate the amount of the phenomena, if it is of suf ficient interest for us to do so.

i 'Philosophical Transactions,' vol. cxlvi. p. 249.