Chemistry, although to a great extent an empirical science, has not been without prophetic triumphs. The existence of the metals potassium and sodium was foreseen by Lavoisier, and their elimination by Davy was one of the chief experimenta crucis which established Lavoisier’s system. The existence of many other metals which eye had never seen was a natural inference, and theory has not been at fault. In the above cases the compounds of the metal were well known, and it was the result of decomposition that was foretold. The discovery in 1876 of the metal gallium is peculiarly interesting because the existence of this metal, previously wholly unknown, had been inferred from theoretical considerations by M. Mendelief, and some of its properties had been correctly predicted. No sooner, too, had a theory of organic compounds been conceived by Professor A. W. Williamson than he foretold the formation of a complex substance consisting of water in which both atoms of hydrogen are replaced by atoms of acetyle. This substance, known as the acetic anhydride, was afterwards produced by Gerhardt. In the subsequent progress of organic chemistry occurrences of this kind have become common. The theoretical chemist by the classification of his specimens and the manipulation of his formulæ can plan out whole series of unknown oils, acids, and alcohols, just as a designer might draw out a multitude of patterns. Professor Cayley has even calculated for certain cases the possible numbers of chemical compounds.[459] The formation of many such substances is a matter of course; but there is an interesting prediction given by Hofmann, concerning the possible existence of new compounds of sulphur and selenium, and even oxides of ammonium, which it remains for chemists to verify.[460]
Prediction by Inversion of Cause and Effect.
There is one process of experiment which has so often led to important discoveries as to deserve separate illustration—I mean the inversion of Cause and Effect. Thus if A and B in one experiment produce C as a consequent, then antecedents of the nature of B and C may usually be made to produce a consequent of the nature of A inverted in direction. When we apply heat to a gas it tends to expand; hence if we allow the gas to expand by its own elastic force, cold is the result; that is, B (air) and C (expansion) produce the negative of A (heat). Again, B (air) and compression, the negative of C, produce A (heat). Similar results may be expected in a multitude of cases. It is a familiar law that heat expands iron. What may be expected, then, if instead of increasing the length of an iron bar by heat we use mechanical force and stretch the bar? Having the bar and the former consequent, expansion, we should expect the negative of the former antecedent, namely cold. The truth of this inference was proved by Dr. Joule, who investigated the amount of the effect with his usual skill.[461]
This inversion of cause and effect in the case of heat may be itself inverted in a highly curious manner. It happens that there are a few substances which are unexplained exceptions to the general law of expansion by heat. India-rubber especially is remarkable for contracting when heated. Since, then, iron and india-rubber are oppositely related to heat, we may expect that as distension of the iron produced cold, distension of the india-rubber will produce heat. This is actually found to be the case, and anyone may detect the effect by suddenly stretching an india-rubber band while the middle part is in the mouth. When being stretched it grows slightly warm, and when relaxed cold.
The reader will see that some of the scientific predictions mentioned in preceding sections were due to the principle of inversion; for instance, Thomson’s speculations on the relation between pressure and the melting-point. But many other illustrations could be adduced. The usual agent by which we melt a substance is heat; but if we can melt a substance without heat, then we may expect the negative of heat as an effect. This is the foundation of all freezing mixtures. The affinity of salt for water causes it to melt ice, and we may thus reduce the temperature to Fahrenheit’s zero. Calcium chloride has so much higher an attraction for water that a temperature of -45° C. may be attained by its use. Even the solution of a certain alloy of lead, tin, and bismuth in mercury, may be made to reduce the temperature through 27° C. All the other modes of producing cold are inversions of more familiar uses of heat. Carré’s freezing machine is an inverted distilling apparatus, the distillation being occasioned by chemical affinity instead of heat. Another kind of freezing machine is the exact inverse of the steam-engine.
A very paradoxical effect is due to another inversion. It is hard to believe that a current of steam at 100° C. can raise a body of liquid to a higher temperature than the steam itself possesses. But Mr. Spence has pointed out that if the boiling-point of a saline solution be above 100°, it will continue, on account of its affinity for water, to condense steam when above 100° in temperature. It will condense the steam until heated to the point at which the tension of its vapour is equal to that of the atmosphere, that is, its own boiling-point.[462] Again, since heat melts ice, we might expect to produce heat by the inverse change from water into ice. This is accomplished in the phenomenon of suspended freezing. Water may be cooled in a clean glass vessel many degrees below the freezing-point, and yet retained in the liquid condition. But if disturbed, and especially if brought into contact with a small particle of ice, it instantly solidifies and rises in temperature to 0° C. The effect is still better displayed in the lecture-room experiment of the suspended crystallisation of a solution of sodium sulphate, in which a sudden rise of temperature of 15° or 20° C. is often manifested.
The science of electricity is full of most 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. Another 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 follows that an electric current passed through such a junction will produce cold. But it is now sufficiently apparent that inversion of cause and effect is a most fertile means of discovery and prediction.
Facts known only by Theory.
Of the four classes of facts enumerated in p. [525] 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 phenomenon which people can verify with their own eyes. But it is surely a matter for greater wonder that a physicist describes and measures phenomena which eye cannot see, nor sense of any kind detect. 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. But there is a class of yet more remarkable cases, in which 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 systematic aberration is constant 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 must also be produced by the sun’s proper motion upon the apparent periods of revolution of the binary stars.