The joint relations of heat and electricity to the metals constitute a new science of thermo-electricity by which Sir W. Thomson was enabled to anticipate the following curious effect, namely, that an electric current passing in an iron bar from a hot to a cold part produces a cooling effect, but in a copper bar the effect is exactly opposite in character, that is, the bar becomes heated.22 The action of crystals with regard to heat and electricity was partly foreseen on the grounds of theory by Poisson.
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.23 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.24
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.25
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.