It is now established that certain elements are related to each other, so that they can, as it were, step into each other’s places without apparently altering the shapes of the crystals which they constitute. The carbonates of iron, calcium, and magnesium, are nearly identical in their crystalline forms, hence they may crystallise together in harmony, producing mixed minerals of considerable complexity, which nevertheless perfectly verify the laws of equivalent proportions. This principle of isomorphism once established, not only explains what was formerly a stumbling-block, but gives valuable aid to chemists in deciding upon the constitution of new salts, since compounds of isomorphous elements which have identical crystalline forms must possess corresponding chemical formulæ.
We may expect that from time to time extraordinary phenomena will be discovered, and will lead to new views of nature. The recent observation, for instance, that the resistance of a bar of selenium to a current of electricity is affected in an extraordinary degree by rays of light falling upon the selenium, points to a new relation between light and electricity. The allotropic changes which sulphur, selenium, and phosphorus undergo by an alteration in the amount of latent heat which they contain, will probably lead at some future time to important inferences concerning the molecular constitution of solids and liquids. The curious substance ozone has perplexed many chemists, and Andrews and Tait thought that it afforded evidence of the decomposition of oxygen by the electric discharge. The researches of Sir B. C. Brodie negative this notion, and afford evidence of the real constitution of the substance,[552] which still, however, remains exceptional in its properties and relations, and affords a hope of important discoveries in chemical theory.
Limiting Exceptions.
We pass to cases where exceptional phenomena are actually irreconcilable with a law of nature previously regarded as true. Error must now be allowed to have been committed, but the error may be more or less extensive. It may happen that a law holding rigorously true of the facts actually under notice had been extended by generalisation to other series of facts then unexamined. Subsequent investigation may show the falsity of this generalisation, and the result must be to limit the law for the future to those objects of which it is really true. The contradiction to our previous opinions is partial and not total.
Newton laid down as a result of experiment that every ray of homogeneous light has a definite refrangibility, which it preserves throughout its course until extinguished. This is one case of the general principle of undulatory movement, which Herschel stated under the title “Principle of Forced Vibrations” (p. [451]), and asserted to be absolutely without exception. But Herschel himself described in the Philosophical Transactions for 1845 a curious appearance in a solution of quinine; as viewed by transmitted light the solution appeared colourless, but in certain aspects it exhibited a beautiful celestial blue tint. Curiously enough the colour is seen only in the first portion of liquid which the light enters. Similar phenomena in fluor-spar had been described by Brewster in 1838. Professor Stokes, having minutely investigated the phenomena, discovered that they were more or less present in almost all vegetable infusions, and in a number of mineral substances. He came to the conclusion that this phenomenon, called by him Fluorescence, could only be explained by an alteration in the refrangibility of the rays of light; he asserts that light-rays of very short length of vibration in falling upon certain atoms excite undulations of greater length, in opposition to the principle of forced vibrations. No complete explanation of the mode of change is yet possible, because it depends upon the intimate constitution of the atoms of the substances concerned; but Professor Stokes believes that the principle of forced vibrations is true only so long as the excursions of an atom are very small compared with the magnitude of the complex molecules.[553]
It is well known that in Calorescence the refrangibility of rays is increased and the wave-length diminished. Rays of obscure heat and low refrangibility may be concentrated so as to heat a solid substance, and make it give out rays belonging to any part of the spectrum, and it seems probable that this effect arises from the impact of distinct but conflicting atoms. Nor is it in light only that we discover limiting exceptions to the law of forced vibrations; for if we notice gentle waves lapping upon the stones at the edge of a lake we shall see that each larger wave in breaking upon a stone gives rise to a series of smaller waves. Thus there is constantly in progress a degradation in the magnitude of water-waves. The principle of forced vibrations seems then to be too generally stated by Herschel, but it must be a difficult question of mechanical theory to discriminate the circumstances in which it does and does not hold true.
We sometimes foresee the possible existence of exceptions yet unknown by experience, and limit the statement of our discoveries accordingly. Extensive inquiries have shown that all substances yet examined fall into one of two classes; they are all either ferro-magnetic, that is, magnetic in the same way as iron, or they are diamagnetic like bismuth. But it does not follow that every substance must be ferro-magnetic or diamagnetic. The magnetic properties are shown by Sir W. Thomson[554] to depend upon the specific inductive capacities of the substance in three rectangular directions. If these inductive capacities are all positive, we have a ferro-magnetic substance; if negative, a diamagnetic substance; but if the specific inductive capacity were positive in one direction and negative in the others, we should have an exception to previous experience, and could not place the substance under either of the present recognised classes.
So many gases have been reduced to the liquid state, and so many solids fused, that scientific men rather hastily adopted the generalisation that all substances could exist in all three states. A certain number of gases, such as oxygen, hydrogen, and nitrogen, have resisted all efforts to liquefy them, and it now seems probable from the experiments of Dr. Andrews that they are limiting exceptions. He finds that above 31° C. carbonic acid cannot be liquefied by any pressure he could apply, whereas below this temperature liquefaction is always possible. By analogy it becomes probable that even hydrogen might be liquefied if cooled to a very low temperature. We must modify our previous views, and either assert that below a certain critical temperature every gas may be liquefied, or else we must assume that a highly condensed gas is, when above the critical temperature, undistinguishable from a liquid. At the same time we have an explanation of a remarkable exception presented by liquid carbonic acid to the general rule that gases expand more by heat than liquids. Liquid carbonic acid was found by Thilorier in 1835 to expand more than four times as much as air; but by the light of Andrews’ experiments we learn to regard the liquid as rather a highly condensed gas than an ordinary liquid, and it is actually possible to reduce the gas to the apparently liquid condition without any abrupt condensation.[555]
Limiting exceptions occur most frequently in the natural sciences of Botany, Zoology, Geology, &c., the laws of which are empirical. In innumerable instances the confident belief of one generation has been falsified by the wider observation of a succeeding one. Aristotle confidently held that all swans are white,[556] and the proposition seemed true until not a hundred years ago black swans were discovered in Western Australia. In zoology and physiology we may expect a fundamental identity to exist in the vital processes, but continual discoveries show that there is no limit to the apparently anomalous expedients by which life is reproduced. Alternate generation, fertilisation for several successive generations, hermaphroditism, are opposed to all we should expect from induction founded upon the higher animals. But such phenomena are only limiting exceptions showing that what is true of one class is not true of another. In certain of the cephalopoda we meet the extraordinary fact that an arm of the male is cast off and lives independently until it encounters the female.