The exceptions which we have lastly to consider are the most important of all, since they lead to the entire rejection of a law or theory before accepted. No law of nature can fail; there are no such things as real exceptions to real laws. Where contradiction exists it must be in the mind of the experimentalist. Either the law is imaginary or the phenomena which conflict with it; if, then, by our senses we satisfy ourselves of the actual occurrence of the phenomena, the law must be rejected as illusory. The followers of Aristotle held that nature abhors a vacuum, and thus accounted for the rise of water in a pump. When Torricelli pointed out the visible fact that water would not rise more than 33 feet in a pump, nor mercury more than about 30 inches in a glass tube, they attempted to represent these facts as limiting exceptions, saying that nature abhorred a vacuum to a certain extent and no further. But the Academicians del Cimento completed their discomfiture by showing that if we remove the pressure of the surrounding air, and in proportion as we remove it, nature’s feelings of abhorrence decrease and finally disappear altogether. Even Aristotelian doctrines could not stand such direct contradiction.
Lavoisier’s ideas concerning the constitution of acids received complete refutation. He named oxygen the acid generator, because he believed that all acids were compounds of oxygen, a generalisation based on insufficient data. Berthollet, as early as 1789, proved by analysis that hydrogen sulphide and prussic acid, both clearly acting the part of acids, were devoid of oxygen; the former might perhaps have been interpreted as a limiting exception, but when so powerful an acid as hydrogen chloride (muriatic acid) was found to contain no oxygen the theory had to be relinquished. Berzelius’ theory of the dual formation of chemical compounds met a similar fate.
It is obvious that all conclusive experimenta crucis constitute real exceptions to the supposed laws of the theory which is overthrown. Newton’s corpuscular theory of light was not rejected on account of its absurdity or inconceivability, for in these respects it is, as we have seen, far superior to the undulatory theory. It was rejected because certain small fringes of colour did not appear in the exact place and of the exact size in which calculation showed that they ought to appear according to the theory (pp. [516]–521). One single fact clearly irreconcilable with a theory involves its rejection. In the greater number of cases, what appears to be a fatal exception may be afterwards explained away as a singular or disguised result of the laws with which it seems to conflict, or as due to the interference of extraneous causes; but if we fail thus to reduce the fact to congruity, it remains more powerful than any theories or any dogmas.
Of late years not a few of the favourite doctrines of geologists have been rudely destroyed. It was the general belief that human remains were to be found only in those deposits which are actually in progress at the present day, so that the creation of man appeared to have taken place in this geological age. The discovery of a single worked flint in older strata and in connexion with the remains of extinct mammals was sufficient to explode such a doctrine. Similarly, the opinions of geologists have been altered by the discovery of the Eozoön in the Laurentian rocks of Canada; it was previously held that no remains of life occurred in any older strata than those of the Cambrian system. As the examination of the strata of the globe becomes more complete, our views of the origin and succession of life upon the globe must undergo many changes.
Unclassed Exceptions.
At every period of scientific progress there will exist a multitude of unexplained phenomena which we know not how to regard. They are the outstanding facts upon which the labours of investigators must be exerted,—the ore from which the gold of future discovery is to be extracted. It might be thought that, as our knowledge of the laws of nature increases, the number of such exceptions should decrease; but, on the contrary, the more we know the more there is yet to explain. This arises from several reasons; in the first place, the principal laws and forces in nature are numerous, so that he who bears in mind the wonderfully large numbers developed in the doctrine of combinations, will anticipate the existence of immensely numerous relations of one law to another. When we are once in possession of a law, we are potentially in possession of all its consequences; but it does not follow that the mind of man, so limited in its powers and capacities, can actually work them all out in detail. Just as the aberration of light was discovered empirically, though it should have been foreseen, so there are multitudes of unexplained facts, the connexion of which with laws of nature already known to us, we should perceive, were we not hindered by the imperfection of our deductive powers. But, in the second place, as will be more fully pointed out, it is not to be supposed that we have approximated to an exhaustive knowledge of nature’s powers. The most familiar facts may teem with indications of forces, now secrets hidden from us, because we have not mind-directed eyes to discriminate them. The progress of science will consist in the discovery from time to time of new exceptional phenomena, and their assignment by degrees to one or other of the heads already described. When a new fact proves to be merely a false, apparent, singular, divergent, or accidental exception, we gain a more minute and accurate acquaintance with the effects of laws already known to exist. We have indeed no addition to what was implicitly in our possession, but there is much difference between knowing the laws of nature and perceiving all their complicated effects. Should a new fact prove to be a limiting or real exception, we have to alter, in part or in whole, our views of nature, and are saved from errors into which we had fallen. Lastly, the new fact may come under the sixth class, and may eventually prove to be a novel phenomenon, indicating the existence of new laws and forces, complicating but not otherwise interfering with the effects of laws and forces previously known.
The best instance which I can find of an unresolved exceptional phenomenon, consists in the anomalous vapour-densities of phosphorus, arsenic, mercury, and cadmium. It is one of the most important laws of chemistry, discovered by Gay-Lussac, that equal volumes of gases exactly correspond to equivalent weights of the substances. Nevertheless phosphorus and arsenic give vapours exactly twice as dense as they should do by analogy, and mercury and cadmium diverge in the other direction, giving vapours half as dense as we should expect. We cannot treat these anomalies as limiting exceptions, and say that the law holds true of substances generally but not of these; for the properties of gases (p. [601]), usually admit of the widest generalisations. Besides, the preciseness of the ratio of divergence points to the real observance of the law in a modified manner. We might endeavour to reduce the exceptions by doubling the atomic weights of phosphorus and arsenic, and halving those of mercury and cadmium. But this step has been maturely considered by chemists, and is found to conflict with all the other analogies of the substances and with the principle of isomorphism. One of the most probable explanations is, that phosphorus and arsenic produce vapour in an allotropic condition, which might perhaps by intense heat be resolved into a simpler gas of half the density; but facts are wanting to support this hypothesis, and it cannot be applied to the other two exceptions without supposing that gases and vapours generally are capable of resolution into something simpler. In short, chemists can at present make nothing of these anomalies. As Hofmann says, “Their philosophical interpretation belongs to the future.... They may turn out to be typical facts, round which many others of the like kind may come hereafter to be grouped; and they may prove to be allied with special properties, or dependent on particular conditions as yet unsuspected.”[557]
It would be easy to point out a great number of other unexplained anomalies. Physicists assert, as an absolutely universal law, that in liquefaction heat is absorbed;[558] yet sulphur is at least an apparent exception. The two substances, sulphur and selenium, are, in fact, very anomalous in their relations to heat. Sulphur may be said to have two melting points, for, though liquid like water at 120° C., it becomes quite thick and tenacious between 221° and 249°, and melts again at a higher temperature. Both sulphur and selenium may be thrown into several curious states, which chemists conveniently dispose of by calling them allotropic, a term freely used when they are puzzled to know what has happened. The chemical and physical history of iron, again, is full of anomalies; not only does it undergo inexplicable changes of hardness and texture in its alloys with carbon and other elements, but it is almost the only substance which conveys sound with greater velocity at a higher than at a lower temperature, the velocity increasing from 20° to 100° C., and then decreasing. Silver also is anomalous in regard to sound. These are instances of inexplicable exceptions, the bearing of which must be ascertained in the future progress of science.
When the discovery of new and peculiar phenomena conflicting with our theories of the constitution of nature is reported to us, it becomes no easy task to steer a philosophically correct course between credulity and scepticism. We are not to assume, on the one hand, that there is any limit to the wonders which nature can present to us. Nothing except the contradictory is really impossible, and many things which we now regard as common-place were considered as little short of the miraculous when first perceived. The electric telegraph was a visionary dream among mediæval physicists;[559] it has hardly yet ceased to excite our wonder; to our descendants centuries hence it will probably appear inferior in ingenuity to some inventions which they will possess. Now every strange phenomenon may be a secret spring which, if rightly touched, will open the door to new chambers in the palace of nature. To refuse to believe in the occurrence of anything strange would be to neglect the most precious chances of discovery. We may say with Hooke, that “the believing strange things possible may perhaps be an occasion of taking notice of such things as another would pass by without regard as useless.” We are not, therefore, to shut our ears even to such apparently absurd stories as those concerning second-sight, clairvoyance, animal magnetism, ode force, table-turning, or any of the popular delusions which from time to time are current. The facts recorded concerning these matters are facts in some sense or other, and they demand explanation, either as new natural phenomena, or as the results of credulity and imposture. Most of the supposed phenomena referred to have been, or by careful investigation would doubtless be, referred to the latter head, and the absence of scientific ability in many of those who describe them is sufficient to cast a doubt upon their value.
It is to be remembered that according to the principle of the inverse method of probability, the probability of any hypothetical explanation is affected by the probability of each other possible explanation. If no other reasonable explanation could be suggested, we should be forced to look upon spiritualist manifestations as indicating mysterious causes. But as soon as it is shown that fraud has been committed in several important cases, and that in other cases persons in a credulous and excited state of mind have deceived themselves, the probability becomes very considerable that similar explanations may apply to most like manifestations. The performances of conjurors sufficiently prove that it requires no very great skill to perform tricks the modus operandi of which shall entirely escape the notice of spectators. It is on these grounds of probability that we should reject the so-called spiritualist stories, and not simply because they are strange.