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 ferromagnetic or diamagnetic. The magnetic properties are shown by Sir W. Thomson 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.2

1 Philosophical Magazine, 4th Series, vol. i. p. 182.
2 Maxwell, Theory of Heat, p. 123.

1

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, 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.

Real Exceptions to Supposed Laws.

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

1 Prior Analytics, ii. 2, 8, and elsewhere.

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. 516521). 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 vapourdensities 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.