adopted the generalization that all substances could exist in all three states. A certain number of 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. Dr. Andrews finds that above 88° Fahr. carbonic acid cannot be liquefied by any pressure he could apply, whereas below this temperature liquefaction is always possible. By analogy it becomes highly probable that even hydrogen might be liquefied if cooled to a sufficiently 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 receive an explanation of a remarkable exception presented by liquid carbonic acid to the general rule that gases expand more by heat than liquids. This liquid carbonic acid was found by Thilorier in 1835 to expand more than four times as much as air; but by the light of Dr. Andrews' experiments we may 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 conden

sation P.

It is an empirical law of the planetary system that all the bodies composing it revolve from west to east; that law is broken, as we have seen, in the cases of one planet and several satellites, probably by the interference of an accidental disturbing force. The law also fails to be true of comets, which, taken as a whole, appear to move according to no single uniform law. This exception, however, is one of limitation only, for in all probability comets, although at present members of our system, have not P Maxwell, Theory of Heat, p. 123.

always been so, but have, in wandering through space, been entangled in our system and retained by the attractive influence of Jupiter, or one of the other larger planets. We must then limit the statement of the law of uniform direction to bodies which are derived from the original constituents of the nebulous mass.

Limiting exceptions occur most frequently in the natural sciences of Botany, Zoology, Geology, &c., the laws of which are almost wholly 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. At one time all the animal remains discovered in the Scottish Old Red Sandstone were fishes or shells, until at last a single small air-breathing reptile occurred opportunely to prevent any hasty conclusions". 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, fertilization 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.

a Prior Analytics,' ii. 2, 8, and elsewhere.

r Murchison's 'Siluria' (1854), p. 254.

Real Exceptions to Supposed Laws.

The exceptions which we have lastly to consider, are perhaps 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. 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 can satisfy ourselves of the actual occurrence of the phenomena, the law must be rejected as illusory. The followers of Aristotle held that nature abhorred 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 generalization 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 has 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 diffraction fringes of colour did not appear in the exact place and of the exact size which calculation showed that they ought to appear according to the conditions of the theory (vol. ii. pp. 145151). One single fact clearly irreconcilable with a theory involves its total 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 very 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 at the beginning, as it were, of this geological age. The discovery of a single worked flint in older strata and in connexion with the remains of extinct mammals was suf ficient 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 Silurian system. As the exami

nation of the strata of the globe becomes more and more complete, our views of the origin and succession of life upon the globe must undergo many changes and ex

tensions.

Unclassed Exceptions.

At every period of scientific progress there will necessarily exist a multitude of exceptional and 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 learn and 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 almost infinitely 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 doubtless 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 in any degree approximated to an exhaustion of nature's powers. The