nothing to do but calculate as exactly as possible the amount of interference, and make allowance for it; the apparent failure of the law under examination should then disappear. But in the second case the results may be much more important. A phenomenon which entirely fails to be explained by any known laws may indicate the interference of some wholly new series of natural forces. The ancients could not help perceiving that the general tendency of bodies downwards failed in the case of the loadstone, nor would the doctrine of essential lightness explain the exception, since the substance drawn upwards by the loadstone is a heavy metal. We now see clearly that there was no breach in the perfect generality of the law of gravity, but that a new form of energy manifested itself in a conspicuous form in the loadstone for the first time. In this case the forces concerned, those of gravity and electrical attraction, have never yet been brought into correlation with each other.

Other sciences show us that laws of nature, rigorously true and exact, may often be developed by those who are ignorant of far more complex phenomena involved in their application. Newton's comprehension of geometrical optics was sufficient to explain all the ordinary refractions and reflections of light. The simple laws of the bending of rays apply to all rays, whatever the character of the undulations composing them. Newton suspected the existence of other classes of phenomena when he spoke of rays as having sides; but it remained for later experimentalists to show that light is a transverse undulation, like the bending of a rod or cord.

Dalton's atomic theory is doubtless true of all chemical compounds, and the essence of it is that the same compound will always be found to contain the same elements in certain definite proportions. Pure calcium carbonate contains 48 parts by weight of oxygen to 40 of calcium,

and 12 of carbon. But when careful analyses were made of a great many minerals, this law often appeared to fail. What was unquestionably the same mineral, judging by its crystalline form and physical properties, would often give varying proportions of its components, and would sometimes contain unusual elements which yet could not be set down as mere impurities. Dolomite, for instance, is a compound of the carbonates of magnesia and lime, but specimens from different places do not exhibit any fixed ratio between the lime and magnesia, and carbonate of iron occasionally forms a real constituent of the mineral. Such facts could be reconciled with the laws of Dalton only by supposing the interference of a new law, that of Isomorphism.

It is now sufficiently established that certain elements are closely related to each other, so that they can, as it were, step into each other's places without apparently altering the form of the compound molecules, or the shape of the crystals which they constitute. The carbonates of iron, calcium, and magnesium, are nearly identical in their crystalline forms, hence they may crystallize 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 most valuable aid to chemists in deciding upon the real constitution of new salts, since those compounds of isomorphous elements which have identical crystalline forms must possess corresponding chemical formula.

We may always expect that from time to time new and extraordinary phenomena will be discovered, and will lead to new views of the laws 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 wholly new relation between light and electricity. The peculiar so-called 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 m, which still, however, remains exceptional in its properties and relations, and affords a hope of important discoveries in chemical theory.

Limiting Exceptions.

We may pass to cases where exceptional phenomena are actually irreconcilable with a law of nature previously regarded as true by philosophers. Error must now be allowed to have been committed, but it is obvious that the error may be more or less extensive. It may be that a law holding rigorously true of the facts actually under notice had been extended by generalization to other series of facts then unexamined. Subsequent investigation may show the falsity of this generalization, and the result must be to limit the law for the future to those objects of which it is really true, while we bring the other classes of objects under distinct generalizations. 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 mPhilosophical Transactions' (1872), vol. clxii. no. 23.

it preserves throughout its course until extinguished. This is indeed but one case of the general principle of undulatory movement, which Sir John Herschel has stated in the most complete manner under the title, 'Principle of Forced Vibrations' (vol. ii. p. 65), and has asserted to be absolutely universal and without exception. But Sir John 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 possessed a beautiful celestial blue tint. Curiously enough the coloured light comes only from the first portion of liquid which the light enters. Similar phenomena in fluor-spar had been described by Sir D. 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 a degradation or alteration in the refrangibility of the rays of light; he asserts, in fact, that light-rays of very short length of vibration in falling upon certain atoms excite undulations of greater length, in total opposition to the principle of forced vibrations. No complete explanation of the mode of change is yet possible, because it evidently 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". It is now also well known that in Calorescence the refrangibility of rays may be increased and the wave-length diminished. Rays of obscure heat and low refrangibility may be concentrated so as to heat a solid sub , and make it give out rays

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Philosophical Tran

vol. cxlii. pp. 465, 548, &c.

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 closely observe gentle waves lapping upon the stones at the edge of a lake or other piece of water, we shall notice that each larger wave in breaking upon a stone gives rise to a series of waves of a smaller order. Thus there must be constantly in progress a degradation in the magnitude of water-waves. The principle of forced vibrations seems then to be too generally stated by Sir John Herschel, but it must be a very difficult question of mechanical theory to discriminate the circumstances in which it does and does not hold true.

We may sometimes foresee the possible existence of exceptions yet unknown by experience, and limit the statement of our discoveries accordingly. Very extensive inquiries have shown that all substances yet examined fall into one of two classes; they are all either ferromagnetic, that is, magnetic in the same way as iron, or they are diamagnetic like bismuth. But it does not thence follow that every substance must be ferro-magnetic 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 Philosophical Magazine,' 4th Series, vol. i. p. 182.

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