phenomena of light. The rainbow had always struck the attention of the most careless observers, and there was no difficulty in perceiving that its conditions of occurrence consisted in rays of the sun shining upon falling drops of rain. It was impossible to overlook the resemblance of the ordinary rainbow to the comparatively rare lunar rainbow, to the bow which often appears upon the spray of a waterfall, or even upon beads of dew suspended on grass and spiders' webs. In all these cases the uniform conditions are rays of light and round drops of water. Roger Bacon had noticed these conditions, as well as the analogy of the rainbow colours to those produced by crystals a. But the knowledge was empirical until Descartes and Newton showed how the phenomena were connected with all the other facts concerning the refraction of light.

There can be no better instance of an empirical truth than that detected by Newton concerning the high refractive powers of combustible substances. Newton's chemical notions were almost as vague as those prevalent in his day, but he observed that certain fat, sulphureous, unctuous bodies,' as he calls them, such as camphor, oils, spirit of turpentine, amber, &c., have refractive powers two or three times greater than might be anticipated from their densities b. The enormous refractive index of diamond, led him with great sagacity to regard it as also of the same unctuous or inflammable nature, so that he may be regarded as predicting the combustibility of the diamond, afterwards demonstrated by the. Florentine Academicians in 1694. Brewster having entered into a long investigation of the refractive powers of different substances, confirmed Newton's assertions, and found that a 'Opus Majus.' Edit. 1733. Cap. x. p. 460.

b Newton's Opticks.' Third edit. p. 249. Leslie's 'Dissertation,' Encyclopædia Britannica, p. 550.

the three elementary combustible substances, diamond, phosphorus, and sulphur, have by far the highest refractive indices known in proportion to their densities, and there are only a few substances, such as chromate of lead or glass of antimony, known to exceed them in absolute power of refraction. The oils and hydrocarbons generally possess an excessive index. But this knowledge remains to the present day purely empirical, no connexion having been pointed out between this coincidence of inflammability and high refractive power, with other laws chemistry or optics. It is worthy of notice, howeve as pointed out by Brewster, that if Newton had argue concerning two minerals, Greenockite and Octahedrite," he did concerning diamond, his predictions would hav proved false. In the present day, the relation of th refractive index to the density and atomic weight of substance is becoming a matter of theory; yet the remain specific differences of refractive power known o on empirical grounds, and it is curious that in hydrog also an abnormally high refractive power has been for to be joined to inflammability.

The science of chemistry, however much its theory 1 have progressed, still presents us with a vast bod empirical knowledge. Not only is it at present hop to attempt to account for the particular group of qua belonging to each element, but there are multitude particular facts of which no further account can be Why should the sulphides of many metals be inte black? Why should a slight amount of phosphoric have so great a power of interference with the crysta tion of vanadic acid d. Why should the compound sil of alkalies and alkaline metals be transparent ? should gold be so highly ductile, and gold and silv c Brewster, Treatise on New Philosophical Instruments,' p. 266, d Roscoe, Bakerian Lecture, 'Philosophical Trans.' (1868), vol. clvii

planation, although they have been studied for two centuries or more. I shall subsequently point out that even the establishment of a wide and true law of nature is but the starting-point for the discovery of exceptions or slight divergences giving a wide scope to empirical discovery.

There is probably no science, I have said, which is entirely free from empirical and unexplained facts. Logie approaches most nearly to this position, as it is merely a deductive development of the laws of thought and the principles of substitution. Yet some of the facts established in the investigation of the inverse logical problem (vol. i. p. 157) may be considered empirical. Mathematical science often yields empirical truths. Why, for instance, should the value of 7, when expressed to a great number of figures, contain the digit 7 much less frequently than any other digits? Even geometry may allow of empirical truths, when the matter does not involve quantities of space, but numerical results and the positive or negative character of quantities, as in De Morgan's theorem concerning negative areas.

Accidental Discovery.

There are not a few cases where almost pure accident has undoubtedly determined the moment when a new branch of knowledge was to be created. The true laws of the construction of crystals were not discovered until Hauy happened to drop a beautiful crystal of calc-spar upon a stone pavement. His momentary regret, at destroying a choice specimen, was quickly removed when, in attempting to join the fragments together, he observed regular geometrical faces, which did not correspond with the external facets of the crystals. A great many more crystals were soon broken intentionally, to observe the

* De Morgan's 'Budget of Paradoxes,' p. 291.

planes of cleavage, and a nearly complete comprehension of the internal structure of crystalline substances was soon the result. Here we see how much more was due to the reasoning powers of the philosopher, than to an accident which must often have happened to other persons.

In a similar manner, a purely fortuitous occurrence led Malus to discover the polarization of light by reflection. The phenomena of double refraction had, of course, been long known, and when engaged in Paris in 1808, in investigating the character of light thus polarized, Malus chanced to look through a double refracting prism at the light of the setting sun, reflected from the windows of the Luxembourg Palace. In turning the prism round, he was surprised to find that the ordinary image disappeared at two opposite positions of the prism. He remarked that the reflected light behaved exactly like light which had been already polarized by passing through another prism. He was induced to test the character of light reflected under other circumstances, and it was eventually proved that polarization is connected by invariable laws with the act of reflection. Some of the most general laws of optics, previously unsuspected, were thus discovered by pure accident.

In the history of electricity, accident has had a large part. For centuries some of the more common effects of magnetism, or frictional electricity, had presented themselves as exceptional and unaccountable deviations from the ordinary course of Nature. Accident must, of course, have first directed attention to such phenomena, but how few of those who witnessed them had any conception of the all-pervading power thus manifested. The very

existence of the so-called galvanism, or electricity of low tension, was unsuspected until Galvani accidentally touched the leg of a frog with pieces of metal. The decomposition of water by voltaic electricity is also said to have been accidentally discovered by Nicholson in 1801,