strikes the reader of the work as the exhaustiveness of his treatment, and the almost infinite power of his insight. If he treats of central forces, it is not any one law of force which he discusses, but many, or almost all imaginable cases, the laws and results of each of which he sketches out in a few pregnant words. If his subject is a resisting medium, it is not air or water alone, nor any one resisting medium, but resisting media in general. We have a good example of his method in the Scholium to the twentysecond proposition of the second book, in which he runs rapidly over many possible suppositions as to the laws of the compressing forces which might conceivably act in an atmosphere of gas, a consequence being drawn from each case, and that one hypothesis ultimately selected which yields results agreeing with experiments upon the pressure and density of the terrestrial atmosphere.

Newton said that he did not frame hypotheses, but, in reality, the greater part of the Principia' is purely hypothetical, endless varieties of causes and laws being imagined which have no counterpart in nature. The most grotesque hypotheses of Kepler or Descartes were not more imaginary. But Newton's comprehension of logical method was perfect; no hypothesis was entertained unless it was definite in conditions, and admitted of unquestionable deductive reasoning; and the value of each hypothesis was entirely decided by the comparison of its consequences with facts. I do not entertain a doubt that the general course of his procedure is identical with that view of the nature of induction, as the inverse application of deduction, which I have advocated throughout these volumes. Francis Bacon held that science should be founded on experience, but he wholly mistook the true mode of using experience, and in attempting to apply his method he ludicrously failed. Newton did not less found his method on experience, but he seized the true method

of treating it, and applied it with a power and success never since equalled. It is wholly a mistake to say that modern science is the result of the Baconian philosophy; it is the Newtonian philosophy and the Newtonian method which have led to all the great triumphs of physical science, and I repeat that the Principia' forms the true Novum Organum.'

In bringing his theories to a decisive experimental verification, Newton showed, as a general rule, an exquisite skill and ingenuity. In his hands a few simple pieces of apparatus were made to give results involving an unsuspected depth of meaning. His most beautiful experimental inquiry was that by which he proved the differing refrangibility of rays of light. To suppose that he originally discovered the power of a prism to break up a beam of white light would be a great mistake, for he speaks of procuring a glass prism to try the celebrated phenomena of colours. But we certainly owe to him the theory that white light is a mixture of rays differing in refrangibility, and that lights which differ in colour, differ also in refrangibility. Other persons might have conceived this theory; in fact, any person regarding refraction as a quantitative effect, must see that different parts of the spectrum have suffered different amounts of refraction. But the power of Newton is shown in the tenacity with which he followed his theory into every consequence, and tested each result by a simple but conclusive experiment. He first shows that different coloured spots are displaced by different amounts when viewed through a prism, and that their images come to a focus at different distances from the lense, as they should do, if the refrangibility differed. After excluding by various experiments a variety of indifferent circumstances, he fixes his attention upon the question whether the rays are merely shattered, disturbed, and spread out in a chance manner,

as Grimaldi supposed, or whether there is a constant relation between the colour and the refrangibility. If Grimaldi was right, it might be expected that any part of the spectrum taken separately, and subjected to a second refraction, would suffer a new breaking up, and produce some new spectrum. Newton inferred from his own theory that a particular ray of the spectrum would have a constant refrangibility, so that a second prism would merely bend it more or less, but not further disperse it in any considerable degree. By simply cutting off most of the rays of the spectrum by a screen, and allowing the remaining narrow ray to fall on a second prism, he proved the truth of this conclusion; and then slowly turning the first prism, so as to vary the colour of the ray falling on the second one, he found that the spot of light formed by the twice-refracted ray travelled up and down, a palpable proof that the amount of refrangibility varied with the colour. For his further satisfaction, he sometimes refracted the light a third or fourth time, and he found that it might be refracted upwards or downwards or sideways, and yet for each coloured light there was a definite amount of refraction through each prism. He completes the proof by showing that the separated rays may again be gathered together into white light by an inverted prism. So that no number of refractions alters the character of the light. The conclusion thus obtained serves to explain the confusion arising in the use of a common lense; with homogeneous light he shows that there is one distinct focus, with mixed light an infinite number of foci, which prevent a clear view from being obtained at any one point.

What astonishes the reader of the 'Opticks' is the persistence with which Newton follows out the consequences of a preconceived theory, and tests the one notion by a wonderful variety of simple comparisons with fact.

It is certainly the theory which leads him to the experiments, and most of these could hardly be devised by accident. The fertility with which he invents new combinations, and foresees the results, subsequently verified, produces an invincible conviction in the reader that he has possession of the truth. Newton actually remarks that it was by mathematically determining all kinds of phenomena of colours which could be produced by refraction that he had 'invented' almost all the experiments in the book, and he promises that others who shall argue truly,' and try the experiments with care, will not be disappointed in the results.

The philosophic method of Huyghens was almost exactly the same as that of Newton, and Huyghens' investigation of the laws of double refraction furnishes almost equally beautiful instances of theory guiding experiment. Double refraction was first discovered by accident, so far as we know, and was described by Erasmus Bartholinus in 1669. The phenomenon then appeared to be entirely exceptional, and the laws governing the two separate paths of the refracted rays were so unapparent and complicated, that even Newton altogether misunderstood the phenomenon, and it was only at the latter end of the last century that scientific men generally began to comprehend its laws.

Nevertheless, Huyghens had, with rare genius, arrived at the true theory as early as 1678. He regarded light as an undulatory motion of some medium, and in his 'Traité de la Lumière,' he pointed out that, in ordinary refraction, the velocity of propagation of the wave is equal in all directions, so that the front of an advancing wave is spherical, and reaches equal distances in equal times. But in crystals, as he supposed, the medium would be of unequal elasticity in different directions, so that a disturbance would reach unequal distances in equal times, and the wave produced would have a spheroidal form. Huy

ghens was not satisfied with an unverified theory. He calculated what might be expected to happen when a crystal of calc-spar was cut in various directions, and he says, 'I have examined in detail the properties of the extraordinary refraction of this crystal, to see if each phenomenon which is deduced from theory would agree with what is really observed. And this being so, it is no slight proof of the truth of our suppositions and principles; but what I am going to add here confirms them still more wonderfully; that is, the different modes of cutting this crystal, in which the surfaces produced give rise to refraction exactly such as they ought to be, and as I had foreseen them, according to the preceding theory.'

The supremacy of Newton's mistaken corpuscular doctrine of light caused the theories and experiments of Huyghens to be disregarded for more than a century; but it is not easy to imagine a more beautiful or successful application of the true method of inductive investigation, theory guiding experiment, and yet wholly relying on experiment for confirmation.

Candour and Courage of the Philosophic Mind.

Perfect readiness to reject a theory inconsistent with fact is, then, a primary requisite of the philosophical mind. But it would be a mistake to suppose that this candour has anything akin to fickleness; on the contrary, readiness to reject a false theory may be combined with a peculiar pertinacity and courage in maintaining an hypothesis as long as its falsity is not actually apparent. There must, indeed, be no prejudice or bias distorting the mind, and causing it to under-estimate or pass over the unwelcome results of experiment. There must be that scrupulous honesty and flexibility of mind, which assigns an adequate value to all