algebraic formula or mathematical problem of any complexity. Professor Clerk Maxwell, indeed, in the preface to his new Treatise on Electricity, has strongly recommended the reading of Faraday's researches by all students of science, and has given his opinion that though Faraday seldom or never employed mathematical formulæ, his methods and conceptions were not the less mathematical in their nature. I have myself protested against the prevailing confusion between a mathematical and an exact science, yet I certainly think that Faraday's experiments were for the most part qualitative, and that his mathematical ideas were of a rudimentary character. It is true that he could not possibly investigate such a subject as magne-crystallic action without involving himself in geometrical relations of some complexity. Nevertheless I think that he was deficient in mathematical deductive power, that power which is so highly developed by the modern system of mathematical training at Cambridge. Faraday was acquainted with the forms of his celebrated lines of force, but I am not aware that he ever entered into the algebraic nature of those curves, and I feel sure that he could not have explained their forms as depending on the resultant attractions of all the magnetic particles. There are even occasional indications that he did not understand some of the simpler mathematical doctrines of modern physical science. Although he so clearly foresaw the correlation of the physical forces, and laboured so hard with his own hands to connect gravity with other forces, it is doubtful whether he understood the doctrine of the conservation of energy as applied to gravitation. Faraday was probably equal to Newton in experimental skill, and in that peculiar kind of deductive power which leads to the invention of simple qualitative experiments; but it must be allowed that he exhibited little of that mathematical power which enabled Newton to follow out intuitively the quantitative results of a complicated problem with such wonderful facility. Two instances, Newton and Faraday, are sufficient to show that minds of widely 1 See also Nature, September 18, 1873; vol. viii. p. 398. different conformation will meet with suitable regions of research. Nevertheless, there are certain traits which we may discover in all the highest scientific minds. The Newtonian Method, the True Organum. Laplace was of opinion that the Principia and the Opticks of Newton furnished the best models then available of the delicate art of experimental and theoretical investigation. In these, as he says, we meet with the most happy illustrations of the way in which, from a series of inductions, we may rise to the causes of phenomena, and thence descend again to all the resulting details. The popular notion concerning Newton's discoveries is that in early life, when driven into the country by the Great Plague, a falling apple accidentally suggested to him the existence of gravitation, and that, availing himself, of this hint, he was led to the discovery of the law of gravitation, the explanation of which constitutes the Principia. It is difficult to imagine a more ludicrous and inadequate picture of Newton's labours. No originality, or at least priority, was claimed by Newton as regards the discovery of the law of the inverse square, so closely associated with his name. In a well-known Scholium 1 he acknowledges that Sir Christopher Wren, Hooke, and Halley, had severally observed the accordance of Kepler's third law of motion with the principle of the inverse square. Newton's work was really that of developing the methods of deductive reasoning and experimental verification, by which alone great hypotheses can be brought to the touchstone of fact. Archimedes was the greatest of ancient philosophers, for he showed how mathematical theory could be wedded to physical experiments; and his works are the first true Organum. Newton is the modern Archimedes, and the Principia forms the true Novum Organum of scientific method. The laws which he established are great, but his example of the manner of establishing them is greater still. Excepting perhaps 1 Principia, bk. i. Prop. iv. chemistry and electricity, there is hardly a progressive branch of physical and mathematical science, which has not been developed from the germs of true scientific procedure which he disclosed in the Principia or the Opticks. Overcome by the success of his theory of universal gravitation, we are apt to forget that in his theory of sound he originated the mathematical investigation of waves and the mutual action of particles; that in his corpuscular theory of light, however mistaken, he first ventured to apply mathematical calculation to molecular attractions and repulsions; that in his prismatic experiments he showed how far experimental verification could be pushed; that in his examination of the coloured rings named after him, he accomplished the most remarkable instance of minute measurement yet known, a mere practical application of which by Fizeau was recently deemed worthy of a medal by the Royal Society. We only learn by degrees how complete was his scientific insight; a few words in his third law of motion display his acquaintance with the fundamental principles of modern thermodynamics and the conservation of energy, while manuscripts long overlooked prove that in his inquiries concerning atmospheric refraction he had overcome the main difficulties of applying theory to one of the most complex of physical problems. After all, it is only by examining the way in which he effected discoveries, that we can rightly appreciate his greatness. The Principia treats not of gravity so much as of forces in general, and the methods of reasoning about them. He investigates not one hypothesis only, but mechanical hypotheses in general. Nothing so much strikes the reader of the work as the exhaustiveness of his treatment, and the unbounded power of his insight. If he treats of central forces, it is not one law of force which he discusses, but many, or almost all imaginable laws, the 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, but resisting media in general. We have a good example of his method in the scholium to the twenty-second proposition of the second book, in which he runs rapidly over many 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 advocate throughout this book. Francis Bacon held that science should be founded on experience, but he mistook the true mode of using experience, and, in attempting to apply his method, 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 a great 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, 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 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 many 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 a 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 varies 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 colour there was a definite amount of refraction through each prism. He completed the proof by showing that the sepa rated 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; he shows that with homogeneous light there is one distinct focus, with mixed light an infinite |