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 Scholium4 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 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,