Newton's theory of gravitation.

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with the analysis at his command. He distinguished between mass and weight, and this was an important point. He also created the theory of attractions, which will be more naturally noted in connexion with his theory of gravitation.

The fundamental principles of Newton's theory of gravitation seem to have occurred to him shortly after he had taken his degree at Cambridge. His reasoning at this time, 1666, appears to have been as follows. He knew that gravity extended to the tops of the highest hills; and he conjectured that it might extend as far as the moon, and be the force which retained it in its orbit about the earth. This hypothesis he verified by the following argument. If a stone is allowed to fall near the surface of the earth, the attraction of the earth causes it to move through sixteen feet in one second. Now Newton, as also other mathematicians, had suspected from Kepler's law that the attraction of the earth on a body would be found to decrease as the body was removed further away from the earth, inversely as the square of the distance from the centre of the earth. He knew the radius of the earth and the distance of the moon, and therefore on this hypothesis could find the magnitude of the earth's attraction at the distance of the moon. Further, assuming that the moon moved in a circle, he could calculate the force that was necessary to retain it in its orbit. In 1666, his estimate of the radius of the earth was inaccurate, and, when he made the calculation, he found that this force was rather greater than the earth's attraction on the moon. This discrepancy did not shake his faith in the belief that gravity extended to the moon and varied inversely as the square of the distance; but he conjectured that some other forcesuch, for example, as Descartes' vortices-acted on the moon as well as gravity.

In 1679 Newton repeated his calculations on the lunar orbit; and, using a correct value of the radius of the earth, he found the verification of his former hypothesis was complete. He then proceeded to the general theory of the motion of a particle under a centripetal force-that is, one directed to a fixed point-and showed that the vector to the particle would sweep over equal areas in equal times. He also proved that, if a particle describes an ellipse under a centripetal force to a focus, the law must be that of the inverse square of the distance from the focus; and, conversely, that the orbit of a particle projected under the influence of such a force would be a conic. In 1684 Halley asked Newton what the orbit of a planet would be, if the law of attraction were that of the inverse square, as was commonly suspected to be approximately the case. Newton asserted that it was an ellipse, and sent the demonstration which he had discovered in 1679. Halley, at once recognising the importance of the communication, induced Newton to undertake the investigation of the whole problem of gravitation, and to publish his results.

It would seem that Newton had long believed that every particle of

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Newton's Principia.

matter attracts every other particle, and suspected that the attraction varied as the product of their masses, and inversely as the square of the distance between them; but it is certain that he did not then know what the attraction of a spherical mass on any external point would be, and did not think it likely that a particle would be attracted by the earth as if the latter were concentrated into a single particle at its centre. Hence he must have thought that his discoveries of 1679 were only approximately true when applied to the solar system. His mathematical analysis, however, now showed that the sun and planets, regarded as spheres, exerted their attractions as if their masses were collected at their centres; and thus his former results were absolutely true of the solar system, save only for a correction caused by the slight deviation of the sun, earth, and planets, from a perfectly spherical form.

The first book of the Principia is given up to the consideration of the motion of particles or bodies in free space either in known orbits, or under the action of known forces, or under their mutual attraction. It is prefaced by an introduction on the science of Dynamics; it also contains geometrical investigations of various properties of conic sections. The second book treats of motion in a resisting medium. The theory of Hydrodynamics was here created, and it was applied to the phenomena of waves, tides, and acoustics. In the third book, the theorems of the first are applied to the chief phenomena of the solar system; and the masses and distances of the planets and (when sufficient data exist) of their satellites are determined. In particular, the motion of the moon, with its various inequalities, and the theory of the tides, are worked out in detail, and as fully as was then possible. Newton also investigated the theory of comets, showed that they belonged to the solar system, and illustrated his results by considering certain special comets. The complete work was published in 1687. A second edition was brought out in 1713 by Roger Cotes of Cambridge (1682-1716) under Newton's direction. The demonstrations throughout are geometrical, but are rendered unnecessarily difficult by their conciseness, and by the absence of any clue to the method by which they were obtained. The reason why the arguments were presented in a geometrical form appears to have been that the infinitesimal calculus was then unknown; and, had Newton used it to demonstrate results which were in themselves opposed to the prevalent philosophy of the time, the controversy as to the truth of his results would have been hampered by a dispute concerning the validity of the methods used in proving them.

The publication of the Principia is one of the landmarks in the history of Mathematics. In it the phenomena of the solar system were shown to be deducible from laws which experience proved to be true on the earth, and thus it brought new worlds within the scope of man's investigations. The conclusions were generally accepted by the leading thinkers of the time; but a generation or so had to pass before

their validity was universally admitted; henceforth, few doubted that the reign of law extended throughout the universe of non-organic matter. Newton further considered the question whether it was possible to explain gravitation as the result of other laws. He could not frame a satisfactory hypothesis, and the problem is still unsolved.

It should be noted that Newton's conclusions could not have been reached, had not observational Astronomy also developed. This was largely due to the excellent work done at Greenwich under Flamsteed (1646-1719), Halley (1656–1742), and Bradley (1692-1762), who successively occupied the position of Astronomer Royal. The last-named explained the aberration of light (1727), and thus obtained an independent determination of the velocity of light.

The achievements of the seventeenth century in Astronomy and Mechanics were so great that they have thrown some of the other work of the time into comparative obscurity. The investigations in Physical Optics were, however, of singular interest. Here again Newton played the leading part. When, in 1669, he was appointed to a professorship at Cambridge, he at first chose Optics for the subject of his lectures and researches; and before the end of that year he had worked out the details of his discovery of the decomposition of a ray of white light into rays of different colours by means of a prism, from which the explanation of the phenomenon of the rainbow followed. In consequence of a chapter of accidents he failed to correct the chromatic aberration of two colours by means of a couple of prisms; hence he abandoned the hope of making a refracting telescope which should be achromatic, and, instead, designed a reflecting telescope, which is of a somewhat different design from those suggested by James Gregory and N. Cassegrain.

We have already explained how Newton deduced the motions of the solar system from the one assumption of universal gravitation. The similar problem in Optics was the possibility of making a single hypothesis from which all the known optical phenomena could be deduced. Two plausible theories of this kind had been already suggested. In one, known as the "corpuscular" or "emission" theory, it is assumed that a luminous object emits corpuscles which hit or affect the eye. In the other, known as the wave or undulatory theory, it is assumed that light is caused by a series of waves in an ether which fills space, the waves being set in motion by pulsations of the luminous body. It would seem that at one time Newton deemed the latter the more probable hypothesis; but, though he could thus account for the phenomena of reflexion, refraction, and colours, it failed (as then propounded) to explain the rectilinear propagation of light; and this he considered fatal to its claims. He accordingly turned to the corpuscular theory, and from it deduced the phenomena of reflexion, refraction, colours, and diffraction. To do this, however, he was obliged to add a somewhat artificial rider, that the corpuscles had alternating fits of easy

C. M. H. V. CH. XXIII.

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Development of Physics.

reflexion and easy refraction, communicated to them by an ether which filled space. His various researches on the subject were embodied in his Optics published in 1704.

The wave theory had been roughly outlined in 1665 by Robert Hooke. It was elaborated in a paper by Huygens in 1678, and expounded at greater length in his Traité de la Lumière, published in 1690. From it Huygens deduced the laws of reflexion, refraction, and double refraction. He was acquainted with the phenomena of polarisation; but he was unable to explain them since he assumed the vibrations in the ether to be longitudinal. It was not until the nineteenth century, when Fresnel worked out the theory on the hypothesis that the vibrations were transverse, that it was put on a satisfactory basis. Huygens was among the most illustrious mathematicians of his age, and the wave theory may be fairly deemed to be due to him. The immense reputation of Newton induced a general acceptance at the time of the corpuscular theory as enunciated by him-an unfortunate result of his extraordinary achievements, and the more curious because his writings show that on some grounds he deemed the wave theory the more probable. In science, as in other subjects, too much reliance should not be placed on individual authority.

The theory of Hydrodynamics, including therein Sound and vibrations of fluids, may be said to have been created by Newton in the second book of his Principia. He determined experimentally the velocity of sound in air and other media. The difficulties of mathematical analysis involved are great, and he was not able to carry the theory very far. In connexion with the theory of Sound, may also be mentioned the names of Brook Taylor, who gave the theory of the transverse vibrations of strings, Joseph Sauveur (1653–1715), and Francis Hauksbee (1650–1713),

As to other physical subjects, we may say that in all of them, at this time, there was intelligent observation and experiment. In particular the subject of Heat was attacked on the right lines by Boyle, Hooke, Newton and others, though the experimental data available were but slight. So, too, as to the work of the time in Electricity, which attracted the attention of Boyle, Halley, Newton, Picard, and Hauksbee.

The death of Newton and the separation of the British school of mathematicians from their continental contemporaries may be taken as marking the close of an epoch. At the beginning of the seventeenth century Mathematics were only just breaking free from their medieval trammels, and Physics in the modern sense were non-existent. In but little more than a century Mathematics had been developed into an instrument of great power; the value of the calculus had been recognised, and the foundations of modern analysis laid; the theories of Mechanics and gravitation had been established; and the problems of Physical Optics had been subjected to mathematical processes. In this extraordinary extension of knowledge all the leading nations of Europe had

Development of the Natural Sciences.-Human Anatomy. 723

taken part. Galileo, Descartes, Fermat, Huygens, Leibniz, and above all, Newton, form a group of workers which will be ever memorable in the history of science; and the fabric of modern Mathematics and Physics is but the superstructure erected on the foundations which they laid.

(2) OTHER BRANCHES OF SCIENCE.

The seventeenth century may, in a broad way, be spoken of as the period during which the Natural Sciences-according to our modern classification of them-Botany, Zoology, Anatomy, Physiology, Geology, and, we may add Chemistry, took definite shape, and began to be built up, each in its own way, as an independent branch of knowledge. The labours of the eighteenth and nineteenth centuries were, in their turn, largely directed towards carrying forward what had then been begun. But the impulse which led to this great development is to be found in the preceding century, or even earlier: in the revolt against the scholastic spirit which formed so large a part of the Renaissance.

The sciences in question, though having their birth partly in mere natural curiosity, sprang largely from the Art of Medicine. The treatment of disease led to enquiry into the structure and action of the body of man, and this in turn to the study of animals. The use of herbs as remedies moved men to observe the features and qualities of plants; and the science of Chemistry, though it began as Alchemy in the search for the transmutation of metals, and continued to be supported by the needs of industrial life, was in the main developed by the desire to find substances which should cure diseases. In the sixteenth century, and long afterwards, the men who were building up the several natural sciences were to be found among the teachers of the medical schools.

Hence it is not wonderful that the first great triumph of the revolt against the scholastic spirit, though it was won in a limited and strictly medical branch of knowledge, namely Human Anatomy, served as a bright example to nearly all the branches of natural knowledge, and exerted a powerful influence upon them.

In Human Anatomy the scholastic spirit remained supreme up to the middle of the sixteenth century. The far-reaching, almost inspired labours of Galen had in quite early times produced a system of doctrines touching the structure and functions of the body of man so complete and consistent that it seemed to supply all that was needed to be known; the study of these things came to mean the study of Galen, the written page was the authority, and enquiry was narrowed to interpretation. In 1543 Andreas Vesalius (1514-64), a young professor at Padua, published a book on the structure of the human body, based, not on what Galen taught, but on what Vesalius had himself seen, and what anybody might