Part 11

Transparency he considers as arising from the particles and their intervals, or pores, being too small to cause reflection at their common surfaces; so that all light which enters transparent bodies passes through them without any portion of it being turned from its path by reflexion.

Opacity, he thinks, arises from an opposite cause, viz., when the parts of bodies are of such a size to be capable of reflecting the light which falls upon them, in which case the light is "stopped or stifled" by the multitude of reflections.

The colours of natural bodies have, in the Newtonian hypothesis, the same origin as the colours of thin plates, their transparent particles, according to their several sizes, reflecting rays of one colour and transmitting those of another.

Among the optical discoveries of Newton those which he made on the inflection of light hold a high place. They were first published in his "Treatise on Optics," in 1707.

III--The Discovery of the Law of Gravitation

From the optical labours of Newton we now proceed to the history of his astronomical discoveries, those transcendent deductions of human reason by which he has secured to himself an immortal name, and vindicated the intellectual dignity of his species.

In the year 1666, Newton was sitting in his garden at Woolsthorpe, reflecting on the nature of gravity, that remarkable power which causes all bodies to descend towards the centre of the earth. As this power does not sensibly diminish at the greatest height we can reach he conceived it possible that it might reach to the moon and affect its motion, and even hold it in its orbit. At such a distance, however, he considered some diminution of the force probable, and in order to estimate the diminution, he supposed that the primary planets were carried round the sun by the same force. On this assumption, by comparing the periods of the different planets with their distances from the sun, he found that the force must decrease as the squares of the distances from the sun. In drawing this conclusion he supposed the planets to move in circular orbits round the sun.

Having thus obtained a law, he next tried to ascertain if it applied to the moon and the earth, to determine if the force emanating from the earth was sufficient, if diminished in the duplicate ratio of the moon's distance, to retain the moon in its orbit. For this purpose it was necessary to compare the space through which heavy bodies fall in a second at the surface of the earth with the space through which the moon, as it were, falls to the earth in a second of time, while revolving in a circular orbit. Owing to an erroneous estimate of the earth's diameter, he found the facts not quite in accordance with the supposed law; he found that the force which on this assumption would act upon the moon would be one-sixth more than required to retain it in its orbit.

Because of this incongruity he let the matter drop for a time. But, in 1679, his mind again reverted to the subject; and in 1682, having obtained a correct measurement of the diameter of the earth, he repeated his calculations of 1666. In the progress of his calculations he saw that the result which he had formerly expected was likely to be produced, and he was thrown into such a state of nervous irritability that he was unable to carry on the calculation. In this state of mind he entrusted it to one of his friends, and he had the high satisfaction of finding his former views amply realised. The force of gravity which regulated the fall of bodies at the earth's surface, when diminished as the square of the moon's distance from the earth, was found to be exactly equal to the centrifugal force of the moon as deduced from her observed distance and velocity.

The influence of such a result upon such a mind may be more easily conceived than described. The whole material universe was opened out before him; the sun with all his attending planets; the planets with all their satellites; the comets wheeling in every direction in their eccentric orbits; and the system of the fixed stars stretching to the remotest limits of space. All the varied and complicated movements of the heavens, in short, must have been at once presented to his mind as the necessary result of that law which he had established in reference to the earth and the moon.

After extending this law to the other bodies of the system, he composed a series of propositions on the motion of the primary planets about the sun, which was sent to London about the end of 1683, and was soon afterwards communicated to the Royal Society.

Newton's discovery was claimed by Hooke, who certainly aided Newton to reach the truth, and was certainly also on the track of the same law.

Between 1686 and 1687 appeared the three books of Newton's immortal work, known as the "Principia." The first and second book are entitled "On the Motion of Bodies," and the third "On the System of the World."

In this great work Newton propounds the principle that "every particle of matter in the universe is attracted by, or gravitates to, every other particle of matter with a force inversely proportional to the squares of their distances." From the second law of Kepler, namely, the proportionality of the areas to the times of their description, Newton inferred that the force which keeps a planet in its orbit is always directed to the sun. From the first law of Kepler, that every planet moves in an ellipse with the sun in one of its foci, he drew the still more general inference that the force by which the planet moves round that focus varies inversely as the square of its distance from the focus. From the third law of Kepler, which connects the distances and periods of the planets by a general rule, Newton deduced the equality of gravity in them all towards the sun, modified only by their different distances from its centre; and in the case of terrestrial bodies, he succeeded in verifying the equality of action by numerous and accurate experiments.

By taking a more general view of the subject, Newton showed that a conic section was the only curve in which a body could move when acted upon by a force varying inversely as the square of the distance; and he established the conditions depending on the velocity and the primitive position of the body which were requisite to make it describe a circular, an elliptical, a parabolic, or a hyperbolic orbit.

It still remained to show whether the force resided in the centre of planets or in their individual particles; and Newton demonstrated that if a spherical body acts upon a distant body with a force varying as the distance of this body from the centre of the sphere, the same effect will be produced as if each of its particles acted upon the distant body according to the same law.

Hence it follows that the spheres, whether they are of uniform density, or consist of concentric layers of varying densities, will act upon each other in the same manner as if their force resided in their centres alone. But as the bodies of the solar system are nearly spherical, they will all act upon one another and upon bodies placed on their surface, as if they were so many centres of attraction; and therefore we obtain the law of gravity, that one sphere will act upon another sphere with a force directly proportional to the quantity of matter, and inversely as the square of the distance between the centres of the spheres. From the equality of action and reaction, to which no exception can be found, Newton concluded that the sun gravitates to the planets and the planets to their satellites, and the earth itself to the stone which falls upon its surface, and consequently that the two mutually gravitating bodies approach one another with velocities inversely proportional to their quantities of matter.

Having established this universal law, Newton was able not only to determine the weight which the same body would have at the surface of the sun and the planets, but even to calculate the quantity of matter in the sun and in all the planets that had satellites, and also to determine their density or specific gravity.

With wonderful sagacity Newton traced the consequences of the law of gravitation. He showed that the earth must be an oblate spheroid, formed by the revolution of an ellipse round its lesser axis. He showed how the tides were caused by the moon, and how the effect of the moon's action upon the earth is to draw its fluid parts into the form of an oblate spheroid, the axis of which passes through the moon. He also applied the law of gravitation to explain irregularities in the lunar motions, the precession of the equinoctial points, and the orbits of comets.

In the "Principia" Newton published for the first time the fundamental principle of the fluxionary calculus which he had discovered about twenty years before; but not till 1693 was his whole work communicated to the mathematical world. This delay in publication led to the historical controversy between him and Leibnitz as to priority of discovery.

In 1676 Newton had communicated to Leibnitz the fact that he had discovered a general method of drawing tangents, concealing the method in two sentences of transposed characters. In the following year Leibnitz mentioned in a letter to Oldenburg (to be communicated to Newton) that he had been for some time in possession of a method for drawing tangents, and explains the method, which was no other than the differential calculus. Before Newton had published a single word upon fluxions the differential calculus had made rapid advances on the Continent.

In 1704 a reviewer of Newton's "Optics" insinuated that Newton had merely improved the method of Leibnitz, and had indeed stolen Leibnitz's discovery; and this started a controversy which raged for years. Finally, in 1713, a committee of the Royal Society investigated the matter, and decided that Newton was the first inventor.

IV.--Later Years of Newton's Life

In 1692, when Newton was attending divine service, his dog Diamond upset a lighted taper on his desk and destroyed some papers representing the work of years. Newton is reported merely to have exclaimed: "O Diamond, Diamond, little do you know the mischief you have done me!" But, nevertheless, his excessive grief is said for a time to have affected his mind.

In 1695 Newton was appointed Warden of the Mint, and his mathematical and chemical knowledge were of eminent use in carrying on the recoinage of the mint. Four years later he was made Master of the Mint, and held this office during the remainder of his life. In 1701 he was elected one of the members of parliament for Oxford University, and in 1705 he was knighted.

Towards the end of his life Newton began to devote special attention to the theological questions, and in 1733 he published a work entitled "Observations upon the Prophecies of Daniel and the Apocalypse of St. John," which is characterised by great learning and marked with the sagacity of its distinguished author. Besides this religious work, he also published his "Historical Account of Two Notable Corruptions of Scripture," and his "Lexicon Propheticum."

In addition to theology, Newton also studied chemistry; and in 1701 a paper by him, entitled "Scala graduum caloris," was read at the Royal Society; while the queries at the end of his "Optics" are largely chemical, dealing with such subjects as fire, flame, vapour, heat, and elective attractions.

He regards fire as a body heated so hot as to emit light copiously; and flame as a vapour, fume, or exhalation, heated so hot as to shine.