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The next step was to determine the law according to which the force thus proved to reside in the sun varied with the distance of the planet. Newton presently showed by a most superb effort of mathematical reasoning, that if the orbit of a planet were an ellipse and if the sun were at one of the foci of that ellipse, the intensity of the attractive force must vary inversely as the square of the planet's distance. If the law had any other expression than the inverse square of the distance, then the orbit which the planet must follow would not be an ellipse; or if an ellipse, it would, at all events, not have the sun in the focus. Hence he was able to show from Kepler's laws alone that the force which guided the planets was an attractive power emanating from the sun, and that the intensity of this attractive power varied with the inverse square of the distance between the two bodies.

These circumstances being known, it was then easy to show that the last of Kepler's three laws must necessarily follow. If a number of planets were revolving around the sun, then supposing the materials of all these bodies were equally affected by gravitation, it can be demonstrated that the square of the periodic time in which each planet completes its orbit is proportional to the cube of the greatest diameter in that orbit.

[PLATE: SIR ISAAC NEWTON'S ASTROLABE.]

These superb discoveries were, however, but the starting point from which Newton entered on a series of researches, which disclosed many of the profoundest secrets in the scheme of celestial mechanics. His natural insight showed that not only large masses like the sun and the earth, and the moon, attract each other, but that every particle in the universe must attract every other particle with a force which varies inversely as the square of the distance between them. If, for example, the two particles were placed twice as far apart, then the intensity of the force which sought to bring them together would be reduced to one-fourth. If two particles, originally ten miles asunder, attracted each other with a certain force, then, when the distance was reduced to one mile, the intensity of the attraction between the two particles would be increased one-hundred-fold. This fertile principle extends throughout the whole of nature. In some cases, however, the calculation of its effect upon the actual problems of nature would be hardly possible, were it not for another discovery which Newton's genius enabled him to accomplish. In the case of two globes like the earth and the moon, we must remember that we are dealing not with particles, but with two mighty masses of matter, each composed of innumerable myriads of particles. Every particle in the earth does attract every particle in the moon with a force which varies inversely as the square of their distance. The calculation of such attractions is rendered feasible by the following principle. Assuming that the earth consists of materials symmetrically arranged in shells of varying densities, we may then, in calculating its attraction, regard the whole mass of the globe as concentrated at its centre. Similarly we may regard the moon as concentrated at the centre of its mass. In this way the earth and the moon can both be regarded as particles in point of size, each particle having, however, the entire mass of the corresponding globe. The attraction of one particle for another is a much more simple matter to investigate than the attraction of the myriad different points of the earth upon the myriad different points of the moon.

Many great discoveries now crowded in upon Newton. He first of all gave the explanation of the tides that ebb and flow around our shores. Even in the earliest times the tides had been shown to be related to the moon. It was noticed that the tides were specially high during full moon or during new moon, and this circumstance obviously pointed to the existence of some connection between the moon and these movements of the water, though as to what that connection was no one had any accurate conception until Newton announced the law of gravitation. Newton then made it plain that the rise and fall of the water was simply a consequence of the attractive power which the moon exerted upon the oceans lying upon our globe. He showed also that to a certain extent the sun produces tides, and he was able to explain how it was that when the sun and the moon both conspire, the joint result was to produce especially high tides, which we call "spring tides"; whereas if the solar tide was low, while the lunar tide was high, then we had the phenomenon of "neap" tides.

But perhaps the most signal of Newton's applications of the law of gravitation was connected with certain irregularities in the movements of the moon. In its orbit round the earth our satellite is, of course, mainly guided by the great attraction of our globe. If there were no other body in the universe, then the centre of the moon must necessarily perform an ellipse, and the centre of the earth would lie in the focus of that ellipse. Nature, however, does not allow the movements to possess the simplicity which this arrangement would imply, for the sun is present as a source of disturbance. The sun attracts the moon, and the sun attracts the earth, but in different degrees, and the consequence is that the moon's movement with regard to the earth is seriously affected by the influence of the sun. It is not allowed to move exactly in an ellipse, nor is the earth exactly in the focus. How great was Newton's achievement in the solution of this problem will be appreciated if we realise that he not only had to determine from the law of gravitation the nature of the disturbance of the moon, but he had actually to construct the mathematical tools by which alone such calculations could be effected.

The resources of Newton's genius seemed, however, to prove equal to almost any demand that could be made upon it. He saw that each planet must disturb the other, and in that way he was able to render a satisfactory account of certain phenomena which had perplexed all preceding investigators. That mysterious movement by which the pole of the earth sways about among the stars had been long an unsolved enigma, but Newton showed that the moon grasped with its attraction the protuberant mass at the equatorial regions of the earth, and thus tilted the earth's axis in a way that accounted for the phenomenon which had been known but had never been explained for two thousand years. All these discoveries were brought together in that immortal work, Newton's "Principia."

Down to the year 1687, when the "Principia" was published, Newton had lived the life of a recluse at Cambridge, being entirely occupied with those transcendent researches to which we have referred. But in that year he issued from his seclusion under circumstances of considerable historical interest. King James the Second attempted an invasion of the rights and privileges of the University of Cambridge by issuing a command that Father Francis, a Benedictine monk, should be received as a Master of Arts in the University, without having taken the oaths of allegiance and supremacy. With this arbitrary command the University sternly refused to comply. The Vice-Chancellor was accordingly summoned to answer for an act of contempt to the authority of the Crown. Newton was one of nine delegates who were chosen to defend the independence of the University before the High Court. They were able to show that Charles the Second, who had issued a MANDAMUS under somewhat similar circumstances, had been induced after due consideration to withdraw it. This argument appeared satisfactory, and the University gained their case. Newton's next step in public life was his election, by a narrow majority, as member for the University, and during the years 1688 and 1689, he seems to have attended to his parliamentary duties with considerable regularity.

An incident which happened in 1692 was apparently the cause of considerable disturbance in Newton's equanimity, if not in his health. He had gone to early morning chapel, leaving a lighted candle among his papers on his desk. Tradition asserts that his little dog "Diamond" upset the candle; at all events, when Newton came back he found that many valuable papers had perished in a conflagration. The loss of these manuscripts seems to have had a serious effect. Indeed, it has been asserted that the distress reduced Newton to a state of mental aberration for a considerable time. This has, apparently, not been confirmed, but there is no doubt that he experienced considerable disquiet, for in writing on September 13th, 1693, to Mr. Pepys, he says:

"I am extremely troubled at the embroilment I am in, and have neither ate nor slept well this twelvemonth, nor have my former consistency of mind."

Notwithstanding the fame which Newton had achieved, by the publication of his, "Principia," and by all his researches, the State had not as yet taken any notice whatever of the most illustrious man of science that this or any other country has ever produced. Many of his friends had exerted themselves to procure him some permanent appointment, but without success. It happened, however, that Mr. Montagu, who had sat with Newton in Parliament, was appointed Chancellor of the Exchequer in 1694. Ambitious of distinction in his new office, Mr. Montagu addressed himself to the improvement of the current coin, which was then in a very debased condition. It fortunately happened that an opportunity occurred of appointing a new official in the Mint; and Mr. Montagu on the 19th of March, 1695, wrote to offer Mr. Newton the position of warden. The salary was to be five or six hundred a year, and the business would not require more attendance than Newton could spare. The Lucasian professor accepted this post, and forthwith entered upon his new duties.

The knowledge of physics which Newton had acquired by his experiments was of much use in connection with his duties at the Mint. He carried out the re-coinage with great skill in the course of two years, and as a reward for his exertions, he was appointed, in 1697, to the Mastership of the Mint, with a salary between 1,200 Pounds and 1,500 Pounds per annum. In 1701, his duties at the Mint being so engrossing, he resigned his Lucasian professorship at Cambridge, and at the same time he had to surrender his fellowship at Trinity College. This closed his connection with the University of Cambridge. It should, however, be remarked that at a somewhat earlier stage in his career he was very nearly being appointed to an office which might have enabled the University to retain the great philosopher within its precincts. Some of his friends had almost succeeded in securing his nomination to the Provostship of King's College, Cambridge; the appointment, however, fell through, inasmuch as the statute could not be evaded, which required that the Provost of King's College should be in holy orders.

In those days it was often the custom for illustrious mathematicians, when they had discovered a solution for some new and striking problem, to publish that problem as a challenge to the world, while withholding their own solution. A famous instance of this is found in what is known as the Brachistochrone problem, which was solved by John Bernouilli. The nature of this problem may be mentioned. It was to find the shape of the curve along which a body would slide down from one point (A) to another point (B) in the shortest time. It might at first be thought that the straight line from A to B, as it is undoubtedly the shortest distance between the points, would also be the path of quickest descent; but this is not so. There is a curved line, down which a bead, let us say, would run on a smooth wire from A to B in a shorter time than the same bead would require to run down the straight wire. Bernouilli's problem was to find out what that curve must be. Newton solved it correctly; he showed that the curve was a part of what is termed a cycloid--that is to say, a curve like that which is described by a point on the rim of a carriage-wheel as the wheel runs along the ground. Such was Newton's geometrical insight that he was able to transmit a solution of the problem on the day after he had received it, to the President of the Royal Society.

In 1703 Newton, whose world wide fame was now established, was elected President of the Royal Society. Year after year he was re-elected to this distinguished position, and his tenure, which lasted twenty-five years, only terminated with his life. It was in discharge of his duties as President of the Royal Society that Newton was brought into contact with Prince George of Denmark. In April, 1705, the Queen paid a visit to Cambridge as the guest of Dr. Bentley, the then Master of Trinity, and in a court held at Trinity Lodge on April 15th, 1705, the honour of knighthood was conferred upon the discoverer of gravitation.

Urged by illustrious friends, who sought the promotion of knowledge, Newton gave his attention to the publication of a new edition of the "Principia." His duties at the Mint, however, added to the supreme duty of carrying on his original investigations, left him but little time for the more ordinary task of the revision. He was accordingly induced to associate with himself for this purpose a distinguished young mathematician, Roger Coates, a Fellow of Trinity College, Cambridge, who had recently been appointed Plumian Professor of Astronomy. On July 27th, 1713, Newton, by this time a favourite at Court, waited on the Queen, and presented her with a copy of the new edition of the "Principia."

Throughout his life Newton appears to have been greatly interested in theological studies, and he specially devoted his attention to the subject of prophecy. He left behind him a manuscript on the prophecies of Daniel and the Apocalypse of St. John, and he also wrote various theological papers. Many other subjects had from time to time engaged his attention. He studied the laws of heat; he experimented in pursuit of the dreams of the Alchymist; while the philosopher who had revealed the mechanism of the heavens found occasional relaxation in trying to interpret hieroglyphics. In the last few years of his life he bore with fortitude a painful ailment, and on Monday, March 20th, 1727, he died in the eighty-fifth year of his age. On Tuesday, March 28th, he was buried in Westminster Abbey.

Though Newton lived long enough to receive the honour that his astonishing discoveries so justly merited, and though for many years of his life his renown was much greater than that of any of his contemporaries, yet it is not too much to say that, in the years which have since elapsed, Newton's fame has been ever steadily advancing, so that it never stood higher than it does at this moment.

We hardly know whether to admire more the sublime discoveries at which he arrived, or the extraordinary character of the intellectual processes by which those discoveries were reached. Viewed from either standpoint, Newton's "Principia" is incomparably the greatest work on science that has ever yet been produced.