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Galileo died on Christmas Day, 1642 — the day of Newton's birth. The further consideration of the grand field of discovery opened out by Galileo with his telescopes must be now postponed, to avoid discontinuity in the history of the intellectual development of this period, which lay in the direction of dynamical, or physical, astronomy.

Until the time of Kepler no one seems to have conceived the idea of universal physical forces controlling terrestrial phenomena, and equally applicable to the heavenly bodies. The grand discovery by Kepler of the true relationship of the sun to the planets, and the telescopic discoveries of Galileo and of those who followed him, spread a spirit of inquiry and philosophic thought throughout Europe, and once more did astronomy rise in estimation; and the irresistible logic of its mathematical process of reasoning soon placed it in the position it has ever since occupied as the foremost of the exact sciences.

The practical application of this process of reasoning was enormously facilitated by the invention of logarithms by Napier. He was born at Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system the tedious arithmetical operations necessary in astronomical calculations, especially those dealing with the trigonometrical functions of angles, were so much simplified that Laplace declared that by this invention the life-work of an astronomer was doubled. Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of Tycho Brahe and Kepler, and was able to improve the Rudolphine tables so much that he foretold a transit of Venus, in 1639, which these tables failed to indicate, and was the only observer of it. His life was short, but he accomplished a great deal, and rightly ascribed the lunar inequality called evection to variations in the value of the eccentricity and in the direction of the line of apses, at the same time correctly assigning the disturbing force of the sun as the cause. He discovered the errors in Jupiter's calculated place, due to what we now know as the long inequality of Jupiter and Saturn, and measured with considerable accuracy the acceleration at that date of Jupiter's mean motion, and indicated the retardation of Saturn's mean motion. Horrocks' investigations, so far as they could be collected, were published posthumously in 1672, and seldom, if ever, has a man who lived only twenty-two years originated so much scientific knowledge. At this period British science received a lasting impetus by the wise initiation of a much-abused man, Charles II., who founded the Royal Society of London, and also the Royal Observatory of Greenwich, where he established Flamsteed as first Astronomer Royal, especially for lunar and stellar observations likely to be useful for navigation. At the same time the French Academy and the Paris Observatory were founded. All this within fourteen years, 1662–1675. Meanwhile gravitation in general terms was being discussed by Hooke, Wren, Halley, and many others. All of these men felt a repugnance to accept the idea of a force acting across the empty void of space. Descartes (1596–1650) proposed an ethereal medium whirling round the sun with the planets, and having local whirls revolving with the satellites. As Delambre and Grant have said, this fiction only retarded the progress of pure science. It had no sort of relation to the more modern, but equally misleading, “nebular hypothesis.” While many were talking and guessing, a giant mind was needed at this stage to make things clear.

7. SIR ISAAC NEwton — LAW of UNIVERSAL GRAVITATION

We now reach the period which is the culminating point of interest in the history of dynamical astronomy. Isaac Newton was born in 1642. Pemberton states that Newton, having quitted Cambridge to avoid the plague, was residing at Wolsthorpe, in Lincolnshire, where he had been born; that he was sitting one day in the garden, reflecting upon the force which prevents a planet from flying off at a tangent and which draws it to the sun, and upon the force which draws the moon to the earth; and that he saw in the case of the planets that the sun's force must clearly be unequal at different distances, for the pull out of the tangential line in a minute is less for Jupiter than for Mars. He then saw that the pull of the earth on the moon would be less than for a nearer object. It is said that while thus meditating he saw an apple fall from a tree to the ground, and that this fact suggested the questions: Is the force that pulled that apple from the tree the same as the force which draws the moon to the earth? Does the attraction for both of them follow the same law as to distance as is given by the planetary motions round the sun ? It has been stated that in this way the first conception of universal gravitation arose."

* The writer inherited from his father (Professor J. D. Forbes) a small box containing a bit of wood and a slip of paper, which had been presented to him by Sir David Brewster. On the paper Sir David had written these words: “If there be any truth in the story that Newton was led to the theory of gravitation by the fall of an apple, this bit of wood is probably a piece of the apple tree from which Newton saw the apple fall. When I was on a pilgrimage to the house in which Newton was born, I cut it off an ancient apple tree growing in his garden.” When lecturing in Glasgow, about 1875, the writer showed it to his audience. The next morning, when removing his property from the lecture table, he sound that his precious relic had been stolen. It would be interesting to know who has got it now!

Quite the most important event in the whole history of physical astronomy was the publication, in 1687, of Newton's Principia (Philosophiae Naturalis Principia Mathematica). In this great work Newton started from the beginning of things, the laws of motion, and carried his argument, step by step, into every branch of physical astronomy; giving the physical meaning of Kepler's three laws, and explaining, or indicating the explanation of, all the known heavenly motions and their irregularities; showing that all of these were included in his simple statement about the law of universal gravitation; and proceeding to deduce from that law new irregularities in the motions of the moon which had never been noticed, and to discover the oblate figure of the earth and the cause of the tides. These investigations occupied the best part of his life; but he wrote the whole of his great book in fifteen months.

Having developed and enunciated the true laws of motion, he was able to show that Kepler's second law (that equal areas are described by the line from the planet to the sun in equal times) was only another way of saying that the centripetal force on a planet is always directed to the sun. Also that Kepler's first law (elliptic orbits with the sun in one focus) was only another way of saying that the force urging a planet to the sun varies inversely as the square of the distance.

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