in which this is described, did not appear till 1661, when it was published by Hevelius of Dantzic. Some of his papers were destroyed by the soldiers in the English civil wars; and his remaining works were finally published by Wallis, in 1673. The passage to which I here specially wish to refer is contained in a letter to his astronomical ally, William Crabtree, dated 1638. He appears to have been asked by his friend to suggest some cause for the motion of the aphelion of a planet; and in reply, he uses an experimental illustration which was afterwards employed by Hooke in 1666. A ball at the end of a string is made to swing so that it describes an oval. This contrivance Hooke employed to show the way in which an orbit results from the combination of a projectile motion with a central force. But the oval does not keep its axis constantly in the same position. The apsides, as Horrox remarked, move in the same direction as the pendulum, though much slower. And it is true, that this experiment does illustrate, in a general way, the cause of the motion of the aphelia of the Planetary Orbits; although the form of the orbit is different in the experiment and in the solar system; being an ellipse with the centre of force in the centre of the ellipse, in the former case, and an ellipse with the centre of force in the focus, in the latter case. These two forms of orbits correspond to a central force varying directly as the distance, and a central force varying inversely as the square of the distance; as Newton proved in the Principia. But the illustration appears show that Horrox pretty clearly saw how an orbit arose from a central force. So far, and no farther, Newton's contemporaries could get; and then he had to help them onwards by showing what was the law of the force, and what larger truths were now attainable.

Newton's Discovery of Gravitation.

[Page 402.] As I have already remarked, men have a willingness to believe that great discoveries are governed by casual coincidences, and accompanied by sudden revolutions of feeling. Newton had entertained the thought of the moon being retained in her orbit by gravitation as early as 1665 or 1666. He resumed the subject and worked the thought out into a system in 1684 and 5. What induced him to return to the question? What led to his success on this last occasion! With what feelings was the success attended? It is easy to make an imaginary connection of facts. "His optical discoveries had recommended him to the Royal Society, and he was now a member. He

there learned the accurate measurement of the Earth by Picard, differing very much from the estimation by which he had made his calculation in 1666; and he thought his conjecture now more likely to be just." M. Biot gives his assent to this guess. The English translation of M. Biot's biography' converts the guess into an assertion. But, says Professor Rigaud,' Picard's measurement of the Earth was well known to the Fellows of the Royal Society as early as 1675, there being an account of the results of it given in the Philosophical Transactions for that year. Moreover, Norwood, in his Seaman's Practice, dated 1636, had given a much more exact measure than Newton employed in 1666. But Norwood, says Voltaire, had been buried in oblivion by the civil wars. No, again says the exact and truth-loving Professor Rigaud, Norwood was in communication with the Royal Society in 1667 and 1668. So these guesses at the accident which made the apple of 1665 germinate in 1684, are to be carefully distinguished from history.

But with what feelings did Newton attain to his success? Here again we have, I fear, nothing better than conjecture. "He went home, took out his old papers, and resumed his calculations. As they drew near to a close, he was so much agitated that he was obliged to desire a friend to finish them. His former conjecture was now found to agree with the phænomena with the utmost precision." This conjectural story has been called "a tradition;" but he who relates it does not call it so. Every one must decide, says Professor Rigaud, from his view of Newton's character, how far he thinks it consistent with this statement. Is it likely that Newton, so calm and so indifferent to fame as he generally showed himself, should be thus agitated on such an occasion? "No," says Sir David Brewster; "it is not supported by what we know of Newton's character." To this we may assent; and this conjectural incident we must therefore, I conceive, separate from history. I had incautiously admitted it into the text of the first Edition.

Newton appears to have discovered the method of demonstrating that a body might describe an ellipse when acted upon by a force residing in the focus, and varying inversely as the square of the distance, in 1669, upon occasion of his correspondence with Hooke. In 1684,

2 Robison's Mechanical Philosophy, vol. iii. p. 94. (Art. 195.) Biographie Universelle.

Library of Useful Knowledge.

5 Historical Essay on the First Publication of the Principia (1838). Robison, ibid.

7 Life of Newton, vol. i. p. 292.

at Halley's request, he returned to the subject; and in February, 1685, there was inserted in the Register of the Royal Society a paper of Newton's (Isaaci Newtoni Propositiones de Motu), which contained some of the principal propositions of the first two Books of the Principia. This paper, however, does not contain the proposition "Lunam gravitare in Terram," nor any of the propositions of the Third Book.

CHAPTER III.

THE PRINCIPIA.

L

Sect. 2.-Reception of the Principia.

ORD BROUGHAM has very recently (Analytical View of Sir Isaac Newton's Principia, 1855) shown a strong disposition still to maintain, what he says has frequently been alleged, that the reception of the work was not, even in this country, "such as might have been expected." He says, in explanation of the facts which I have adduced, showing the high estimation in which Newton was held immediately after the publication of the Principia, that Newton's previ ous fame was great by former discoveries. This is true; but the effect of this was precisely what was most honorable to Newton's countrymen, that they received with immediate acclamations this new and greater discovery. Lord Brougham adds, "after its appearance the Principia was more admired than studied;" which is probably true of the Principia still, and of all great works of like novelty and difficulty at all times. But, says Lord Brougham, "there is no getting over the inference on this head which arises from the dates of the two first editions. There elapsed an interval of no less than twenty-seven years between them; and although Cotes [in his Preface] speaks of the copies having become scarce and in very great demand when the second edition appeared in 1713, yet had this urgent demand been of many years' continuance, the reprinting could never have been so long delayed." But Lord Brougham might have learnt from Sir David Brewster's Life of Newton (vol. i. p. 312), which he extols so emphatically, that already in 1691 (only four years after the publication), a copy of the Principia could hardly be procured, and that even at that

time an improved edition was in contemplation; that Newton had been pressed by his friends to undertake it, and had refused.

When Bentley had induced Newton to consent that a new edition should be printed, he announces his success with obvious exultation to Cotes, who was to superintend the work. And in the mean time the Astronomy of David Gregory, published in 1702, showed in every page how familiar the Newtonian doctrines were to English philosophers, and tended to make them more so, as the sermons of Bentley himself had done in 1692.

Newton's Cambridge contemporaries were among those who took a part in bringing the Principia before the world. The manuscript draft of it was conveyed to the Royal Society (April 28, 1686) by Dr. Vincent, Fellow of Clare Hall, who was the tutor of Whiston, Newton's deputy in his professorship; and he, in presenting the work, spoke of the novelty and dignity of the subject. There exists in the library of the University of Cambridge a manuscript containing the early Propositions of the Principia as far as Prop. xxxiii. (which is a part of Section vii., about Falling Bodies). This appears to have been a transcript of Newton's Lectures, delivered as Lucasian Professor: it is dated October, 1684.

Is Gravitation proportional to Quantity of Matter?

It was a portion of Newton's assertion in his great discovery, that all the bodies of the universe attract each other with forces which are as the quantity of matter in each: that is, for instance, the sun attracts the satellites of any planet just as much as he attracts the planet itself, in proportion to the quantity of matter in each; and the planets attract one another just as much as they attract the sun, according to the quantity of matter.

To prove this part of the law exactly is a matter which requires careful experiments; and though proved experimentally by Newton, has been considered in our time worthy of re-examination by the great astronomer Bessel. There was some ground for doubt; for the mass of Jupiter, as deduced from the perturbations of Saturn, was only 1070 of the mass of the sun; the mass of the same planet as deduced from the perturbations of Juno and Pallas was 45 of that of the Sun. If this difference were to be confirmed by accurate observations and calculations, it would follow that the attractive power exercised by Jupiter upon the minor planets was greater than that exercised upon

Saturn. And in the same way, if the attraction of the Earth had any specific relation to different kinds of matter, the time of oscillation of a pendulum of equal length composed wholly or in part of the two substances would be different. If, for instance, it were more intense for magnetized iron than for stone, the iron pendulum would oscillate more quickly. Bessel showed' that it was possible to assume hypothetically a constitution of the sun, planets, and their appendages, such that the attraction of the Sun on the Planets and Satellites should be proportional to the quantity of matter in each; but that the attraction of the Planets on one another would not be on the same scale.

Newton had made experiments (described in the Principia, Book iii., Prop. vi.) by which it was shown that there could be no considerable or palpable amount of such specific difference among terrestrial bodies, but his experiments could not be regarded as exact enough for the requirements of modern science. Bessel instituted a laborious series of experiments (presented to the Berlin Academy in 1832) which completely disproved the conjecture of such a difference; every substance examined having given exactly the same coefficient of gravitating intensity as compared with inertia. Among the substances examined were metallic and stony masses of meteoric origin, which might be supposed, if any bodies could, to come from other parts of the solar system.

CHAPTER IV.

VERIFICATION AND COMPLETION OF THE NEWTONIAN THEORY.

THE

Tables of the Moon and Planets.

HE Newtonian discovery of Universal Gravitation, so remarkable in other respects, is also remarkable as exemplifying the immense extent to which the verification of a great truth may be carried, the amount of human labor which may be requisite to do it justice, and the striking extension of human knowledge to which it may lead. I have said that it is remarked as a beauty in the first fixation of a theory that its measures or elements are established by means of a few

1 Berlin Mem. 1824.