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their distances from the bodies which they attract, the motion of the moon ought not only to depend upon its gravity towards the earth, but also to be influenced by the action of the sun; for this effect, though exceedingly weakened by the distance, ought not to be wholly imperceptible in the result.

Thus Newton ceased to doubt; and after having been, during so many years, kept in suspense about this eminently important law, he had no sooner recognized its truth, than he penetrated instantly to its most remote consequences, pursued them all with a vigour, a perseverance, and a boldness of thought, which, till that time, had never been displayed in science. Indeed it seems hardly probable that it will, at any future time, be the destiny of another human being to demonstrate such wonderful truths as these; that all the parts of matter gravitate towards one another, with a force directly proportional to their masses, and reciprocally proportional to the squares of their mutual distances; that this force retains the planets and the comets round the sun, and each system of satellites around their primary planets; and that, by the universally communicated influence which it establishes between the material particles of all these bodies, it determines the nature of their orbits, the forms of their masses, the oscillations in the fluids which cover them, and, in fine, their smallest movements, either in space or in rotation upon their own axes, and all conformably to the actually observed laws. The finding of the relative masses of the different planets, the determination of the ratio of the axes of the earth, the pointing out the cause of the precession of the equinoxes, and the discovery of the force exercised by the sun and the moon in causing the tides, were the sublime objects which unfolded themselves to the meditations of Newton, after he had discovered the fundamental law of the system of the universe. Can we wonder at his having been so much excited as not to have been able to complete the calculation which was leading him to a conviction that the discovery was achieved?

It was now that he must have experienced intense satisfaction at having so profoundly studied the manner in which physical forces act, and at having sought by so many experiments to comprehend, and exactly to measure their different effects. More particularly

must he have been delighted at having created that new calculus, by means of which he was enabled to develope the most complicated phenomena, to bring to light the simple elements of motion, and thus to obtain the forces themselves from which the phenomena result; and finally, to re-descend from these forces to the detail of all their effects: for, with equal talent, had he not possessed this instrument of investi gation, the complete unfolding of his discovery would have been impossible. But, possessing the means, he had only to apply them; and thus he saw the constant object of his hope attained. Henceforward, he devoted himself entirely to the enjoyment of these delightful contemplations; and during the two years that he spent in preparing and developing his immortal work, Philosophiae naturalis Principia Mathematica, he lived only to calculate and to think. Oftentimes lost in the contemplation of these grand objects, he acted unconsciously: his thoughts appearing to preserve no connexion with the ordinary concerns of life. It is said, that, frequently on rising in the morning, he would sit down on his bedside, arrested by some new conception, and would remain for hours together, engaged in tracing it out, without dressing himself. He would even have neglected to take sufficient nourishment, had he not been reminded by others of the time of his meals.*

It was only by the uninterrupted efforts of solitary and profound meditation, that even Newton was able to unfold all the truths he had conceived, deductions and which were but so many from his great discovery. We may learn from his example, on what severe conditions even the most perfect intellect is able to penetrate deeply into the secrets of nature, and to enlarge the bounds of For himself, he human attainments. well knew, and willingly confessed, the inevitable necessity of perseverance and

The following anecdote is told on this subject. Dr. Stukely, an intimate friend of Newton, called upon him one day when his dinner was already served up, but before he bad appeared in the diningroom. Dr. Stukely having waited some time, and becoming impatient, at length removed the cover from a chicken, which he presently ate, putting the

bones back into the dish and replacing the cover. After a short interval, Newton came into the room,. and after the usual compliments, sat down to dinner, but on taking up the cover, and seeing only the bones of the bird left, he observed with some little surprise, I thought I had not dined, but I now had that I have."

constancy in the exercise of his attention, in order to develope the power of thought. To one who had asked him on some occasion, by what means he had arrived at his discoveries, he replied, "By always thinking unto them;" and at another time he thus expressed his method of proceeding. "I keep the subject constantly before me, and wait till the first dawnings open slowly by little and little into a full and clear light." Again, in a letter to Dr. Bentley, he says, "If I have done the public any service this way, it is due to nothing but industry and patient thought." With such tastes and habits, the complete command of his own time, and of his own ideas, was his highest enjoyment. Thus, notwithstanding the importance of the results he had obtained, Newton was not eager to establish a title to them by publication, and perhaps he would have even longer delayed giving them to the world had an accidental circumstance not induced him to do so. About the beginning of 1684, Halley, one of the greatest of the English astronomers, and, at the same time, one of the most enlightened and active minds that have ever cultivated science, formed the idea of employing the Theorems of Huygens on central forces, to determine the tendency in the different planets to recede from the sun, by virtue of their revolutions about that body, their orbits being considered as circular. From the ratios discovered by Kepler between the times of these revolutions, and the major axes of the orbits, he recognized these tendencies to be reciprocally as the square of the distances of each planet from the sun, so that the attraction which this luminary exerts to keep them in their places, must also vary according to the same law. This was precisely the idea that Newton had conceived in 1666, and from which he had drawn the same consequence. But there was yet a long way from this, to the rigorous calculation of curvilinear motions when the law of the force is given. Halley perceived the difficulty of this step, and after having in vain endeavoured to remove it, he consulted Hooke, at Sir Christopher Wren's house, without, however, receiving any light on the subject, although Hooke had boasted before them both that he had completely resolved this grand question. At last, impatient to see an idea unfolded, which appeared to him so fertile in consequences, Halley went to Cambridge in

1692, purposely to confer with Newton on the subject. It was then that Newton showed to him a Treatise on Motion, in which Halley found the desired solution. This treatise, with some additions, afterwards formed the two first books of the Principia. It would appear that, at this time, Newton had already introduced, and explained some parts of it, in his lectures at Cambridge. Halley, delighted at seeing his hopes realized, requested Newton to confide to him a copy for insertion in the registers of the Royal Society, in order to secure to him the honour of so important a discovery. Although Newton had an extreme repugnance to expose himself in the arena of literary intrigue, where he had, on a former occasion, wasted his time, and sacrificed his tranquillity, Halley, by repeated entreaties, at length succeeded in his object. On returning to London, Halley announced his success to the Royal Society, who repeated the request by means of Aston, at that time their secretary. But, though Newton kept his word to Halley, personally, by sending him a copy of his treatise, he did not then wish it to be communicated, having still many things to complete.* It was not till the following year, that Dr. Vincent presented, in Newton's name, this work, which was destined to make so great a revolution in science. Newton dedicated it to the Royal Society, who showed itself able to appreciate such an honour. It decided that the work should be printed immediately at its own expense, and addressed to the author, by Halley, a letter of thanks expressed in the most honourable terms.

Hooke, who probably had for some time past conceived in his mind similar ideas, without having been able to bring them to perfection, had no sooner understood the object of Newton's treatise, and heard of the admiration with which it was received, than he claimed for himself the priority of the discovery of the law of attraction varying inversely as the square of the distance. His reclamation was so violent, that Halley thought it necessary to notice it in his official letter to Newton, and to say that Hooke expected Newton to mention in his preface, that the priority was due to him. We will here quote the answer of

Birch, Hist. R. S. vol. iv. p. 370.

Newton*, (dated Cambridge, 26th June, 1686,) especially as it will enable us to trace more clearly the progress and developement of his ideas throughout this important research.

"In order to let you know the case between Mr. Hooke and me, I give you an account of what passed between us in our letters, so far as I could remember; for 'tis long since they were writ, and I do not know that I have seen them since. I am almost confident by circumstances, that Sir Christopher Wren knew the duplicate proportion when I gave him a visit; and then Mr. Hooke, by his book Cometa, written afterwards (1678), will prove the last of us three that knew it. I intended in this letter to let you understand the case fully, but it being a frivolous business, I shall content myself to give you the heads of it in short, viz. that I never extended the duplicate proportion lower than to the superficies of the earth, and before a certain demonstration I found the last year, have suspected it not to reach accurately enough down so low; and therefore in the doctrine of projectiles never used it, nor considered the motion of the heavens, and consequently Mr. Hooke could not, from my letters, which were about projectiles, and the regions descending hence to the centre, conclude me ignorant of the theory of the heavens. That what he told me of the duplicate proportion was erroneous, namely, that it reaches down from hence to the centre of the earth-that it is not candid to require me now to confess myself in print then ignorant of the duplicate proportion in the heavens, for no other reason but because he had told it me in the case of projectiles, and so upon mistaken grounds accused me of that ignorance;-that, in my answer to his first letter, I refused his correspondence; told him I had laid philosophy aside, sent him only the experiment of projectiles (rather shortly hinted, than carefully described) in compliment, to sweeten my answer, expected to hear no further from him, could scarce persuade myself to answer his second letter, did not answer his third, was upon other things, thought no further of philosophical matters than his letters put me upon it, and therefore may be allowed not to have had my thoughts about me so well at that time. That, by the same

This letter is printed in the Biographia Brit

tannica.-Art. Hooke.

reason, he concluded me ignorant of the rest of that theory I had read before in his books. That, in one of my papers, writ (I cannot say what year, but I am sure some time before I had any correspondence with Mr. Oldenburg, and that's above fifteen years ago) the proportion of the forces of the planets to the sun reciprocally duplicate to their distances from him, and the proportion of our gravity to the moon's conatus recedendi a centro terræ is calculated, though not accurately enough. That, when Huygenius put out his treatise de Horologio Oscillatorio, a copy being presented to me, in my letter of thanks to him I gave those rules in the end thereof a particular commendation for their usefulness in computing the forces of the moon from the earth, and the earth from the sun, in determining a problem about the moon's phase, and putting a limit to the parallax, which shews that I had then my eye upon the forces of the planets arising from their circular motion, and understood it; so that a while after, when Mr. Hooke propounded the problem solemnly in the end of his Attempt to prove the motion of the earth, if I had not known the duplicate proportion before, I could not but have found it now. Between ten and eleven years ago, there is an hypothesis of mine registered in your books, wherein I hinted a cause of gravity towards the earth, sun, and planets, with the dependence of the celestial motions thereon; in which the proportion of the decrease of gravity from the superficies of the planet (though for brevity sake not there expressed) can be no other than reciprocally duplicate of the distance from the centre; and I hope I shall not be urged to declare in print that I understood not the obvious mathematical conditions of my own hypothesis; but grant I received it afterwards from Mr. Hooke, yet have I as great a right to it as to the ellipsis. For as Kepler knew the orb to be not circular but oval, I guessed it to be elliptical; so Mr. Hooke, without knowing what I have found out since his letters to me, can know no more but that the proportion was duplicate quam proxime at great distances from the centre, and only guessed it to be so accurately, and guessed amiss in extending that proportion down to the very centre; whereas Kepler guessed right at the ellipsis, and so Hooke found less of the proportion than Kepler did of the

ellipse, there is so strong an objection against the accurateness of this proportion, that without my demonstrations, to which Hooke is yet a stranger, it cannot be believed by a judicious philosopher to be anywhere accurate. And so, in stating this business, I do pretend to have done for the proportion as for the ellipse, and to have as much right to the one from Hooke and all men, as to the other from Kepler, and, therefore, on this account also, he must, at least, moderate his pretences. The proof you sent me I like very well: I designed the whole to consist of three books; the second was finished last summer, being short, and only wants transcribing, and drawing the cuts fairly. Some new proportions I have since thought of, which I can as well let alone. The third wants the theory of comets. In autumn last, I spent two months in calculations to no purpose, for want of a good method, which made me afterwards return to the first book, and enlarge it with divers propositions, some relating to comets, others to other things found out last winter. The third I now design to suppress. Philosophy is such an impertinently litigious lady, that a man had as good be engaged in lawsuits, as have to do with her. I found it so formerly, and now I am no sooner come near her again, but she gives me warning. The two first books, without the third, will not bear so well the title of Philosophic Naturalis Principia Mathematica; and, therefore, I had altered it to this, De Motú corporum libri duo; but, upon second thoughts, I retain the former title, 'twill help the sale of the book, which I ought not to diminish now 'tis yours."

Newton then adds, in a postscript, "Since my writing this letter, I am told by one who had it from another lately present at one of your meetings, how that Mr. Hooke should make a great stir, pretending I had all from him, and desiring they would see that he had justice done him. This carriage towards me is very strange and undeserved; so that I cannot forbear in stating the point of justice, to tell you further that he has published Borelli's hypothesis in his own name; and the asserting of this to himself, and completing it as his own, seems to me the ground of all the stir he makes. Borelli did something and wrote modestly. He has done nothing, and yet written in such a way, as if he knew, and had suf

ficiently hinted all but what remained to be determined by the drudgery of calculations and observations, excusing himself from that labour, by reason of his other business; whereas he should rather have excused himself by reason of his inability-for it is very plain, by his words, he knew not how to go about it. Now is not this very fine? Mathematicians that find out, settle, and do all the business, must content themselves with being nothing but dry calculators and drudges; and another that does nothing but pretend and grasp at all things, must carry away all the invention, as well of those that were to follow him, as those that went before. Much after the same manner were his letters writ to me, telling me that gravity in descent from hence to the centre of the earth was reciprocally in a duplicate ratio of the altitude that the figure described by projectiles in that region would be an ellipsis, and that all the motions of the heavens were thus to be accounted for; and this he did in such a way, as if he had found out all, and knew it most certainly. And upon this information, I must now acknowledge, in print, I had all from him, and so did nothing myself but drudge in calculating, demonstrating, and writing upon the inventions of this great man; and yet, after all, the first of these three things he told me is false, and very unphilosophical; the second is as false; and the third was more than he knew, or could affirm me ignorant of, by anything that passed between us in our letters. Nor do I understand by what right he claims it as his own; for as Borelli wrote long before him, that, by a tendency of the planets towards the sun, like that of gravity or magnetism, the planets would move in ellipses: so Bullialdus wrote, that all force respecting the sun as its centre, and depending upon matter, must be in a reciprocally duplicate ratio of the distance from the centre, and used that very argument for it, by which you, Sir, in the last Transactions, have proved this ratio in gravity."

The remainder of this letter offering no other historical details, we will not continue the quotation; but the extremely curious reply of Halley to Newton is well worthy of attention. It is dated 29th June, 1686. Halley begins by encouraging Newton not to heed the effects of Hooke's expostulations with the Royal Society, and then continues,

According to your desire, I waited upon Sir C. Wren, to inquire of him, if he had the first notion of the reciprocal duplicate proportion from Mr. Hooke? his answer was, that he himself, very many years since, had had his thoughts upon making out the planet's motions by a composition of a descent towards the sun and an impressed motion; but that at length he gave over, not finding the means of doing it. Since which time Mr. Hooke had frequently told him that he had done it, and attempted to make it out to him, but that he never was satisfied that his demonstrations were cogent. And this I know to be true, that in January, 1683, I having, from the sesquialterate proportion of Kepler, concluded that the centripetal force decreased in the proportion of the squares of the distance reciprocally, came on Wednesday to town, from Islington, where I met with Sir C. Wren and Mr. Hooke, and falling in discourse about it, Mr. Hooke affirmed, that upon that principle all the laws of the celestial motions were to be demonstrated, and that he himself had done it. I declared the ill success of my attempts; and Sir Christopher, to encourage the inquiry, said, that he would give Mr. Hooke, or me, two months time to bring him a convincing demonstration thereof; and besides the honour, he of us that did it should have from him a present of a book of forty shillings. Mr. Hooke then said he had it, but that he would conceal it for some time, that others, trying and failing, might know how to value it, when he should make it public. However, I remember that Sir Christopher Wren was little satisfied that he could do it; and though Mr. Hooke then promised to show it to him, I do not find that, in that particular, he has been so good as his word. The August following, when I did myself the honour to visit you, I then learned the good news, that you had brought this demonstration to perfection, and you were pleased to promise me a copy thereof, which I received with great satisfaction; and thereupon took another journey to Cambridge, on purpose to confer with you about it, since which time it has been entered upon the register-books of the society. Mr. Hooke, according to the philosophically ambitious temper he is of, would, had he been master of a like demonstration, no longer have concealed it, the reason he told Sir Christopher and me now ceasing.

But now he says that it is but one small part of an excellent system of nature, which he has conceived but has not yet completely made out; so that he thinks not fit to publish one part without the other. But I have plainly told him, unless he produce another differing demonstration, and let the world judge of it, neither I nor any one else can believe it. After the meeting of the Royal Society, at which your book was presented, being adjourned to the Coffee-house, Mr. Hooke did there endeavour to gain belief, that he had some such things by him, and that he gave you the first hint of this invention; but I found they were all of opinion that nothing thereof appearing in print, nor on the books of the Society, you ought to be considered as the inventor. And if in truth he knew it before you, he ought not to blame any one but himself, for having taken no more care to secure a discovery which he puts so much value on." Halley concludes, by conjuring Newton, in the name of science, not to suppress the third volume through disgust at the conduct of an envious rival. Happily he succeeded, and Newton has, in a scholium,* generously mentioned Wren, Hooke, and Halley, as having all three recognized in the celestial motions the existence of an attraction reciprocally proportional to the square of the distance.

Newton's Principia appeared complete in 1687. We may form some idea of the novelty and profundity of the discoveries which it contained, on learning that, when it was first published, not more than two or three among Newton's contemporaries were capable of understanding it; that Huygens himself, a man whose mind was particularly suited to appreciate its merit. only in part adopted the idea of gravitation, and that merely as regarded the heavenly bodies, while he rejected its influence between the separate particles of matter-being preoccupied by the hypothetical ideas he had formed respecting the cause of gravity; that Leibnitz, perhaps through rivalry, or perhaps by a prepossession in favour of his own metaphysical system, completely mistook the beauty and the certainty of the method employed by Newton in this work, and even went so far as to publish a dissertation, in which he endeavoured to demonstrate the same truths on different principles;

Book 1, Prop. 4.

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