dependent on the value assigned to the earth's would be an elliptical curve or eccentric radius. Employing the value derived from ellipsoid;' terms too vague and indefinite to the commonly received estimate of 60 miles show that he had any distinct idea of elliptic to the degree, he found the resulting actual orbits, while he did not even pretend to give deflexion considerably less than that which a demonstration. the theory required. He, consequently, desisted from the inquiry, and turned his attention to other subjects.

But other eminent persons were, about the same time, incessantly attempting the solution of questions closely allied to this. Hooke in the same year read a paper to the Royal Society, in which the combination of a projectile and a central force was clearly explained as producing revolution in an orbit, accompanied by an experimental illustration, the very same in principle as that of Horrox, whose claims he altogether omits to mention. He, indeed, slightly improved the form of the experiment, and enlarged it by attaching a smaller ball, which was made to circulate round the larger so as to represent the earth and moon; but he does not seem to have been at all aware of the whole force of Horrox's illustration as regards the motion of the apsides.

In 1673, Huyghens had applied the laws of dynamics to the motion of bodies in circular orbits. Such an investigation would hold good in the celestial motions if the planetary orbits were circles, and this was clearly seen by several of those engaged in the subject at that time. But this would not be exact. And the difficulty was to apply the same principles to elliptic orbits, and connect, by a physical relation, the other laws of Kepler.

In 1673 Edmund Halley, then an undergraduate of Queen's College, Oxford, transmitted some mathematical papers to the Royal Society, which at once established his pre-eminent ability in those sciences. most important of them was the calculation of the place of a body revolving in an elliptic orbit, according to Kepler's laws;-a problem proposed by Kepler himself, not admitting of exact geometrical solution, and to which Seth Ward had previously proposed A few years later, Hooke exemplified in a a useful practical approximation. This inmore detailed manner the nature of motion troduced him to the scientific world, and led in an orbit, in a paper entitled 'An Attempt to his expedition, in 1676, to St. Helena, to to Prove the Motion of the Earth,' &c., observe the southern stars. Returning in which appears in the Philosophical Transactions for 1674. Here, though he lays down very clearly some of the dynamical principles, yet, with respect to the law by which the central force varies with the distance, he distinctly says he has not yet experimentally verified it.

In 1678, in his work De Cometa, he, however, states the law to be the inverse square. In 1679, Hooke wrote to Newton, most probably, we may suspect, with the view of sounding him, requesting him to furnish a demonstration of the motion of the earth, (as he observes in a letter written some years afterwards,) not telling him at first the proportion of gravity to the distance, nor what was the curved line that was thereby made.' Newton, however, unwilling to be drawn into this discussion, excused himself as being engaged on other studies, and added (as he says) in compliment, to sweeten his answer,' the suggestion of a problem-In what line will a body fall from a great height to the earth, taking into account the earth's rotation? This not only referred to a practical proof (then important) of the earth's rotation; but the accurate solution of it would imply a knowledge of the law of gravitation. In December 4, 1679, Hooke read a paper to the Royal Society on this subject, in which he maintained that the path of the falling body

the following year, he settled near London, in the rural retirement of Islington, and soon after became assistant-secretary to the Royal Society. At a much later period he was appointed Savilian Professor of Geometry at Oxford.

Halley anxiously directed his attention to the great problem of the solar system; and expressly mentions (in a letter to Newton at a later period) that in January 1684, he concluded, " from the sesquialter proportion of Kepler, that the centripetal force decreased in proportion to the squares of the distances." But he was unable to proceed further in the application of this law of force to the elliptic orbits of the planets. Full of the subject, and anxious to obtain any help in the solution, he journeyed to London from Islington on a Wednesday, to be ready to attend the Royal Society's meeting on Thursday; and there meeting with Wren and Hooke, an interesting discussion ensued, in the course of which Wren candidly mentioned that he had, some years before, attempted the problem of elliptic orbits, but had failed, while Hooke boasted that he had a solution of it, which he kept a secret; but which he neither then, nor ever afterwards, produced, though urgently pressed to do so, and with the temptation, to him

Letters, i. 226, &c.

With a

so potent, before him of present distinction, measurement, it immediately struck him that and the security of an indisputable claim to the value of the earth's radius was the erronepriority for the future. ous element in his first calculation. These various points, settled in detail as to feverish interest in this result little imagined all their particulars, with the utmost care, by by those present, hastily noting down the our author, we have here collected in the value thus assigned, he hurried home, resumorder of the narrative in a brief sketch; be-ed his calculation with the new value, and cause they distinctly determine the precise position in which the investigation of the law of gravity stood before the final step was taken by Newton; and the exact share which each of his predecessors in the attempt could fairly claim-points on which much misapprehension has prevailed.

having proceeded some way in it, was so overpowered by nervous agitation at its anticipated result, that he was unable to go on, and requested a friend to finish it for him-when it came out, exactly establishing the inverse square as the true measure of the moon's gravitation, and thus furnishing the key to the whole system.

Newton's first calculation, as we have seen, failed, from not having adopted the common Stirring as this incident no doubt is, we but erroneous estimate of the earth's radius. fear the dry facts now brought together, must We have already noticed that better determi- somewhat qualify our acceptance of it. Those nations had been made long before, and it of our readers who have visited the Royal seems hardly possible that they could have Society's apartments, have of course seen a been unknown to him. In particular, the large antique volume bound in velvet with measurement of Snell is fully stated in a work gilt clasps, in whose vellum pages members of Varenius on geography; of which, it ap-on their admission sign the obligation-and pears from one of Newton's own letters to Collins,* in edition was published at Cambridge in 1672, to which he himself contributed, by superintending the drawing of the diagrams.

is, then, difficult to understand why he should not have at once repeated his calculanon with a more correct datum; or rather why he should have calculated, even in the first instance, upon so obviously faulty a basis. It is true that, by an accidental coincidence, the chief numbers concerned were, on that estimate, all multiples of 60, which of course greatly facilitated the computation; but this can hardly afford a sufficient explanation.

they have doubtless been shown, in a page belonging to the year 1675, among other signatures, in a clear upright hand, the name of Isaac Newton. He was then personally present on that occasion. But from a variety of circumstances alluded to by our author, it is almost a matter of certainty, that he did not attend any meeting of the society for some years afterwards, especially in the year 1682. On the other hand, it is hardly conceivable that on the day of his admission he did not hear something of Picard's measurement, so much discussed at the time. Though constantly resident at Cambridge after this, it appears that he duly received the 'Philosophi cal Transactions,' and therefore must have known it in 1676. In every way, therefore, is almost impossible that he should have first learnt it, as stated, in 1682.

But we have more positive testimony, in his own statements, that he had used some more correct value, and obtained a satisfactory conclusion considerably before this period.

The far more precise determination made by Picard (giving the length of the degree 69% miles) was described in detail in a work pub-it lished in a splendid form at the press of the Louvre, in 1671, (and not, as stated, in the 'Biographia Britannica,' 1679.) Few copies, indeed, were printed, and the work was little known; but the results were circulated-a communication of them being made to the Royal Society on January 11, 1672, and discussions of the subject taking place there in 1675, recorded in the Philosophical Transactions' for 1676, and again in 1682, besides being referred to by Flamstead in 1677.

After the memorable discussion with Wren and Hooke, in August 1684, Halley visited Newton at Cambridge with the hope of ob taining some help in the grand problem. It was then that Newton informed him of his original attempt;-which he again described. Nevertheless, Newton, from the time of the in a letter, (a few years later,*) by saying failure of his first very rough trial, seems to that he had (about 1666) made an investigahave discontinued all inquiry on the subject; tion, on the assumption of the law of the and the received history of his resumption of inverse square, of the moon's gravity, which it is well known to be briefly this:-Being he had calculated, though not accurately present at a meeting of the Royal Society in enough.' But in his conversation with Hal1682, and hearing the discussion of Picard's ley, he further stated that he afterwards suc‐

* Letters, ii. 322.

VOL IV. No.I.

8

*

Essay, 51.

cessfully renewed his calculation; expressly from his conversations with Newton. He says adding, that it was the inquiry of Hooke with merely, that in 1684, at Halley's request, respect to falling bodies, in 1679, which led Newton resumed his calculations, and obhim to do so, but that he thought no further on the subject, being then engaged in other pursuits, and threw aside the papers.

tained a successful result, now using Picard's measure. This was somewhat enlarged upon by Dr. Robison, (though it does not appear from what authority,) who describes Newton as learning Picard's value at a meeting of the Royal Society: when, on his return home, follows the calculation scene before given.

To this M. Biot adds conjecturally, that it probably took place in 1682. And lastly, in the translation of M. Biot's Article for the Society of Useful Knowledge, the probability is converted into certainty. On such authority, however, it is not surprising that later writers should have repeated the narrative.

This capital result formed the clue to the whole system; but there was still much to be done in working it out. Later in the same year, (1684,) Halley paid Newton a second visit, and on December 10, he communicated to the Royal Society the result of his application, but without going into any detail of the discoveries.

But further, we must recollect that his first rough calculation with regard to the moon, involved only the consideration of a circular orbit, whereas the main difficulty was in the general case of elliptic motion. Now, in a subsequent letter to Halley, Newton expressly says that Hooke's letters to him were the occasion of his finding the method of determining figures,' (the forms of the orbits of revolving bodies,) which, when I had tried in the ellipsis, I threw the calculation by, being upon other studies, and so it rested for about five years, till upon your request I sought for the papers. * Being, however, unable to find these precious documents, he soon after supplied the deficiency from his own original resources, by working out the whole anew; that is, both the calculation of the moon's gravity and the whole theory of elliptic motion. 'He composed near a dozen propositions,' says Dr. Pemberton, (Essay, app. In February 1685, a short statement of the 51,) containing the outline of these investiga- main propositions, including the demonstrations. It was on this occasion, as far as ap- tion of elliptic motion, was communicated pears, that he for the first time employed to the Royal Society by Newton, and entered Picard's value of the earth's radius; and thus established a more perfect coincidence of theory and observation. The result was communicated to Halley in November 1684. This account of the case displays in a singular degree the peculiarities of Newton's character, in the indifference with which he Now, several writers have assigned 1683 seemed to regard the most important results as the date of this communication, most proof his greatest intellectual efforts;-doubtless bably on the authority of a passage in the from the unconscious ease with which he Commercium Epistolicum, in which this date made them. It is further remarkable, that is assigned, though from what we have already in a letter to Halley some time after,† New-seen of the progress of the business, it maniton expressly says, that he had collected the festly cannot be correct: moreover, Mr. law of the inverse squares from Kepler's theorems, in 1661; which shows that even at a much earlier period he was in possession of at least some general apprehension of the theory of central forces.

upon their Register. This valuable record has, for the first time, been printed in the essay before us,† and it is remarkable that its contents exactly accord with the description of 'about a dozen propositions,' which he composed on a former occasion.

Rigaud has carefully ascertained that no such notice occurs in the records of the Royal Society, while there is a distinct minute on December 10, 1684, of Halley's representation of Newton's results, in which a request is made to him to send the full account of them.

But there is a further circumstance connected with this point. There are now, first published, two memoranda, which exist in Newton's handwriting in the Macclesfield collection-not exactly copies, but to the same purport-in which he speaks generally of his first communication of his discoveries: in one copy, with a date 1683; in the other it

* Art. Newton, in the Biographic Universelle. + Appendix, p. 1.

was evidently originally the same, but the 3 | to the analyzed elements of the motion; and has been altered to a 4. The document is these elements again recombined by the aid without a date, but most probably is of a of that refined idea, the basis of the fluxional much later period, when Newton may not calculus, but which, in its geometrical form, have accurately remembered the year.' * Still was called by Newton 'prime and ultimate the error is remarkable, and we shall see that ratios.' unwarrantable use (at least) was made of it. On the 25th of April 1686, the complete Memoir (equivalent to the first book of the Principia) was presented, and, in part, read at a meeting of the Royal Society. The second book appears to have been sent in March 1687, though no formal notice of it is found. The third, which completes the whole, was communicated April 6, 1637.

It was by nothing more than a happy adaptation of these elementary combinations, applied to the conic geometry of the ancients, that Newton proved the path of a body moving under the influence of a projectile and a central force (the latter inversely as the square of the distance) to be always one of the conic sections, and under certain conditions an ellipse. Thence immediately reIn a letter in the Macclesfield collection,† sulted the necessary truth of the other law of Newton says The book of the Principles Kepler, (in the language of the old geometers,) was writ in about seventeen or eighteen the sesquialter proportion of the times and months, whereof about two were taken up distances. A vast multitude of mathematical with journeys, and the MS. was sent to the consequences from these principles now Royal Society in spring 1686; and the shortness of the time in which I wrote it, makes me not ashamed of having committed - some faults.'

crowded upon Newton's mind, which he poured forth in rich profusion on the pages of the Principia; applying to a vast number of truths in physico-mathematical science, And when we consider the actual nature and more or less referring to cases occurring and contents of the work, our surprise is ex- in the system of the world. But the most cited rather that it should have been produc-material were those relating to the attraced at all in so marvellously short a time, than tions of bodies, and the motions of a system that it should have imperfections. The mere subject to mutual attractions. composition, arrangement, transcription, and In immediate connection with the lastrevision, would have occupied the time, in named views it was, that Horrox's theory of the case of most writers, supposing the mate- the moon, and his experiment showing the rials collected. In a word, we can only re-motion of the apsides, were now to receive gard the fact of the singularly rapid produc- their physical demonstration, and to be provtion of such a work as a palpable proof, that ed real representations of the laws of nature. the author must have had at least all its When Newton began to apply the theory of main doctrines fully developed in his mind a universal gravitation to the motion of the long time before, though they very probably moon, he soon perceived that the cause of its may have lain there dormant and neglected; inequalities was to be found in the same and appearing to himself obvious truths, he principle which occasioned the general ellipwas indifferent to drawing them out in form, tic revolution; in other words, that gravitaor putting them on record, until urged by the tion which influenced it with respect to the importunities of his friends. earth, also affected it by the action of the sun. In a word, that as every part of the planetary world attracts every other part, so every portion of the planetary motions is more or less modified by every other portion. In the instance of the moon, more particularly, the motion of the apsides was shown to be a direct consequence of the same general principle.

Anxiously as all philosophers had been seeking for the truths disclosed in the Principia, yet the novelty of the whole train of thought by which they were there developed, was startling to their apprehensions. The complete investigation of the elliptic theory involved several material steps of a kind entirely foreign to the conceptions even of the best mathematicians. The demonstration of Kepler's empirical laws as necessary dynamical truths, involved ideas entirely novel. The proof of the equable description of areas, not merely as applying to the planets, but as an universal theorem, astonished the tardy geometricians by the rapidity with which it was educed from the simple composition of forces, and an elementary theorem of Euclid applied Essay, Appendix, p. 66. + Essay, p. 92.

Under all the circumstances, it is more surprising that Newton should have carried the investigation so far as he did, than that he should have failed, from a remarkable oversight, in establishing one portion of the truth in the lunar theory; in which the error afterwards became so manifest, that the fate of the whole theory of gravitation was vibrating in the balance, which was only at length turned in its favor by the happy suggestions of Clairault.

It should also be remarked, as was pointed was in a fever of anxiety to be immortalized out by Flamstead, that in one passage in the in that chronicle. He accordingly persuaded Principia, Newton has inadvertently as- Aubrey to write to Wood, suggesting, as if cribed to Halley a great part of what is due from himself, the propriety of blazoning to Horrox. It is, however, a manifest mistake to say, (as Martin, the compiler of the Biographia Philosophica,' does,) that Newton' made Horrox's theory the groundwork of all his astronomy.' He is, however, confessedly a writer of no authority, and we should not have noticed this remark, had it not been unaccountably adopted by Dr. Hutton in his 'Mathematical Dictionary.'

In our sketch of the preceding history, we have clearly enough pointed out what real approaches towards Newton's discovery had been made by others, and the precise point at which they had failed. The reading of his paper at the Royal Society was followed by high and just encomiums. And from what we have seen of the character of Hooke, we shall not be surprised to find him, after the meeting, loudly disparaging its merits; setting up a claim to priority on his own part; and in no measured terms demanding justice, and even insinuating a charge of plagiarism. After what we have stated, it will not be necessary to go into those claims, or Newton's reply to them. Nor need we remark the candid manner in which, in the Principia, he acknowledges the claims of Wren, Hooke, and Halley, in regard to circular orbits; unless it be to point out the extraordinary version of the passage given by Dr. Thomson, in his History of the Royal Society, where he observes,Newton, in his "Principia," informs us, that the doctrine of gravitation had occurred to Hooke and Halley about the same time that it did to himself.'-(P. 340.)

Hooke's achievements. Aubrey, however, being unacquainted with science, Hooke inserted a detailed statement of his claims, and also made some other alterations in the letter which Aubrey had drawn up. The original having been examined, the different handwritings fully explain the mode of its composition. As an amusing specimen we will give it-the words in brackets marking Hooke's erasures, and the italics his additions :—

September 15, 1689. 'Mr. Wood!—Mr. R. Hooke, R.S.S., did, in Ano 1670, write a discourse, called an attempt to prove the motion of the earth, which he then read to the Royal Society, but printed it in the beginning of the year 1674*..... to Sir John Cutler, to whom it is dedicated, wherein he has delivered the theory of explaining the celestial motions mechanically. His words are these, pages 27, 28, viz:

(Here a space is left.)

'About nine or ten years ago Mr. Hooke wrote to Mr. Isaac Newton of Trinity College, Cambridge, to make a demonstration of [it] this theory, not telling him at first the proportion of the curved line that was thereby made. the gravity to the distance, [and] nor what was

'Mr. Newton, [did express,] in his answer to the letter, did express that he had not though of it; and, in his first attempt about it, he calculatel the curve by supposing the attraction to be the same at all distances; upon which Mr. Hooke told him in his next letter the whole of his hypothesis; said that the gravitation was reciprocal to the square of the distance, which would make the motion in an ellipsis, in one of whose foci the sun being placed, the aphelion and perihelion of the planet would be opposite to each other in the same line, which is the whole celestial theory concerning which Mr. Newton had made a demonstration, not at all owning that he received the

Hooke, however, was not to be satisfied. Some years later we meet with a curious instance of the pertinacity of his mortified vanity in still urging his already refuted pre-first intimation of it from Mr. Hooke. Likewise,

tensions.

In 1813 there was printed a collection of letters from originals in the Bodleian Library, together with some other documents from the MSS. of Aubrey in the Ashmolean Museum. Among these is a letter from Aubrey to Anthony Wood, relative to Hooke's pretensions, which, as there printed, is nearly unintelligible. But Mr. Rigaud has elicited the whole state of the case, at once explaining the obscurity of the letter, and putting in an amusing light both Hooke's egregious vanity and insatiable desire of celebrity at the expense of others, and his friend Aubrey's simplicity. The fact was simply this-Hooke hearing that Wood was engaged on the Athena Oxonienses,

Book iii. p. 35, schol.

Mr. Newton has, in the same book, printed some other theories and experiments of Mr. Hooke's as that about the oval figure of the earth and sea. without acknowledging from whom he had [i them, though he had not sent it up with the other parts of his book till near a month after this thear when it served to help to answer Dr. Wallis h was read to the Society by R. H., [Mr. Hooke. arguments produced in the R. S. against it.

In the attempt to prove the motion of the earth. &c., printed 1674; but read to the Royal Society 1671, page 27, line 31.

(Here follows a long quotation from the paper.

'Mr. Wood!-This is the greatest discovery in nature that ever was since the world's creation fore. I know you will do him right. I hope you It never was so much as hinted by any man be

The words are here illegible.