733 



PRINCIPIA. 



PRINCIPIA. 



734 



fifteenth, and serving to blend the two, as well as to augment the 

 volume of sound. 



PRINCI'PIA, the contracted title of the ' Philosophise Naturalis 

 Principia Mathematica,' the great work of Newton, the publication of 

 which is the most remarkable known epoch in the history of science. 

 The title-page of the first edition is : ' Philosophise Naturalis Principia 

 Mathematica. Autore Is. Newton, Trin. Coll. Cantab., Soc. Matheseos 

 Professore Lucasiano, et Societatis Regalis Sodali. Imprimatur. S. 

 I'.'pys, Reg. Soc. Pneses, Julii 5, 1686. Londini Jussu Societatis 

 Regioe ac Typis Josephi Streater. Prostat apud plures Bibliopolas. 

 Anno MDCLXXXVII.' 



We entirely pass over the common story of the fall of an apple. 

 [NEWTON, hi Bioo. Div.] It appears in the rough copy left among 

 Newton's papers of the information furnished to Fontenelle for his 



>f Newton : but as Fontenelle did not give it, though very much 

 given to anecdote, it may be inferred that Mrs, Conduitt, Newton's 

 niece, struck it out before it was sent. It is clear however that New- 

 ton first thought on the subject in 1666. With reference to the story 

 of his laying by the theory until Picard's measure of the earth was 

 brought to his notice in 1682, it appears that Picard's ' Mesure 

 de la Terre ' was published in 1672, and much discussed at the Royal 

 Society in the years following.* Moreover Dr. Pemberton, who de- 

 rived his information from Newton himself, states most explicitly (in 

 his preface) that a letter from Hooke gave occasion to his resuming his 

 old thoughts, and that he then used Picard's measure. This letter 

 from Hooke, the subject of which was the curve in which a falling 

 body descends to the earth, taking into account the earth's motion, is 

 clearly made out to have been written in 1679, which is therefore the 

 date of Newton's resumption of his attempt, not 1682, as generally 

 stated. The new attempt, as every one knows, was more successful, 

 but Newton did not write any treatise nor contemplate any publica- 

 tion ; he traced out the foundation of his system, and threw aside his 

 papers. In January ,t 1684, Halley had concluded, from Kepler's third 

 law, that the centripetal force on the planets (supposed to move in 



) was as the inverse square of the distance. Not being able to 

 proceed further, he applied to Huoke and Wren, the former of whom 

 (ri't-'ssed to have solved the whole problem, but would communicate 

 nothing ; the latter declared that he had long given over the question 

 from inability to succeed. In August following, Halley paid a visit to 

 Newton at Cambridge, who informed him that he had solved the 

 problem, but tea* not obit la lay his hand on the pa/xn ichich contained 

 his solution, so completely had he thrown the subject aside. After 

 Halk-y's departure, he worked the theorems out again, and transmitted 

 them to Halley through Mr. Paget, the mathematical master at Christ's 

 Hospital. On receipt of this communication, in November, Halley 

 immediately paid another visit to Cambridge, to gain more informa- 

 tion, and to induce Newton to pursue the inquiry. December 10, 

 1 >i^ t, Hallry stated at the Royal Society that " he had lately seen Mr. 

 Nrwton at Cambridge, and that he had shown him a curious treatise 

 ' I >. Motu,' which, upon liis desire, he said was promised to be sent to 

 the Society, to be entered upon then* register." Halley and Paget were 

 accordingly deputed to keep Newton in mind of his promise (a singular 



'ling, showing how well the Society knew Newton's indifference 

 about communicating), and the consequence was, that about the middle 

 of February, 1685, a communication (that previously made to Halley, 

 enlarged), entitled '..Isaac! Newtoni Propositiones de Motu,' was sent 

 and registered : it contains what were afterwards the main theorems 

 of the early sections of the Principia, direct and inverse, relating to 

 n-iitiii:t:il fon.-fs. No Priucipia as yet existed, and even this basis 



uly recently been written down satisfactorily. Newton writes to 

 Mr. Aston, Sec. U.S., in acknowledging the news of the above entry, 

 " I designed them for you before now, but the examining several 

 tilings has taken a greater part of my time than I expected, and a great 

 deal of it to no purpose. And now I am to go into Lincolnshire for a 

 month or nix weeks. Aftericards I int< it as soon as I can 



niently." ( February 23, 1685.) On this Mr. Rigaud well re- 

 marks, " The Principia was not a protracted compilation from memo- 

 randa which might have been written down under the impression of 

 different trains of thought : it had the incalculable advantage of being 

 sed by one continued effort, during which the mutual bearing 

 of the sevtral parts \v;m vividly present to the author's mind." On 

 the 21st of April, 1880, Halley announced to the Royal Society that 

 Mr. Newton " had an incomparable Treatise on Motion almost ready 

 for the press;" and on the 28th of the same month Dr. Vincent J 

 presented the manuscript of tin; first book to the Society, who referred 

 the question of printing to the Council, and the production of a report 

 upon the contents to Halley. May Hi, the Society decided that the 

 work should be printed forthwith in quarto, Ac.; and hence it lias 



Rinaud mentions that Newton must bare been acquainted with the mea- 

 sures of Snell and Norwood, the result of the former of which appears in his 

 own edition of Varcnius. The latter, there can be no doubt, he did not trust ; 

 and as to the former, we hare shown [MILK] that in this very edition of 

 Virenins, he had allowed grow errors to pass as to tlio measures of bis own 

 country. It may be inferred that he had not much to do with the details of it. 



t That U, what we call 1684 ; Halley writes 1083-4. [PeaioDS or lltvni.v- 

 Tios.] All the following dates are for a year beginning in January. 



t This gentleman has been (wrongly) supposed to have been the hnnband of a 

 lady to whom Xewton was attached in early life. 



always been supposed that the Society paid the expenses of printing, 

 though the title-page only bears " jussu Societatis," &c., and not 

 " jussu et sumptibus," as usual where it bore the expenses. But Mr. 

 Rigaud quotes the minute of the Council of the Society of the 2nd o 

 June, confirming the vote of the Society to the extent of resolving 

 " that Mr. Newton's book be printed," but adding that " E. Halley 

 shall undertake the business of looking after it, and printing it at his 

 own charge, which, he engaged to do." The fact was, that when the 

 Council came to consider the Society's vote of the 19th of May, they 

 found there was no money ; a work of Francis Williighby, ' De Historia 

 Piscium,' published " jussu et sumptibus," in 1686, had so reduced 

 their funds, that they were obliged to pay then- officers in copies of 

 this very book about fishes. 



In the meanwhile arose a controversy with Hooke, the universal 

 claimant, who, when the first part of the manuscript was presented by 

 Vincent, asserted that he had discovered the law of the inverse squares, 

 and had communicated that and other discoveries to Newton. The 

 heads of the paper on which he founds his claim are given at length in 

 HOOKE, ROBERT, in Bioo. Div., and they show that though he had (in 

 common with several others) some very correct notions on the subject, 

 he had not even arrived at the knowledge of the law of the inverse 

 squares, though that had been propounded by BOUILLAUD [Bioo. Div.]. 

 Mr. Rigaud enters at great length into this question ; if we were to 

 do the same, we should take an advanced position, and before we 

 attempted to show that Hooke did not write any part of the substance 

 of the Principia, we should require reasonable proof that he would 

 have been able to read and understand the mathematical part of it 

 when written : an/1 not until this had been given, which we are con- 

 vinced could not be given from Hooke's writings, should we consider 

 it necessary to enter on the first point. Had it not been for Halley, 

 this trumpery claim of Hooke's would have produced serious con- 

 sequences. Newton, easily disgusted by controversy, and having ob- 

 served that physical questions generally gave rise to it, proposed (in 

 a letter to Halley, June 20, 1686) to omit the third book altogether, 

 which contains the actual application of the first two books to the 

 existing universe. He says, " 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 have no sooner come near her again, but she gives 

 me warning. The two first books, without the third, will not so well 

 bear the title of ' Philosophic Naturalis Principia Mathematica,' and 

 therefore I had altered it to this, ' De Motu Corporum Libri Duo," 

 but upon second thoughts, I retain the former title. 'Twill help the 

 sale of the work, which I ought not to diminish now 'tis yours." 

 Halley had to soothe this irritation, and prevent thu consequences ; 

 and as the letter in which he did this is very curious, and has never 

 been printed altogether, except by Mr. Rigaud, the surpassing interest 

 which everything connected with the I'rincipia excites will justify our 

 giving it entire, particularly as it is the original voucher for several of 

 the most important circumstances connected with the publication : 





 " London, 29 June, 1C86. 



" Sir, I am heartily sorry that in this matter, wherein all mankind 

 ought to acknowledge their obligations to you, you should meet witli 

 anything that should give you disquiet ; or that any disgust should 

 make you think of desisting in your pretensions to a lady whose 

 favours you have so much reason to boast of. 'Tis not she, but your 

 rivals, envying your happiness, that endeavour to disturb your quiet 

 enjoyment ; which, when you consider, I hope you will see cause to 

 alter your resolution of suppressing your third book, there being 

 nothing which you can have compiled therein, which the learned 

 world will not be concerned to have concealed. Those gentlemen of 

 the Society to whom I Have communicated it, are very much troubled 

 at it, and that this unlucky business should have happened to give 

 trouble, having a just sentiment of the author thereof. According to 

 your desire in your former, I waited upon Sir Christopher 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 the making out tho 

 planets' motions by a composition of a descent towards the sun, and 

 an impressed motion ; but that at length he gave it 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 coyrnt. 

 And this I know to be true, that in January, 1683-4, I, having, from the 

 considerations of the sesquialter proportion of Kepler, concluded that 

 the centripetal force decreased in the proportion of the squares of tho 

 distances reciprocally, came on Wednesday to town, where I met with 

 Sir Christopher Wren and Mr. Hooke, and falling in discourse about it, 

 Mr. Hooke affirmed, that upon that principle all the laws of thu 

 celestial motions were to be demonstrated, and that he himself h;id 

 done it. I declared the ill-success of my own attempts ; and Sir 

 Christopher, to encoui aje the inquiry, said that he would give Mr. 

 Hooke, or me, two months' time to bring him a convincing demon- 

 stration thereof; and, besides the honour, he of us, that did it, should 

 have from him a present of a book of forty shillings. Mr. Huoke then 

 said, that he had it, but he would conceal it for some time, that others 

 trying and failing might know how to value it, when he should make 



