<423>

APPENDIX.

<424> <425>

APPENDIX.

No. I.

(Referred to in page 32.)

AFTER publication of the second edition of the Principia, when an erroneous interpretation had been given of the Scholium, Newton was very anxious that the motive under which he wrote it, and the precise meaning which he attached to it, should be understood. I have, therefore, given in page 30 an explanation of his views, which is more full than that quoted in the note from Raphson; but I have found another MS. in which an additional motive is stated. "And because," he says, "Mr. Leibnitz had published those elements (meaning those in the Lemma) a year and some months before, without making any mention of the correspondence which I had with him by means of Mr. Oldenburg ten years before that time, I added a Scholium, not to give away the Lemma, but to put him in mind of that correspondence, in order to his making a public acknowledgement thereof before he proceeded to claim that Lemma from me."[1]

DRAUGHT COPIES OF THE SCHOLIUM TO THE LEMMA. SCHOLIUM.

In literis quæ mihi cum Geometra peritissimo G. G. Leibnitio, anno 1676, intercedebant, cum significarem me compotem esse methodi analyticæ determinandi Maximas et Minimas, ducendi Tangentes, quadrandi figuras curvilineas, conferendi easdem inter se, et similia peragendi queæ in terminis surdis æque ac in rationalibus procederent, et Tractatus duos de hujusmodi rebus scripsisse, alterum quem Barrovius, anno 1669, ad Collinium misit, et alterum anno 1671 in quo hanc methodum prius exposueram; cumque fundamentum hujus methodi literis trans <426> positis hanc sententiam involventibus (Data Equatione quotcunque fluentes quantitates involvente Fluxiones invenire et vice versa,) celarem, specimen vero ejusdem in curvis quadrandis subjungerem et exemplis illustrarem; et cum Collinius Epistolam, 10 Decem. 1672 datam, a me accepisset in qua methodum hanc descripseram et exemplo Tangentium more Slusiano ducendarum illustraveram, et hujus Epistolæ exemplar mese Junio anno 1676 in Galliam ad D. Leibnitium misisset, et vir clarissimus sub finem mensis Octobris, in reditu suo e Gallia per Angliam in Germaniam, epistolas meas in manu Collinii insuper consuluisset: incidit is tandem in methodum similem sub diversis verborum et notarum formulis, et mense Junio sequente specimen ejusdem in Tangentibus more Slusiano ducendis ad me misit, et subjunxit se credere methodum meam a sua non abludere presertim cum quadraturæ curvarum per utranque methodum faciliores redderentur. Methodi vero utriusque fundamentum continetur in hoc Lemmate.

Almost the whole of the Scholium printed in the first and second editions of the Principia is put in Italics, in order to show the change upon it which Sir Isaac had proposed for the third edition.

In the other two forms of the Scholium, written on the same sheet with the preceding, the first and second half of it are partly transposed; and at the end of one of them after in hoc Lemmate, are the words et hæc methodus plenius exponitur in Tractatu.

It is singular that both Newton and Cotes should have permitted the words annis abhinc decem to remain in the second edition, seeing that in 1713, thirty-seven years had elapsed. In the draughts, however, of the Scholium under consideration, the more correct words anno 1676 are substituted.

I have found another draught of the Scholium, distinctly written, without any important correction, which differs only from the printed one in the first edition of the Principia in the following points: —

1. After ducendi tangentes the words quadrandi figuras curvilineas are added.

2. After procederet, the words methodumque exemplis illustrarem are added; and

3. Before celarem, the word eandem is inserted.

<427>

No. II.

(Referred to in page 34.)

John Wallis, D. D., the author of the following letter, was one of the most distinguished mathematicians of the seventeenth century. He was born at Ashford in Kent on the 23d November 1616. He studied at Emanuel College, Cambridge, and was a Fellow of Queens'. In 1644 he was chosen one of the Secretaries to the Westminster Assembly of Divines, and in 1649 Savilian Professor of Geometry at Oxford. Between the years 1654 and 1662 he carried on a keen controversy with Hobbes. His principal work is his Arithmetica Infinitorum, published in 1655.[2] His works, both theological and mathematical, were published by the curators of the University of Oxford in 1699, in 3 vols. folio. He died at Oxford on the 28th October 1703, and was in the 82d year of his age when he wrote the two following letters: —

1. — LETTER FROM WALLIS TO NEWTON.

"OXFORD, April 30, 1695.

"SIR,

"I thank you for your letter of April 21st by Mr. Conon. But I can by no means admit your excuse for not publishing your Treatise of Light and Colours. You say you dare not yet publish it. And why not yet? Or if not now, when then? You add, lest it create you some trouble. What trouble now more than at another time. Pray consider how many years this hath layn upon your hands already, and while it lyes upon your hands it will still be some trouble; (for I know your thoughts must still running upon it.) But when published that trouble will be over. You think, perhaps, it may occasion some letters (of exceptions) to you, which you shall be obliged to answer. What if so? 'Twill be at your choice weather to answer them or not. The Treatise will answer for itself. But are you troubled with <428> no letters for not publishing it? I suppose your other friends call upon you for it as well as I, and are as little satisfied with the delay. Meanwhile you lose the reputation of it, and we the benefit, so that you are neither just to yourself nor kind to the public. And perhaps some other may get scraps of the notion and publish it as his own; and then 'twill be his, not yours, though he may perhaps never attain to the tenth part of what you be already master of. Consider that 'tis now about thirty years since you were master of these notions about Fluxions and Infinite Series; but you have never published aught of it to this day, (which is worse than nonumque prematur in annum.) 'Tis true I have endeavoured to do you right in that point. But if I had published the same or like notions without naming you, and the world possessed of another calculus differentialis instead of your fluxions: how should this or the next age know of your share therein? And even what I have said is but playing an after game for you to recover (precariously ex postliminio what you had let slip in its due time. And even yet I see you make no great haste to publish these letters[3] which are to be my vouchers for what I say of it. And even these letters at first were rather extorted from you than voluntary. You may say, perhaps, the last piece of this concerning colour is not quite finished. It may be so, (and perhaps never will,) but pray let us have what is; and while that is printing, you may (if ever) perfect the rest. But if, during the delay, you chance to die, of those papers chance to take fire, (as some others have done,) 'tis all lost both as to you as to the public. It hath been an old complaint that an Englishman never knows when a thing is well, (but will still be overdoing,) and thereby loseth, or spoils many times what was well before. I own that modesty is a virtue, but too much diffidence (especially as the world now goes) is a fault. And if men will never publish aught till it be so perfect that nothing more can be added to it, themselves and the public will both be losers. I hope, Sir, you will forgive me this freedom, (while I speak the sense of others as well as my own,) or else I know not how we shall forgive these days. I <429> could say a great deal more, but if you think I have said too much already, pray forgive this kindness of

"Your real friend and humble servant,

"JOHN WALLIS.

"Dr. Gregory gives you his service."

2. — LETTER FROM WALLIS TO NEWTON.

The following letter, written more than two years afterwards, is partly on the same subject, but is interesting from the message which it contains from Leibnitz in the postscript of a letter to Wallis, dated May 28, 1697: — [4]

Oxoniæ, Julii 1, 1697.

"CLARISSIME VIR,

"Accepi nuper a D. Leibnitio literas Hanoveræ datas Mai 28, 1697. In quibus cum nonnulla sint quæ te quadamtenus spectant, liberem tibi suis verbis exponere, viz., 'Si qua esset occasio, D. Newtono, summi ingenii viro (forte per amicum) salutem officiosissimam a me nunciandi, eumque meo nomine precandi ne se ab edendis præclaris meditationibus diverti pateretur, beneficio hoc a te petere auderem. Item methodum Fluxionum profundissimi Newtoni cognitam esse methodo mea differentiali non tamen animadverti, potquam opus ejus ad lucem prodiit, sed etiam professus sum in Actis Eruditorum; et alios quoque monui. Id enim candori meo convenire judicavi non minus quam ipsius merito. Itaque communi nomine designare soleo Analyseos Infinitesimalis (quæ latius quam Methodus Tetragonisto patet) interim; quemadmodum et Vietiana et Cartesiana methodus, Analyseos Speciosa nomine venit; discrimina tamen nonnulla supersunt. Ita fortasse Newtoniana et mea differunt in nonnullis." Hæc ea verbatim transcripsi ex nobilissimi Leibnitii literis ut videas id ab exteris etiam desiderari, quod ego non tantum petii sed obtestatus sum aliquoties, aliique mecum, nec tamen hactenus obtinuimus ut quæ apud te primis desideratissima ederentur. Quippe cum hoc aut negas aut differs; non tantum tuæ famæ sed et bono publico deesse videris. Duas illas Epistolas (longiusculas et refertissimas) <430> anno 1676 scriptas (unde ego Excerpta quædam antehac edidi) curabo ego (nisi me id vetes) subjungi volumini cuidam meo (jam aliquandiu sub prælo) quamprimum per præli moras licebit. Tuam de Lumine et Coloribus Hypothesin novam (cujus aliquot specimina jam ante multis annis dederis) quam per annos (si recte conjicio) triginta apud te supprimere dictum est, spero ut propediem edendam cures; ut quam ego insignem Naturali Philosophiæ accessionem jaMdudum existimavi et publice deberi: Quam et Prælo fuisse diu paratam audio.) Idem dixerim de pluribus quæ apud te latent, quorum ego non sum conscius. Hæc interim raptim monenda duxi.

"Tuus ad officia,

"JOHANNES WALLIS.

"I put it into this form, that if you think it proper you may desire Dr. Sloan to insert it in the Transactions."[5]

The letter is addressed on the back,

"To MR. ISAAC NEWTON, Controller

of the Mint at The Tower,

LONDON."

The first paragraph of this message to Newton, in the preceding letter, is given in Leibnitz's letter to Wallis, as printed in the third volume of his works, and the following reason is assigned for withholding the rest of the message: — [Sequebantur pauca quæ rem Mathematicam non spectant.] — Wallisii Opera, tom. iii. p. 680.

In Wallis's reply to Leibnitz, dated July 30, 1697, he says, — "Quæ Newtonum spectant, ad eum scripsi tuis verbis, simulque obtestatus sum meo nomine ut imprimi curet quæ sua supprimit scripta. Quod et sæpe ante feceram, sed hactenus in cassum." — Ibid. p. 685.

<431>

No. III.

(Referred to in page 61.)

The Abbé Anthony Conti, or Conty, whose name appears so prominently in the Fluxionary controversy, was a noble Venetian, who obtained some distinction as a philosopher and a poet. He was born at Padua on the 22d January 1677, and, at the age of twenty-two, he retired to Venice into the Congregation of the Oratoire, where he became a priest, and remained nine years. Disgusted with the scholastic philosophy of the day, he studied Bacon and Locke, and devoted himself to the studies of mathematics, natural philosophy, and natural history, which he prosecuted at Padua. Having gone to Paris, where he was a favourite in society, he met with M. Remond de Montmort, an eminent mathematician, who accompanied him to England to observe the great solar eclipse of the 15th April 1715. He was then introduced to Newton, and was on very intimate terms with him. He took a great interest in his controversy with Leibnitz, but being acquainted also with the German philosopher, he found it difficult to take an impartial course between the two extreme opinions of the day. We shall meet with him again when we come to the consideration of Newton's Chronology, which was the ground of a serious difference with its author.[6] Conti wrote a philosophical poem entitled Il Globo de Venere/>, and four tragedies, which were published at Venice in 1739. He died at Padua on the 6th March 1749.

The following very interesting letter,[7] referred to in the text, was written to Brook Taylor, one of the committee who drew up the report on the Commercium Epistolicum.

<432>

1.— LETTER OF THE ABBE CONTI TO BROOK TAYLOR.

"MONSIEUR,

"Je m'en vais vous expliquer en peu de mots les raisons qui m'ont engagé dans la querelle de Mons. Newton et de M. Leibnitz, Mr. Newton me pria d' assembler à la Société les Ambassadeurs et les autres Ministres étrangers. Il souhaitait qu'ils assistassent à la collation qu'on devoit faire des papiers originaux, qui se conservent dans les archives de la Société avec d'autres lettres de M. Leibnitz. Mr. le Baron de Kirmansegger[8] vint à la Société avec les Ministres des Princes; et après que la collation des papiers fut faite, il dit tout haut, que cela ne suffisoit pas, que la véritable méthode pour finir la querelle, c'étoit que Mr. Newton luy-même écrivit une lettre à Mr. Leibnitz dans laquelle il luy proposât les raisons et en même tems luy demandât des réponses directes. Tous les Ministres des Princes qui étoient présents goûtèrent l'idée de Mr. Kirmansegger; et le Roy même à qui on la proposa le soir, l'approuva, ayant dit tout cela à Mr. Newton, cinque ou six jours après il m'escrivit une lettre pour envoyer à Mr. Leibnitz à Hanover. Mr. Newton, peut-il dire que je l'ay prié de m'adressér cette lettre? Cependant la nécessité, de l'envoyer à Hanover, et de l'accompagner d'une des miennes m'engagea dans la querelle. La lettre qui fut portée à Hanover par le Baron de Discau, resta plus d'un mois à Londres. Madme la Comtesse de Kirmansegger la fit traduire en François par M. Coste: le Roy la lut et l'aprouva fort, en disant que les raisons étoient très simples et tràs claires, et qu'il étoit difficile de répondre à des faits. J'ay lu à Mons. Newton la lettre que j'escrivois à Mons. Leibnitz; c'est Mr. de Moivre qui me l'avoit corrigé et j'en conserve encore la brouillon: Mr. de Moivre y-avoit ajouté quelque chose à l'égard de la manière équivoque dont Mr. Leibnitz avoit proposé le problême. Mr. Leibnitz fut fort irrité de la lettre que je luy avois envoyée, comme il paroit par sa réponse, et par des expressions assez fortes qu'il avoit avancées contre moy dans ses lettres à S. A. R. la Princesse de Galles. Il écrivit plusieurs lettres pour sa justification que j'ay donné à Mons. Newton à proportion qu'elles <433> m'ont tombés dans les mains, Mr, Newton en fit une espèce de réponse qui fut imprimée avec la première lettre à la fin de l'Histoire des Fluxions; les lettres que Mr. Leibnitz m'avoit addressées, furent aussi imprimées dans le même livre; et Mr. Leibnitz (evidently a mistake for Mr. Newton ) en fit non seulement ôter mon nom; mais encore ne me fit aucune part qu'on les imprimoit. Quand Mr. de Mesaus[9] luy proposa de les imprimer de nouveau en Hollande, il luy donna son approbation, et dit même qu'il luy fourniroit quelque autre petit papier. J'ignore ce qui est arrivé d'après, parce que j'ay quitté l'Angleterre. On dit que Mr. Newton a changé de sentiment et qu'il se plaint de moy de l'avoir engagé dans la querelle avec Mr. Leibnitz; je le prie très humblement de réfléchir à des faits qui sont incontestables; et par lesquels il paroit assez que je n'ay eu d'autre part à la question qu'autant qu'il voulut bien m'en faire. J'ay essuyé tous les reproches des Allemans, et de Mr. Leibnitz luy-même pour soutenir ses raisons. Je les ai aussi soutenus en France où malgré tout ce qu'on a l'addresse de luy écrire en Angleterre, on n'est pas trop dans ses intérêts comme il pense. J'ai pense un jour me brouiller avec un grand mathématicien, chez une Dame, où on parloit de cette dispute; il soutenoit que tous les argumens du Commercium Epistolicum n'etoient pas concluans; et que Mr. Newton n'y avoit aucune part, non plus qu'aux lettres qu'on avoit imprimées par son ordre. J'aurois bien d'autres choses à dire la-dessus; mais je suis las d'entendre parler d'une matière qui n'est pas agréable. On a voulu me commettre avec Mr. Newton, et je ne sçay pas pourquoi; je l'ay toujours honoré et respecté; et je luy ay toujours dit la vérité sans aucun intérêt: mais si les plaintes continuent, je ne pourray pas me dispenser de faire imprimer la simple histoire d'un fait, qui fera voir au public que je n'ay pas prétendu me mêler dans cette querelle pour acquérir du nom. Mr., je suis

"Votre très humble et tràs obéissant serviteur,

"CONTY."

"A Paris, ce May 22, 1721."

<434>

The following is the only letter from Conti to Newton which I have found among the Portsmouth Manuscripts: —

2. — LETTER FROM THE ABBE CONTI TO SIR ISAAC NEWTON.

HANOVER, 10 Decembre, 1716.

"MONSIEUR,

"Je vous demande pardon si je n'ay pas pu vous écrire jusque à cette heure. Je suis tombé malade depuis que je suis icy, et je ne suis pas encore revenu de ma maladie. Je n'ay vu ni Le Roy,[10] ni La Cour, et je suis obligé de garder la chambre depuis vingt jours.

"M. Leibniz est mort; et la dispute est finie. Il a laissé plusieurs lettres et plusieurs manuscrits qu'on imprimera, aussi des manuscrits d'autres sçavants, une qui est Traité de M. Des-Cartes qui n'est point paru jusque ici. Il y a des Dialogues sur les articles de la Téodicea; une instruction au Prince Eugène sur les exercices militaires; une instruction au Czar pour faire fleurir les arts et les sciences dans son pais; beaucoup des remarques sur la langue universelle, et sur I'étimologie des mots. Comme je espère que le Roy me donnea la permission de voir les papiers je remarquerai s'il y a quelque chose touchant votre dispute, mais peut-etre qu'on cachera ce qui ne fait point d'honneur à la mémoire de M. Leibnitz. On a commencé de travailler sur sa vie. M. Wolfius aura le soin d'écrire tout ce qui appartient aux Mathématiques.

'M. Leibnitz a travaillé pendant toute sa vie à inventer des machines qui n'ont point réussi. Il a voulu faire une espèce de moulin à vent pour les mines, un carosse qui tire sans chevaux, un carosse qui se change, un chaire à porteur, et un charette; jusque des Souliers à ressort. Il y a deux modelles de sa machine arithmétique, mais elle est très composée, et on en dit qu'elle n'est à la fin que la machine de Pascal multipliée.

"Vous aurez vu l'insolente dissertation, qu'on a imprimée dans les actes de Lipsic au mois de Juin. M. Bernoulli prétend à cette heure d'être l'inventeur de calcul intégral. Je suis sûr que la dissertation vous fera rire.

<435>

"Je ne sçay pas si l'ambassadeur de Venise vous a prié de proposer à la Societé Royal M. le Marquis Orsi Sénateur de Bologne, et un de plus grand sçavants que nous avons en Italie. Il est célèbre en France par plusieurs livres qu'il a écrit, et il est un Seigneur qui a beaucoup de mérite et de talent. On dit qu'il a refusé autrefois d'être Cardinal. Il s'est addressé a moi pour vous prier de cette grace, et je le fais volontiers, car je connois les mœurs et le sçavoir de M. le Marquis Orsi.

"Si il y aura quelque chose de nouveau touchant l'affaire de M. Leibnitz je vous en informerai avec toute l'exactitude. Il n'y a peut-être un personne plus intéressé pour votre gloire que moy. J'en ay l'obligation, et même l'inclination. Je suis avec tout la zèle, et en vous priant de faire mes compliments à Madame votre nièce.

"Monsieur,

Votre très-semble {sic} et tres obéissant serviteur,

"CONTI."

<436>

No. IV.

(Referred to in pages 65, 82.)

M. Pierre Remond de Montmort, to whom Bernoulli addressed the letter mentioned in the text, was born in Paris on the 27th October 1678. He came to London in 1700, when he made the acquaintance of Newton. He visited Dr. Gregory at Oxford, who showed him his Commentary on the Principia, and who afterwards told him in the course of their correspondence, that he was preparing a new edition of the Principia under Sir Isaac's eye, a task which he did not live to execute. This fact is mentioned in a short letter to Sir Isaac himself,[11] in which he begs his acceptance of his newly published work Essai d' Analyse sur les Jeux de Hazard, and expresses his sorrow for the death of Gregory. In 1704 he purchased the estate of Montmort, close to the residence of the Duchess D'Angoulême, whose niece and god-daughter, Mademoiselle de Romicourt, he married. He corresponded with Leibnitz, the Bernoullis, and other distinguished mathematicians, both in England and on the continent, by whom he was much esteemed, both as a geometer and a member of society. He was particularly attached to our countryman Brook Taylor, by whom several of his letters have been preserved. He paid a second visit to England in 1715, and was a great admirer, as we shall afterwards see, of the beauty and accomplishments of Miss Catherine Barton, Sir Isaac Newton's niece. He was elected in 1716 one of the Académiciens Libres of the Academy of Sciences. When on a visit to Paris in 1719, he was seized with small-pox, and died on the 7th October 1719, deeply lamented by the population of the three parishes which belonged to him.

The history of the very interesting letter from Bernoulli which forms this Appendix, is curious, and is given by Montmort himself in a long letter to Newton, written in bad English, and dated March 27, 1718. It contains messages from the two Bernoullis, together with an extract of Nicolas Bernoulli's paper <437> on Trajectories,[12] and a part of the following letter which he did not know had been previously in the hands of Newton.

When Bernoulli had learned that Newton did not approve of the challenge made to the English mathematicians, he communicated "the whole story of that affair" to Montmort, and desired him to send to Newton an extract of his letter. Montmort, lest he should annoy Newton by "giving him the trouble of an answer," sent the extract to Brook Taylor, and never learned from him that it had been forwarded to its destination. The following is the extract found among Sir Isaac's papers: —

LETTER FROM JOHN BERNOULLI TO M. REMOND DE MONTMORT.

"Avril 8, 1717.

"Je vous proteste, Mons. que je n'ai jamais eu la pensée de me commettre avec Messieurs les Anglois, ni d'entrer en lice, quand même quelqu'un d'eux m'attaqueroit, bien loin de les défier le premier; le temp et le repos me sont trop précieux pour les consumer en vaines disputes; mais voici, ce qui c'est. Mons. Leibnitz m'ayant demandé si je ne pouvois pas luy fournir quelque problême pour le proposer à Messieurs les Anglois et en particulier à M. Keil pour la solution duquel seroit requise une adresse particulière dont on ne put s'aviser aisément sans la connoissance de quelques unes des méthodes que nous avions trouvées dans le temps que j'étois encore en Hollande et que M. Leibnitz ne trouvoit pas apropos d'en faire part encore au public, me priant pour cela de menager le secret afin de s'en servir un jour utilement contre ceux qui voudroient nous braver, comme il arrive aujourdhuy. Pour faire donc plaisir à Monsr. de Leibnitz, j'ay imaginé un problême qui me paroissoit avoir les qualités telles qu'il pouvoit souhaiter. Je luy en fis part avec une double solution, afin qu'il pût, s'il le jugeoit apropos, le proposer aux Anglois mais sous son nom. J'ay sujet d'être étonné de voir que M. Leibnitz m'ait produit comme auteur, et proposant de ce problême, et cela malgré moy et même à mon insçu. Vous aurez donc la bonté de désabuser Mr. Newton de <438> l'opinion où il est à cet égard; et de l'assurer de ma part que je n'ai jamais eu le dessein de tenter messieurs les Anglois par ces sortes de défis, et que je ne désire rien tant que de vivre en bonne amitié avec luy, et de trouver l'occasion de luy faire voir combien j'estime son rare mérite, en effect je ne parle jamais de luy qu'avec beaucoup d'éloges. Il seroit pourtant à souhaiter qu'il voulùt bien prendre la peine d'inspirer à son ami Mr. Keill des sentiments de douceur et d'équité envers les étrangers, pour laisser chacun en possession de ce que luy appartient de droit, et à juste titre, car de vouloir nous exclure de toute prétention, ce seroit une injustice criante. Voicy cependant le problême dans les propres termes que je l'ay communiqué a Mons. Leibnitz, puisque vous temoignez le désirer."

BERNOULLI'S PROBLEM.

"Super Recta AG tanquam Axe ex puncto A, educere infinitas curvas, qualis est ABD, ejus naturæ ut radii osculi in singulis punctis B et ubique ducti BO secentur ab axe AG in C in data ratione, ut nempe sit BO : BC :: 1 : n. Deinde construendæ sunt Trajectoriæ EBF primas curvas ABD normaliter secantes."

Figure

In his correspondence with Montmort, Bernoulli expressed the greatest anxiety to be on good terms with Newton. In a letter, dated March 17, 1718, he desires to know if Montmort has sent the preceding extract to Newton, and implores him again to disabuse the English of the false opinion that he and his nephew have any design of entering into disputes with them, or diminishing the value of Newton's discoveries; and he asks <439> him, as a special favour, to do this in reference to Mr. Newton, whose esteem and friendship are very precious to him.

Montmort, in reply to this letter, stated that these expressions in reference to Newton and the English would not be considered very compatible with the Epistola pro eminente Mathematico, which he had inserted in the Acts of Leipsic, and he gave him very frankly his opinion of that letter Bernoulli replied to this letter in the following words, which Montmort sent to Newton: —

"Je ne m'en suis mêlé en aucun façon, ni de la forme que mon ami vouloit donner à la réponse, ni des expressions dont il se serviroit, et que je n'approuve pas toutes. Il m'a qualifié de titres que je n'ai jamais eu la vanité d'ambitionner. Avec cela il M. Keill d'une manier qui ne peut qu'aigrir son esprit. Cela ne me plaisoit pas. J'aurois souhaité que mon apologiste eust dit les choses simplement et nettement sans toucher sur personalités. Certe que je luy aurois recommandé avec empressement s'il m'avoit communiqué son dessein, lorsqu'il m'offrit par une lettre obligeante de vouloir défendre ma cause contre M. Keill me priant seulement de luy envoyer les preuves authentiques lesquels je ne pouvois pas luy refuser."

Fontenelle justly remarks, in his Eloge on Montmort, that though he was more connected with the English than with the Germans by personal acquaintance, yet he was perfectly neutral between the rival analysts, always speaking the truth to both parties, and in a tone which made truth acceptable. See p. 274, and APPENDIX, No. XIX.

While this correspondence was going on, Varignon had been endeavouring to effect a reconciliation between Newton and Bernoulli. See p. 291, and APPENDIX, No. XXI.

<440>

No. V.

(Referred to in pages 76, 80.)

In the 24th Chapter of this Volume, the reader will find some account of James Wilson, M.D., the editor of Robins' Mathematical Tracts, the friend of Pemberton, and the editor of his Course of Chemistry.

1. — LETTER FROM A. B., [JAMES WILSON, M.D.,] TO SIR ISAAC NEWTON.

"LONDON, December 15, 1720.

"SIR,

"I saw the other day, in the hands of a certain person, several mathematical papers, which, he told me, were transcribed from your manuscripts. They chiefly related to the doctrine of series and fluxions, and seemed to be taken out of the Treatises you wrote on those subjects in the years 1666 and 1671. I was not permitted to peruse them thoroughly, but one of the papers I particularly took notice of, and it contained a deduction of your Binomial Theorem from a corollary in your Quadratures, with some improvement, as a series for the rectangle under any two dignities of two binomials. These papers, I observed, had been very incorrectly copied, so that I endeavoured all I could to dissuade the possessor of them from getting them printed, of which nevertheless he seemed very fond. I therefore thought it behoved me to acquaint you with this matter, and, as I have not the honour to be known to you, I believed the less troublesome way to do it would be that of a letter.

"And now, Sir, permit me to say, that it is the earnest desire of everybody conversant in these subjects, that you would be pleased to publish yourself what you have formerly written; for this would effectually prevent their being ever printed incorrectly and unworthy of yourself. Nor ought you to deny that pleasure to your well-wishers and admirers, in reading your noble inventions of this kind, whereof you have expressed yourself to have been so sensible at the time you first made these <441> discoveries. Your analysis Per Æquationes Numero Terminorum Infinitas, Quadraturas, &c., give us so exquisite a delight, that when we read your letters to Mr. Oldenbourgh, and your remarks on Leibnitz's reply to your letter to the Abbot Conti, we glow, as it were, with a desire of seeing all that you wrote on these subjects in 1671, and the years preceding. I have heard, indeed, that you were prevented from publishing one Treatise, by reason it had in it the Determination of the Radius of Curvity, which Huygens published afterwards in his Horologium. But this objection can now be of no force, since the world has been lately informed by your letter written to Mr. Collins in 1672, Decemb. 10, that you had applied your method ad resolvendum abstrusiora problematum genera de curvitatibus, &c., long before the publication of Huygens's book. Nor indeed was this unknown to Apollonius in respect to the Conick Sections, as appears from his Fifth Book. It was a very great satisfaction to your countrymen and friends to observe, that by the happy discovery of Mr. Collins's papers, you had an opportunity of triumphing over such disingenuous persons, who laboured all they were able to defraud you of the honour of some of your inventions. But such is the force of prejudice on some minds, that you cannot but observe that there are in the world dishonest men, who, contrary to their own conscience and knowledge, still raise a clamour on this head. To shame, therefore, such obstinate people, to make your right to those inventions evident to all, even the least knowing in these matters, and to put an end for ever to all disputes, the best method would be to publish all that you have formerly written on this subject, whereby we should have an exact and adequate notion of fluxions and their uses, which cannot be had from what has been delivered by others. But as they produced these things abroad first, those that are learners have recourse to their writings, and consequently mention them as the authors thereof. This has happened through your own backwardness in giving to the world what you had discovered so long ago. However, there is still a way left to retrieve all; for, as their pretended methods are grounded on the notion of indivisibles, so they have given a wrong idea of what you alone had found out, and have erred <442> egregiously, when they even attempted to apply Second, &c., Differences, as they call 'em, to mathematical figures. This, tho' they cannot but be now at length very sensible of, yet by their cavils they would dissemble their being conscious of their errors.' But these would be so apparent to every eye, if you would publish all your papers, that those who had a mind to be rightly instructed in these matters, would have recourse alone to your immortal writings; so that all succeeding mathematicians would constantly mention with honour the Series, Fluxions, &c., of the great Newton, when the differentials and integrals of Leibnitz and Bernoulli shall be quite forgotten.

"I am, your most obedient and most humble servant,

"A. B."

"P.S. — I had just the liberty to transcribe the Theorem I mentioned at the beginning of my letter, and it was this: —

P+PQ¯λ×M+MN¯μ=PλMμ+λ×QAμ×N1+λ-1×QBμ-1×N+λ+μ¯×NQA2+λ-2×QCμ-2×N+λ+μ-1¯×NQB3+λ-3xQDμ-3xN+λ+μ-2¯xNQC4etc.

"Amongst the papers I likewise observed that there were some which deduced even the first principles of geometry from the fluxions of points, &c.

"I have since met with another person, who told me he had likewise a copy of your manuscripts. But he would not let me <443> see them, or inform me how he came by them. I imagine, when you sent any of your friends your papers, the person they got to transcribe them took a double copy, which is a frequent practice, in order to make profit by it; so that they are in different hands. To prevent these things being ever published incorrectly, the only way is to let them come abroad yourself; for to declare that such papers as shall be published without your knowledge or consent, are imperfect and faulty, will not be sufficient to deter some bookseller or another from adventuring on the printing them for the hopes of gain. Nor need the publishing them be any trouble to you; for any of your friends would gladly undergo the labour of seeing them correctly printed.

"In the introduction to your Quadratures, you have given us an exact idea of fluxions, but it is too short, and does not instruct us how the superior fluxions are represented by Lines. The truth is, the trifling objections that are made by your antagonists would never have been raised, if you had given us your papers, where your fluxions are illustrated by various examples. And is not this a pity, since you have pleased to permit the publication of your illustrating the common algebra. Nothing less than this can make all foreigners and prejudiced persons acquiesce, and at length to acknowledge you to be the inventor of a method that is so admirably suited both to the investigating and demonstrating the most difficult mathematical truths."

2. — LETTER FROM JAMES WILSON, M.D., TO SIR ISAAC NEWTON.

"LONDON, 21st January 1720-21."

SIR,

"As some time ago I presumed to let you know that I had seen copies of several of your manuscripts, and having since been permitted to transcribe some of them, I take the liberty to send them to you, that you may compare them with the originals, to see after what manner they have been copied. They contain three problems, which I take to be the 2d, 3d, and 4th <444> of your Treatise wrote in 1671. Here is also a paper in English containing five problems, which I guess to be part of that which you have mentioned in your remarks on Leibnitz's letter to the Abbot Conti, as dated 13th November 1665. The other papers seemed to have not been so well copied as these, so I did not write them out. They contained, I observed, several problems, as to find the curvature and areas of curves, and to compare curves together, &c. There was also a paper containing six examples, showing how to deduce the areas of curves from the tables in your Quadratures, with Constructions and Synthetick Demonstrations. It concluded with saying, that it was here judged proper to demonstrate by the means of moments, as it had an analogy to what the ancients have done on the like occasions. I have been likewise told by one that he had a copy of a manuscript of yours, entitled Geometria Analytica, which he highly prized, but this I never saw.

"When I had the honour of seeing you at Mr. Innys's shop, you was pleased to object against publishing these manuscripts; that you apprehended it would occasion disputes concerning their antiquity. The followers of Leibnitz are, it is true, an obstinate sort of people, and bo proof, however clear, seems sufficient to make them lay aside their prejudices, yet on such an occasion I cannot think they should be more than ordinarily exasperated; for thereby you will not do more than by what yon have said, when you published your Quadratures, and in your remarks on Leibnitz's reply to your letter to the Abbot Conti. The publishing indeed of the Commercium Epistolicum raised their fury, because that not only proved you to be the inventor of fluxions, but moreover made it appear that their master was a plagiary. However, notwithstanding this, the defamatory writings they spread abroad on that occasion were without a name, as if they were ashamed of them; and the person who has been charged as the author of them, has since thought fit to deny it. But suppose this should raise ever so great a clamour, I cannot see that you need be concerned the least about it, for, in publishing these papers, you would not pretend to vindicate to yourself the right to these inventions from their antiquity; for that you rely on the arguments that are drawn from the <445> papers contained in the Commercium Epistolicum, which the Leibnitians themselves do not pretend to say, are not of an older date than their master's letter of June 21, 1677.

"But then I think these papers ought to be published on many accounts. By that means young mathematicians will be able readily to perceive the force of the arguments contained in the Commercium Epistolicum, and in its admirable abridgment, before they receive the least prejudice from the cavils of your antagonists. These, I think, are now all reduced to this, that it does not appear from the Commercium that you were acquainted with the true characteristic and algorithm of fluxions or differences, before their master. The weakness of this cavil would appear evident even to the most prejudiced, if you would publish all your papers. Again, your Book of Quadratures, which all intelligent persons must own is the perfectest piece that ever saw the light, seems not to be well understood by foreigners, (and perhaps not by some at home;) for otherwise a certain confident person durst not lay claim to many things contained in it, under the notion of his integral calculus. But the publishing your papers would enable all to see the beauties of that noble Treatise; and this is now absolutely necessary, since there are pretenders in the world to these inventions. Lastly, as various copies of your manuscripts, more or less imperfect, are got abroad, nothing but causing them to be printed yourself can prevent their coming out incorrect and mangled, which ought not to be the fate of such excellent things.

"I am, Sir, with the profoundest respect,

"Your most obedient and most humble servant,

"JAMES WILSON.

"P.S. — I humbly desire that, when you have perused these papers, you would be pleased to seal them up, and to leave them with your servants, that I may have them again upon calling for them some time or other.

"At page 48 of the Commercium Epistolicum, it is said by Mr. Collins, that the doctrine of Series, &c., was the subject of your lectures at Cambridge, and that these lectures were reserved <446> there, which, if so, they might afford convincing proofs of your right to these inventions.

"In your remarks on Leibnitz's reply to your letter to the Abbot Conti, I think you seem too readily to acknowledge that Leibnitz might have found out by himself your method of an arbitrary series; for in a Scholium of your Principia, you say that one of the things which you concealed under a cypher, in your letter of October 24, 1676, was 'Data Æquatione quotcunque Fluentes quantitates involvente, Fluxiones invenire, et vice versa.' Now, might not Leibnitz by that means be helped to decypher what was besides concealed in that letter? Amongst which was that very method of assuming a series, which he did not publish till some years after you had helped him to a key in the Scholium above-mentioned.

"I hope you will pardon this freedom, for it is not my purpose to go on in troubling you thus with impertinent letters.

"Sir, I am your most obedient

"And most humble servant,

"JAMES WILSON."

<447>

No. VI.

(Referred to in page 100.)

LETTER FROM SIR ISAAC NEWTON TO DR. THOS. BURNET.

"Sir,

"Your argument, p. 118, I acknowledge good against those who suppose only hills and mountains taken out of ye sea, and it may be good agt those who suppose all ye earth higher than ye sea taken out thence, but one who would have mountains and ye sea made by removing earth from one place to another, might suppose (if it were necessary) all the earth a quarter of a mile or half a mile lower than the top of the seas, or then the lowest valleys, or even lower than that, was thrown out of ye deep. But the opinion being to me absurd, I say no more of it. I could wish I was as well satisfied wth your argument about ye oval figure of ye earth, for it seems hard to me that a constant force applied to stretch a membrane, (as you figuratively term ye atmosphere) should make it shrink, unless you suppose it at first overstretched by a tumultuary force, and so to return by way of undulation, and that the limus of ye earth hardened while it was at ye ebb. But whatever may be ye reason of the earth's figure, you desire my opinion what that figure is. I am most inclined to believe it spherical, or not much oval; and my chief reason for that opinion is ye analogy of ye planets. They all appear round so far as we can discern by telescopes, and I take ye earth to be like ye rest. If its diurnal motion would make it oval, that of Jupiter would much more make Jupiter oval, the vis centrifuga at his equator, caused by his diurnal motion being 20 or 30 times greater than the vis centrifuga at ye equator, caused by the diurnal motion of ye earth, as may be collected from the largeness of his body and swiftness of his revolutions. The sun also has a motion about his axis, and yet is round. What may be argued from ye dimensions of ye earth's shaddow collected by lunar eclipses I cannot tell, nor what from ye measures on ye earth answering to a degree in several latitudes, not knowing how exactly those measures were made or the latitudes of places taken.

<448>

"You seem to apprehend that I would have the present face of the earth formed in ye first creation. A sea I believe was then formed, as Moses expresses, but not like ye sea, but with an eaven bottom without any precipices or steep descents, as I think I exprest in my letter. Of or present sea, rocks, mountains, &c., I think you have given the most plausible account. And yet if one would go about to explain it otherwise, philosophically, he might say that as saltpetre dissolved in water, though ye solution be uniform, crystallizes not all over ye vessel alike, but here and there in long barrs of salt; so the limus of ye chaos, or some substances in it, might coagulate at first, not all over ye earth alike, but here and there in veins or beds of divers sorts of stones and minerals. That in other places wch remained yet soft, the air wch in some measure subsided out of the superior regions of ye chaos, together wth ye earth or limus by degrees extricating itself gave liberty to the limus to shrink and subside, and leave the first coagulated places standing up like hills; which subsiding would be encreased by the draining and drying of that limus. That the veins and tracts of limus in the bowels of those mountains also drying and consequently shrinking, crackt and left many cavities, some dry, others filled with water. That after the upper crust of the earth by the heat of the sun, together with that caus'd by action of minerals had hardened and set; the earth in the lower regions still going closer together left large caverns between it, and the upper crust filled with ye water, wch upon subsiding by its weight, it spread out by degrees till it had done shrinking, which caverns or subterraneal seas might be the great deep of Moses, and if you will, it may be supposed one great orb of water between ye upper crust or gyrus and the lower earth, though perhaps not a very regular one. That in process of time many exhalations were gather'd in those caverns which would have expanded themselves into 40 or 50 times the room they lay in, or more, had they been at liberty. For if air in a glass may be crowded into 18 or 20 times less room than it takes at liberty, and yet not burst the glass, much more may subterranean exhalations by the vast weight of ye incumbent earth be keept crowded into a less room before they can in any place lift up and burst that <449> crust of earth. That at length somewhere forcing a breach, they by expanding themselves, forced out vast quantities of water before they could all get out themselves, wch commotion caused tempests in ye air, and thereby great falls of rain in spouts, and all together made ye flood, and after the vapours were out, ye waters retired into their former place. That the air wch in ye beginning subsided with ye earth, by degrees extricating itself, might be pent up in one or more great caverns in the lower earth under ye abyss, and at ye time of ye flood, breaking out into ye abyss, and consequently expanding itself, might also force out ye waters of ye abyss before it. That the upper crust or gyrus of earth might be upon the stretch before ye breaking out of ye abyss, and then by its weight shrinking to its natural posture, might help much to force out the waters. That the subterraneal vapors which then first break out and have ever since continued to do so, being found by experience noxious to man's health, infect the air and cause that shortness of life wch has been ever since the flood. And that several pieces of earth either at ye flood or since falling, some perhaps into ye great deep, others into less and shallower cavities, have caused many of those phenomena we see on ye earth, besides the original hills and cavities.

"But you will ask how could an uniform chaos coagulate at first irregularly in heterogeneous veins or masses to cause hills. Tell me then how an uniform solution of saltpetre coagulates irregularly into long bars; or to give you another instance, if tinn (such as the pewterers bring from ye mines in Cornwel to make pewter of) be melted and then let stand to cool till it begin to congeal, and when it begins to congeale at ye edges, if it be inclined on one side for ye more fluid part of ye tin to run from those parts wch coagulate first, you will see a good part of ye tin congealed in lumps which after the fluider part of ye tin which congeals not so soon is run from between them, appear like so many hills, with as much irregularity as any hills on ye earth do. Tell me ye cause of this, and ye answer will perhaps serve for the chaos.

"All this I write not to oppose you, for I think the main part of your hypothesis as probable as that I have here written, if not <450> in some respects more probable. And tho' the pressure of ye moon or vortex, &c., may promote ye irregularity of ye causes of hills, yet I did not in my former letter design to explain the generation of hills thereby, but only to insinuate how a sea might be made above ground in your own hypothesis before the flood, besides the subterranean great deep, and thereby all difficulty of explaining rivers, and the main point in wch some may think you and Moses disagree might be avoyded. But this sea I not [do] not suppose round the equator, but rather to be two seas in two opposite parts of it where the cause of ye flux and reflux of or present sea deprest ye soft mass of ye earth at that time when ye upper crust of it hardened.

"As to Moses, I do not think his description of ye creation either philosophical or feigned, but that he described realities in a language artificially adapted to ye sense of ye vulgar. Thus when he speaks of two great lights, I suppose he means their apparent not real greatness. So when he tells us God placed these lights in ye firmament, he speaks I suppose of their apparent not real place, his business being not to correct the vulgar notions in matters philosophical, but to adapt a description of the creation as handsomely as he could to ye sense and capacity of ye vulgar. So when he tells us of two great lights, and ye stars made ye 4th day, I do not think their creation from beginning to end was done the 4th day, nor in any one day of ye creation, nor that Moses mentions their creation, as they were physicall bodies in themselves, some of them greater than this earth, and perhaps habitable worlds, but only as they were lights to this earth, so therefore though their creation could not physically [be] assigned to any one day, yet being a part of ye sensible creation which it was Moses's design to describe, and it being his design to describe things in order according to the succession of days, allotting no more than one day to one thing, they were to be referred to some day or other, and rather to the 4th day than any other, if they [the] air then first became clear enough for them to shine thro' it, and so put on ye appearance of lights in ye firmament to enlighten the earth. For till then they could not properly be described under ye notion of such lights, nor was their description under that notion to be deferred after they had <451> that appearance, tho' it may be the creation of some of them was not yet completed. Thus far, perhaps, one might be allowed to go in ye explaining ye creation of ye 4th day, but in ye third day for Moses to describe ye creation of seas when there was no such thing done neither in reality nor appearance, me thinks is something hard, and that ye rather becaus if before ye flood there was no water but that of rivers, that is, none but fresh water above ground, there could be no fish but such as live in fresh water, and so one half of ye fift day's work will be a non entity, and God must be put upon a creation after ye flood, to replenish one half of this terraqueous globe wth whales, and all those other kinds of sea fish we now have.

"You ask what was that light created the first day? Of what extent was the Mosaical chaos? Was ye firmament, if taken for ye atmosphere so considerable a thing as to take up one day's work? and would not ye description of ye creation have been complete without mentioning it? To answer these things fully, would require comment upon Moses whom I dare not pretend to understand: yet to say something by way of conjecture, one may suppose that all ye planets about or sun were created together, there being in no history any mention of new ones appearing or old ones ceasing. That they all, and ye sun too, had at first one common chaos. That this chaos, by ye spirit of God moving upon it became separated into several parcels, each parcel for a planet. That at ye same time ye matter of ye sun also separated from the rest, and upon ye separation began to shine before it was formed into that compact and well defined body we now see it. And the preceding darkness and light now cast upon ye chaos of every planet from the solar chaos, was the evening and morning, wch Moses calls ye first day, even before ye earth had any diurnall motion, or was formed into a globular body. That it being Moses design to describe the origination of this earth only, and to touch upon other things only so far as they related to it, he passes over the division of ye general chaos into particular ones, and does not so much as describe ye fountain of that light God made, that is, ye chaos of ye sun, but only wth respect to the chaos of the earth, tells us that God made light upon the face of ye deep where darkness was before. Further, <452> one might suppose that after ye chaos was separated from ye rest, by ye same principle wch promoted its separation, (wch might be gravitation towards a centre,) it shrunk closer together, and at length a great part of it condensing, subsided in ye form of a muddy water or limus, to compose this terraqueous globe. The rest wch condensed not, separated into two parts, the vapors above and the air, wch being of a middle degree of gravity ascended from ye one, descended from ye other, and gathered into a body stagnating between both. Thus was the chaos at once separated into three regions, the globe of muddy waters below ye firmament, the vapors or waters above the firmament, and ye air or firmament itself. Moses had before called the chaos the deep and the waters, on ye face of wch ye spirit of God moved, and here he teaches the division of all those waters into two parts, with a firmament between them: wch being the main step in ye generation of this earth, was in no wise to be omitted by Moses. After this general division of ye chaos, Moses teaches a subdivision of one of its parts, that is, of the miry waters under ye firmament into clear water, and dry land on the surface of the whole globous mass, for wch separation nothing more was requisite then that ye water should be drained from ye higher parts of ye limus to leave them dry land, and gather together into ye lower to compose seas. And some parts might be made higher than others, not only by ye cause of ye flux and reflux, but also by ye figure of ye chaos, if it was made by division from ye chaos of other planets, for then it could not be spherical. And now while the new planted vegetables grew to be food for animals, the heavens becoming clear, for ye Sun in ye day, and Moon and starrs in ye night, to shine distinctly through them on the earth, and so put on ye form of lights in ye firmament, so that had men been now living on ye earth to view the process of ye creation, they would have judged those lights created at this time. Moses here sets down their creation as if he had then lived, and were now describing what he saw. Omit them he could not, without rendering his description of the creation imperfect in ye judgment of ye vulgar. To describe them distinctly as they were in themselves, would have made ye narration tedious and confused, amused ye vulgar, and become a philosopher more <453> then a prophet. He mentions them, therefore, only so far as ye vulgar had a notion of them, that is, as they were phenomena in ye firmament; and describes their making only so far, and at such a time, as they were made such phenomena. Consider, therefore, whether any one who understood the process of ye creation, and designed to accommodate to ye vulgar not an ideal or poetical, but a true description of it as succinctly and theologically as Moses has done, without omitting any thing material wch ye vulgar have a notion of, or describing any being further then the vulgar have a notion of it, could mend that description wch Moses has given us. If it be said that ye expression of making and setting two great lights in ye firmament is more poetical then natural, so also are some other expressions of Moses, as when he tells us the windows or floodgates of heaven were opened, (Gen. vii.,) and afterwards stopped again, (Gen. viii.;) and yet the things signified by such figurative expressions are not ideall or moral, but true. For Moses, accommodating his words to ye gross conceptions of ye vulgar, describes things much after ye manner as one of ye vulgar would have been inclined to do had he lived and seen ye whole series of what Moses describes.

"Now for the number and length of ye six days: By what is said above, you may make the first day as long as you please, and ye second day too, if there was no diurnal motion till there was a terraqueous globe, — that is, till towards ye end of that day's work. And then if you will suppose ye earth put in motion by an eaven force applied to it, and that ye first revolution was done in one of our years, in the time of another year there would be three revolutions, of a third five, of a fourth seaven, &c., and of ye 183d year, 365 revolutions, that is, as many as there are days in our year, — and, in all this time, Adam's life would be increased but about 90 of or years, wch is no such great business. But yet I must profess I know no sufficient naturall cause of ye earth's diurnal motion. Where natural causes are at hand, God uses them as instruments in his works, but I doe not think them alone sufficient for ye creation, and therefore may be allowed to suppose that, amongst other things, God gave the earth its motion by such degrees, <454> and at such times, as was most suitable to ye creatures. If you would have a year for each day's work, you may, by supposing day and night was made by the annual motion of the earth only, and that the earth had no diurnal motion till towards the end of ye six days. But you'l complain of long and dolefull nights; and why might not birds and fishes endure one long night as well as those and other animals endure many in Greenland; or rather why not better then the tender substances wch were growing into animals might endure successions of short days and nights, and consequently of heat and cold? For what think you would become of an egge or embryo wch should frequently grow hot and cold? Yet if you think ye night too long, its but supposing the Divine operations quicker. But be it as it will, me thinks one of the Tenn Commandmts given by God in Mount Sina, prest by divers of ye prophets, observed by or Saviour, his Apostles, and first Christians for 300 years, and with a day's alteration by all Christians to this day, should not be grounded on a fiction. At least divines will hardly be persuaded to [be]lieve so.

"As I am writing, another illustration of ye generation of hills, proposed above, comes into my mind. Milk is as uniform a liquor as the chaos was. If beer be poured into it, and ye mixture let stand till it be dry, the surface of ye curdled substance will appear as rugged and mountainous as the earth in any place. I forbear to describe other causes of mountains, as the breaking out of vapours from below before the earth was well hardened, — the settling and shrinking of ye whole globe after ye upper regions or surface began to be hard. Nor will I urge their antiquity out of Prov. viii. 25, Job xv. 7, Psalm xc. 2, but rathe beg yor excuse for this tedious letter, which I have ye more reason to do, because I have not set down any thing I have well considered, or will undertake to defend."

There is no signature to this letter, but the whole is distinctly written in Sir Isaac's hand, and almost without any corrections or interlineations, which is very unusual in his manuscripts.

<455>

No. VII.

(Referred to in page 104.)

PART OF A LETTER FROM SIR ISAAC NEWTON ON FLAMSTEED'S SPECULATIONS RESPECTING THE SUN, THE ACTION OF HEATED MAGNETS, AND THE MOTION OF COMETS.

Concerning the experiment that a magnet loses its magnetism by heat, some have indeed supposed the sun to be cold, but I believe Mr. Flamsteed is not of this opinion, for they may as well affirm culinary fire to be cold. For we have no argument of its being not, but that it heats and burns things that approach it, and we have the same argument of the sun being hot. Were we ten times nearer him, no doubt, we should feel him an hundred times hotter, for his light would be there an hundred times more constipated, and the experiment of the burning glass shews that his heat is answerable to the constipation of his light. So then were a body hard by the sun, his light being there about 50,000 times more constipated, his heat would be 50,000 times greater than we feel it in a hot summer day, which is vastly greater than any heat we know on earth. Now, though the inward part of the sun were an earthy gross substance, yet if the liquid shining substance which Mr. Flamsteed supposes to swim upon it, be then hot, it will heat the matter within as certainly as melted lead would heat an iron bullet immersed in it. Nor is it material whether the liquid matter on the sun be of any considerable thickness. An iron bullet would heat as fast in a quart as in an ocean of melted lead, this difference only excepted, that the bullet would cool a small quantity of lead more than a great one. If then the liquid matter swimming on the sun be but so thick as not to be cooled by the central parts, (as it must be), it will certainly heat the central parts, for it imparts heat to the contiguous matter as fast as if it were thicker, and keeps of all cool environing mediums, (the instrument of cooling things,) from coming near the central parts to cool them. By which means the <456> central parts must become as hot, as if the hot fluid matter surrounding it equalled the whole vortex. The whole body of the sun, therefore, must be red hot, and consequently void of magnetism, unless we suppose its magnetism of another kind from any we have, which Mr. Flamsteed seems inclinable to suppose.

As for a great magnet exercising its directive virtue more strongly than its attractive on a small one, it holds in all cases I had opportunity to observe, and till a contrary instance can be brought, I am inclined to believe it holds generally. Mr. Flamsteed puts a case of a little magnet thrown violently by a great one. In this case, certainly, the motion of the small magnet neither helps nor hinders any part of the operation of the great magnet upon it, only that it shortens the time the great magnet has to operate in. Were the great magnet thrown along by the side of the little one, that it might have time enough to work on it, no doubt it would direct it as well as attract it. For do not magnets thus operate when trajected through the air in a ship under sail, more swiftly about the centre of the earth by the diurnal motion thereof, still more swiftly about the sun by the annual motion! And were the greater of the two magnets stopped, would it operate otherwise? Surely not. It would only want time to operate in. And if for want of time it directed not, much less would it attract or repel. If an instance could be found where a projected magnet is attracted or repelled by a fixed one, but not directed, it would be material. But such an instance, I doubt, will scarce be found. But if for want of time to perform the magnetical operations in, it be neither sensibly attracted, repelled, nor directed, it is nothing to the purpose. On the other hand, I add, that a resting magnet, if it have a large sphere of activity, so that it may have time to perform its operations before the projectile magnet be out of its reach, it will direct more strongly than attract, and I give this instance of it. Let the earth represent the great resting magnet, the mariner's needle a small one: this is directed as strongly by the earth when the ship is in its swiftest motion under sail, as when it rests, so far as observations have hitherto been made, and consequently were the ship ten times swifter, would still be as <457> much directed, and yet so little attracted by the earth as not to become sensibly heavier thereby. The case is the same with a comet continuing long within the reach of the sun's magnetism.

The instance of a bullet shot out of a cannon, and keeping the same side forward, may be a tradition of the gunners, but I do not see how it can consist with the laws of motion, and therefore dare venture to say that upon a fair trial it will not succeed, excepting sometimes by accident. The trial may be thus made upon a spell or bridge such as school-boys play with: lay a large ball, one hemisphere of which is white, the other black. Either hemisphere lying upwards, strike the edge of the bridge to make the ball rise, and if the ball receive not any circulating motion from the stroke, you will see the hemisphere which is laid upwards continue upwards as well falling as rising. If I did not know the event of the experiment by the reason of it, yet I could guess at it by what I have observed of a hand-ball tossed up.

To the foregoing objections may be added this: — If the comet be attracted in its access to the sun, and repelled in its recess, and so being continually accelerated would be swifter in its recess than in its access, contrary to what Mr. Flamsteed and others believe. For the magnetic repulse continually urging the comet to the sun, would make it go away faster and faster continually.

Another objection may be this: — Let S be the sun, ABCD the line of the comet's motion, according to the hypothesis, ABC that part in which the comet is attracted, CDF that part Figure <458> in which it is repelled. When the comet comes at C, being there neither attracted nor repelled, it ought to proceed on in the line of the determination of its motion CV, and verge neither to D on the one hand, nor to E on the other; but when it is advanced a little farther, and begins to be repelled, the repulse will not make it verge from the line of its motion's direction CV towards the sun, but drive it from the sun, that is it does not make it verge from CV towards D, but towards E, and so go away in the line CE. But I should have put the point where it begins to be repelled a little sooner, as at K. If to avoid this difficulty the comet be made to pass between the sun and us, that supposition is urged by the difficulty mentioned in my former letter. But all these difficulties may be avoided by supposing the comet to be directed by the sun's magnetism as well as attracted, and consequently to have been attracted all the time of its motion, as well as in its recess from the sun, as in its access towards him, and thereby to have been as much retarded in its recess as accelerated in his access, and by this continual attraction to have been made to fetch a compass about the sun in the line ABKDF, the vis centrifuga at C overpowering the attraction and forcing the comet there, notwithstanding the attraction, to begin to recede from the sun."

The date of the letter, of which this was intended to form a part, is April 16, 1681.

<459>

No. VIII.

(Referred to in page 114.)

LETTER FROM SIR ISAAC NEWTON TO DR. COVEL.

"Sr,

"I have had an account of the solemnity of the Proclamation; and I am glad to understand it was performed wth so much decence by the wiser and more considerable part of ye university, and generosity on yor part. The next thing is a book of verses. If you do it at all, ye sooner ye better. Concerning ye new Oaths wch you are to administer, I need not give instructions to you about their legality. But because many persons of less understanding (whom it may be difficult to persuade) will scruple at them, I will add my thoughts to yours, that you may have the fuller argument for convincing them, if I can add anything to what you have not thought of; ffor, seeing these Oaths are the main thing that ye dissatisfied part of ye University scruple, I think I cannot do the University better service at present than by removing the scruples of as many as have sense enough to be convinced wth reason. The argument I lay down in the following propositions: —

"1. Fidelity and Allegiance sworn to ye King is only such a ffidelity and obedience as is due to him by ye law of ye land; ffor were that ffaith and allegiance more than what the law requires, we should swear ourselves slaves, and ye King absolute; whereas, by the law, we are ffree men, notwithstanding those Oaths.

"2. When, therefore, the obligation by the law to ffidelity and allegiance ceases, that by the Oath also ceases; ffor might allegiance be due by the oath to one person, whilst by the law it ceases to him and becomes due to another, the oath might oblige men to transgress the law and become rebells or traitors; whereas the oath is a part of the law, and therefore ought to be so interpreted as may consist wth it.

"3. Fidelity and Allegiance are due by ye law to King Wil <460> liam, and not to King James. For the Statute of 25 Edw. 3, wch defined all treasons against ye King, and is ye only statute to that purpose, by the king understands not only a king de jure and de facto, but also a king de facto, though not de jure, against whom those treasons lye. Whence the Ld Chief Justice Hales, in his Pleas of the Crown, page 12, discoursing of that statute, tells us that a king de facto and not de jure, is a king within that Act, and that treason against him is punishable, tho' the right heir get the crown. And that this has been the constant sense of the law, Sr Robt. Sawyer also, upon my asking him about it, has assured me. And accordingly, by another statute in the first of Hen. 7, 'tis declared treason to be in arms against a king de facto, (such as was Richard the Third,) tho' it be in behalf of a king de jure. So then by ye law of ye land all things are treason against King William wch have been treason against former kings; and therefore the same fidelity, obedience, and allegiance wch was due to them is due to him, and by consequence may be sworn to him by ye law of ye land. Allegiance and protection are always mutuall; and, therefore, when K. James ceased to protect us, we ceased to owe him allegiance by ye law of ye land. And, when King W. began to protect us, we begun to owe allegiance to him.

"These considerations are in my opinion sufficient to remove ye grand scruple about the oaths. If ye dissatisfied party accuse the Convention for making ye P. of Orange King, 'tis not my duty to judge those above me; and therefore I shall only say that, if they have done ill, 'Quod fieri non debuit, factū valet.' And those at Cambridge ought not to judge and censure their superiors, but to obey and honour them according to the law and the doctrine of passive obedience.

"Yesterday a bill for declaring the Convention a Parliament was read ye 2d time and committed. The Committee have not yet finished their amendments of it. There is no doubt but it will pass. I am in haste,

"Yor most humble Servant,

"IS. NEWTON.

"LONDON, Feb. 21, 1688-9."

<461>

No. IX.

(Referred to in page 121.)

LETTER FROM JOHN LOCKE TO MR. NEWTON.

"LONDON, 26th July 1692.

"SIR,

"Finding noe better conveyance, I have sent you the 8th Chapter by Martin the carrier. It was delivered to his owne hands yesterday. I would beg yu, if yu have soe much leisure, to read, correct, censure, and send it back by the same hand this weeke, else I fear the presse will stay. I deferred it soe long, in hopes to send all together by a safe hand, missing that I have ventured but one chapter at once. As soon as this comes back, I will send the next.

"Mr. Boyle has left to Dr. Dickson, Dr. Cox, and me, the inspection of his papers. I have here inclosed sent you the transcript of two of them that came to my hand, because I knew you desired it. Of one of them I have sent you all there was; — of the other, only the first period, because it was all you seemed to have a minde to. If you desire the other periods, I will send you them too. If I meet with anything more concerning the process he communicated to you, you shall have it; and if there be anything more in relation to any of Mr. Boyle's papers, or anything else wherein I can serve you, be pleased to command,

"Sir,

"Your most affectionate and most humble servant,

"J. LOCKE.

"First Period.

"℞ ℔ x, cleanse it well with ℔ j of flowers of in 24 hours. To these ℔, take ℥ ij of minerel soap u 2, shake it with the , so as it may first imbody with it, and afterwards, by further agitation, be spued out by it. This worke may last 24 hours or <462> more. To the same , adde ℥j more of the soape, and worke as before. This doe 7 times. Then before any Durca be added, the matter must be kept in agitation as before for at least 7 days, for 'twill be the better (if it be forced in) adding no soap to it. The soap being to make it throw out any feculency that may lie concealed in in the forme of a powder, whereby the will remain the purer.

"℞ lb j of choice , and grind with it for 2 or 3 hours, or longer, if need be, ℥ j of our dry soap, till it have been aaa with it, and thrown out again in the form of an unpromising powder. Then put to it another dram of the soap, and proceed as before. Afterwards adde a 3d dram, and set aside the powder that will be thrown out as formerly, and thus impregnate the liquor with ℥ j after another, till you have incorporated with it, as far as you can doe it, by grinding a whole ounce."

<463>

No. X.

(Referred to in page 128.)

LETTER FROM DR. BENTLEY TO SIR ISAAC NEWTON.

"Feb. 18, 16923.

"HOND SIR,

"Understanding yt the publication of my sermons might be delayed a while without any damage to ye bookseller, I have kept them in my hands, and shall keep them a little longer. And, though there were yet several matters in them, about which I would have purchased your opinion at no small rate, nevertheless I had not presumed any further to interrupt your worthy design with questions from a stranger. But yr unexpected and voluntary favour by the last post doth encourage me to request you, yt you would run over this abstract and thread of my first unpublished sermon; and to acquaint me with what you find in it yt is not conformable to truth and your hypothesis. My mind would be very much at ease, if I have that satisfaction, before ye discourses are out of my power.

"Proved, in ye 6 son 'That ye present system of ye world cannot have been eternal. So yt matter being eternal (according to ye Atheists) all was once a chaos, yt is, all matter was evenly or near upon evenly diffused in the mundane spaces.'

"I proceed therefore in this 7th to shew, ye matter in such a chaos could never naturally convene into this or a like system. To which end we must consider some systematical phænomena of ye present world. And

"(1.) All bodies around our earth gravitate, even ye lightest comparatively, and in their natural elements.

"(2.) Gravity or ye weight of bodies is proportional to ye quantity of matter, at equal distances from ye center.

"(3.) Gravity is not peculiar to terrestrial bodies, but common to all ye planets and ye sun. Nay the whole bodies of sun and planets mutually gravitate toward one another; and in a <464> word 'all bodies gravitate toward all. This universal gravitation or attraction is ye τὸ φαινόμενον or matter of fact, for ye demonstration of which I must referr you to . . . . . Indeed as to the cause and origin of this gravity he was pleased to determin nothing. But you will perceive in the sequel of this discourse ye it is above all mechanism or power of inanimate matter, and must proceed from a higher principle and a divine energy and impression.' (I have written these words at large, yt you may see if I am tender enough, how I engage your name in this matter.)

"(4.) Now if gravity be proportional to ye qty of matter, there is a necessity of admitting a vacuū.

"(5.) And to estimate wh proportion ye void space in our system may bear to ye solid mass. Refined gold (though even yt be porous, because dissoluble in and aqua regia, and ye tanted non impossibility yt the figures of its corpuscles should be adapted for total contact) is to common water as 19 to 1, and water to common air as 850 to 1, so yt gold is to air as 16,150 to 1, so ye yt void space in the textur of con air is 16,150 times as big as ye solid mass. And because air hath an elastick endeavour to expand itself, and ye space it occupies, being reciprocally as its compression, the higher it is, 'tis ye less compressed and more rarefied, and at ye hight of a few miles it has some million parts of void space to one of real bodie; and at ye hight of 1 terr. semid, (as . . . . hath calculated,) tis so very tenuious, yt a sphære of our common air (already 16,150 parts nothing) expanded to ye thinness of yt region would more than take up ye whole orb of Saturn, which is many million millions of times bigger than all ye globe of ye earth: and yet higher above yt, ye rarefaction gradually increases in immensum. So yt the whole concave of ye firmament, except sun, planets, and atmospheres, may be considered as a mere void.

"(6.) Esto hypothesis; That every fixt starr is a sun; so yt the proportion of void space to matter yt is found in our sun's vortex will near upon hold in ye rest of ye mundane space. [I know what Kepler says, Epitome Astron. p. 36, therefore quæro, if this hypothesis may pass.] Allow then yt the globe of ye earth is entirely solid and dense, and yt all ye matter of our sun, pla <465> nets, atmospheres, and æther, is about 50,000 times as much as ye bulk of ye earth. Astronomers will bear us witness yt we are liberal enough. Now the Orbis Magnus (7000 terr. diam. wide) is 343,000,000,000 times as big as the whole earth, and therefore is 6,860,000 times as big as all ye matter of our system. But by the doctrine of ye parallaxis, we cannot well allow less (in ye Copernican hypothesis) than 100,000 diam. of ye Orb Mag: for the diameter of ye firmament. So yt the whole concave of ye firmament is (in ye 3plic. Prop.) 1,000,000,000,000,000 times as big as ye sphære of ye Orbis Magnus, and therefore (multiplying this by 6,860,000) it is 6,860,000,000,000,000,000,000 times as big as all ye matter of our system. So yt if all yt matter was eavenly disperst in ye concave of ye firmament, every corpuscle would have a sphære of void space around it 68,600 . . . . times bigger than its own dimensions: and ye diameter of ye sphære would be above 19,000,000 times longer than ye diameter of ye corpuscle, (supposing ye corpuscle to be sphærical.) And further, because of ye equal sphæres of other corpuscles about yt corpuscle, ye void space about every corpuscle becomes twice as wide as it was, having a diam. compounded of ye diameter of its own sphære, and ye 2 semidiameters of ye sphæres of ye 2 next corpuscles opposite, so yt every atom has a void space about it 8+68,600 . . . . times as big as ye atom, and would be distant 19,000,000 times its own length (if sphærical) from any other corpuscle. And by ye same supposition of equal diffusion in ye whole surface of ye void sphære about every atom whose diam. is 38,000,000 times as long as ye diam. of ye atoms, there can be no more than 12 atoms placed at equal distances from ye central one and from each other, (like ye center and angles of an icosaedron.) So yt lastly, every atom is not only so many million millions of times distant from any other atom, but if it should be moved and impelled (without attraction or gravitation) to ye length of yt distance, it is many more million millions odds to an unit, that it doth not hit and strike upon one of those 12 atoms. But ye proportion of this void to matter within our firmament, may hold in all ye other mundane spaces beyond it. [The measure of ye Orbis M. 7000 terrest. diam. and of ye firmamēt 100,000 diam. of ye Orbis Magnus I take from And: Tac <466> quet, being round numbers. If you substitute better instead of them, ye calculation may be soon altered.]

"I am aware, yt half of ye diameter of ye firm: should be allowed for ye radij of ye several vortices of ye next fixt stars, so yt the space of our sun's vortex should be diminished, as 8 to 1. But because ye semr. of ye firm. may be immensely greater thā we supposed it, we think yt abatement not worth considering.

"(1.) Now the design of all this is to shew, which (if ye premises be granted) is evident at first sight, yt in ye supposition of such a chaos, no quantity of common motion (without attraction) could ever cause these stragling atoms to convene into great masses and move, as they do in our systē, a circular motion being impossible to be produced naturally, unless there be either a gravitation or want of room.

"(2.) And as for gravitation, 'tis impossible yt that should either be coeternal and essential to matter, or ever acquired by it. Not essential and coeternal to matter; for then even our system would have been eternal (if gravity could form it) against our Atheists' supposition, and what we have proved in our last. For let them assign any given time, yt matter convened from a chaos into our system, they must affirm yt before yt given time matter gravitated eternally without convening, which is absurd. [Sir, I make account, yt your courteous suggestion by your last, yt a chaos is inconsistent with ye hypothesis of innate gravity, is included in this paragraph of mine.] And again, 'tis unconceivable, yt inanimate brute matter should (without a divine impression) operate upon and affect other matter without mutual contact; as it must, if gravitation be essential and inherent in it.

"(3.) But then if gravitation cannot be essential to matter, neither could it ever be acquired by matter. This is self-evident, if gravitation be true attraction. And if it be not true attraction, matter could never convene from a chaos into a system like ours, (paragraph 1.) Nay, even now, since ye forming of our system, gravitation is inexplicable otherwise than by attraction. 'Tis not magnetism, as you have shewn. 'Tis not ye effect of vortical motion; because it is proportional to ye Q of matter, for if the earth was hollow, there would be no less weight <467> of bodie in ye air (according to vortices,) than if it was solid to ye centre: there would be no less pressure toward ye sun, if ye whole space of ye sun were a mere void, than if a dense bodie. Again: A vortical motion, without gravitation antecedent to it, supposeth and requirs, either an absolute full, or at least a dense texture of ye æthereal matter; contrary to what is proved before, and what appears from ye motions of comets: and besides, as you have shewn, it contradicts ye phænomena of ye slower motion of planets in Aphelijs qua Perihelijs, and ye sesquialteral proportion of yr periodical motions to their orbs. In a word, if gravity be not attraction, it must be caused by impulse and contact; but yt can never solve universal gravitation, in all scituations, lateral as well as descending, &c., according to ye phænomena of your hypothesis.

"[Sir, to my conceptions, universal gravitation, according to your doctrine, is so impossible to be solved mechanically, yt I was much surprised to see you warn me what I ascribed to you, for you pretended not to know ye cause of it. As to innate gravity, you perceive yt it is wholy against my purpose and argumentation. If I used ye word, it was only for brevity's sake. But I must needs desire your judgment of wt is here deliver'd to yt purpose. I look't a little into Hugenius de la Pesanteur, when it newly came out, and I well remember that it cannot be reconciled to your doctrine; and Varignon's book I read, which, besides yt it cannot explain universal gravity, is confuted by ye most vulgar phænomena. He makes long filets of materia subtilis reach from ye top of ye earth's vortex to ye earth. All bodies descend yt are in ye lower half, because ye superior part of ye filets are ye longer. All ascend in ye higher half, for ye contrary reason. But in ye middle of them there is a considerable space of equilibriū, indifferent both to ascent and descent, wch he calls espace de repose, and in yt ye moon moves in a circle without ascending or descending very well. Therefore, in ye filets of ye Sun's vortex, all ye space between Mercury and Saturn is an espace de repose a small distance for ye equilibrium; so much longer than ye whole half of ye filets from Mercury to ye body of ye Sun.]

"(4.) But though we could suppose gravitation essential to <468> matter, or rather supervene into matter while it was diffused in a chaos, yet it could never naturally constitute a system like ours.

"(1.) For if matter be finite, and seeing extension is not matter, ye summe of ye mundane matter must consist of seperate parts divided and disterminated by vacuum; but such parts cannot be positively infinite, any more than there can be an actually and positively infinite arithmetical summe, which is a contradiction in terms. It may be said yt all bodies have infinite puncta, so yt there are infinite summs. Indeed at yt rate all numbers are infinite, as containing infinite fractions. Even fractions themselves are infinite. But such puncta are not quanta, so yt the case is different toto genere. Can a positive summe contain infinite ones, twos, or infinite given fractions? Can it have infinite quota and quanta as ye atoms we speak of are? I say, then, if matter be finite, it must be in a finite space. But, then, by universal gravity, in an even diffusion, all matter would convene in one mass in ye middle of ye space, and, if never so unevenly diffused, all would convene still into one mass, though not in ye middle of ye mundane space, but in ye center of ye common gravity.

"(2.) Nay, though we suppose it once constituted, even then, even now, all would convene together in a finite system. I grant, yt if ye whole world was but one sun, and all ye rest planets moving about him, they would not convene; but in several fixt starrs yt have no motion about each other, they, with their systems of planets, would all convene in ye common center of mundane gravity, if ye present world was not sustained by a Divine power.

"[Sir, in a finite world, where there are outward fixt starrs, this seems plainly necessary; but in ye supposition of an infinite space, let me ask your opinion. I acquiesce in your authority, yt in matter diffused in an infinite space, 'tis as hard to keep those infinite particles fixt at an equilibrium, as poise infinite needles on their points upon an infinite speculum. Instead of particles, let me assume fixt starrs, or great fixt masses of opake matter, is it not as hard yt infinite such masses in an infinite space should maintain an equilibrium, and not convene toge <469> ther; so yt, though our system was infinite, it could not be preserved but by ye power of God.]

"(3. ) Moreover, in such a chaos, though gravity should supervene to matter, ye planets could never acquire their transverse motions about ye sun, &c. If they were formed in ye same orbs they now move in, they could never begin to move circularly; ye ætherial matter could not impress it, for ye is too thin, and is indifferent to east or west, as appears from comets. Nor could gravity act in a horizontal line, as they move in where there is no inclination nor descent. Now, therefore, suppose the planets to be formed in some higher regions, and first descend towards the sun, wherby they would acquire their velocities; but then they would have continued their descent to ye sun unless a Divine power gave them a transverse motion against yt vast impetus yt such great bodies must fall with; so yt on all accounts there's a necessity of introducing a God.

"[As to what you cite from Blondel, I have read ye same in Hon. Fabri's Astronomia Physica, and Galilæo's System, p. 10 and 17, who adds, yt by the velocity of Saturn, one may compute at what distance from ye sun it was formed, according to ye degrees of acceleration found out by himself in the progression of odd numbers. (But he must surely have erred, not knowing wt you have since shewn, yt ye velocity of descent as well as weight of bodies decreases as ye square of ye distance increases,) and yt there is yt proportion of ye distances and velocities of all ye planets quam proxime, as if they all dropt from ye same hight. (But you seem to reject this, saying, yt the gravitation of ye sun must be doubled at ye very moment they reach their orbs.) I confess I could make no use of ye passage of Galilæo and Fabri, because I could not calculate, so yt I said no more, but in general as above, and ye rather because I knew that there must be some given hights, from whence each of them descending, might acquire their present velocities. But I own, yt if I could understand ye thing, it would not be only ornamental to ye discourse, but a great improvement of ye argument for a Divine power; for I think it more impossible yt they should be all formed naturally at ye same yn at various distances; and 'tis ye miracle of all miracles if they were naturally formed <470> at such intervals of time, as all of them to arrive at their respective orbs at ye very same moment, which is necessary, if I rightly conceive your meaning about doubling ye sun's attraction; for if Mercury fell first, and when he reached his own orb, ye sun's attraction was doubled. That continuing doubled, ye descents of ye succeeding planets would be proportionably accelerated, which would disturb ye supposed proportion betwixt Mercuries velocity and theirs.

"Hond. Sir, This is ye contents of ye former sermon; ye latter is an argument of a divine goodness from ye meliority in our system, above what was necessary to be in natural causality. I hope I shall have no need to give you more trouble in yt. But, Sir, while I am writing this, I have received a letter from my bookseller, calling away for ye press. Let me but begg of you, by the next post, some brief hints what you approve of, and what not; for I have resolved to expect your answer, let him be never so clamorous. Sr, I heartily ask your pardon for giving you the trouble of this, which I must increase likewise by another piece of boldness in desiring your good leave to present you with my 8 poor discourses when these 2 last are made publick.

"Sir, I am your most obliged & hu. sert,

"R. BENTLEY.

"For

The Hond. MR. ISAAC NEWTON,

Math. Prof, and Fellow

of TRINITY COLLEGE, in

CAMBRIDG.

"Post-Paid 5.'

<471>

No. XI.

(Referred to in page 147.)

LETTER FROM SAMUEL PEPYS TO MR. NEWTON.

"Dec. 21, 1693.

"SIR,

"If to what you have done, and which I can in noe wise sufficiently acknowledge your favour in, it could bee excusable to come once more to you upon ye same errand; it should bee to aske you whether B's disadvantage (in his contest with A) bee anything different under his obligation to fling 2 sixes at one throw with 12 dyes, from what it would bee were he to doe it twice with 6 dyes at a time out of one box, or at once out of 2 boxes with that number in each. I being yet (must owne) unable to satisfy my selfe touching ye difference, i.e., how it arises, though at ye same time you have putt mee beyond all doubt of A's having ye advantage in ye maine of B. Nor must I conceale my being at ye same losse how to comprehend, even flinging 12 dyes at one throw out of a single box, (ye sayd dyes being tinged 12 greene, 12 blew), they being lesse provided for turning up a six with either of these different-coloured parcells while flung together out of ye same box, then were ye 6 blew to bee throwne out of one box, and ye 6 greene from another; in which latter case, I presume each of them severally would bee equally entitled to the producing of a six with A's 6 white ones, and by consequence of 2 when flung together.

"I am conscious enough that this is but fumbling, and that it arises only from my not knowing how to make ye full use of your Table of Progressions; but pray bee favourable to my unreadinesse in keeping pace with you therein, and give mee one line of farther help. I am most thankefully, deare Sir,

"Your obliged and most humble

"and faythful servt,

"S. PEPYS."

<472>

No. XII.

(Referred to in page 152.)

1. — LETTER FROM DR. JOHN MILL TO MR. NEWTON.

"MY MOST HONOURED FRIEND,

"I am heartily sensible of your many signal favours and civilities to me when last at Cambridge. I hope you have not forgot your kind promise of remarking in paper your thoughts of the varieties you have met with in the Apocalypse. Whatever I have not observed already in my book, I would willingly add in my Appendix which is going on, and will have many things in it very considerable. My book, as long as it is with you, is in as safe hands as I can desire. If you please, you may take the first fair opportunity of conveying it hither. I think the best way will be by our Oxford carrier, if the waters be low enough. You may send for him, and put the book, carefully packed up, into his own hands. And if your servant go along with him and see it put up in his pack, it will do well; we cannot be too careful in a matter of this consequence. I have been mighty curious since I saw you last, in observing something which I have all along slighted as trivial hitherto, the points of distinction in the old Alexandrian copy. And now I find them extraordinary accurate and regular; there is but one note for all manner of distinctions indeed, and 'tis at the top of a word, as our modern Greek colon (:), but then 'tis placed with such exactness and caution everywhere, as to distinguish the notions and ideas in each clause and sentence, infinitely better than we could do with all our modern apparatus of distinctions. I am so very fond of their way of distinguishing the text, that I could heartily wish, when I collated the Beza MS., I had marked all the distinctions. For a last, may I presume to beg your favour to transcribe any one single page in the Greek, and to point it exactly according to the copy, 'twill be a mighty obligation.

<473>

"My most humble service to my noble worthy friend, your master, as also to Dr. Covel. He put an Arabic charm in my hands, which I have not yet returned. The next return of the carrier he shall surely receive it, with a translation of some part of it. I hope our common friend Mr. Laughton is well. Pray give him my thanks for all civilities.

"But I doubt I trespass upon your time and studies. I wish you all imaginable health and happiness, and remain ever, with the greatest sincerity of affection,

"Worthy Sir,

"Your most obedient humble servant,

"JO. MILL.

"ST. EDMOND HALL, OXON.

Novr. 7, 1693.

"These for the truly honor'd Mr. Professor NEWTON,

at his lodgings in Trinity College,

"CAMBRIDGE."

"2. — LETTER FROM MR. NEWTON TO DR. JOHN MILL.

"SR,

"I feare you think I have kept yor book too long: But to make some amends for detaining it so long, I have sent you not only my old collations so far as they vary from yours, but also some new ones of Dr. Covil's two MSS; ffor I have collated them anew, & sent you those readings wch were either omitted in yor printed ones, or there erroneously printed. In collating these MSS., I set the readings down in the margin of yor book, & thence transcribed them into a sheet of paper, wch you will find in your Book at ye end of ye Apocalyps, together wth my old collations, & a copy of a side of Beza's MS. The collations I send you of Dr Covil's two MSS. you may rely upon; ffor I put them into Mr. Laughton's hand wth ye two MSS., & he compared them wth ye MSS. and found them right. In the other collations you will find that Stephens made several omissions & <474> some other mistakes, in collating the Complutensian edition, tho' its probable that he collated this edition wth more diligence & accurateness than he did any of ye MSS. Where I have noted any readings of ye Alexandrin MS., I desire you would collate that MS. again wth my readings, because I never had a sight of it. I could not observe any accurateness in ye stops or commas in Beza's MS. You may rely upon the transcript of something more then a side of it, wch you will find in your Book at ye end of the Apocalyps. In your little MS. book, which I return you, tyed up together wth your New Testament, you will find those transcripts yon desired out of MSS., except two, wch were in such running hands yt I could not imitate them, nor did it seeme worth the while, ye MSS. being very new ones. — I am, in all sincerity,

"Yr most humble & most obedient servant,

"IS. NEWTON.

"TRIN. COLL. CAMBRIDGE,

Jan. 29, 16934"

This letter is followed by one leaf headed Spicilegia Variantium Lectionum in Apocalypsi ex MSS. Sin. et Cov. 2. It is written on both sides, and appears to be the "sheet" referred to in line 8 of Newton's letter. After this come two leaves containing three pages of various readings in the Apocalypse, which appeared to be "my old Collations," referred to in line 3d of the letter.

<475>

No. XIII.

(Referred to in page 119.)

TABLE OF REFRACTIONS SENT BY FLAMSTEED TO NEWTON.

I have thought it right, for the reasons mentioned in the note on page 169, to give the following table of refractions, communicated by Flamsteed to Newton, on the 11th October 1694, which has been omitted in the copy of the letter published by Mr. Baily in his Life of Flamsteed, p. 134.

Distantia visa a vertice.× Refr. and . Refr. simplex. Distantia visa a vertice.× Refr. and . Refr. simplex.
77° 00′2′ 00″3′ 30″88° 40′[13]19′ 30″
80 003 405 1088 5220 50
81 004 005 3089 0021 30
82 005 00 89 1123 20
83 006 00 89 2024 20
84 007 00 89 2725 30
85 008 00 89 3026 30
86 0010 00 89 3827 10
87 0012 3014 0089 4428 30
87 3013 30 89 4929 20
88 0016 00 89 5130 00
88 2517 25 89 5531 00
88 3518 45 90 0232 03
<476>

No. XIV.

(Referred to in page 203.)

LETTER FROM MR. FLAMSTEED TO MR. NEWTON.

THE OBSERVATORY, Jan. 2, 16989.

"SIR,

"I was in your neighbourhood on Saturday last, but thought it [not right] to disturb you with a visit when I had nothing to offer [excepting] my respects, and the usual wishes of many happy years,                 this. I had not troubled you now, but that on my way home I received a letter from Dr. Wallis, in which he mentions that I have received the packet (that is my [letter] on the parallax of the pole star,) and at the same time I received another letter from one in London, which desired me not to PRINT ANY PARAGRAPH OF THE LETTER WHICH SPEAKS OF YOUR GIVING MR. NEWTON OBSERVATIONS OF THE MOON. He is a friend of both of you, but he does not give his REASONS WHY. I thought but to acquaint you with it, and desire your advice upon it. Sr, I wrote my letter to Dr. Wallis in great haste, and when I had much other business in my hands, in November last, and to silence some busy people who are always asking why I did not print, I took occasion to let them know, that since the year 1689, when I was first fitted for it, I have been laying in a stock of observations to rectify the places of the fixed stars; that in 1694 I rectified my solar tables, and laid a foundation for the reclassification of the fixed stars; that in 1695 I furnished you with 150 observed places of the moon, and with the places also calculated from my tables, in order to the correction and restitution of her theory: That I had tables for abridging the labour (usually employed in calculating the stars' places from my data) under my hands and others, to make the catalogue more useful, and I wrote my letter in English, and the good Doctor having promised me a week's work as a recompense for my pains, I sent him word <477> that I would excuse that, if he would save me the labour of putting it into Latin. It was then but three sheets which (he accepting the condition) I sent him, and thereby gained time to copy six months' observations from my books, and furnish my country calculators with the right ascensions, &c., of the stars in the southern constellations, to calculate their longitudes and latitudes from. In a fortnight's time I received two of the three sheets from the Doctor loose in a wrapper, from Dr. Gregory, with directions to leave them, when perused, (for him to return,) at Mr. Hindmarsh's, a bookseller's shop, where the nonjurats resort, in Cornhill. The third sheet soon followed, but on perusal of them I found it was requisite to add almost another, to explain some places where I had been too short, or where the Doctor, not having thoroughly understood my meaning, (by reason he had not seen my instruments, nor was acquainted with my methods,) had not expressed it as I would myself. This took me up more time than I expected, which made me to send my packet by the post, lest Dr. Gregory should not convey it so soon to the Doctor as I desired. However, I gave Dr. Gregory notice that I had returned it, and he was as diligent to write to Dr. Wallis as above, for what occasion I know not. I shall give you the whole paragraph wherein I have mentioned my accommodation of you with materials, and I assure you I have not mentioned you on that account any where besides in my letter, onely [in] the book I have, where I shew that if we allow the nutation, this parallax must be greater, as much as it is. My words are these: — 'Contraxeram etiam cum Do Newtono doctissimo tunc temporis in academia Cantabrigiensi Professore necessitudinem cui lunæ loca ab observationibus meis ante habitis deducta 150 dederam, cum locis simul è tabulis meis ad earum tempora supputatis tum similia in posterum prout assequerer promiseram cum elementis calculi mei in ordine ad emendationem theoriæ lunaris Horroccianæ qua in re spero eum successus consecuturum expectationi suæ pares.'

"Sr, this is the paragraph, and all of it. I think there is not near so much in it as I acknowledge to myself, and (I have heard from other worthy gentlemen) you have acknowledged to them, and therefore cannot think it was from any intimation of <478> yours (tho' he says it wd be displeasing to you if it were printed,) but out of a design to ingratiate with you that he put an arrest upon this paragraph. I think the word Horroccianæ may be omitted, tho' I put it in because you allow that theory as far as it goes, you found the faults of it by the differences from my observation. He was a countryman, and tho' your theory will be new in that (tho' you give us the reasons, and derive it from natural cause,) yet he gave the groundplot, and it will be an honour both to you and me to do him justice.

"Sr, My observations lie the king and nation in at least 5000lb I have spent above 1000lb. out of my own pocket in building, instruments, and hiring a servant to assist me now near 24 years. 'Tis time for me (and I am now ready for it) to let the world see I have done something that may answer this expense, and I therefore hope you will not deny me the honour of having said that I have been useful to you in your attempts to restore the theory of the moon. I might have added the observations of the comets, places given you formerly of the superior planets, and observations at the same time with the moons, but this I thought wd look like boasting, and therefore I forbore it.

"I desire you would please to let me know by a line whether Dr. Gregory ever shewed you my letter, I mean Dr. Wallis his translation of it, which I think I have altered in the paragraph above from what it was, but cannot say in what words, because I returned the Doctor his copy, with my transcript of it enlarged and altered, together; but whenever 'tis printed, you will find it agree with the copy above exactly.

"Sr, I am told Dr. Gregory is to be tutor in mathematics to the Duke of Gloucester, which place, I was told some months ago (when the settling of his household was first discourst of) was designed for me. To make a variance betwixt you and me and Dr. Wallis, and to engage you to procure him the favour of Mr. Montague, I am apt to believe he recommends himself in this business. He thinks, perhaps, it will depreciate me, and keep me from being his competitor. Let him not trouble himself. I have an interest much beyond his whenever I please to move that way, but I do not think the Duke yet fit for a mathe <479> matical tutor, or that he will be this four or five years. I hate flattery, and shall not go to court on this account till I am sent for, or have notice that I am desired. That place might, indeed, afford me the opportunity of procuring help for my assistance, or I could defray the charges out of pay; but I fear it would be as prejudicial to me otherwise, and therefore shall not move to traverse the Doctor's designs, except he force me to it by his treacherous behaviour.

"Sr, I beg an answer to this letter speedily, and you need tell me no more but that you have seen the paragraph before, or not seen it; that you gave such orders to Dr. Gregory or not, that I may return an answer to Dr. Wallis; and hereafter, if any such flatterers as he come to say any thing to you that may tend to make a difference betwixt us, pray tell them you will inform me, and you will forthwith be rid of them. I shall always use the same course towards you, whereby a friendship that began early may continue long and be happy to both of us, which, through God's blessing, I hope it may, at least I shall always endeavour it, being ever, Sr,

"Your most affectionate friend and humble servant,

"JOHN FLAMSTEED, M.R.

"Pray enquire what company Dr. Gregory keeps, that you may not be deceived in his character. The Scotch think to carry all before them by the Bp of Salisbury, whom I esteem, (next the Bp of Wester above the rest of the clergy,) but I cannot think him wise in placing his countrymen about the young Duke.

"To MR. ISAAK NEWTON

Warden of the Mint,

at his house in German Street, near

St. James's, London. — These present."

Owing to the great decay of the paper, the first lines of this letter are hardly legible.

<480>

No. XV

(Referred to in page 225.)

ARTICLES OF AGREEMENT BETWEEN CHURCHILL, FLAMSTEED, AND THE REFEREES.

"Articles of agreement made this day of October,[14] in the fourth year (1705) of the reign of our Sovereign Lady Anne, by the grace of God Queen of England, Scotland, France, and Ireland, Defender of the Faith, &c., between the Honourable Francis Robarts, Esq., Sir Chr. Wren, Kt., Sir Is. Newton, Kt., David Gregory, Doctor of Physic, and John Arbuthnot, Doctor of Physic, on the one part; Mr. John Flamsteed, Her Majesty's Astronomer at the Observatory in Greenwich, on the other part; and Mr. Aunsham Churchill of parish, in London, on the third part.

"Whereas His Royal Highness Prince George of Denmark, out of his great generosity and propension to encourage arts and sciences, hath been pleased to defray the charges of printing all the Astronomical Observations of the said Mr. John Flamsteed made at the said Observatory, in a book entitled Historia Cœlestis, and to refer the care and management of the said impression to the said Fr. Robarts, Esq., Sr Chr. Wren, Sr Is. Newton, Dr. Gregory, and Dr. Arbuthnot; and whereas the said referees, by and with the consent of the said Mr. John Flamsteed, have treated with the said Mr. Aunsham Churchill for printing the same, it is hereby covenanted and agreed between the said parties as followeth:—

"I. That the said Aunsham Churchill shall print, or cause to be printed, four hundred copies, well corrected, and only four hundred copies of the said Historia Cœlestis, upon the same paper, and with the same letter with the paper and letter in the specimen hereunto annexed; and for every 400 copies of every <481> sheet so printed off, shall receive the sum of thirty and four shillings.

"II. That for making the impression correct, the said A. Churchill, at his own proper cost and charges, send the corrected proof of every sheet to the place appointed, or to be appointed by the said referees, to be there further corrected, compared with the original, and allowed by the said Mr. J. F. or his order, before the same be printed off.

"III. That the said Mr. J. F., or his said order, shall have access to the press at all times, and be allowed to stand by the same while the said number of 400 copies of any sheet or sheets shall be printed off, and then to break the press without delay, let, hindrance, or molestation of or from him the said A. Ch. , or his printer, or printers, their servants or agents, or any of them, on any pretence whatever.

"IV. That the 400 copies of every sheet, within 14 days after the same shall be printed off, shall, at the charge of the said A. Ch., be sent to the order of the said referees, to be kept for his Royal Highness till the whole be printed off, excepting the two last copies of the sheet, or two copies last printed off, which, at the charges of the said A. Ch., shall be sent the one to the said J. Fl., or his order, the other to the order of the said trustees, to be examined and collated with the last proof, and with the original papers of the said Mr. J. F.; and that every sheet in which any error shall be found, which is not the error of the copy, be corrected, and shall be reprinted at the sole cost and charges of the said A. Ch., both for paper and printing.

"V. That the said A. Ch. shall set five sheets per week, abating only a sheet for every holiday, provided that the said A. Ch. be supplied with sufficient MS. copy, and that sufficient dispatch be made in correcting the proof-sheets.

"VI. That within two months after the said book shall be in the press, the said referees, or the major part of them, shall sign an order for the said A. Ch. to receive of the Treasurer of His R. Highness the sum of three hundred pounds, advanced in part of payment, for the paper and printing of the said book. And after the impression of the said book shall be finished, the said referees, or the major part of them, shall sign an order for the <482> said A. Ch. to receive the remainder of the money which, after the rate of 34s. per sheet, shall then be due to him, the said A. Ch., for the paper and printing of the whole impression.

"VII. That the said A. Ch. shall not have, or claim, or endeavour to have, any right, title, or interest, either in the original copy or in the printed copies or any part thereof."

On another leaf of the same sheet, though not immediately following the preceding articles, I find the following articles relating to Flamsteed, which, like the preceding, are written in Newton's own hand, and afford ample materials for the defence of the referees.

ARTICLES OF AGREEMENT BETWEEN FLAMSTEED AND THE REFEREES.

"I. That the book shall be printed in two volumes, the first to consist of three parts, namely: —

"1st, The catalogue of the fixed stars.

"2d, The observations of the fixed stars, planets, &c., by the sextant, telescope, and micrometer, from the year 1675 to the year 1689 inclusively; and

"3dly, The places of the planets and comets computed from those observations, together with a general Preface.

"The second to consist of two parts, viz.: —

"1st, Observations made by the wall quadrant, telescope, and micrometer in and after the year 1689, until the finishing of the impression.

"2dly, The places of the planets and comets computed from them.

"II. That Mr. Flamsteed shall, with all convenient speed, prepare and deliver in to the said referees or their order, fair and correct copies of his Catalogue of the fixed stars, and of the observations to be printed in the two volumes, with fair and correct schemes in folio, of the figures of eclipses, and other telescopic phenomena, to be graved in copper plates. And that within months he shall deliver in to the said referees a fair copy of the observations to be printed in the second volume.

"III. That the said Mr. John Flamsteed shall, with all con <483> venient despatch, compute, or cause to be computed, the places of the planets which remain to be computed, and deliver in to the said referees fair and correct copies of all their true places, computed from the observations and well corrected, to be printed in the two volumes at the end of the Observations.

"IV. That after the first volume shall be printed off, the said referees shall sign an order for the said Mr. Flamsteed to receive of the trustees of His Royal Highness, for the charges of copying the same, and correcting the press, the sum of fifty pounds, and for the charges of computing the apparent longitudes and latitudes of the planets in that volume (not exceeding hundred l. and lat.) after the rate of 1s. 6d. per place; and for computing the true longitudes and latitudes of the moon from the apparent places, not exceeding        places, after the rate of 1s. 6d, per place. And after the second volume shall be printed off, they shall sign a like order for the said Mr. John Flamsteed to receive £50 more for copying and correcting the same, after the rate of 6d. (?) per place for computing the places of the other planets in longitude and latitude, not exceeding        places, and after the rate of 1s. 6d. per place, for computing the true longitudes and latitudes of the moon, not exceeding        places, provided the computation be performed exactly to the satisfaction of the said referees.

"V. That the said John Flamsteed shall suffer the said referees, or their order, or any of them, to collate the said fair MS. copies and schemes, and also the printed copies, with all or any of the original papers in his custody, from whence the said MS. copies and schemes were taken, and with the first minutes from whence those papers were drawn up, and for that end shall, at the request of the said referees, lend the said papers and minutes, or any part of them, to the order of the said referees, the person to whom they are lent giving a receipt for the same.

"VI. That the said Mr. John Flamsteed shall, before next Michaelmas,[15] fairly describe schemes in folio of a fit size for the book containing the figures of the eclipses and other telescopical observations proper to be described, of the same magnitude as in the MS., and shall assist a graver with his directions for graving <484> the same in copper-plate, and examine the plates and correct their faults, so that the schemes may be exact, and the said [graver] shall roll off, or cause to be rolled off, four hundred schemes from every plate, upon four hundred sheets of the same paper with that of the book, to be bound up with the book in such a manner that they may be laid open readily and conveniently."

On the back of the folio page which contains the preceding articles, and immediately after them, I find the following paragraph, which is not numbered, but which seems to be an alternative mode of paying Flamsteed instead of the one in Art. IV.

"That the said referees, or the major part of them, shall also sign orders for the said Mr. John Flamsteed, to receive of the said Treasurer of H. R. H. the sum of two hundred and [fifty] pounds for his charges in agents, servants to calculate observations, copy papers and schemes, and correct the press, the one half thereof to be paid so soon as the first volume of the said book shall be printed off,[16] and the other half thereof to be paid as soon as the second volume of the said book shall be printed off, provided the same Mr. John Flamsteed shall well and truly observe, perform, fulfil, and keep all and singular the articles, covenants, and agreements above-mentioned, specified and declared, which on his part ought to be observed, performed, fulfilled, and kept."

Immediately after this, I find the following additional article in reference to A. Churchill.

"That the said Mr. A. Ch. shall be bound in £1000 to perform, the articles on his part."

It is obvious that Flamsteed was acquainted with these articles, as he refers to Article V. in his letters to A. and F. Churchill of the 24th May and the 7th June 1706, and in his letter to Sir Christopher Wren. — See Baily's Flamsteed, pp. 224, 225, and 88, line 5.

<485>

No. XVI.

(Referred to in page 237.)

The following are the cancelled and the substituted paragraphs in Flamsteed's letter to Sir Christopher Wren, dated 19th July 1708: —

The following is the concluding paragraph in the original letter, but cancelled in the copy inserted by Mr. Baily in Flamsteed's Autobiography: —

"I am not only willing, but desirous, that the press should proceed to finish the first volume of Observations. I have spoke to Mr. Hodgson to take care of correcting the second proofs, and with him I shall leave the six sheets to be added; which when they are wrought off, Sir Isaac Newton has 175 sheets of the second volume in his hands, that the press may proceed with whilst I am completing the Catalogue, so there need be no stop on my account, as there never was, nor hereafter shall be, God sparing me life and health, and prospering, as I firmly believe he will, my sincere endeavours.

"I am, with all due respect, and for all your favours,

"Yr grateful and obliged humble servt.,

"JOHN FLAMSTEED, M. R.

"I think to send a copy of this letter to Mr. Roberts, and doubt not but he will imparte the contents of it to Sir Isaack Newton."

N.B. — The last three lines of the letter, from "I am, &c., to M. R.," and the postscript, are in Flamsteed's hand-writing.

The following are the concluding paragraphs substituted in the pretended copy taken from the original by Flamsteed himself: — [17]

"I am as willing as you can be that the press may proceed: but to have it hurried on at this time, when I cannot possibly <486> look after it, and only to find a printer in work who at other times has neglected it, would be a piece of folly, for which I am confident all the referees would condemn me. I must therefore entreat them that this resolve be suspended till my return out of the country; when, God sparing me life and health, I hope, with the assistance of the referees, to put the press into such a method, as it may have no stops, if any heed may [be] given to my advice.

"I beg your pardon for so long a letter: the occasion has forced me to be more troublesome than I ought to one of your age and employment. If you excuse me now I hope no further occasion will be of repeating it: and I shall ever own myself,

"Sir, your most obliged and humble servant,

"JOHN FLAMSTEED, M.R."

<487>

No. XVII.

(Referred to in pages 226, 240.)

The following document, which I found in a state of decomposition, contains an account of the expense incurred by the Prince's referees, and also that which was incurred by the Government in completing the Historia Cœlestis, as edited by Halley. It is in Sir Isaac Newton's handwriting, and on the back of a folio containing his observations on Bernoulli's letter of the 7th June 1713: —

"Charge.

"I received of Edward Nicolas, Esq., at one time, £250, at another, £125 — total received,£37500
"Upon reckoning with the Prince's administrators, I paid back the balance of the account, the same being2530
£349170

"Discharge.

"Paid to Mr. Churchill for paper and printer,£194170
"To Mr. Flamsteed for his copy,12500
"To Mr. Machin, for correcting the copy by the minute-book and examining some calculations,[18]3000
£349170

"Some time after this Dr. Halley undertook to finish the book, and the referees of the Prince acted no further, and after <488> the work was finished and the accounts stated, moneys were impressed to me without account to pay them off.

"Charge.

"Received,£364150

"Discharge.

"Paid to Mr. Churchill for paper and printing,£98110
"Paid for designing and graving the draughts and rolling off the plates,1164712
"Paid to Dr. Halley,15000
£36415712

"Besides £20 paid to Senr Catenaro, which I did not bring to account."[19]

See Flamsteed's Autobiography, p. 102, where he has given an impertinent account of these transactions. Flamsteed met Newton at the Exchequer, when he was "passing his accounts there concerning the disbursement of the Prince's monies." He told Flamsteed of the additional £20 given to Catenaro, but he did not tell him that he paid it out of his own pocket; and Flamsteed considers it as part of the Prince's money, "thrown away by Newton only to shew his liberality." The above Charge and Discharge is the account which Mr. Baily tells us he was not able to get a sight of. — Baily's Flamsteed, p. 102, note.

<489>

No. XVIII.

(Referred to in page 241.)

LETTER FROM SIR ISAAC NEWTON TO MR. FLAMSTEED.

"SIR,

"By discoursing with Dr. Arbuthnot about your Book of Observations which is in the press, I understand that he has wrote to you by her Majesty's order, for such observations as are requisite to complete the Catalogue of the Fixed Stars,[20] and you have given an indirect and dilatory answer. You know that the Prince had appointed five gentlemen to examine what was fit to be printed at his Highness's expense, and to take care that the same should be printed. Their order was only to print what they judged proper for the Prince's honour; and you undertook, under your hand and seal, to supply them therewith, and thereupon your Observations were put into the press. The Observatory was founded to the intent that a complete catalogue of the fixed stars should be composed by observations to be made at Greenwich, and the duty of your place is to furnish the observations. But you have delivered an imperfect catalogue, without so much as sending the observations of the stars that are wanting, and I hear that the press now stops for want of them. You are, therefore, desired either to send the rest of your catalogue to Dr. Arbuthnot, or at least to send him the Observations which are wanting to complete it, that the press may proceed. And if instead thereof you propose any thing else, or make any excuses or unnecessary delays, it will be taken for an indirect refusal to comply with her Majesty's order. Your speedy and direct answer and compliance is expected."

This draft of a letter to Flamsteed must have been written immediately after the 23d of March 1711, the date of Flam <490> steed's answer to Dr. Arbuthnot's application in the name of the Queen, on the 14th of the same month. In the letter to Arbuthnot, which Newton justly characterizes as "indirect and dilatory," Flamsteed tells him that "a great deal more help is requisite, and must he procured to calculate the new Tables and the planets' places therefrom, to render the work complete, worthy of the British nation, the name it bears, her Majesty's patronage, and to commend the memory of his Royal Highness to posterity;" and he proposes that he should discourse with him a few hours, and, for that purpose, come and dine with him. The Royal Observatory was founded, as Newton states, to form a complete catalogue of the fixed stars, and Flamsteed was made Astronomer-Royal, or Astronomical Observator, as he was then called, for this very purpose.

<491>

No. XIX.

(Referred to in page 274.)

LETTER FROM M. MONTMORT TO BROOK TAYLOR.

"Avril 12, 1716.

"Ce seroit dommage que ce bon vin fut bu par des commis de vos douanes: étant destinè pour des bouches philosophiques, et la belle bouche de Mademoiselle Barton. Je suis infiniment sensible à l'honneur qu'elle (Mlle Barton) me fait de se souvenir de moy. J'ai conservé l'idée du monde, la plus magnifique de son esprit, et de sa beauté. Je l'aimois avant d'avoir l'honneur de la voir, comme nièce de Mr. Newton, prevenu aussi de ce que j'avois entendu dire de ses charmes même en France. Je l'ai adorée depuis sur le temoignage de mes yeux, qui m'ont fait voir en elle, outre beaucoup de beauté, l'air le plus spirituel et le plus fin. Je crois qu'il n'y a plus de danger que vous luy fassiez ma déclaration. Si j'avois le bonheur d'estre auprès d'elle; je serais aussitot et aussi embarassé que je le fus la première fois. Le respect et la crainte de luy deplaire m'obligeroit ce [de] me taire et à luy cacher mes sentimens. Mais à 100 lieues loin et separé par la mer je crois qu'un amant peut parler sans être temeraire, et une dame d'esprit souffrir des déclarations sans qu'elle puisse se reproché[r] d'avoir trop d'indulgence. Il vint icy, il y a quelques jours, une personne de sa part. Je n'y étois pas, vous pouvez croire qu'il fût bien reçu par Madme de Montmort aussitot qu'il se fut nommé de Madelle Barton. Il ne voulust point dire ce que l'amenoit, il dit seulement qu'il reviendroit. Madme de Montmort jugea que c'est une personne qui fait icy des commissions pour des personnes de qualité d' Angleterre. Je voudrais bien que Madlle Barton voulust m'honorer du soin du luy faire les emplettes et de me faire son comissionaire. Outre le plaisir de servir une si belle personne j'aurais celui de m'acquitter envers Mr. Newton d'une partie des obligations que je luy ai."

<492>

No. XX.

(Referred to in page 278.)

EXTRACTS FROM SWIFT'S LETTERS TO STELLA, IN WHICH MRS. BARTON AND LORD HALIFAX ARE MENTIONED.

"1710, Sept. 28. — I dined to-day with Mrs. Barton alone at her lodgings."[21]

"1710, Oct. 1. — To-morrow I go with Delaval, the Portugal envoy, to dine with Lord Halifax at Hampton Court."

"1710, Oct. 13. — Lord Halifax is always teasing me to go down to his country house,[22] which will cost me a guinea to his servant, and twelve shillings coach hire, and he shall be hanged first. Is not this a plaguy silly story? But I am vexed at the heart, for I love the young fellow, and am resolved to stir up people to do something for him. He is a Whig, and I'll put him upon some of my cast Whigs, for I have done with them, and they have, I hope, done with this kingdom for our time."

"1710, Oct. 14. — What, another! I fancy this is from Mrs. Barton; she told me she would write to me, hut she writes a better hand than this."

"1710, Nov. 28. — Lord Halifax sent to invite me to dinner, where I staid till six, and crost him in all his Whig talk, and made him often come over to me."

"1710, Nov. 30. — To-day I dined with Mrs. Barton alone."

"1710, Dec. 19. — I visited Mrs. Barton."

<493>

"1711, Jan. 23. — I called at Mrs. Barton's, and we went to Lady Worsley's,[23] where we were to dine by appointment."

"1711, Jan. 24. — As for my old friends, I never see them, except Lord Halifax, and him very seldom."

"1711, March 7. — Mrs. Barton sent this morning to invite me to dinner, and there I dined just in that genteel manner that M. D. (Stella and Dingley) used, when they would treat some better sort of body than usual."

"1711, April 3. — I was this morning to see Mrs. Barton. I love her better than any body here, and see her seldomer. Why really now, so it often happens in the world that when one loves a body best — psha, psha, you are so silly with your moral observations."

"1711, April 10. — I have been visiting Lady Worsley and Mrs. Barton to-day."

"1711, May 29. — Pr'ythee, don't you observe how strangely I have changed my company and manner of living? I never go to a coffee-house; you hear no more of Addison, Steele, Henley, Lady Lucy, Mrs. Finch, Lord Somers, Lord Halifax, &c."

"1711, July 6. — An ugly rainy day; I was to visit Mrs. Barton."

"1711,July 18. — To-day I took leave of Mrs. Barton, who is going into the country."

"1711, Oct. 9. — I lodge, or shall lodge by Leicester Fields. . . . Did I tell you that my friend Mrs. Barton has a brother drowned, that went on the expedition with Jack Hill? He was a Lieutenant-Colonel, and a coxcomb; and she keeps her chamber in form, and the servants say she receives no messages."

"1711, Oct. 14. — I sat this evening with Mrs. Barton; it is the first day of her seeing company; but I made her merry enough, and we were three hours disputing upon Whig and Tory. She grieved for her brother only for form, and he was a sad dog."

"1711, Oct. 25. — I sat this evening with Mrs. Barton, who is my near neighbour."[24]

"1711, Nov. 20. — I have been so teased with Whiggish dis <494> course by Mrs. Barton and Lady Betty Germaine,[25] never saw the like. They turn all this affair of pope-burning into ridicule, and indeed they have made too great clutter about it, if they had no real reason to apprehend some tumults."

"1711, Nov. 28. — I am turned out of my lodging by my landlady, but I have taken another lodging hard by in Leicester Fields."

"1711, Dec. 16. — I took courage to-day, and went to Court with a very cheerful countenance. It was mightily crowded; both parties coming to observe each other's faces. I avoided Lord Halifax's bow till he forced it on me, but we did not talk together."

After reading the preceding passages, it would be difficult to understand how Mrs. Barton, whom Swift esteemed and loved, could have ever resided under the roof of Lord Halifax as his mistress.

The following letter[26] endorsed by Swift, "My old friend Mrs. Barton, now Mrs. Conduitt," is the only one of hers that has been preserved: —

GEORGE STREET, November 29, 1733.

"SIR,

"Mrs. Barber did not deliver your letter till after the intended wedding brought me hither. She has as much a better title to the favour of her sex than poetry can give her, as truth is better than fiction, and shall have my best assistance. But the town has been so long invited into the subscription, that most people have already refused or accepted, and Mr. Conduitt has long since done the latter. I should have guessed your holiness would rather have laid than called up the ghost of my departed friendship, which since you are brave enough to face, you will find divested of every terror, but the remorse that you were abandoned to be an alien to your friends, your country, and yourself. Not <495> to renew an acquaintance with one who can twenty years after remember a bare intention to serve him, would be to throw away a prize I am not now able to repurchase; therefore, when you return to England, I shall try to excel in, what I am very sorry you want, a nurse. In the mean time I am exercising that gift to preserve one who is your devoted admirer.

"Lord Harvey has written a bitter copy of verses upon Dr. Sherwin, for publishing, as 'tis said, his Lordship's epistle, which must set your brother Pope's spirits all a working. Thomson is far advanced in a poem of 2000 lines, deducing liberty from the patriarchs to the present time, which, if we may judge from the press, is now in full vigour. But I forget I am writing to one who has the power of the keys of Parnassus, and that the only merit my letter can have is brevity. Please therefore to place the profit I had in your long one to your fund of charity, which carries no interest, and to add to your prayers and good wishes now and then a line to

"Sir, your obedient humble servant,

"C. CONDUIT."

"Mrs. Barber, whom I had sent to dine with us, is in bed with the gout, and has not yet sent me her proposals."[27]

<496>

No. XIX.

(Referred to in page 291.)

1. — LETTER FROM VARIGNON TO NEWTON.

"Nobilissimo Doctissimoque Viro

"D. D. Newtono Equiti Aurato

"Regiæ Societatis Anglicanæ Præsidi Dignissimo

"S. P. D. Petrus Varignonius.

"Exoptatissimam mihi Effigiem tui, quâ me donare dignatus es, vir humanissime ac munificentissime, gaudenti gratissimoque animo nuper accepi. Tui spectandi percupidus capsam statim distraxi, evolutâque telâ, in hujus effigiei vultu et fronte et oculis quasi spirans mihi visum est tuum summum atque eminens ingenium cum oris dignitate conjunctum, etiamnumque videtur. Paucis post diebus venit ad me Cl. Taylorus (quatuor abhinc vel quinque mensibus hic habitans) qui eam intutus attente, suo usus conspicillo, tibi simillimam esse pro certo mihi affirmavit; quod admodum me delectavit ac delectat. Porro sculptam alteram tui imaginem, jam inde a decem circiter annis habebam ex dono amici Angli (Oxoniensis nomine Arnold) qui cum me sæpius de te magnalia loquentem audisset, reversus Londinum, illinc eam ad me misit, pergratam mihi fore existimans: recte quidem. Sed cum Sculpta tui similitudinem ex vero non effingat æeque ac picta, hanc nihilominus semper exoptavi, quâ nunc mihi datur videre tandem illustrissimum ac doctissimum eum virum quem amplius triginta annos summâ veneratione colebam ob ingentia ejus merita presertim in Mathesim quam promovit et auxit immensum, cujusque legibus astrictam primus demonstravit esse Naturam. Quantas autem pro tanto dono (quod antea pecuniæ summâ quâvis emissem si aliunde quam a perhonorifica mihi tuæ liberalitatis magnificentiâ obtinere potuissem) gratias agere tibi debeam, optime <497> intelligo et intime sentio. Sed tantas ut eas expedire verbis nequeam; nec etiam eas quas habeo tibi maximas pro eo quod me monuit Cl. Moivræus te non dedignari mei quoque imaginem quam nudiusquartus idcirco misi Do Ayres (capellano D. D. Equitis Sutton, excellentissimi legati vestri apud nos) in longiore capsula volutatam, quam pridie mihi officiosissime promiserat se missurum fore Londinum ad Dum Preverau (apud D. D. Craggs Sanctioris consilii Anglicani commentariensem) ut eam tibi reddat, quam benigne accipias rogo. Vale, mihique tuorum in me Beneficiorum æternum memori favere perge.

"Dabam Parisiis, Die 28th Novemb. 1720, N. S.

"P.S. — Post Scriptam hanc Epistolam D. Nicole ex Angliâ recens me invisit ac monuit, dum apud te pranderet, aut cœnaret, propinasse te toti generatim academise nostrtæ Parisiensi, speciatimque Cl. Fontenelle, ac etiam mihi; pro quo honore novas habeo tibi gratias et ago maximas. Contemplatus etiam Dus Nicole pictam effigiem tui, de eâ censuit penitus idem ac D. Taylorus, nimirum eam tibi persimilem esse; quod raeum de eâ obtentâ gaudium auxit."

2. — LETTER FROM NEWTON TO VARIGNON.

"Viro celeberrimo Dno Abbati Varignon Regio Mathesis Professori et Academiæ Scientiarum Socio apud Parisienses

Is. Newtonus S. P. D.

"Clarissime Dno,

"Accepi Historiam et Commentaria ex Archivis Academiæ Scientiarum pro anno 1719, pro quibus gratias tibi reddo quammaximas. Accepi etiam schedam primam Libri de Coloribus elegantem sane et specie nobilem. Et ne Dnus Montalanus expensa moleste habeat dabo illi libras viginti sterlingas, et expensa compingendi libros insuper solvam. Gratias tibi reddo quamplurimas quod insinuasti libros plures amicis donandos esse, scilicet Cardinali Polignac, et filio Cancellarii, et Bibliothecæ Academiæ. Vellem et alios donandos esse filio et nepoti D. <498> Joannis Bernoullii, et alios Abbati de Comitibus,[28] et P. Sebastian, et D. Remond. Sed et gratias tibi maximas reddo quod onus in te suscipere digneris conferendi correctiones Dni Coste et Dni Moyvre inter se, et quod optimum videbitur eligendi; ut et emendandi qæcunque alia occurrerint. Metuebam utique ne correctiones Dni Coste, inter plurima tua negotia, molestiam nimiam tibi crearent. Sed cum hocce onus in te suscipere non dedigneris, eo magis me tibi obligasti. Schema tuum libris singulis præfigendum probo, sed nondum a Pictore delineatum est. Pictorem mox adibo.

"In sententia mathematici Judicis quam D. Leibnitius D. Joanni Bernoullio ascripsit, publice accusor plagii. Et epistola quam D. Bernoullius ad me misit, et qua se talem sententiam scripsisse negavit, videbatur ad me missa ut remedium contra injuriam illam publicam: et eo nomine licentiam mihi datam esse putabam diluendi injuriam illam auctoritate De Bernoullii, præsertim cum is me non prohibuerit. Attamen Epistolam illam non nisi privatim communicavi, et Keilio nullam dedi licentiam aliquid evulgandi ex eadem, et multo minus scribendi contra Bernoullium ob ea quæ in Epistola illa mihi amice scripserat. Et hac de causa Keilium quasi liti studentem vehementer objurgavi: sed ille jam mortuus est.[29]

"Conqueritur D. Bernoullius quod ipsum vocavi hominem novum, et mathematicum fictum, et Equitem erraticum. Sed contra Bernoullium nondum coepi scribere. Hsec omnia dixi scribendo contra Leibnitium, et ejus argumenta repellendo.

"1. Dixerat utique D. Leibnitius Keilium esse hominem no <499> vum et rerum anteactarum parum peritum cognitorem, id est, hominem qui floruit post tempora Commercii quod Leibnitius habuit cum Oldenburgio: et idem objeci Leibnitio Bernoullium judicem constituenti, cui utique commercium illud antiquum annis plus triginta post mortem Oldenburgii ignotum fuerat.

"2. Cum D. Leibnitius sententiam Judicis mathematici Bernoullio ascriberet, vocavi judicem illum mathematicum vel fictum mathematicum, id est, mathematicum qui vere author esset sententiæ illius, vel fingebatur esse author. Nam cum Bernoullius ab authore sententiæ illius citabatur tanquam ab authore aversus, dubitabam utrum ille author esset, necne. Et Bernoullius ipse literis ad me datis affirmavit se non fuisse authorem.

"3. D. Leibnitius in Epistola sua prima ad Abbatem de Comitibus quæstionem de primo methodi differentialis inventore deseruit, et ad disputationes novas confugit de gravitate universali et qualitatibus occultis et miraculis et vacuo et atomis et spatio et tempore et perfectione mundi: Et sub finem Epistolæ Problema Bernoullii ex Actis Eruditorum desumptum proposuit mathematicis Anglis: Et initio proximæ suæ ad abbatem Epistolæ contulit banc novam controversiam cum duello, scribens se nolle in arenam descendere contra milites meos emissarios, sed cum ipse apparerem, se lubenter mihi satisfactionem daturum. Et ad hæc omnia alludens non contra Bernoullium sed contra Leibnitium scripsi in observationibus meis in hanc ejus Epistolam, ubi dixi quod Epistolæ et chartæ antiquæ (ex mente Leibnitii scilicet) jam abjiciendæ sunt, et Quæstio (de primo methodi inventore) deducenda est ad rixam circa Philosophiam et circa res alias: et magnus ille Mathematicus quem D. Leibnitius judicem sine nomine constituit, jam velum detrahere debet (secundum Leibnitium scilicet) et a partibus Leibnitii stare in hac rixa, et chartam provocatoriam ad mathematicos in Anglia per Leibnitium mittere quasi duellum, vel potius bellum, inter milites meos emissarios (uti loquitur) et exercitum discipulorum in quibus se felicem jactat; methodus esset magis idonea ad Quæstionem de primo inventore dirimendam quam examinatio veterum et authenticorum scriptorum, et scientiæ mathematicæ imposterum factis nobilibus equitum erraticorum vice argumentorum ac Demonstrationum implendæ essent.

<500>

"Hoc totum contra Leibnitium scripsi, et non contra Bernoullium. Leibnitius Bernoullium constituit judicem. Leibnitius eundem ex judice constituit advocatum. Leibnitius Commercium Epistolicum fugit quasi a judice suo condemnatum. Leibnitius vice Quæstionis de primo Inventore disputationes novas de Quæstionibus Philosophicis proposuit, et Problema tanquam a Bernoullio misit a Mathematicis Anglis solvendum. Leibnitius fuit eques ille erraticus qui vice argumentorum ex veteribus et authenticis scriptis desumendorum, introduxit alias disputationes, quas ipse contulit cum duello. Ad hoc duellum ille me provocavit methodi infinitesimalis gratia. Hæc methodus erat virgo illa pulchra pro qua eques noster pugnabat. Quæstionem de primo methodi hujus inventore per victoriam in hoc duello dirimere sperabat, et Virginem lucrari non examinatis veteribus et authenticis scriptis in Commercio Epistolico editis, per quæ Quæstio illa dirimi debuisset. Problemata mathematica proponi possunt exercitii gratia, sed non ad dirimendas lites alterius generis: et solus Leibnitius eadem in hunc finem proposuit.

"Hæc tibi scripsi non ut in lucem edantur, sed ut scias me nondum cum Bernoullio lites habuisse. Contra ilium nondum scripsi, neque in animo habeo ut scribam: nam lites semper fugi.

"Ds. Moivreus mihi dixit D. Bernoullium picturam meam optare: sed ille nondum agnovit publice me methodum fluxionum et momentorum habuisse anno 1672, uti conceditur in Elogio D. Leibnitii in Historia Academiæ vestræ edito. Ille nondum agnovit me in Propositione prima Libri de Quadraturis, anno 1693 a Wallisio edita, et anno 1686 in Lem. 2 Lib. 2. Princip. synthetice demonstrata, Regulam veram differendi differentialia dedisse, et Regulam illam anno 1672 habuisse, per quam utique curvaturas curvarum tunc determinabam. Ille nondum agnovit me anno 1669, quando scripsi Analysin per series, methodum habuisse quadrandi curvilineas accurate, si fieri possit, quemadmodum in Epistola mea 24 Octob. 1676, ad Oldenburgium data, et in Propositione quinta Libri de Quadraturis, exponitur; et Tabulas Curvilinearum quæ cum Conicis Sectionibus comparari possunt per ea tempora a me compositos fuisse. Si ea <501> concesserit, quæ lites prorsus amovebunt, picturam meam haud facile negabo. Vale.

"DABAM LONDINI,

26 Sept. 1721. St. Vet."

Varignon, in replying to this letter on the 9th December 1721, N.S., acknowledges having received it by the hands of M. Arlaud,[30] "qui gratissime mihi de te narravit, et cum quo ad multam usque noctem honorificentissime de te sum collocutus." Then follows the paragraph relating to Bernoulli, which we have already given in page 292, and the letter concludes with some details respecting the frontispiece and diagrams for the French edition of his Optics, then publishing under the superintendence of Varignon.

<502>

No. XXII.

(Referred to in pages 18, 231. )

1. — LETTER FROM JOHN BERNOULLI TO NEWTON.

"Viro Illustrissimo atque Incomparabili Isaaco Newtono S.P.D. Johannes Bernoulli.

"Opticam tuam Angl. à te mihi dono datam nuper accepi missu Celeb. Varignonii, à quo etiam exemplar Lat., sicut intelligo, accepturus sum. Pro utroque hoc egregio munere non minus quam pro aliis jam sæpius mihi acceptis tanquam totidem tuæ erga me benevolentiæ signis nunc demum debitas persolvo gratias, quas, quod fateor, dudum persolvere debuissem. Noli, quæso, officii hujus neglecti causam imputare animo ingrato et beneficiorum immemori, à quo semper quam maxime abhorrui; noli etiam credere, me ideo minus ingentia tua merita coluisse. Quin potius, si quid fidei verba mea merentur, id tantum ex silentio meo colligas velim, quod te divini ingenii virum, cui parem non habet ætas nostra, ego præ summa veneratione compellare non audebam; certe ne nunc quidem auderem, nisi nuper, quod animum addidit, intellexissem, juxta stupendas ingenii dotes etiam comitatis et affabilitatis virtutem usque adeo esse tibi connatam, ut ab inferioris conditionis hominibus, qualem me lubens profiteor, litteras accipere plane non detrectes. Cæterum quanti æstimaverim tuam amicitiam, qua, uti percepi ex litteris virorum clariss. Monmortii et Moivrei, me antehac dignatus es, eosdem hos viros antestor, ac præsertim quidem Moivreum, qui ea de re luculentissimum testimonium coram perhibere poterit. Sed nescio qui factum, ut post accensam facem feralis illius belli, quod maximo scientiæ Mathematicæ probro ante aliquot annos exortum inter quosdam utriusque nationis Britannicæ et Germanicæ Geometras, ego nec Britannus nec Germanus sed Helvetius, qui à partium studio alienissimus sum, et quidvis potius facerem, quam aliorum litibus me sponte immiscere, gratia tamen tua, ut fama fert, exciderim. <503> Quod si ita esset, quamvis contrarium sperem, non possem non credere, hocce infortunium fuisse mihi conflatum à supplantatione quorundam sycophantarum, qui ex rabida quadam aviditate sibi suisque popularibus ædificandi monumenta ex ruderibus destructæ aliorum existimationis et famæ, nos omnes non-Anglos insontes cum sontibus, ni statim per omnia applaudere velimus, acerbissimis contumeliis proscindunt. Itaque non dubito quin tibi, vir maxime, de me quoque multa falsa et conficta fuerint narrata, quæ gratiam, qua apud te flagravi, si non delere, saltem imminuere potuerunt. Sed non est ut multis me excusem: provoco ad scripta mea quæ extant; docebunt quam singulari cum laude de te tuisque inventis, quavis data occasione, locutus fuerim. Ecquis aliter posset, qui magnitudinem meritorum tuorum considerat? Quam mirabundus autem etiamnum illa deprædicem atque extollam quovis loco et tempore, privatim æque ac publice, in litteris, in sermonibus, in orationibus, in prælectionibus, illos loqui sinam qui me legunt, qui me audiunt. Sane si quid sapio, gratior erit posteritati commemoratio meritissimæ tuæ laudis à nobis instituta, utpote ex sincero animo et calamo profecta, quam nonnullorum ex vestratibus immodicus ardor (non dico te laudandi, nam satis laudari non potes, sed) tibi omnia, etiam ea quæ ipse non desideras, arrogandi, et exteris relinquendi nihil. Fallunt haud dubie, qui me tibi detulerunt tanquam auctorem quarundam ex schedis istis volantibus, in quibus forsan non satis honorifica tui fit mentio. Sed obsecro te, vir inclyte, atque per omnia humanitatis sacra obtestor, ut tibi certo persuadeas, quicquid hoc modo sine nomine in lucem prodierit, id mihi falso imputari. Non enim mihi est in more positum, talia protrudere anonyma quæ pro meis agnoscere nec vellem nec auderem. At vero non sine dolore audivi, te in quibusdam Epistolis libro (quem non vidi) cl. Raphsoni annexis ita de me loqui, ut inde concludi possit, quod me suspiceris auctorem nescio cujus scripti sine nomine publicati, et quod suspicio ista tibi subnata sit ex litteris quibusdam Leibnitii, qui me Auctorem esse affirmaverit. Quale fuerit illud scriptum jam non inquiro, interim certum te volo, à me non esse profectum, si præsertim tibi, quem tanti facio, non usquequaque esset decorum; absit autem ut credam Leibnitium, virum sane opti <504> mum, me nominando fucum vobis facere voluisse; credibile namque potius est ipsum vel sua vel aliorum conjectura fuisse deceptum; qua in re etsi data opera me offendere noluerit, non tamen omni culpa vacabat, quod tam temere et imprudenter aliquid perscripserit, cujus nullam habebat notitiam; fecisset utique melius, si antea ex me ipso quid de re esset rescivisset. Sed festinabat vir bonus, existimans forsan, causam suam aliquid inde roboris accepturam, parum sollicitus, utrum mihi incommoda necne futura esset conjecturalis illa relatio. Sed tandem absolvo, hoc unum maxime in votis habens, ut, nullo relicto dubio, tibi liquidissime constet animi in te mei integritas atque candor conjunctus cum perpetua tui admiratione atque veneratione, ut constet quoque me grata et memori mente usque et usque recolere qæ in me contulisti favoris et amoris signa. Non enim sum nescius, quantum tibi debeam non solum pro splendidis Librorum tuorum muneribus, quibus me subinde mactasti, sed et pro honorifica mei in vestram Societatem Reg. Scient. receptione, quippe quam ex tua commendatione mihi contigisse omnino perspectum habeo. Quod superest, Vale, Vir Illustrissime, atque mihi immortalium tuorum meritorum cultori studiosissimo fave. Dabam Basileæ, a. d. iii. Non. Quintil.[31] MDCCXIX.

2. — LETTER FROM JOHN BERNOULLI TO NEWTON.

"Prænobili ac Toto Orbe Celeberrimo Viro D. Isaaco Newtono S. P. D. Joh. Bernoulli.

"Litteræ Tuæ insigni voluptate me affecerunt, Vir Illustrissime. Ex iis intellexi Te, neglectis litibus mathematicis, eadem me prosequi benevolentia et amicitia, qua me olim dignatus fueras. Facis certe prout decet virum candidum et generosum, qui non facile patitur sibi eos designari, quos amore suo dignos judicat. Qualis sit epistola illa, de qua dicis quod sit 7 Junii 1713 data ad D. Leibnitium, mihi non constat. Non memini ad illum eo die me scripsisse, non tamen omnino negaverim, <505> quandoquidem non omnium epistolarum à me scriptarum apographa retinui. Quodsi fortassis inter innumeras quas ipsi exaraveram una reperiretur, quæ dictum diem et annum præ se ferret, pro certo asseverare ausim, nihil in ea contineri quod probitatis nomen tuum ullo modo convellat, neque me unquam ipsi veniam dedisse, ut quasdam ex Epistolis meis in publicum ederet, et talem imprimis quæ tibi, etsi contra spem et voluntatem meam, non arrideret. Quocirca denuo te rogo, vir illustr., velis tibi persuasum habere, mentem mihi nunquam fuisse aliter de te loqui quam de viro summo, nedum existimationem tuam vel probitatem sugillare. Absit ut dicam, te famam apud exteras Gentes captasse; spero tamen, te non respuere elogia à nobis ultro oblata, utpote sincera et te digna, atque adeo magis acceptanda quam quæ ex immoderato partium studio offeruntur. Quod tibi jam seni (cui incolumitatem per novum quem propediem auspicabimur annum et per multos secuturos ex animo apprecor) non liceat studiis mathematicis incumbere, acerbe dolebit Orbis eruditus, quem hucusque ditasti tot stupendis inventis. Ego quidem nondum senex, ad senium tamen vergo, aliisque distringor negotiis, ut nec mihi amplius fas sit rei mathematicæ tam sedulam operam dare, uti solebam. Quod memoras, vir Amplissime, de libro Raphsoni, eum scil. iterum impressum esse cum nonnullis Leibnitii epistolis, in quibus affirmet, me Auctorem esse prædictæ epistolæ (quæ quid contineat probitati tuæ injurium hariolari non possum) hoc certe liti sopiendæ non conducit; ipsum vero librum Raphsoni fortasse nunquam videbo, quia ejusmodi libri ex Hollandia huc raro deferuntur. Hoc interim considerari à vestratibus vellem, si per testimonia certandum esset, melius id fieri adducendo alias epistolas quam a Leibnitio scriptas, quippe qui in propria causa non haberi potest pro idoneo teste. Sunt mihi epistolæ virorum quorundam doctorum ex nationibus nullam in hac lite nationali partem habentibus, quas si publici juris facerem, nescio an illi ex vestratibus, qui tanto cum fervore ad injurias usque mecum expostulant, magnam inde gloriandi causam acquirerent. Habeo inter alia documenta authentica apographum à D. Montmortio nuper defuncto mathematico, ut nosti, dum viveret perdocto atque nulli parti addicto, utpote Gallo; habeo, inquam, apographum ab eo mihi transmissum ali <506> cujus epistolæ, quam ipse ad cl. Taylorum scripserat 18 Decemb. 1718, et quæ vel sola magnam litis partem dirimeret, sed non ex voto Taylori cæterorumque ejus sequacium.[32] Ab istis autem evulgandis libenter abstinebo, modo vestri desinant, quod pacis causa optarem, nostram lacessere patientiam. Lubens credo quod ais de aucto Corollario 1, Prop. xiii. Lib. 1. Operis tui incomparabilis Princip. Phil., hoc nempe factum esse antequam hæ lites cœperunt, neque dubitavi unquam, tibi esse demonstrationem propositionis inversæ quam nude asserueras in prima Operis Editione; aliquid dicebam tantum contra formam illius asserti, atque optabam, ut quis analysin daret qua inversse veritatem inveniret à priori, ac non supposita directa jam cognita. Hoc vero, quod te non invito dixerim, à me primo præstitum esse puto, quantum saltem hactenus mihi constat. Unum superest, quod pace tua monendum habeo. Retulit mihi nuperrime Amicus quispiam ex Anglia redux, me esse ejectum ex numero Sodalium Illustr. vestræ Societ. Reg., id quod collegerit ex eo quod nomen meum non repererit in Catalogo Londini viso Sociorum (in ampla scheda annuatim imprimi solita) pro anno 1718. Et quominus dubitarem monstravit mihi librum aliquem Anglicum impressxim an. 1718, cui titulus Magnæ Britanniæ Notitia, ubi in parte postrema pag. 144 videre est Catalogum Membrorum exterorum Societatis Regiæ, atque in illo nomen Agnati mei, sed meo nomine, quod miror, prorsus exulante. Liceat ergo ex te quærere, utrum ex decreto Illustr. Societatis fuerim expunctus, et quid peccaverim vel quonam delicto ejus indignationem in me concitaverim, an vero Secretarius (qui ni fallor turn temporis fuit Taylorus) propria auctoritate me proscripserit. Quid? ideone locum in illustri hoc corpore mihi non ambienti tam honorifice obtulissetis, ut postea tanto turpius ex eo me ejiceretis? Hoc equidem ob insignem vestram æquitatem suspicari vix possum. Quare enixe te rogo, vir Nobilissime, ut quid ea de re sit me quantocyus {sic} facias certiorem. Vale, ac mihi studiosissimo tui porro fave. Dabam Basileæ, a d. xxi. Decemb. MDCCXIX.

<507>

3. — LETTER FROM JOHN BERNOULLI TO NEWTON.

"Illustrissimo atque Nobilissimo Viro Isaaco Newtono S. P. D. Joh. Bernoulli.

"Ad te iterum venio, Vir Inclyte, ut iteratas persolvam gratias pro novo munere quo me beasti, nec me tantum, sed et filium meum atque Agnatum. Accepi nimirum tria inter nos tres distribuenda Exemplaria nitidissime compacta Optices tuæ Parisiis nuper editæ, quæ Cl. Varignonius, paulo ante obitum suum, cunctis qui sinceritatem cum eruditione conjunctam amant vehementer lugendum, mihi nomine tuo transmiserat. Etsi nesciam quid sit quo hanc tuam erga me meosque munificentiam demeruerim aut postea demereri possim; id saltem persuasum tibi habeas, vir maxime, neminem esse qui immortalia tua inventa ex vero rerum pretio pluris æstimet et simul sincerius quam ego. Hoc cumprimis quod de Lumine et Coloribus systema pro ingenii tui sagacitate felicissime eruisti me summum habet admiratorem; inventum sane quovis ære perennius et à posteritate magis quam nunc fit suspiciendum. Sunt enim qui illud partim ex invidia partim ex imperitia obtrectare non verentur, quin et cum nihil habent quod pretium ejus imminuat, audent inventionis laudem tibi surripere eamque sibi arrogare. En exemplum in quodam Hartsoekero, homine inepto et in Geometria prorsus hospite, qui in opusculo aliquo in lucem protruso perfricta fronte sustinet novam tuam Colorum theoriam eorumque diversam refrangibilitatem sibi dudum notam variisque experimentis perspectam fuisse, antequam quicquam ea de re inventum à te aut evulgatum fuisset, quod apud me summam excitavit indignationem, sicut et hoc quod reliquas tuas rerum Physicarum explicationes utut ingeniosissimas, præsertim quæ ad systema planetarium spectant, ubi omnia cum phænomenis tam mirifice consentiunt, admodum salse et scoptice traducit, quamvis de rebus istis non aliter argumentetur quam cæcus de colore, nec mirum, siquidem homo sit ἀγεωμέτρητος et omnis humanitatis expers, nemini parcens, imo summorum virorum atque de re mathematica ac philosophica optime meritorum famam arrodere non dubitans. Ita ut mirer, neminem ex ves <508> tratibus adesse, qui tuam, Vir Illustrissime, existimationem vindicet contra rudem et barbarum hominem. Ad me quod attinet, fateor me ab illo tractari multo acerbius; nihil enim injuriarum est, nihil aculeorum quod in me non sparserit, idque non aliam ob causam quam quod aliquis ex meis discipulis phosphorum meum mercurialem ab illius morsibus defenderit. Licet indignus sit homo cui ego respondeam, unum tamen est quod me magnopere urit; scilicet, ut me omnium risui exponat, impudentissime comminiscitur, me mihimet ipsi tribuisse titulum excellentis Mathematici, et, ut calumniæ crimen à se amoliatur, te, Vir Illustrissime, ejus Auctorem facit, dum locum citat ex tomo 2. Collectaneorum Di. Desmaiseaux, (Recueil de diverses piéces), p. 125, l. 32, ubi loqueris de epistola illa 7 Junij 1713, quam Leibnitius à me scriptam esse contenderat, et in qua prout erat impressa in scheda illa volante 29 Julij 1713, elogium illud, sed quod parenthesi includebatur, mihi erat adscriptum. Hinc malitiose colligit calumniator, quasi insinuare volueris, me eò arrogantiæ processisse ut hunc mihi titulum sumserim, cum tamen te voluisse contrarium dicere luculentissime pateat ex verbis quæ locum citatum immediate sequuntur, quibus nimirum fateris in eadem illa epistola per Leibnitium altera vice edita in Novis Litterariis citationem parenthesi inclusam esse omissam; unde sponte fluit Auctorem epistolæ non fuisse Auctorem parentheseos, sed hanc fuisse insertam ab eo qui schedam volantem 29 Julij edidit; possum itaque haberi pro Auctore Epistolæ, et tamen non haberi pro Scriptore elogii parenthetici. Interim quicquid sit, calumnia Hartsoekeri in te magis quam in me redundat, eam enim ex verbis tuis maligne detortis elicere conatur. Quid igitur faciendum status, ut innocentia in tutum collocetur apud eos qui Collectanea Desmaisavii non viderunt, libentissime equidem ex te ipso intelligerem, si qua responsione me dignari volneris. Quod superest, te, Vir Nobiliss., rogatum volo nomine Celeb. nostri Scheuchzeri, vestræ Societatis Regiæ Socii, ut Filio ipsius, qui nunc Londini agit, te accendendi alloquendique copiam indulgeas; id namque in maxima laude sibi ponet, quod viderit summum Philosophorum et Mathematicorum Principem. Vale, et me Nominis tui Cultorem perpetuum amare perge. Dabam Basileæ, a. d. vi. Febr. MDCCXXIII.

<509>

No. XXIII.

(Referred to in page 298.)

Brook Taylor, LL.D., the son of John Taylor of Bifrons House in Kent, was born on the 18th August 1685, and died on the 29th December 1731. In 1701 he was admitted into St. John's College, Cambridge, where he entered upon the study of mathematics and natural philosophy. In 1708 he wrote his treatise "On the Centre of Oscillation." In 1712 he was elected a fellow of the Royal Society, and in the same year he presented to that body his paper "On the Ascent of Water between two Glass Planes." His most important works, — his Methodus Incrementorum, and his treatise On the Principles of Linear Perspective, were published in 1715. In the following year he paid a visit to Count Remond de Montmort and the Abbè Conti in Paris, with the first of whom he maintained a friendly correspondence. He was chosen Secretary to the Royal Society on the 13th January 1714, an office which he resigned on the 21st October 1718. In the following letters he appears as one of the champions of Newton in the fluxionary controversy.

1.— LETTER FROM BROOK TAYLOR TO SIR ISAAC NEWTON.

"Sir,

"The great loss to our family of my good dear mother, has made it necessary for me to make haste home, and I find the circumstances of our family will not suffer me to be in town before the rising of the Royal Society; wherefore I am under the necessity to beg the favour of you, Sir, to excuse me for not attending you in Crane Court, and that you will be pleased to get M. Desaguliers, or some other person, to do the Secretary's business at the meetings of the Society; and I hope I shall another time have an opportunity of making the Society some amends for my present absence.

<510>

"Upon my coming to London on Tuesday night, I found a letter from Mr. Montmort, dated the 31st March, N.S., wherein he gives me the following account of what passed at the French Academy relating to D. Keill's paper, which it seems they don't care to print.

"'Le plus grand nombre s'est opposé à faire imprimer le morceau de Mr. Keill dans les mémoires de l'Académie par la raison que Mr. Keill est étranger à l'Académie, et que cela est contre les Statuts. Je pris la parole, represéntai 1o que le morceau est excellent; 2o que M. Newton est attaqué dans les mémoires par M. Nas Bernoulli qui non plus que Mr. Keill n'est pas Membre de L' Académie; 3o que s'il étoit jamais permis de faire exception à une règie générale, c'estoit en faveur d'un aussi grand homme que M. Newton. Je compte qu'il sera imprimé s'il est avoué et reconnu de Mr. Newton ou de Mr. Halley au nom de la Société Royale.'[33]

"These are Mr. Montmort's own words, which I thought it my duty to communicate to you, not knowing what sort of an account Mr. Fontenelle may have given in his letter to Dr. Halley.[34] Mr. Montmort, in all his letters to me, seems to take a particular pleasure in expressing the great respect he has for you, Sir; and in one of his last he tells me he has sent to me a hamper of champagne wine, and begs your acceptance of 50 bottles of it.[35] I can send it from hence either by land carriage or by water, if you will be pleased to let me know whither I shall direct it. I will send it as soon as it comes to my hand. Pray, Sir, do me the favour to make my most humble service acceptable to Mrs. Barton. — I am,

"Sir,

"Your most faithful and most obedient servant,

"BROOK TAYLOR.

"BIFRONS, near CANTERBURY,

22d April 1716.

"To Sir IS. NEWTON."

<511>

2.— EXTRACT OF A LETTER FROM M. MONTMORT TO BROOK TAYLOR, dated Jan. 22, 1717.[36]

"Pour moi je soutient {sic} icy et je l'ai toujours soutenu hautement que M. Newton a été maître du Calcul différentiel et intégral avant tout autre géomètre, et que dès l'année 1677 il sçavoit tout ce que les travaux de M. Leibnitz et M. Bernoulli ont découvert depuis."

3.— LETTER FROM M. MONTMORT TO BROOK TAYLOR.

"MONTMORT, ce 18 Decr. 1718.

"Je suis très persuadé, Monsieur, que vous n'avez point eu dessein de vous faire honneur de ce qui n'étoit point à vous, et de vous l'approprier; outre que vous avez l'esprit et le cœur trop élevé pour être capable d'une telle petitesse, vous êtes trop riche de votre propre fond pour avoir besoin du bien d'autruy. Je crois que quand vous avez donné au public vostre excellent livre Methodus Incrementorum, vous étiez peu instruit de l'histoire des nouvelles découvertes. Je croirois même que vous ne l'estes pas assez à présent pour un homme destiné comme vous à jouer un grand rolle parmy les Sçavants de ce siècle. Les connaissances historiques inutiles à la vérité pour la perfection de l'esprit sont absolument néecessaires à un autheur qui faute de les avoir court risque de porter des jugemens injustes, de bâtir sur le fond d'autruy contre son intention, de mal apprécier le mérite des autheurs, et enfin de se tromper dans de faits dont un lecteur sévère suppose qu'on est instruit parcequ'on devroit l'être. En voici quelques uns dont il est apropos que vous ayez connaissance.

"Mr. Huygens est inventeur de la théorie de centres d'oscillations, et de percussion. M. Jacques Bernoulli l'a rendue plus claire, plus facile, et plus parfaite. Voyez les Mémoires de l'Académie en 1703 et 1704. M. J. Bernoulli ayant cru qu'on y pouvoit ajouter quelque chose, a donné en 1714 dans ces Mémoires un beau morceau sur cette matière. Je crois qu'il a <512> donné un second dans les Actes de Leipsic. Je ne sçai quand, car je ne les ai pas ici. Il est vrai que Mrs Bernoulli ny M. Leibnitz n'ont point donné dans les journaux de Leipsic les analyses de la chaînette, de la courbure d'une voile enflée par le vent, et de celle que prend un linge pressé par le poid d'un fluide qu'il contient; mais il me semble que les solutions qu'ils ont donnés de ces problêmes sont trés justes. J'ai parmy mes vieux papiers des démonstrations de tout ce que M. Jac. Bernoulli a avancé en 1691 p. 288 de l'identité qu'il y a entre la chaînette et la courbe de la voile, et aussi entre la courbe du linge et l'élastique. Vous trouverez dans la nouvelle théorie de la manœuvre des vaisseaux publié en 1714 les analyses des courbes velaria, catenaria, lintea. Je n'adjouterai point que ces analyses couvrent depuis plus de 25 ans entre les mains de plusieurs géomètres de toutes nations; à qui M. Jean Bernoulli a communiqué les leçons manuscriptes qu'il avoit fait, ètant à Paris pour M. Le M. de l'Hôpital. Toutes ces analyses à l'exception de celle de la courbe élastique s'y trouvent. Je les ai vu dans un manuscript de ces leçons que le P. Reyneau tira in 1692 d'un ami de M. Bernoulli. Le fait est constant, et j'en suis temoin avec peut-être plus de cent personnes, mais je n'admets que les monuments publics telles qu'est l'impression.

"Il y avoit quelque chose a redire à ce que M. Jac. Bernoulli avoit donnè en 1694 touchant la courbure des ressorts. Il a perfectionné cette matière dans les mémoires de l'Académie de l'année 1705. Je me souviens dans ce moment que l'analyse des chaînettes se trouve dans la solution que M. Jac. Bernoulli a donne en 1701 de son probleme des Isoperimetres. II est vray Mr. que la solution que Mr. Jean Bernoulli a donné en 1706 dans les mémoires de l'Académie du prob. des Isopérimètres n'est pas exempte de faute. Il a eu le bonheur de s'en appercevoir le 1er, et avant que d'estre relevé par d'autres. Vous en verrez une nouvelle et très belle solution dans les Actes de Leipsic au mois de Janvier de cette année. Sa méthode est fondé sur la considération de trois élémens contigus de la courbe au lieu qu'il n'en considéroit que deux dans celle qui a paru en 1706. Elle n'est presque point différente dans le fond de celle de Monsr.. Herman qui ne me plait pas moins. Elles sont toutes deux <513> entées sur celle de feu M. Bernoulli. Il la regarde comme son chef-d'œuvre: c'est un morceau d'une grande force, et qui me paroit surpasser en difficulté toutes les productions de ce jour. Je sçai bon gré au pauvre defaut d'avoir tenu ferme à soupçonner et dire qu'il y avoit faut et paralogisme dans l'analyse de son frère, et de n'avoir pas lâché ces 50 ecus qui n'étoient pas bien gagnés.

"Je ne sçai si vous sçavez que M. De la Hire en 1702 dans les Mémoires de l'Académie, et M. Herman dans les Journaux de Leipsic un peu de temps après, ont entrepris de déterminer la courbe que décrit un rayon de lumière passant dans notre Atmosphère. Je crois qu'il y a faute dans M. de la Hire. Je ne me souviens pas de ce qui m'a paru il y a quelques années de la solution de M. Herman; vous en jugerez et de ce qu'ils disent sur la densité de l'Atmosphére.

"J'ay étè fort surpris de trouver ce qui suit dans votre lettre. 'As to the owning of any one as inventor or improver of the method, besides Sir Isaac Newton, I knew of none. I saw nothing anywhere that seemed to me an improvement upon what Sir Isaac had published. I was sensible that several had applied the method with good success, and understood pretty much of it; but I always took Sir Isaac Newton not only for the inventor, but also for the greatest master of it.' Je pense comme vous Mr. sur le mérite de Mr. Newton. Je parle toujours comme d'un homme au dessus des autres, et qu'on ne peut trop admirer. Mais je ne puis m'empêcher de combattre l'opinion où vous estes que le Public a reçu de Mr. Newton, et non de M. Leibnitz et Bernoulli les nouveaux calculs, et l'art de les faire servir à toutes les recherches qu'on peut faire en Géométrie. C'est une erreur de fait. Il vaut mieux que moi qui n'ay là dessus aucune prévention, ni rien qui me porte à en avoir, qui fait profession d'estre votre amis, et qui le suis plus sans comparaison que des Géomètres Allemands que je n'ai jamais vu; il vaut mieux, dis je, que je vous fasse remarquer la fausseté qu'un adversaire à qui vous donneriez avantage sur vous et qui vous reprocheroit avec apparence de vérité que votre zèle pour la gloire de vostre nation vous rend partiel et vous fait oublier toutes les règles de l'equité. Je n'examinerai point ici les droits de <514> Mrs. Newton et Leibnitz à la première invention du calcul différentiel et intégral. Je vous rapporterai quand vous voudriez le détail des réflexions qu'un long et sérieux examen m'a fourni, et j'espère que vous n'en serez pas mécontent. Je veux seulement vous faire remarquer qu'il est insoutenable de dire que Mrs. Leibnitz et Bernoulli ne sont pas les vrays et presque uniques promoteurs de ces calculs. Voici mon raisonnement, jugez en. Ce sont eux et eux seuls qui nous out appris les règles de différentier et d'intégrer, la manière de trouver par ces calculs les tangentes des courbes, leur pointes d'inflexion et de rebroussement, leurs plus grandes, et leurs plus petites ordonnées, les développés les caustiques par réflexion, et par réfraction, les quadratures des courbes, les centres de gravité, ceux d'oscillation, et de percussion, les problêmes de la méthode inverse des tangentes, tels que celuycy par ex. qui donne tant d'admiration à M. Huygens en 1693 trouver la courbe dont la tangente est à la partie interceptè de l'axe en raison donné. Ce sont eux qui les premiers ont exprimé des courbes méchaniques par les équations différentielles, à en abaisser les dimensions, et à les construire par les logarithmes, ou par des rectifications des courbes quand cela est possible; et qui enfin par de belles et nombreuses applications de ces calculs aux problêmes les plus difficiles de la Méchanique tels que sont ceux de la chaînette, de la voile, l'élastique, de la plus viste déscente, de la paracentrique, nous ont mis et nos neveux dans la voye des plus profondes découvertes. Ce sont là des faits sans réplique. Il suffit pour s'en convaincre d'ouvrir les journaux de Leipsic. Vous y verrez les preuves de ce que j'avance. Personne hors M. le M. de l'Hospital qu'on peut joindre en partie à ces Messieurs quoiqu'il ait été disciple de M. Jean Bernoulli, n'a paru avec eux sur la scène jusqu'en 1700 ou environs. Je compte pour rien ce que M. Carré en France et M. Moivre en Angleterre, de même M. Craige donnèrent dans ce temps ou peu auparavant; tout cela n'etoit rien en comparaison de ce qu'on nous avoit donné dans les Actes de Leipsic. Il est vray Mr. que les Principes Math. de. M. Newton ont paru en 1686 [1687]; ce sçavant ouvrage peut donner lieu de croire que M. Newton sçavoit dès-lors de ces calculs tout ce qu'on sçait aujourdhuy, M. Bernoulli même. Je ne veux pas disconvenir, et c'est une question à part. Mais il est <515> sûr au moins que ce livre n'apprend rien de ces calculs, si ce n'est le lemme, 2d page 250, 1ère èdit., mais vous sçavez qu'il ne contient que la 1ère et plus simple règle de prendre les différences, ce que M. Leibnitz avoit fait avec plus d'étendue en 1684. Je dois adjouter que dans le 2de volume de M. Wallis imprimé en 1693 on trouve plus au long les règles de ces calculs, mays quoyque ce morceau soit propre à nous donner une grande idée de ce qu'en sçavoit alors Mr. Newton, il n'en apprend pas plus que l'on en trouvoit dans les journaux de Leipsic. On trouve en 1697 une solution de Mr. Newton du problême de la plus viste déscente, mais comme il n'y a point d'analyse, et qu'on ne sçait point la route qu'il a suivie, cela ne touche point à ma proposition qui est que depuis 1684, 1ère date publique de la naissance du calcul différentiel et intégral, jusqu'en 1700 ou environ, où je suppose qu'il avoit acquis presque toute la perfection qu'il a aujourdhuy, personne n'a contribué à le perfectionner que Mrs. Leibnitz et Bernoulli, à moins qu'on n'y veuille joindre pour quelque part M. le M. l'Hospital à qui ils avoient de bonne heure révelé leur secrets. Qui apparemment en seroient encore pour tous les Géomètres d'aujourdhuy s'ils avoient voulu les tenir cachés à l'imitation de Mr. Newton, qui à mon avis a du avoir la clef de ceux là ou des pareils dès le temps qu'il a donné son fameux ouvrage, Ph. Nat. Ppia Math. On ne peut rien le plus beau ni de meilleur en son genre que le traité de Mr. Newton De Quadratura Curvarum, mais il est venu bien tard. La date de l'impression de cet ouvrage est fâcheuse, non pour Mr. Newton, qui a acquis tant de gloire que l'homme le plus ambitieux n'en pourroit désirer davantage, mais pour quelques Anglois qui semblent porter envie à ceux qui ont découvert et publié les 1ers ces nouvelles méthodes qui ont portés si long la Géométrie."

<516>

No. XXIV.

(Referred to in page 300.)

letter from james stirling to sir isaac newton.

"Sir,

"I had the honour of your letter about five weeks after the date. As your generosity is infinitely above my merite, so I reackon myself ever bound to serve you to the utmost; and, indeed, a present from a person of such worth is more valued by me than ten times the value from another. I humbly ask pardon for not returning my grateful acknowledgements before now. I wrote to Mr, Desaguliers to make my excuse, while, in the meantime, I intended to send a supplement to the papers I sent; but now I'm willing they be printed as they are, being at present taken up with my own affair here, wherewith I won't presume to trouble you, having sent Mr. Desaguliers a full account thereof.

"I beg leave to let you know, that Mr. Nicholas Bernoulli proposed to me to enquire into the curve which defines the resistances of a pendulum, when the resistance is proportional to the velocity. I enquired into some of the most easy cases, and found that the pendulum, in the lowest point, had no velocity, and consequently could perform but one half oscillation, and then rest. Bernoulli had found that before, as also one Count Ricato, which I understood after I communicated to Bernoulli what occurred to me. Then he asked me how in that hypothesis of resistance a pendulum could be said to oscillate, since it only fell to the lowest point of the cycloid, and then rested. So I conjecture that his uncle sets him on to see what he can pick out of your writings, that may any ways be cavilled against, for he has also been very busy in enquiring into some other parts of the Principles.

"I humbly beg pardon for this trouble, and pray God to prolong your daies, wishing that an opportunity should offer <517> that I could demonstrate my gratefullness for the obligations you have been pleased to honour me with.

"I am, with the greatest respect. Sir,

"Your most humble and most obedient servt,

James Stirling.

"Venice, 17 August 1719, N. St.

"P.S. — Mr. Nicholas Bernoulli, as he hath been accused by Dr. Keill of an ill-will towards you, wrote you a letter some time ago to clear himself. But having in return desired me to assure you, that what was printed in the Acta Paris. relating to your 10 Prop. lib. 2, was wrote before he had been in England, sent to his friends as his private opinion of the matter, and afterwards published without so much as his knowledge. He is willing to make a full vindication of himself as to that affair whenever you'll please to desire it. He has laid the whole matter open to me; and if things are as he informs me, Dr. Keill has been somewhat harsh in his case. For my part, I can witness that I never hear him mention your name without respect and honour. When he shewed me the Acta Eruditorum, where his uncle has lately wrote against Dr. Keill, he shewed me that the theorems there about quadratures are all corollarys from your Quadratures; and whereas Mr. John Bernoulli had said there, that it did not appear by your construction of the curve, Prop. 4, lib. 2, that the said construction could be reduced to logarithms, he presently shewed me Coroll. 2 of the said Proposition, where you shew how it is reduced to logarithms, and he said he wondered at his uncle's oversight. I find more modesty in him as to your affairs than could be expected from a young man, nephew to one who is now become head of Mr. Leibnitz's party; and, among the many conferences I've had with him, I declare never to have heard a disrespectful word from him of any of our country but Dr. Keill."

<518>

No. XXV.

(Referred to in page 300.)

LETTER FROM FONTENELLE TO SIR ISAAC NEWTON.

"Monsieur,

"Je suis chargé par L' Académie Royale des Sciences d'avoir l'honneur de vous remercier de la nouvelle Edition que vous avez envoyée de vos Principes des Mathématiques de la Philosophie Naturelle. Il y a déjà plusieurs années que cet excellent ouvrage est admiré dans toute l'Europe, et principalement en France, où l'on sait bien connaître le mérite étranger. Mais présentement, Monsieur, que vous avez une place dans notre Académie, nous prétendons, en quelque façon que vous n'êtes plus étranger pour nous, et nos Savants qui ont quelque droit de vous appeler leur Confrère prennent une part plus particulière à votre gloire. On peut sans témérité vous prédire qu'elle sera immortelle par les deux Livres que vous avez publiés, oà il brille de toutes parts un si heureux génie de découvertes, et où ceux-même qui savent le plus trouvent tant à apprendre.

"L'Académie vous prie Monsieur de lui faire quelque fois part de vos nouvelles productions ainsi que font Messrs. Leibnitz, Bernoulli, et les autres Savants étrangers qu'elle a adoptés. Il n'est pas surprenant qu'elle cherche à se faire honneur de ce qu'elle vous possède. — Je suis,

"Monsieur,

"Votre très humble et très obéissant serviteur,

"FONTENELLE,

"Sec. Perp. de l'Ac. Roy. des Sc.

"à Paris, ce 4 Fév. 1714."

<519>

No. XXVI.

(Referred to in page 300.)

LETTER FROM DR. DERHAM TO SIR ISAAC NEWTON.

"UPMINSTER, Feb. 20, 17123.

MUCH HOND SR

"As I was perusing the Commerc. Epist. wch ye R. S. honoured me with, it came into my mind, that in some of Mr. Collins's lrs to Mr. Towneley of Lanc., (now in my hands,) there was something relating to that subject; and looking over Mr. Towneley's papers, I found a long lr of Mr. Collins's, giving a sort of historical account of the matter, That in Sept. . . . . Mercator published his Logar., one of wch he sent to Dr. Wallis, &c. . . . another to Mr. Barrow, who thereupon sent him up some papers of Mr. Newton, (now his successor,) by wch, and some other communications, &c., it appears ye sd method was invented some years before by Mr. Newton, and generally applied. . . . Then follows an account of your method, and of Mr. Gregorie's performance in yt kind, with what Mr. Gregory had written to him about it in Feb. 1671, and Jan. 1672, &c.

"There is a great deal more, too long to speak of; but if you think the papers may be of use to you, at your request I will bring them wn I next come to London, to be looked over or transcribed; but I am engaged not to part with any of them out of my power. I have also divers of Mr. Sluse's lrs, and other papers of his, from Rome and Leige, to Mr. Towneley, but they being in French, I cannot as yet give any account whether there be any thing relating to your matter in them. Not meeting you when I was last in town, I shall take this occasion to acquaint you yt I have tried Mr. Huygens's glass of 122 feet at , , , and , and some fixt ; and I hope shortly to have a view of also. I believe it by far the best long glass I ever looked through, representing these celestials very clear and well. But I can hardly think Mr. Huygens could see <520> tollerably through it with the eye-glass accompanying it, wch is but 6 inches focus; I, therefore, make use of eye-glasses of a larger focus. I am not yet so well accommodated for strict observations with this glass as to tell you any thing of Sat., &c., for I am forced to raise a long ladder and send my man up with the glass. Neither have I a good eye-glass to my mind, only some spectacle-glasses. But would you, or some other of my friends that have interest enough, procure me a small Prebend, to enable me to be at charges without injuring my wife and children, I promise you I would stick at no charge to get an apparatus for this noble glass, to make it as serviceable to the R. S. as in me lies; and to accomplish some other matters also for their service. Be pleased to excuse my presumption thus upon your friendship and favour, wch I desire may be no otherwise troublesome to you then if any thing happens in your way, and you have no other friend capable of it, you would, for the service of the R. S. as well as myself, think of me, and at the same time pardon,

"Most Hond Sr,

"Your affectionately humble servant,

"Wm. Derham.

"If you have any commands, direct to Upminster, near Rumford, Essex, by the general post."

In another letter, which possesses no interest, dated May 11, 1714, he requests Newton to fulfil his promise of giving him his "castigations" for a third impression of his Physico-Theology.

<521>

No. XXVII.

(Referred to in pages 308, 410.)

LETTER FROM POPE TO MR. CONDUITT.

"SR,

"I make use of the liberty you gave me, of a free criticisme, in the inclosed; without any formalityes, or asking an excuse from you in my turn. I think nothing can be more proper than the first part of your dedication, which relates to the author of the work: Whatever thoughts flow from that, or take rise from that, render your compliment to the Queen (in my opinion) the more graceful as well as the more just (and proper for you as a relation, and intrusted with so valuable a depositum.) As to what depends not on that, I would only wish you avoided as much as possible the common topicks of dedications and addresses: Your real subject (I mean both Sir Isaac Newton and Her Majesty), will shine of themselves; and a shortness, a dignity, and plainness will become them. For instance I cannot but think, yt after yu have said, that Sr Isaac carried arts and sciences in a few years farther than all others had in whole ages; it flattens if not contradicts it, to add afterwds yt in the present reign they may be advanced to a much greater height. I wd omit that paragraph wch I have marked between two crosses ×. It takes very much from the praise of Sr I. N., and I fear unjustly, to imagine that any Prince's reign can make Newtons, however it might incourage or admire them.

"I mean in general only that I wd shorten those parts wch are mere panegyric, independent on the occasion the book and author give you: the character of sincerity wch yu so rightly touch upon in the King, I wd keep exactly as it is, and anything in short that is characteristical. I prefer (since your commands are, that I shd chuse what I like) the column on the right hand: only in one place I think what you say of the Queen's encouragement of arts, is almost a repetition of the same thing elsewhere. I have marked it by inclosing yt passage with a line and two crosses × ×. The rest I believe may stand.

<522>

"Upon the whole I really approve it; and you ought to pardon my freedom, since you caused it. If I am ever so much in the wrong, it will be at least an instance of my good intention. I am ashamed to be so particular in things of so little importance as my objections, which are indeed so very slight. But the apprehension that you might soon want the papers, and the consciousness that I could not be serviceable enough to you to excuse a longer delay, made me write this, rather than wait for an opportunity of talking with you. Methinks yu should end the dedication with returning once more to Sir Isaac Newton. What little I've added, is only a hint to that effect. I am sincerely of opinion that your dedication is very just, and decent, and well judged. I cd wish it were inlarged with some Memoirs and Character of him, as a private man. I doubt not his life and manners wd make a great Discovery of Virtue and Goodness and Rectitude of heart, as his works have done of Penetration and ye utmost Stretch of human knowledge. — I am, Sir, your most obedient humble servant,

"Twickenham,                      "A. Pope.

"Novr. 10th, 1727."

The following are the additions referred to in the letter, and written upon a separate leaf: —

"Yr Majesty does not think these instructions and entertaining pursuits below your exalted station; and yourself a proof that the abstruser parts of them are not beyond ye reach of yr sex," &c.

"Formed by such models?

"That liberty and knowledge (as this glorious prospect gives us reason to hope) may be equally and jointly perpetuated; and that the bright example set in this reign by the Royal patrons of both, may be transmitted with the sceptre, to those of the same great line: to ye end that this age may be as illustrious, and this nation as distinguished, for every other felicity and glory; as it is, and ever must be, for having been honoured with such a man as Sir Isaac Newton, is the most sincere prayer of,

"Madam, may it please yr Majesty, &c."

<523>

No. XXVIII.

(Referred to in page 341.)

In 1831, soon after the publication of my Life of Sir Isaac Newton, I received the following letter from Dr. Burgess, Bishop of Salisbury, who had distinguished himself by several learned and able works in defence of the doctrine of the Trinity.

"Salisbury, Nov. 30, 1831.

"Sir,

"I beg your acceptance of the enclosed pages, which were occasioned by the perusal of your very interesting Life of Sir Isaac Newton, which I read with great pleasure, till I came to the statement of the contents of Sir Isaac's Dissertation on 1 John v. 7, and 1 Tim. iii. 16. I thought the restatement of his opinions on these subjects injurious to his memory, as he had expressly and anxiously suppressed them. I was desirous of counteracting the present abuse of Sir Isaac's authority by Socinians and Unitarians, but I was unwilling to deliver these pages to the public, without communicating them to yourself. — I am, Sir,

"With very sincere respect,

"Your obedient Servant,

"T. Sarum."

The pages thus enclosed by the Bishop, bore the title of Appendix on Sir Isaac Newton's suppression of his Dissertation on 1 John v. 7, and 1 Tim. iii. 18. It consisted of ten printed pages, and contained the following criticisms on my work.

"The name of Sir Isaac Newton has been lately employed by Socinians and Unitarians, in opposition to the doctrine of the Trinity, on the authority of a Tract, which he anxiously and deliberately suppressed. Dr. Brewster, in his recent publication of the Life of Sir Isaac Newton, has, it is much to be regretted, done the same injustice to the memory of Sir Isaac <524> by his restatement and revival of the general contents of the suppressed Dissertation on the controverted verse of St. John, and by omitting to notice Sir Isaac's suppression of the Tract. The preceding Remarks on the general Tenour of the New Testament had hardly left the press, when I first met with Dr. Brewster's Life of Sir Isaac Newton in the 24th volume of the Family Library. The popularity of the work, of which Dr. Brewster's volume is a very interesting portion, has induced me to add this Appendix to my Remarks, in order to counteract, as far as may be, the injury done to the name of Sir Isaac Newton, and its influence on public opinion."

"The revival and restatement of these abortive criticisms are injurious to the memory of the writer, because it omits to notice that the Tract which contains them was deliberately and anxiously suppressed." — Pages 81, 82.

As soon as I received the preceding letter, and its enclosure, I informed the Bishop of the great mistake which he had committed, in charging me with having injured the memory of Sir Isaac Newton, by omitting to notice that he had suppressed his Tract. I directed his attention to page 274 of the work, in which I had not only mentioned the fact, but had even printed at full length Newton's own letter to Locke suppressing his Dissertation. To this letter I received the following answer: —

"Palace, Salisbury, Dec. 10, 1831.

"Sir,

" . . . I am still more sorry that I should have overlooked, or rather not have seen, at the time I printed my Appendix, the account in your work to which your letter directs me, and which I have since read, of the suppression of the Dissertation. The pages of your work (281-284) containing the statement of Sir Isaac Newton's opinions and paraphrase, were shewn to me by a friend, and as they contained no allusion to the suppression of the Dissertation, I was led to suppose that you had altogether omitted to notice it. When I reprint my Appendix, I shall certainly correct my oversight. — I am, Sir,

"Your obedient Servant,

"T. SARUM."

<525>

I am unwilling to characterize the incompatibility of the statements contained in these two letters, but having overlooked the offence at the time, I may now express my surprise, that after having committed such a gross error, Dr. Burgess never thought of correcting it, either by reprinting the few pages of his Appendix, or by inserting a fly leaf in his volume.

The charge of having injured Sir Isaac Newton, and of having produced, by "the revival and restatement of his abortive criticisms," an influence on public opinion which it was necessary for Dr. Burgess to counteract, is too ridiculous to require refutation. The Bishop himself, in his "Tracts on the Divinity of Christ,"[37] has quoted from this very Dissertation, in order to shew that it is not Antitrinitarian, and yet he denounces others for following his example. He has referred also, times without number, to the subject of Newton's Arian tendencies, and thus compelled his readers to peruse the very Dissertation of which he is afraid. Such an attempt to stifle the truths of history is of very rare occurrence. Dr. Horsley, the great champion of the Trinity, did not scruple to give importance to Newton's Dissertation, by publishing it along with the Principia; and I should have betrayed the trust committed to me, had I not given an account of the theological writings of a man, who was described by one Bishop as "knowing more of the Scriptures than them all," and by another as having "the whitest soul" he ever knew.

<526>

No. XXIX.

(Referred to in page 276.)

IRENICUM: OR ECCLESIASTICAL POLITY TENDING TO PEACE.

THESIS 1.

"The cities of the Israel before the Babylonian captivity were governed by elders, who sat in the gate of the city, and put the laws of Moses in execution, and had a place of worship in or near the gate, and sometimes a high place for sacrificing upon a neighbouring hill. — See Deut. xix. 12, and xxi. 19, 20, 21, and xxii. 18, 19, and xxv. 7, 8, and Ruth iv. 2, and Josh. xx. 4, and Psal. vii. 4-8. And in this sense it is said that the gates of hell, that is the magistrates in the gates of idolatrous cities, shall not prevail against the true Church of Christ.

THESIS 2.

"The government of the Jewish Church being dissolved by the Babylonian captivity, was restored by the commission of Artaxerxes Longimanus, king of Persia, to Ezra, authorizing him to set magistrates and judges to judge the people who knew the laws of God, and to teach them who knew them not, and to execute judgment upon those who would not do the Law of God and the law of the king, whether it were unto death or to banishment, or to confiscation of goods, or to imprisonment.

"For the forming of this government being left to the discretion of Ezra, it may be presumed that he would pursue the ancient form of Jewish government so far as it was practicable. — See Ezra x. 14.

THESIS 3.

"The government then set up by Ezra was by courts of judicature, composed of elders; the highest court being the Sanhedrim, composed of 70 elders, originally instituted by Moses; and <527> the second court being composed of 23 elders in the outward gate of the temple; and the other courts sitting in the synagogues of the cities, and being composed of the elders of the city, not more in number than 23, not fewer than three. — See Matt. x. 17, and xxiii. 34; Luke xii. 11, and xxi. 12.

THESIS 4.

"The government set up by Ezra continued till the days of Christ, and was then extended over all the Roman Empire; and the Jews, by the permission or connivance of the Romans, erected synagogues wherever they were sufficiently numerous to do it; and the elders of cities were called rulers of their synagogues. — See Acts xv. 21, Matt. x. 17, and xxiii. 34, and Luke xii. 11, and xxi.12.

THESIS 5.

"The same government continued among the converted Jews of the circumcision in the regions of Phœnicia, Syria, &c., till the end of the fourth century, or longer, and the chief ruler of the synagogue was called by them the Prince of the Synagogue.

THESIS 6.

"The same government was propagated from the Jews to the converted Gentiles, the name of synagogues being changed to that of churches, and the name of Chief Rulers and Princes of the Synagogues unto that of Presidents and Bishops, the Bishop being the President of the Council of Elders, called in the Greek Presbyters, and the Presbyters in the Council being at length called Prebendaries, from the allowances made to them out of the revenues of the Church for their attendance. But the name of churches was of a larger extent, being given also to single assemblies in private houses, and other places not attended with a Board of Elders, and collectively to the churches of a kingdom or nation, or in the whole world.

THESIS 7.

"It is therefore the duty of bishops and presbyters to govern the people according to the laws of God and the laws of the king, <528> and in their councils to punish offenders according to those laws, and to teach those who do not know the laws of God; but not to make new laws in the name of either God or the king.

THESIS 8.

"The Church is constituted, and her extent and bounds of communion are defined by the laws of God, and these laws are unchangeable.

THESIS 9.

"The laws of the king extend only to things that are left indifferent and undetermined by the laws of God, and particularly to the revenues and tranquillity of the Church, to her courts of justice, and to decency and order in her worship; and all laws about things left indifferent by the laws of God ought to be referred to the civil government.

THESIS 10.

"The king is supreme head and governor of the Church in all things indifferent, and can nominate new bishops and presbyters to succeed in vacant places, and deprive and depone them whenever they may deserve it.

THESIS 11.

"The being of the Church doth not depend upon an uninterrupted succession of bishops and presbyters for governing her; for this succession was interrupted in the time of the Babylonian captivity until Ezra, by the commission of Artaxerxes, appointed new governors. And therefore if it should be again interrupted, the Christian people, by the authority or leave of the king, may restore it. The Christian church was also in being before there was a Christian synagogue.

THESIS 12.

"All persons baptized are members of Christ's body called the Church, even those who are not yet admitted into the communion of the synagogue of any city. For all members circumcised were members of the Church of the Jews in the time of the Babylonian <529> captivity before Ezra restored their polity. And in the days of Ahab, when there remained only 7000 in Israel who had not bowed the knee to Baal, these were the true Church of God, though without an external form of government; and the worshippers of Baal under their external form of government were a church of idolaters, such a church, as in scripture, is called the synagogue of Satan, who say they are Jews and are not, a false church with regard to the God whom they worshipped. And the three thousand baptized by Peter were a Christian church, though they had not yet a bishop, or presbyter, or synagogue, or form of government.

THESIS 13.

"By imposition of hands men are admitted into the communion of the synagogue of a city, and by excommunication they are deprived of that communion, and return into the state they were in by baptism alone, before they were received into communion by imposition of hands, except the sin for which they were excommunicated; and by new imposition of hands they may be received into communion again without new baptism, and therefore by excommunication they do not lose the privilege or benefit of baptism.

THESIS 14.

"Men are not to be excommunicated without breaking one or more of the articles upon which they are admitted into communion. For this would be to alter the bounds of communion settled by the laws of God in the beginning of the Gospel.

THESIS 15.

"To impose any article of communion not imposed from the beginning is a crime of the same nature with that of those Christians of the circumcision who endeavoured to impose circumcision, and the observation of the law upon the converted Gentiles. For the law was good if a man could keep it, but we were to be saved not by the works of the law, but by faith in Jesus Christ; and to impose those works as articles of communion, was to make them necessary to salvation, and thereby to make void the faith in <530> Jesus Christ. And there is the same reason against imposing any other article of communion which was not imposed from the beginning. All such impositions are teaching another gospel.

THESIS 16.

"To refuse communion with any church or synagogue merely upon account of the laws of the king in matters indifferent, unless these laws are imposed not merely as laws of the civil government, but as articles of religion and communion, is disobedience to the king, and schism in relation to the Church.

THESIS 17.

"To distinguish churches from one another by any difference in customs or ceremonies, or in other laws than the laws of God, is improper, and tends to superstitions. And if the distinction occasions a breach of communion, the person insisting upon it as a matter of religion is guilty of the schism. For the distinction being taken from things which are only of human authority and external to religion, ought not to be considered as a part of religion, nor to enter into the definition of a Church.

THESIS 18.

"The fundamentals or first principles of religion are the articles of communion taught from the beginning of the Gospel in catechising men in order to baptism and admission into communion; namely, that the catechumen is to repent and forsake covetousness, ambition, and all inordinate desires of the things of this world, the flesh, and false gods called the devil, and to be baptized in the name of one God, the Father, Almighty, Maker of Heaven and Earth, and of one Lord Jesus Christ, the Son of God, and of the Holy Ghost. — See Heb. v. 12, 13, 14, and vi. 1, 2, 3.

THESIS 19.

"After baptism we are to live according to the laws of God and the king, and to grow in grace and in the knowledge of our Lord Jesus Christ, by practising what they promised before bap <531> tism, and studying the Scriptures, and teaching one another in meekness and charity, without imposing their private opinions, or falling out about them.

THESIS 20.

"The commission to teach and baptize was given to the Apostles as the disciples of Christ, and to their disciples, and the disciples of their disciples, to the end of the world, there being no bishops or presbyters or church government yet instituted among the Christians. But after the institution of governments, the governors appointed men to catechize and baptize, except in cases of necessity, where the original right returned. For Tertullian has told us that in his days the rule was, In casu necessitatis quilibet laicus tingit."

These Theses were called Positions in the original MS., but the term Thesis was afterwards substituted. We have placed them according to their number, and not as in the manuscript.

<532>

No. XXX.

(Referred to in page 350.)

QUÆRIES REGARDING THE WORD ὅμοούσιος.

QUÆRE 1. Whether Christ sent his apostles to preach metaphysics to the unlearned common people, and to their wives and children?

QUÆRE 2. Whether the word ὁμοούσιος ever was in any creed before the Nicene; or any creed was produced by any one bishop at the Council of Nice for authorizing the use of that word?

QUÆRE 3. Whether the introducing the use of that word is not contrary to the Apostles' rule of holding fast the form of sound words?

QUÆRE 4. Whether the use of that word was not pressed upon the Council of Nice against the inclination of the major part of the Council?

QUÆRE 5. Whether it was not pressed upon them by the Emperor Constantine the Great, a catechumen not yet baptized, and no member of the Council?

QUÆRE 6. Whether it was not agreed by the Council that that word should, when applied to the Word of God, signify nothing more than that Christ was the express image of the Father? and whether many of the bishops, in pursuance of that interpretation of the word allowed by the Council, did not, in their subscriptions, by way of caution, add τουτ᾽ ἐστιν ὁμοιούσιος.

QUÆRE 7. Whether Hosius (or whoever translated that Creed into Latin) did not impose upon the Western Churches by translating ὁμοούσιος by the words unius substantiæ, instead of consubstantialis? and whether by that translation the Latin Churches were not drawn into an opinion that the Father and Son had one common substance, called by the Greeks Hypostasis, and whether they did not thereby give occasion to the Eastern <533> Churches to cry out, presently after the Council of Sardica, that the Western Churches were become Sabellian?

QUÆRE 8. Whether the Greeks, in opposition to this notion and language, did not use the language of three Hypostases, and whether in those days the word Hypostasis did not signify a substance?

QUÆRE 9. Whether the Latins did not at that time accuse all those of Arianism who used the language of three Hypostases, and thereby charge Arianism upon the Council of Nice, without knowing the true meaning of the Nicene Creed?

QUÆRE 10. Whether the Latins were not convinced, in the Council of Ariminum, that the Council of Nice, by the word ὁμοούσιος, understood nothing more than that the Son was the express image of the Father? — the acts of the Council of Nice were not produced for convincing them. And whether, upon producing the acts of that Council for proving this, the Macedonians, and some others, did not accuse the bishops of hypocrisy, who, in subscribing these acts, had interpreted them by the word ὁμοιούσιος in their subscriptions?

QUÆRE 11. Whether Athanasius, Hilary, and in general the Greeks and Latins, did not, from the time of the reign of Julian the Apostate, acknowledge the Father, Son, and Holy Ghost to be three substances, and continue to do so till the schoolmen changed the signification of the word hypostasis, and brought in the notion of three persons in one single substance?

QUÆRE 12. Whether the opinion of the equality of the three substances was not first set on foot in the reign of Julian the Apostate, by Athanasius, Hilary, &c. ?

QUÆRE 13. Whether the worship of the Holy Ghost was not first set on foot presently after the Council of Sardica?

QUÆRE 14. Whether the Council of Sardica was not the first Council which declared for the doctrine of the Consubstantial Trinity? and whether the Council did not affirm that there was but one hypostasis of the Father, Son, and Holy Ghost?

QUÆRE 15. Whether the Bishop of Rome, five years after the death of Constantine the Great, A. C. 341, did not receive appeals from the Greek Councils, and thereby begin to usurp the universal bishopric?

<534>

QUÆRE 16. Whether the Bishop of Rome, in absolving the appellants from excommunication, and communicating with them, did not excommunicate himself, and begin a quarrel with the Greek Church?

QUÆRE 17. Whether the Bishop of Rome, in summoning all the bishops of the Greek Church to appear at the next Council of Rome, A. C. 342, did not challenge dominion over them, and begin to make war upon them for obtaining it?

QUÆRE 18. Whether that Council of Rome, in receiving the appellants into communion, did not excommunicate themselves, and support the Bishop of Rome in claiming appeals from all the world?

QUÆRE 19. Whether the Council of Sardica, in receiving the appellants into communion, and decreeing appeals from all the churches to the Bishop of Rome, did not excommunicate themselves, and become guilty of the schism which followed thereupon, and set up Popery in all the West?

QUÆRE 20. Whether the Emperor Constantius did not, by calling the Council of Millain and Aquileia, A. C. 365, abolish Popery? and whether Hilary, Lucifer, . . . . . . were not banished for adhering to the authority of the Pope to receive appeals from the Greek Councils?

QUÆRE 21. Whether the Emperor Gratian, A. C. 379, did not, by his edict, restore the universal bishopric of Rome over all the West? and whether this authority of the Bishop of Rome hath not continued ever since?

QUÆRE 22. Whether Hosius, St. Athanasius, St. Hilary, St. Ambrose, St. Hierome, St. Austin, were not Papists?[38]

<535>

No. XXXI.

( 362.)

DE METALLO AD CONFICIENDUM SPECULUM COMPONENDO ET FUNDENDO.

"℞ cupri partes 11 vel 12, stanni optimi partes 4, arsenici albi partem 1. Cupro liquefacto injiciatur arsenicum, et cum baculo ligneo bene commisceantur agitando. Dein Stannum etiam in frusta divisum injiciatur, et massa iterum agitetur celeriter, atque omnibus sic bene commistis in formam absque mora infundantur.

"Nota 1. Quod Stannum celerrime liquefiat, et massam deinde per fumos suos porosam reddat si diutius stet super ignem ut intentius incalescat.

"2. Massa itaque si iterum fundenda est non debet plusquam ad liquefactionem incalescere.

"3. Potest cuprum antequam miscetur cum stanno, purgari liquefaciendo et injiciendo in 12 uncias cupri liquefacti, primo unciam unam arsenici ac duas tresve uncias antimonii crudi, deinde tres vel quatuor uncias salis nitri per vices, donec totus sal deflagraverit. Tunc massa frigefacta abjiciatur scoria salinosa, et iterum fundatur metallum injicianturque novi salis nitri duæ tresve unciæ per vices, donec totus deflagraverit, ut prius; eritque satis depuratum si sal supernatans post refrigerium albus exierit; sin secus, tertio liquefaciendum est cum sale. Sed interea summe cavendum est a fumis arsenici.

"Ex cupro sic purgato componi potest metallum cum arsenico et stanno ut supra; sed compositio habebitur fortius reflectens et (quantum conjicio) magis resistens ærugini si omisso arsenico injiciatur ad duodecim partes cupri liquefacti, primo una pars Zineti seu Margaritæ albæ et una pars reguli antimonii per se sine te facti, deinde quatuor partes stanni ut supra. Signum optimæ compositionis est ut metallum instar vitri læve appareat ubi frangitur.

<536>

"4. Si metallum in formam infusum, inter refrigerandum in fragmenta sponte dissiliat, id arguit nimium esse stanni pro quantitate cupri. Quare tunc aliquantulum novi cupri, puta duodecima pars totius masssæ per se pendenda est huic fuso injicienda reliqua massa diffracta.

"5. Metallum sic formatum debet esse satis crassum ne inter terendum et poliendum vel minime flecti queat. Majori enim ἀχριβεία debent metalla ad usus opticos formari quam vitra. Quæ ego pro tubo septem fere digitorum fudi, erant quadrantem digiti circiter crassa, duosque digitos lata. Primò quidem formabam tenuiora, et minus lata, sed ex illis nihil perfectum construere potui."

<537>

No. XXXII.

(Referred to in pages 393, 396.)

OBSERVATIONS ON THE FAMILY OF SIR ISAAC NEWTON.

In the year 1705, Sir Isaac Newton gave into the Herald's Office an elaborate pedigree, stating, upon oath, that he had reason to believe that John Newton of Westby, in the county of Lincoln, was his great-grandfather's father, and that this was the same John Newton who was buried in Basingthorpe Church on the 22d December 1563. This John Newton had four sons, John, Thomas, Richard, and William Newton of Gunnerly, the last of whom was great-grandfather to Sir John Newton, Bart. of Hather. Sir Isaac considered himself as descended from the eldest of these, he having, by tradition from his kindred ever since he can remember, reckoned himself next of kin (among the Newtons) to Sir John Newton's family.

The pedigree, founded upon these and other considerations, was accompanied by a certificate from Sir John Newton of Thorpe, Bart., who states that he had heard his father speak of Sir Isaac Newton as of his relation and kinsman; and that he himself believed that Sir Isaac was descended from John Newton, son to John Newton of Westby, but knoweth not in what particular manner.

The pedigree of Sir Isaac, as entered at the Herald's Office, does not seem to have been satisfactory either to himself or to his successors, as it could not be traced with certainty beyond his grandfather; and it will be seen from the following interesting correspondence, that, upon making farther researches, he had found some reason to believe that he was of Scotch extraction.

EXTRACT OF A LETTER FROM THE REV. DR. REID OF GLASGOW TO DR. GREGORY OF EDINBURGH, DATED MARCH 14, 1784.

"I send you on the other page an anecdote respecting Sir Isaac Newton, which I do not remember whether I ever hap <538> pened to mention to you in conversation. If his descent be not clearly ascertained, (as I think it is not in the books I have seen,) might it not be worth while to inquire if evidence can be found to confirm the account which he is said to have given of himself? Sheriff Cross was very zealous about it when death put a stop to his inquiries.

"When I lived in Old Aberdeen above twenty years ago, I happened to be conversing over a pipe of tobacco with a gentleman of that country, who had been lately at Edinburgh. He told me that he had been often in company with Mr. Hepburn of Keith, with whom I had the honour of some acquaintance. He said that, speaking of Sir Isaac Newton, Mr. Hepburn mentioned an anecdote, which he had from Mr. James Gregory,[39] professor of Mathematics at Edinburgh, which was to this purpose: —

"Mr. Gregory being at London for some time after he resigned the mathematical chair, was often with Sir Isaac Newton.[40] One day Sir Isaac said to him, 'Gregory, I believe you don't know that I am connected with Scotland.' — 'Pray how, Sir Isaac?' said Gregory. Sir Isaac said he was told that his grandfather was a gentleman of East Lothian; that he came to London with King James at his accession to the crown of England, and there spent his fortune, as many more did at that time, by which his son (Sir Isaac's father) was reduced to mean circumstances. To this Gregory bluntly replied, 'Newton a gentleman of East Lothian? I never heard of a gentleman of East Lothian of that name.' Upon this Sir Isaac said, 'that being very young when his father died, he had it only by tradition, and it might be a mistake,' and immediately turned the conversation to another subject.

"I confess I suspected that the gentleman who was my author had given some colouring to this story, and therefore I never mentioned it for a good many years.

"After I removed to Glasgow, I came to be very intimately acquainted with Mr. Cross, then Sheriff of Lanark, and one day <539> at his own house mentioned this story, without naming my author, of whom I expressed some diffidence.

"The Sheriff immediately took it up as a matter worth being inquired into. He said he was well acquainted with Mr. Hepburn of Keith, (who was then alive,) and that he would write him to know whether he ever heard Mr. Gregory say that he had such a conversation with Sir Isaac Newton. He said he knew that Mr. Keith, the ambassador, was also intimate with Mr. Gregory, and that he would write him to the same purpose.

"Some time after, Mr. Cross told me that he had answers from both the gentlemen above mentioned, and that both remembered to have heard Mr. Gregory mention the conversation between him and Sir Isaac Newton, to the purpose above narrated, and at the same time acknowledged that they had made no farther inquiry about the matter.

"Mr. Cross, however, continued the inquiry, and a short time before his death, told me that all he had learned was, that there is, or was lately, a baronet's family of the name of Newton in West Lothian or Mid-Lothian, (I have forgot which:) That there is a tradition in that family, that Sir Isaac Newton wrote a letter to the old knight that then was, (I think Sir John Newton of Newton was his name,) desiring to know what children, and particularly what sons he had, their age, and what professions they intended: That the old baronet never deigned to return an answer to this letter, which his family was sorry for, as they thought Sir Isaac might have intended to do something for them."

Several years after this letter was written, a Mr. Barron, a relation of Sir Isaac Newton, seems to have been making inquiries respecting the family of his ancestor, and in consequence of this the late Professor Robison applied to Dr. Reid, to obtain from him a more particular account of the remarkable conversation between Sir Isaac and Mr. James Gregory, referred to in the preceding letter. In answer to this request, Dr. Reid wrote the following letter, for which I was indebted to the late Sir John Robison, Sec. R.S.E., who found it among his father's manuscripts.

<540>

LETTER FROM DR. REID TO PROFESSOR ROBISON RESPECTING THE FAMILY OF SIR ISAAC NEWTON.

"Dear Sir,

"I am very glad to learn by yours of April 4, that a Mr. Barron, a near relation of Sir Isaac Newton, is anxious to inquire into the descent of that great man, as the family cannot trace it farther, with any certainty, than his grandfather. I therefore, as you desire, send you a precise account of all I know; and am glad to have this opportunity, before I die, of putting this information in hands that will make the proper use of it, if it shall be found of any use.

"Several years before I left Aberdeen (which I did in 1764,) Mr. Douglas of Feckel, the father of Sylvester Douglas, now a barrister at London, told me, that, having been lately at Edinburgh, he was often in company with Mr. Hepburn of Keith, a gentleman of whom I had some acquaintance, by his lodging a night at my house, at New Machar, when he was in the rebel army in 1745. That Mr. Hepburn told him, that he had heard Mr. James Gregory, professor of mathematics, Edinburgh, say, that, being one day in familiar conversation with Sir Isaac Newton at London, Sir Isaac said, 'Gregory, I believe you don't know that I am a Scotchman?' — 'Pray, how is that?' said Gregory. Sir Isaac said he was informed that his grandfather (or great-grandfather) was a gentleman of East (or West) Lothian: that he went to London with King James I. at his accession to the crown of England: and that he attended the Court in expectation, as many others did, until he spent his fortune, by which means his family was reduced to low circumstances. At the time this was told me, Mr. Gregory was dead, otherwise I should have had his own testimony, for he was my mother's brother. I likewise thought at that time, that it had been certainly known that Sir Isaac had been descended from an old English family, as I think is said in his Eloge before the Academy of Sciences at Paris, and therefore I never mentioned what I had heard for many years, believing that there must be some mistake in it.

<541>

"Some years after I came to Glasgow, I mentioned, (I believe for the first time,) what I had heard to have been said by Mr. Hepburn, to Mr. Cross, late sheriff of this county, whom you will remember. Mr. Cross was moved by this account, and immediately said: 'I know Mr. Hepburn very well, and I know he was intimate with Mr. Gregory; I shall write him this same night, to know whether he heard Mr. Gregory say so or not.' After some reflection, he added, 'I know that Mr. Keith, the ambassador, was also an intimate acquaintance of Mr. Gregory, and as he is at present in Edinburgh, I shall likewise write to him this night.

"The next time I waited on Mr. Cross, he told me that he had wrote both to Mr. Hepburn and Mr. Keith, and had an answer from both, and that both of them testified that they had several times heard Mr. James Gregory say, that Sir Isaac Newton told him what is above expressed, but that neither they nor Mr. Gregory, as far as they knew, ever made any farther inquiry into the matter. This appeared very strange both to Mr. Cross and me, and he said he would reproach them for their indifference, and would make inquiry as soon as he was able.

"He lived but a short time after this; and in the last conversation I had with him upon the subject, he said, that all he had yet learned was, that there was a Sir John Newton of Newton in one of the counties of Lothian, (but I have forgot which,) some of whose children were yet alive; that they reported that their father, Sir John, had a letter from Sir Isaac Newton, desiring to know the state of his family, what children he had, particularly what sons, and in what way they were. The old knight never returned an answer to this letter, thinking probably that Sir Isaac was some upstart, who wanted to claim a relation to his worshipful house. This omission the children regretted, conceiving that Sir Isaac might have had a view of doing something for their benefit.

"After this I mentioned occasionally in conversation what I knew, hoping that these facts might lead to some more certain discovery, but I found more coldness about the matter than I thought it deserved. I wrote an account of it to Dr. Gregory, <542> your colleague, that he might impart it to any member of the Antiquarian Society, who he judged might have the curiosity to trace the matter farther.

"In the year 1787, my colleague, Mr. Patrick Wilson, professor of astronomy, having been in London, told me on his return that he had met accidentally with a James Hutton, Esq. of Pimlico, Westminster, a near relation of Sir Isaac Newton, to whom he mentioned what he had heard from me with respect to Sir Isaac's descent, and that I wished much to know something more decisive on that subject. Mr. Hutton said, if I pleased to write to him he would give me all the information he could give. I wrote him accordingly, and had a very polite answer, dated at Bath, 25th December 1787, which is now before me. He says, 'I shall be glad, when I return to London, if I can find in some old notes of my mother, any thing that may fix the certainty of Sir Isaac's descent. If he spoke so to Mr. James Gregory, it is most certain he spoke truth. But Sir Isaac's grandfather, not his great-grandfather, must be the person who came from Scotland with King James I. If I find any thing to the purpose, I will take care it shall reach you.'

"In consequence of this letter I expected another from Mr. Hutton when he should return to London, but have never had any. Mr. Wilson told me he was a very old man, and whether he be dead or alive, I know not.

"This is all I know of the matter, and, for the facts above-mentioned, I pledge my veracity. I am much obliged to you, Dear Sir, for the kind expressions of your affection and esteem, which, I assure you, are mutual on my part, and I sincerely sympathize with you on your afflicting state of health, which makes you consider yourself as out of the world, and despair of seeing me any more.

"I have been long out of the world by deafness and extreme old age. I hope, however, if we should not meet again in this world, that we shall meet and renew our acquaintance in another. In the meantime, I am, with great esteem, dear Sir, yours affectionately,

"Tho. Reid.

"Glasgow College, 12th April 1792."

<543>

This curious letter I published in the Edinburgh Philosophical Journal for October 1820. It excited the particular attention of the late George Chalmers, who sent me an elaborate letter upon the subject; but as I was at that time in the expectation of obtaining some important information through other channels, the letter was not published. This hope, however, has been disappointed. A careful search was made at my request through the charter-chest of the Newtons of Newton in East Lothian, by Mr. Richard Hay Newton, the representative of that family, but no document whatever has been found that can throw the least light upon the matter. It deserves to be remarked, however, that Sir Richard Newton, the alleged correspondent of Sir Isaac, appears to have destroyed his correspondence; for though the charter-chest contains the letters of his predecessors for some generations, yet there is not a single epistolary document either of his own or of his lady's.

Hitherto the evidence of Sir Isaac's Scottish descent has been derived chiefly from his conversation with Mr. James Gregory; but I am enabled to corroborate this evidence by the following information, derived, as will be seen, from the family of the Newtons of Newton. Among various memoranda in the handwriting of Professor Robison, who proposed to write the life of Sir Isaac, are the following: —

"1st, Lord Henderland informed me in a letter dated March 1794, that he had heard from his infancy that Sir Isaac considered himself as descended from the family of Newton of Newton. This he heard from his uncle Richard Newton of Newton, (who was third son of Lord William Hay of Newhall.") "He said that Sir Isaac wrote to Scotland to learn whether any descendants of that family remained, and this (it was thought) with the view to leave some of his fortune to the family possessing the estate with the title of baronet. Mr. Newton not having this honour, and being a shy man, did not encourage the correspondence, because he did not consider himself as of kin to Sir Isaac," &c.

"2d, Information communicated to me by Hay Newton, Esq. of that Ilk, 18th August 1800."

"The late Sir Richard Newton of Newton, Bart., chief of <544> that name, having no male children, settled the estate and barony of Newton in East Lothian county upon his relation, Richard Hay Newton, Esq., son of Lord William Hay."[41] — "It cannot be discovered how long the family of Newton have been in possession of the barony, there being no tradition concerning that circumstance further than that they came originally from England at a very distant period, and settled on these lands." — " The celebrated Sir Isaac Newton was a distant relation of the family, and corresponded with the last baronet, the above-mentioned Sir Richard Newton."

In writing to James Watt on the 3d May 1797, Professor Robison says, — "I believe I told you that I had been on the hunt to find documents of Sir Isaac Newton's Scotch extraction, and that he himself firmly believed that his grandfather was a younger son of Sir — — Newton of that Ilk, in East Lothian, and wrote to the last man of the family requesting information whether some of the younger sons did not attend James VI. when he succeeded to the Crown of England? I am still in hopes of finding that letter."[42]

The preceding documents furnish the most complete evidence that the conversation respecting Sir Isaac Newton's family took place between him and Mr. Gregory; and the testimony of Lord Henderland proves that his own uncle, Richard Newton of Newton, the immediate successor of Sir Richard Newton, with whom Sir Isaac corresponded, was perfectly confident that such a correspondence took place.

All these circumstances prove that Sir Isaac Newton could not trace his pedigree with any certainty beyond his grandfather, and that there were two different traditions in his family, one which referred his descent to John Newton of Westby, and the other to a gentleman of East Lothian who accompanied King James VI. to England. In the first of these traditions he seems to have placed most confidence in 1705, when he drew out his traditionary pedigree; but as the conversation with Professor James Gregory respecting his Scotch extraction took place <545> twenty years afterwards, namely, between 1725 and 1727, it is probable that he had discovered the incorrectness of his first opinions, or at least was disposed to attach more importance to the other tradition respecting his descent from a Scotch family.

In the letter addressed to me by George Chalmers, I find the following observations respecting the immediate relations of Sir Isaac: — "The Newtons of Woolsthorpe," says he, "who were merely yeomen farmers, were not by any means opulent. The son of Sir Isaac's father's brother was a carpenter called John. He was afterwards appointed gamekeeper to Sir Isaac, as lord of the manor, and died at the age of sixty in 1725. This John had a son John, who was Sir Isaac's second cousin, and who became possessed of the whole land estates at and near Woolsthorpe, which belonged to the great Newton, as his heir-at-law. John became a worthless and dissolute person, who very soon wasted this ancient patrimony, and, falling down with a tobacco-pipe in his mouth when he was drunk, it broke in his throat, and put an end to his life at the age of thirty years, in 1737."[43]

The following account of Sir Isaac's heir-at-law is given by the Rev. Mr. Mason, Rector of Colsterworth, in a letter to Mr. Conduitt, dated March 23, 1727, three days after Newton's death: — "This morning I received from you the melancholy news of that truly great and good gentleman's death. Sir Is. N. I have, according to your desire, made Sir Isaac's heir and representative, who is the bearer of this, acquainted with it, but, God knows, a poor representative of so great a man; but this is a case that often happens. There are two families of the Newtons in this parish, both descended from the second and third brothers of Sir Isaac's father. The second brother was Robert Newton, from whom the bearer of this, John Newton, is descended. The third was Richard, from whom descends Robert Newton, now living in this parish, so that, without dispute, John Newton, the bearer, is heir to the estate not devised by will."

<546>

No. XXXIII.

(Referred to in page 412.)

LETTER FROM SIR ISAAC NEWTON TO A FRIEND.

"SR,

"Before I received yors I had an account from Mr. Parish of ye arbitration, and thereupon wrote to Mr. Parkins to know how ye indentures run, and to Mr. Storer, to know distinctly what it is that his son Oliver deposes. I had a speedy answer from Mr. Parkins, whereby I understand that Mr. Storer is bound to leave all things in a tenantable repair, by a clause which you do not mention; but from Mr. Storer I have not yet received an answer, and therefore cannot write to you what I designed for putting an end to these differences.

"When I met Mr. Storer and his sons at Wolstrope, yt is at Lady-day last, I was satisfied with the removal of ye wheat hoval and with ye thatch of ye houses in view, as I went up ye yard to ye house. I do not say yt there was no faults, for I am short-sighted, and did not (yt I remember) go close to ye barn, not being then minded to call Mr. Storer to a strickt account for repairs. Thence we went into ye orchard, and I was pleased with ye repairs of ye slated house, but told Mr. Storer's sons yt he was an ill husband with ye drain below, and he promised it should be scoured. Then turning to Robin's house I pointed to two very faulty places in the thatch, and Mr. Storer's son confessed it rained in, and promised it should be mended. Thence I went into ye dwelling-house to receive Mr. Storer's rent, and when he was going to pay it he told me yt his son found boards for ye gutters of ye Lucome windows wch I was to pay for, but ye bill was lost, and so desired yt I would allow 30s for these boards. Alter some words, I put it to him whether he could honestly affirm ye yt boards were worth so much. He answered he could not, but he hoped I would not stand with him for a small matter. To wch I presently answered yt I would not <547> stand with him, and so remitted 30s of his rent on account of ye bill wch he said was lost. About a fortnight after coming to Colsterworth, I was three or four times at Wolstrope, and one of those times going into ye garden I found ye walls ruinous, and in going through ye pales between ye garden and ye house, I observed yt they and ye great gates were much out of order. At yt time also ye pales were wanting to ye swine-coat and some of ye long pales pluckt off from ye cow-house. At yt time I heard also yt they had carried away ye fence from ye new quick in ye clay-field, and made money of it. Mr. Storer represents yt ye hedge was decayed and grown useless before; but this is to excuse one fault with another, for Mr. Storer was to keep it in repair, I paying for ye wood. After I understood these things, I was called out of ye country before I could speak with Mr. Storer, and afterwards, in hay time, I had notice yt ye Linghouse was ruinous, for want of repair, and that Mr. Storer's son refused to repair it. Soon after a friend viewed the tenements, and sent me an acct of those things out of repair whh I had observed, and some other things also whh I had not noted. And at that time, or some time after, I understood that Mr. Storer's son refused absolutely to do any repairs, and had treated Will. Cottam with ill language about it. Whereupon, considering that they had not repaired Robin's house, and left divers other things out of repair, and that Mr. Storer's son, living wt his father, and being his father's agent, cd not persist in a refusal of repairs, witht his father's knowledge and encouragement, I resolved to call the father to a general acct for repairs, whh cd not be done but by suit, and because the son was concerned in the aforesaid hedge, I resolved to sue them both, and this the rather because his son had disparaged the living at Lady-day in my hearing, I being of opinion that he did it as well behind my back as before my face, to hinder me of tenants who might put me upon calling them to account for repairs. This was the occasion of the suit which I tell you, that you may understand I was not rash in beginning it, as Mr. Storer endeavours to persuade his friends.

"I hear 'tis represented I shd be well pleased wt repairs at Lady-day, and allow Mr. Storer 30s on that acct, and say that <548> things were better in repair than when Mr. Burch left them. But I have told you that the 30s was in discharge of a bill, and respected only the slating of the house, whh was done at my charges, and if I was pleased with what I had repaired, what is that to Mr. Storer? Because I eased [him] of repairs of the side of the house, there is the more reason that he shd leave other things in good repair. He was indeed at the charge of carriages, but that was a bargain, and I have, on the other hand, allowed him 30s for boards, whh perhaps were not worth half the money. And if I was kind to him in that, he is very disingenuous to turn it to my disadvantage. For this is to snap me by the fingers for giving him bread.

"Whether I said that things were left better in repair by Mr. Storer than by Mr. Burch I do not remember, and if it be understood generally, it's manifestly false. For I cd not say so of Robin's house, because I complained of its being out of repair, nor of the garden walls, because I had not then viewed them, nor of the gates and pales, because I did not see any repairs of late done to them, nor cd I say so of the repairs of anything for whh I now sue. But of the slated house, and, if you please, of all the houses taken one with another, I might, and do now say, that they were better in repair when Mr. Storer left than when he entered. But then I add, that this is nothing to Mr. Storer's purpose, for 'tis my charge of 11lb 10s in slating, which makes amends for all the rest. And if I have repaired the main building substantially, that must not excuse Mr. Storer from repairing what belongs to his own share. So you see that what Mr. Storer alleges himself amounts to nothing. In short, as I did not begin this suit without just occasion, so now I have begun it I do not intend to end it without satisfaction. If Mr. Storer will send me a satisfactory answer to my last, I'll endeavour to make a final end in my next, but if he goes on to misrepresent things, I'll solicit Mr. Parish to give you another meeting. I thank you for undertaking the office of an arbitrator, and that you may inherit the blessing promised to peace-makers, is the hearty wish of —

"Cambridge, Jan. llth, 878."

<549>

No. XXXIV.

(In reference to pages 381, 382.)

ALTERATIONS AND ADDITIONS MADE IN THE THIRD EDITION OF THE PRINCIPIA.

After perusing Pemberton's letters to Newton, I drew up a list of the additions made to the Principia in the third edition, and of the more important alterations upon the second, in so far as they could be gathered from the letters. It occurred to me, however, that some of his distinguished successors in Cambridge must have had occasion to notice these additions and alterations, and I accordingly applied to J. C. Adams, Esq., of Pembroke College, who has obligingly favoured me with the following interesting communication: —

"I have made no regular comparison of the several editions of the Principia, except with reference to some special points. Some of the differences, however, which I have noticed between the 2d and 3d editions, I will mention below.

"The proof that Newton was acquainted with the true principles of calculating the motion of the moon's apogee, and that he had actually determined that motion to a considerable degree of approximation, is supplied hy a scholium which follows prop. 35 of the 3d book in the first edition. In the subsequent editions this scholium is greatly enlarged, but the evidence on the point above mentioned is unfortunately omitted.

"In the correspondence between Newton and Cotes, published by Mr. Edleston, I can find no allusion to the old scholium.[44]

"Many have supposed that Newton intended to find the motion of the moon's apogee in the 2d corollary to prop. 45 of his 1st book, p. 141, but this is a complete mistake. In the 1st and 2d editions no reference whatever is made to the moon in this corollary, and in the 3d edition is added the remark, 'Apsis lunæ est duplo velocior circiter,' for the express purpose of pointing out that the corollary is not applicable to the case of <550> the moon. In fact, the disturbing force, the effect of which is found in this corollary, is only one part of the sun's disturbing force on the moon, and to the other part the method of the corollary is plainly inapplicable.

"To the 2d edition of the Principia, at page 419, (451 of 3d,) there is added a very elegant proposition by Machin and Pemberton, respecting the motion of the moon's node. It may be thus stated: — The mean rate of motion of the sun from the moon's node is a mean proportional between the rates of motion with which the sun separates from the node when in syzygy and quadrature respectively. I may mention that when stated in this form, the proposition is equally applicable to the motion of the moon's apogee. (See p. 553, bottom.)

"I will now mention some of the other changes which I have noticed in the 3d edition.

"Lemma 11, Cor. 4, p. 31, 2d edit. last line, 'quamque alias sesquialteram dicunt,' is omitted in 3d edit.

"Prop. 4, Cor. 1, p. 38, two lines, from 'centripetæ sunt' to 'in ratione,' are omitted.

"Cor. 2, p. 39, one and a half line, from 'centripetæ sunt' to 'in ratione,' is omitted.

"Prop. 8, p. 44, line 14, 'Circulo' is changed into 'Semicirculo;' and in the scholium, p. 45, 'Et simili argumento corpus movebitur,' is changed into 'Et argumento haud multum dissimili corpus invenietur movere.'

"Prop. 10, Cor. 2, p. 47, for 'ad axes alteros,' is substituted 'ad idem punctum axis communis.'

"At the end of corollary 1, prop. 13, p. 59, 53,[45] is added, 'Eademque velocitate.'[46]

"Prop. 14, Cor. p. 54, after 'QT×SP,' is added, 'quæ dato tempore describitur.'

"Prop. 17, page 57, line 8, 'Sit istud L,' is changed into 'Sit L coni sectionis latus rectum.'

"At the end of prop. 17, p. 64, 57, is added the sentence, 'Nam si corpus,' &c.[47]

<551>

"Scholium to prop. 21, p. 65, at the beginning the sentence ending with 'potest' is added.

"Near the end of the scholium to prop. 31, p. 112, 104, Ward's name is omitted.

"At the end of corollary 19 to prop. 66, p. 182, 167, is added, 'Nisi quatenus motus fluendi,' &c.

"At end of corollary 20 to same prop., p. 183, 168, are added 15 lines, 'Nisi quod loca maximarum,' &c.

"In book ii. p. 246, 226, the Leibnitz scholium is replaced by another.

"To prop. 13, p. 269, 250, a short scholium is added.

"To prop. 14, p. 274, 252, a scholium is added.

"At end of scholium to prop. 22, p. 292, 270, the sentence is added, 'Cæterum per experimenta constat,' &c.

"At the end of corollary 3, prop. 29, p. 303, 280, the clause, 'Quæ et generalior sit,' &c., is omitted.

"Page 292, 2d edit., 'Denique cum receptissima Philosophorum ætatis hujus,' is changed into 'Denique cum nonnullorum,' &c.

"Page 314, Lemma 5, the second paragraph is added, 'Hæc ita,' &c.

"Page 316, Cor. 1, 'duplicata' is omitted in the 3d line.

"Page 317, prop. 39, a scholium of 7 lines is added.

"Page 325, Exp. 13, 'Mense Junio 1710,' is added.

"In book iii., at the end of Regula iii. p. 389, 358, is added, 'Attamen gravitatem corporibus essentialem esse minime affirmo,' &c. Also Regula iv. is added.

"Phenom. i., p. 390, 359, Pound's observations of the elongations of Jupiter's satellites are given. The account of phen. ii. is enlarged. To phen. iii. is added, 'Hos enim luce a sole,' &c.[48]

"Phen. iv., the periodic times of the planets are added.

"Prop. 4, p. 397, 364, Huygens's determination of the force of gravity by means of the pendulum, is cited at greater length, &c. A scholium is added.

"Prop. 5, p. 399, 365, a short scholium is added.

"Prop. 8, corollary 1, p. 406, 370, the masses of the planets are changed.

<552>

"Prop. 10, p. 407, 373, 'Ostendimus utique in scholio,' &c., is added.

"Prop. 17, p. 411, 377, a short paragraph is added on the rotation of Jupiter and of the Sun. Also reference is made to Mercator and Cassini.

"Prop. 19, p. 413, 378. Some changes are made in the account of measurements of degrees; and in the 3d edit., Pound's measures of the polar and equatorial diameters of Jupiter are given.

"Prop. 20, p. 418. A paragraph in p. 384 of 2d edit., 'Hæc ita se habent,' &c., is omitted; as is also another in p. 387, on the figure of the earth, derived from the measures of Picart and Cassini.

"Prop. 24, p. 424, 390, 'Vis solis vel lunæ,' &c., is added.[49]

"Scholium to prop. 35, of 3d edit. The paragraph 'Si computatio accuratior desideretur,' &c., in p. 425 of 2d edit., is omitted.

"Two corollaries are added to prop. 37, p. 471 of 3d edit.

"The fig. to Lemma 10, p. 490, 431 of 3d edit., is simpler than in the former editions.

"In p. 497 of 3d edit., the places of stars compared with the comet of 1680, are given according to Pound.

"Prop. 42, p. 523, of 3d edit., Bradley's observations of the comet of 1723 are given. A paragraph at the end of this prop. at p. 481 of edit. 2, attributing the acceleration of the moon's motion to an increase of the mass of the earth, due to the condensation of vapours from the interplanetary spaces, is omitted in the 3d edit.

"Many of the above changes and additions are very trifling, but I thought I might as well mention what I had noted."

From the letters of Pemberton, I have collected the following additions and alterations, which are not mentioned by Mr. Adams. The pages are numbered as in the second edition.

Page 9, line 14, vas placed after postquam at Pemberton's request.

<553>

Page 17, after Lemmate 23, ejusque corollario is added. Pemb.[50]

" 19, line 10, after retardantur, a whole page nearly is added on the fall of heavy bodies; and for hujus ætatis, in line 14, is substituted ætatis superioris. Newton had made it ætatis novissimæ, but Pemberton says that superioris is Ciceronian.

" 20, line 16, after corpus A, we read (ut ita dicam) in chordam arcus TA quæ velocitatem ejus exhibet, ut habeatur, &c. Line 10 from bottom, quiescens added after corpus B. Pemb.

" 42, Cor. 3 is considerably changed at Pemberton's desire.

" 46, line 4, aliæ inserted after diametri. Pemb.

" 51, line 7, opposita substituted for conjugata. Pemb.

" 51, 52, the diagrams greatly simplified. Pemb.

" 59, 60, Pemberton suggests a change on Prop. 17, which is not adopted.

" 64, line 16, after Positione three new lines are added in place of the last seven lines of Cas. 1. Cas. 2 is also changed. Pemb.

" 79, a paragraph of six lines is added to Prop. 24, by Newton; but Pemberton proposes to have the leaf cancelled, and demonstrates, at some length, the truth of the paragraph which he wishes to substitute. See this Volume, p. 381.

" 87, lines 14 to 18 slightly changed. Pemb.

" 147, lines 13-15 altered by Pemberton.

" 249, Cor., two lines, 'Si centro C, &c.' are added at the beginning.

" 299, line 14, a slight alteration by Pemberton.

" 300, par. 2. See p. 155, note.

" 303, line 16 from bottom, finge is substituted for concipe.

" 305, line 14, after debet, the paragraph is greatly enlarged.

" 321, the second paragraph of Exp. 3 is greatly altered by Pemberton.

<554>

Page 326, after the table, there is inserted an account, occupying two pages, of Desaguliers' experiments in 1719. In the fine paper copy of the third edition, the word ambientis following concavæ, in the third line of the Additions, is struck out. See Horsley, Newtoni Opera, tom. ii. p. 427, note.

" 333, line 21, at expandent, Pemberton adds an explanatory note.

" 364, line 4 from bottom, after revolvantur, is inserted manente lege gravitatis.

" 367, line 5, after proxime, the words uti calculis quibusdam initis, are changed into uti calculo quodam inito.

" 376, Pemberton proposes to leave out the last sentence of the page Et hi motus, &c., but it was not done.

" 376, Prop. 14, Pemberton proposes to alter Cor. 1, but it was not done.

" 377, the whole of Prop. 17 is new, and greatly enlarged.

" 378, Prop. 19 is greatly changed. A paragraph of five lines, and placed at the beginning of the Proposition about Norwood's measurement of a degree, is new. The first paragraph in the 2d edit. is greatly altered.

" 379, the first paragraph is altered.

" 381, the two last paragraphs are greatly changed, and Pound's measures of Jupiter's oblateness are given in a table followed by two new paragraphs.

" 384, paragraph first, and the three last lines of paragraph second, omitted at Pemberton's suggestion.

" 386, 387, more than a page is omitted, and a large paragraph "Virga ferrea," &c., added, Pemb.

" 389, line 3, a prioribus Astronomis non observatæ substituted for nondum observatæ.

" 389, line 32-34, Pemberton suggests "a brief hint at the principle whence the precept contained in this line was deduced," but it is not given.[51]

<555>

Page 390, line 19, an additional reference is made to the new Cor. 20, Prop. 66, Lib. 1. Pemb.

" 415, at the end of this page is added a scholium with Machin's two Propositions on the motion of the moon's nodes. Pemberton suggested the reference to what had been done in his Epistola ad Amicum de Cotesii Inventis, pp. 6 and 7.

" 427, line 2, "25472 ut supra in Prop. 19," is substituted for "85820;" and in line 8, "85472," for "85820."

" 430, 431, the latter half of Cor. 7. is greatly altered.

" 433, the diagram and letters are altered. Pemb.

" 464, line 23, fere is omitted. Pemb.

" 467, line 7, Pemberton says that this is inconsistent with Optics, Qu. 1{illeg}, but no change is made.

" 469, line 23, and 471, lines 27, 28, objected to by Pemberton, but not changed.

" 472, Pemberton criticises the explanation of the ascent of vapour from comets' tails, and proposes to substitute Sectionibus Conicis for Ellipticis, but no change is made.

" 474, line 17, Lusitania for Portugallia. Pemb.

" 481, Before the paragraph beginning line 7-19, Vapores, &c. , mentioned by Mr. Adams, is inserted an account, occupying a page, of the great star in Cassiopeia, seen in November 1572, by Cornelius Gemma. The paragraph beginning with Vapores, and ending with Migrare, immediately follows it; but the last paragraph, beginning with Decrescente, is omitted.

In place of omitting, as he has done, the long paragraph, "Si computatio," as in the Scholium, to Prop. 35, lib. iii. pp. 415 and 463 of third edition, Sir Isaac drew it up in a different form, which I find written as follows on the back of one of Pemberton's letters, without a date:[52] — "Ut radius ad sinum <556> distantiæ Lunæ a Sole ita angulus quidam Q ad Variationem secundam si Lunæ lumen augetur, addendam si diminuitur. Sic habebitur . . . . longitudo Lunæ Angulus vero Q ex observationibus determinandus est. Et interea pro eodem usurpari potest angulus 1′ 45″ donec accuratius determinetur." "It does not appear," says Mr. Adams, to whom I sent the paragraph, "why it was not inserted, as it describes what is now called the Parallactic inequality, and the co-efficient given is not far from the truth. Owing to the want of the paragraph, the process of finding the moon's longitude terminates very abruptly."

[1]

The words in Italics are an interlineation.

[2] See this Volume, page 8.

[3] The letters on Fluxions in Wallis's Works, vol. ii. pp. 391-396.

[4] The letter of Leibnitz is dated 28th March, though in the title prefixed to it by Wallis, and in the following letter, the date is made 28th May.

[5] This memorandum is placed at the very foot of the page, apparently for the purpose of its being cut off.

[6]

Conti's defence of himself, referred to in note 2, page 305, is published without his name in the Bibliothèque Francaise for May and June 1726. Amsterdam, pp. 182-193.

[7]

From the Life of Brook Taylor, p. 121.

[8]

Kilmansegg or Kilmansegger.

[9]

Des Maizeaux.

[10]

Conti was a great favourite of the King, who had invited him to Hanover, and with whom he dined every day.

[11]

Dated Paris, 16th February 1709.

[12]

See page 68.

[13]

Dist. vera 89°.

[14]

Flamsteed says that they were dated November 10.

[15]

October 11, 1706.

[16]

See Baily's Flamsteed, p. 261.

[17]

See Baily's Flamsteed.

[18]

Flamsteed mentions this sum as given to one of Newton's servants for assisting him in the calculations.

[19]

The "Figures for the frontispieces and capitals" were engraved by Catenaro, who, upon "complaining that the first agreement was too hard a bargain," received £20 additional.

[20]

Flamsteed, in his petition to the Queen, December 29, 1710, distinctly states that his Catalogue of 3000 Fixed Stars was finished and ready to be transcribed. <490> "I have made further advances." he adds, "than 'tis proper to mention here, and might have presented your Majesty with the whole work perfected before this time, if his Royal Highness's noble intentions had not been prevented, and my endeavours continually obstructed by those who ought, and whose duty I conceive it was, to have seconded and promoted both." — Baily's Flamsteed, p. 278.

[21]

This is the only place where Swift speaks of Mrs. Barton's lodgings; and it is important to observe, that Newton was at that very time removing from Chelsea to St. Martin's Street, so that Mrs. Barton was probably occupying lodgings for a short time while the house was preparing for her uncle. It is quite clear also, from the extracts dated October 9, 25, and November 28, 1711, that Mrs. Barton was living at Newton's house in Leicester Fields. At this time, too, Mrs. Barton, at Swift's request, carried a message from Bolingbroke to Newton. — See this volume, p. 267, and Edleston's Correspondence, &c., Lett. xxi. p. 36.

[22]

Had Mrs. Barton lived with Halifax, Swift, who "loved her better than any body in London," would not have been teased by the invitation.

[23]

The wife of Sir Robert Worsley, Bart., and only daughter of Viscount Weymouth.

[24]

Mrs. Barton lived with Newton in Martin Street, Leicester Fields.

[25]

Professor De Morgan says that Mrs. Barton's intimacy with Swift was probably through Halifax. It was more probably through Lady Betty Germaine, whom Swift had known from her childhood. Lady Betty was a daughter of the Earl of Berkeley, to whom Swift had been chaplain and private secretary. Many of her letters to Swift are published in his Correspondence.

[26]

Swift's Works, vol. xvii. p. 101. Edit. Edin. 1784.

[27]

Mrs. Barber was a great friend and favourite of Swift. She was the author of a volume of poems, which were dedicated to the Earl of Orrery, and the proposals here referred to, were probably proposals to publish her poems by subscription. — See Swift's Works, vol. xvii. p. 77, and vol. xviii. p. 55.

[28]

The Abbé Conti. Newton must have forgotten or forgiven the offence which he had taken at the Abbé, for having "assisted Leibnitz in engaging him in new disputes." See pp. 305, 306, and APPENDIX No. III. p. 431. The conduct of the Abbé in reference to his Chronology appears to have revived the former feelings of Newton.

[29]

John Keill was born in Edinburgh in 1671, and studied mathematics there under David Gregory, whom he accompanied to Oxford in 1694, having obtained one of the Scotch Exhibitions in Balliol College. He acquired a high reputation at Oxford as a teacher of the Newtonian philosophy, by apparatus provided by himself. His Introductio ad Veram Physicam appeared in 1701, and his Introductio ad Veram Astronomiam in 1708. He was appointed Savilian Professor of Astronomy at Oxford in 1710, and in 1711 he entered the lists against Leibnitz and Bernoulli, as the able and staunch champion of Newton, as will be seen in the first two chapters of this volume. He died in 1721, in the 50th year of his age.

[30]

M. Arlaud, an eminent Swiss painter, who resided in Paris, and improved some of the diagrams for Coste's French translation of Newton's Optics, which appeared in 1722. — See Edleston's Correspondence, &c., p. 88.

[31]

July 5th.

[32]

This letter will be found in p. 511, sect. 3.

[33]

This letter is published in the Contemplatio Philosophica, pp. 84-88.

[34]

See Edleston's Correspondence, &c., p. 187.

[35]

This is the wine mentioned in p. 491, as intended for Miss Barton.

[36] This letter is published at the end of Keill's letter to Bernoulli.

[37]

He even says that Newton wrote against 1 John v. 7, as other orthodox persons have done. Page xxi. Tracts, &c. Lond. 1820.

[38]

The Quæries after No. 14 are not numbered in the original.

[39]

The nephew of the celebrated James Gregory, the Inventor of the Reflecting Telescope.

[40]

This must have been after October 1725. — See pp. 385, 387.

[41]

This entail was executed in 1724, a year or two before Sir Richard's death.

[42]

Origin and Progress of the Mechanical Inventions of James Watt. By James Patrick Muirhead, Esq., A.M. Vol. ii p. 252. Lend. 1854.

[43]

See this volume, page 410, note.

[44]

There is a slight allusion to it in the Correspondence, &c., p. 109.

[45]

The first number for the page is the number in the 3d edition, and the second number is that in the 2d edition.

[46]

Suggested by Pemberton.

[47]

Id.

[48]

Suggested by Pemberton.

[49]

Suggested by Pemberton.

[50]

The word Pemb. indicates that the alteration was made at the suggestion of Pemberton.

[51]

If Newton had complied with Pemberton's suggestion, all the difficulties connected with the motion of the moon's apogee would have been avoided. The para <555> graph to which Pemberton's suggestion relates, viz., "Diminui tamen debet motus Augis sic inventus in ratione 5 ad 9 vel 1 ad 2 circiter, ob causam quam hic exponere non vacat," clearly implies that Newton knew the reason.

[52]

In this letter Pemberton calls Newton's attention to lines 24, 25, 26, 27, of page 341, and asks him to compare them with the second paragraph of the Scholium to <556> Prop. 34, Book ii. p. 300; "for," he says, "if what is inserted in these lines before us be universally true, without any restriction, how can what is delivered in that paragraph be of any use in the forming of ships?"

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