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Her character, as delineated by her husband with somewhat of mathematical precision, is this: "that she was virtuous without

"blemish,

of the Greenwich Observations, which will be a work of good use, especially as it is now freed from the trifles it was loaded with. Sir, I have one thing which I would trouble you with further, and that is, to let me know what lectures, or other papers of Sir Isaac Newton's, remain in your University unpublished. This may be done at your leisure. It would be a great satisfaction to me, if I could be any way serviceable to you here at London; and should readily embrace any'opportunity to approve and express myself. what I am exceedingly obliged to be,

Your most affectionate friend,.

And faithful servant,

William Jones

From the Same to the Same.

Sjr, London, Oct. 25, 1711.

The favour of your account of Sir Isaac's papers left at Cambridge, I return you my hearty thanks for; and, as you have some further considerations about the Doctrine of Differences, I am assured that they cannot but be valuable; and if a few instances of the application were given, perhaps it would not be amiss. Having tarried some time for a convenient opportunity, I was obliged to send you at last Moreton's book by the carrier, though it will only satisfy you that Dr. Gregory had but a very slender notion of the design, extent, and use of lib. 3d of the Principia. I hope it will not be long before you find leisure to send me what you have further done on this curious subject. No excuse must be made against the publishing of them, since with respect to reputation, I dare say it will be no way to your disadvantage. I have nothing of news to send you, only the Germans and French have in a violent manner attacked the philosophy of Sir Isaac Newton, and seem resolved to stand by Des Cartes. Mr. Keil, as a person concerned, has undertaken to defend and answer some things, as Dr. Friend and Dr. Mead do in their way, the rest. I would have sent you the whole controversy, was I not sure that you know those only are most capable of objecting against his writings, that least understand them. However, in a little time, you wilL see some of them in the Philosophical Transactions.

I am, Sir,

Very much your friend and servant,

William Jones. c Answeh ** blemish, generous without extravagance, frugal but not nig"gard, cheerful but not giddy, close but not sullen, ingenious

"but

Answer to the foregoing, by Mr. Cotes.

Dear Sir,

I have received Moreton's book. I thank you for the favour you did mie in sending it. I have looked over what relates to his way of interpolation; but I find no cause from thence to make any alteration. The controversy concerning Sir Isaac's philosophy is a piece of news that I had not heard of. I think that philosophy needs no defence, especially when attacked by Cartesians. One Mr. Green, a fellow of ClareHall, seems to have nearly the same design with those German and French objectants, whom you mention. His book is now in our press, and almost finished I am told; he will add an Appendix, in which he undertakes also to square the circle. I need not recommend his performance any further to you.

I am, Sir, your obliged friend,

And humble servant,

R. C.

From Mr. Jones to Mr. Cotes.
Dear Sir, London, Jan. 11, 1711-12.

I have sent you here enclosed the copy of- a letter, that I found among Mr. Collins's papers, from Sir Isaac Newton to one Mr. Smith. The contents thereof seem in a great measure to have relation to what you are about, as being the application of the Doctrine of Differences to the making of tables; and for that reason I thought it might be of use to you, so far as to see what has been done already. I shewed this to Sir Isaac: he remembers that he applied it to all sorts of tables. I have more papers of Mr. Mercator's, and others, upon this subject; though I think none so material to your purpose as this. I should be very glad to see what you have done upon this subject all published; and I must confess, that unless you design a large volume, it were much better to put them into the Philosophical Transactions, for that would sufficiently preserve them from being lost, which is the common fate of small single tracts, and at the same time, to save the trouble and expense of printing them, since the subject is too curious to •expect any profit from it; and besides now, as the Royal Society having done themselves the honour of choosing you a member, something from you cannot but be acceptable to them. Sir Isaac himself expects these things of you, that I formerly mentioned to him as your promise.

I am, Sir, your much obliged friend, and humble servant,

William Jones.

From ** but not conceited, of spirit but not passionate, of her com"pany cautious, in her friendship trusty, to her parents dutiful,

"and

From Mr. Jones to Mr. Cotes.
Sih; London, Feb. 6th, 1712-15.

The Royal Society having ordered one of their books for you, and another for Mr. Saunderson, also one for Trinity-College library, and one for the University library; I would not lose the opportunity of paying you my respects, by sending them. I need not tell you the occasion and design of that collection. You will see readily, that it affords such light concerning what it relates to, as could not easily have been discovered any other way; it also shews, that your gieat predecessor, whose illustrious example I do'nt doubt but you follow, never employed his time about things ordinary. I have no mathematical intelligence to send you. Mr. Keil thinks he has discovered a very easy and practical solution of the Keplerean problem. If Moreton's book is of no use to you, please to send it to me, though I fear it will yield me but small assistance, having occasion for variety' of modern solstitial meridian altitudes of the Sun, such as may be depended upon. Helvetius, Flamstead, and the French observations, seem defective. I should be glad to be informed where I can be supplied best. I am extremely pleased to find that Sir Isaac's book is so near being finished; and it is not less agreeable to me to hear, that your own book is in such forwardness. You are much in. the right of. it to print your lectures and other papers, in a book by itself: it is better than. to have them lie up and down among other things. What I formerly proposed as to the putting of things in the Philosophical Transactions, is only fit for a sheet or two, but not exceeding that. I very much long to see those valuable pieces, and hope you will let me know in what time I may expect them.—Do me the justice to believe, that I am, with. all sincerity,

Your most humble servant,

William Jones.

From the Same to the Same.
Sib, London, April 2Qth, 17 IS.

Ever since I received your very kind letter, and Moreton's book, I waited for an opportunity of sending you some old manuscripts I had by me, and at last am obliged to venture them by the carrier. They relate, in some measure, to the method of Differences: the folio one, I find, was written by one Nath. Torperly, a Shropshire man, who, when young, was amanuensis to Vieta, but afterwards writ against him. He was coternporary with Briggs. The book, I think, can be of no other use to you than in what relates to the history of that method, and in having the satisfaction of seeing

what "and to her husband ever faithful, loving, and obedient." She had by nature a strong understanding, which was improved by his conversation and 'instruction. Under his tuition she became a considerable proficient in Algebra, and with a view to qualify herself for the office of preceptor to her sister's son, who was destined to a maritime profession, made herself perfect in Trigonometry, and the Theory of Navigation. Mrs. Jones, after the death of her husband, was urgently and repeatedly solicited, by the Countess of Macclesfield, to remain at Sherborne Castle; but having formed a plan

what has been formerly done on that subject. I am mightily pleased to see the end of the Principia, and return you many thanks for the instructive index, that you have taken the pains to add, and hope it will not be long before we shall see the beginning of that noble book. I shall be in some pain till I hear that you have received my old manuscript, it being a favourite purely on account of some extravagancies in it; but I shall think it safe in your hands.

I am, Sir,

Your affectionate friend, and humble servant,

William Jones.

From the Same to the Same.
Dear Sib, London, July Wth, 1713.

It is impossible to represent to you, with what pleasure I received your inestimable present of the Principia, and am much concerned to find myself so deeply charged with obligations to you, and such I fear as all my future endeavours will never be able to requite. This edition is indeed exceedingly beautiful, and interspersed with great variety of admirable discoveries so very natural to its great author; but it is more so from the additional advantage of your excellent preface, which I wish much to get published in some of the foreign journals; and since a better account of this book cannot be given, I suppose it will not be difficult to get it done. Now, this great task being done, I hope you will think of publishing your papers, and not let such valuable pieces lie by. As to what you mentioned in your last, concerning my old manuscripts, though for my part I know of nothing worth your notice publicly in them, but, if you do find any, the end of my sending them is the better answered; and you know that you may do as you please. <

I amj Sir,

Your most obedient servant,

William Jones.

for for llie education of her son, with an unalterable determination to pursue it, and being apprehensive that her residence at Sherborne might interfere with the execution of it, she declined accepting the friendly invitation of the Countess, who never ceased to retain the most affectionate regard for her.

In the plan adopted by Mrs. Jones for the instruction of hers on, she proposed to reject the severity of discipline, and to lead his mind insensibly to knowledge and exertion, by exciting Ins curiosity, and directing it to useful objects. To his incessant importunities for information on casual topics of conversation, which she watchfully stimulated, she constantly replied, read, and you will know; a maxim, to the observance of which he always acknowledged himself indebted for his future attainments. By this method, his desire to learn became as eager as her wish to teach; and such was her talent of instruction, and his facility of retaining it, that in his fourth year he was able to read, distinctly and rapidly, any English book. She particularly attended at the same time to the cultivation of his memory, by making him learn and repeat some of the popular speeches in Shakespeare, and the best of Gay's Fables.

If, from the subsequent eminence of Sir William Jones, any general conclusion should be eagerly drawn in favour of early tuition, we must not forget to advert to the uncommon talents both of the pupil and the teacher.

In common cases, premature instruction has often been found to retard, rather than accelerate, the progress of the intellectual faculties; and the success of it so much depends upon the judgment of the tutor, and the capacity of the scholar, upon the skill of the one, as well as upon the disposition and powers of the other, that it is impossible to prescribe a general rule, when instruction ought

to

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