The polite terms in which you are pleased to express your estimate of that portion of my “Introduction” which has been printed, could not fail to give pleasure to the writer. And the kind conclusion of your letter claims more than formal thanks: it is, in commercial phrase, a draft upon the affections, which the heart is ready and willing to pay. I intend to indulge myself in the high gratification of making a visit to Monticello next July; and regret that I could not, without great inconvenience have done so last summer. With an ardent curiosity to see the University, considerations, I cannot call them hopes, are connected, which make me desirous1 to see you, as soon as the duties in which I am engaged shall permit.

There is something in the organization of Wm & Mary which, independently of location or other permanent disadvantages, must forever prevent it from being prosperous or successful: and while I sincerely congratulate the friends of the University, on their success in the late session of the legislature, in its favour, I am inclined to think, that when it goes into operation, we shall scarcely have occasion to open the doors of the old College. Even at present there is no reputation to be acquired here; and no encouragement to activity or zeal.

Your comparative view of the French and English writers on mathematical and physical science is that which I have long entertained. Two great works however, in the english language, those of Young and Robison, may be regarded as exceptions to the general standard of the english writers on the various subjects of mechanical philosophy. Yet, I confess, I am not a convert to the theory of light and heat which is so ably defended by the former; the theory of undulations in a diffused universal medium. The latter, in his system of mechanical philosophy, which is delivered in the happiest style of an experienced teacher, avails himself of the best and latest investigations of his cotemporaries of every country. He is indeed very severe in his occasional remarks, on the earlier continental writers, who opposed the system of Newton; and on those who, afterwards, laboured to diminish the splendour of that great mans reputation. But to his own distinguished cotemporaries, and more immediate predecessors, he extends all that amenity and respect which enlightened genius should indulge towards kindred2 minds. Aepinus,3 Euler, Boscovich, Clairaut, Lagrange, Bossut, Buat, Coulomb, and Laplace, are among those whose names most frequently grace his pages. The British Chemists have, perhaps, better maintained their ground in the struggle for preeminence, for the last twenty years, than the mathematical philosophers. The discoveries of Davy, and the systematic labours of Murray are, alone, monuments to british talent.

The fluxional notation and ideas must, undoubtedly, give place to the differential method, in England and in this country, at no distant period. The clearness and facility of the latter compared with the obscurity and difficulty of the former, in the hands of beginners, will soon fix the destiny of the two methods. The best scotch mathematicians have already decided in favour of the differential method. The new Eding Encycloa edited by Brewster, has an admirable treatise on this calculus, in which, the only thing fluxional to be found, is the title. The writer acknowledges his regret that there is not, in the english language, any work which presents a competent view of this calculus, in its present improved form. He has, however certainly done much towards the removal of the cause of that regret, by giving a copious view of this branch of mathematical science, in its most finished state. All ideas of velocities are rejected, and even all geometrical appeals. It is treated4 rather as a part of universal arithmetic, and in a manner purely analytical. But it is written for the learned; at least, students, who have made the usual proficiency in our colleges to entitle them to a first degree, would rarely be capable of proceeding to the study of that treatise. Something is required in a more simple and elementary form for general use. And we may hope, that this want in the english aids to instruction shall soon be supplied: the information which you recently received, with respect to the impressions at Cambridge, encourages this expectation. In the mean time a translation of the elementary work of Bourguet, or of5 Garnier, on this subject, would be very useful in our public institutions. My second son, whom I call the mathematician, has almost completed a translation of the “Élémens du Calcul Differrentiel” of Bezout, for the use of his younger brother who is already an expert algebraist: the work of Bezout being the only elementary one to which he has access, that treats the subject by the theory of infinitessimals. He has himself been engaged in reading the more abstruse, and more perfect treatise, in Brewsters Encyclopa   Although we have a pretty large library in the college, we have very few books of real use to the professors, unless those on metaphysics, or what has been pompously denominated the Philosophy of mind, are to be esteemed as such. We have a great deal of old Theology and of old science. At present indeed we have the works of Bezout and Laplace, and some choice books on Chemistry; and also the systems of natural and mechanical philosophy of Young and Robison, which after three years of solicitation were imported, and received last summer. And of course we have access to most of the old writers on Physics and mechanics from Archimedes to Newton. But it was rather a strange circumstance, that soon after I came to this place, the Principia of Newton, the works of Pemberton and Maclaurin, the optics of Smith, the mechanics of Emmerson and of Vince, with almost every useful work in my department, at that time in the library, disappeared; and did not reappear for nearly three years after, although I openly lamented the want of that assistance they could have afforded me, destitute as I then was of better helps. I had unfortunately considered my situation as that of a servant of the community rather than the servant of an individual, and have been duly corrected for the heretical sentiment. I would not presume to mention these things to you, did I not know, that you take a peculiar interest in the progress of education, and particularly, perhaps, in the schemes of public institution, established, in the country which owes to yourself and to your associates of the revolution, for nearly half a century, so many and so great obligations.

I have hesitated to trouble you with the present letter, aware that the correspondence which, at your advanced period of life, you may still find agreeable to sustain, must be with old, and probably very distant friends. But reflecting, that to read is less fataguing than to write, and that an acknowledgement was really due for that assurance of welcome which you have been so good as to give me, I came to the determination to tender it in this form. And with my thanks for the personal favour, and the sentiments of purest respect, I remain your obt Servt