I take the liberty of sending you a copy of a little work which I prepared for the use of one of my classes in Wm & Mary. I intended to have sent it to you last year, but was induced to defer doing so from the expectation that I should before now, have found it convenient to get the diagrams engraved. The state of this institution, however, does not encourage me to incur the expense; and perhaps it as useful as it is, to the student, who must take the diagrams at the black board, and draw out a fair copy for himself. One of my former pupils has furnished the copy of diagrams which I send you, from notes, taken when he attended my lectures. I believe they are correct with respect to litteral references; a little distortion of the figure occasionally occurs.

The book, if I may call it so, presents a greater number of typographical errors than might be expected in so few pages. I prepared the manuscript in Richmond during the vacation; and by the time the printers had procured the mathematical signs from Philadelphia the period of the vacation was nearly expired. I was desirous of having a few copies for the immediate use of my class, and the printers, although unaccustomed to this kind of work, wished to proceed with the job. I have corrected the copy which I send you with a pencil.

The printing of so small a volume on a subject so copiously and so ably treated by many writers, appears to require an apology. My principal object is indicated in the title page; but I had particular motives connected with my situation. The text book which I am required to employ, is the American edition of Cavallo’s Natural Philosophy. This edition differs from the English one, in the omission of several very pleasing popular views, and in the addition of a great number of abstruse investigations and of insulated theorems on difficult subjects. The matters omitted would be calculated to make the student love the science; those which are added are very well adapted to frighten beginners, as few of them can be read, but by men who are already familiar with several of the higher branches of the mathematics. Besides, the work of Cavallo is not by any means sufficiently comprehensive with respect to the elementary physico-mathematical principles to prepare any student, whatever may be his talents, to advance in order and without collateral reading, to the successful study of the additions made made by the american editor. yet a little more than three years ago, at the instance of a member of our faculty, whose slight acquaintance with arithmetic limits his mathematical attainments, it was ordered by the Visiters, that the students in the Nat. Philosophy class should be required to recite formally from that book, page by page, without any omission or selection of matter. The object of that individual was to destroy that class.

The students who attend our courses are generally very deficient in preparatory schooling; and a great proportion of them seem to be altogether incapable of steady application, from the want of early discipline. My “Introduction &c” was arranged in some measure with a view to the improvement of mental discipline; its plan being convenient for regular recitals at the black board, or otherwise: and with the hope, that a familiar acquaintance with the principles it contains, would enable the student in Nat: Phil: (who is duly prepared in mathematics) to pursue a more general reading, with satisfaction and enjoyment; and to encounter future difficulties in the science, with confidence and alacrity.

In the year 1803 the Revd James Wood of Cambridge England, published a synopsis of elementary principles, on a plan for ready recital, under the title of “Principles of Mechanics, intended for the use of the students of the University.” At one time I had thoughts of employing that work as an auxiliary to our text book. But upon further consideration it appeared to me too meagre in its form, too much of a skeleton; nor did I admire either his method or taste. I have followed what is perhaps, a very common, and certainly a very natural inclination. A professor who loves the science which he teaches will be fond of treating it in a manner as a favourite child, by dressing it according to his own fancy, and by presenting it in that attitude, which he supposes may most effectually secure to it, at first sight an approving glance, as a kind sentiment.

The demonstrations of the 14th 35th 68th and 93d propositions are by my second son, who is now in his 20th year—he has a very extraordinary passion for the mathematical and physical sciences. Three or four other demonstrations are taken, without alteration, from the writings of Dr Robison and Dr Thomas Young. All the rest if the work is in my own method and language, my general guides being Newton, Robison, Mouge, Young, &c.