had stood, merely by the note it sounded. Dr. Saunderson had a peculiar method of performing arithmetical calculations, by an ingenious machine and method, which has been called his "Palpable Arithmetic, and is particularly described in a piece prefixed to the first volume of his Algebra. That he was able to make long and intricate calculations, both arithmetical and algebraical, is a thing as certain as it is wonderful. He had contrived for his own use, a commodious notation for any large numbers, which he could express on his abacus, or calculating table; and with which he could readily perform any arithmetical operation by the sense of touch only, for which reason it was called his "Palpable Arithmetic." His calculating table was a thin smooth board, a little more than a foot square, raised upon a small frame so as to lie hollow; which board was divided into a great number of little squares by lines intersecting one another perpendicularly, and parallel to the sides of the table, and the parallel lines only one tenth of an inch from each other, so that every square inch of the table was thus divided into one hundred little squares. At every point of intersection, the board was perforated by small holes, capable of receiving a pin; for it was by the help of pins stuck up to the head through these holes, that he expressed his numbers. He used two sorts of pins, a larger and a smaller sort; at least, their heads were different, and might easily be distinguished by touch. Of these pins he had a large quantity in two boxes, with their points cut off, which always stood ready before him when he calcu lated. The writer of that account describes particularly the whole process of using the machine, and concludes, "He could place and displace his pins with incredible nimbleness and facility, much to the pleasure and surprise of all the beholders; he could even break off in the middle of a calculation, and resume it when he pleased, and could presently know the condition of it, by only drawing his fingers gently over the table." Saunderson's method of calculation deserves particular notice, not merely because it is the production of a blind man, but because it is calculated to be useful to such of the blind as may make mathematics their study. Many blind philosophers of great eminence have derived advantages from Saunderson's invention; it has enabled them to make out their long and difficult calculations, which they perhaps never would have been able to accomplish without its assistance. Among those I may mention the names of Grenville, Moyes, and Ward. For a more particular description of this curious contrivance, the reader is referred to the following letter from M. Diderot to a lady: "This Saunderson, madam, is an author deprived of sight, with whom it may not be foreign to our purpose to amuse you. They relate prodigies of him; and of these prodigies there is not one, which his progress in the Belles Lettres and his mathematical attainments do not render credible. The same instrument served him, for algebraical calculations, and for the construction of rectilineal figures. You would not, perhaps, be sorry that I should give you an ex plication of it, if you thought your mind previously qualified to understand it; and you shall soon perceive that it pre-supposes no intellectual preparations, of which you are not already mistress; and that it would be extremely useful to you, if you should ever be seized with the inclination of making long calculations by touch." (See Transactions of the French Academy.) Mr. Saunderson, in mathematical learning, was equal to any of his time; and in the capacity of a teacher, perhaps superior to all. Whatever pieces, therefore, the world might be favoured with from so excellent a master, could not fail of meeting with a kind reception; and his work on the method of fluxions, though far from being a complete system of the fluxionary calculus, will prove of the utmost advantage to students in this branch of science. That perspicuity, that simple analysis and elegant construction, for which Dr. Saunderson was so remarkable and so justly celebrated, appear throughout this whole treatise. The consummate master and finished teacher are here fully displayed, in a judicious choice of examples, and the perspicuous method of solving and applying them. 'What the Doctor has given us," (says a learned writer very justly,) "upon Mr. Cotes's Logometria is particularly valuable, as by his intimate acquaintance with that extraordinary person, he may be presumed to have understood his writings better than any one at that time living, Dr. Smith only excepted, to whose superior genius and faithful care the world is so much indebted for the improvement, as well as the preser vation of Mr. Cotes's Works. But we are much mistaken if the latter part of this treatise, (we mean his explanation of the chief propositions of Sir Isaac Newton's Principia,) does not prove as valuable as what he has given us on the writings of Mr. Cotes. Every person who has attempted the arduous study of Sir Isaac's Principia, must be sufficiently acquainted with the difficulties of fully comprehending the demonstrations in that illustrious author. Dr. Saunderson has removed many of these difficulties; and thereby rendered the study of the Principia much pleasanter and easier than it was before." We have already observed, that this treatise is not a complete system of the Fluxionary Calculus; its readers must therefore, be previously acquainted with the elementary parts of Fluxions, or be assisted, viva voce, by a master. With either of these helps, he will find it one of the most useful treatises that has hitherto appeared on the subject. AUTHORITIES. HUTTON'S Mathematical Dictionary-NICHOLSON's Philosophical Journal-REID's Inquiry into the Human Mind-London Monthly Critical Review. THE LIFE OF LEONARD EULER, Professor of Mathematics in the Royal Academy of Saint Petersburgh, and Member of the Royal Societies of London, Berlin, Paris, Vienna, and Stockholm. "To him the motion of each orb was known, AMONG those eminent Philosophers who, by their lives and writings, have rendered so much service to mankind, is Leonard Euler; a man whose cultivated mind, and high intellectual attainments, and above all, his deep and unaffected piety, have rendered him the ornament of his country, and will transmit his name to posterity, not only as one of the greatest men but also as one of the best the world has ever yet produced. LEONARD EULER was the son of a Clergyman in the neighbourhood of Basil, and was born on the 15th G |