Mathematick" and the other books mentioned were actually printed; they existed only in manuscript copies. From the above it appears that about 1724 the mathematical course at William and Mary was quite equal to that in either of the two New England colleges. We must, of course, guard ourselves against the impression that full and exhaustive courses were given in algebra, geometry, surveying, and navigation. As is pointed out by the author himself, the merest rudiments only were imparted.

Reverend Jones was succeeded by Alexander Irvine, and he in turn by Joshua Fry. Fry was educated at Oxford, and, after coming to this country, was made master of the grammar school connected with William and Mary, and later, professor of mathematics in the college. In company with Peter Jefferson, the father of Thomas Jefferson, he made a map of Virginia. He also served on a commission appointed to deter mine the Virginia and North Carolina boundary line. He was succeeded in 1758 by William Small.

A few years before the outbreak of the Revolutionary War William and Mary College had among her students several who afterwards rose to prominence; she had four who became signers of the Declaration of Independence, and also the illustrious Thomas Jefferson, who became the author of this great document. At William and Mary, Jefferson was a passionate student of mathematics. The college long exercised the duties of the office of surveyor-general of the Colony of Virginia. Thomas Jefferson's father was a practical surveyor, who had been chosen in 1747 with Joshua Fry, then professor of mathematics at Willam and Mary, to continue the boundary line between Virginia and North Carolina.

When Thomas Jefferson, at the age of seventeen, entered the Junior class, he came into intimate relation with Dr. William Small, of Scotland, who was then the professor of mathematics. As an instructor he had the happy gift of making the road of knowledge both easy and profitable. In his Autobiography Jefferson says: "It was my great good fortune, and what probably fixed the destinies of my life, that Dr. William Small, of Scotland, was then professor of mathematics, a man profound in most of the useful branches of science, with a happy talent of communication, correct and gentlemanly manners, and an enlarged and liberal mind. He, most happily for me, became soon attached to me, and made me his daily companion when not engaged in the school; and from his conversation I got my first views of the expansion of science, and of the system of things in which we are placed."

In 1773 Thomas Jefferson was appointed surveyor of the county of Albemarle. But the college of Williamsburg left its stamp upon Jef ferson, not merely as a qualified surveyor, but also as a statesman, philosopher, economist, and educator. We dwell with special interest upon his association at college with Dr. Small, because in later years, when filling the office of President of the United States, we shall marvel at the rich fruits his early association with a lover of exact science brought

forth. It was during Jefferson's administration that a systematic plan of conducting the Government surveys of the great North-West Territory was initiated; it was during his administration that the great work of the U. S. Coast Survey was first inaugurated. He took also great interest in the enlargement of the U. S. Military Academy. In these great movements the personal interest and enlightened zeal of Jefferson himself were the primary motive power. His biographers tell us that he was the first discoverer of the formula for constructing the mouldboard of a plow on mathematical principles. He wrote to Jonathan Williams on this subject, July 3, 1796: "I have a little matter to communicate, and will do it ere long. It is the form of a mould board of least resistance. I had some years ago conceived the principles of it, and I explained them to Mr. Rittenhouse." We quote the following to show that even in his old age he still loved the favorite study of his youth. Said he in a letter to Col. William Duane, dated October, 1812, "When I was young, mathematics was the passion of my life. The same pas sion has returned upon me, but with unequal powers. Processes which I then read off with the facility of common discourse, now cost me labor and time, and slow investigation." Of interest are also certain passages in a course of legal study which he drew up for a young friend: Before you enter on the study of law a sufficient groundwork must be laid. Mathematics and natural philosophy are so useful in the most familiar occurrences of life and are so peculiarly engaging and delightful as would induce every one to wish an acquaintance with them. Besides this, the faculties of the mind, like the members of the body, are strengthened and improved by exercise. Mathematical reasoning and deductions are, therefore, a fine preparation for investigating the abstruse speculations of the law." Among the books in mathematics recommended by Jefferson to his young friend are, Bezout's Cours de Mathématique-the best for a student ever published; Montucla, or Bossut, Histoire des Mathématiques; Astronomy-Fergu son, and Le Monnier or De Lalande.

It should not be left unmentioned here that George Washington once applied to the College of William and Mary for an elective course in land surveying, and that he received his first commission as county surveyor from the faculty of the college. In this connection we can not refrain quoting a passage from the excellent monograph by Dr. Herbert B. Adams on the College of William and Mary. "It is interesting," says he, "to trace the evolution of men as well as of institutions. It is generally known that Washington began his public life as a county surveyor, but, in all probability, few persons have ever thought of his service in that office as the historical and economic germ of his political greatness. Most people regard this early work as a passing incident in his career, and not as a determining cause, and yet it is possible to show that Washington's entire public life was but the natural out

* Circular of Information of the Bureau of Education, No. 1, 1887, p. 30.

growth of that original appointment given him in 1749, at the age of seventeen, by the College of William and Mary. That appointment, in the colonial days of Virginia, was the equivalent of a degree in civil engineering, and it is interesting to observe what a peculiar bias it gave to Washington's life before and after the Revolution."

Professor Small's successors in the mathematical chair at William and Mary were Rev. Thomas Gwatkin, George Blackburn, Ferdinand S. Campbell, Robert Saunders, Benjamin S. Ewell, and Thomas T. L. Snead.

UNIVERSITY OF PENNSYLVANIA.

The University of Pennsylvania was chartered in 1755, and was known before the Revolution as the College, Academy, and Charitable School of Philadelphia. The celebrated Dr. William Smith, D. D., was the first provost. He was a man of great learning and superior executive ability. Under his administration, previous to the outbreak of the Revolution, the college made marvellous progress. The teachers were men of well-established reputation throughout the colonies. Dr. Smith, who was very fond of mathematical studies, gave lectures on mathematics, natural philosophy, astronomy, and rhetoric. In 1769 he appears as one of the founders of the American Philosophical Society. The first volume of the transactions of that society contains accurate observations by Rittenhouse and himself of the transits of Venus and Mercury. Associated with him at the college as professor of mathematics, from 1760 to 1763, was Hugh Williams. He was a graduate of the institution, and a minister. Afterward he studied medicine abroad and then practiced in Philadelphia. He took great in. terest in astronomy, and observed the transit of Venus and Mercury for the Philosophical Society.

Theophilus Grew is also mentioned as a mathematical instructor. Rev. Ebenezer Kinnersley, Franklin's assistant in his electrical experiments, gave instruction in physics. "In this institution," says Dr. Smith, "there is a good apparatus for experiments in natural philosophy, done in England by the best hands and brought over from thence in different parcels. There is also in the experiment room an electrical apparatus, chiefly the invention of one of the professors, Mr. Kinnersley, and perhaps the completest of the kind now in the world." The courses of study mapped out by Dr. Smith are preserved in his works.* According to this, the mathematical and physical instruction during the three years at college was as follows (in 1758):

First year.-Common and decimal arithmetic reviewed, including fractions and the extraction of roots; algebra through simple and quadratic equations, and logarithmical arithmetic; first six hooks of Euclid.

Second year.-Plane and spherical trigonometry; surveying, dialing, navigation; eleventh and twelfth books of Euclid; conic sections; fluxions; architecture, with fortification; physics.

Third year. Light and color, optics, perspective, astronomy.

*William Smith's Works, 1803, p. 238.

There is given, in addition to this, the following list of "books recommended for improving the youth in the various branches."

First year.-Barrow's Lectures, Pardie's Geometry, Maclaurin's Algebra, Ward's Mathematics, Keil's Trigonometry.

Second year.-Patoun's Navigation, Gregory's Geometry and Fortification; Simson's Conic Sections; Maclaurin's and Emerson's Fluxions.

Third year.-Helsham's Lectures; Gravesande; Cote's Hydrostatics; Desaguliers; Muschenbroec; Keil's Introduction; Martin's Philosophy, Maclaurin's View of Sir Isaac Newton's Philosophy, Rohault per Clarke.

It appears that the instruction was given by lectures, the books of which the above is a partial list, were (says Dr. Smith) "to be consulted occasionally in the lectures, for the illustrations of any particular part; and to be read afterwards, for completing the whole." How closely this advanced curriculum of Dr. Smith was adhered to, and how nearly his ideal scheme came to be realized in the actual work of the college, we have no means of determining. This much is certain, that before the Revolution the institution attracted a large number of students. According to Dr. Smith, the attendance in the college alone went as high as one hundred, while the total attendance, including the pupils of the academy and charity schools, surpassed three hundred. Of the course of study which he planned for the institution, it has been said by competent judges that "no such comprehensive scheme of education then existed in the American colonies."

But there followed a reaction. Political troubles at the beginning of the Revolutionary War broke up the institution. The authorities of the college were accused of disloyalty, and in 1779 the charter was annulled by the Provincial Assembly, and the college estate vested in a new board. Dr. Smith was ejected, and in 1791 there was organized the "University of Pennsylvania." Many years elapsed before the institution regained the popularity it enjoyed before the war.

SELF-TAUGHT MATHEMATICIANS.

The mathematicians mentioned in the previous pages were all men engaged in the profession of teaching. But, strange as it may seem, the most noted mathematician and astronomer of early times was not a professor in a college, nor had he been trained within college walls. We have reference to David Rittenhouse. He was born near Germantown, Pa., in 1732. Until about his eighteenth year, he was employed on his father's farm. The advantages for obtaining an education in rural districts were then exceedingly limited, but the elasticity of his genius was superior to the pressure of adverse fortune. At the age of twelve he came in possession of a chest of carpenter's tools, belonging to an uncle of his, who had died some years previously. This chest contained, besides the implements of trade, several elementary books treating of arithmetic and geometry. This humble coffer was to him an invaluable treasure, for the tools afforded him some means of exercising

the bent of his genius toward mechanics, while the books early led his mind to those pursuits for which it was pre-eminently fitted. While a boy he is said to have covered the fences and plows on his father's farm with geometrical figures. At the age of seventeen he constructed a wooden clock.

The delicacy of his constitution and the irresistible bent of his genius induced his parents to yield to his oft-repeated wish of giving up farming, and to procure for him the tools of a clock and mathematical instrument maker. Rittenhouse now worked diligently with his tools during the day, and at night spent a portion of his time which should have been passed in taking repose in the prosecution of his studies. His success seems to have been extraordinary, for his biographers assert that before the age of twenty he was able to read the Principia, and that he had discovered the method of fluxions without being aware that this had already been done by Newton and Leibnitz. In Sparks's American Biography we read that since Newton in his Principia "follows the synthetic method of demonstration and gives no clue to the analytic process by which the truth of this proposition was first discovered by him, Rittenhouse began to search for the instrument which might be applied to the purpose of similar discoveries, and in his researches attained the principles of the method of fluxions."

Dr. Rush, in his eulogy on Rittenhouse, says in the same way: "It was during the residence of our ingenious philosopher with his father in the country that he made himself master of Sir Isaac Newton's Principia, which he read in the English translation of Mr. Motte. It was here, likewise, he became acquainted with the science of fluxions; of which sublime invention he believed himself, for a while, to be the author, nor did he know for some years afterwards that a contest had been carried on between Sir Isaac Newton and Leibnitz for the honor of the great and useful discovery. What a mind was here! Without literary friends or society, and with but two or three books, he became, before he had reached his four and twentieth year, the rival of two of the greatest mathematicians in Europe."

Our information concerning the studies of our young philosopher is so scanty, that we find it impossible to determine the exact range of his thoughts or the consequences that flowed from them. Not the slightest information as to the exact nature of his alleged invention has been preserved. He himself seems to have attached no weight to it. We are of the opinion that his invention, whatever it may have been, was not of sufficient importance to deserve the name of an "invention of fluxions." If Rittenhouse actually made an invention of such transcending magnitude before the age of twenty, and at a time when he had hardly begun his scientific studies, how is it that he made not the slightest approach to any similar discovery during the forty-four years of his maturer life? Though always a passionate lover of scientific pursuits, he made no original contributions whatever to the science of