issue, supplemented by Halsted's Mensuration. The analytic geometry used is Puckle's Conic Sections. Until the present year (1888-89) Byerly's Calculus has been taught. Post-graduate courses in mathematics are now offered to students.

The present mathematical course is as follows (catalogue 1887-88): The Freshman class will study algebra, solid geometry, spherics, mensuration, plane and spherical trigonometry, with their applications to surveying, navigation, etc. The Sophomore class will study analytical geometry, graphic algebra, and theory of equations.

The Junior class will study analytical geometry of three dimensions, differential and integral calculus. This course of study will embrace the applications of the calculus to mechanics and physics.

The Senior class will study determinants, quaternions, invariants, and quantics.

In the higher classes will be discussed the history and logical structure of the mathematical sciences, and the logical theory of the calculus, the theory of limits, and the infinitesimal method.

Text-books.-Wentworth's Complete Algebra; Halsted's Geometry (John Wiley & Sons, New York); Halsted's Mensuration, 3d Ed. (Ginn & Co.); Wentworth's Trigonometry, Surveying, and Navigation; Graphic Algebra, by Phillips & Beebe; Puckle's Conic Sections, 5th Ed.; Smith's Solid Geometry; Newcomb's Differential and Integral Calculus; Theory of Equations, by Burnside and Panton, 2d Ed.; Muir's Determinants; Scott's Determinants; Salmon's Modern Higher Algebra, 4th Ed.; Hardy's Quaternions.

Engineering students are required to take the four-years' course; science students, the studies for the first three years; arts students, those of the first two years; and letters students, those of the first year. Two post-graduate courses are offered:

I. A course preparatory to original investigation in the objective sciences. This will include infinitesimal calculus, the method of least squares, kinematic, linkage, differential equations, the calculus of finite differences.

Text books.-Williamson's Differential Calculus, Williamson's Integral Calculus, Clifford's Kinematic, Forsyth's Differential Equations, Boole's Differential Equations, Boole's Calculus of Finite Differences, Merriman's Method of Least Squares.

II. A course preparatory to original investigation in the subjective sciences. This will include projective geometry, the theory of numbers, the algebra of logic, the theory of probability, non-Euclidian geometry.

Text-books.-Cremona's Projective Geometry; Lejeune Dirichlet's Zahlentheorie, 3d Ed.; Macfarlane's Algebra of Logic; Boole's Laws of Thought; Todhunter's History of the Theory of Probability; Frischauf's Absolute Geometrie.

The catalogue for 1887-88 gives one student taking post-graduate studies in mathematics.

The university is open to both sexes. "A number of young ladies still show that they are capable of mastering even the abstruse modern developments of this oldest of the sciences." (Professor Halsted, June, 1888.)

WASHINGTON UNIVERSITY.

Up to the date of writing we have not been able to secure the infor mation desirable for a sketch of the mathematical teaching at this university, but an excellent biographical notice of Professor William

Chauvenet, the first professor of mathematics at Washington University, has been written for us by his son, Regis Chauvenet, now presi dent of the State School of Mines, at Golden, Colo. Professor William Chauvenet ranks among the coryphæi of science in America. He and Benjamin Peirce have done more for the advancement of mathematical and astronomical science, and for the raising to a higher level of the instruction in these subjects, than any other two Americans. It is our wish, on that account, to place before the reader a somewhat full sketch of the life and works of Professor William Chauvenet. The biograph ical notice above referred to is as follows:

"William Marc Chauvenet, father of the subject of this sketch, was born at Narbonne, France, in 1790, and came to the United States in 1816. He was the youngest of four brothers, another of whom also came to this country but has left no descendants. William Marc was a man of education and culture, versed in several languages, and a constant reader. He came to America, however, in connection with a manufacturing enterprise which had its headquarters in New York, with a branch at Boston. The latter department was under Mr. Chauvenet's charge, and here he married, in 1819, Miss Mary B. Kerr, of Roxbury. This was before a heavy defalcation in the New York house, which broke up the enterprise so badly that all investments in it proved to be total losses. Mr. Chauvenet having an idea that rural life would suit his taste, bought a small farm close to Milford, Pike County, Pa., and it was here that his only child, William Chauvenet, was born, May 24, 1820.

"By the advice of friends Mr. Chauvenet soon gave up his attempt at farming, and settled in Philadelphia, where his son grew to manhood. His rapid progress at school attracted such attention from his instructors, especially in mathematics, that his father easily yielded to their advice, and sent him to Yale College, where he graduated in 1840, 'facile princeps' in mathematics, and high in standing in all other branches. The honorary societies, Phi Delta Kappa' and 'Chi Delta Theta,' denoting respectively the fifteen of highest standing and the fif. teen best writers of the class, each claimed him as a member.

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"Upon his return to his home be was, after a brief incumbency in a subordinate position, appointed professor of mathematics in the Navy. Late in 1841 he married Miss Catherine Hemple, of Philadelphia. Shortly after this he served a brief term on a United States vessel, as instructor to midshipmen, but did not go upon a foreign cruise, and was soon detailed to the Naval Asylum,' then situated at Philadelphia. Here midshipmen were sent at that time, to receive instruction and examinations, principally in mathematics and the theory of navigation. The young professor was struck with the imperfections in the education of naval officers, and it was very largely through his efforts, aided by such influences as he could bring to bear on the matter, that a commission was appointed to draft a plan for a fixed 'Naval Academy,' corre

sponding to the Military Academy at West Point. Six naval officers constituted this commission, Professor Chauvenet being of the number. The appointment of so young a man (he was but twenty-four at the time) on a commission of such importance indicates what must have been his record, and the impression he made upon his seniors in years and rank.

"The Naval Academy was formally called into existence in the year 1845, being located at Annapolis, Md. Professor Chauvenet was appointed to the chair of mathematics, and resided at the academy until his resignation from the Navy in 1859.

"It was not long after this change of residence that he began to plan his work on trigonometry, which was published in 1850. Its title, 'A Treatise on Plane and Spherical Trigonometry,' partly indicated that it was not a students' class book merely, but that it took up most of the more advanced applications of the subject. It soon assumed the posi tion it still retains as the standard reference work in its line.

"Some time before this publication, Professor Chauvenet had persuaded his father to retire from business and accept a position at the academy. He came as instructor in the French language, and remained at his post until his death in 1855.

"It having been decided to erect an astronomical observatory at the academy, Professor Chauvenet was made professor of astronomy and put in charge of the observatory. As he became more and more interested in his work, the idea of his next treatise, 'Spherical and Practical Astronomy,' grew upon him, and, just previous to his resignation, had assumed such form that he issued a prospectus for its publication as a subscription work. This was never carried out.

"In 1859 he was notified that his application for the professorship of mathematics at Yale College would be followed by his election to that position. Almost simultaneously with this came a call to St. Louis, Mo., where he was offered the same chair in the then newly-established Washington University. After much deliberation he accepted the latter, and removed with his family (including at that time his mother) to St. Louis, in the fall of 1859.

"Chancellor Hoyt, who was at the head of the 'Washington' at this time, died early in the 'sixties,' and Professor Chauvenet was elected to the vacancy. He still continued his duties as professor of mathematics, however, and now resumed his work on the 'Astronomy.' The risks of publication were great, and his means did not enable him to guarantee the publishers against loss. The Civil War was in progress, and the time seemed inopportune for such an undertaking. It was to the liberality of certain friends, chiefly to the initiative of Mr. (afterward Judge) Thomas T. Gantt, of the St. Louis bar, that a guarantee fund was raised, sufficient in the opinion of the publishers to prevent any loss to them. The work, in two octavo volumes, was published in 1863. "Few works of a scientific nature, by American authors, have been 881-No. 3-16

received with such universal favor, by those competent to judge of its merits, as was this. Its reputation was quite as great in Europe as here, while of course it is not (as it was never intended to be) a treatise much known outside of scientific, and more especially astronomical, circles. Its scope, and the rigorous methods adopted, are sufficiently indicated in the author's preface. It retains to-day its standard character, as fully as when this was first recognized by the scientific world upon its publication.

"Professor Chauvenet's mother died in St. Louis, not long after the appearance of the Astronomy, and it was but a few months later that the first symptoms of the disease that proved finally fatal to him, made their appearance. Partial recovery and resumption of his duties was followed by a long period of alternating hopes and fears, during which time he tried in vain different parts of the United States, from South Carolina to Minnesota. During this illness he worked at his only elementary publication, the 'Geometry,' which he undertook, partly because he had long thought that the popular texts of the day were marked by too strict an adherence to strictly 'Euclidian' methods, and partly be cause he wished to provide an income for his family, by the publication of a text for which he had reason to suppose there would be a larger sale than was possible with advanced treatises. The publication of this work shortly antedated his death, which occurred at St. Paul, Minn., December 13, 1870.

"Professor Chauvenet left, so to speak, two distinct impressions behind him. By far the larger circle, in numbers, of those who knew him, were of those to whom his scientific attainments, though known, were as traditions merely, since they were in a field whose extent was to them only a matter of vague conjecture. To these he left the impression of a man of wide and varied culture, and keen critical taste. Probably few scientists of distinction were more keenly interested in lines outside of their own specialties. He was not only a critic in music, but to his latest day a pianist of no mean ability, always expressing a preference, in his own playing, for the works of Beethoven, which he rendered with an interpretation which never failed to excite the admiration of musicians whose execution surpassed his own. His knowledge of English literature was extensive, but he read and re-read a few authors, at least in the latter part of his life, and his great familiarity with many of these gave point to the old adage, 'fear the man of few books,' though perhaps not in the sense in which these words were originally intended. He was a ready writer, and contributed at times reviews, partly scientific, to various journals. His style was clear and unaffected, while, in the review of a pretentious or ignorant author, he had the gift of a delicate sarcasm, so light at times as only to be visible to one reading between the lines. For other pretenders he could drop this mask, and write with severity; but only twice in his life, to the knowledge of the present writer, did he ever do so. In addition to his more important writings,

he was the author of a 'Lunar Method,' still used in the Navy, and invented a device called the 'great circle protractor,' by which the navigator is enabled (knowing his position) to lay down his course on a 'great circle' of the globe, without further calculation. This invention was purchased by the United States Government not long after the close of the Civil War.

"Professor Chauvenet's scientific reputation needs little comment on the part of the present writer. He was one of a group of scientists in his own or cognate lines, who were the first to secure recognition abroad, as well as at home, for the position of the exact sciences in the United States. Among his more intimate scientific friends were Benjamin Peirce and Wolcott Gibbs (Harvard), Dr. B. A. Gould, and many others whose names are as household words in the history of scientific progress in this country. At the formation of the National Academy of Sciences he was one of the prominent members. But while his scientific reputation will outlast his personal memory, it is doubtful if to those who knew him, even of his scientific associates, it will ever be as present as his strong personal attractiveness, the result at once of an easy and varied culture, and of a simple dignity of character, which impressed alike his family, his friends, and his pupils. His family, consisting at the time of his death of his wife, four sons, and a daughter, are all still living (1889)."

The only mathematical book written by Chauvenet and not mentioned in the above sketch is a little book entitled Binomial Theorem and Logarithms, published in 1843 for the use of midshipmen at the Naval School, Philadelphia.

As regards the quality of Professor Chauvenet's books, Prof. T. H. Safford, of Williams College, says: "This excellent man and lucid writer was admirably adapted to promote mathematical study in this country. His father, a Frenchman of much culture, trained him very thoroughly in the knowledge of the French language, even in its niceties. They habitually corresponded in that language; and the son was enabled to study the mathematical writings of his ancestral country in a way which enabled him to reproduce in English their ease and grace of style, as well as their matter. In these respects his works are far more attractive than those of ordinary English writers; his Trigonometry is much the best work on the subject which I know of in any language; his Spherical and Practical Astronomy is frequently quoted by eminent continental astronomers; and his Geometry has raised the standard of our ordinary text-books, of which it is by far the best existing."*

Chauvenet's books, especially his Geometry, have been used in the best of our schools. Recently a revised edition of his Geometry has been brought out by Professor Byerly, of Harvard. Among the chief modifications made by him are the following: (1) The "exercises," which

* Mathematical Teaching, by Prof. T. H. Safford, 1887, p. 9.