Magazine conducted by Dr. Martin. His energies were stimulated, and he became a leading contributor to our periodicals. He astonished his friends by his skill in solving difficult problems, and their admiration for his talents became almost unbounded. His mathematical mind had received the first stimulus from our elementary periodicals. Had he not died in the prime of life, he might have done good original work, provided he had begun to look higher than merely to the solution of difficult problems in our elementary journals. The solving of problems is very beneficial at first, but it becomes a waste of time if one confines himself to that sort of work. The solution of problems is not a high form of mathematical research, and should serve merely as a ladder to more ambitious efforts.

Another journal devoted mainly to the solution of problems is the School Messenger, now called the Mathematical Messenger, edited and published bi-monthly by G. H. Harvill, at Ada, La. One of the ablest contributors to it is J. W. Nicholson, professor of mathematics at the Louisiana State University. The Messenger commenced February, 1884.

The Annals of Mathematics is the continuation, under a new name and different form, of the Analyst. It is edited and published at the University of Virginia by Prof. Ormond Stone and Prof. William M. Thornton. It is of somewhat higher grade than the Analyst, though more elementary than the American Journal of Mathematics. It contains more articles on mathematical astronomy and other subjects of applied mathematics than the American Journal. Our distinguished mathematical astronomer, G. W. Hill, contributes several articles in his specialty. Profs. Asaph Hall, R. S. Woodward, H. A. Howe, and William M. Thornton contribute various articles on applied mathematics. Professor Oliver, of Cornell, has several papers, one on "A Projective Relation among Infinitesimal Elements," and another on the "General Linear Differential Equation." Prof. W. W. Johnson writes "Glaisher's Factor Tables," the "Distribution of Primes," and other subjects. Professor Halsted gives his demonstration of Descarte's theorem and Euler's theorems. The name of Bohannan, now professor at Ohio University, appears often. Prof. O. H. Mitchell, of Marietta College, discusses the equation of the second degree in two variables. Prof. R. H. Graves has geometrical articles; William E. Heal writes on repetends; S. T. Moreland, on the momental ellipsoid; J. F. McCullogh, on Rolle's theorem. A little space in each number is devoted to the proposing and solving of problems. The list of contributors is too large to be given here in full.

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When Professor Sylvester became actively connected with the Johns Hopkins University, in 1877, the university established the American Journal of Mathematics, for the publication of original research in pure and applied mathematics. It was the design that this should not be a journal devoted to the publication of solutions to problems, but that it

should be of so high a grade as to command a place by the side of the best European journals of mathematics. It is a source of pride to us that this great aim has been reached. The American Journal of Mathematics is to-day as well known and as highly respected in Europe as in America. Among its contributors are found not only the leading scientists of America, but also such foreign investigators as Cayley, Clifford, Crofton, Faà de Bruno, Frankland, De Gasparis, Glashan, Hammond, Hermite, Kempe, Lipschitz, Loudon, Lucas, MacMahon, Muir, Petersen, Poincaré, Roberts, Weichold, and G. P. Young.

The subject which has received most attention in the American Journal of Mathematics has been Modern Higher Algebra. The contributions of Sylvester on this subject loom large. In Volume I is found "a somewhat speculative paper" entitled, "An Application of the New Atomic Theory to the Graphical Representation of the Invariants and Covariants of Binary Quantics," followed by appendices and notes relating to various special points of the theory.* Sylvester contributed various memoirs on binary and ternary quantics, including papers by himself, with the aid of Dr. Franklin, containing tables of the numer. ical generating functions for binary quantics of the first ten orders, and for simultaneous binary quantics of the first four orders, etc. The list of his articles is too extensive to be mentioned here. Since his return to England he has contributed to the Journal a series of "Lectures on the Theory of Reciprocants," reported by J. Hammond.

The larger number of American contributions are from persons who were, or still are, connected with the Johns Hopkins University, either as teachers or students. Dr. W. E. Story, of the Johns Hopkins University, has written on "Non-Euclidean Trigonometry," "Absolute Classification of Quadratic Loci, etc.," and other, chiefly geometrical, subjects. Dr. T. Craig has contributed numerous papers, mainly on the theory of functions and differential equations. Dr. F. Franklin has aided Professor Sylvester in the preparation of papers, and has also made various independent contributions. After the return to England of Professor Sylvester, Professor Newcomb became editor-in-chief. His valuable articles have been noticed elsewhere. Among the contributors who were once students at the Johns Hopkins University, but are now not connected with it, are E. W. Davis, W. P. Durfee, G. S. Ely, G. B. Halsted, A. S. Hathaway, O. H. Mitchell, W. I. Stringham, C. A. Van Velzer, A. L. Daniels, C. Veneziani, D. Barcroft, and J. C. Fields. The Journal has two lady contributors, Mrs. C. Ladd Franklin, of Baltimore, and Miss C. A. Scott, of Bryn Mawr College. The great memoir on "Linear Associative Algebra," by Benjamin Peirce, was published in the American Journal of Mathematics; also articles by his son, C. S. Peirce, on the "Algebra of Logic" and the "Ghosts in Diffraction Spectra." Papers on applied mathematics have been written by Professor Rowland, of the Johns Hopkins University, and George

* Vide Professor Cayley's article on Professor Sylvester in Nature, January 3, 1889.

William Hill, of the Nautical Almanac Office. Mr. Hill has done admirable work in mathematical astronomy. For his researches on the lunar theory, published in the American Journal, and for other astronomical papers, published elsewhere, he was awarded the gold medal of the Royal Astronomical Society, in 1887.* Among the writers for the American Journal is Prof. W. W. Johnson, of the U. S. Naval Academy at Annapolis. He is also a frequent contributor to leading European journals, and commands a place among the very foremost of American mathematicians. In the list of American writers to the Journal are H. T. Eddy, J. W. Gibbs, E. McClintock, A. W. Phillips, J. Hagen, E. W. Hyde, H. B. Fine, and others of no less power and originality.

THE U. S. COAST AND GEODETIC SURVEY.

In giving the origin of the U. S. Coast Survey it is desirable to begin with a sketch of the preliminary training of its first superintendent, Ferdinand R. Hassler. He was born in the town of Aarau, Switzerland, in 1770. He was sent to the University of Bern to study law, but he soon drifted into mathematics and became a favorite pupil of Prof. John G. Tralles.† Tralles and Hassler undertook the topographical survey of the Canton of Bern. In 1791 a base-line was measured, and a net of triangles established. The instruments on hand being found insufficient for long distances new ones were ordered from Ramsden, in London. On the receipt of these, in 1797, the survey was resumed, but soon discontinued. The conquering armies of the French came marching into Switzerland. The feeble republic was forced to submit to the dictatorial orders of the war minister of France, which required, among other things, that the places then occupied by the Swiss engi. neers should be vacated and filled by French. A swarm of sixty French engineers appeared, but soon disappeared without accomplish. ing anything. The revolutionary tendencies of the times and the unsettled state of the country induced Hassler to quit Switzerland. His fatherland seemed to bear no roses for him. Having landed in Phila delphia, in October, 1805, he formed the acquaintance of Prof. Robert Patterson and Mr. Garnet, of New Brunswick, to whom he showed his mathematical books and instruments.

About this time Congress was considering the feasibility of a survey of the coasts and harbors. Professor Patterson sent to President Jef ferson a sketch of Hassler's scientific career in Switzerland, and Mr. Clay, the Representative from Philadelphia, in 1806, asked Hassler whether he would be willing to undertake the survey, in case that the

* Vide Monthly Notices on the Royal Astronomical Society, Vol. XLVII, No. 4, February, 1887.

+ Translation from the German of Memoirs of Ferdinand Rudolph Hassler, by Emil Zschokke, published in Aarau, Switzerland, 1877, with Supplementary Documents, published in Nice, 1882.

Government should decide upon one. Mr. Hassler was, of course, willing. The law authorizing the survey was passed in February, 1807. Hassler received one of the twelve circulars which were sent to scientific men for plans of the contemplated survey. By the direction of President Jefferson, a commission (formed, it appears, of the very gentlemen who had proposed plans, excepting Mr. Hassler) examined the various plans at Professor Patterson's, in Philadelphia. They rejected their own projects and recommended to the President the one suggested by Mr. Hassler. The survey proposed by him was of a kind that had never been previously attempted in this country; it was to be a triangulation, and the sides of the triangles were to be from ten to sixty miles in length, such as had, at that time, just been executed in France and was in progress in England. The project was quite in advance of the science of our country. It was fortunate for us that a man of Mr. Hassler's learning, ability, and mechanical ingenuity was available to the Government. He had, meanwhile, been appointed by Jefferson professor at West Point. This position he resigned after three years, and accepted the professorship of mathematics at Union College, Schenectady, N. Y. Politics delayed the work of the survey. The first thing to be done was to procure the necessary instruments. In 1811 Hassler was sent to England by our Government to direct the manufacture of suitable instruments. Shortly after his arrival in Great Britain the War of 1812 broke out, and he was four years in London, in the disagreeable position of an alien enemy, and half the time left by our Government without compensation. He returned to this country in 1814, with a splendid collection of instruments, which had cost nearly forty thousand dollars.

In August, 1816, a formal agreement between the Government and Mr. Hassler was reached, to the effect that he should undertake the execution of the survey. He immediately entered upon the preliminary steps of reconnoitering and the numerous collateral experiments necessary for such a survey. Two preliminary base-lines were measured: One in New Jersey, in the rear of the Highlands, on North River, and nearly six miles in length; the other on Long Island, and of about five miles. Down to the year 1818 eleven stations were occupied, forming the elements of 124 triangles.

To a scientific man, familiar with the many preliminary details which are indispensable to accurate scientific work, but which do not always appear in the ultimate results, the progress which Hassler was making would have seemed highly satisfactory. Congress, however, was displeased. In April, 1818, Mr. Hassler received official notice that he was suspended, accompanied with the remark that the little progress hitherto made in the work had caused general dissatisfaction in Congress. Possibly the feeling on the part of American engineers against this foreigner because he had been preferred to one of them had something to do with this suspension. To Hassler this was a very severe blow; his

brightest hopes seemed dashed into fragments. A year or two later he prepared a defense of himself. He wrote an account of his plans and methods and published it in the Philosophical Transactions of Philadelphia (Vol. III, New Series, 1825). By this article he hoped to vindicate his schemes. It attracted the attention of scientific men everywhere. It was reviewed by leading astronomers in Europe-Bessel, Struve, Schumacher, Férussac, Francœur, Krusenstern, and others—all agreeing that Mr. Hassler's plans were good, and testifying to his inventive genius for solving the difficulties of the Coast Survey, as well as to the certainty that his plans, if carried out, would lead to success. Bessel was certainly a competent judge, for, in addition to his theoretical knowledge, he had had experience in geodetic work in Germany. He had words of only the highest praise for Hassler's scheme.*

After his suspension from the survey, Hassler engaged in various occupations. For a while he was a farmer in northern New York. He afterward went to Jamaica, Long Island, and then to Richmond, Va., giving lessons in mathematics to sons of prominent men. While in Richmond he published his Elements of the Geometry of Planes and Solids, 1828. His Elements of Analytic Trigonometry appeared in 1826. Subsequently he published an Arithmetic, Astronomy, and Logarithms and Trigonometric Tables, with introductions in five languages.

After twelve years in rural retreat, Hassler was recalled to official activity. He became United States gauger, and then was intrusted, from 1830 to 1832, with the difficult mission of regulating the standards of weights and measures throughout the United States, which at that time were very various.

In 1828 the question of the Coast Survey was again agitated. The Secretary of the Navy reported to Congress favorably on Hassler's work, which had been suspended so suddenly ten years previously. The Secretary said that "he [Hassler] had accomplished all that was possible in so short a time." In 1832 Mr. Hassler was re-instated, with the title of "Superintendent of the United States Coast Survey."

In the interval from 1818 to 1832 nothing of permanent value had been accomplished. Attempts had been made to survey portions of the coast, under the direction of the Navy Department, but there had been no general or connected survey. The charts prepared had been expen. sive and unsafe, and not very creditable to the country.

In 1832 began the most successful and most famous period in Mr. Hassler's life. Though sixty-two years old, there still glowed in him the fire of youth. The survey was begun with vigor. He had a traveling carriage prepared for him, which conveyed him rapidly to all parts of the survey. In this carriage he could seat himself at a writing table or dispose himself for sleep. The work was prosecuted according to the plans first laid out by him. He labored under the great disadvantage of having no skilled assistants. His corps of workmen had all to be

* Vide Silliman's Journal, Vol. IX, p. 225.