work astronomical instruments were needed. President Jefferson ordered the purchase from London of a transit instrument, a telescope, an astronomical clock, and a sextant. The first principal meridian began at the mouth of the Great Miami; the second at a point 5 miles south-west of the confluence of Little Blue River with the Ohio; the third at the confluence of the Ohio and the Mississippi Rivers; the fourth at the junction of the Illinois and Mississippi; the fifth at the mouth of the Arkansas River. A large number of other meridians, or "base-lines," have since been established.*

In view of the fact that our Government has had, all in all, nearly 3,000,000 square miles of land to sell or to otherwise dispose of, and that the sale had always to be preceded by a survey, it must be evident that there was a demand for surveyors. They could earn a comparatively easy subsistence while a student of pure mathematics might have gone a begging for a living. About 1816 a friend of Comte in this coun try warned that French mathematician and philosopher against the purely practical spirit that prevailed in this new country, and against coming here, by saying: "If Lagrange were to come to the United States he could only earn his livelihood by turning surveyor."

MATHEMATICAL JOURNALS.

The number of mathematical journals published in this country since the beginning of this century is much greater than one might suppose. A full historical sketch of these periodicals has been given by Dr. David S. Hart in the Analyst (Vol. II, pp. 131-8, 1875), and we shall make free use of his valuable article.

The oldest mathematical journal in America was the Mathematical Correspondent. It was established by gentlemen in New York and other cities, who had long felt the want of a periodical which should do for America what the Ladies' Diary had done for England. George Baron was editor-in-chief. It was to be issued quarterly. The first number was issued in New York City on May 1, 1804. Only eight numbers ever appeared. An essay in this magazine on Diophantine analysis, by Robert Adrain, was the first attempt to introduce the study of this subject in America.

The main cause of the discontinuance of the journal lies in the prej. udice which the editors, who were of Hibernian descent, entertained against American authors. A contributor, who called himself "A Rabbit," was permitted by the editors to sneer at several works written by American authors, such as Shepherd, Pike, Walsh, and others. The editors themselves also spoke in the most contemptuous manner of Col. Jared Mansfield, the superintendent of the Military Academy at West Point. Baron advertised on the cover of No. 2 of the Correspondent a

For further information on the early surveys, see Niles's Register, Vol. XII, pp. 97, 406; Vol. XVI, p. 362,

lecture delivered by him in New York, which contains, as he says, "a complete refutation of the false and spurious principles ignorantly imposed on the public in the new American Practical Navigator, written by N. Bowditch." The sub-editors endorsed the above. But some of these attacks, especially " A Rabbit's," seem to have created trouble, and on p. 154 the editor says: "A Rabbit' will not in any future number be permitted to propose questions concerning the blunders of stupid Shepherds; we had rather soar aloft with the eagle than waddle in the mud with the goose." For some hidden reason, Baron resigned the editorship. Many of the subscribers neglected to pay, and the paper soon died out.

The next periodical was the Analyst, or Mathematical Museum, edited by Robert Adrain. The first number was published in Philadelphia in 1808. Five numbers only appeared. We have spoken of this periodical at some length when we wrote about Robert Adrain. It contained the valuable original work of Adrain on the Law of Probability of Errors. Besides the editor, N. Bowditch, Alexander M. Fisher, and Melatiah Nash were among the contributors to the Analyst.

In 1818, William Marrat became editor of the Scientific Journal, which was published at Perth Amboy, N. J., in monthly numbers. Nine numbers are all that are known to have appeared. The cause of the discontinuance seems to have been the departure of Mr. Marrat for England. In 1825 Robert Adrain started in New York a second periodical, the Mathematical Diary, which was published quarterly during the first two years and annually during the last two. The last number contains an excellent likeness of Lagrange, and a sketch of his life. After the first year the editorship of the journal passed into the hands of James Ryan, the author of several mathematical works. In the preface to the first number of the Mathematical Diary, Robert Adrain said: “The principal object of the present little work is to excite the genius and industry of those who have a taste for mathematical studies by affording them an opportunity of laying their speculations before the public in an advantageous manner. It is well known to mathema

ticians that nothing contributes more to the development of mathematical genius than the efforts made by the student to discover the solutions of new and interesting questions." These words may have been prompted by his own experience. We have already pointed out how the Analyst, which was edited by him seventeen years previously, was the medium of publishing the first proofs of the all important Law of the Facility of Error in Observations.

Nearly all the more prominent mathematicians of America were contributors to the Diary. Among them were Robert Adrain, N. Bowditch, Theodore Strong, Eugene Nulty, Benjamin Peirce, Benjamin Hallowell, William Lenhart, M. O'Shannessy, Henry J. Anderson, and others.

In 1832 the publication was suspended on account of an unfortunate

quarrel among the mathematicians. Mr. Samuel Ward, a then recent graduate of Columbia College, had in part the management of the last number, in which he inserted a dialogue, written by himself, exhibiting in a ridiculous light Henry J. Anderson, then professor of mathematics at Columbia College. High words passed between the parties and their friends, which resulted in the complete breaking up of the Mathemati cal Diary. Samuel Ward was afterward editor of Young's Algebra. In later years he followed wholly different pursuits. He became known in Washington as the "king of the lobby," and as the giver of the best dinners of any man in America.

According to Dr. Hart, a journal called the Mathematical Companion, was started by John D. Williams in 1828, and continued for four years. The periodical, says Dr. Hart, was evidently gotten up as a rival of the Mathematical Diary. The writer has never seen a copy of this periodi cal. There is one in the Harvard library. Mr. Williams had many opponents, and a bitter contest was carried on between the two parties. He finally issued his fourteen famous "challenge problems," directed against all the mathematicians in America, excepting only Dr. Bowditch, Professor Strong, and Eugene Nulty. Six of these are impossible. All the others have been solved by several persons.t

The periodicals which we have named were devoted entirely to math. ematics. In addition to these there were publications which were given

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* Dr. Artemas Martin sends us the full title of the journal, as found in Bolton's Catalogue of Scientific and Technical Periodicals, 1665 to 1882, published by the Smithsonian Institution, p. 360-"The Mathematical Companion, containing new researches and improvements in the mathematics, with collections of questions proposed and resolved by ingenious correspondents. Edited by Williams; 1 vol., 18 mo., New York, 1828-31."

In the Educational Notes and Queries, edited by W. D. Henkle, Vol. II, No. 11, January, 1876, will be found a copy of a communication to a newspaper made by John D. Williams in 1832, containing the "fourteen challenge problems," and beginning as follows:

"Messrs. Editors.—It is this day six months since, under the signature of Diophantus, I proposed through the medium of your paper to the mathematicians of America, a collection of problems in Diophantine analysis. No correct solution having as yet been received to the whole of them, I take this opportunity to fulfill my pledge to furnish such, and inclosed they will come to your hands. I now desire to re-propose them for the ensuing six months; and shall except from my challenge the Hon. Nathaniel Bowditch, LL. D.,. etc., of Boston, Mass.; Mr. Eugene Nulty, of Philadel phia; and Prof. Theodore Strong, of Rutgers College, New Brunswick, N. J., only. The list of gentlemen challenged stands then as follows: Prof. Robert Adrain, University of Pennsylvania; Henry J. Anderson, Columbia College, N. Y.; Benjamin Peirce, Harvard University, Cambridge, Mass.; Mr. J. Ingersoll Bowditch, Boston, Mass.; Marcus Catlin, Hamilton College, Clinton, N. Y.; M. Floy, jr., New York; C. Gill, Sawpitts Academy, N. Y.; L. L. Inconnew, Cincinnati, Ohio; Benjamin Hallowell, Alexandria, Va.; Samuel Ward, 3rd New York-it being presumed that there are none in the United States with the exception of the above list would think of attempting their solution." Then follow the fourteen questions. All problems being in Diophantine analysis would tend to show that this subject was then a comparatively favorite study.

to science, or to useful information in general, but which gave part of their space to a "mathematical department." Foremost among these was the Ladies and Gentlemen's Diary, or United States Almanac, etc., edited by Melatiah Nash, for the years 1820, '21, '22. It contained much valuable information in astronomy and philosophy, enigmas, charades, queries, and mathematical problems, to be answered in the succeeding numbers. Other almanacs which generally contained mathematical · problems were Thomas's Almanac, published at Worcester, Mass., which existed for more than one hundred years; the Maine Farmer's Almanac; two publications, each called the "Farmers' Almanac ;" the Knickerbocker Almanac; the Anti-Masonic Almanac, commenced in 1828 at Rochester, N. Y. Other journals having a mathematical department were the American Monthly Magazine, commenced in New York in the year 1817; the Portico, which was started in Baltimore in 1816 and continued two or three years.

The mathematical journals spoken of were all of the most elementary kind, and, excepting No. IV of the Analyst, which contained Adrain's investigations on least squares, added nothing to the stock of mathematical science. These journals had an educational rather than scientific value. The proposal and solution of problems was the main work done by their contributors. Now, it will certainly be admitted that solving problems is one of the lowest forms of mathematical work. The existence of mathematical journals shows that since the beginning of this century there always were some persons interested in mathematics, but the number was so small that mathematical journals never were a financial success. All the early mathematical periodicals had merely an ephemeral existence.

881-No. 3-7

III.

THE INFLUX OF FRENCH MATHEMATICS.

During the latter part of the eighteenth century we see the French people rising with fearful unanimity, destroying their old institutions, and upon their ruins planting a new order of things. With this period begins the interest in popular education in France. A new impetus was given also to higher scientific education, which continued to be far in advance of that of the rest of Europe.

In 1794 was opened in Paris the Polytechnic School and in the fol lowing year the Schools of Application. The Polytechnic School gained a world-wide celebrity. The professors at this institution were men whose names are household words wherever science has a votary. Lagrange, Lacroix, and Poisson laid the basis to its course in analytical mathematics; Laplace, Ampère, and others to that of analytical me chanics and astronomy. Descriptive geometry and its applications had for their first teachers the founder of this science, the illustrious Monge and his celebrated pupils, Hachette and Arago.

The success of the Polytechnic School was phenomenal. It was the nurse of giants. Among its pupils were Arago, Biot, Bourdon, Cauchy, Chasles, Duhamel, Dupin, Gay-Lussac, Le Verrier, Poncelet, Regnault. The Polytechnic School is of special interest to those who live in America, because the U. S. Military Academy at West Point was a germ from it. || Compared with the French mathematicians who flourished at the beginning of this century the contemporary American professors were mere Liliputians. The masterpieces of French scholars were unknown in America. What little mathematical knowledge existed here came to us through English channels. For that reason that epoch was called the period of the influx of English mathematics. As compared with colonial times, considerable attention was paid to mathematical studies during that period. But there was still a great dearth in original thinkers on mathematics among us. The genius of our people was ex ercised in different fields, and so the little science we had was borrowed from others.

But the time came when French writers were at last beginning to make their influence felt among us. We recognized their superiority over the English and profited by it. Mathematical studies received a new impetus. But even then ours was not the glory of the sun, but

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