A 8 At Excepting the statement in the next to the last sentence, viz., that lim lim A8 is determinate and indeterminate, we claim that Dr. Fisher has establim At lished the fundamental principles of the Differential Calculus in a simple, rigorA8 lim A8 Δι ous, and logical manner. By the principle of Limits, the lim lim At' that is to say, the limit of the quotient of two variables equals the quotient of their limits. Then if one is determinate the other is determinate, or if one is indeterminate the other is indeterminate. They are, however, both determinate. The statement that dt is used instead of 0 to preserve the trace of the quantity that vanished will be considered by many mathematicians as the rankest sort of mathematical heresy, the reanimating of Berkeley's "ghost of departed quantities." But here too Dr. Fisher's position is absolutely impregnable, for, since is, per se, indeterminate, but determinate by the equation by which, in every case, it is defined, it may be replaced by the ratio of any two quantities 0 which preserves the ratio that defines So in the case above, 0 0 can be 0 0 preserve the ratio 32t. But 0 be preserved by d8 dt second, ds being a variable, and dt a constant ; third, ds both being variables. Each of these three ways of viewing ds dt is used in the Calculus. This method to preserve the trace of the quantities which vanished, and ds and dt can represent large or small parts of 8 and t. There are in general three possible ways by which the ratio 32t can First, ds being considered a constant, and dt a variable; is replaced by or the quotient of any other two quantities which of exposition is used in my classes with the result that students are enabled to use the Calculus, not as a machine by which to grind out problems, but as an instrument of research. The American Monthly Review of Reviews. Monthly Magazine. Edited by Dr. Albert Shaw. vance. Single Number, 25 cents. The American Co., 13 Astor Place, New York City. An International Illustrated The American Monthly Review of Reviews for October has several articles of unusual interest to women readers. Miss Frances Willard tells the story of the World's W. C. T. U. movement; Mrs. Ellen M. Henrotin, president of the General Federation of Women's Clubs, outlines the benefits of those organizations; Mrs. Sheldon Amos, of England, writes of a London Women's Club, and Miss Mary Taylor Blauvelt contributes an enlightening article on the opportunities for women at the English universities. B. F. F. The Arena. An Illustrated Monthly Magazine. Edited by John Clark Ridpath, LL. D. Price, $2.50 per year in advance. Single Number, 25 cents. Boston: The Arena Co. The Arena for October continues the battle for reform. The number is especially interesting and in some parts brilliant; it is in all parts aggressive and courageous. Hon. Charles A. Towne's article, "The New Ostracism," is in the author's best vein of critical analysis. In the course of the discussion he attacks with great vigor the plutocratic interference with professors in colleges and universities. Herman E. Taubeneck continues his cogent statistical attack on consecrated wealth. Judge Walter Clark sends out a powerful plea for the establishment of public rights over semi-public interests and institutions. The Editor of The Arena continues with unabated vigor his onslaught on the organized forces of plutocracy. His article, "Prosperity: the Sham and the Reality," is one of his strongest and best. Dr. Ridpath's exposition of the bottom purposes and methods of the money power is as caustic as it is true. Mary Platt Parmelee's article on the Political Philosophy of the Father of American Democracy is an original and forceful argument for popular liberties. B. O. Flower is again at his best pace in "The Latest Social Vision,” in which he discusses the merits of Bellamy's "Equality." Perhaps the most radical and defiant article in the number is "The Dead Hand in the Church," by Rev. Clarence Lathbury, in which he attacks with destructive criticism the domination of the dead past over the living present in the church. "Hypnotism in its Scientific and Forensic Aspects" is the subject of an interesting and useful article by Marion L. Dawson. "Suicide: Is It Worth While?" is the caption of Charles B. Newcomb's startling study of one of the most interesting and painful themes of the age. The "Plaza of the Poets" is rich with the contributions of Ironquill, Junius Hempstead, Clinton Scollard, Reubie Carpenter, and Helena M. Richardson; while "The Editor's Evening" sparkles with its usual gems of social and poetical philosophy. Under "Book Reviews" the charming poems of Madison Cawein are set forth with merited commendation. B. F. F. The Open Court. A Monthly Magazine Devoted to the Science of Relig ion, and the Religion of Science, and the Extension of the Religious Parliament Idea. Edited by Dr. Paul Carus. T. J. McCormack, Assistant Editor, and E. C. Hegeler and Mary Carus, Associate Editors. Price, $1.00 per year in advance. Single Copies, 10 cents. Chicago and London: The Open Court Publishing Co. The following is the table of contents of the November number: "An Introduction to the Study of Ethnological Jurisprudence," by the Late Justice Albert Hermann Post, Bremen, Germany; "History of the People of Israel from the Beginning to the Destruction of Jerusalem by the Chaldeans," by C. H. Cornill, Professor of Theology in the University of Koenigsberg; "The Religion of Science; the Worship of Beneficence," by James Odgers Knutsford, England; "Death in Religious Art," by the Editor; "Vivisection from an Ethical Point of View: A Controversy," by Prof. Henry C. Mercer, and others; "Leonhard Euler," a biographical sketch by T. J. McCormack; "The Sacred Books of the Buddhists," by Albert J. Edmunds; "Brief Notes on some Recent French Philosophical Works;" Book Reviews, and Notes. Among the book reviews is a just estimate or criticism of "Finkel's Mathematical Solution Book;" the review contains about a page and a half, and is written by Assistant Editor T. J. McCormack. B. F. F. THE AMERICAN MATHEMATICAL MONTHLY. VOL. IV. Entered at the Post-office at Springfield, Missouri, as Second-class Mail Matter. NOVEMBER, 1897. BIOGRAPHY. VASILIEV. No. 11. BY GEORGE BRUCE HALSTED. LEXANDER VASILIEVITCH VASILIEV was born August 24 (old style), 1853, at Kazan. His father, orientalist already academician, was then Professor of Chinese Literature at the University of Kazan. His mother was a daughter of Simonov, Professor of Astronomy in Lobachevski's time and his predecessor as Rector. In 1855 on the transference of the Oriental Faculty to St. Petersburg, Vasiliev's father removed thither. In 1870 Vasiliev finished the course of the fifth St. Petersburg gymnasium as goldmedalist. The love for mathematics, awakened in the gymnasium, where in Class VI. he studied Sturm's Differential Calculus, carried him to the mathematical department of the University of St. Petersburg, which then boasted Somov and the great Chebishev (Tchébychev). As result of his earnest studies for 1870-73 appears the work "On the separation of roots," crowned with a gold medal. In 1874 on his taking his first degree he was invited by the University of Kazan to begin there his teaching as Privat-docent. Though he had planned to continue his studies at Berlin, he accepts this invitation to his birthplace and begins in November, 1874. His Dissertatio pro venia legendi was entitled "On the separation of the roots of simultaneous equations." In January 1875 he begins to lecture on Functiontheory, all his scholars being older than the professor. |