Scientific Serials

Abstract

Bulletin of the American Mathematical Society, November 1897.—The number opens with an account, by Prof. Osgood, of the proceedings at the International Congress of Mathematicians held at Zürich in August last. The transactions of the Congress, which was attended by about two hundred mathematicians, together with the papers read, or presented, are to be published in full.—Prof. J. McMahon performs a like work for the Detroit meeting of the American Association for the Advancement of Science. An analysis of the twenty-one papers presented to the Section is given. One of these communications was an account of stereoscopic views of spherical catenaries and gyroscopic curves by Prof. Greenhill, who was present at the meeting, and to whom the Section “is also indebted for instructive remarks made in connection with many of the other papers.” Then follow five papers read before the American Mathematical Society, viz. before the Chicago Section (April 24, 1897): Quaternions as members of four-dimensional space, by Prof. A. S. Hathaway. Note on the invariants of n points, by Dr. E. O. Lovett, is another communication which was made at the same meeting.—Dr. Lovett contributes also a note on the fundamental theorems of Lie's theory of Continuous Groups (October 30). The object of the note is to call attention to a misapprehension, if not an error, in a paper, by J. E. Campbell, on a law of combination of operators bearing on the theory of continuous transformation groups, read at the March 11 meeting of the London Mathematical Society (Proc, vol. xxviii. pp. 381–390). The fourth paper is one read at the Toronto meeting, August 16. It is an interesting short note by Prof. T. F. Holgate, and is entitled, “A geometrical locus connected with a system of coaxial circles.” The writer's object is to find the locus of points through which three lines can be drawn tangential to three circles of a coaxial system in pairs.—Condition that the line common to n–1 planes in an n space may pierce a given quadric surface in the same space, by Dr. V. Snyder, was read at the Detroit meeting mentioned above. The note is a generalisation of a proof recently given by the author (criteria for nodes in Dupin's cyclides) of the geometric significance of a certain determinant.—Dr. E. W. Brown gives a valuable analysis of Prof. H. Lamb's Hydrodynamics. Of this the reviewer writes: “The author is to be congratulated on the completion of a task which will earn him the gratitude of all those who are now, or may in the future be, interested in Hydro dynamics.—In the Notes are particulars of the British Association meeting at Toronto, in so far as it concerned mathematicians.—Other matters are a list of the mathematical courses for the winter semester (1897–98) in the Universities of Göttingen, Leipzig, Munich, Vienna and Strassburg.