Abstract
Bulletin of the American Mathematical Society, January. —“On the stability of a sleeping top” is the abstract of a lecture delivered by Prof. Klein before the Society at the Princeton meeting, October 17, 1896. It will be remembered that Prof. Klein delivered four lectures “On the theory of the top,” at the sesquicentennial celebration of the University. In these latter an attempt was made to simplify the formulæ for the motion of a top by turning to account the methods of the modern theory of functions. The later lecture before us considers from the same standpoint a much more elementary question, viz. the stability of a top rotating about an axis directed vertically upwards. The point of support is supposed to be fixed. When the rotation is very rapid the behaviour of the top is as if its axis were held fixed by a special force. Some interesting results are arrived at.—Bibliography of surfaces and twisted curves, by Dr. J. E. Hill, consists mainly of extracts from a paper read before the Society in May last. It attempts to represent a compilation and classification of all articles, with certain exceptions, upon these surfaces and curves which have been published during the present century. The paper itself should be, judging from these extracts, extremely useful to students.—Linear differential equations is a review, by Prof. M. Bôcher, of Schlesinger's “Handbuch der Theorie der Linearen Differentialgleichungen,” and, like the previous work by Prof. Bôcher in the Bulletin, is thorough. The writer's conclusion is that though the book fails to meet some of the demands which it seems to him may fairly be made of a handbook, it is certain to fill an important place in a mathematical library, owing to the great amount of information which it contains in accessible form.—Messrs. R. W. Willson and B. O. Peirce furnish a table of the first forty roots of the Bessel equation Jo(x) = o with the corresponding values of J1(x). This is a paper which was presented to the Society at its summer meeting, September 1, 1896.—The final article, not counting the notes and publications, is entitled “Notes on the Theory of Bilinear Forms,” and is by Prof. H. Taber. It was read at the November meeting.
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Scientific Serials. Nature 55, 380–381 (1897). https://doi.org/10.1038/055380b0
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DOI: https://doi.org/10.1038/055380b0