Abstract
American Journal of Mathematics, vol. x. No. 1 (Baltimore: Johns Hopkins University, 1887).—The number opens with the concluding lecture (the 33rd) of Prof. Sylvester's course on the theory of reciprocants, in which is investigated the differential filiation of a cubic curve having a given absolute invariant S3/T2. A supplemental “lecture”, is supplied by the reporter (Mr. Hammond) from the lecturer's surplus material: this “constitutes probably the most difficult problem in elimination which has been effected up to the present time.” All admirers of Prof. Sylvester's brilliant genius will be glad to have the fine presentment of his features which accompanies this number.—Algebraic surfaces of which every plane section is universal in the light of dimensional geometry is devoted to a proof and to illustrations, by Mr. E. H. Moore, Jun., of a theorem due to Picard, viz. “Les seules surfaces algébriques dont toutes les sections planes sont unicursales sont les surfaces réglées unicursales et la surface du quatrième degré de Steiner.”—Mr. Morgan Jenkins, in a paper on Prof. Cayley's extension of Arbogast's method of derivations, presents in a simplified form results given by the elder mathematician in a memoir printed in the Phil. Trans, (read December 1860).—Properties of a complete table of symmetric functions, by Capt. P. A. Macmahon, R.A., establishes some remarkable features of a tabulation set forth by Mr. Durfee in vol. v. of the Journal.—Oskar Bolza, in his article on binary sextics with linear transformations into themselves, considers those binary sextics which remain unchanged (or are only changed by a constant factor) for certain linear transformations of the variables.—Prof. Cayley follows with the sequel to his memoir on the transformation of elliptic functions (vol. ix.), and Prof. Woolsey Johnson closes the number with the symbolic treatment of exact linear differential equations.
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Scientific Serials . Nature 37, 71 (1887). https://doi.org/10.1038/037071a0
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DOI: https://doi.org/10.1038/037071a0