Abstract
American Journal of Mathematics, vol. xi. No. 4 (Baltimore, July 1889).—Prof. Cayley opens the number with a resumption of his memoir on the surfaces with plane or spherical curves of curvature (pp. 293-306).—The circular cubic with double focus on itself is treated by Schröter and Durège (Crelle, Bd. v.). Mr. F. Morley, writing on the geometry of a nodal circular cubic (pp. 307-16), gives a geometrical account, illustrated by figures, of the case when the curve, in addition, is nodal. Some properties of the special case when the inflexion is at infinity are given by Dr. Booth (Quarterly Journal, vol. iii.) in his discussion of the logocyclic curve (cf. vol. i. of his “Collected Papers,” cap. xxx.).—The next paper supplies a defect in MM. Briot and Bouquet's “Propriétés des fonctions définies par des équations differentielles “(Journ. de l'École Pol., cap. xxxvi.): it is entitled, “On the Functions defined by Differential Equations, with an extension of the Puiseux polygon construction (see Journ. de Math, pures et appliquées, i. 15) to these equations” (pp 317-28), and is written by Mr. H. B. Fine.—In the memoir “Sur les solutions singulières des équations différentielles simultanées” (pp. 329-72), M. Goursat extends results obtained by M. Darboux to simultaneous differential equations and to equations of higher order.—The number, and volume, concludes with a note by J. C. Fields, on the expression of any differential coefficient of a function of any number of variables by aid of the corresponding differential coefficients of any n powers of the function, where is the order of the differential coefficient (pp. 388-96)—All these papers are, of course, purely mathematical: there is a physical paper (pp. 373-87) by Prof. H. A. Rowland, entitled “Electro magnetic Waves and Oscillations at the Surface of Conductors.” The calculations are founded on Maxwell's equations. “In these equations occur two quantities, J and ψ. Maxwell has given the reasons for rejecting ψ, and has shown that neither J nor ψ enter into the theory of waves. In order, however, that there shall be no propagation of free electricity in a non-conductor, the components of the electric force must satisfy the equation of continuity, and this leads to components of the vector potential satisfying the same equation, and J = o therefore. I have satisfied myself that there is absolutely no loss of generality from these changes.”
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Scientific Serials. Nature 40, 334 (1889). https://doi.org/10.1038/040334b0
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DOI: https://doi.org/10.1038/040334b0