Abstract
American Journal of Mathematics, vol. x. No. 3 (Balti more, April).—The number opens with an article by M. E. Goursat, “Surfaces telles que la somme des rayons de courbure principaux est proportionnelle à la distance d'un point fixe an plan tangent”(pp. 187–204), in which are discussed some surfaces of a somewhat more general character than those treated of by M. Appell in the last number of the Journal. The title sufficiently indicates the scope of the memoir, which in part touches upon work accomplished by Riemann.— “Remarks on the Logarithmic Integrals of Regular Linear or Differential Equations5r (pp. 205–24), by Karl Heun, follows up Fuchs's investigations (Journal für Mathematik, Ixviii. p. 376). The author has else where shown that the Fuchs equations are not independent of each other when the differential equation is of a higher order than the second, and in this paper he deduces, from elementary considerations, the minimum number of conditions on which the existence of logarithms depends. In addition he gives several theorems concerning the pseudo-singular points.—Mr. C. H. Chapman, in his article “On Some Applications of the Units of an n-fold Space ” (pp. 224-42), obtains a proof of the rule for multiplying two determinants of the nth order by the principles of quaternions.—In “A Problem suggested in the Geometry of Nets of Curves and applied to the Theory of Six Points having Multiply Perspective Relations”(pp. 243–57), Mr. E. H. Moore discusses matters treated of by Von Staudt, Clebsch, Klein, and others.—Adopting the definition of orientation given by Laguerre, M. G. Humbert generalizes results previously obtained by Laguerre and himself in a memoir entitled “Sur Fomentation des systemes de droites”(pp. 258–81), and also brings together some interesting properties of the hypocycloid given already by Cremona and Darboux.
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Scientific Serials . Nature 38, 164–165 (1888). https://doi.org/10.1038/038164a0
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DOI: https://doi.org/10.1038/038164a0