Abstract
American Journal of Mathematics, vol. xxii. No. 1, January.—Appareil à liquide pour l'intégration graphique de certains types d'équations différentielles, by M. Petrovitch, is a continuation of the article, “Sur l'intégration hydraulique des équations différentielles,” by the same author (vol. xx. No. 4). The article describes an apparatus, exceedingly easy to construct, which gives a means of solving certain equations, “intégrables analytiquement, mais il est commode pour les applications d'avoir une methode rapide et sûre pour la construction mécanique de leurs courbes intégrates.”—The next paper, proof that there is no simple group whose order lies between 1092 and 2001, by G. H. Ling and G. A. Miller, continues the search begun by Hölder, and carried on by F. N. Cole and Burnside.—T. F. Holgate contributes a note additional to a former piper on certain ruled surfaces of the fourth order. The surface for which the nodal lines are real and distinct, F54, and that for which the nodal lines are coincident, F64, were previously discussed, but no mention was made of the surface for which the nodal lines are imaginary, though the existence of such a surface must have been in mind at the time. From the geometrical standpoint a study of the separate surfaces is of considerable interest.—H. F. Stecker's non-Euclidian properties of plane cubics is an interesting discussion on the lines of Clifford and Story.—Dr. E. O. Lovett gives two notes (1) on the differential invariants of Goursat and Painlevé, and (2) a supplementary note on projective invariants (see the April No. of the last volume).—Certain sub-groups of the Betti-Mathieu group is a slight addition to a dissertation by Dr. L. E. Dickson (Annals of Mathematics, 1897; cf. also the July No. (1899) of the American Journal).—Dr. W. H. Metzger gives a brief note on the excess of the number of combinations in a set which have an even number of inversions over those which have an odd number.—On Lie's theory of continuous groups, by E. W. Rettger, following up Study's and Taber's work, investigates the two- and three-parameter sub-groups of the general projective group in two variables, and of the general homogeneous linear groups in three variables, enumerated by Lie on pp. 288, 519 of his Continuerliche Gruppen, and his aim is to show that singular transformations occur among the transformations of many of these sub-groups.—V. Snyder writes on lines of curvature on annular surfaces having two spherical directrices. Several interesting geometrical results are given.
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Scientific Serials . Nature 61, 457 (1900). https://doi.org/10.1038/061457a0
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DOI: https://doi.org/10.1038/061457a0