Scientific Serial

Abstract

Bulletin of the American Mathemalical Sociely, April, 1901. —Prof. F. N. Cole opens with an account of the proceedings at the February meeting of the Society in New York City, and, in addition to the titles of the nineteen papers communicated, gives an abstract of several of them. Three of the papers are ptinted. Their titles are: (i) Green's functions in space of one dimension, by, Prof. M. B´cher. The results arrived at are given, but the proofs and further developments are reserved (2) Possible triply asymptotic systems of surfaces, by Dr. L. P. Eisenhart. This supplements a note by the author, in the January Bulletin, entitled, “A demonstration of the impossibility of a triply asymptotic system of surfaces.” Instead of the general negation previously given, the author now gives the qualified one: The only triple systems of surfaces cutting mutually in the real asymptotic lines of these surfaces are composed of properly associated families of hyperboloids of one sheet and hyperbolic paraboloids; (3) Note on Hamilton's determination of irrational numbers, by Dr. H. E. Hawkes. The purpose of the note is to call attention to Hamilton's use of the partition (Schnitt) in his definition of certain irrational numbers (Trans. of the R. Irish Academy, vol. xvii. 1837, p. 293)—On a system of plane curves having factorable parallels, by Dr. V. Snyder, was read before the December meeting of the Society. The type of scrolls contained in a linear congruence, and having factorable asymptotic lines, gives rise to a class of plane curves whose parallels have a similar property (cf. a paper by the author, in the American Jonrnal of Mathematics, vol. xxiii., on a special form of annular surface). Mr. Bromwich gives a very uselul analysis of Dr. P. Muth's “Theorie und Anwendung der Elementartheiler” (1899, xvi. and 236 pp.), and hopesthat the book may induce its readers to take up the special part of invariant theory treated in it. Mr. Bromwich has done good work in this direction (see Proc. of London Math. Soc. vol. xxxii. 1900, p. 98), where he gives a list of papers on the subject—Short notices follow of Dr. R. Fricke's “Kurzgefasste Vorlesungen üer Verschiedene Gebiete der höheren Mathematik, mit Berüchsichtigung der Anwendungen” (1900), and Dr. R. Böger's “Ebene Geometrie der Lage”(1900), both by Prof. H. S. White.—The notes are very copious and interesting, giving account of the courses of lectures in the Continental and home Universities, and the usual new publications close the number.