THE organization of an "International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics" has been suggested. Information in regard to the proposed society can be obtained from Messrs. P. Molenbroek, The Hague, Holland, and S. Kimura, Yale University, New Haven. B. G. TEUBNER of Leipzig has an unusually large number of mathematical works in preparation. To begin with the history of mathematics, the second part of Vol. III of MORITZ CANTOR'S "Vorlesungen über Geschichte der Mathematik," covering the period from 1700 to 1726, is announced. The third part, which is to conclude this standard work, will carry the historical account to the year 1759. The excellent edition, by I. L. Heiberg and H. Menge, of the complete works of Euclid ("EUCLIDIS Opera omnia," Greek text with Latin translation) of which Vols. I-V and Vol. VII have appeared before, will be brought to a close this year by the appearance of Vol. VI, which contains the "Data" edited by Dr. Menge. As the second volume of Paul Tannery's edition of Diophantus ("DIOPHANTI ALEXANDRINI Opera omnia cum Graecis commentariis ") is in press, we are now in possession of most carefully prepared texts of the four classics of Greek mathematics: Euclid, Archimedes, Apollonius, and Diophantus. A complete edition of the works of Ptolemy, by Berger, Boll, Heiberg, and others, is in preparation. In modern mathematics Teubner is also publishing several sets of collected works. The second part of Vol. I of HERMANN GRASSMANN'S mathematical writings, edited by Professor F. Engel, contains the "Ausdehnungslehre" of 1862, and will probably be out before the end of the present year. Two more volumes are to follow. The mathematical volume of JULIUS PLÜCKER'S "Wissenschaftliche Abhandlungen," edited by Professor A. Schoenflies, has just appeared; the physical volume will be edited by Dr. F. Pockels. The first volume of LEOPOLD KRONECKER'S "Vorlesungen," which appeared in 1894, has now been followed by the first volume of his "Gesammelte Werke"; each of these two series will consist of four volumes. P. STÄCKEL and F. ENGEL'S "Theorie der Parallellinien von Euklid bis auf Gauss, eine Urkundensammlung," and O. BIERMANN'S "Elemente der höheren Mathematik," appeared during the last few months. The following works are announced as in press: a German translation, by M. Lukat, of LUIGI BIANCHI'S "Geometria differenziale"; a new work by Professor CARL NEUMANN, "Allgemeine Untersuchungen über das Newton'sche Princip der Fernwirkungen"; the first volume of a "Theorie der doppelt periodischen Funktionen einer Veränderlichen," by Professor MARTIN KRAUSE; the second part of Vol. II, as well as Vol. III, of Professor ERNST SCHRÖDER'S "Vorlesungen über die Algebra der Logik"; and the long expected "Geometrie der Zahlen," by Professor HERMANN MINKOWSKI. The printing of the first part of a new work by Professor SOPHUS LIE and Dr. GEORG SCHEFFERS, "Geometrie der Berührungstransformationen," is nearly completed, and the work will probably appear in December. Among other works announced as soon forthcoming, we may mention: L. SCHLESINGER, "Handbuch der Theorie der linearen Differentialgleichungen," Vol. II; O. STOLZ, “Grundzüge der Differential- und Integralrechnung," Vol. II; R. STURM, "Die Gebilde ersten und zweiten Grades der Liniengeometrie in synthetischer Behandlung," Vol. III; P. GORDAN, "Vorlesungen über Invariantentheorie," Vol. III; and W. WIRTINGER, “Untersuchungen über Thetafunktionen," a memoir which was awarded the Benecke prize by the Philosophical Faculty of the University of Göttingen in 1895. A work on automorphic functions, by Professor FELIX KLEIN and Dr. ROBERT FRICKE, is also in preparation. In applied mathematics Teubner announces the second volume of the fourth edition of WÜLLNER'S " Experimental-Physik"; Vol. VIII of FRANZ NEUMANN'S "Vorlesungen über mathematische Physik: Vorlesungen über die Wärme"; a second part to Professor CARL NEUMANN'S "Elektrische Kräfte"; Vol. II of A. STEINHEIL and E. Vorr's "Handbuch der angewandten Optik"; and MARTIN, "Die Folgerungen der Bodenreinertragstheorie" (in 3 vols.), Vol. II. AMONG the announcements of MM. Gauthier-Villars et Fils of Paris we notice the fourth (and last) volume of G. DARBOUX's "Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal"; a first fascicule (352 pp.) of this volume has appeared. Of MERAY's "Leçons nouvelles sur l'analyse infinitésimale et ses applications géométriques" the second volume has been issued, while the third and fourth ("Questions analytiques classiques; applications géométriques") are in preparation. The third and last volume of FERMAT's works is in press. CAUCHY'S "Euvres complètes" are progressing slowly; vols. 1, 4, 5, 6, 7, 8 of series I, and vols. 6, 7, 8, 9, 10 of series II have appeared so far; vol. 9 of the first series is nearly ready. Eleven of the thirteen volumes of the magnificent edition of LAPLACE's works are ready; the twelfth is in press. PICARD'S valuable "Traité d'analyse" is in its third volume, of which two parts (390 pp.) have appeared; the fourth and final volume, on partial differential equations, is in preparation. The second volume of J. TANNERY and MOLK's "Éléments de la théorie des fonctions elliptiques" is still in press; the whole work will comprise four volumes. Of B. NIEWENGLOWSKI'S "Cours de géométrie analytique," Vol. I was issued in 1894, Vol. II in 1895; the third ("Géométrie dans l'espace, avec une note sur les transformations en géométrie, par E. Borel ") is in press. The fourth volume of TISSERAND'S "Traité de mécanique céleste" has not yet appeared, but is printing; the second volume of BAILLAUD'S "Cours d'astronomie" will soon be out; and a portion of the second volume of P. APPELL'S "Traité de mécanique" has been issued, while the remaining part and Vol. III are in preparation. In the number of Nature for October 3 is a long list of forthcoming scientific works. Among the works announced are the following: "The year-book of scientific and learned societies of Great Britain and Ireland," comprising lists of the papers read before societies engaged in fourteen departments of research during 1895, to be published by C. Griffin & Co.; "The Indian calendar," containing complete tables for the verification of Hindu and Mohammedan dates for a period of 1600 years (A.D. 300 to 1900) for the whole of India, by ROBERT SEWELL, in collaboration with SANKARA BALKRISHNA DIKSHIT, with a table of eclipses by Dr. SCHRAM, to be published by Swan Sonnenschein & Co; "A practical trigonometry, for the use of engineers, architects, and surveyors," by HENRY ADAMS, to be published by Whittaker & Co.; "Miscellaneous papers," by the late Professor H. HERTZ, translated by D. E. Jones, "Elements of geometry," by GEORGE C. EDWARDS, "CHRISTIANSEN'S mathematical physics," translated by W. F. Magie, "Rigid dynamics," by W. J. LOUDON, "Elements of co-ordinate geometry," by S. L. LONEY, and "Elementary trigonometry," by CHARLES PENDLEBURY, to be published by Macmillan & Co. "Dynamics," by P. G. TAIT, to be published by A. & C. Black; "An introduction to the algebra of quantics," by E. B. ELLIOTT, to be published by the Clarendon Press; and, to be published by the Cambridge University Press, "Catalogue of scientific papers, compiled by the Royal Society of London,” 1874-1883, Vol. XI; "Scientific papers of JOHN COUCH ADAMS," Vol. I, edited by his brother, W. G. Adams, with a memoir by Dr. J. W. L. Glaisher; "Collected mathematical papers of ARTHUR CAYLEY," Vol. IX; "Treatise on spherical astronomy," by Sir ROBERT S. BALL; HEATH'S "Treatise on geometrical optics," second edition; "Treatise on Abel's theorem," by H. F. BAKER; "Treatise on the Lunar theory," by E. W. BROWN; "Elementary treatise on electricity and magnetism," by J. J. THOMSON; "Treatise on geometrical optics," by R. A. HERMAN; "Euclid," Books XI and XII, by H. M. TAYLOR; and "Mechanics and hydrostatics; part 3, hydrostatics," by R. T. GLAZEBROOK. THE announcements of Ginn & Co. include: "Problems in differential calen!us," by W. E. BYERLY; "Molecules and the molecular theory of matter," by A. D. RISTEEN; and "Plane and solid geometry," by W. W. BEMAN and D. E. SMITH. NEW PUBLICATIONS. HIGHER MATHEMATICS. ABRAHAM IBN ESRA. Sefer Ha-Mispar. Das Buch der Zahl. Ein hebräisch-arithmetisches Werk aus dem 12ten Jahrhundert. Uebersetzt und erläutert von M. Silberberg. Frankfurt am Main, 1895. 8vo. 10 and 198 pp. Illustrated. Mk. 4.00 ANNUAIRE DE L'ÉCOLE POLYTECHNIQUE pour l'an 1895. Avec des notes scientifiques, historiques et statistiques et le Mémorial de l'École. Paris, 1895. 8vo. 308 pp. Mk. 2.00 BLANK (F.). Ueber die geodätischen Curven auf einem körperlichen Kreisringe. [Progr.] Gera, 1895. 4to. 24 pp. Illustrated. Mk. 1.50 CALINON (A.). Le géométrie à deux dimensions des surfaces à courbure constante. Paris, Gauthier-Villars, 1895. 8vo. Fr. 2.50 CAYLEY (A.). Collected mathematical papers. Vol. VIII. Cambridge, University Press (New York, Macmillan), 1895. 4to. 4 and 570 pp. 25s. CHISHOLM (G.). Algebraisch-gruppentheoretische Untersuchungen zur sphärischen Trigonometrie. [Diss.] Göttingen, 1895. 8vo. 68 pp. 3 plates. Mk. 2.00 DARBOUX (G.). Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal. (In 4 vols.) Vol. IV: Déformation infiniment petite et représentation graphique. Paris, Gauthier-Villars, 1895. 8vo. ler fasc., pp. 1-352. Whole volFr. 15.00 ume DELASSUS (E.). Sur les équations linéaires aux dérivées partielles à caractéristiques réelles. [Thèse.] Paris, Gauthier-Villars, 1895. 4to. 67 pp. Fr. 3.50 GRASSMANN (R.). Die Formenlehre der Mathematik in strenger Formelentwicklung. 4 Teile in 1 Bande, nebst Formelbuch. Stettin, Grassmann, 1895. 8vo. 5 and 12 and 242 pp.; 12 and 189 pp. ; 9 and 132 pp.; 3 and 39 pp.; Formelbuch: 24, 27, 14, and 5 pp. Illustrated. Mk. 10.00 HOFER (F.). Histoire des mathématiques depuis leurs origines jusqu'au commencement du XIXe siècle. 4e édition. Paris, Hachette, 1895. 16mo. 3 and 609 pp. Fr. 4.00 HURWITZ (J.). Ueber eine besondere Art der Kettenbruch-Entwicklung complexer Grössen. [Diss.] Halle, 1895. 8vo. 50 pp. 1 plate. ISRAEL-HOLZWART (K.). Grundlagen und Methoden des tabellarischen Rechnens. Frankfurt am Main, 1895. 4to. 58 pp. Illustrated. Mk. 1.50 JACOBI (C. G. J.). Ueber die vierfach periodischen Functionen zweier Variabeln, auf die sich die Theorie der Abel'schen Transcendenten stützt. (1834.) Herausgegeben von H. Weber. Aus dem Lateinischen übersetzt von A. Witting. Leipzig, Engelmann, 1895. 8vo. 40 pp. Cloth. Mk. 0.70 JACOTTET (C.). Göttingen, 1895. Ueber die allgemeine Reihenentwicklung der Potentialfunction nach Lamé'schen Producten. [Diss.] 8vo. 48 pp. Illustrated. KOVALEVSKY (S.). See LEFFLER (A. C.). Mk. 1.20 KOVALEWSKY (S.). Souvenirs d'enfance de Sophie Kovalewsky, écrits par elle-même, et suivis de sa biographie par Mme A. Ch. Leffler, duchesse de Cajanello. Paris, Hachette, 1895. 16mo. 10 and 334 pp. Fr. 3.50 KRONECKER (L.). Werke, herausgegeben auf Veranlassung der Königl. Preussischen Akademie der Wissenschaften von K. Hensel. (In 4 vols.) Vol. I. Leipzig, Teubner, 1895. 4to. 10 and 484 pp. 1 portrait. Mk. 28.00 KLEIN (F.). Ueber die Beziehungen der neueren Mathematik zu den Anwendungen. Antrittsrede, gehalten am 25. Oktober 1880 bei Uebernahme der damals an der Universität Leipzig neuerrichteten Professur für Geometrie. (Besonderer Abdruck aus Band XXVI der Zeitschrift für mathematisch-naturwissenschaftlichen Unterricht.) Leipzig, Teubner, 1895. 8vo. 12 pp. Vol. XI: LAPLACE. Œuvres complètes, publiées sous les auspices de l'Académie Paris, Fr. 20.00 LEFFLER (A. C.). Sonya Kovalevsky: a biography. By Anna Carlotta Leffler, duchess of Cajanello, and sisters Rajevsky: being an account of her life, by Sonya Kovalevsky. Translated by A. de Furuhjelm and A. M. Clive Bayley, with a biographical note by Lily Wolffsohn. London, Unwin, 1895. 8vo. 380 pp. 6s. Sonia Kovalevsky: biography and autobiography. I: Memoir by by A. C. Leffler (Edgren), duchessa di Cajanello. II: Reminiscences of childhood, written by herself. Translated into English by Louise von Cossel. London, Scott (New York, Macmillan), 1895. 12mo. 316 pp. Frontispiece. $1.25 LJUNGH (A. T.). Ueber isoptische und orthoptische Kurven. [Diss.] Lund, 1895. 8vo. 50 pp. 1 plate. LONEY (S. L.). The elements of co-ordinate geometry. London and New York, Macmillan, 1895. 12mo. 10 and 420 pp. Cloth. $1.25 MANAIRA (A.). Sopra una certa rappresentazione piana dell' elissoide di rivoluzione e sulla applicazione di essa ai calcoli geodetici. Padova, Prosperini, 1895. 8vo. 56 pp. 1 plate. |