Dominion of

The most important periodicals for mathematics, and among the most important in the world, are : Annali di Matematica Pura ed Applicata (1858+) a continuation of Annali di Scienze Mate matiche (1850-57) which may possibly be regarded as a develop ment of Raccolta di Lettere ed altri Scritti intorno alla Fisica ed alle Matematiche ; R. Accademia dei Lincei, Rome, Rendiconti (1884+), Memorie (1876+) ; and Prince Boncom pagni's Bullettino di Bibliografia e di Storia delle Scienze Mate matiche e Fisiche (1868-87), Rome. Among many other periodi cals are : R. Accademia delle Scienze dell' Istituto di Bologna, Memorie (1850+) and Rendiconto (1829+) ; Giornale di Mate matiche (1863+) (Battaglini) ; R. Accademia delle Scienze Fi siche e Matematiche, Naples, Rendiconti (1862+) and Atti (1864) ; R. Accademia della Scienze di Torino, Atti (1865+) and Memoire (1759+) ; University of Rome, Facolta di Scienze, Semi nario Matematico, Rendiconti (1914+) ; Archivio di Storia della Scienza (1919+) ; Bollettino di Bibliografia e Storia delle Scienze Matematiche (1898-1922) (Loria) continued as a supplement to the secondary school journal Il Bollettino di Matematica (1902+) ; Periodico di Matematiche, various titles (1886+) organ of Society Italiana "Mathesis"; Istituto G. Ferraris, Ras segna di Matematica e Fisica (1920+), Rome; and Giornale di Matematica Finanziaria (1922-F). Scientia (I 907+ ) contains popular articles of value.

JAPAN.

The Physico-Mathematical Society of Japan (Nippon Silgaku-Buturigakkwai) founded in 1884, has published proceed ings (kizi, 1884+), the first two volumes (1884-1887) being in Japanese, and the rest mainly in English. The Tohoku Mathe matical Journal (19Ir+) is now published by the Imperial Uni versity at Sendai. Under the auspices of the National Research Council of Japan have already been published (1924-28) five volumes of The Japanese Journal of Mathematics, Transactions and Abstracts. Two other English periodicals containing some advanced mathematical work are : Science Reports, First series, Mathematics, Physics, Chemistry (1912+) also published by the Imperial University at Sendai ; and Journal of the Faculty of Science, Imperial University of Tokyo, Section I, Mathematics, Astronomy, Physics, Chemistry (1925+). The latter is the con tinuation of Journal of the College of Science, Imperial University at Tokyo (1887-1925).

There is also Journal of The Mathematical Association of Japan for Secondary Education, in Japanese (title excepted) (1919+).

NORWAY.—The Norsk Matematick Forening, founded at Oslo in 1918, has as its official organ, Norsk Matematisk Tidsskrif (1919+). The Society is publishing also Norsk Matematisk For enings Skrifter (1921 ) , and Sophus Lie Gesammelte Abhand lungen (1922+ ) . Archiv for Mathematik og Naturvidenskab (1876+), Oslo, and Norske Videnskabs-akademie i Oslo, Mathe matisk-naturvidenskabelig Klasse, Skrif ter (1894+) contain some valuable mathematical material.

POLAND.

The Polskie Towarzystwo Matematyczne (Societe Polonaise de Mathernatique) was founded at Cracow in 1919, and one volume of Rozprawy (1921), in Polish, was published.

This was continued by annual volumes (1922+) of Rocznik (Annales) in French. A Polish supplement (Dodatek) is also issued (19a2+). Among the older periodicals are two published in Warsaw: Prace Matematycznofizyczne (1888+) and Wiad mo'ci Matematyczne (1897+). A new Warsaw periodical of much importance, devoted entirely to the theory of aggregates, is Fundamenta Mathematicci (1920+). Another publication valu

able for its mathematical material is Akademija umifjetnaci, Bulletin International, Cracow (1889-190o), in French and Ger man ; Bulletin International, Classe des Sciences .Mathematiques et Naturelles, Serie A (190I+); and Memoires, Classe des Sci ences Mathematiques et Naturelles, Serie A (1928+).

PORTUGAL.

Jornal de Sciencias Mathematicas e Astronomicas (1877-1902), Coimbra, of the Academia Polytechnica do Porto, was continued as the Academia's Annees Scientificos (1905-21), and then as Anais da Faculdade de Sciencias do Porto (1927+). Under the auspices of the Accademia Real das Sciencias de Lisboa, has been published Jornal de Sciencias Mathematicas, Physicas e Naturaes (i866+).

RUMANIA.—The Societatea "Gazeta Matematica," with about II() members, was founded at Bucharest in 1909, and Gazeta Mate matica foae lunara de Matematici elementare si speciale pentru ugul Scoalelor secundare, speciale superioare (1895-0, became its official organ Among numerous minor mathematical serials of Rumania is the monthly Revista Matematiai din Timipara (192I+), published at Timisoara. Some advanced mathematical work has been published in Bulletin Mathematique de la Societe Roumaine des Sciences, Bucharest (1892+) ; and Academie Rou maine, Bucharest, Annales (1867+), and Section Scientifique, Bulletin (1912 ) .

RUSSIA.—At Moscow in 1864 was organized a Circle of lovers of mathematics which in 1867 developed into the important Moscow Mathematical Society (Moskovskoe Matematicheskoe Obshchestvo). This organization founded and carried on Mate maticheskii Sbornik (1866+). Another important society is Khar'kovskoe Matematicheskoe Obshchestvo, founded in 1879. Its Communications (1879-1918) were continued as Annales Scientifiques des Institutions Savants de l'Ukraine, section mathematique (1924-28) which were continued as Com munications de la Societe mathematique de Kharkow (1927+). A third society is at the University of Kazan, Fiziko-Matema ticheskoe Obshchestvo, about 106 members, whose Bulletin (Lsviestiza) (1891+) was the continuation of the physics-mathe matics section (188o-9o) of the society of naturalists of the Uni versity. Bibliographia Mathematica Rossica (1896-190o) was a supplement to lzvieseda. A fourth society is Leningradskoe Fiziko-Matematiceskoe Obshchestvo, founded in 1892, and with about 8o members. The first volume of Journal de la Societe Physico-Mathematique de Leningrade appeared in 1927. Much of mathematical importance appears in the various publications of the Academy of Sciences, Leningrad (1726+).

Fiziko-matematicheskiza nauki v ikh nastoiashchem s proshed skein (1885-1905), edited and conducted by Bobynin was im portant for its bibliographical and historical articles and supple ments.

SOUTH AFRICA.—Some mathematical papers are to be found in Royal Society of South Africa, Transactions (1908+), Cape Town; and in South African Journal of Science (1903+) of the South African Association for the Advancement of Science.

SPAIN.—The Sociedad Matematica Espanola founded at Ma drid in 1910 published a Revista (1911-1917). This was contin ued (1919+) as Revista Matematica Hispano-Americana, pub lished under the auspices of the Sociedad and of the Laboratorio y Seminario Matematico of the University. This Seminario has also issued some Publications (1916+). The R. Academia Espanola, Memorias (1870+), Madrid, contains mathematical material.