524 SCIENCE PROGRESS 



dences (Abbildungen). M. Frdchet (38) gives an extension of 

 the theorem which Borel based on one of Heine to the theory 

 of abstract aggregates. 



Arithmetic and Theory of Numbers. — A. Schreiber (12) gives 

 arithmetical and geometrical considerations on the "golden 

 section." E. Cahen (32) studies the best sequence of approxi- 

 mation to a given number. J. H. Baudet and F. Schuh (50) give 

 some properties of certain fractions. Cf. also M. Kiseljak (62). 



Questions in indeterminate analysis are dealt with by 

 W. de Tannenberg (34), E. Maillet (39), and F. Pollaczek (57) ; 

 congruences by S. Bergmann (62), A. Arwin (63-4), and V. Voss 

 (27) ; binary quadratic forms by G. Humbert (32, two papers) ; 

 division of the circle by S. Szilard (55), G. Rados (54), and A. 

 Loewy (15) ; partition of numbers by L. von Schrutka (59) ; 

 various numerical functions by J. G. van der Corput (50) and 

 K. Szilysen (53) ; the theory of algebraic numbers by J. A. 

 Schouten (22), Ph. Fiirtwangler (58, 60), M. Bauer (55, second 

 paper), O. Muhlendyck (62), A. Ostrowski (18), K. Hensel 

 (18-19), an d E. Landau's (70). book of 191 8 ; and Borel's theorem 

 on " normal " numbers by W. Sierpinski (40) and H. Lebesgue 

 (40). 



Algebra. — An extension of Rolle's theorem to the case of 

 many variables is given by M. T. Beritch (36) ; the solubility 

 of equations is considered by G. Rados (52) ; the theory of 

 Galois' groups by E. Noether (22) and F. Seidelmann (22) ; 

 the determination of roots by M. Bauer (55), E. Balint (55), 

 and K. Bohlin (65) ; and C. Runge (13) gives graphical methods 

 for finding complex roots. Algebraic forms are discussed by 

 E. Waelsch (56, 57) and Gy. Farkas (53) ; combinatory 

 analysis by G. Usai (47), F. Schuh (50), and J. du Saar (51) ; 

 determinants and symmetric functions by Sir T. Muir (1, two 

 papers), G. Frobenius (12), C. Kostka (19), and O. Szasz (62-3) ; 

 matrices by H. T. Burgess (9) and A. Loewy (14, 24) ; and 

 rational substitutions by P. Fatou (34), G. Julia (34, 35) and 

 S. Lattes (34, 35). 



C. C. Bramble (Amer. Journ. Math. 1918, 40, 351-65) 

 derives a collineation group isomorphic with the group of 

 the doable tangents of the plane quartic. The isomorphisms 

 of the general, infinite group with two generators are studied 

 by J. Nielsen (25), and the primitive, metacyclic congruence 

 groups with three or four variables by G. Bucht (64). 



