RECENT ADVANCES IN SCIENCE 355 



America delivered in 191 7 on Gaston Darboux (i 842-191 7). 

 Both papers contain valuable sketches of Darboux's work, 



G. A. Bliss {Bull. Amer. Math. Soc, 26, 1920), in a presidential 

 address, gives, in addition to an interesting account of the recent 

 history of the Calculus of Variations, a new method of treating 

 the second variation. 



The following papers have also been published : 



Weiner, N., Bilinear Operations Generating all Operations Rational in 



a i2 Domain, Ann. Math., 21, 1920. 

 RiTT, J. F., On the Iteration of Rational Functions, Trans. Amer. Math. Soc, 



21, 1920. 

 Storlow, S., Remarques sur les ensembles de mesure nuUe a plusieurs 



dimensions, Comptes Rendus, 171, Sept. 20, 1920. 

 Bray, H. E., A Green's Theorem in Terms of Lebesgue Integrals, Ann. Math., 



21, 1920. 

 Daniell, p. J., Stieltjes' Derivatives, Bull. Amer. Math. Soc, 26, 1920. 

 Neder, L., Konvergenzbesitztum der Potenzreihen Stetiger Funktionen auf 



dem Rande des Konvergenzkreises, Math. Zeitschrift, 6, 1920. 

 Neder, L., Uber die Fourier Koeffizienten der Funktionen von Beschrank- 



ter Schwankung, Math. Zeitschrift, 6, 1920. 

 Bohr, H., Zur Theorie der allgemeinen Dirichletschen Reihen, Math. Ann., 



79, 1919. 

 Perron, O., Beitrag zur Theorie der Divergenten Reihen, Math. Zeitschrift 



6, 1920. 

 KojiMA, J., Theorems on Double Series, TShoku Math. Journ., 17, 1920. 

 Appell, Paul, Sur I'^lement simple de la decomposition des fonctions double- 



ment p^riodiques de troisieme espece, Acta Math., 42, 1920. 

 Hardy, G. H., On the Representation of a Number as the Sum of any Number 



of Squares and in Particular of Five, Trans. Amer. Math. Soc, 21, 1920. 

 Petrovitch, Michel, Propri6t6s arithmetiques d'une classe de nombres 



rationnels. Bull. Soc Math. France, 48, 1920. 

 Hardy, G. H., On Two Theorems of F. Carlson and S. Wigert, Acta Math., 



42, 1920. 

 MacMahon, p. a.. On the Partitions into Unequal and into Uneven Parts, 



Quart. Journ., 49, 1920. 

 LoEWY, A., Beglertmatrizen und Lineare Homogene Differentialausdriicke, 



Math. Zeitschrift, 7, 1920, 

 ScHMEiDER, W., Bemerkungen zur Theorie der Abzahlbaren Abelschen 



Gruppen, Math. Zeitschrift, 6, 1920. 

 Carver, W. B., and King, Estella F., A Property of Permutation Groups 



Analogous to Multiple Transitivity, Bull. Amer. Math. Soc, 26, 1920. 

 Miller, G. A., Groups involving only Operators whose Orders are Divisors 



of Four, Tohoku Math. Journ., 17, 1920. 

 CooLiDGE, J. L., Hermetian Metrics, Ann. Math., 22, 1920. 

 Bell, E. J., Representation in Homogeneous Forms, Ann. Math., 21, 1920. 

 Du Pasquier, L. G., Sur la theorie des nombres hypercomplexes a co- 



ordonn^es rationnelles. Bull. Soc. Math., France, 48, 1920. 

 Wilson, W. H., On Certain Related Functional Equations, Bull. Amer. Math. 



Soc, 26, 1920. 

 Smirnoff, V... Sur quelques points de la theorie des Equations differentielles 



lineaires du second ordre et des fonctions automorphes, Comptes Rendus, 



171, Sept. 20, 1920. 

 Malmquist, J., Sur les fonctions k un nombre fin de marches satisfaisant 



k une quatre difi6rentielle du premier ordre, Acta Math., 42, 1920. 



