RECENT ADVANCES IN SCIENCE n 



H. F. Baker {Phil. Trans. A, 191 6, 216, 130-86) considers 

 certain linear differential equations of astronomical interest. 



N. Kuylenstierna (Arkiv for Mat. 1916, 11, No. 10) continues 

 his researches on the analytic solutions of two simultaneous 

 linear finite-difference equations of the first order. 



E. del Vecchio (ibid. No. 1 1) integrates two parabolic equa- 

 tions. 



L. Schlesinger (Jahresber. der D.M.V. 24, 84-123; Math. 

 is term. ert. Budapest, 191 6, 34, 129-53, 3 l6 ~3 6 ) writes on the 

 theory of linear integro-differential equations. 



W. L. Hart {Amer. Journ. Math. 191 7, 39, 4 7~ 2 4) dis- 

 cusses certain properties of infinite linear systems of ordinary 

 differential equations in infinitely many variables, which are 

 analogous to some connected with the notion of fundamental 

 sets of solutions, of those of finite linear systems with a finite 

 number of variables. It may be remarked that Ritt (i9*7 '> 

 Science Progress, 191 7, 12, 12) considered a problem of a 

 different type ; the results of E. H. Moore (1908) are not of the 

 nature of those obtained in the present paper ; the general 

 systems of von Koch (1899), F. R. Moulton (191 5), and Hart 

 (191 7; see Science Progress, 191 8, 12, 547) do not include 

 the system of the present paper ; while the results of Hilde- 

 brandt (191 7 ; Science Progress, 191 7, 12, 12) generalise the 

 theorems on finite systems in such a way that the notion of the 

 determinant of the fundamental sets of solutions is retained, 

 whereas in the present paper the matrices of the fundamental 

 sets need not possess determinants. 



J. A. Bullard (Amer. Journ. Math. 191 7, 39, 43<>-5 ) shows 

 how certain properties of a group of linear homogeneous trans- 

 formations can be obtained at once from the charateristic 

 equation of the general infinitesimal transformation of the 

 group, and thus how the type of structure is in part determined 

 immediately from the infinitesimal transformations of such a 

 group without the determination of the adjoint group. 



On various points of potential theory, see A. Wangerin 

 (Nova Acta der K. Leop. Carol. Akad. 191 5, 1-80) and G. Prasad 

 (Bull. Calcutta Math. Soc. 1916, 6, 3—1 1 ; 191 7, 8, 33-4°)- 



Geometry. — B. P. Haalmeijer (Nieuzv Archie f voor Wiskunde, 

 191 7, 12, 152-60) discusses " convex regions" in the theory 

 of sets of points. 



There is an excellent and detailed review by R. C, Archibald 



