194 SCIENCE PROGRESS 



29), G. Szego (29), O. Blumenthal (28), C. H. Miintz (19), E. 

 Fischer (15, 17), J. A. Schouten (47), E. Jahnke (12), G. Julia 

 (3S> 33), an d H. B. A. Bockwinkel (47). 



Analysis. — G. Prasad (Bull. Calcutta Math. Soc, 191 8, 9, 

 1-9) studies in a number of typical cases the question of the 

 existence of the normal derivate of the Newtonian potential 

 due to a surface distribution having a discontinuity of the 

 second kind. B. Datta (Amer. Journ. Math., 1919, 41, 133-42) 

 obtains by a new method the chief results of C. Niven (1880) 

 on the non-stationary state of heat in an ellipsoid, and shows 

 how this method can be applied to arrive at new results in the 

 case of the ellipsoid with three unequal axes. A. E. Jolliffe 

 (Proc. Cambridge Phil. Soc, 191 9, 19, 191— 5) proves a generalisa- 

 tion of the theorem previously proved on certain trigonometrical 

 series which have a necessary and sufficient condition for 

 uniform convergence by T. W. Chaundy and himself (cf. 

 Science Progress, 191 6, 11, 269). S. R. Ranganathan 

 (Journ. Indian Math. Soc, 191 9, 11, 50-6) establishes the 

 Fourier expansion of Bernoulli's polynomials, and deduces the 

 sums of certain interesting types of series in a finite form. 



On the theory of functions of real variables, cf. E. Landau 

 (13), J. Wolff (49), H. Bremekamp (49), M. T. Beritch (33, 34), 

 G. Julia (34), C. J. de la Vallee Poussin (34, 35), A. Denjoy 

 (31), T. Fort (10), G. Pick (15), W. G. Simon (10), P. J. Daniell 

 (10), A. F. Andersen (11), J. Kiirschak (21), C. Carath£odory 

 (28), H. Hahn (25), S. Bernstein (22), J. Peres (34, 35), O. 

 Szasz (21, 26, 30), B. Jekhowski (32), and K. Knopp (13). On 

 the general theory of analytic functions, cf. Valiron (32, 33), 

 O. Szasz (26), W. Schmeidler (22), R. Konig (21, 23), P. Stackel 

 (21), J. Schur (21), L. Lichtenstein (20, two papers), S. Lattes 

 (33), J- F. Ritt (32), G. Faber (30), and H. Bohr (19) ; on 

 conformal representation and so on, cf. H. Bohr (29), C. Cara- 

 theodory and H. Rademacher (11), P. I. Helwig (48); on 

 special functions, cf. G. N. Watson (40, 43), O. Szasz (26), G. 

 Pick (25), E. Hilb (25), N. Nielson (11), H. B. A. Bockwinkel 

 (45), J. C. Kluyver (45), N. G. W. H. Beeger (49), L. Crijns (49), 

 W. C. Post (50), and E. Hecke (15). 



S. Banerji (Bull. Calcutta Math. Soc, 191 8, 9, 43-58) treats 

 in detail the problem of the forced vibrations of a hetero- 

 geneous string, which is a case of boundary problems of ordinary 

 differential equations. A. L. Nelson (Amer. Journ. Math., 191 9, 



