io SCIENCE PROGRESS 



point. C. N. Moore (Bull. Amer. Math. Soc. 191 7, 24, 145-9) 

 gives a continuous function whose development in Bessel's 

 functions of order zero is not summable at a certain point : 

 this function is analogous to a function given by Fejer (1910), 

 whose Fourier development diverges at a point, but the proof 

 of the non-summability follows different lines from FejeVs proof 

 of the divergence for his example. 



W. Gross (Sitzungsber . der K. Akad. der Wiss. in Wien, 

 191 5, 124 (Ha), 1017-37) applies the well-known process of 

 " Poisson's summation " to Fourier's series, Cesaro's mean, and 

 Riemann's summation. 



W. H. Young (Compt. Rend. 1916, 163, 427-30, 975-8 ; 191 7, 

 164, 82-5, 267-70) continues his work on the theory of the 

 convergence of Fourier's series. On the subject of Fourier's 

 series M. Fekete (Math, es term. ert. Budapest, 191 6, 34, 759— 

 86), and I. Priwaloff (Rend, del Circ. mat. di Palermo, 191 6, 41, 

 202-6) also write. 



D. F. Barrow (Annals of Math. 191 7, 19, 96-105) gives a 

 simple method of compounding frequency functions when 

 they can be represented by Fourier's series. It is applicable 

 over a wide range of problems, yields formulae which represent 

 exactly the frequencies and from which numerical results can 

 be obtained with relative ease, and is most useful where a few 

 frequencies are to be compounded — that is, where the asymp- 

 totic solution is not very exact. 



P. R. Rider (Amer. Math. Monthly, 191 7, 24, 420-22) gives 

 a short intrinsic equation solution of a problem proposed and 

 solved by Euler in his book of 1744, which is usually solved by 

 the methods of the calculus of variations. 



J. Radon (Sitzungsber. der K. Akad. der Wiss. in Wien, 191 6, 

 125 (I la], 221-43, 241-58) has papers on (1) the application of 

 the calculus of variations to the general problem of the cate- 

 nary, and (2) an extension of the concept of" convex functions " 

 in this calculus. 



Expositions and extensions of Volterra's theory of " func- 

 tions of lines " are given by E. Pascal (Rend, dell' Accad. di 

 Napoli, 1914,20, 40-48, 68-77,85-91, 104-11) and P. Dienes 

 (Math. 6s term. ert. Budapest, 1916, 34, 154-94, 656-92), and 

 H. B. A. Bockwinkel (Versl. Kon. Akad. van Wet. Amsterdam, 

 25) has several articles on the " complete transmutations " 

 important in the functional calculus, 



