REVIEWS 



MATHEMATICS 



The Theory o£ Functions of a Real Variable and the Theory of Fourier's 

 Series. Second Edition, in two volumes. Vol. I. By E. W. Hobson, 

 Sc.D., LL.D., F.R.S., Sadleirian Professor of Pure Mathematics, 

 and Fellow of Christ's College in the University of Cambridge. [Pp. 

 xvi + 671.] (Cambridge : at the University Press, 192 1. Price 

 455. net.) 



The first edition of this work appeared in 1907. The time which has elapsed 

 since then has been a period of great activity in the development of the 

 Theory of Functions of a real variable. In order to give an account of the 

 present position of the subject, Dr. Hobson has expanded his book into two 

 volumes, of which only the first has at present appeared. This volume, 

 in which the matter has been partly rewritten and considerably enlarged, 

 treats the theory of number, the descriptive and metric properties of sets 

 of points, transfinite numbers and order-types, functions of a real variable, 

 the Riemann integral and the Lebesgue integral, and, finally, non-absolutely 

 convergent integrals. In the chapter on Transfinite Numbers and Order- 

 types the situation with respect to the controversy connected with axiom 

 variously called the Multiplicative Axiom, the Principle of Selection, and 

 Zermelo's Axiom is reviewed, but no attempt has been made to give dogmatic 

 decisions. The status of this axiom remains undefined. The author has, 

 however, made a point of giving, where possible, proofs of theorems which 

 do not depend on the assumption of the axiom, and of pointing out in other 

 cases that the axiom has been assumed. 



D, M. Wrinch. 



The Pruiciple of Relativity, being Original Papers by A. Einstein and 

 H. Minkowski, translated into English by M. N. Saha and S. N. Bose, 

 with an historical introduction by P. C. Mahalanobis, University of 

 Calcutta. [Pp. xxiii-|- 186.] (Calcutta : Pubhshed by the University, 

 1920.) 



The University of Calcutta has done English-speaking people a service by 

 putting into their hands an English translation of what will always be the three 

 classical papers in the literature of the Principle of Relativity, a principle 

 which must be recognised to have come to stay and to be of the utmost 

 significance for the future of physical science, since it makes possible the re- 

 conciliation of Newton's simple system of dynamics with what the philosophers 

 have always held must be true in regard to the relative nature of position 

 and motion. We have here first the paper of 1905, in which Einstein first 

 put the view that the recognition of the relative nature of a scale of time acts 

 as a sufficient explanation of the dif&culties of reconciling the electro-magnetic 

 theory of light with the experiments of Michelson and Morley. In this paper 

 he completes and rounds off the electron theory of Lorentz as a theory of the 

 constitution of matter, replacing the hypothesis of the contracting electron 



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