REVIEWS 659 



both in. extent and in depth ; more and more different functions have been 

 investigated and, at the same time, known functions have been dissected 

 more and more carefully so as to learn something of their essence, the real 

 variable. 



Another matter which is continually in the author's mind is his disagree- 

 ment with the point of view of the mathematicians, such as Lebesgue and 

 Denjoy, who insist too much upon generality, who wish to discover proposi- 

 tions which shall be true, not only of all functions that have been constructed, 

 but of all functions that ever will be. As he points out, the discovery of 

 continuous functions without derivatives does not prevent the study of 

 continuous functions which have derivatives from playing an important part 

 in analysis. One will probably agree with him in not being much concerned 

 with functions which would require an infinite number of words for their 

 definition. F. P. W. 



Theorie des Nombres. Par M. Kraitchik. [Pp. ix + 230.] (Paris : 

 Gauthier-Villars et Cie., 1922. Price frs. 25.) 



The object of this work is the actual solution of congruences ; it is not 

 concerned with general theory. The author has invented graphical and 

 mechanical methods which enable the processes of groping or sifting 

 (tatonnement ou criblage) to be carried on systematically and with a certain 

 facility ; he prints 60 pages of numerical tables of linear factors of quadratic 

 forms, of factors of 2" ± i, and of the squares of numbers less than a million ; 

 the type of these might certainly be better. There is an interesting introduc- 

 tion by M. d'Ocagne, the creator of the science of Nomography. 



F. P. W. 



ASTRONOMY 



Sidelights on Relativity. By Albert Einstein, Ph.D. Translated by 

 G. B. Jeffery, D.Sc. and W. Perrett, Ph.D. [Pp. 56.] (London : 

 Methuen & Co., 1922. Price 35. 6d. net.) 



The translations of two addresses by Einstein are given in this small 

 volume. The first, entitled " Ether and the Theory of Relativity," was 

 delivered on May 5, 1920, in the University of Leyden. With the development 

 of the theory of relativity, previous conceptions of the ether had of necessity 

 to be modified. One school of thought was for abandoning the conception 

 entirely ; another considered it necessary to retain it. Here we have Ein- 

 stein's own views ; a few quotations may summarise these. " The ether 

 of the general theory of relativity is a medium which is itself devoid of 

 all mechanical and kinematical qualities, but helps to determine mechanical 

 (and electromagnetic) events." The gravitational and electromagnetic fields 

 are distinguished : " There can be no space nor any part of space without 

 gravitational potentials : for these confer upon space its metrical qualities 

 without which it cannot be imagined at all. The existence of the gravitational 

 field is inseparably bound up with the existence of space. On the other 

 hand, a part of space may very well be imagined without an electromagnetic 

 field." Hence " our present view of the universe presents two realities which 

 are completely separated from each other conceptionally, although connected 

 causally, namely, gravitational ether and electromagnetic field, or — as they 

 might also be called — space and matter." 



The second address, " Geometry and Experience," was delivered before 

 the Prussian Academy of Science on January 27, 1921. It deals with the 

 fundamental conceptions on the basis of geometry, the meaning of non- 

 Euclidean geometry, and the question as to whether the universe is spatially 

 finite or infinite. 



H. S. J. 



