September i, 1923] 



NATURE 



319 



whereby this fraudulent undercutting could be pre- 

 vented. 



(3) The researches on synthetic dyes have not en- 

 grossed the attention of continental chemists to the 

 exclusion of the study of natural colouring matters, and 

 the present monograph, well printed on paper of pre- 

 War quality, is a good indication of the interest taken 

 by Swiss chemists in the border-line science of bio- 

 chemistry. The subjects dealt with include a summary 

 of the methods employed in obtaining balsams and 

 resins and in subjecting these materials to systematic 

 decompositions. The appropriate methods of proxi- 

 mate analysis are also indicated. The larger section 

 of the work is devoted to the identification and prepara- 

 tion of the most important vegetable colouring matters. 

 The detailed information supplied on this abstruse 

 subject is supplemented by many references to original 

 memoirs, and there is an adequate index. The brochure 

 is the eighty-fourth section of the comprehensive hand- 

 book of experimental methods in biology being issued 

 under the editorship of Dr. Emil Abderhalden, the 

 well-known physiologist. 



Relativity Problems. 



Sidelights on Relativity. By Prof. A. Einstein. I. 

 Ether and Relativity. II. Geometry and Experi- 

 ence. Translated by Dr. G. B. Jeffery and Dr. W. 

 Perrett. Pp. iv + 56. (London : Methuen and Co., 

 Ltd., 1922). 35. 6d. net. 



PARTICULARLY since the introduction of the 

 theory of relativity, the problem of the ether 

 has been a bone of contention among physicists. 

 They have been divided into two camps ; one unwilling 

 to let go the idea of an ether, though perhaps in 

 modified form, and the other seeing in the theory 

 of relativity, if not the negation of an ether, at least 

 something that rendered it no longer necessary. In 

 view of this, it is to be welcomed that Prof. Einstein's 

 inaugural lecture on " Ether and the Theory of 

 Relativity," which was delivered in 1920 at the 

 University of Leyden, has been made accessible to the 

 English scientific pubhc. 



" The endeavour toward a unified view of the nature 

 of forces leads to the hypothesis of an ether," and in 

 the first lecture in this book is to be found an excellent 

 account of the various phases through which the 

 ether-conception passed in the forward trend of 

 physical research. The ether gradually became divested 

 of its mechanical properties until, with the advent 

 of the special theory of relativity, it was deprived of 

 the " last mechanical characteristic which Lorentz had 

 still left it "—its " immobility." But " to deny the 

 ether is ultimately to assume that empty space has 



NO. 2809, VOL. 112] 



no physical qualities whatever," a view with which 

 the fundamental facts of mechanics do not harmonise. 



" According to the general theory of relativity 

 space is endowed with physical qualities ; in this 

 sense, therefore, there exists an ether. According to 

 the general theory of relativity space without ether 

 is unthinkable ; for in such space there would not 

 only be no propagation of light, but also no possibiUty 

 of existence for standards of space and time (measuring- 

 rods and clocks), nor therefore any space-time intervals 

 in the physical sense. But this ether may not be 

 thought of as endowed with the quality characteristic 

 of ponderable media, as consisting of parts which may 

 be tracked through time. The idea of motion may 

 not be applied to it." 



The second lecture, on " Geometry and Experience," 

 is an expanded form of an address delivered in 192 1 

 to the Prussian Academy of Science in Berlin. In 

 geometry, " axioms are free creations of the human 

 mind. All other propositions of geometry are logical 

 inferences from the axioms," and " the matter of 

 which geometry treats is first defined by the axioms," 

 or what Schlick aptly calls " implicit definitions." 

 But geometry first becomes a natural science " by 

 the co-ordination of real objects of experience with 

 the empty conceptual framework of axiomatic geo- 

 metry." " Geometry predicates nothing about the 

 relations of real things, but only geometry together 

 with the purport of physical laws can do so." The 

 question as to the nature of the structure of a continuum 

 is a physical one to which experience must supply the 

 answer, and we must acknowledge Riemann's geometry 

 to be correct " if the laws of disposition of practically 

 rigid bodies are transformable into those of the bodies 

 of Euclidean geometry with an exactitude which 

 increases in proportion as the dimensions of the part 

 of space-time under consideration are diminished." 



The question of the spatial finiteness or otherwise 

 of the universe appears to be definitely a " pregnant 

 question in the sense of practical geometry." Einstein 

 discusses this problem in its various aspects from the 

 view-point of the results of the general theory of 

 relativity, and shows how, by the use of an analogy 

 in two dimensions, we may form a mental picture of 

 a three-dimensional universe which is finite, yet 

 unbounded, and not Euclidean, but spherical. He 

 aims at showing " that the human faculty of visualisa- 

 tion is by no means bound to capitulate to non- 

 Euclidean geometry." 



To all lovers of logical and exact thought who are 

 interested in the developments that have arisen in 

 the wake of the theory of relativity, this book can 

 be warmly recommended. The work of translation 

 has been admirably done, and much of Xhe. finesse of 

 expression characteristic of Einstein's writings has 

 been retained. 



