160 SCIENCE PROGRESS 



expresses geometrical properties as equations in these measures. Now between 

 the measures of the six distances determined by four points and between the 

 measures determined by two points and two lines there are relations : they are 

 called eliminants. Thus geometrical properties are reduced to algebraical equa- 

 tions involving eliminants. 



After the statement in the briefest terms of the object and scope of the book 

 given partly in a preface and partly in an introduction of seven pages, Mr. Thompson 

 commences his task of elaborating finite and differential geometry, and in performing 

 this gives us about no pages of solid, serried ranks of symbols. A little more 

 bread and a little less sack would have formed a more palatable fare. The no 

 pages too, are not of ordinary strength : they are composed largely of that very 

 concentrated essence which the Cambridge mathematician dignifies as examples. 



The book is strictly confined to two dimensions and the author gives no indica- 

 tion of any attempt which he may have made to extend the method to three 

 dimensions. Indeed he has deliberately cut himself off from the ordinary notation 

 by using a, b, . . . for points and a, /3, . . . for lines, thus leaving no simple choice 

 of symbols for planes. It is perhaps a little unfair to criticise an author for not 

 including matter which he has distinctly excluded by his title, but it would be 

 unwise to expect a very wide acceptance of a novel notation in plane geometry 

 which does not allow of extension to three dimensions. 



C. 



PHYSICS 



The Principle of Eelativity. By E. J. Cunningham, M.A. [Pp. xiv + 221.] 

 (Cambridge : at the University Press, 1914. Price gs. net.) 



The belief in the existence of a medium for the propagation of electromagnetic 

 radiation has become so definite, that when the Principle of Relativity was first 

 propounded about ten years ago, a so-called insuperable objection was at once 

 raised to it, viz. that it did away with the possibility of an objective ether. Further 

 it was asserted that the principle introduced views about space and time much too 

 artificial to be reconciled with the intuitive notions which we already possessed 

 concerning those two modes of perception. 



It must be granted that the present volume goes a long way towards destroying 

 the force of both these objections. Perhaps its greatest merit is the very careful 

 analysis to which are subjected all such concepts as mass, force, momentum, 

 energy, with which dynamical and electrical theory are concerned. The author 

 shows that the standards of space and time as employed in dynamics are not, as 

 frequently supposed, absolutely defined for us apart from natural phenomena. The 

 existence of such absolute standards is an assumption of Newtonian theory, only 

 justifiable by the simplicity which it introduces into the co-ordination of phenomena, 

 and not based on any philosophic doctrine. As far as dynamical and electrical 

 theory is concerned, if there comes to us knowledge of phenomena which cannot 

 be fitted into the Newtonian scheme, except by hypotheses concerning the con- 

 stitution of matter, hitherto unsuspected and having no a priori justification, there 

 is nothing contrary to scientific procedure in laying aside any attempt to formulate 

 such hypotheses, and in endeavouring to correlate our new knowledge by a revisal 

 of our concepts of space and time and by an acceptance of standards of those 

 which are not absolute, but vary with the frame of reference in which measure- 

 ments are being carried out. 



Briefly the new knowledge has been gained by all those experiments which 



