rKESIDENx's ADDRESS — SECTION A. 17 



For example, if space axes are taken rotating with the earth, the con- 

 ditions certainly do not hold. The Principle of Relativaty can be 

 summarized roughly as follows :— 



The statement of any physical relationship remains unchanged by 

 any transformation of co-ordinates which leaves the values of g , 



unaltered at infinity. 



Various attempts have been made to remove the limitation on the 

 Principle, arising from the necessity of the invariance of g at infinity. 

 The most important are those of Einstein and de Sitter. Both get rid 

 of the difficulty of the conditions at the boundary by removing the 

 boundary itself and postulating a si^ace-time fourfold which is un- 

 bounded as a sphere or an anchor ring in three-dimensional space is 

 unbounded. 



In Einstein's scheme the space-time fourfold, apart from local 

 modifications due to the presence of matter, is specified by 



ds^ = - R\dx' + sin^ x('^^^' + •^"^' ^'^W)^ + ^^'• 

 The spacial region is thus the surface of a hypersphere of radius R 

 and the time is rectilinear. 



The Law of Gravitation is modified, but the modification is insufficient 

 to cause observable changes in verifiable predictions. 



The general curvature of space-time is attribiited to unperceived 

 world matter 



One great difficulty in accepting the theory lies in the re -introduction 

 of the distinction between time and space. De Bitter's hypothesis 

 makes 



ds^ = - R\dx- + sin' xl^/^' + «i"' ^#'j + cos^ x(^/^ 

 which transforms into 



-K' [doj' + sin= cj [dC' + sin^ ^{^6' + sin^ ddcf>'')}] 

 under the substitutions 



sin x =' sin ^ sin to 

 tan {it/R) = cos ^ tan oj. 



This is free from the objection that it re-introduces an absolute 

 time, but, on the other hand, it would fail to satisfy the followers 

 of Mach in that it derives the inertial frame, that is the frame of reference 

 determined by the earth's rotation, from a curvature of space-time which 

 is postulated to fit the facts and is derived from nothing material. It 

 does not, in short, satisfy Freundhch's second postulate. C. D. Broad, 

 writing in the Hihhert Journal of April, 1920, points out that too much 

 stress must not be placed on this postulate. Einstein attributes his 

 rotational effects to unperceived world matter, de Sitter simply uses a 

 curved space time. In theory the world matter is capable of being 

 perceived, but in actual fact it is not perceived. Broad concludes a 



