i82 SCIENCE PROGRESS 



talking high metaphysics. The generahsed theory of relativity 

 seems to be high metaphysics enshrined in imposing algebra. 

 . . ." In the main, however, the examination of the theory 

 is proceeding on lines of sober scientific argument, untainted 

 by prejudices that suggest national differences. Writers like 

 E. Picard, P. Painleve and others, give us carefully thought out 

 and cautiously expressed statements, which are of great value 

 to such as do wish to understand the theory and its physical 

 consequences. 



Of great interest is a further paper by P. Painleve {Comptes 

 Rendus, 174, 1922, 1137-43), who sets out the fundamental 

 postulates of the classical theory of the Newtonian mechanics, 

 and compares them with those of the Einsteinian theory. In 

 addition Painleve indicates briefly his own standpoint— one 

 that has much to recommend it in the eyes of the ordinary 

 apphed mathematician, who wishes to combine caution with 

 progress. The writer retains the fundamental basis of 

 EucKdean geometr}^, but postulates that in the neighbourhood 

 of gravitating matter the geometrical properties of sohd bodies 

 are changed in accordance with the coefficients in a quadratic 

 differential expression ds- similar to that underlying Einstein's 

 work. A further communication is promised on the subject. 



S. Zaremba (Journ. de Math, pitres et appL, (9) I, 1922, 

 105-39) gives a critical examination of the foundations of the 

 theory. He claims that the consequences that are drawn by 

 relativists from the fundamental postulates of their theory, do 

 not really follow from them. Zaremba holds that the theory 

 needs completion in its essentials, and is somewhat doubtful 

 if this will ever take place. (See also Comptes Rendus, 174, 

 1922, 1416-18.) 



Keen opposition to the theory is again expressed by 

 J. Le Roux {Comptes Rendus, 174, 1922, 924-7, and Journ. de 

 Math, pares et appl., (9) I, 1922, 205-53). The latter paper 

 consists of a discussion of the restricted theory of relativity. 

 Le Roux claims that the Michelson and Morley experiment does 

 not necessarily lead to the modifications of our conceptions of 

 time and space involved in the restricted theory— which in 

 his opinion is quite useless. He examines the mathematics 

 of waves emitted by moving sources and finds that the 

 geometry of the Lorentz transformation is given by what he 

 calls " ellipsoidal interference waves." Le Roux concludes : 

 Einstein's restricted principle of relativity is either a super- 

 fluity or an absurdit}^, according to the domain of its applica- 

 tion." Opposition to the theory is also the burden of a paper 

 by E. Wiechert {Phys. Zeit., xxiii, 1922, 25-8), who is incHned 

 to support the older relativity views of Mach as against 

 Einstein's " Standpunktsrelativitat." 



