[" 820 ] 



LXXXVII. On Uniform Rotation, the Principle of Rela- 

 tivity, and the Michel son-Morley Experiment. By J. W. 

 Nicholson, M.A., JD.Sc, Professor of Mathematics in the 

 University of London* . 



SOME discussion has taken place recently with regard to 

 the bearing of the principle o£ relativity on problems 

 of uniform rotation. Usually the validity of an application 

 of this principle has been assumed. The principle may be 

 regarded from two points of view. In the first place, it may 

 be postulated, as by Einstein and others, for the case of 

 uniform translation, in the form of a general law underlying 

 the description of electromagnetic phenomena, quite apart 

 from its actual analytical origin. Secondly, it may be de- 

 rived, as originally by Larmor, from the result of an analytical 

 transformation applied to the variables in a set of equations 

 occurring in electromagnetic theory. When approached 

 from this standpoint, it is endowed with a mode of proof 

 which is otherwise lacking, although invested with certain 

 difficulties of detail. For the case of a system in uniform 

 translation, a complete correlation between the sequence 

 of events in this system referred to axes moving with 

 it, and the sequence in a corresponding fixed system, 

 can be established. This correlation is contained to any 

 order of approximation in the equations developed by Larmor, 

 who, however, in his treatise, discussed the more detailed 

 theory of the matter only to the second approximation needed 

 for the description of the null result of such experiments as 

 that of Michelson and Morley, or the efforts of Lord Eayleigh 

 and Brace to detect a double refraction in bodies on account 

 of the earth's motion. Subsequent writers, following Lorentz 

 and Einstein, have developed the detailed theory to any 

 relative magnitude of the velocity of translation to that of 

 light. 



The principle of relativity, in the case of uniform velocity 

 of translation, was thus suggested at first by analysis, although, 

 in the words of Lorentz, the scaffolding by which it was 

 originally built up has been removed, and the principle 

 postulated a priori as giving a consistent account of pheno- 

 mena. But when consideration is directed from motion of 

 translation to motion of uniform rotation, it appears that a 

 corresponding analytical basis has not been given to the 

 principle, and the two points of view begin to diverge. It 



* Communicated by the Author. 



