Woolard— Generalized Relativity and Gravitation. 4:27 



the earth relative to the aether, we should have measured 

 the absolute velocity of Newtonian mechanics. There 

 are several experiments which should enable us to do this 

 quite easily, the most famous being the so-called Michel- 

 son-Morley experiment 4 ; but in every one of the numer- 

 ous instances in which these experiments have been 

 accurately performed, they have failed to give the 

 slightest evidence of the expected effects. Hence, the 

 statement of the Principle of Relativity, that "it is 

 impossible by means of physical experiments to deter- 

 mine the absolute velocity of a body through space. ' ' 



4. The theory of electricity and magnetism, based 

 upon experimental evidence, gives us a set of equations 

 for the conditions existing in an electromagnetic field. 

 Let the systems of - rectangular coordinates (x, y, z, t) 

 and (x' , y' , z' , t'), t referring to time, be moving relative 

 to one another with a uniform motion of translation 

 without rotation; let the origins of the two systems 

 coincide at the initial epoch ; then it is clear that 



X = X — at | 



z'=z-yt f {l > 



t' = t 



According to what we said above, the Newtonian equa 

 tions of motion are unchanged by a transformation of 

 this type ; when we try to extend electrodynamics to 

 moving systems in this way, however, we find that the 

 equations are changed fundamentally. It is found that 

 they are unchanged by a transformation of the type 



(2) 



where v is the velocity of motion, and c, as always, is the 

 velocity of light. Now, in order to explain the fact that 

 we cannot detect the motion of the earth relative to the 



* Cunningham, Eelativity and the Electron Theory, pp. 16-21 ; Carmichael, 

 Theory of Eelativity, 1913, pp. 10-13. 



a*' 



t 



y 

 t' 



= P(x 



— y 



-vt) - 



-4) 



P 



= {i- 



^ 



