8 Bateman, The Physical Aspect of Time. 



practically sufficient to determine the relation between 

 the two systems of measurement in certain cases, as, for 

 instance, when the i5's are moving with a uniform velocity 

 relative to the A's* 



It is found that in the case of uniform relative motion 

 the units of length and time in the two systems are 

 different, and that two events occurring at different points 

 of space may appear to be simultaneous according to 

 measurements made by the A's, and not appear to be 

 simultaneous according to measurements made by the i5's. 

 Also, the shape of a bod}' is theoretically different 

 according to the two series of measurements, but the 

 difference is so very slight as to be unnoticeable. 



The fact that the electromagnetic equations have the 

 same form in the two systems of coordinates, indicates, 

 that as far as our observations of electromagnetic pheno- 

 mena are concerned, a uniform motion of a system of 

 observers would remain undetected. This, of course, is 

 in accordance with the view that position and motion are 

 purely relative, and that the term absolute motion is 

 meaningless. 



* The transformation for the case of uniform velocity was given by 

 Voiyt, Larmor and Lorentz, it is 



y'^y, z'^z, /■ = . 



'' — / ^rs » J' —J' > - — - , ' — _ 



This transformation makes 



{x\ - .r'„)2 + (v\ -y'„y- + (;\ - ='„)= - c-i/\ - /',)-^o, 

 a consequence of 



{x,-s„_r- + {y,-y^J"+{Z;-z,r--c-H/,-f„y'=o. 



It can be shown that any transformation of coordinates which leaves the 

 last equation unaltered is such that the electrodynamical equations are 

 unaltered in form. See papers by E. Cunningham and the author in the 

 Proccedivgs of the London Mathematical Society (1910). 



