by means of these equations of transformation. So long as we restrict ourselves to those systems of reference among all others that emerge out of each other as a result of transformations of the above type, there is no sense in talking of absolute rest or absolute motion. For we may freely decide to regard either of two systems moving in such a way as the one that is at rest or in motion. According to classical mechanics it was, indeed, believed that only the Galilei-transformations could come into question when we were concerned with referring equivalent systems of reference to each other according to the principle of relativity. This, however, is not the case. The recognition of the fact that other equations of transformation may come into question for this purpose, and, indeed, may be chosen to suit the facts of observation which are to be accounted for, the recognition of this fact is the characteristic feature of the "special" theory of relativity of Lorentz-Einstein which replaced that of Galilei-Newton. Lorentz's fundamental equations of the electrodynamics of moving matter led to it. This system of electrodynamics, which is in satisfactory agreement with observation, is founded, in contradistinction to Hertz's theory, on the view of an absolutely rigid ether at rest. Its fundamental equations assume as its favoured system the co-ordinate system that is at rest in the ether.
These fundamental electrodynamical equations of Lorentz, however, change their form if, in them, we replace the co-ordinates
,
,
,
of a system of reference, initially chosen, by the co-ordinates