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' of a system moving uniformly and rectilinear with respect to the former by means of the transformation relationships. Must we infer from this that systems of reference which are moving uniformly and rectilinearly with respect to each other are not equivalent as regards electrodynamic events, and that there is no relativity principle of electrodynamics? No, this inference is not necessary, because, as remarked, the principle of relativity of classical mechanics with its group of equations of transformation does not represent the only possible way of expressing the equivalence of systems of reference that are moving uniformly and rectilinearly with respect to each other. As we shall show in the sequel, the same postulate of relativity may be associated with another group of transformations. Nor did experiment seem to offer a reason for answering the above question in the affirmative. For all attempts to prove by optical experiments in our laboratories on the earth the progressive motion of the latter gave a negative result ([Note 2]). According to our observations of electrodynamic events in the laboratory the earth may be regarded equally well as at rest or in motion; these two assumptions are equivalent.
This led to the definite conviction that in fact a principle of relativity holds for all phenomena, be their character mechanical or electrodynamic. But there can be only one such principle, and not one for mechanics and another for electrodynamics. For two such principles would annul each other's effects because we should be able to derive a favoured system from them in the case of events in which mechanical and electrodynamical events occur in conjunction, and this favoured system would allow us to talk with sense of absolute rest or motion with regard to it.
The one escape from this difficulty is that opened up by Einstein. In place of the relativity principle of Galilei and Newton we have to set another which comprehends the events of mechanics and electrodynamics. This may be done, without altering the postulate of relativity formulated above, by setting up a new group of transformations, which refer the co-ordinates of equivalent systems of reference to one another. The fundamental equations of mechanics must, certainly, then be remodelled so that they preserve their form when subjected to such a transformation. Starting-points for this remodelling were already given. For it had been found empirically that Lorentz's fundamental equations of electrodynamics allowed new kinds of transformations of co-ordinates, namely, those of the form