is small compared to
, the difference between the two types of transformations becomes negligible.
[45] As a matter of fact the appellation “FitzGerald contraction” should also be abandoned in Einstein’s theory, since FitzGerald and Lorentz had always regarded the contraction in the light of a real physical contraction in the stagnant ether. Nevertheless, if the reader realises the difference in the two conceptions of the contraction, it will simplify matters to retain the original name.
[46] It is necessary to take both of these conditions into account. If, for instance, we limited ourselves to the invariance of light’s velocity without taking into consideration the relativity of velocity, transformations such as
;
would also satisfy our requirements, and these would not be the Lorentz-Einstein transformations and would not be in accord with the relativity of Galilean motion.