but
Thus the Galilei-Newton principle of relativity of classical mechanics and the Lorentz-Einstein "special" principle of relativity differ only in the form of the equations of transformation that effect the transition to equivalent systems of reference ([Note 3]).
Moreover, the relation of these two different transformation formulæ to each other comes out clearly in the circumstance that the equations of transformation of Galilei and Newton may be derived by a simple passage to the limit from the new equations of Lorentz and Einstein. For if we assume the velocity
of each system with respect to the other to be very small compared with the velocity of light
, so that the quotient
or