Lorentz transformations are valid only in t-time, whereas classical mechanics employs $\tau $-time. Since classical mechanics is supposed to be valid in any Galilean frame, i.e. any frame in uniform motion relative to the substratum, it becomes important to find the transformations which should replace the Lorentz formulae when we pass from one Galilean frame to another. These are determined in the present paper, on a simple convention as to the measurement of time in a Galilean frame. They prove to differ from Lorentz formulae, but have closely allied properties. In particular, they yield Einstein's relative-velocity formulae, which are thus seen to be more general than the Lorentz formulae themselves.