We remember that Newtonian relativity expressed the fact that mechanical phenomena, hence the laws of mechanics regulating these mechanical phenomena, remained unchanged when we passed from one Galilean frame to another. The significance of this statement is as follows:
To begin with, when we wish to fix the position of a body in our frame, it is also necessary to specify the instant of time at which the body occupies this position. We thus have four co-ordinates to take into consideration: three for space,
,
,
; and one for time,
. If, now, we change our frame of reference, taking our stand in some other Galilean system, which is in motion with respect to the first, these co-ordinates will change in value or will be transformed. For instance, if a body remains at rest at the meeting point of the three axes of our first frame, its co-ordinates will always be