It follows that if in a Galilean frame we place side by side, at rest, an optical clock, a vibrating atom, a piece of radium gradually losing its mass, and a top revolving without friction, the time determinations defined by all these phenomena will be identical, since all these are perfectly isolated from external influences. To be more precise, if a sodium atom vibrates so many times per second, as measured by the optical clock of its Galilean system, it should still vibrate exactly the same number of times per second (as measured by the clock of the frame) even if the constant velocity of the Galilean frame (with respect to some standard Galilean frame) has been changed to some other constant velocity. In short, all physical phenomena at rest in a frame would evolve at exactly the same rate in terms of the optical clock of the frame, regardless of the magnitude of the Galilean motion of the frame; since, according to the special principle of relativity, this absolute Galilean motion is entirely meaningless. If observation, by any chance, should prove that the relative rates of vibration of the atom and the clock were to vary according to the Galilean frame in which we set them, we should have a physical means of differentiating one Galilean frame from another, hence of determining the velocity of our frame through the ether; and the special principle of relativity would have to be abandoned. Assuming, therefore, Einstein’s premises to be correct, we must agree that the vibrations of the optical clock constitute as perfect a means of determining congruent intervals of time as it is possible for physicists to obtain. Finally, we see that in any Galilean frame exactly the same [Pg 233] time-determinations would be obtained whether we made use of an optical clock, a top spinning on its axis without friction, a vibrating atom, or a mechanical clock, provided all these bodies were at rest as a whole in our Galilean frame. Consider, then, two Galilean frames, each containing an optical clock and a top spinning without friction on its axis. If, when the two frames are brought to relative rest, side by side, the two tops are spinning at exactly the same rate, both executing rotations per second when measured in terms of their respective clocks, then exactly the same correlation must exist when the Galilean frames are moving apart. It is therefore a matter of indifference whether the observers in the frames measure time by means of their optical clocks or by means of the rotations of their tops.