, necessarily obtains a different measure for the velocity of propagation of the same action. This was to hold for every finite velocity
. Only infinite velocity was to be distinguished by the singular property that it was to come out in every system independently of its state of motion as having exactly the same value in all the measurements, namely, the value infinity.
This hypothesis—for we are here, of course, dealing only with a purely physical hypothesis—immediately suggested itself. Without further test there was no support for supposing that also a finite velocity, namely, the velocity of light, which the naïve point of view is inclined to endow with infinitely great velocity, would manifest the same singular property.
The fact, however, which the Michelson-Morley experiment helped us to become aware of was that the law of propagation for light is, for the observer, independent of any progressive motion of his system of reference, and has the property of isotropy (that is, equivalence of all systems) (cf. [Note 2]), so that it immediately suggests itself to us that the velocity of light is to be considered as having the same value for all systems of reference. The recognition of the fact thus arrived at was, without doubt, a surprise, but it will appear less strange to those who bear in mind the particular rôle of the velocity of light in the equations of Maxwell, the foundation of our theory of matter.
In consequence of this peculiarity, the velocity of light occurs in the equations of kinematics as a universal constant. To understand this better we pursue the following argument. Long before the advent of the questions of electrodynamic phenomena in moving bodies we might, on grounds of principle, have suggested quite generally the question: how are the co-ordinates in two systems of reference that are moving uniformly and rectilinearly with respect to each other to be referred to each other? We should have been able to attack the purely mathematical problem with a full consciousness of the assumptions contained in the hypotheses, as was actually done later by Frank and Rothe ([Note 4]). We then arrive at equations of transformation that are much more general than those written down on [p. 9]. By taking into account the special conditions that nature manifests to us, for example the isotropy of space, we may derive from them particular forms, the hypothetical assumptions contained in which come clearly to view. Now, in these general equations of transformation a quantity occurs that deserves special notice. There are "invariants" of these equations of transformation, that is, quantities that preserve their value even when such a transformation is carried out. Among these invariants there is a velocity. This signifies the following: if an effect propagates itself in one system with the velocity
, then in general the velocity of propagation of the same effect in another system is other than