Now if, instead of restricting ourselves to any particular phenomenon, we consider all phenomena of the same type, such as all mechanical or all electrodynamic phenomena, we know that these phenomena in their aggregate satisfy the requirements of certain general laws or equations: the laws of mechanics or the laws of electrodynamics, as the case may be. To say, therefore, that Galilean motion or velocity is relative so far as a certain type of phenomenon is concerned means that the general laws governing such types of phenomena remain unchanged [Pg 120] in form when we pass from one Galilean frame to another. Expressed mathematically, this means that when the space and time transformations are applied to the general laws, these laws or equations are transformed into equations possessing exactly the same mathematical appearance; they are then said to have been transformed into themselves. When the transformations were applied to the general laws of mechanics, these laws suffered no change in form; and this fact constituted the mathematical expression of the Newtonian or mechanical principle of the relativity of Galilean motion. But when the transformations were applied to the equations or laws of electrodynamics, a distinct change in form was noted; the laws or equations lost their simple appearance. This suggested that the electrodynamical laws as accepted by classical science held only in their simple form for a privileged Galilean frame, which for reasons of symmetry was naturally assumed to be one at rest in the stagnant ether. But then, the laws changing in form according to the Galilean frame to which they were referred, it followed as a necessary consequence that electromagnetic experiments should pursue a different course and yield different results according to the frame in which the observer and his instruments were placed. It should then be possible to discover the magnitude of the velocity of the frame through the ether by means of electromagnetic or optical experiments, so that once again, independently of any particular ether hypothesis, mathematical reasoning as well as commonplace reasoning confirmed the physical reality of velocity through the ether.