1. The time is absolute; the time of an event, ', relatively to ' is the same as the time relatively to . If instantaneous signals could be sent to a distance, and if one knew that the state of motion of a clock had no influence on its rate, then this assumption would be physically established. For then clocks, similar to one another, and regulated alike, could be distributed over the systems and ', at rest relatively to them, and their indications would be independent of the state of motion of the systems; the time of an event would then be given by the clock in its immediate neighbourhood. 2. Length is absolute; if an interval, at rest relatively to , has a length , then it has the same length relatively to a system ' which is in motion relatively to . If the axes of and ' are parallel to each other, a simple calculation based on these two assumptions, gives the equations [Pg 26] of transformation This transformation is known as the "Galilean Transformation." Differentiating twice by the time, we get Further, it follows that for two simultaneous events, The invariance of the distance between the two points results from squaring and adding. From this easily follows the co-variance of Newton's equations of motion with respect to the Galilean transformation (21). Hence it follows that classical mechanics is in accord with the principle of special relativity if the two hypotheses respecting scales and clocks are made. But this attempt to found relativity of translation upon the Galilean transformation fails when applied to electromagnetic phenomena. The Maxwell-Lorentz electromagnetic equations are not co-variant with respect to the Galilean transformation. In particular, we note, by (21), that a ray of light which referred to has a velocity , has a different velocity referred to ', depending upon its direction. The space of reference of is therefore distinguished, with respect to its physical properties, from all spaces of reference which are in motion relatively to it (quiescent æther). But all experiments have shown that electromagnetic and optical phenomena, relatively to the earth as the [Pg 27] body of reference, are not influenced by the translational velocity of the earth. The most important of these experiments are those of Michelson and Morley, which I shall assume are known. The validity of the principle of special relativity can therefore hardly be doubted.