where _r__{AB} is the length of the moving rod, measured in the stationary system. Therefore the observers stationed with the watches will not find the clocks synchronous, though the observer in the stationary system must declare the clocks to be synchronous. We therefore see that we can attach no absolute significance to the concept of synchronism; but two events which are synchronous when viewed from one system, will not be synchronous when viewed from a system moving relatively to this system. § 3. Theory of Co-ordinate and Time-Transformation from a stationary system to a system which moves relatively to this with uniform velocity. Let there be given, in the stationary system two co-ordinate systems, _i.e._, two series of three mutually perpendicular lines issuing from a point. Let the X-axes of each coincide with one another, and the Y and Z-axes be parallel. Let a rigid measuring rod, and a number of clocks be given to each of the systems, and let the rods and clocks in each be exactly alike each other. Let the initial point of one of the systems (_k_) have a constant velocity in the direction of the X-axis of the other which is stationary system K, the motion being also communicated to the rods and clocks in the system (_k_). Any time _t_ of the stationary system K corresponds to a definite position of the axes of the moving system, which are always parallel to the axes of the stationary system. By _t_, we always mean the time in the stationary system. We suppose that the space is measured by the stationary measuring rod placed in the stationary system, as well as by the moving measuring rod placed in the moving system, and we thus obtain the co-ordinates (_x_, _y_, _z_) for the stationary system, and (ξ, η, ζ) for the moving system. Let the time _t_ be determined for each point of the stationary system (which are provided with clocks) by means of the clocks which are placed in the stationary system, with the help of light-signals as described in § 1. Let also the time τ of the moving system be determined for each point of the moving system (in which there are clocks which are at rest relative to the moving system), by means of the method of light signals between these points (in which there are clocks) in the manner described in § 1. To every value of (_x_, _y_, _z_, _t_) which fully determines the position and time of an event in the stationary system, there correspond a system of values (ξ, η, ζ, τ); now the problem is to find out the system of equations connecting these magnitudes. Primarily it is clear that on account of the property of homogeneity which we ascribe to time and space, the equations must be linear.