Out of the totality of natural phenomena, we can, by successive higher approximations, deduce a coordinate system (_x_, _y_, _z_, _t_); by means of this coordinate system, we can represent the phenomena according to definite laws. This system of reference is by no means uniquely determined by the phenomena. _We can change the system of reference in any possible manner corresponding to the above-mentioned group transformation G_{c}, but the expressions for natural laws will not be changed thereby._ For example, corresponding to the above described figure, we can call _t′_ the time, but then necessarily the space connected with it must be expressed by the manifoldness (_x′_ _y_ _z_). The physical laws are now expressed by means of _x′_, _y_, _z_, _t′_,—and the expressions are just the same as in the case of _x_, _y_, _z_, _t_. According to this, we shall have in the world, not one space, but many spaces,—quite analogous to the case that the three-dimensional space consists of an infinite number of planes. The three-dimensional geometry will be a chapter of four-dimensional physics. Now you perceive, why I said in the beginning that time and space shall reduce to mere shadows and we shall have a world complete in itself. II Now the question may be asked,—what circumstances lead us to these changed views about time and space, are they not in contradiction with observed phenomena, do they finally guarantee us advantages for the description of natural phenomena? Before we enter into the discussion, a very important point must be noticed. Suppose we have individualised time and space in any manner; then a world-line parallel to the _t_-axis will correspond to a stationary point; a world-line inclined to the _t_-axis will correspond to a point moving uniformly; and a world-curve will correspond to a point moving in any manner. Let us now picture to our mind the world-line passing through any world point _x_, _y_, _z_, _t_; now if we find the world-line parallel to the radius vector OA′ of the hyperboloidal sheet, then we can introduce OA′ as a new time-axis, and then according to the new conceptions of time and space the substance will appear to be at rest in the world point concerned. We shall now introduce this fundamental axiom:— _The substance existing at any world point can always be conceived to be at rest, if we establish our time and space suitably._ The axiom denotes that in a world-point, the expression _c²__dt²_ - _dx²_ - _dy²_ - _dz²_