We wish to picture to ourselves the whole relation graphically. Let (_x_, _y_, _z_) be the rectangular coordinates of space, and _t_ denote the time. Subjects of our perception are always connected with place and time. _No one has observed a place except at a particular time, or has observed a time except at a particular place._ Yet I respect the dogma that time and space have independent existences. I will call a space-point plus a time-point, _i.e._, a system of values _x_, _y_, _z_, _t_, as a _world-point_. The manifoldness of all possible values of _x_, _y_, _z_, _t_, will be the _world_. I can draw four world-axes with the chalk. Now any axis drawn consists of quickly vibrating molecules, and besides, takes part in all the journeys of the earth ; and therefore gives us occasion for reflection. The greater abstraction required for the four-axes does not cause the mathematician any trouble. In order not to allow any yawning gap to exist, we shall suppose that at every place and time, something perceptible exists. In order not to specify either matter or electricity, we shall simply style these as substances. We direct our attention to the _world-point_ _x_, _y_, _z_, _t_, and suppose that we are in a position to recognise this substantial point at any subsequent time. Let _dt_ be the time element corresponding to the changes of space coordinates of this point [_dx_, _dy_, _dz_]. Then we obtain (as a picture, so to speak, of the perennial life-career of the substantial point),—a curve in the _world_—the _world-line_, the points on which unambiguously correspond to the parameter _t_ from +∞ to -∞. The whole world appears to be resolved in such _world-lines_, and I may just deviate from my point if I say that according to my opinion the physical laws would find their fullest expression as mutual relations among these lines. By this conception of time and space, the (_x_, _y_, _z_) manifoldness _t_ = 0 and its two sides _t_ < 0 and _t_ > 0 falls asunder. If for the sake of simplicity, we keep the null-point of time and space fixed, then the first named group of mechanics signifies that at _t_ = 0 we can give the _x_, _y_, and _z_-axes any possible rotation about the null-point corresponding to the homogeneous linear transformation of the expression _x²_ + _y²_ + _z²_. The second group denotes that without changing the expression for the mechanical laws, we can substitute (_x_ - α_t_, _y_ - β_t_, _z_ - γ_t_ for (_x_, _y_, _z_) where (α, β, γ) are any constants. According to this we can give the time-axis any possible direction in the upper half of the world _t_ > 0. Now what have the demands of orthogonality in space to do with this perfect freedom of the time-axis towards the upper half? To establish this connection, let us take a positive parameter c, and let us consider the figure _c²__t²_ - _x²_ - _y²_ - _z²_ = 1