which is seen to be a modified extension to four dimensions of the equation for $S$. We must measure $t$ in the same units as $x$, $y$, $z$. By taking the constant velocity of light (300,000 kilometres per second) as unit velocity, we can measure in length or time indiscriminately. [8] We will analyse briefly this equation as it epitomizes the Special Theory of Relativity. If the World-Frame had been Euclidean the equation would have been $$\Omega^2 = (dx)^2 + (dy)^2 + (dz)^2 + (dt)^2$$ but this would not satisfy the "transformation equations" which resulted from the Special Theory. These transformation equations arose directly from a reconciliation between two observed facts; (a) the observed agreement of all natural phenomena with the "Restricted Principle of Relativity"--a principle which shows that absolute rectilinear motion cannot be established--(as regards mechanics this was recognized by Newton; the Michelson-Morley and other experiments showed this principle also applied to optical and electro-dynamical phenomena); and (b) the observed disagreement of optical and electro-dynamical phenomena (notably the constancy of light velocity) with the laws of dynamics as given by classical mechanics, e.g., in regard to the compounding of relative velocities. Einstein effected this reconciliation by detecting a flaw in classical mechanics. He showed that by regarding space and time measurements as relative to the observer--not absolute as Newton defined them--there was nothing incompatible between the Principle of Relativity and the laws of dynamics so modified. Newton's definitions were founded on conception. Einstein's recognition of the relativity of space and time is based on observation. Equation (1) shows that the geometry of the World-Frame referred to an inertial system is semi-Euclidean (hyperbolic), and that space and time measurements are relative to the observer's inertial reference system. The equation shows that the World-Frame has a certain geometrical character which we distinguish as four-dimensional "flatness." It is everywhere alike (homaloidal). Its flat character is shown by the straight line nature of the separation-interval and of the system to which it is most simply referred. Thus we have found two absolute features in the World-Frame--(1) Its geometrical character--"flatness"; (2) The separation-interval--which can be expressed in terms of measurable variables called space and time partitions, this partitioning being dependent on the observer's motion. We are now in a position to explore the World-Fabric. Already we see that, studied under inertial conditions (free of force), it agrees with the World-Frame. THE WORLD-FABRIC The General Theory of relativity is largely concerned with the investigation of the World-Fabric. Consider the World-Frame to be disturbed. We may regard this disturbance, which manifests itself in physical phenomena, as energy, or more correctly "action."