Many diverse experiments have been made, and they all agree in concluding that a man who assumes the earth to be at rest will find by measurement that the velocity of light is the same in all directions. Furthermore, when the same man turns his attention to interstellar or interplanetary phenomena, and assumes the sun to be at rest, he will again find the velocity of light to be the same in all directions. These are well-attested experiments made at long intervals of time. This is the exact contingency contemplated above. Again the velocity of light _in vacuo_ has recently taken on a new dignity. It used to be one among other wave velocities such as the velocity of sound in air, or in water, or the velocity of surface waves in water. But Clerk Maxwell discovered that all electromagnetic influences are propagated with the velocity of light, and now modern physical science half suspects that electromagnetic influences are the only physical influences which relate the changes in the physical world. Accordingly the velocity of light becomes the fundamental natural velocity, and experiment shows that our judgment of its magnitude is not affected by our choice of the framework at rest, so long as we keep to a set of dynamical axes. These experiments on light have been confirmed by other electromagnetic experiments not involving light. Thus we are driven to equations (II), where V is the velocity of light. The first conclusion to be drawn from equations (II) is that two people who make different choices of bodies at rest will disagree as to their measuring rods in the way described above. There is no peculiar difficulty about that. The only wonder is that all people agree so well in their judgments as to metrical systems. A mathematical angel would naturally expect incarnate men to be in violent disagreement on this subject. But the case of time is different. For simplicity of statement we speak of A as at O, and B as at O′. We remember that O′ is moving relatively to O with velocity _v_ in direction OO′. Suppose A and B are looking in this direction; and they both measure their time from the instant when they met, as O′ passed over O. Then we have T = ((_t_ - _vx_)/V^2)/((1 - _v_^2)/V^2). Now, suppose we consider all the events all over space which A considers to have happened simultaneously at the time _t_. The events of this set which occurred anywhere on a plane perpendicular to OO′ at a distance _x_ in front of O (according to A's reckoning), will have occurred according to B's reckoning at the time T as given above. Let us fix our attention on the fact that B does not consider all these events to be simultaneous. For let T_{1}, and T_{2} be B's times for such events on planes _x__{1}, and _x__{2}. Then T_{1} - T_{2} = _v_(_x__{2} - _x__{1})/(V^2 - _v_^2).