(1) Objects on B's system appear to A to be shorter in the direction of relative motion than they appear to B. (2) This opinion is reciprocal. B thinks that A's measurements on A's system are too great. (3) Similarly for times: each observer thinks that the other's clocks have a slower rate than his own, so that B's durations of time appear shorter to B than to A, and conversely. (4) Events which appear simultaneous to A do not in general appear so to B, and conversely. (5) Lengths at right angles to the direction of motion are unaffected. (6) These effects vary with the ratio of the relative velocity to that of light. The greater the relative velocity, the greater the effects. They vanish if there is no relative velocity. (7) For ordinary velocities the effects are so small as to escape notice. The remarkable point however is their occurrence rather than their magnitude. (8) The observers similarly form different estimates of the velocities of bodies on each other's systems. The velocity of light however appears the same to all observers. Taking into account these revised views of lengths and times the mechanical principle of relativity may be extended to physical laws generally as follows: All unaccelerated frames of reference are equivalent for the statement of the general laws of physics. In this form the statement is called the Special, or Restricted, Principle of Relativity, because it is restricted to unaccelerated frames of reference. Naturally the laws of classical mechanics now require some modification, since the suppositions of unalterable lengths and times no longer apply. THE FOUR DIMENSIONAL CONTINUUM