You may remember that points along the track of any material body (necessarily moving with a speed less than the velocity of light) are in the absolute past or future of one another; they are not absolutely “elsewhere”. Hence the length of the track in four dimensions is made up of time-like relations and must be measured in time-units. It is in fact the number of seconds recorded by a clock carried on a body which describes the track.[17] This may be different from the time recorded [Pg 126] by a clock which has taken some other route between the same terminal points. On p. 39 we considered two individuals whose tracks had the same terminal points; one of them remained at home on the earth and the other travelled at high speed to a distant part of the universe and back. The first recorded a lapse of 70 years, the second of one year. Notice that it is the man who follows the undisturbed track of the earth who records or lives the longest time. The man whose track was violently dislocated when he reached the limit of his journey and started to come back again lived only one year. There is no limit to this reduction; as the speed of the traveller approaches the speed of light the time recorded diminishes to zero. There is no unique shortest track; but the longest track is unique. If instead of pursuing its actual orbit the earth made a wide sweep which required it to travel with the velocity of light, the earth could get from 1 January 1927 to 1 January 1928 in no time, i.e. no time as recorded by an observer or clock travelling with it, though it would be reckoned as a year according to “Astronomer Royal’s time”. The earth does not do this, because it is a rule of the Trade Union of matter that the longest possible time must be taken over every job. Thus in calculating astronomical orbits and in similar problems two laws are involved. We must first calculate the curved form of space-time by using Einstein’s law of gravitation, viz. that the ten principal curvatures are zero. We next calculate how the planet moves through the curved region by using Einstein’s law of motion, viz. the law of the longest track. Thus far the procedure is analogous to calculations made with Newton’s law of gravitation and Newton’s law of motion. But there is a remarkable addendum which applies only [Pg 127] to Einstein’s laws. Einstein’s law of motion can be deduced from his law of gravitation. The prediction of the track of a planet although divided into two stages for convenience rests on a single law. I should like to show you in a general way how it is possible for a law controlling the curvature of empty space to determine the tracks of particles without being supplemented by any other conditions. Fig. 5