126 GRAVITATION— THE LAW 



corded by a clock which has taken some other route 

 between the same terminal points. On p. 39 we con- 

 sidered 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 cal- 

 culate the curved form of space-time by using Einstein's 

 law of gravitation, viz. that the ten principal curva- 

 tures 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 New- 

 ton's law of gravitation and Newton's law of motion. 

 But there is a remarkable addendum which applies only 



