134 GRAVITATION— THE LAW 



greater than the third side. There is an analogous, but 

 significantly different, law for the time-triangle, viz. two 

 of the sides (not any two sides) are together less than 

 the third side. It is difficult to picture such a triangle 

 but that is the actual fact. 



Let us be quite sure that we grasp the precise mean- 

 ing of these geometrical propositions. Take first the 

 space-triangle. The proposition refers to the lengths of 

 the sides, and it is well to recall my imaginary discus- 

 sion with two students as to how lengths are to be 

 measured (p. 23). Happily there is no ambiguity 

 now, because the triangle of three events determines a 

 plane section of the world, and it is only for that mode 

 of section that the triangle is purely spatial. The propo- 

 sition then expresses that 



"If you measure with a scale from A to B and from 

 B to C the sum of your readings will be greater than the 

 reading obtained by measuring with a scale from A to C." 



For a time-triangle the measurements must be made 

 with an instrument which can measure time, and the 

 proposition then expresses that 



"If you measure with a clock from A to B and from 

 B to C the sum of your readings will be less than the 

 reading obtained by measuring with a clock from A to C." 



In order to measure from an event A to an event B 

 with a clock you must make an adjustment of the clock 

 analogous to orienting a scale along the line AB. What 

 is this analogous adjustment? The purpose in either 

 case is to bring both A and B into the immediate 

 neighbourhood of the scale or clock. For the clock that 

 means that after experiencing the event A it must travel 

 with the appropriate velocity needed to reach the locality 

 of B just at the moment that B happens. Thus the 

 velocity of the clock is prescribed. One further point 



