150 GRAVITATION— THE EXPLANATION 



large and the radius of curvature small. The rods 

 therefore are small, and there will be more of them in 

 $i£i than the picture would lead you to expect. If the 

 earth chooses to go to E 2 the curvature is less sharp; 

 the greater radius of curvature implies greater length 

 of the rods. The number needed to stretch from S ± to 

 E 2 will not be so great as the diagram at first suggests; 

 it will not be increased in anything like the proportion 

 of S ± E 2 to S ± E X in the figure. We should not be sur- 

 prised if the number turned out to be the same in both 

 cases. If so, the surveyor will report the same distance 

 of the earth from the sun whether the track is EE ± or 

 EE 2 . And the Superintendent of the Nautical Almanac 

 who published this same distance some years in advance 

 will claim that he correctly predicted where the earth 

 would go. 



And so you see that the earth can play truant to any 

 extent but our measurements will still report it in the 

 place assigned to it by the Nautical Almanac. The 

 predictions of that authority pay no attention to the 

 vagaries of the god-like earth; they are based on what 

 will happen when we come to measure up the path that 

 it has chosen. We shall measure it with rods that adjust 

 themselves to the curvature of the world. The mathe- 

 matical expression of this fact is the law of gravitation 

 used in the predictions. 



Perhaps you will object that astronomers do not in 

 practice lay measuring rods end to end through inter- 

 planetary space in order to find out where the planets 

 are. Actually the position is deduced from the light 

 rays. But the light as it proceeds has to find out what 

 course to take in order to go "straight", in much the 

 same way as the metre rod has to find out how far to 

 extend. The metric or curvature is a sign-post for the 



