PREDICTIONS FROM THE LAW 151 



light as it is a gauge for the rod. The light track is in 

 fact controlled by the curvature in such a way that it is 

 incapable of exposing the sham law of curvature. And 

 so wherever the sun, moon and earth may have got to, 

 the light will not give them away. If the law of curva- 

 ture predicts an eclipse the light will take such a track 

 that there is an eclipse. The law of gravitation is not a 

 stern ruler controlling the heavenly bodies; it is a kind- 

 hearted accomplice who covers up their delinquencies. 



I do not recommend you to try to verify from Fig. 6 

 that the number of rods in SiE t (full line) and SJL 2 

 (dotted line) is the same. There are two dimensions of 

 space-time omitted in the picture besides the extra dimen- 

 sions in which space-time must be supposed to be bent; 

 moreover it is the spherical, not the cylindrical, curvature 

 which is ,the gauge for the length. It might be an 

 instructive, though very laborious, task to make this 

 direct verification, but we know beforehand that the 

 measured distance of the earth from the sun must be 

 the same for either track. The law of gravitation, ex- 

 pressed mathematically by G^ u — Xg^ t means nothing 

 more nor less than that the unit of length everywhere 

 is a constant fraction of the directed radius of the world 

 at that point. And as the astronomer who predicts the 

 future position of the earth does not assume anything 

 more about what the earth will choose to do than is 

 expressed in the law G tLV ^=Xg lxl/i so we shall find the 

 same position of the earth, if we assume nothing more 

 than that the practical unit of length involved in measure- 

 ments of the position is a constant fraction of the directed 

 radius. We do not need to decide whether the track is 

 to be represented by EE ± or EE 2 , and it would convey 

 no information as to any observable phenomena if we 

 knew the representation. 



