128 GRAVITATION— THE LAW 



we might wish. You will realise the possibility that, 

 given two ridges as in Fig. 5, it may be impossible to 

 join them by an intervening valley without the illegal 

 kind of curvature. That turns out to be the case. Two 

 perfectly straight ridges alone in the world cannot be 

 properly joined by empty space and therefore they can- 

 not occur alone. But if they bend a little towards one 

 another the connecting region can lie smoothly and sat- 

 isfy the law of curvature. If they bend too much the 

 illegal puckering reappears. The law of gravitation is 

 a fastidious tailor who will not tolerate wrinkles (except 

 of a limited approved type) in the main area of the 

 garment; so that the seams are required to take courses 

 which will not cause wrinkles. You and I have to sub- 

 mit to this and so our tracks curve towards each other. 

 An onlooker will make the comment that here is an 

 illustration of the law that two massive bodies attract 

 each other. 



We thus arrive at another but equivalent conception 

 of how the earth's spiral track through the four-dimen- 

 sional world is arrived at. It is due to the necessity of 

 arranging two ridges (the solar track and the earth's 

 track) so as not to involve a wrong kind of curvature in 

 the empty part of the world. The sun as the more 

 pronounced ridge takes a nearly straight track; but the 

 earth as a minor ridge on the declivities of the solar 

 ridge has to twist about considerably. 



Suppose the earth were to defy the tailor and take a 

 straight track. That would make a horrid wrinkle in the 

 garment; and since the wrinkle is inconsistent with the 

 laws of empty space, something must be there — where 

 the wrinkle runs. This "something" need not be matter 

 in the restricted sense. The things which can occupy 

 space so that it is not empty in the sense intended in 



