n CONCEPTS OF SPACE AND TIME 29 



of gravitation. In other words, the man in the cage will 

 think that he and the cage and the object therein are all 

 acted upon by gravitation. What is really due to accelera- 

 tion appears to be a case purely and simply of gravitation. 

 Thus we see acceleration and gravitation are really the same 

 phenomena and only different in appearance to observers. 

 Acceleration and gravitation are, in fact, equivalent expres- 

 sions. Einstein's closed cage may yet become as historic 

 as Newton's falling apple. 



Now take rotation, which is simply a special case of 

 acceleration. And let us imagine an observer situated on a 

 rotating or revolving plane circular disc and proceeding to 

 measure the area of the disc and the rate at which it is 

 revolving. He has two identical clocks, one of which he puts 

 near the centre of the disc and the other near the circum- 

 ference in order to take some time measurements. When he 

 proceeds to take the time of the clock near the centre he 

 finds that it moves more slowly than when he proceeds to 

 read the clock placed near the circumference. We have al- 

 ready seen why this is so. The motion of the disc at the 

 centre is nil, and its motion at the circumference quite 

 marked, and the times of identical clocks at these two points 

 will therefore vary to the moving observer. And similarly 

 the rate of any identical clock will vary according to the dis- 

 tance of its position on the surface of the disc from the cen- 

 tre, as the motions of all points on the disc will differ accord- 

 ing to their distance from the centre. He then proceeds to 

 apply identical measuring rods and finds the same continual 

 variation. He finds that the identical measuring rods vary 

 in length according to their position on the disc; one placed 

 on the circumference is shorter than one placed near the 

 centre. And the differing lengths of the rods will measure 

 up different spaces. The observer will become utterly 

 confused, and will finally conclude that the spaces on the 

 disc are not the same everywhere and in all directions, but 

 appear to vary in all directions and to be twisted, warped, 

 and curved. Or, as we would say, the space of the disc is 

 not straight-line homogeneous uniform Euclidean space, but 



