A NEW LAW OF GRAVITATION 119 



Do not imagine that this preliminary change of con- 

 ception carries us very far towards an explanation of 

 gravitation. We are not seeking an explanation; we 

 are seeking a picture. And this picture of world- 

 curvature (hard though it may seem) is more graspable 

 than an elusive tug which flits from one object to 

 another according to the point of view chosen. 



A New Law of Gravitation. Having found a new pic- 

 ture of gravitation, we require a new law of gravitation; 

 for the Newtonian law told us the arcounr. of the tug 

 and there is now no tug to be considered. Since the 

 phenomenon is now pictured as curvature the new law 

 must say something about curvature. Evidently it must 

 be a law governing and limiting the possible curvature 

 of space-time. 



There are not many things which can be said about 

 curvature — not many of a general character. So that 

 when Einstein felt this urgency to say something about 

 curvature, he almost automatically said the right thing. 

 I mean that there was only one limitation or law that 

 suggested itself as reasonable, and that law has proved 

 to be right when tested by observation. 



Some of you may feel that you could never bring your 

 minds to conceive a curvature of space, let alone of 

 space-time; others may feel that, being familiar with 

 the bending of a two-dimensional surface, there is no 

 insuperable difficulty in imagining something similar for 

 three or even four dimensions. I rather think that 

 the former have the best of it, for at least they escape 

 being misled by their preconceptions. I have spoken of 

 a "picture", but it is a picture that has to be described 

 analytically rather than conceived vividly. Our ordinary 

 conception of curvature is derived from surfaces, i.e. 



