u6 GRAVITATION— THE LAW 



gravity vanishes, so that he can remain at rest without 

 support — without hammering. He looks up and sees 

 apples falling at the surface of the earth, and as before 

 ascribes this to a mysterious tug which he calls gravita- 

 tion. The apple looks down and sees Newton approach- 

 ing it; but this time it cannot attribute Newton's accelera- 

 tion to any evident hammering. It also has to invent 

 a mysterious tug acting on Newton. 



We have two frames of reference. In one of them 

 Newton is at rest and the apple is accelerated; in the 

 other the apple is at rest and Newton accelerated. In 

 neither case is there a visible cause for the acceleration; 

 in neither is the object disturbed by extraneous ham- 

 mering. The reciprocity is perfect and there is no ground 

 for preferring one frame rather than the other. We 

 must devise a picture of the disturbing agent which will 

 not favour one frame rather than the other. In this 

 impartial humour a tug will not suit us, because if we 

 attach it to the apple we are favouring Newton's frame 

 and if we attach it to Newton we are favouring the 

 apple's frame.* The essence or absolute part of gravi- 

 tation cannot be a force on a body, because we are en- 

 tirely vague as to the body to which it is applied. We 

 must picture it differently. 



* It will probably be objected that since the phenomena here dis- 

 cussed are evidently associated with the existence of a massive body (the 

 earth), and since Newton makes his tugs occur symmetrically about that 

 body whereas the apple makes its tugs occur unsymmetrically (vanishing 

 where the apple is, but strong at the antipodes), therefore Newton's 

 frame is clearly to be preferred. It would be necessary to go deeply into 

 the theory to explain fully why we do not regard this symmetry as of 

 first importance ; we can only say here that the criterion of symmetry 

 proves to be insufficient to pick out a unique frame and does not draw 

 a sharp dividing line between the frames that it would admit and those 

 it would have us reject. After all we can appreciate that certain frames 

 are more symmetrical than others without insisting on calling the sym- 

 metrical ones '"right"' and unsymmetrical ones 'wrong'. 



