228 Professor A. S. Eddington [Feb. 1, 



analogy brings out the point that the theory is an explanation of the 

 real nature of our measures rather than of gravitation. We offer no 

 explanation why the particle always takes the path of least effort— 

 perhaps, if we may judge by our own feelings, that is so natural as to 

 require no explanation. More seriously, we know that in consequence 

 of the undulatory theory of light, a ray traversing a heterogeneous 

 medium always takes the path of least time ; and one can scarcely 

 resist a vague impression that the course of a material particle may be 

 the ray of an undulation in five dimensions. What concerns gravita- 

 tion more especially is that we have offered no explanation of the 

 linkages by which the hurdles rearrange themselves on a definite plan 

 when disturbed by the presence of a gravitating particle ; that is a 

 point on which a mechanical theory of gravitation ought to throw 

 light. 



From the constant of gravitation, together with the other 

 fundamental constants of nature— the velocity of light and the 

 quantum of action — it is possible to form a new fundamental unit 

 of length. This unit is 7 x 10"-^ centimetres. It seems to be 

 inevitable that this length must play some fundamental part in any 

 complete interpretation of gravitation. (For example, in Osborne 

 Reynold's theory of matter this length appears as the mean free- 

 path of the granules of his medium.) In recent years great progress 

 has been made in knowledge of the excessively minute ; but until 

 we can appreciate details of structure down to the quadrillionth or 

 quintillionth of a centimetre, the most suVjlime of all the forces of 

 nature remains outside the purview of the theories of physics. 



[A.S.E.] 



APPENDIX. 



Outline of the Mathematical Theory of Einstein's Law 

 OF Gravitation. 



The fundamental formula, by which from measurements we infer 

 the relative positions of objects in a space defined by three rectangular 

 co-ordinates, x, y, z, is — 



ds- = dx" -h dy"- 4- dz"- (1) 



where ds is the measured element of length, and the right-hand side 

 refers to the inferred positions. Experiments are concerned with fields 

 of gravitation which from the present point of view must be regarded 

 as extremely weak, so the formula must be taken as applying strictly 

 only in the absence of gravitation. (We have no proof that in a strong 

 gravitational field the formula would be self-consistent, i.e. that measured 

 space would be Euclidean.) 



