804 Prof. A. S. Eddington on the 



•r 



formed at the point tends to a particular volume, then 

 there exists at every point in the world a definite locus, viz. 

 the boundary of: the electron (averaged if necessary) which 

 could potentially exist at that point. This locus must 

 express some property of the structure o£ the field-entity ; 

 and it appears inevitable that the locus must be ihe locus 

 of curvature* of the world at that point. The locus will 

 be judged to be a sphere of constant radius, not through 

 any intrinsic shape or size (since shape and size are relative 

 terms and cannot be intrinsic), but because our actual 

 criterion of symmetry and scale at different points in the 

 world rests ultimately on this locus. The whole principle 

 of physical measurement rests on the convention that 

 direction and position are not in themselves relevant to 

 measurement, so that measurement conventionally assigns 

 extension in such a way that the extensional properties 

 of the unit of material structure are on the average 

 independent of position and direction. The mathematical 

 expression of our conclusion that the locus of curvature 

 is a sphere of constant radius leads at once to Einstein's 

 law of gravitation. 



I think there can be little doubt that the law of 

 gravitation arises in this way, through the fact that we 

 have to study the structure of the field-entity with 

 apparatus whose parts are themselves constituted in relation 

 to the structure of the field-entity, so that the intrinsic 

 properties of the field-entity disappear in the vicious circle. • 

 The law is not of the nature of a constraint (such as Least 

 Action) imposed on the field-entity, but expresses the prin- 

 ciple of measurement t- Admittedly the argument makes 

 certain jumps, appealing to broad principles instead of 

 following through a full theory of structure; and this is 

 necessitated by our present ignorance of the details of 

 material structure. That brings me back to the first 

 contention in this paper ; we cannot separate off the 

 field-laws as a province of physics fully understood and 



* This is, of course, not the locus of the centre of curvature, which 

 lies in some fifth dimension which does not exist. In each direction 

 a radius is drawn proportional to the radius of curvature of the corre- 

 sponding section. 



t Cf. E. Cunningham, 'Relativity and the Electron Theory/ 2nd edition, 

 p. 137. " The law of gravitation becomes the condition which singles 

 out a measure-system." But whereas he appears to consider that our 

 actual measure- system is determined so as to give the greatest possible 

 simplicity to the laws of nature, I consider that it is determined by the 

 structure of the measuring appliances which we have to use. 



