£02 Prof. A. S. Eddington on the 



OQj be the comparison-length in the direction OP], and 

 k the constant fraction, so that 



OP 1= £OQi. 



Then our real meaning is that the locus of P l5 i. e. the 

 boundary of the electron, is similar to and in a constant 

 ratio to the locus of Qj. 



The statement that the electron is a sphere of constant 

 size appears in two aspects. First it may be a statement 

 of empirical fact. In that case our comparison-locus Qt is 

 a metre-sphere, that is to say a locus constructed in a 

 specified manner with a material scale, which we take by 

 definition as our standard of constant size (at different 

 times and places) and of spherical symmetry. That this 

 materially constructed sphere should be similar to and in 

 a constant ratio to the surface of an electron, presumably 

 results from the conditions determining the extension of 

 rigid bodies. We cannot trace the connexion in detail 

 because of our ignorance of material structure : but it 

 seems possible to see the connexion from broad principles. 

 If electrons were always elongated north and south we 

 should scarcely trust a pair of compasses constructed of 

 electrons to keep an unvarying distance when turned from 

 east-west to north-south ; and we should expect a drop 

 of water at rest and undisturbed to exhibit a similar axial 

 character. But if the electrons are spherical, that is to 

 say if the extensional properties of our units of material 

 structure are symmetrical, then there is nothing to show 

 why our materially constructed locus Q x should deviate 

 from symmetry in one direction rather than another. Thus 

 in conventionally assigning spherical shape to our locus Q 1? 

 we are virtually assigning spherical shape to the electron *. 



But our original statement as to the shape and size of the 

 electron referred not to an empirical fact, but to a readily 

 understood consequence of its unknown laws of formation. 

 In this case reference to a metre-sphere is obviously irre- 

 levant. The comparison-locus Qi implied in the statement 



* It may be asked, How about the ring-electron P In that case, 

 the electron-structure possible at any poiut is not unique since the 

 ring can have different orientations. Our statement as to sphericity 

 must be taken to refer, not to a single electron, but to the average 

 of a large uumber taken at random. Perhaps the explicit intro- 

 duction of the statistical average for the electron assists the argument, 

 for statistical averages are evidently concerned in all properties of 

 matter in bulk, so that there now appears a closer connexion between 

 the causes determining the two loci OPi and OQi. 



