Tlie Relativity of Field and Matter. 801 



to be a law specialising the structure of tbe field-entity, 

 and only redeemed from arbitrariness by tbe fact that it is 

 the most simple law of the kind possible ; but regarded 

 as a property of matter (relative to the field-entity) it is 

 scarcely more than a truism and does not specialise the 

 structure of matter. It would be difficult, if not impossible, 

 to devise a theory of material structure for which this law 

 was not obeyed *. 



Consider an isolated electron. The details of the manner 

 in which such a structure comes to exist in space are 

 unknown ; but it is unnecessary to have a detailed theory 

 to understand one consequence of these unknown laws, 

 viz. that the electron is always of constant size and shape. 

 But the statement that the electron is always formed of 

 a particular size raises the question : Size, relative to what ? 

 There is no meaning in absolute size. The statement can 

 only mean that the radius of the electron is always a parti- 

 cular fraction of some other comparison-length. A little 

 consideration shows that the comparison-length must be 

 located at the same place and have the same direction as the 

 radius considered ; direct comparison is only possible in 

 that case. Equality of lengths in different, directions can 

 only be tested by a process equivalent to turning something- 

 material from one direction to the other — a procedure which 

 really begs the question. For example, to test whether two 

 radii of the electron OP], OP2 are equal, we may imagine 

 the electron turned round so that the original radius OPi 

 falls into the position OP 2 and note whether its extremity 

 falls on P 2 . But if the test succeeds, it really demonstrates 

 nothing about the shape (relative or absolute) of the 

 electron ; it only shows that an electron has "no memory " 

 so that an electron which has been turned round from 

 another position is identical in extension with an electron 

 newly created at the spot. Lorentz's "contracted electron" 

 would fulfil this test just as well as a spherical electron, 

 since the radius would contract or expand as the rotation 

 took place. 



Thus the statement that the radius of an electron has 

 a particular size implies that there is at the same spot 

 and in the same direction a comparison-length of which 

 it is a fixed fraction ; and the statement that all the radii 

 are equal means that each radius is the same fraction o( 

 the comparison-length in the corresponding direction, hot 



* This conclusion was reached by analytical methods in Proc. Roy, 

 Soc. A, vol. xcix. p. 104. I have here separated it from the mathe- 

 matical setting in which it first appeared. 



