704 Dr. C. V. Burton : Notes on 



thus constituted the form of argument developed in § 13- 

 For the electron is conceived as having a vacuous spherical 

 nucleus, for which mobility is only postulated in general 

 terms, the kinematics of the motion of the nucleus not being 

 so far imaginable. If it be allowed that this difficulty of the 

 nucleus may have some unforeseen solution, the whole 

 problem of the mobility of the electron is left lacking in that 

 precision which would be essential to a strict investigation. 

 Whether or not a configuration of strain self-locked by the 

 reuniting of sundered and relatively twisted surfaces is 

 capable in this case of being moved freely through the 

 medium without involving fresh breaches of continuity, must 

 be judged rather from an instinctive standpoint. Having 

 had the advantage of discussing this point with Professor 

 Larmor, who has cleared my mind of a misapprehension, I 

 express with some hesitation my outstanding difference of 

 view regarding this question of mobility. 



15. The method of regarding such problems outlined in 

 § 11 above may be more helpful. If the medium in the 

 unstrained state is stable for every possible type of displace- 

 ment, no locked distribution of infinitesimal strain can possess 

 that special lability of equilibrium which is an essential of 

 free mobility ; but if the medium itself is labile in regard to 

 certain types of strain, the aspect of the problem is clearly 

 modified. The form then assumed by the question is this : 

 the supposed transference of a self-locked strain-distribution 

 from one position to another in the medium is equivalent to 

 the superposition of a determinate differential strain. Is 

 this latter of such a type as could be imposed on the originally 

 unstrained medium, without breach of continuity and without 

 the expenditure of work? If so, the transference of the 

 strain-figure through the medium can take place freely ; 

 otherwise it cannot. The hypothetical medium with which 

 we have to deal is one in which small non-rotational strains 

 (but no others) can be produced without any resistance being- 

 encountered ; that is, without work being done. Consider, 

 then, a pair of equal spherical vacuous cavities at any dis- 

 tance apart in the unstrained medium : we have to enquire 

 what non-rotational strains could be imposed on the system ; 

 the differential aspect of the non-rotational condition being- 

 equivalent to irrotationality of the motion of the medium at 

 each instant. Supposing all velocity-components to vanish 

 at infinity, the only motion which could instantaneously be 

 taking place, without building up opposing reactions from 

 the elasticity of the (incompressible) medium, would be that 

 arising from changes of shape, size, or position of the cavities. 



