448 SCIENCE PROGRESS 



pressure and also to (/a 2 — i), both of which relations are con- 

 tradicted by experiment. 



There remains only one other theory which need be 

 seriously considered and which has been advanced indepen- 

 dently by Livens 1 and Havelock. 2 This theory will be 

 discussed in somewhat greater detail as, in the author's opinion, 

 it is probably the correct one. It has been mentioned above 

 that it is certain that, under the conditions of the experiments, 

 an actual increase in the density of the metallic vapour in the 

 arc takes place simultaneously with an increase in the pressure 

 of the surrounding gas. It is to this density change in the 

 incandescent vapour that the present theory attributes the 

 observed displacement. The theories of Larmor and of 

 Richardson both attempted to explain it by means of some 

 influence exerted by the surrounding gas, and in both cases 

 they were found incapable of accounting for a displacement 

 of the observed magnitude. No account was taken by them 

 of the neighbouring metallic atoms of the same free period. 

 Richardson 3 indeed expressly ruled these out ^of consideration 

 by asserting that their effect is to cause only a broadening of 

 the lines, unaccompanied by any displacement, but no reasons 

 were given to justify the statement. 



Thus the present theory is concerned with the vibrations 

 emitted, not by a single vibrator, but by an aggregate of similar 

 vibrators with the same free period. The method of procedure 

 consists in forming the equation of motion of a typical electron 

 and then making a summation with respect to all the electrons 

 in a unit of volume. The essential point of the theory consists 

 in the introduction into that equation of a force acting upon the 

 electron and arising from the electric polarisation of the sur- 

 rounding medium. It is assumed in order to satisfy theoretical 

 requirements that each electron may be surrounded by a sphere 

 of a radius sufficiently large for it to contain a great number of 

 electrons, but yet, at the same time, small when compared with 

 the wave length : the matter inside this sphere is imagined 

 removed. Then if a single electron is placed at its centre O, 

 the force on this electron when an electric field of strength E is 

 acting is not simply eE, as it would be if the electron were 



1 Phil. Mag. p. 268, August 191 2. 



2 Astroph. Journ. 35, p. 304, 191 2. 

 5 ]Loc. cit. ante, p. 563. 



