572 Prof. 0. W. Richardson on a Theory of the 



same direction as that in the present investigation. This dis- 

 agreement is usually attributed to the existence of undiscovered 

 absorption-bands in the ultraviolet, although, as will be shown 

 below, it is questionable whether any such hypothesis is 

 necessary. 



The second reason for the discrepancy is one which must 

 be universally operative, and arises from our having neglected 

 the effects of the other electrons in the atom. The preceding- 

 theory would be exact on the supposition that the electrical 

 properties of each atom were due to a single doublet placed 

 at its centre. We have reasons for believing that each atom 

 contains a considerable number of electrons, and consequently 

 of possible doublets. According to J. J. Thomson's most recent 

 estimate, this number is proportional to the atomic weight of 

 the atom and is of the same order of magnitude. It is thus 

 necessary to take into consideration the way in which the 

 behaviour of any given electron under assigned conditions is 

 affected by the presence of the other electrons in the atom. 



In developing our theory, we have supposed that a doublet 

 inside an atom A produced the same field of force in the 

 neighbourhood of a distant atom B as if the doublet were 

 immersed in free aether. That this will not in general be the 

 case is seen at once by considering the extreme case where 

 the number of additional doublets in A is indefinitely great. 

 In this case, the atom will behave like a sphere of specific 



3\ 



inductive capacity # = 1 + 2— 3-% where a is the radius of the 



atom and the summation is extended over all the doublets in 

 it ; so that the electric field due to a doublet at the centre of 

 A will give rise to an external field which is everywhere 

 smaller than the value used on p. 560 in the ratio 3//e+ 2. One 

 way of looking at the question is to regard the other electrons 

 in A as disposing themselves in such a way as to shield 

 external points from the field of the doublet. On account of 

 the finite number of the electrons and their definite geometric 

 arrangement, the above method of looking at the question is 

 only a crude approximation, but it is evident that in any 

 given case the field near B due to the .sth doublet in A will 

 be cut down in a certain ratio <y s depending on the orientation 

 of the doublet in the atom A. 



The doublet induced in B will also be reduced in a similar 

 manner, since the electric field at a point inside B will be 

 smaller than that outside. It will not, however, be necessary 

 to correct for this, as it can be shown that it has really been 

 allowed for in the dispersion theory on which formula (10) 

 is based. It may be worth while briefly indicating the way 



