8 Mr. W. Sutherland on the 



of the sphere of radius R, which is 27rR 2 /3. ^ ^ ne sphere 

 is regarded as having a rigidity W, the angle through which 

 the sphere of radius R is sheared is 3eF/27rR 2 W. This dis- 

 places one electron relatively to the other by the amount 

 3^Fr/47rR 2 W, and therefore 3<? 2 Fr/47rR 2 W is the electric 

 moment in the direction of F which F has produced in the 

 pair of electrons. This gives in an atom an average intensity 

 of electrization, analogous to intensity of magnetization, of 

 amount 3VF?y477- 2 R 2 Wa 3 , where a is the radius of the atom. 

 The corresponding average electric intensity in the atom is 

 47r/3 times this, and may be denoted by F'. This produces 

 induced electrization F'(K — l)/47r, where K is the dielectric 

 capacity of the atom, and the electric intensity clue to this is 

 F'(K — 1). This is the intensity which acts upon the consti- 

 tutive electron pairs of the atom. With a tj^pical pair of 

 these constitutive electrons in this field of electric force 

 derived from the special inner pair of electrons we proceed 

 just as we have done with that special pair in the field F. 

 Let there be n of these constitutive pairs of electrons in the 

 atom, each of electric moment ecr. The domain of each, or 

 its share of the volume of the atom, is 47ra 3 /3w. Let w be 

 the rigidity of each pair of constitutive electrons. This is 

 different from W because we cannot assume that all the 

 constitutive pairs are directed in the same way. Indeed, 

 within the atom similar considerations apply to those which 

 I have pointed out in the theory of the electric origin of 

 cohesion. In each pair of constitutive electrons the opposite 

 forces are eF', which may be assumed to act over area 

 27t<t 2 /3, so the angle through which the pair is sheared is 

 3tfF'/27rcr 2 itf, and so the average distance through which each 

 electron of the pair is displaced is SeF'a/^Tr^w, giving 

 electric moment oe 2 F'cr/4:Tr<7 2 iv. For the n pairs the total 

 moment will be n times this. For the whole electric moment 

 generated in the atom by F we have 



3e 2 Fr / 1 , 3(K-1>*V 



4ttR 2 W 



(""ESS?) «> 



To carry this farther we must express W and w by means 

 of the formula given in "The Electric Origin of Rigidity 

 and Consequences " (Phil. "Mag. [6] vii. p. 417), with K = l, 



namely ' w-?^ <W. _2tt£W 



W ~ 3 (2a) 6 ' lL ~ 3 (2a) 6 ' ' ' ' ^ a) ' 



Let v be the domain of the atom, that is, the ??th part of 

 the volume through which n atoms are distributed, then the 



