24 Mr. W. Sutherland on 



the sphere, so that the special pair of electrons has an electric 

 moment er oppositely directed to that of the whole atom, 

 which is denoted by es. This electric moment es produces 

 the external electric field of cohesion, and it produces the 

 internal field in which the special pair of electrons vibrates. 

 The special negative electron is attracted by the positive 

 with a force (e 2 /r <i )(r z lli 3 ) = e 2 rlR 3 , and comes to rest in the 

 internal field at the distance defined by the equation 

 r/R 3 = s/a 3 , where a is radius of atom. If displaced in any 

 direction at right angles to r the negative electron of inertia 

 i oscillates with a frequency (V/^OV^tt. I£ displaced in 

 the direction of r it oscillates with the same frequency. 

 Thus the negative electron has three degrees of freedom in 

 which its frequency is the same. Moreover, this frequency 

 is the same for all atoms, if R is the same for all, and that is 

 why it is stipulated above that R is to be an absolute con- 

 stant. It is assumed that there is a fundamental period of 

 vibration the same for all atoms, because in the Balmer- 

 Rydberg formula l/\ = w = w — &/(ra + f0 2 the parameter b 

 has nearly the same value for many series of spectral 

 lines in many elements. The frequency bV (V= velocity of 

 light) is a fundamental constant of Nature, such that 1/Yb 

 might yet furnish a natural unit of time, R being an asso- 

 ciated natural unit of length. In the non-metals there is a 

 tendency for es to be proportional to a 3 , so that if the 

 frequency is constant and R also, then r is nearly constant 

 in the non-metals. In the metals of the Li and Be families 

 es is proportional to a, so that r is inversely proportional to 

 a 2 , yet the fundamental frequency is constant. 



By means of the constitutive pairs of electrons and the 

 special pair in the atom a theory of dielectric capacity is 

 reached in the following way. The electric axes of the pairs 

 in matter free from external electric action are distributed 

 at random as regards their direction. Thus an average 

 direction for a single representative pair when an electric 

 intensity is applied to the matter is that at right angles to 

 the intensity. The average pair of electrons is subjected to 

 a shearing stress by the action of the external electric 

 intensity, so also is the special pair, and also the atom as a 

 whole. If in each case we introduce the corresponding- 

 rigidity we derive the associated strain which gives the whole 

 electric displacement caused by the external electric intensitv. 

 In this way we obtain the dielectric capacity of any atom. 

 For the atom of a metal in its compounds the result obtained 

 is (6), namely, 



(N , -])V=(N-l)B = CB 2 / 3 + DB 2 ' 3 (N 2 -l)/ f >, 



