4 Mr. W. Sutherland on the 



is at distance r from it on the axis of electrization. Let the 

 one electron be displaced through the small distance as at 

 right angles to the axis and the other through — as, then if i 

 is the inertia of each, the equation of motion is 



,d 2 as _ e 2 s x 

 l di 2 ~~~~a?'r> 



with frequency (e 2 s/a z ri)i/2TT. 



The instability requiring constraint takes the significance 

 from this case, which is mentioned only in preparation for 

 the following. Imagine with Kelvin the positive electron 

 uniformly distributed through a sphere of radius R. The 

 same effect would be produced if the positive electron moved 

 at random with a sufficiently high velocity within a sphere 

 of radius R. Then if the negative electron is within the 

 same sphere of radius R, but at distance r from its centre, 

 the force which it experiences from the positive electron is 

 (e 2 /r 2 ) (r 3 /R 3 ) —e 2 rfR z . In the atom the negative electron 

 comes to rest at distance r given bv 



e~r 

 W 



(1) 



and now the equilibrium is stable, given that the positive 

 electron is constrained as stipulated. For simplicity let us 

 make the centre of this sphere of radius R coincide with 

 that of the atom of radius a. Then for small displacement as 

 of the negative electron at right angles to r, which is parallel 

 to the electrization of the atom^ the equation of motion is 



id*as/dt 2 = - {e 2 r/W)asfr= - A/R 3 



with frequency /= {e 2 /Wi)hJ27r. 



Again, for a small displacement z of the negative electron 

 parallel to the electrization the equation of motion is 



id 2 z/dt 2 = -e 2 z/W, 



with again the same frequency. In each of the three degrees 

 of freedom of the negative electron the period of vibration 

 is the same. If R is an absolute constant, this frequency is 

 the same for all atoms. 



The first thing to do then is to see whether the equation 



Yb = 33 x 10 14 = {e 2 /UH) V2tt .... (2) 



leads to a possible and probable value of R. The quantity 

 about which there is most uncertainty is i, its average value 



