Electric Origin of Rigidity and Consequences. 427 
of small pitch on the surface of the atom, so that for finding 
T it may be treated as though the path of each electron were 
a circle of radius a. The electric attraction is the centripetal 
force, and so Iv*/a=é/K(2a)*, where I is the inertia of an 
electron, assumed to be the same for both electrons; thus 
7=Ta/v=2ratl*Kefe. . . . . (18) 
Here K denotes the dielectric capacity of the stuff of the 
atom, not quite the same as the average for the atoms and 
their interspace. It is well worth noticing as another ex- 
ample of duality, that the period thus caleulated is propor- 
tional to the period of vibration of any one doublet in the 
field of force due to all the others, on the supposition that 
the doublet moves free of constraint from the atom, just as 
we assumed in the above ealeulation of +. The time of 
vibration being 
27 (moment of inertia / moment of couple)? 
is equal to 
2a] 2 2 1 
¥. eee eee =? 3a? 1K /ear\2 
2m — ae 2ar(3a° 1K /e*r) 
if s=2a, o=e/4a*, and factor 1/3 is used. 
This is nearly the same as (13). The value of r calculated 
in each of these ways is independent of the temperature, and 
therefore of the electrokinetic energy impressed on the 
doublet by the atom. It is the same as the period calcu- 
lated on the assumption that all the electric energy of a 
doublet is kinetic energy: for if © is the velocity of rotation 
for this, then 
4C0?= N= 27e’s?/3K(2a)’, and C=2e’l, 
2 : ae 
T= = 20 (3a° 1K /e*a)?. 
0) 
Substituting in (12) for 7 the value given in (13), we have 
y= KepWeArGazl.. 2. . . ., (¥4) 
To express @ the simplest assumption we can make is that 
the chance of the occurrence of conditions favourable to the 
breaking up of two adjacent doublets will be proportional 
to the: ratio’ of the free spaces between the atoms to the 
volume of the atoms, this ratio being a measure of the 
freedom of the atoms to move. In section 3 we took the 
angular velocity of the atoms to be proportional to 68. Thus 
