422 Mr. W. Sutherland on the 
3. The Division of Molecular Electric Energy into Electro- 
static and Electrokinetic as shown by the T. emperature 
Variation of Rigidity in Metals. 
The theory of rigidity leads as follows to a fundamental 
principle concerning the partition of electric energy. Let 
us denote the electrostatic ener gy associated with matter per 
unit volume in a metal at absolute zero by W?, and assume 
that » the rigidity at 0 represents the electrostatic energy at 
that temperature, denoted by w?, then by (1). 
w? @? 
Now as a metal is heated up from zero to @ its atoms have 
an increasing amplitude of motion which at @ is proportional 
to 6@ the.expansion; and it may be assumed that, just as in 
harmonic motion mean velocity is pr oportional to mean 
amplitude, so the angular velocity of atoms of metal at @ is 
proportional tu 6@ or equal to c@, where ¢ is a constant for 
any & given metal. If, then, the difference between W2 and 
w? exists as rotator y energy C6?, we have the equation 
W?—w?=Cé@?. 
But at the melting-point rigidity vanishes and w?=0, so 
that when 0=T we find W?=C'?, and thus 
w? ne 0° 
Wty ME 
The above, then, are the assumptions by which I propose 
to give a dy namical meaning to (1). The fraction 62/T? re- 
presents that fraction of the original electrostatic energy at 
absolute zero which is converted into electrokinetic energy 
on raising the temperature to 8. The combined existence of 
electrostatic and electrokinetic energies in the same pair of 
electrons may be conceived by imagining the electrons to 
travel over the surface of the atom in curves similar to screws 
having a small pitch so that the motion parallel to the axis 
of the screw is negligible in comparison with that round it. 
The average distance along the axis of the screw between 
the two electrons is the distance s which gives the pair of 
electrons the electric moment es. The electrokinetic energy 
of motion round this axis and the electrostatic energy due to 
separation of the charges along the axis, may both be regarded 
as a store of directed ener gy of total amount W?2 per unit 
volume. In this way we conceive a possible source of phe- 
nomena in which the total energy W? predominates, and of 

