490 Mr. W. Sutherland on the 
is equal to half the square of the shear multiplied by the 
original electric energy e?/rK. Thus the rigidity of a pair 
of electrons is their electrostatic energy. To obtain a simple 
dynamical representation of a metal we may use the fiction 
of three laminar distributions, and then, by the definition of 
rigidity and Maxwell’s expression Qro?/K for the energy in 
unit volume of a dielectric, we get by a similar argument to 
that just used for a pair of electrons the result 
Nalt niet 
3K” (mp)? ~ 
This demonstrates the electric origin of rigidity at absolute 
zero. At higher temperatures kinetic effects have to be 
taken into account as well as the static. Rigidity is of 
electrostatic origin, but its variation with temperature is a 
simple kinetic phenomenon. I find (Physical Review, x. 
1900) that R. A. Fessenden, in America, for some time has. 
been advocating the electric origin of cohesion and rigidity, 
though in spite of considerable insight and imagination he 
has not, to my knowledge, Palani his ideas w ith sufficient 
precision for a working physical theory. 
Reinganum, who has investigated the electric origin of 
cohesion (Physikalische Zeitschr ift, 1900, Ann. der Ph. 14] ae 
1903), has, in the second of these papers, considered the 
tensile strength of metals in a general way without special 
attention to rigidity. 

2. The Consequent Nature of Atomic Vibration. 
In section 6 of “The Cause of the Structure of Spectra” 
(Phil. Mag. [6] ii.) the mechanical period of vibration of an 
atom of metal was calculated in the following way. N the 
rigidity of the metal at absolute zero must be the rigidity of 
its monatomic molecule. The velocity of propagation of a 
shearing stress through the atom must be (N/p);- But as 
N = Iro?/3K, this takes the form o(27/dpK):. Since the 
linear dimension of the atom is (m/p)3 or 2a, the period of 
vibration of the atom is 
2a)o(2m/3pK)?. ee 
On account of the electric origin of rigidity, the period of 
mechanical vibration is expressed in terms of the electric 
properties of the atom. Accordingly, without the interven- 
tion of the idea of rigidity, we can calculate and interpret 
this vibration as an electrical-mechanical analogue of the 
vibration of an ordinary magnet. The inertia of the atom 
