DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
331 
if e be the charge of electricity per unit volume, or if we write v x , v 2 . . . for the 
momenta corresponding to u lf u 2 . . . we see that the energy may be expressed as 
1 
(1 + /ce) 
KM 
(G6) 
Then if e be increased by Se this "part of the energy, which is measured by the 
temperature, will be diminished by 
f V , V J 1 *Se 
{%%) ' ' * i(l + «c ) 2 
( 67 ) 
or if Ke be small we may put 1/(1+ xe) 3 equal to 1, and write © where © is the 
temperature for 
so that (67) becomes 
{ U \ U \) { U 2 U 2\ 
S©= —@/<8e 
( 68 ) 
Thus if k be positive the temperature of the body will be diminished by communicating 
to it a positive charge of electricity, or electricity will behave like a substance with 
real specific heat. Since the electromotive force in an unequally heated conductor 
= —d(Kd)/dx, when k is positive the current goes from the hot to the cold parts of 
the wire, but when this is the case, what Sir William Thomson calls the “specific 
heat of electricity in the conductor,” is negative. In this case we see that the 
temperature of the body will fall or rise according as a charge of positive or negative 
electricity is communicated to it: when k is negative or the “ specific heat of electricity 
in the conductor ” positive, the temperature will rise when a positive and fall when a 
negative charge of electricity is communicated to the body. These effects have, as 
far as I know, never been observed. 
Another relation between heat and electricity is afforded by the phenomenon of 
pyroelectricity. This phenomenon is well illustrated by a crystal of tourmaline which 
when warmed becomes positively electrified at one end, which we shall call the 
positive end, and negatively electrified at the other, which we shall call the negative 
end. Sir William Thomson has shown that this phenomenon can be explained by 
supposing that there is an electric displacement in the tourmaline depending upon the 
temperature. Now if {uu] involves the coordinates which fix the electric displace¬ 
ment we can easily see that there must be such an effect. For take the case of a 
tourmaline crystal whose axis is taken as the axis of x, the positive direction of the 
axis being that drawn from the negative to the positive ends of the crystal; let p be 
the electric displacement parallel to this axis, and suppose that in the expression for 
the energy per unit volume there is the term 
