332 
MR. J. J. THOMSON ON SOME APPLICATIONS OF 
.(69) 
where 4>(p) merely denotes some function of p and © denotes the temperature as 
before. By Lagrange’s equation we see that there will be an electromotive force 
parallel to the axis of x and equal to 
.(70) 
so that if K be the specific inductive capacity of the tourmaline the electric displace¬ 
ment will be 
.(7i) 
and this will depend upon the temperature, which is all that is required for Sir William 
Thomson’s explanation. Let us now consider the effect of the term </>(y>)© upon the 
temperature. We see, as in the last case, that the part of the energy on which the 
temperature depends may be expressed in the form 
{ttpq} {u 2 u 2 } 
+ ... 
1 + 
(72) 
where i\, v, 2 , . . . v a will remain constant, so that if p be increased by Sp the tempera¬ 
ture will be diminished by 
and we may write this as 
LW 
S©=—© 
{l + 0(p)p 
P(p) 
i + <Mp) 
■ ■ ■ ( 73 ) 
. . . (74) 
As the positive direction of x is that drawn from the negative to the positive ends 
of the crystal the electric displacement in this direction must be positive, hence we 
see from equation (71) that <f>(p) is positive; but if <£'( p ) be positive we see from 
equation (74) that when p is increased the temperature will fall. Thus if we take a 
tourmaline crystal and place it in an electric field so that the line joining the negative 
end of the crystal to the positive is in the direction of the electric force, the tem¬ 
perature of the tourmaline crystal will fall when the strength of the field is increased 
and rise when it is diminished. 
§ 8. We know that when there are inequalities both of strain and temperature in a 
circuit made of one kind of substance there will be an electromotive force acting round 
the circuit, but if the strain be uniform this E.M.F. will vanish however the tempera¬ 
ture may vary provided it remains continuous, while if the temperature be uniform 
the E.M.F. Avill vanish however the strain may vary from point to point. 
Let us suppose that the circuit consists of a wire of which ds is an element of arc, 
