480 PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
so that equation (6) becomes 
= 2 * (! f-f+f- F )+ sv '< —* + 8T - 
substituting for P from (5), we have 
rlT 
SQ = % ~~ Sp + 8T X -p SV ? constant.. (9) 
Now, if p enters into the expression for the kinetic energy due to the motion of the 
molecules of the body, it must enter as a factor into all the terms expressing this 
energy, otherwise the phenomenon symbolised by p would be more affected by the 
motion of particular molecules than by that of others. Thus T x must be of the form 
when T 3 does not involve p. 
Thus 
f(p) t 3 
f = 3 
f (p) 
T l5 
and therefore, by (9), 
so that 
SQ = 
r f (p) 
/ (p) 
SQ _ ^ /(p) 
Ti 
/ (p) 
Ti Bp + STi + § V {p constant); 
^ , S» + S log T, + SY( - P constan T 
/(P) Z 8 i T x 
• ( 10 ) 
Since T x is assumed to be proportional to the absolute temperature, and since the 
first two terms on the right-hand side of the equation are perfect differentials, we 
see that, in order that SQ jd should be a perfect differential, 
STfjt, constant) 
must be one too. 
The state of the body is determined if w r e know the value of the p coordinates and 
the temperature, so that SY, when p is constant, may be written as 
dV 
dd 
where dV/d0 is very large when the temperature is near the melting or the boiling 
points of the substance. 
