492 
PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
where is a constant, p the density of the gas in the state A, 6 the absolute 
temperature, v 1 the mean potential energy of unit mass of the gas ; = plpO, r p being 
the pressure of the gas. 
Since pv = £ we may write this as 
f(A 1 0 + R 1 <Hog ^y-oi) .(26) 
The value of L for the gas in state B is similarly 
V (v + KA logf -%), .(27) 
where letters with the suffix 2 denote for gas in the state B quantities corresponding 
to those denoted by the same letters with the suffix 1 for gas in the state A. The 
value of L for the whole system equals the sum of (26) and (27). 
Let us suppose that a mass B£ of the gas in the state A gets decomposed; then, if 
Bp be the increase in the mass of the gas in the state B, we have Bp = B£. The change 
in the positional part of L for the system is 
- §£ ( A x e + Rj# log ^ - Rj0 - y x ) + Bp (A,e + n, 2 e 1 og ^ - K 2 e - y 3 ) ; 
but Bp = Bg, and when the system is in a steady state the variation of L vanishes, so 
that we have 
{A 1 -A 2 + (R,-R 2 ))^ + R 1 «log^-R^log^ V -(V 1 -V 3 )=0 . . (28) 
If two of the molecules of the gas in the state B make up one of those in the state 
A, that is, if the gas on dissociation splits up into two components, we have 
R 3 = sRp 
Making this substitution, equation (28) becomes 
Rilog^ + A 1 -A s + R 1 = ^^ , 1 .(29) 
where a is a constant. 
If the density of the mixture of normal and dissociated gas be B, and the density of 
the normal gas at the same density and pressure cl, then we have 
8 £ + 7 ] 
+ 2t? 5 
