THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
275 
just the same amount of work could still be gained by mixing given volumes of them 
in a reversible manner as if they were gases wholly unlike ; but the transpiration 
pressure would then be infinitesimally small and the time of transpiration infinitely 
great.^ It is thus impracticable to proceed to a limit, and no paradox is here involved 
such as the assertion that a finite amount of work could be gained by mixing two 
gases which are practically identical in properties. A similar apparently paradoxical 
limiting case might be formulated as reg’ards osmotic pressure of a dissolved substance 
very nearly identical with the solvent. 
60. The law of Henry that the density of dissolved gas is in a constant ratio s to 
its density as it exists free in the surrounding atmosphere, is involved in the osmotic 
law, and conversely may be employed to verify it. In circumstances of equilibrium 
the potential of free energy of the dissolved gas (in Gibbs’ sense) must be the same in 
the liquid and the atmosphere; that is, the removal of an elementary portion of the 
gas from the liquid to the atmosphere must not alter the free energy of the whole. 
Thus the difference of the free energies of the dissolved gas per unit mass, when its 
partial pressure in the liquid is changed from 2^1 to j)- 2 , is equal to the difference of the 
free energies of the gas per unit mass in the surrounding atmosphere Avhen its partial 
pressure is changed from pjs to 2 ^- 2 /^' The latter difference is by Lord Rayleigh’s 
principle, independent of what other gases may also be present in the atmosphere : it 
is thus Ipdv, where joi’ = R'd for the unit mass of gas, and is therefore at constant 
temperature R'd log 2^i!P2- This does not involve s, and therefore the difference of 
the free energies of the dissolved gas at two different densities is the same as if it 
existed in the free gaseous state at those densities : and this carries with it identity 
for the two states as regards all relations of available eneigy and work. Conversely, 
the law of Henry follows as aboA^e, by the principle of available energy, from the 
circumstance that the molecules of the dissoRed gas are outside each others’ spheres 
of molecular action, independently of any picture that we may form of the process of 
exchanges in evaporation and absorption. 
It is a confirmation of the soundness of this thermodynamic theory, that the law 
of osmotic pressure for dissolved gases is immediately involved in, and might have 
been predicted from, the equations given by von Helmholtz in 1883,t in a discussion 
of their energy relations in connexion Avith the theory of galvanic polarization. 
* The assumption is involved that the gases are really different and that means exist for separating 
them. [The fact that the amount of available energy at our command depends on the control we have 
learned to exercise over physical processes does not detract from the objective validity of that conception 
as a deduction from general principles of molecular theory, as has often been suggested (c/. §49 sztpra) : 
any more than our possible complete ignorance of some forms of total enei’gy would give to the idea of 
energy itself a subjective aspect.] 
t “Zur Thermodynamik Chemischer Vorgiinge,” III., ‘ Monats. Berl. Akad.,’ May, 1883, especially 
equations (4) and (o) ; ‘ Abhandlungen,’ III., pp. 101-114. The law had however been arrived at quite 
explicitly by Willaed Gibbs as early as 18/6 in his discussion of the general theory (p. 226). Recently 
the argument has been carefully formulated by Lord Rayleigh, ‘ Nature,’ Jan. 14, 1897: cf. also a 
2 N 2 
