1897.] Mr Larmor, On the theory of Osmotic Pressure. 241 



polarization *, involve in fact an implicit prediction of the osmotic 

 law. This circumstance, that the law of osmotic pressure, as 

 regards dissolved gases, is tacitly involved in von Helmholtz's 

 equations, does not of course confer on him a position in the actual 

 development of the subject. 



But the theory of osmotic pressure can I think be placed on a 

 purely abstract basis independently of the law of solubility of gases, 

 which would then assume the form of a deduction from it. The 

 broad principles on which this is to be done have been in fact 

 laid down in a precise and very general manner, but without special 

 application, by Willard Gibbs as early as 1875, in his fundamental 

 development of the laws of mechanical availability of energy-f". 

 The following position is, I believe, sound. Each molecule of the 

 dissolved substance forms for itself a nidus in the solvent, that is, 

 it sensibly influences the molecules around it up to a certain 

 minute distance so as to form a loosely connected complex, in the 

 sense not of chemical union but of physical influence. The laws of 

 this mutual molecular influence are unknown, possibly unknowable ; 

 but provided the solution is so dilute that each such complex is, 

 for very much the greater part of the time, out of range of the 

 influence of the other complexes, as for instance are the separate 

 molecules of a free gas, then the principles of thermodynamics 

 necessitate the osmotic laws. It does not matter whether the 

 nucleus of the complex is a single molecule, or a group of molecules, 

 or the entity that is called an ion : the pressure phenomena are 

 determined merely by the number of complexes per unit volume. 

 To determine the osmotic forces, we must know the change in 

 available energy that is involved in dilution of the solution by 

 further transpiration of the pure solvent into it. In finding that 

 change, the laws of mutual action between molecules of the dissolved 

 substance are not required : for there is actually no action between 

 them, and as soon as the solution becomes so concentrated that 

 such mutual action between the complexes comes in, the theory is 

 no longer exact. Nor are the laws of mutual action between the 

 molecules of the dissolved substance and those of the solvent 

 required, because the effect of transpiration of more of the solvent 

 into the solution is not in any way to alter the individual com- 

 plexes. The change in available energy of the system, on dilution, 

 thus solely arises from the expansion of the complexes into a larger 

 volume ; and it can be traced into exact correlation with the change 



* H. von Helmholtz, " Zur Thermodynamik chemischer Vorgange in"; in 

 collected papers Vol. in. pp. 105—114, especially his equation (4), and the theory of 

 diffusion at the end. [The law had also been formulated explicitly in this manner 

 by Willard Gibbs as early as 1876, loc. cit. infra, p. 227.] 



t Trans. Connecticut Academy, Nov. 1875, p. 138, "Effect of a Diaphragm 

 (Equilibrium of Osmotic forces)." 



