242 Mr Larmor, On the theory of Osmotic Pressure. [Jan. 25, 



of available energy that occurs in the expansion of a gas. This 

 argument meets the objection that a true theory should involve a 

 knowledge of the molecular actions between the various molecules. 

 It would seem that with just the same cogency it might be argued 

 that a real investigation of the connexion of the alteration of the 

 freezing point of a liquid by pressure and its change of volume on 

 freezing should involve a knowledge of the individual molecular 

 actions in the liquid : and so it would, had we not the means of 

 evading considerations of molecular constitution that is afforded by 

 Lord Kelvin's great principle of dissipation, which is for this very 

 reason at the basis of all physical theory. 



There is however one point to be remembered, namely, that the 

 theoretical osmotic pressure is a limiting value which may not be 

 reached by an actual arrangement, unless we can be certain that it 

 works reversibly and so without heating effects. 



The remark has been made by Lord Kelvin, that the connexion 

 between Henry's law and the osmotic law must break down when 

 the solution of the gas is accompanied by change in its state of 

 molecular aggregation. It is also probable from the fundamental 

 ideas as to dissociation and aggregation, that such change would 

 usually be partial, and not uniform over all the dissolved molecules ; 

 so that it is not to be expected that Henry's law would in such 

 circumstances hold good. The point in which the argument, as 

 set forth in precise form by Lord Rayleigh*, becomes then inap- 

 plicable, is that the gas expelled from solution by the osmotic 

 process must be considered as emerging in the actual state of 

 aggregation differing from that of its free condition, and its return 

 to the latter state involves further change of available energy. 



If the considerations above stated, which will be most suitably 

 developed in detail in another connexion, are valid, it follows, that 

 Professor Poynting's*f* recent suggestion with a view to evading the 

 necessity of the ionic dissociation hypothesis cannot avail, as it 

 would not lead to the desired value for the osmotic pressure : that 

 pressure depends on the number of molecular complexes involving 

 the dissolved substance that exist on the dilute solution, but not 

 on their individual degrees of complexity. 



* Nature, loc. tit., p. 254. t Phil. Mag. Oct. 1896. 



