32 MOLECULAR WEIGHT AND POLYMERISM 



body possess as gas or vapour, in order that it may, on 

 absorption, follow Henry's law ? and the answer is that the 

 gas or vapour must, at equal temperature and concentration, 

 exercise a pressure equal to the osmotic pressure of the 

 same substance in the dissolved state. 



The proof of this may be given in a form due partly to 

 me l , partly to Lord Rayleigh 2 , and partly given in a private 

 correspondence with Dr. Donnan. 



Before entering on the proof, which deals with osmotic 

 pressure and semipermeable membranes, i. e. membranes 

 that only allow the solvent to pass, it may be remarked 

 that any notion one may form as to the mechanism 

 producing osmotic pressure, or the action of semipermeable 

 membranes, is without influence on the reasoning. Thus 

 the question whether the pressure is produced by the 

 solvent or by the dissolved body can 

 be left out of consideration ; so too, 

 whether it is dependent on collisions 

 or by attractive forces. The action 

 of the membrane too, whether it is as 

 a sieve, or by means of absorption, 

 is indifferent. All this is the case 

 because the proof to be given is based 

 Fig. 4. 1 on thermo-dynamics, and is conse- 



jquently free from assumptions on the 

 mechanism. Moreover it is plain that two semipermeable 

 membranes cannot give different osmotic pressures, for that 

 would allow of a perpetuum mobile; thus let the ring 

 (Fig. 4) be supposed filled with solution on the right, and 

 solvent on the left, separated by two semipermeable mem- 

 branes above and below, which give osmotic pressures 

 amounting to p { and p. 2 respectively. Such a difference of 

 pressure p l p 2 would then give rise to a flow, which, as 

 all the conditions remain unchanged, would never cease. 



After these remarks, let us proceed to the actual proof. 

 By means of a reversible cyclic process carried out at 



1 Zeitschr.f. Phys. Chcm. I. 488. 2 Nature, 55. 253. 



