778 ANNUAL EEPORT SMITHSONIAN INSTITUTION^ 1913. 



was found the link which he needed. He considers first the process 

 of distillation of water vapor, which goes from pure water toward a 

 solution, owing to the lesser tensions of the latter; he then examines 

 the passage of water which goes through semipermeable membranes 

 from the pure solvent toward a solution, owing to osmotic pressure; 

 com2:)aring the two phenomena with each other, he recognizes their 

 parallelism. 



But that is not enough. He had applied to equilibrium in gases 

 one of his equations which is at bottom only the result of a com- 

 bination of Clapeyron's equation and the laAV of the gaseous state, 

 and wished to find out if this equation was equally applicable to solu- 

 tions. He observes now that by means of semipermeable walls, and 

 by substituting osmotic pressure for gaseous, it is possible for him to 

 reproduce for solutions the cycles and the reversible modifications 

 which have led him to deduce the equation for gases. 



There results the necessary consequence that the laws of gases must 

 also hold for osmotic pressure. He verifies the existing data and 

 finds that the laws of Boyle and Gay-Lussac are in fact confirmed by 

 the measurements of Pfeffer, and that consequently the principle of 

 Avagadro must be applicable. Isotonic solutions must be equi- 

 molecular. And since the law of the gaseous state is applicable to 

 solution, he calculates, according to the measurements of Pfeffer, the 

 value of the constant R^ and to his great surprise finds that the 

 numerical value of this is with great approximation equal to that 

 obtained for gases; the gaseous pressure and osmotic pressure exer- 

 cised by a given quantity of dilute substance under a definite volume 

 are equal. 



From this moment the understanding is complete; the analogy 

 between the gaseous state and that of dilute solutions is established. 

 Van't Hoff is not slow in making clear the relations which connect 

 the osmotic pressure with the diminution of tension of vapor, with 

 the elevation of the boiling point and the lowering of the freezing 

 point of solutions. Thus, he includes in the law set forth above the 

 empirical rules already worked out by Raoult. It is thus that the 

 direct measurement of osmotic pressure and indirect measurement, 

 such as tensimetric, ebullioscopic, and cryoscopic determinations, 

 which are much more exact and easier to carry out, lead to a deter- 

 mination of the molecular size of the substances dissolved. Our 

 knowledge of the molecular state of bodies, limited at first to sub- 

 stances obtainable in gaseous form, is thus found extended to all 

 soluble substances. What a revolution this extension produced in all 

 domains of chemistry and allied sciences is so well Imown that it 

 need not be dwelt upon. 



This theory was set forth for the first time in its entirety in three 

 memoirs presented simultaneously on October 14, 1885, to the Royal 



