OSMOTIC PRESSURE 23 



required to counterbalance this tendency toward endosmose 

 is always the same for the same concentration of the solu- 

 tion, and for different concentrations is found to be propor- 

 tionate to the number of molecules dissolved in the unit 

 volume. Whether this osmotic pressure be due to the motions 

 of the dissolved molecules or to the attraction of some other 

 sort which they exert upon the solvent, it is evident that 

 the effect must depend upon the number of molecules per 

 unit volume only when the molecules of the dissolved body 

 are free to act independently of each other, as do the mole- 

 cules of a gas. What the real kinetic energy of the molecules 

 in such a solution is, we do not decide by drawing this con- 

 clusion. Even if it be as great as in a gas, the great resist- 

 ance which a solvent opposes to diffusion shows that there 

 is a force which greatly diminishes the external effect of this 

 kinetic energy; it can never, therefore, have occurred to 

 van 't Hoff to claim that osmotic pressure is to be measured 

 externally in the same absolute unit as gaseous pressure. 

 But this opinion seems to have gained a foothold, so that 

 the kinetic treatment of the subject is combated by M. 

 Pupin, 1 on the ground that the kinetic energy of the mole- 

 cules in a solution ought to burst the containing vessel when 

 it was concentrated to what would correspond, in the gaseous 

 state, to a volume under the pressure of many atmospheres. 

 For this reason he demands that osmotic pressure should be 

 treated as a static phenomenon. To the writer, Dr. Pupin 

 appears to confound molar and molecular kinetics. Because 

 the mass as a whole is in equilibrium and at rest, it does not 

 follow that the molecules must be; in fact very few physicists 

 would care to call any force static in the sense that it was 

 not occasioned by kinetic forces held in equilibrium for the 

 moment. 



1 Dissertation, Der osmotische Druck, etc., University of Berlin, 1889. 



