October 2, 1896.] 



SCIENCE. 



463 



which is impervious to the passage of sugar 

 and of many other substances. With such 

 cells the osmotic pressure was measured 

 and was found, to be surprisingly great. 

 For a one and a-half per cent, solution 

 of saltpetre it is more than three atmos- 

 pheres. For sea water it would be about 

 twenty atmospheres. Pfeffer's experiments 

 were made with reference to their bearing 

 on the action of organic cells and on other 

 physiological questions, and it was eight 

 years later before their extraordinary the- 

 oretical importance was pointed out by 

 van't Hoif. 



A careful study of the experimental data 

 given by Pfeffer and others leads to the 

 following conclusions : 



First, the osmotic pressure is directlj' 

 proportional to the concentration of the 

 solution. 



Second, the osmotic pressure is directly 

 proportional to the absolute temperature. 

 In establishing this law the experiments of 

 Soret* are of especial interest. He sub- 

 jected a solution of copper sulphate, con- 

 tained in a vertical tube, to a temperature 

 of 80° near the top and of 20° at the bot- 

 tom. Under these circumstances the con- 

 centration increases below and diminishes 

 above. After equilibrium was established 

 it was found that the per cent, of copper 

 sulphate in the two parts of the solution 

 was inversely as the absolute temperature. 

 The analogy with what would take place 

 in a gas under the same conditions is 

 clear. 



Third, solutions which are isotonic at a 

 given temperature contain in unit volume 

 the same number of molecules of the dis- 

 solved substance. Another statement of 

 the same law, which gives it also a quan- 

 titative expression, is that the osmotic 

 pressure of a solution is the same as though 

 the dissolved substance existed as a gas 

 within the same space. The osmotic pres- 

 sure of a one per cent, solution of sugar 



may be calculated by the same formula* 

 which we should use to calculate the pres- 

 sure exerted by one gram of a gaseous 

 body having a molecular weight of 342 and 

 contained in a volume of 100.6 cubic centi- 

 meters. 



Every one recognizes, of course, that the 

 laws which have been given for osmotic 

 pressure are identical with the laws or 

 Boyle, of Charles and of Avogadro for gases. 

 Yan't Hoff pointed out this analogy very 

 clearly, but he did not give any clear ex- 

 planation of what he considered as the real 

 cause of the phenomena of osmose. He 

 spoke, from the purely empirical side, of 

 of the attraction which the solution exerts 

 for pure water. ^ Ostwald in his Lehrbuch*^ 

 is even more careful. He speaks of the cell 

 as conducting itself as though there is with- 

 in it a partial vacuum for water. These ex- 

 pressions are very similar to those of the 

 older text-books, which speak of the expan- 

 sion of gases as due to the repulsion of their 

 particles for each other, and appear to me 

 equally misleading and unsatisfactory. In 

 a later paper, ^ in reply to a criticism by 

 Lothar Meyer,^ van't Hoflf gives a clearer 

 explanation in terms of the kinetic theory. 



If we have a gas in a confined space and 

 introduce into it a small amount of some 

 volatile liquid the vapor of the liquid will 

 rise and fill the space very nearly as though 

 the gas were not present, and when equi- 

 librium is reached the pressure will equal 

 the original pressure of the gas plus the 

 vapor pressure of the liquid. The expla- 

 nation is that the pressure exerted on the 

 surface of the liquid by the gas is not that 

 of continuous matter, but is due to the 



* p^ 760XT. 



342X0.045X0.1006X273 

 In this formula, 

 T = Absolute temperature. 

 342 -= Molecular weight of cane sugar. 

 0.045 = One-half the weight of a liter of hydrogen. 

 0.1006 = Volume in liters of 100 grams of the solu- 

 tion. 



