86 J. van't Hoff on the Function of Osmotic Pressure 



On integration this equation gives, on the assumption of 

 constant volume, 



— = constant; 



that is, the osmotic pressure is proportional to the absolute 

 temperature, provided concentration (which is here equiva- 

 lent to the volume of a gas) remain constant ; and this is 

 entirely in accordance with Gay-Lussac's law connecting the 

 pressure and temperature of gases. 



Experimental Proof (Determination of the osmotic pressure 

 at different temperatures). — Let us compare this theoretical 

 conclusion with the experimental data furnished by Pfeffer 

 (pp. 114-115). He found that the osmotic pressure increases 

 with rise of temperature ; it will be seen that, although his 

 results do not furnteh a conclusive proof of the correctness of 

 the theorem, yet there is a most striking correspondence 

 between experiment and theory. If we calculate from one of 

 two experiments at different temperatures the osmotic pres- 

 sure to be expected in the other, by help of Gay-Lussac's law, 

 and compare it with the experimental result, we have the 

 following series : — 



1 . Solution of cane-sugar. 



Pressure at 32°, found . . . 544 millim. 

 Pressure at 14°' 15, calculated . 512 „ 

 „ „ found . . 510 ,, 



2. Solution of cane-sugar. 



Pressure at 36°, found . . . 567 „ 



Pressure at 15 0, 5, calculated . 529 „ 



„ „ found . . 520'5 „ 



3. Solution of sodium tartrate. 



Pressure at 36°*6, found . . 1564 „ 



Pressure at 13°* 3, calculated . 1443 „ 



„ „ found . . 1431*6 „ 



4. Solution of sodium tartrate. 



Pressure at 37°*3, found . . 983 „ 



Pressure at 13°*3, calculated . 907 „ 



„ „ found . . 908 „ 



Comparison of the Osmotic Pressure by Physiological 

 Methods. — In the same manner that support has been lent to 

 the application of Boyle's law to solutions (viz. that different 

 substances in isotonic solutions retain their equality of 

 osmotic pressure so long as their respective concentrations are 

 reduced to the same fraction), so the application of Gay- 

 Lussac's law receives support by the fact that this isotonic 



