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



And introducing the concentration, or the active mass 0, in- 

 stead of the pressure proportional to it, 



%(a lt i n \og O lt — a l i t log C,) = constant. 

 This is Guldberg's and Waage's law in a logarithmic form, 

 differing from the former statement only by the introduc- 

 tion of the value i. 



It remains to be shown that in this new form it agrees 

 better with experimental results ; and as a knowledge of the 

 correct value of i is necessary, we must deal with aqueous solu- 

 tions, for sufficient experimental data are to be had only with 

 such. 



XI. Determination of'\ for Aqueous Solutions. 



As Avogadro's law has been proved for solutions by four 

 separate lines of argument, there are four ways in which the 

 deviations, i. e. the values of i, may be determined. But that 

 one which depends on the lowering of the melting-point has 

 been so thoroughly proved experimentally that we shall con- 

 fino ourselves to its use. 



Reverting to the cycle which, on p. 95, was employed to 

 prove the applicability of Avogadro's law to solutions, the re- 

 lation was found : — 



100 W* 



= 2T 



where the second term refers to the work done in removing or 

 adding that amount of the solvent in which a kilogram- 

 molecule of the substance was dissolved ; that term must 

 therefore be multiplied by i : — 



In this manner a simple means of determining the value of i 

 is apparent. The value of i is from the above equation pro- 

 portional to t, i. e. to the molecular depression of temperature, 

 for the other data (T = absolute melting-point, W = heat of 

 fusion of solvent) are constant. Now 18*5 is the molecular 

 depression for cane-sugar, which from p. 91 is seen to follow 

 Avogadro's law accurately ; hence i = l ; and for other bodies 

 i is their respective depressions divided by 18*5. Almost 

 identical results are arrived at by using in the above equation, 

 instead of Tand W, the values for ice, viz. 273 and 79 ; they 

 will therefore be employed in the following calculations. 



XII. Proof of the Modified Law of Guldbcrg and Waage. 

 In employing the relation proposed for the purpose of 

 comparison with the results of Guldberg and Waage's formula, 



