TRANSACTIONS OK SECTION B. 617 



and Avogadro in the case of gases are equally applicable to dissolved substances if 

 the osmotic pressure of the dissolved molecules be substituted for the pressure 

 of the gas. 



While van't Hoff was able to establish a thermodynamic relation between the 

 csraotic pressure of a dissolved substance aud the molecular lowering of vapour 

 pressure, the molecular lowering of the freezing-point of solutions furnishes a 

 rational basis for the empirical generalisations of Raoult, and of Babo and WLillner. 



In van"t Hoff's thermodynamical argument the solutions are assumed to be 

 very dilute, and Leuce experimental veritication is specially important for the case 

 of such solutions. 



I have found that in the case of aqueous solutions of sugar and urea the agree- 

 ment between the value calculated by van't Hoff by means of the equation 



t = ^J^^ (which must equal 1-89 if W = 79 kal., and is 1-87 if W = 80 kal.) and 



the observed value of the constant is excellent. Even in the case of alcohol the 

 values do not vary by more than \h per cent, from 1"87 — a difference which may 

 be accounted for by the difficulty of determining exactly the percentage of alcohol 

 in a solution from its density. That this is the case is shown by the fact that the 

 value 1 '84 or 1 85 is observed for all concentrations. It is also possible to calculate 

 van't Hoff's constant without determining the freezing-point of water in the 

 following way : Sugar, urea, and alcohol are not electrolytes, i.e., are in water only 

 very slightly dissociated. We can, therefore, determine the relation between con- 

 centration and depression of freezing-point, starting from a solution of any conA'enient 

 concentration, where an ice cap is not formed, instead of from pure water, and thus 

 eliminate the influence of any error in the determination of the freezing-point of 

 water. From these observations made with my thermometers divided to 0°'01 

 and 0°-001 I have been able to establish van't Hoff's constant by a second inde- 

 pendent method. Also, if the results obtained by Loomis with a thermometer read- 

 ing to 0°01 are similarly treated, the van't Hoff's constant becomes evident in the 

 case of sugar, less evident in the case of water and alcohol, though the variations 

 are so great that the probable error is greater than he suspected, and the concentra- 

 tion of the solution was probably wrongly determined. 



We proceed to the generalisation of Arrhenius. Yan't Hoff showed by four 

 different methods that a law analogous to that of Avogadro was valid for solution 

 of non-electrolytes like cane-sugar. It then became of importance to account for 

 exceptional cases in which the depression of the freezing-point was abnormal, and 

 in particular the cases of salts, acids, and bases in aqueous solutions. The explana- 

 tion was given when Arrhenius showed that by two independent, quite different 

 methods, the observation of the lowering of the freezing-point and of the electrical 

 conductivity of a solution, the same value could be obtained for the factor i, which 

 denotes the ratio of the pressure actually exerted by the substance to the pressure 

 which the substance would exert if it consisted entirely of undissociated molecules. 

 This law, which is of special importance owing to the light thrown by the 

 dissociation-theory on various physical and chemical problems, must, like those 

 of van't Hoff already mentioned, be more valid in very dilute solutions, and 

 should at first be verified for them. For sugar, urea, alcohol, which are bad con- 

 ductors of electricity, we have found normal depression and a constant 1'89 or 

 1-87. For KCl, SO^H.,, dichloracetic acid, trichloracetic acid, and nitrobenzoic 

 acid, which are good conductors and show at the same time abnormal depression, 

 I found that the degrees of the dissociation from the lowering of freezing-point and 

 from the electrical conductivity are nearly the same. 



It is obviously desirable "that Ostwald's dilution law, one of the laws of the 

 action of masses, and a most important foundation for the theory of dissociation, 

 should be verified by determinations of freezing-points, just as it has been verified 

 by determinations of electrical conductivity ; and for the reasons already stated the 

 experimental verification is most important in the case of the most dilute solutions. 

 The effect of experimental error in the calculation is here very considerable, and the 

 freezing point methods hitherto in use have not been sufficiently delicate to verify 

 the dilution law. The more accurate method already referred to has to a large 



