234 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 



solutions, and might be expected to be of use in showing their 

 relation to one another. I need not refer here to the more 

 obvious of such deductions, as, for example, the properties of 

 non-electrolytes, or of electrolytes at extreme dilution, but may 

 restrict myself to cases in which both constants k and I play a 

 part. 



The ratio of P to P will be 



r w 



For dilute electrolytes throughout a certain range of concentra- 

 tion, and through a wider range in the case of non-electrolytes, 

 a varies but slightly with n. Throughout such range the 

 coefficient of n in the above expression will thus vary but 

 slightly. Hence, n being small, 



-= =A". 



r w 



approximately, where e is the base of Napier's logarithms and 

 A a constant. Arrhenius,* Reyherf and WagnerJ have found 

 this result to hold in the case of the viscosity of both classes of 

 solutions. 



The difference between P and P^ will be 

 P-P w =(k+(l-k}a)n. 



and for the reason just given, will, throughout a certain range 

 of low concentration, wider in the case of non-electrolytes than 

 in that of electrolytes, be approximately proportional to n. 

 This form of the expression obviously includes such laws as 

 Raoult's for vapour tensions, and van 't Hoff's for the depression 

 of the freezing point in non-electrolytes, as well as the approxi- 

 mate proportionality of the rotation of the plane of polarisation 

 to concentration. It has recently been verified by Kohlrausch 

 and Hallwachs's observations on density, they having found 



* Ztschr. f. phys. Chemie, i, (1887) p. 285. 



t Ibid, ii, (1888), p. 753. 



t Ibid, v, (1890), p. 31. 



Wied. Ann., liii, (1894), p. 36. 



