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 1 play a 
part. 
The ratio of P to P,, will be 
= eae: ee, 
w Ww 
For dilute electrolytes throughout a certain range of concentra- 
tion, and through a wider range in the case of non-electrolytes, 
« varies but slightly with ». Throughout such range the 
coefficient of m in the above expression will thus vary but 
slightly. Hence, m being small, 
k+(l-k)a 
i ae ) 17 
n 
ae =o =A’; 
approximately, where e is the base of Napier’s logarithms and 
A aconstant. Arrhenius,* Reyhert and Wagner} have found 
this result to hold in the ease of the viscosity of both classes of 
solutions. 
The difference between P and P,, will be 
P-P,,=(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 2. 
This form of the expression obviously includes such laws as 
Raoult’s for vapour tensions, and van ’t Hoft’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. 
