220 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 
test the applicability to sufficiently dilute solutions, of such an 
expression, V1Z., 
P=P,, + hie) lon iy. newe ane eee eee (1) 
where P is the numerical value of any property (density, &), 
Pw that of the same property of water under the same physical 
conditions, n the molecular concentration of the solution, 2. e., 
the number of gramme-equivalents of the dissolved substance 
per unit volume of the solution, « the ionization-coefficient am 
and (1—e)n consequently the numbers of dissociated and undis- 
sociated gramme-equivalents per unit of volume respectively, 
and k and l constants, which may be spoken of as ionization- 
constants, which will vary with the solvent, the substance 
dissolved, the property to which they apply, the temperature, 
and the pressure, but not with the concentration of the solution. 
The formula can obviously apply only to properties for 
which P, has a finite value. ‘hus it is inapplicable to electrical 
resistance, for which Pw would have a practically infinite value. 
SIMPLE SOLUTIONS. 
In order to test the applicability of the above expression I 
have determined the ionization-constants for the density, thermal 
expansion, viscosity, surface-tension, and refractive index of 
solutions of Sodium and Potassium Chlorides, by the aid of 
observations made by Bender *, Briickner +, and Rother ~. 1 
selected these observations as a first instalment, not because of 
their precision (for in one or two cases more exact observations 
are available), but because these observers, in all cases but one, 
determined the values of the above properties for mixtures of 
solutions as well as for simple solutions. I selected the above 
chlorides partly because I thought it well to begin with salts of 
simple molecular structure, but largely also because, for the pur- 
pose of calculating the conductivity of mixtures of them (as 
described in my paper on this subject §), I had already obtained 
interpolation formule and curves which, judged by the results 
* Wied. Ann. vol. xxii. (1884) p, 184, and vol. xxxix. (1890) p. 89. 
+ Ibid. vol. xlii. (1891) p. 293. t Ibid. vol. xxi. (1884) p. 576. 
§ Trans. N.S. Inst. Sci. ix. (1896) p. 101; and Phil. Mag. [5] xli. (1896) p. 276. 
