244 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 
That no satisfactory conelusion ean be drawn from experi- 
ments of this kind, unless conducted at extreme dilution, may 
be shown roughly in the case of density by the aid of the 
results obtained above. For we may assume that the ionization- 
constants for density obtained above will not be very different 
from those which would be derived from observations made at 
greater dilution*. We know from Kohlrausch and Hallwachs’s 
observations that if ap and bp represent NaCl and 4Na,CO, 
respectively, (P_,—P,,) /n will have the value 0:0139 for solu- 
tions containing ‘005 grm.-equivalents per litre, and that for 
NaCl and HCl it will have the value of 0:0235. We may 
assume that for NaCl and KCl it will be about ‘02. From the 
values of / for these salts we find the first two terms of (12) to 
be ‘0,64. If we assume / to have half the mean value of J for 
NaCl and KCl, the third term will amount to —'0,98. The 
tirst three terms thus amount to about ‘0,54, or say 3 per cent. 
of the value of fa P/N. Thus, observations of the kind 
referred to, for density, could give no satisfactory result, even if 
conducted at this very great dilution, At a dilution of ‘001 
grm.-molecules per litre, the first three terms of (12), calculated 
in the same way, amount to ‘0,1, or about 05 per cent of 
(P.— P,,)/n. A proved independence of p at this dilution 
would be more satisfactory. 
Observations at such extreme dilutions, in the case of most 
properties of solutions, are probably impracticable. But they 
are fortunately unnecessary for the settling of the question 
under consideration. For if the values of the ionization- 
constants for any property have been obtained as above from 
observations over a range extending to great, though not neces- 
sarily extreme, dilution, the values so obtained may fairly be 
assumed to apply very approximately to much greater dilutions ; 
and from the values of Ll» +0, L+H, L+L, ete, thus 
obtained, it may readily be determined whether or not Lt 
is independent of the ions p, qg, ete. Unfortunately, Kohlrausch 
and Hallwachs’s observations on specific gravity are not suffi- 
ciently numerous for this purpose. 
* Mr. E. H. Archibald, one of my studenus. tells me that for magnesium sulphate 
Kohlrausch and Hallwachs’s data give & = *05063 and J = "066887. 
