TO THEIR STATE OF IONIZATION 
MACGREGOR. 235 
that between concentrations of 0.005 and 1 gramme-equivalent 
per litre, (P—P,,)/n varies in the case of certain salts and 
acids only by from 5 to 20 per cent, and in the case of sugar 
only by 1.5 per cent. 
VARIATION OF TEMPERATURE AND OTHER COEFFICIENTS WITH 
CONCENTRATION. 
The temperature-coefficient of any property of a solution 
of given concentration will be 
oP Ok ol ok da 
WwW =, ps tia -  ) — 
16P ot * ot ne (Sy a apt ag (7) 
P ot ea ES a 
The pressure-coefficient will have the same form, p being 
written for t. The concentration-coeflicient will be 
Ja 
1 sp_ b+ (« ie i”) 
Pon P,,tkn+(l--k)an 
In the case of a solution of a given salt of given concentration, 
temperature, and pressure, «#, ”, and @’s rates of change have 
definite values the same for all properties. For moderately 
dilute solutions, da/st, da/sp*, and 6«/9n are all small, and da/%t 
and ga/sn at least have the same sign. Also the k’s and l’s for 
the different properties all depend upon the mutual action 
between molecules and solvent, and may thus he expected to 
have more or less closely related values. We may therefore 
expect not only that the coefficients of one kind for the various 
properties of solutions of a given salt will vary with concentra- 
tion in a somewhat similar manner, but also that the variation 
with concentration of all the coefficients, but especially the 
temperature and pressure-coefticients, will exhibit a certain 
family likeness. It is obviously not to be expected that the 
variation will be exactly similar in any case. 
This family likeness bas been observed in the case of the 
temperature-coefficients for electrical conductivity and fluidity 
*Thave not seen Réntgen’s paper, on which the statement that d«/dp is small is 
based. The Fortschritte der Physik reports Tammann as quoting him to that effect. 
2 
