TO THEIR STATE, OF IONIZATION MACGREGOR. 235 



that between concentrations of 0.005 and 1 gramme-equivalent 

 per litre, (P PJ/'W- 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 



<5P rffc (SI Sk\ 7 Sa 

 +-r,n+( TL--T. }an+(l-4e)-r.n 



1 dP^ 6t 6t ^ 6t 6t ' 6i (7) 



P 6t ~ P w + kn + (l-k)an 



The pressure-coefficient will have the same form, p being 

 written for t. The concentration-coefficient will be 



r ) 



6n J (g) 



w + kn + (lk)an 



In the case of a solution of a given salt of given concentration, 

 temperature, and pressure, a, n, and a's rates of change have 

 definite values the same for all properties. For moderately 

 dilute solutions, <ja/<tf, 6aJ6p*, and 6u/^n are all small, and da/ty 

 and da/An at least have the same sign. Also the fc's and I's for 

 the different properties all depend upon the mutual action 

 between molecules and solvent, and may thus be 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-coefficients, 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 has been observed in the case of the 

 temperature-coefficients for electrical conductivity and fluidity 



* I have not seen Rontgen's paper, on which the statement that 6a/fip is small is 

 based. The Fortschritte der Physik reports Tammann as quoting him to that effect. 



2 



