102 Prof. J. G-. MacGregor on the Relation of the Physical 



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

 temperature, and pressure, a, n, and as rates of change have 

 definite values the same for all properties. For moderately 

 dilute solutions, cWc^> (Wdi?*> an d "d»fdn are all small, 

 and ~dx/~dt and 'da/'dn afc least have the same sign. Also the 

 Fs and l'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 concentration in a somewhat similar manner, 

 but also that the variation with concentration of all the coeffi- 

 cients, 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 

 by Grotrian f, who found that, in general, with increasing 

 concentration both of these temperature-coefficients undergo 

 changes in the same sense. GrossmannJ claimed to have 

 proved these coefficients to be equal ; but afterwards withdrew 

 the claim as based on an error §. Kohlrausch and Hallwachs 

 also have noticed for very dilute solutions a close similarity 

 between the curves representing the density and the con- 

 ductivity respectively of the same salt as functions of the 

 concentration. 



The following tables show that this family likeness extends, 

 to a greater or less extent, to all the coefficients for at any 

 rate a considerable number of the properties of solutions. 

 The tables include some of Grotrian' s coefficients with others 

 calculated from the observations of Kohlrausch, Bender, 

 Bruckner, Rother, Rontgen and Schneider ||, Fink% and 

 Timberg**. The coefficients are in almost all cases mean 

 values, the ranges of temperature &c. to which they apply, 

 though the smallest for which data are available, being not in 



* I have not seen Rontgen's paper, on which the statement that ^afdp 

 is small is based. The Fortschritte der Physik reports Tainuiann as 

 quoting him to that effect. 



t Wied. Ann. viii. (1879) p. 552. 



X Ibid, xviii. (1883) p. ll9. 



§ See Kohlrausch, Wied. Ann. xxvi. (1885) p. 224. 



|| Wied. Ann. xxix. (1886) p. 194. 



H Ibid. xxvi. (1885) p. 505. 

 ** Ibid. xxx. (1887) p. 545. 



