104 Prof. J. G. MacGregor on the Relation of the Physical 



all cases the same. As I wish to show only a general simi- 

 larity, it is not necessary to specify the ranges. The tempe- 

 ratures &c. of the lower limits of the ranges are also not in 

 general exactly the same. The data of the tables are thus not 

 exactly comparable ; but they are sufficiently so for my 

 purpose. The heading n stands for gramme-equivalents per 

 litre. 



A glance at these tables shows that, if regard be had to 

 sign, Grotrian's conclusion as to the temperature-coefficients 

 for conductivity and fluidity applies to all the coefficients for 

 all the properties tested. A given change of concentration 

 produces a change in the coefficients in the same sense. Too 

 much importance, however, must not be attached to this ; for 

 it is obvious that if we had tabulated, say, the coefficients for 

 conductivity, surface-tension, viscosity, and specific volume, 

 it would have been found that the changes produced in the 

 first two would have been in the opposite sense to those pro- 

 duced in the last two. But it is interesting to note that the 

 expectation suggested by the above formulae is distinctly 

 realized. 



At very great dilution of electrolytes the temperature- 

 coefficient becomes, approximately, 



i% =(t + »g)/< p --'». • ■ • « 



the pressure-coefficient having the same form. The concen- 

 tration-coefficient becomes 



!g = Z/(P» + nZ) (10) 



If we compare (9) and (10) with (7 J and (8), it becomes 

 obvious that the variation with concentration of the tempe- 

 rature and pressure-coefficients will probably be more closely 

 related at low than at high concentrations ; but that the 

 opposite will be true of the concentration-coefficients. Ac- 

 cordingly, having plotted Grotrian's coefficients and those of 

 the above tables as functions of the concentration, I find that 

 the temperature-coefficient curves are in general more closely 

 similar at low than at high concentrations ; but that this is 

 not the case for the concentration-coefficient curves. In the 

 case of the pressure-coefficients the data are insufficient. 



A corresponding similarity holds for the absorption-spectra 

 of solutions, though it cannot be expressed in coefficients. In 

 a former paper * I have shown that for all solutions for which 



* Trans. Roy. Soc. Can. ix. (1891), sec. 3, p. 27. 



