TO THEIR STATE OF IONIZATION MACGREGOR. 239 



data were available, the absorption spectra were similarly 

 affected by elevation of temperature and increase of concen- 

 tration. 



THE OCCASIONAL CONSTANCY IN THE DIFFERENCE BETWEEN THE 

 MOLECULAR VALUES OF PROPERTIES OF SOLUTIONS HAVING 

 THE SAME MOLECULAR CONCENTRATION. 



The difference between the values per gramme-equivalent of 

 any property for two simple solutions, 1 and 2, of different 

 electrolytes but of the same concentration, will be 



(P l -PJ/n=k 1 -kg l + (^-A^) 1 - (I 2 ~k t )a 2 (11) 



Now a in all cases diminishes as n increases. Provided there- 

 fore, the values of the ( &)'s have the same sign, and the rates 

 of change of the as with concentration are inversely propor- 

 tional, or approximately so, to the (l k)'s of their respective 

 solutions, we shall have (Pj P 2 )/7i exactly or approximately 

 constant. If we regard (? l P 2 ) /n as approximately constant 

 when its absolute value changes with n only to a small extent, 

 then the more nearly the (l k's) and the a's are inversely 

 proportional to one another the more nearly constant will 

 (P l P 2 )/n be. If, however, we regard this quantity as con- 

 stant when its values for different values of n differ from one 

 another by only a small percentage, then the magnitude of the 

 (l k)'s becomes of importance, and we may have (P 1 P 2 )/r* 

 approximately constant, even though the (I &)'s may be far 

 from being inversely proportional to the a's. 



In the case of certain solutions of moderate strength, this 

 approximate constancy of (P 1 P 2 )/n has been observed by 

 Valson and Bender* for the density and the refractive index, 

 by Wagner -f- for viscosity constants, and by Jalm J for the 

 electro-magnetic rotation of the plane of polarization ; and a 

 very close approximation to constancy in the case of the specific 



* Wied. Ann., xxxix, (1890), p. 89. 



t Ztschr. f. phys. Chemie, v. (1890), p. 31. 



t Wied. Ann., xliii, (1891), p. 280. 



