232 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 
Both Bender* and Briickner} obtained their results from 
numerous series cf observations, in each of which a solution of 
given concentration of one salt was mixed in succession, in equal 
volumes, with a number of solutions of different concentrations 
of a second salt having one ion in common with the first. The 
values of the property under consideration were determined 
both for the simple solutions and for the mixtures, and the 
arithmetic means of the values for the constituents of the 
several mixtures were found. Curves were then plotted with 
molecular concentrations of the simple solutions of the second 
salt as abscissee, aud the observed values for the mixtures and 
the arithmetic means of the values for the constituents, respec- 
tively, as ordinates. The “corresponding” solutions were 
indicated by the points of intersection or contact of these curves. 
In all cases the two curves for each series are found to run very 
close together, so close that it 1s impossible to determine exactly 
at what points they touch or cross; and when the observational 
errors admitted by the authors are taken into account, they 
must be considered to be within touching or crossing distance 
at considerable distances on each side of the points at which 
Bender and Brickner assumed them to be contact or to inter- 
sect. I have plotted a number of these curves so as to indicate 
accurately all significant figures, and have found, on taking 
possible errors of observation into account, that in no case can a 
more definite conclusion be drawn than that “ corresponding ” 
solutions have pretty nearly the simple relations as to concen- 
tration claimed by the authors. I1t is not necessary to enter 
into details ; but I may, by way of illustration, give the follow- 
ng = 
* Wied. Ann. xxii. (1884) p. 184, and xxxix. (1890) p. 89. 
+ Ibid. xlii. (1891) p. 293. 
