232 RELATION OF PHYSICAL PROPERTIES OF AQUEOUS SOLUTIONS 



Both Bender* and Briicknerf 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 abscissae, and 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. 

 Jn all cases the two curves for each series are found to run very 

 close together, so close that it is 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 Bruckner 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. It is not necessary to enter 

 into details ; but I may, by way of illustration, give the follow- 

 ing : 



* Wied. Ann. xxii. (1884) p. 184, and xxxix. (1830) p. 89. 

 t Ibid. xlii. (1891) p. 293. 





