108 MR J. Y. BUCHANAN ON THE 



For the purpose of discussing the changes of displacement produced in a constant 

 quantity of water by the dissolution of successive quantities of a salt in it, we compare 

 them with those which would take place under one of two hypotheses. 



§ 40. First Hypothesis. — It is assumed that, when a quantity of salt, insufficient for 

 saturation, is dissolved in a quantity of water, it takes possession of the quantity of 

 water which it requires in order to produce a saturated solution, and saturates it, after 

 which the saturated solution disseminates itself through the remaining water, forming 

 a simple mixture with it. 



To take a particular case : — Let the constant quantity of water be 1 kilogram, 

 and, when saturated with the particular salt used, let it take up 4 gram-molecules 

 of it. When 1 gram-molecule of the salt has been dissolved in it, let the displace- 

 ment of the solution so produced be r030 kilogram. We have then one-fourth of the 

 water saturated by the first gram-molecule of salt added, producing an increment of 

 displacement amounting to 30 grams. Let us now add a second gram-molecule of 

 salt. There are 750 grams of free water remaining, and of these the second gram- 

 molecule of salt takes possession of 250 grams, with which it forms a saturated 

 solution ; and this, with the 250 grams saturated water already present, disseminates 

 itself through the remaining 500 grams of free water, and forms a homogeneous mixture 

 of the two liquids. 



If the increment of displacement produced by the dissolution of the first gram- 

 molecule was 30 grams, that produced by the dissolution of the second must be the 

 same, because it has been produced by an exact repetition of the first operation ; and 

 the total displacement after addition of the second gram-molecule salt must be 

 1"060 kilogram. Similarly, when the third gram-molecule has been dissolved, the 

 total displacement will be 1'090 kilogram, and, when the fourth gram-molecule 

 has been added, and saturation has been reached, the displacement must be 

 ri20 kilogram. 



The numerical criterion, therefore, by which to decide if the aqueous solution 

 of a particular salt follows this law is that, for equal additions of salt dissolved in a 

 constant quantity of water, equal increments of displacement are produced. 



If, by A, we represent the displacement of the solution produced by dissolving 

 n parts of the salt in a constant quantity of water, then the above criterion finds 

 expression in the equation : 



— = Const. 

 dn 



^41. Second Hypothesis. — It is assumed that, when a quantity of salt, insufficient 

 to produce saturation, is dissolved in a quantity of water, it exercises no selection, 

 but salinifies every particle of the water alike, producing a homogeneous solution of 

 uniform concentration, and that, when a second quantity of salt, equal to the first, 

 is dissolved in this solution, it intensifies its salinity uniformly and produces an 

 increased displacement, which bears the same proportion to that of the first solution 



