SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 109 



as the displacement of the first solution bore to that of the original quantity of water ; 

 further, that when a third, equal, quantity of salt is added to the solution of the second 

 quantity, it intensifies its salinity uniformly and produces an increased displacement, 

 which bears the same relation to that of the second solution as the displacement of 

 the second solution bore to that of the first, and as that of the first bore to that of 

 the original water ; and so on. 



As we may consider the equal quantities of salt successively added to the constant 

 quantity of water to be as small as we please, our imagined process of solution becomes 

 more and more nearly continuous. 



If we represent by \ the displacement of the constant quantity of water, and by 

 r the ratio of its displacement to A^, that of the solution produced by the dissolution 



of the first of a series of n equal quantities of salt, then '^= ^ and is the common ratio 



of the displacement of each solution to that of the succeeding one in the series. 

 Then the displacement of the solution after the n*^ portion of salt has been dissolved 

 is expressed by the equation : 



This equation expresses the fact that, when the quantities of salt dissolved in a 

 constant quantity of water form an arithmetical series, the displacements of the 

 respective solutions so produced form a geometrical series ; consequently the logarithms 

 of these displacements form an arithmetical series. 



A convenient numerical criterion, therefore, by which to decide if the 

 aqueous solution of a particular salt follows this law, is furnished by the degree of 

 conformity of the observed displacements with those calculated on the basis of the 

 equation : 



1M^ = Const. 

 dn 



To take an example : — As before, let the constant quantity of water be 1 

 kilogram,^ which becomes saturated when 4 gram-molecules of the salt used are 

 dissolved in it. When the first gram-molecule has been dissolved in it, let the 

 displacement of the solution so produced be 1030 kilogram. As the displacement of 

 the water was TOGO kilogram, the effect of the first operation has been to increase 

 the total displacement in the proportion 1000 : 1 '030 = 1*030. When the second 

 gram-molecule of salt is dissolved, it, by hypothesis, increases the displacement of the 

 solution containing the first gram-molecule in the same proportion as the dissolution 

 of the first gram-molecule increased that of the water, that is, in the proportion 

 rOOO : 1*030 ; consequently the displacement of the solution containing the first two 

 gram-molecules of salt must be (1*030)1 Similarly, when the third gram-molecule 

 has been dissolved, the total displacement must be (1*030)^; and, when the fourth 

 gram-molecule has been dissolved and saturation has been produced, the displacement 

 must be (1*030)\ 



