SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 105 



the solution we have replaced water by KCl in the proportion of 2-665 grams KCl per 

 gram of water. 



We have carried out the calculation for the volume of a litre of initial water and 

 final solution. It is much simpler when we take the volume displaced by the weight 

 W of the solution, or A = W/S. 



For the solution 1/2 KCl +1000 grams water A =1014-001 Gt. We then take 

 1014'00l grams of water, and we add KCl, removing at the same time pure water so as 

 to preserve the constant displacement 1014-001 Gtt. We may imagine that equal small 

 portions of KCl added take possession of the amount of water required to form with it 

 a solution of the concentration (1/2 KCl +1000 grams water), and that the remainder 

 of the water is uncontaminated. We proceed on this principle with the fractional 

 dissolution of the salt and removal of water so as to keep the displacement constant. 

 When we have removed 14001 grams of water, we find that we have dissolved 

 37-3 grams or 1/2 KCl in the 1000 grams of water remaining. 



But the operation so described is one of substitution. Consequently it is legiti- 

 mate to regard solutions as products of substitution. In fact, the result of the 

 operation is that we have replaced 14-001 grams of water by 1/2 KCl, so that the 

 substitution has taken place at the rate of 28-002 grams or r555 gram-molecules 

 of water per gram-molecule of KCl. 



If we turn to Table No. 82, the first table in Class E, we find the first entry in the 

 fourth column is 28-00 as the value oi v/m, or the mean increment of displacement per 

 gram-molecule of KCl in the solution (1/2 KC1+ 1000 grams of water) at 19-5° C. 



The tables of Class D give a summary of the Increments of Displacement, v, 

 caused by the dissolution of m grm.-mol. of salt in 1000 grams of water at diff'erent 

 temperatures. Here 1; = A — 1000. The arrangement of the tables in this class 

 is similar to that of Class C. 



The tables in Class E enable us to see at a glance the comparative volumetric 

 efi"ect of dissolving different quantities of diff'erent salts in 1000 grams of water. 

 Each entry in these tables is derived from the corresponding entry, v, in the corre- 

 sponding table of Class D, by increasing it in the proportion w : 1, whence we obtain 

 the values v/m. 



§ 38. In the following table we have solutions of the eighteen salts of the 

 double ennead (MR, MRO3) for which m = l/16. It gives under w the weight of 

 1/16 gram-molecule of the salt dissolved in 1000 grams of water; under S, the specific 

 gravity of this solution at 19-5° C, referred to that of distilled water at the same 

 temperature as unity ; and under v, the increment of displacement caused by dissolv- 

 ing 1/1 G gram-molecule of the salt in 1000 grams of water, expressed in grams of 

 distilled water having the temperature 19-5° C. 



The solutions are arranged in three groups, each group containing six solutions of 

 salts having the same metallic base (K, Rb, or Cs). These six solutions fall into two 

 groups of three, or triads, the first three being the salts having the general formula MR, 



TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 14 



