SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. Ill 



(column 2) by that of the distilled water which it displaces (column 4), are entered in 

 column 3 of the table under Sa- 



Let us now apply the second hypothesis, as specified in § 41. The fundamental 

 solution is that for which m = 1/2 and if = 80 grams, the displacement of which is taken 

 as 1-020 kilogram ; its logarithm is therefore 0-0086001. 



The log-displacement of the solution for which m = 1 is then 



log Aj = 2 X 0086001 = 0-0172002, 

 and the log-displacements entered in column 5 under A^ are obtained from the equation 



logA,„ = 0-0172002xm. 



The values of the displacements corresponding to these logarithms are given in 

 column 6 under A^. The quotient obtained by dividing the weight of the solution 

 (column 2) by the corresponding displacement (column 6) gives the specific gravity of 



the solution, -r- = S^, the values of which are given in column 7. 

 Al 



For the value of m= 1/2 the numbers in columns 3 and 7, and in columns 4 and 6, 

 are of course identical. For values of m greater than 1/2 the values of Aj^ are always 

 greater than those of A^, and for values of w less than 1/2 they are less ; but, as the 

 value of m increases the difference A^— A^ increases, so that when m = 10, A^— Aj^^ = 

 0-085947. When the value of m diminishes, the difference A^ — A^ diminishes also. 

 If we turn to the specific gravities, we see that, in the case where m= 1/32, S^ — &£ = 

 — 0-000012, so that, at this concentration, it is still possible to determine by observa- 

 tion whether the change of displacement with change of concentration has taken place 

 according to the terms of the first or the second hypothesis. For greater dilutions the 

 differences of specific gravity approach too nearly to the probable uncertainty of the 

 observations to make this possible. 



§ 43. If we study the tables in this memoir, we shall find that in the solutions of 

 the majority of the salts the values of dAjdni and vjm reach a minimum for values of m 

 in the vicinity of 1/32, and they increase whether the concentration of the solution is 

 increased or diminished. At concentrations corresponding to m>2 a number of the salts 

 give solutions which conform nearly to the arithmetic law of the first hypothesis. The 

 salts which furnish solutions which conform most closely to this law are those which 

 contain at least one of the elements Li, Cs, or I. In the ennead MR, after the caesium 

 salts and the iodides come some of the rubidium salts and the bromides ; the remainder 

 of the bromides and nearly all the chlorides conform more nearly to the geometric law 

 of the second hypothesis, and some of them may be said to conform exactly to it. 



§ 44. From the equation log A,„- 0-0172002 x m it follows that A„^ = (1-0404)"'. 

 Therefore, if the solutions of a salt follow strictly the law expressed by our second 

 hypothesis, the general expression for the displacement of a solution containing m.MR 

 in 1 kilogram of water, when the displacement for any particular value of m — for 

 instance, for m = 1 — is Aj, is A^ = A^"*. 



