104 MR J. Y. BUCHANAN ON THE 



varies inversely as the square root of the number of observations, the mean probable 

 error of the mean specific gravity derived from any number of series s is as follows : — 



s = 1 



2 



3 



4 



5 



6 



7 



8 



9 



±)-„ = 7-39 



5-22 



4-27 



3-69 



3-30 



3-02 



2-79 



2-61 



2-46 



Further, the probable error of the mean of one series being zb7'39, and each series 

 consisting of nine individual observations, the probable error of a single observation 

 must be 3 x 7"39 = ±22-17 in the sixth place, or ±2*22 in the fifth place. 



§ 36. Following the tables of Class B we have those of Class C, which give a sum- 

 mary of the specific gravities of the solutions of diff"erent salts at difi'erent temperatures. 

 The salts included in each table have a common acid or a common base. Thus the 

 first table of the class contains only chlorides, the second only bromides, and so on. 

 These tables furnish the means of comparing the effect of concentration and of the 

 specific nature of the salt dissolved on the specific gravity of the solution. 



§ 37. The specific gravity, S, of one of our solutions expresses the weight in kilograms 

 of the quantity of the solution having the composition m.MR grams of salt plus 1000 

 grams of water, which exactly displaces 1 kilogram of distilled water having the 

 temperature T. When we compare the specific gravities of the difi'erent solutions, we 

 are considering equal volumes of those solutions ; but the proportion between the salt 

 and the water present in this volume of solution is different for different solutions. 

 Therefore the specific gravities of the solutions alone do not offer a simple theme for 

 discussion. 



The values of W, on the other hand, contain always the constant quantity of water 

 in which the different salts are dissolved in quantities proportional to their molecular 

 weights. It follows, therefore, that the values of (W— 1000) = w are always exactly 

 proportional to the molecular weights of the salts used. 



If the increments of specific gravity (S— 1) were also proportional to the molecular 

 weight of the salt dissolved, the quotient W/S = A would be constant for all the solutions 

 of the different salts having the same molecular concentration. This is not found to be 

 the case. The increments of specific gravity do not follow the periodic law exactly, 

 although in the nature of things they cannot depart very far from it. 



But we may consider the specific gravity of a solution from another point of view. 

 Let us consider a kilogram of water having the temperature T ; it fills a certain space 

 which we may call 1 litre (Lx). We propose to make the solution having the con- 

 centration 1/2 KCI4- 1000 grams of water by dissolving portions of the salt KCl in the 

 water, but removing so much pure water from the litre-flask as to keep the sum of the 

 volumes of water and salt always equal to the litre. When we have in this way 

 prepared our litre of (1/2 KCl -f- 1000 grams water), it weighs 1022"98 grams, and is 

 composed of 36*78 grams KCl and 986'20 grams of water. As we started with 1000 

 grams of water, we have had to remove 13*8 grams of it in order to make room for 

 the 36*78 grams KCl which have been dissolved. Consequently, in the construction of 



