SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 103 



logarithm of the corresponding highest value of A. With this, and the corresponding 

 values of c? log A, the log-displacement of each solution can be at once obtained. 



In Class A there are thirty-seven tables ; of these, twenty-four relate to solutions 

 of chlorides, bromides, iodides, and nitrates of the alkalies and alkaline earths, the 

 specific gravities of which have been determined with two hydrometers. The values 

 of S given for each value of m in each of these tables is the mean of two groups 

 of series of nine observations each, each group being made with a different hydro- 

 meter. The hydrometers chiefly used were Nos. 17 and 21, and for each value of m 

 either three or four series of observations were made with each of these hydrometers. 

 The mean of each series is the mean of nine independent values of the specific gravity, 

 so that the final mean, S, is the mean of 72 independent observations when four 

 series have been made with each hydrometer, and the mean of 54 independent 

 observations when three series have been made with each hydrometer. 



§ 35. In the tables of Class B, we have the particulars of the series of observations 

 made with hydrometers 21 and 17 respectively from which the final mean value of S 

 in the table is obtained. In the tables of this class m has the same signification 

 as in those of Class A ; S21 gives the mean specific gravity for the particular value 

 of m derived from .S21 series of observations made with hydrometer No. 21 ; S17 the 

 mean specific gravity similarly obtained from Sy, series made with hydrometer No. 17. 

 The final mean derived from s ( = s^i -t- s-^-j), the sum of these series, is found under S. 

 Under r^ we have the probable error of S calculated by the method of least squares, 

 and under d, the maximum departure of the mean of any individual series from the 

 mean specific gravity, S. Numbers under r^ and d are expressed in units of the sixth 

 decimal place. 



For each table of Class A referring to specific gravities derived from observations 

 with two hydrometers a corresponding table of Class B has been prepared. In the 

 twenty-four tables of Class B there are 189 entries under S, r^, and d respectively. 

 Summing those under s, we find that the experimental material on which these tables 

 are founded consists of 1227 series, whence the mean number of series of observations 

 per solution is 6 '49. Each series consists of nine individual observations, and when 

 each of them is compared with the corresponding observation made under the same 

 conditions in distilled water, they give a mean per solution of 58-4 independent 

 observations of the ratio of the weight of a given bulk of the saline solution to the 

 same bulk of distilled water, both liquids being at the same temperature. The 1227 

 series accounted for in the twenty-four tables correspond to 11,043 independent 

 observations of the hydrometric displacement, from each of which the specific gravity 

 of the solution in which the instrument floated is deducible. 



The sum of the values of r^ in the twenty-four tables is 5487, which divided by 

 189 gives dz2-90, in the sixth decimal place, as the mean probable error of the mean 

 specific gravity found for any one of' the solutions. We have seen that this depends 

 on a mean of 6-49 series per solution; therefore, admitting that the probable error 



