170 



MR J. Y. BUCHANAN ON THE 



illustrated by quoting the results of five series of observations, each series consisting 

 of eleven independent observations made in a solution of calcium chloride containing 

 6*3 gram-molecules of OaCl2 in 1000 grams of water. The table includes, by the 

 method of least squares, the estimation of the probable error ^' of a single observation, 

 and 7'o that of the arithmetical mean of each series. 



It will be seen from the example given in § 86 that we obtain a series of differences 

 between the consecutive readings corresponding to added weights of 0"1 gram, and, 

 to take the first case, 0"1 gram immerses 10"50 mm. of stem, an added weight of 0"0095 

 would be required to immerse 1 "0 mm. of stem. 



When a series of readings has been made in the experimental solution with the 

 hydrometer whose constants are known, the weight of solution displaced to a given scale 

 division, which is one of the actual readings, is known, and the total weight of the 

 hydrometer when floating at the same division in distilled water is obtained. With 

 these data the calculation of the specific gravity of the solution is made. 



An example will illustrate this method : — 



Taking the first reading in series No. 1, using hydrometer A : 



1st Heading — 



4'0 grams added weight immersed 13*9 mm. 



Corrected weight of hydrometer =188"53748 grams. 



Volume of enclosed air == 108*56 c.c. 



Weight of enclosed volume of air = 0*12880 ,, 



Added weight = 4*00000 „ 



192-66578 

 Correction for exposed stem (weight of 0*9 c.c. air) = — 0*00106 



Weight of solution displaced to 13*9 mm. 



= 192-66472 



Weight of distilled water displaced to 13*9 mm. 

 Corrected weight of hydrometer 

 Weight of enclosed volume of air 



Added weight to immerse 13*0 mm. 



•9 mm. 



Stem correction (weight of 0*9 c.c. air) 



= 136 

 = 



•11132 

 *13592 



136 

 = 

 = 



•24724 

 41042 

 •00837 



136 

 = -0 



66603 

 00110 



Weight of distilled water displaced to 1 3 9 mm. = 136*66493 



c, .n . 192*66472 



Specific gravity = ^gg.^^^gg = 1 "409760. 



