SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 35 



§ 15. Correction for Departure of the Mean Reading from 50 mm. — If the mean 

 reading, R, be exactly 50 mm., then the weight which must be added to the 

 hydrometer to immerse it to the 50-mm. mark is the mean added weight, w. 



If, however, the mean reading, R, be less or greater than 50, the mean added 

 weight must be increased or diminished by the weight, dw^, which would increase or 

 diminish the immersion by the difference df between the observed mean reading, R, and 

 50. The calculation of this correction, dw^, is best explained by taking the series of 

 observations, XVII. 73, Table A^, as an example. In this case the mean reading, R, is 

 5072, and (if = 50 - 5072 = -072 (Knew). 



The immersion in the whole series of observations is increased by 89 '2 mm. 

 of the stem by an addition of O'SOO gram. Hence an increase of 1 mm. in the 



stem immersion is caused by the addition of - = 0*00897 gram, and a difference of 



^ 89-2 * 



072 mm. in the immersion must be produced by the weight 0"00897 x — 072 — — 0'0064 

 gram, which is the required correction, dw^ (line n). 



As the mean reading, R, is in this case greater than 50, the weight required to 

 immerse the hydrometer to 50 mm. must be less than the mean added weight, w, by 

 the amount of the correction, dw^, and is, therefore, 0'925 — 0'0064 = 0"9186 gram 

 (line o). If the mean reading, R, were less than 50 mm., the correction, dwr, would 

 be calculated in the same manner, but would require to be added to the mean added 

 weight. 



§ 16. Correction for Temperature. — The weight required to be added to the hydro- 

 meter to cause it to float at the 50-mm. mark in distilled water of the mean observed 

 temperature of 15'01° C, as found above, is 0*9186 gram. A correction {dwt, line q) 

 must now be applied to reduce the displacement observed at the mean temperature, 

 T, to the standard temperature, T, which is in this case 15*00° C. Before this can 

 be done we must determine the value of dw^ for 0*01° C. at 15*00° C. This is 

 found as follows. A series of observations is made with the hydrometer in distilled 

 water at various temperatures, the results of which are expressed in a curve, having 

 displacements as abscissae and temperatures as ordinates. Suppose we wish to 

 find the temperature correction at, say, 23*00° C, we proceed as follows. Draw 

 horizontal lines through T = 23"5° and T = 22*5° C, cutting the curve at a and h 

 respectively. From a drop a perpendicular on ch, meeting it at c. Then the length 

 ac represents 1° C, while ch is the difference in the total displacement for this 1° 

 difference in the temperature. Knowing the value of the abscissa OX in grams per 

 unit length, say grams per millimetre, we measure accurately the length ch and 

 multiply it by this constant. This gives us the value of dwt for 1° difference of 

 temperature at 23° C. The value of dwt per 0*01° C. is simply the former figure 

 divided by 100. This process is repeated at each of the temperatures at which 

 observations are being made. 



The value of dwt in grams per 0*01° C. at 15*00° C. has been taken as 0*00026. 



