SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 47 

 distilled water, and let h' = that of the solution, then the two displacing weights are 



XT/ I JJ 



H + h and H' + h\ and the specific gravity is S^ = ^ — j- ■ The data given in the 



Smithsonian Tables, Nos. 124 and 126, enable us to arrive at the value of h for distilled 

 water. Table No. 124, and at those of h! for certain solutions of the salts included 

 in Table No. 126. In the following table the effect of introducing the weight of 

 the meniscus in the hydrometric determination of the specific gravity of some of the 

 solutions contained in Smithsonian Table No. 126 has been calculated. The tabular 

 specific gravity (col. h) furnished by the Smithsonian Tables is taken to represent the 

 hydrometric specific gravity arrived at without taking into account the influence of the 

 meniscus. From this, and using the surface-tension of distilled water, and that of the 

 solutions furnished by the Smithsonian Tables given in columns d and e, the hydro- 

 metric specific gravity of the same solution, having regard to the weight of the 

 meniscus, is calculated and entered in column I. The details of this calculation are as 

 follows. In column a we have the formula of the salt in solution, in column h the 

 specific gravity of the solution. In column c is the temperature, and in column e is the 

 surface-tension of the solution at that temperature. The surface-tension of distilled 

 water at the same temperature is given in column d. In columns d and e the values 

 of the surface-tension are expressed in dynes per centimetre. Accepting 1/981 gram as 

 the pressure which balances the force of 1 dyne, the weight, in milligrams, of liquid 

 lifted by 1 centimetre of glass is obtained by multiplying the entries in the fourth 

 column by TO 19. If the circumference of the stem of our hydrometer were exactly 

 1 centimetre, this would be the weight of the meniscus. 



The circumference of the stem of hydrometer No. 17, the one which has been most 

 frequently used, is 1*062 centimetre; therefore, to get the weight in milligrams of the 

 meniscus supported by it, we must multiply the entry in column d by 1*019x1 "062 

 = 1-0822. 



Consider the first line of the table. The salt dissolved is NaCl. Taking the 

 total weight of hydrometer No. 17 when floating at the 50th division in distilled water 

 to be 1817105 grams (col. h), and multiplying this number by r036 (col, 6), the 

 tabular specific gravity of the least concentrated solution of NaCl quoted in the table, 

 we obtain 188 "2521 (col. i) as the displacing weight of this hydrometer when floating 

 at the 50th division in NaCl solution of the specific gravity r0360. The surface- 

 tension of distilled water at 20° C. is given (col. d) as 72-8 dynes per centimetre. 

 Multiplying this by r0822, we obtain 78*8 milligrams (col. / ) as the weight of the 

 meniscus of distilled water. Similarly, multiplying 7 7 '6, the surface-tension of the NaCl 

 solution in dynes per centimetre, by r0822, we obtain 84'0 milligrams (col. g) as the 

 weight of the meniscus of this solution supported by the stem of hydrometer No. 17. 

 We have, then, after taking account of the influence of meniscus, for the displacing weight 

 of the hydrometer when floating in distilled water, 1817105 -f- 0-0788 = 181-7893 grams 

 (col. j), and for that of the hydrometer when floating at the same division in NaCl solu- 



