82 



TABLES 58-59. 



REDUCTIONS OF WEIGHINGS IN AIR TO VACUO. 



TABLE 58. 



When the weight M in grams of a body is determined in air, a correction is necessary for the 

 buoyancy of the air equal to M 5 (i/d i/dj) where 8 = the density (wt. of I ccm in grams 

 = 0.0012) of the air during the weighing, d the density of the body, d t that of the weights. 

 5 for various barometric values and humidities may be determined from Tables 153 to 155. The 

 following table is computed for 5 = 0.0012. The corrected weight = M + kM/iooo. 



TABLE 59. Reductions of Densities in Air to Vacno. 



(This correction may be accomplished through the use of the above table for each separate 

 weighing.) 



If s is the density of the substance as calculated from the uncorrected weights, S its true den- 

 sity, and L the true density of the liquid used, then the vacuum correction to be applied to the 

 uncorrected density, s, is 0.0012 (i s/L). 



Let Ws = uncorrected weight of substance, Wi = uncorrected weight of the liquid displaced 

 by the substance, then by definition, s = LW S /Wj. Assuming D to be the density of the 

 balance of weights, W s {i +0.0012 (r/S i/D)}and Wi {i +0.0012 (i/L i/D)}are the 

 true weights of the substance and liquid respectively (assuming that the weighings are made 

 under normal atmospheric corrections, so that the weight of i cc. of air is 0.0012 gram). 



W s {i + 0.0012 (i/S i 

 Then the true density 



But from above W s /Wi 



Wi {i + 0.0012 (i/L i/D) } 



s/L, and since L is always large compared with 0.0012, 

 S s = 0.0012 (i s/L). 

 The values of 0.0012 (i s/L) for densities up to 20 and for liquids of density i (water), 

 0.852 (xylene) and 13.55 (mercury) follow : 



(See reference below for discussion of density determinations). 



SMITHSONIAN TABLES. 



Johnston and Adams, J. Am. Chem. Soc. 34, p. 563, 1912. 



