TABLE 35.— EFFECT OF AIR ON WEIGHING 

 Reductions of weighings in air to vacuo 



69 



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 MS(l/d — 1/rfi) where 5 = the density (wt. of 1 cm 3 in 

 grams = 0.0012) of the air during the weighing, d the density of the body, di that of the 

 weights. 8 for various barometric values and humidities may be determined from Tables 

 631-632. The following table is computed for 5 = 0.0012. The corrected weights 

 M + *M/1000. 



TABLE 36.— REDUCTIONS OF DENSITIES IN AIR TO VACUO 



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

 rate weighing.) 



If j is the density of the substance as calculated from the uncorrected weights, S its true 

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

 to the uncorrected density, s, is 0.0012 (1 — s/L). 



Let W , = uncorrected weight of substance, IV i = uncorrected weight of the liquid dis- 

 placed by the substance, then by definition, s = LWJWi. Assuming D to be the 

 density of the balance of weights, W,{\ + 0.0012(1/5" — \/D)} and H^i{l+ 0.0012 

 (1/L — l/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 1 cm 3 of air is 0.0012 gram). 



Then the true density S = 



W,{\ +0.0012(1 AS*— !/£>)} 

 Wi{l+0.0012(l/L — 1/D)} 



But from above W,/W\ = s/L, and since L is always large compared with 0.0012, 

 S — j = 0.0012(1— s/L) 



The values of 0.0012(1 — s/L) for densities up to 20 and for liquids of density 1 (water), 

 0.852 (xylene), and 13.55 (mercury) follow: 



SMITHSONIAN PHYSICAL TABLES 



