394 VAPOR-DENSITIES. 



below half an atmosphere the experiments both of Naumann and of 

 Troost show a deficiency of density as compared with the formula. 

 For an indefinite diminution of pressure, there can be little doubt that 

 the real density, like the value given by the formula, approaches the 

 theoretical value 2'073. The greatest excess in numbers obtained by 

 experiment is '07 ; the greatest deficiency is "19, which occurs at 

 59'7 mm ; the next in order of magnitude is *11, which occurs more than 

 once. These discrepancies are certainly such as may be accounted 

 for by errors of observation. They do not appear to be greater than 

 we might expect on the hypothesis of the entire correctness of the 

 formula. On the other hand, the agreement is greater than we should 

 expect, if we reject the theory on which the formula was obtained. 

 It is about such as we might expect in a suitable formula of inter- 

 polation with three constants, which have been determined by the 

 values of the density for one atmosphere, for half an atmosphere, and 

 for infinitesimal pressures. But we must regard the actual formula, 

 in its application to this single temperature, as having only two 

 constants, of which one is determined so as to make the formula give 

 the theoretical value for infinitesimal pressures, and the other so as to 

 make it agree with the experiments of Cahours at the pressure of one 

 atmosphere. 



An entirely different method has been employed by Horstmaim* 

 to determine the vapor-density of this substance. A current of dried 

 air is forced through the liquid acid, which is heated to promote 

 evaporation, and the mixture of air and vapor is cooled to any olesired 

 temperature, with deposition of the excess of acid, by passing upward 

 through a spiral tube in a suitable bath. The acid is then separated 

 from the air, and the quantity of each determined. It is assumed that 

 the air is exactly saturated with vapor on leaving the coil, and that it 

 has the temperature of the bath. If we know the pressure of saturated 

 vapor for that temperature, and assume the validity of Dalton's law, 

 it is easy to calculate the density of the vapor. For the pressure 

 of the air is found by subtracting the pressure of the vapor from 

 the total pressure (the experiments were so conducted that this 

 was the same as the actual pressure of the atmosphere), and the 

 ratio of the weights of the acid and the air obtained by analysis, 

 divided by the ratio of their pressures, will give the ratio of their 

 densities. The pressures of saturated vapor employed by Horstmann 

 are those given by Landolt,t and differ greatly from the determina- 

 tions of Regnault, in some cases being nearly twice as great, a 

 difference noticed but not explained by Landolt, who however gives 



* Berichte der deutschen chemischen GeadlscTiaft, Jahrg. iii (1870), S. 78 ; and Jahrg. xi 

 (1878), 'S. 1287. 

 t Lieb. Ann., suppl. vi (1868), p. 157. 



