VAPOR-DENSITIES. 401 



from the memoir cited, except that the correction of the barometric 

 pressures has been applied by the present writer in accordance with 

 the data furnished in that memoir. The two next columns contain 

 the values of P 2 and P 3 . These would naturally be calculated from 

 M 2 and M 3 by equations (15). But since the values of M 2 and M 8 

 have not been given explicitly, those of P 2 and P 8 have been calculated 

 from the recorded values of ?r and 8. Since the weight of the possible 



7*2 

 perchloride is ^^M 2 , we have 



7'2M 2 ta_7-2 



= 2-22v7r == TT 3> 

 Moreover, 



P-7T = P 3 -P 2 , 



since both members of the equation express the pressure due to the 

 excess of the protochloride. The values of P 2 and P 3 were obtained 

 by these equations. 



The eighth column of the table gives the values of p calculated 

 from the preceding values of t c , P 2 , and P 3 , by equation (16); and the 

 last column, the difference of the observed and calculated values of p. 

 The average difference is 18 mm , or a little more than two per cent., the 

 observed pressure being almost uniformly less than the calculated 

 value. This deficiency of pressure is doubtless to be accounted for 

 by a fact which MM. Troost and Hautefeuille have noticed in this 

 connection. The protochloride of phosphorus deviates quite appre- 

 ciably from the laws of Mariotte, Gay-Lussac, and Avogadro, the 

 product of the volume and pressure of a given quantity of vapor at 

 180 and the pressure of one atmosphere being 1*548 per cent, less 

 than at the same temperature and the pressure of one-half an atmo- 

 sphere.* Now we may assume as a general rule that when the 

 product of volume and pressure of a gas is slightly less than the 

 theoretical number (calculated by the laws of Mariotte, Gay-Lussac, 

 and Avogadro) the difference for any same temperature is nearly pro- 

 portional to the pressure.! It is therefore probable that between 

 160 and 180, at pressures of about one atmosphere, the product of 

 volume and pressure for protochloride of phosphorus is somewhat 

 more than three per cent, less than the theoretical number. The 

 experiments of Wurtz, as exhibited in Table IX, show that the 

 pressure, and therefore the product of volume and pressure (we may 

 evidently give the volume any constant value as unity), in a mixture 

 consisting principally of the protochloride is on the average a little 

 more than two per cent, less than is demanded by theory, the differ- 

 ences being greater when the proportion of the protochloride is 



* Troost and Hautefeuille, Comptes fiendus, vol. Ixxxiii (1876), p. 334. 

 t Andrews, " On the Gaseous State of Matter," Phil. Trans., vol. clxvi (1876), p. 447. 

 G.I. 20 



