VAPOE-DENSITIES. 377 



In the case of a mixture of C1 2 , PC1 3 and PC1 5 , equation (3) will 

 have three terms distinguished by different suffixes. To fix our ideas, 

 we may make these suffixes 2 , 3 and 5 , referring to C1 2 , PC1 3 and PC1 5 

 respectively. Since the constants a 2 , a s and a 5 are inversely propor- 

 tional to the densities of these gases, 



and we may substitute , , - - for dm*,, cZm 8 and dm s in equation (3), 



a z a s a s 

 which is thus reduced to the form 



log mL = _ A _ B logj + C (7) 



& m 2 m 3 t 



If we eliminate m 2 , m 3 , m 6 by means of the partial pressures Pvp$,p 6 , 

 we obtain 



when A', B', like A, B and C, are constants. If the chlorine and the 

 protochloride are in such proportions as arise from the decomposition 

 of the perchloride, p z =p 3 and 4> 2 > 3 = (p 2 +> 3 ) 2 . In this case, there- 

 fore, we have 



It will be seen that this equation is of the same form as equation (5), 

 when p 5 in (9) is regarded as corresponding to p 2 in (5), and p 2 +p B in 

 (9), which represents the pressure due to the products of decomposition, 

 is regarded as corresponding to p l in (5), which has the same signifi- 

 cation. It follows that equation (5), as well as (6), which is derived 

 from it, may be regarded as applying to the vapor of perchloride of 

 phosphorus, when the values of the constants are properly determined. 

 This result might have been anticipated, but the longer course which 

 we have taken has given us the more general equations, (7) and (8), 

 which will apply to cases in which there is an excess of chlorine or 

 of the protochloride. 



If the gas-mixture considered, in addition to the components 

 capable of chemical action, contains a neutral gas, the expressions for 

 the energy and entropy of the gas-mixture should properly each 

 contain a term relating to this neutral gas. This would make it 



C 7YL 



necessary to add c n m n to the coefficient of dt in (1), and n n to the 



c 



coefficient of dt in (2), the suffix n being used to mark the quantities 

 relating to the neutral gas. But these quantities would disappear 

 with the elimination of dt, and equation (3) and all the subsequent 

 equations would require no modification, if only p and D are estimated 

 (in accordance with usage) with exclusion of the pressure and weight 



