Variation in the Pressure of Saturated Vapours. 43 



equation in (3), we have 

 dp 



AD dt - r Q~( c ~ Cl H T ~" T °) . (4/) 



If, as before, c— c x be considered as constant, then this equation 

 can be integrated. By taking T and T x at the correspond- 

 ing p and p x as limits, we find, after an easy transposition, 



Here log is Brigg's logarithm, m the modulus ; 



log m= 1-3622157. 



J. Bertrand, by assuming that a vapour has the properties 

 of a perfect gas at any temperature, obtained the formula* 



8 

 l gp = *-.y-y\ogT, .... (6) 



in which a, /9, and 7 are arbitrary constants, whose arbi- 

 trariness this savant took advantage of in order to bring the 

 pressures calculated from this formula in closest agreement with 

 the results of observation, or, more truly speaking, with those 

 calculated by means of interpolation-formulse from observed 

 pressures. The expression previously found by A. Dupre for 

 vapour-pressures can be put into the same form. 



This investigator, instead of making my assumption as to 

 the constancy of c — Ci, took Regnault's empirical formula 



r=za—bt, 



and assumed it to be true for all vapours. Then, from equa- 

 tion (3), we have 



dp 

 A -r. dt a — bt 



whence it is easy to obtain a formula of the form (6). 



Equation (5) also does not essentially differ from (6). 

 Indeed it can be transformed thus : 



log^=logp + -^(logTo + wO+^jjfjr 



-(.AD ,mT » + Al)Jf-AD lo S T - 



* Thermodynamique, p. 92. 



