Variation in the Pressure of Saturated Vapours. 47 



theoretical basis ; this explains its accordance with the results 

 of experiments. 



The same formula may be deduced upon other bases. 

 According to Southern and (Brighton's law, the inaccuracy 

 of which was, however, proved by Regnault's experiments, 

 the heat of vaporization does not depend upon the pressure on 

 the surface of a liquid remaining constant at all temperatures. 

 If this law were true, then instead of equation (4) we should 

 have the less accurate one 



r=r . 

 Then equation (4') would be converted into the following: — 



dt _ 



^0 



1 



P~ 



"AD 



' rp2' 



whence by integration we obtain equation (r). 



Thus Southern's inaccurate law and equation (r) proceed 

 from one and the same supposition, that c — c l is negligible 

 compared with r. This is sufficiently near the truth, and 

 may be regarded as the very first approximation. 



From the preceding we have the right to conclude that 

 Roche's formula, although roughly, still presents a law of 

 nature. All the other empirical formulae — Young's, Arago's, 

 Dulong's, Tredgold's, Cariolis', and others, and among them 

 Biot's — have no theoretical basis, and with the exception of 

 the latter do not satisfy the results of experiments. It is true 

 that Biot's formula gives vapour-pressures very nearly ap- 

 proaching those found by experiment ; but this is not due to 

 its representing in itself the nature of a vapour, but because 

 of the large number (five) of arbitrary coefficients, or, in 

 geometrical language, because the curve expressed by Biot's 

 formula has a large number (five) of points common to the 

 curve of the actual vapour-pressures in a state of saturation. 



3. Let us investigate the curve expressed by the equation (5), 

 taking as abscissae the absolute temperatures T ; and as ordi- 

 nates the pressures p. From this formula it is easy to obtain 



Po V 1 / 

 Here x=- >* y y = -—., and y-\-xT is a perfectly definite 



and constant quantity for every vapour. Let 



