tO^ M. 11. Clausius on the Mov^htg Force of Heat, 



By means of this equation let 5 be eliminated from (Va.) ; neg- 

 lecting the quantity o", which, when the temperature is not 

 very high, disappears iu comparison with s, we obtain 



^' 1 dp ^ r 



pTt" Ail(fl +7p* 



If the second assumption that r is constant be made here, we 

 obtain by integration 



^;?i" A.R(a + lOO)(a4-0' 

 where p^ denotes the tension of the vapour at 100°. Let 



/-100=T, « + 100=«, and -^^^^^ =^; 



we have then 



log^ = ^ (21.) 



^Pi a + T ^ 



This equation cannot of course be strictly correct, because the 

 two assumptions made during its development are not so. As 

 however the latter approximate at least in some measure to the 



tinith, the fonnula expresses in a rough manner, so to speak, 



the route of the quantity log — ; and from this it may be per- 



Pi 

 ceived how it is, when the constants « and jS are regarded as 



arbitrary, instead of representing the definite values which their 

 meaning assigns to them, that the above may be used as an em- 

 pirical formula for the calculation of the tension of vapours, 

 without however considering it, as some have done, to be cam- 

 ple tely true theoretically. 



Our next application of equation (Ya.) shall be to ascertain 

 how far the vapour of water, concerning which we possess the 

 most numerous data, diverges in its state of maximum density from 

 the law of M. and G. This divergence cannot be small, as car- 

 bonic acid and sulphurous acid gas, long before they reach their 

 points of condensation, exhibit considerable deviations. 



The equation (Vflf.) can be brought to the following foi-m : 



' p dt 



Were the law of M. and G. strictly true, the expression at the 

 left-hand side must be very nearly constant, as the said law 

 would according to (20.) immediately give 



