16 M. R. Clausius on the Moving Force of Heat, 



and hence we obtain, as the analytical expression of the maxim, 

 apphcablc to vapours at their maximum density, the equation 



J+o-A=A(,-<.)f (III.) 



If, instead of the above maxim, the assumption that the quan- 

 tity of heat is constant be retained, then, according to (7.), in- 

 stead of equation (III.) we must set 



|+^-*=o- («•) 



And this equation, although not exactly in the same form, has 

 been virtually used heretofore to determine the value of the quan- 

 tity h. As long as the law of Watt is regarded as true, that the 

 sum of the latent and sensible heat of a quantity of steam at its 

 maximum density is the same for all temperatures, and conse- 

 quently that 



It +'=*'' 



it must be inferred that for this fluid k also is equal ; this, 

 indeed, has been often asserted, by saying that when a quantity 

 of vapour at its maximum density is compressed in a vessel im- 

 pervious to heat, or suffered to expand in the same, it will remain 

 at its maximum density. As, however, Regnault* has corrected 

 the law of Watt so that we can set with tolerable accuracy 



^+c=0'305, 



the equation (8.) gives for h also the value 0*305. It follows 

 from this, that a portion of the steam in the impermeable vessel 

 must be precipitated by compression, and that it cannot retain 

 its maximum density after it has been suffered to expand, as its 

 temperature does not decrease in a ratio corresponding to the 

 decrease of density. 



Quite otherwise is it if, instead of equation (8.), we make use 

 of equation (III.). The expression on the right-hand side is 

 from its nature always positive, and from this follows in the first 

 place that h is less than 0'305. It will be shown further on 

 that the value of the said expression is so great that h becomes 

 even negative. Hence we must conclude that the above quan- 

 tity of vapour will be partially precipitated, not by the compres- 

 sion, but by the expansion ; when compressed, its temperature 

 rises in a quicker ratio than that corresponding to the increase 

 of density, so that it does not continue at its maximum density. 



This result is indeed directly opposed to the notions generally 

 * M^, de VAcad.y vol. xxi. 9th and 10th Memoirs, 



