Nature aifd their Mutual Dfyctidihce. 19 



of the temperature only, viz. 



f{6) - w 



a p° /i,k(l+U0) 



If we take the total differential of the right member of equa- 

 tion (37) in a case where w is constant, then it must be =0; 

 we consequently get 



but according to the formulas (20) and (38) 



r 



- : ----- 



Po 

 which, substituted above, gives 



Po -^o 



:ed above, gives 



— l v ; v 



whence follows 



dp add 



(40) 



7 



This differential equation for the elastic force of steam in pro- 

 portion to the temperature, when the steam is at maximum den- 

 sity, is exactly what Baron Wrede has earlier found ; but as this 

 formula has been criticised- in Dove's Repertorium der Physik, 

 vol. vii. p. 231, as not being exact, a direct proof of its correct- 

 ness, under the supposition of w being constant, will perhaps 

 not be unnecessary. 



It is known that Poisson, by means of formula (36), has proved 

 that when the quantity of heat contained in an aeriform body is 

 denoted by w, then w must be such a function of p and p that it 

 satisfies the differential equation 



dw dw n 



7, p, and p having the same signification as above. 



But we know that this equation is integrated by putting 



pdp—rypdp = and dw = 0; 



for if the integrals of these two equations are respectively de- 

 noted by 



M = a and w — b, 



when they are supposed to be resolved with regard to the arbi- 

 trary constants a and b } then we know that 



M = F(w), 



C2 



