or 



mid the Laws regarding the Natare of Heater jLQ^ 



(§)=^"- ■■i".i 



Let us now make a corresponding application to the process 

 of evaporation represented by fig. 4. The quantity of heat in 

 that case transmitted from A to B was 



rdm-^ i-jr -\-c—h\dmdt'y 



for which_, neglecting the differentials of the second order^ we 

 may set simply 



rdm. 



The quantity of work thereby produced was 



{s—iT)-~-dmdt, 

 and hence we obtain the equation ,. 



{s—o)~~' dm.dt 1 



rdm C 



or 



'•=c.(--)J (V.) 



These, although not in the same form, are the two analytical 

 expressions of the principle of Carnot as given by Clapeyron. In 

 the case of vapours, the latter adheres to equation (V.), and con- 

 tents himself with some immediate applications thereof. For 

 gases, on the contraiy, he makes equation (IV.) the basis of a 

 further development ; and in this development alone does the 

 partial divergence of his result from ours make its appearance. 



We will now bring both these equations into connexion with 

 the results furnished by the original maxim, commencing with 

 those which have reference to permanent gases. 



Confining ourselves to that deduction which has the maxim 

 alone for basis, that is to equation (II«.), the quantity U which 

 stands therein as an arbitrary function of v and / may be more 

 nearly determined by (IV.) j the equation thus becomes 



dQ=^B + n{^-Ayogv']dt+^'dv, {lie.) 



in which B remains as an arbitrary function of t alone. 



If, on the contrary, we regard the incidental assumption also 



