S62 ^r. CLAPEYROX ox the motive power of heat. 



of the liquid corresponding to the temperature t of the body A, andy> 

 that which corresponds to the temperature t — dt of the body V>,hh 

 the increase of volume due to the vapour formed in contact with the 

 body A, A A that which is due to the vapour formed after the body A 

 has been removed, the formation of which has reduced the temperature 

 by the quantity dt; we have seen, I say, that the quantity of action de- 

 veloped by the transmission of the latent caloric furnished by the body 

 A, [and transmitted] from that body to the body B, is measured by the 

 quadrilateral figure cdef. Now this surface is equal, if we neglect the 

 infinitely small quantities of the second order, to the product of the vo- 

 lume cd by the differential of the pressure dh — ek. Naming p the 

 pressure of the vapour of the liquid corresponding to the temperature t, 



p will be a function of t, and we shall have dh — ek= t^ ^^• 



erf will be equal to the increase of volume produced in water when it 

 passes from the liquid into the gaseous state, under the pressure p, at a 

 corresponding temperature. If we call p the density of the liquid, c that 

 of the vapour, and v the volume of the vapour formed, I v will be its 



weight, and — will be the volume of the liquid evaporated. The in- 



P 

 crease of volume owing to the formation of a volume v of vapour will 



therefore be 



The effect produced will therefore be 



.^rf<. 

 dt 



The heat, by means of which this quantity of action has been pro- 

 duced, is the latent caloric of the volume v of vapour formed; let k be 

 a function of t representing the latent caloric contained in the unity 

 of volume of the vapour furnished by the liquid subjected to experiment, 

 at a temperature t, and under a corresponding pressure, the latent ca- 

 loric of the volume v will be k v, and the ratio of the effect produced 

 to the heat expended will be expressed by 



(-;)'; 



0-1) 



"^Pdt 



dt 



k 

 We have demonstrated that it is the greatest which can possibly be 

 obtained ; that it is independent of the nature of the liquid employed, 

 and the same as that obtained by the employment of the permanent gases: 



now we have seen that this is expressed by — , C being a function of t 

 independent of the nature of the gases; we shall therefore also have 



