from Air when it undergoes a given Condensation. 91 



and find that their indications agree for a long range of tem- 

 perature, we must infer that the supposed principle is true in 

 nature for the whole of the interval, and that equal quantities 

 of absolute heat have uniformly caused equal expansions on 

 both scales. 



In an air-thermometer, or, vvliich is the same thing, in a 

 mass of air under a constant pressure, the rise of temperature 

 is proportional to the increment of volume. Wherefore, since 

 both the absolute heat and the heat of temperature keep pace 

 with the increase of volume, it follows that their difference, 

 that is, the latent heat, must follow the same law of variation. 



And, because it is proved that equal increments of latent 

 heat correspond to equal rises of temperature and to equal 

 increments of volume, we may employ the dilatation of a mass 

 of air to measure the accumulation of latent heat, just as we 

 employ it to measure the increase of temperature. Let u' de- 

 note the volume of the fluid, at some fixt temperature, sup- 

 pose zero of the thermometrical scale ; and, the pressure be- 

 ing constant, put o for the volume when the temperature has 

 been raised to t, and the latent heat i has combined with the 

 air : then, a and /3 being two constants, it is evident that we 

 shall have, o = u' (1 + «t)\ , .^ 



„ = u'(l+i3i)/ ^"^^ 



When u' and u are the same in the two formulae, the two 

 factors 1 + a T and 1 + /3 ? are equal : consequently, 



/3e = aT, and^ = -^. 



The fraction — is therefore the proportion of the latent heat 

 to the rise of temperature for the same dilatation of the fluid ; 

 a proportion which, as has been shown, is constant so long 

 as the air-thermometer continues to be an exact measurer of 



heat. 



The first of the two formulae necessarily supposes that the 

 air has varied under a constant pressure; but the second 

 is true in whatever manner the volume has changed from 

 u' to V. 



Let f' and § denote the respective densities when the vo- 

 lumes are u' and o : then -^ — —, and hence we derive these 

 other expressions, viz. 



^" — • (B) 



? 



l + ar I 

 = -^ I 



N2 Of 



