of Air under Volume and under Pressure, 335 



cation with the atmosphere is opened, restoring the external 

 pressure, whereby the density within is increased frooa r to m. 

 The density of the air which has re-entered will thus be dimi- 

 nished from e to 77^5 and its mass will he m — r. 



Now, from what was formerly shewn of the air-thermometer, 

 the heat evolved by the compression of the rarified mass r, will 

 be to that absorbed by the dilatation of the re-entered mass 



m — r, as r log — to — {m — r) log — . Their difference or 



^^S \ \) \§ \ i^ay therefore represent the change of 

 temperature by the true scale, or the heat evolved by a mass of 



— J 



f - y. But the mixed mass is m^ and, therefore, the rise in its 



temperature on the same scale, is- log -j ("")"'("■) \ = 



Hence, i the rise of temperature in the mass w, reckoned on 

 the common scale, is equal to what any mass of air at the tem- 

 perature T would undergo by increasing its density from unit 



to — J - j"» = g. Wherefore, if the specific heat of air under 



a constant volume, be to that under a constant pressure, in the 

 constant ratio of 1 to 1 + ^, we have i =: i% — • 1 1= 



-^1 1 I, from the law of Boyle. Hence, p =— , 



and 



loff — 



° m 



logg 

 To find the value of r when the surplus heat, or 



log -j — ( jm I — - log -, is a maximum, -we have 



