the Air-Thermometer. 335 



consequence is, that all the subsequent part of that memoir con- 

 nected with the hypothesis is erroneous. 



Let t be the temperature of a mass of air, g its density, and 

 p the pressure. Then, from known principles, 



p = 6c(l+aO*-- (A). 



a being the expansion for 1°, and h another constant. 



When the quantity of heat in a body varies, it is evident that 

 the variations of temperature on the common scale must be, ca- 

 teris paribus, inversely as the specific heat. From the above 

 equation making p and § respectively to vary with t, whilst the 

 other is constant, we have 



dt=z .dp, and dt = — — .de. 



ap ^ a^ ^ 



Also when the quantity of heat changes in the mass of air, 

 let this change be denoted by q ; then the specific heat will be 



proportional to -^. Hence the specific heat of air under a con- 



stant volume will be to that under a constant pressure as 



^.p.^-.^.A.k, 



whence 



Now, supposing k constant, we have by integrating 

 ? = B (^log^ — log^) 4-C; 



and if, whilst gf = o, we reckon the pressure and density to be- 

 come each equal unit at the same instant, then C = o ; hence 



? = S (;^ log/? — log ?^ (B). 



To determine the proper form of this integral, M. Poisson 

 deemed it necessary to assume an additional hypothesis ; but in 

 that assumption both he and M. Laplace have deceived them- 

 selves. The value they give to q is 



\ a / ^ oae 



* It must be observed, that, though the indications of an air-thermometer 

 be here used, no stress is laid on the theori/ of that instrument. 



