8 Mr. Ivory on the Lwjos of the Condensation and Dilatation 



Again, at the 1st and 3rd epochs, the elasticities being the 

 same, the products of the densities by the factors for tempe- 

 rature will be equal : wherefox'e, 



J \-\-ar-^xi-\-a6 



and by substituting the value of 8g — §*§, 



o l--|-a7- + aj-|-a^ 



In this expression 8' i is the heat disengaged while the density 

 acquires the increment S' g. MM. Gay-Lussac and Welter 

 have made a series of experiments between the temperatures 

 — 20** and 40" of the centigrade thermometer, and between 

 the pressures O^'lil and l^'^G ; and they have found that the 

 quantity e has in every case very nearly the same value. The 

 equation is therefore generally true, at least within a great 

 range. As the small variations may be considered as diffe- 

 rentials, we obtain by integrating, 



g^= C X (1 + «T + ««■ + aS), 



and the determination of the constant is equivalent to making 

 the origmal temperature equal to t + 9, instead of t. Where- 

 fore, puttmg d = 0, we get 



e 1+aT + ai 



? = — r+^7~' 



the original density being unit, and the first temperature t. 



In the particular experiment of MM. Clement and Des- 

 ormes, the numerical quantities are as follows, 



h — F= O^'OOSei 

 /i" _ /;' = 0"-01021 

 e = 0-3492. 

 By another similar experiment of MM. Gay-Lussac and 

 Welter, the value of e comes out equal to 0*3 7244. In both 

 these determinations e is very nearly ^ ; and it is not impro- 

 bable, as I shall show below, that this is the true value. 

 Adopting it, for the present, as an approximation, we get 



? = V-T+r. — ) • (^^ 



In the experiments from which we have deduced the last 

 formula, the only cause of a variation of temperature is the 

 condensation and dilatation of the air. But in the manner 

 we have viewed the subject, it is proved that g is always the 

 same function of the heat of combination, whatever be the 

 sources of temperature. It follows, therefore, that the form 

 of the function <$) is determined generally by the formula (B). 

 Hence we obtain the following expressions for the tempera- 

 ture, 



