170 On the Elastic Force, Density, and Temperature of Gases. 



has not been allowed to expand : let the temperature it will be 

 raised be (e -I- a>) degrees, and the elastic force will be also in- 

 creased. Then we have 



r= (/(€+*>) 



= C€, 



C € + < 



= 1+-. 



c e e 



Now if no caloric be lost, <o is the temperature which would 

 be lost by the air when allowed to expand until it had got its 

 original elastic force, and the value is got from the expression 



Again, e is found from the law of Dalton and Gay-Lussac, 

 since the pressure was supposed constant, in terms of the rare- 

 faction, as follows : — 



Let v Q be the volume of a gas at the freezing-point, 

 v ... ... 0° above freezing, 



^ ... ... (d + e)° 



then 



v = v o (l+x0) 



i/ = t; o (l+a(0 + e)) 



and 



vt __ 1 + aO -f ate _ -, , ae 



v ~~ v 



ae 



or _ S(l + «fl) 



l+*0 



a 



and 



</~ 1+ € - 1+ 8(l+«0) 



Putting the value of «= j^, and that of €^='2077, we have 



d~ ^2359.(1 + ad)' 



or the ratio of the two specific heats is unity very nearly for 

 small condensations and rarefactions. 



London, July 28, 1853. 



