Density, and Temperature of Gases. 169 



Td express the rarefaction in numbers, 



Let v be the volume of a gas when the pressure is p ; 



Let v 1 be the volume of a gas after an expansion and the 



pressure has become p' ; 

 Let also 8 be the rarefaction or negative condensation ; 



then 8= = - — f—, by Boyle's law, since the change of 



temperature is small. 



Now comparing the last of the observations with the second, 

 it appears that the difference of the temperatures varies as the cube 

 of the rarefaction ; or if we put co l for the difference when the rare- 

 faction is one, and co that for any other rarefaction 8, we have 



HO* 



.*. CO = (D l 8 3 , 



which is the fourth law discussed at the commencement of the 

 paper. 



To find co i we must employ the largest value of 8 in the best 

 trial, which was the second in the table, where 



o> = 2°, 



* 63-40 

 29-80' 

 and these give 



co l =0°'2077. 



Employing this as the constant in the formula a> = a> i S 3 , the 

 values of co in the last column of the table were calculated ; and 

 we see that they confirm the accuracy of the formula, on com- 

 paring them with the observations. 



We are now able easily to find the ratio of the specific heat of 

 air at a constant pressure to that for a constant volume. 



Using a notation and method like that of Poisson, Traite de 

 Mecanique, vol. ii. p. 644, let c = the capacity of air for heat at a 

 constant pressure = the quantity of caloric which will raise the 

 temperature of one grain of air, 1° Fahrenheit ; 



Let r be the quantity which will raise it e degrees ; then 



r=ce. 



Again, let c ! = the capacity of air for heat at a constant 

 volume or density 

 = the quantity of caloric which will raise one 

 grain of air 1° Fahrenheit, under this con- 

 dition ; 



then the quantity V will raise it more than e degrees, since it 



