hy Dy)ia])iical Action in the Compression of Gas. 15 



two sets of variables, both of which correspond to a position 

 of equilibrium, the second of which positions may be any 

 whatever. But in the case of our experiment, the second 

 position of equilibrium is absolutely determinate. The only 

 magnitude arbitrarily assumed was the disturbing force/; and 

 that alone has determined the particular values of both 8v and 

 St, for which the disturbance / first becomes equilibrated and 

 replaced by Sp. There must be, therefore, a second equation 

 belonging to these three values exclusively, and by combining 

 which with the former any two of the quantities may be 

 determined from the knowledge of the third. This equation, 

 obtained from the experiment itself, was found tohe dv = v. jS. dt, 

 where /S is a constant quantity. From the two equations 

 vdp — pdv=2n'oidt and p)dv=^pv . (3 .dt, we obtain a third, 

 vdp =pv . (a + ^)dt, which gives the increment of temperature 

 corresponding to a given increment of energy. 



As an example, let 1 lb. of air at temperature 32° sustain a 

 pressure of 2116 lbs. to the square foot, and occupy a volume 

 = 12'393 cubic feet, and let an additional weight of/ lbs. to 

 the square foot be suddenly put upon it, whereby it is com- 

 pressed into a volume v^ and its temperature is raised to 33°. 

 The value ofpv will be in this case 26,224 cubic-foot pounds. 

 The values of a and /3 now generally received as most accurate, 

 are approximately u = '002, 0= '005, and oe.-\-^ = '007. Also, 

 since, when dt = 1°, dv = '005 v = '062,SLnd therefore t'^ = 12*33 1 , 

 substituting these values, the equation 



V .dp =(«-!- ^) pv . dt 



gives us w/jo = '007 X 26,224 = 183*6 cubic-footpounds; and 

 therefore /= '007^0 = 14*8 lbs. per square foot, and ^^ = 2130*8 

 lbs., and p^dv = 132'l cubic-footpounds. 



Therefore an additional weight of 14*8 lbs. to the square 

 foot, imposed upon the gas already in equilibrium under a 

 pressure of 2116 to the foot, will compress it through "062 

 cubic foot, and raise its temperature by 1° F. 



To explain this result from thermodynamical principles : — 

 To raise 1 lb. of air by 1° F. a quantity of heat ='2375 or 

 |g of unity must have been created. ' And in this case vdp or 

 183*6 is the amount of energy which has created it. There- 

 fore f f X 183*6 is the energy which would generate one unit of 

 heat in the gas. But f-^ x 183*6 = 773 cubic-foot pounds; — a 

 coincidence with the value obtained by Joule which is truly 

 marvellous, since all the data here made use of were known 

 long before the conception of the dynamical origin of this heat. 



The whole energy of the volume of air at 32° was in the 

 first instance pv = 26224:. But after the condensation and 



