by Dynamical Action In the Compression of Gas. 17 



which may be put under the form 



dj) = '007 .p,dt 



is independent of di\ It expresses that if the equilibrium 

 of the forces is disturbed by a force of seven thousandths 

 of the original pressure, the temperature of the gas will 

 vary 1° F. And this will be the case whatever dv is, i. e. 

 whether the gas is condensed or rarefied, much or little. 

 But the same disturbing force produces, simultaneously with 

 the heat, a certain amount of condensation. The equation 

 dv = 'OODvdt proves this. And if the gas was originally not 

 only in equilibrium, but also quiescent (that is, neither in a 

 condition of actual expansion nor of condensation), then the 

 effect of the disturbing force will be simply as stated above, 

 to condense the gas. But the gas may be in a condition of 

 thermostatic expansion (see above), as for instance the atmo- 

 sphere about us while the barometer is falling uniformly. 

 If this expansion enlarges the volume in a given time more 

 than the action of the disturbing force condenses it in the 

 same time, the same rise of temperature will take place as 

 before, but the gas will be rarefied. In this case, however, the 

 expansion, as the fall in the barometer, will not be uniform, 

 but retarded. So likewise, a gas is cooled during a retarded 

 condensation. 



We have shown that by the dynamic employment of the 

 energy (ot-\-/3)pv, the temperature is raised 1°F., and the air 

 is condensed by the quantity ^v. Conversely, if the expan- 

 sive force is suddenly increased beyond the compression in 

 the same proportion, the air will expand itself hjBv, and one 

 degreee of temperature will be lost and vis viva equal to the 

 energy (u-^-jS) pv will be gained, either by the rising piston 

 of the engine, or the cannon-ball in the cannon. If this is 



repeated - ( = 491) times, the air will be deprived of all its 



heat, it will be expanded by — of its volume, and the cannon 



ball will have acquired vis visa = pv. In the case of 



1 lb. of atmospheric air at 32° and barometrical pressure 

 30 in., this is about 92,000 foot-pounds. This is the total 

 energy of the air, being all the dynamical work that can be 

 got out of it. 



All these consequences of the dynamic theory of heat, are 

 now propounded, as far as I know, for the first time. No 

 account of any one of these cases is given in any existing 

 work on this subject, nor any help to get an answer to such 



Phil. Mag. S. 5. Vol. 4. No. 22. July 1877. C 



