Mr. W. J. M. Rankine on the Mechanical Action of Heat. 115 



(12.) The ordinary mode of expressing the specific heats of 

 gases is to state their ratios to that of an equal volume of atmo- 

 spheric air at the same pressure and temperature. 



When — is a very small fraction, specific heats of unity of 



T 



volume of a perfect gas are given by the equations 

 nMKv = ^ I 



1/1 x\ (24) 



That is to say, the specific heat of unity of volume at constant 

 volume is inversely proportional to the fraction by which the 

 ratio of the two specific heats exceeds unity ; a conclusion already 

 deduced from experiment by Dulong. 



The following is a comparison of the ratios of the apparent 

 specific heats .under constant pressure, of unity of volume of 

 oxygen and hydrogen respectively, to that of atmospheric air, as 

 deduced from equation (24), with those determined experimen- 

 tally by De la Roche and Berard. 



Ratio -p^Ml^'lifi^- 

 mMKp (atmos. air) 



Gas. By theory. By experiment. 



Oxygen 0973 0-9765 



Hydrogen .... 0-973 0-9033 



This comparison exhibits a much more close agreement between 

 theoiy and experiment than has been hithei-to supposed to exist, 

 the errors in the constants employed having had the effect of 

 making the ratio 1 4- N seem greater for atmospheric air than 

 for oxygen and hydrogen, while in fact it is smaller. 



To treat the other substances on which both M. Dulong and 

 MM. De la Roche and Berard made experiments as perfect gases, 

 would lead to sensible errors. I have therefore confined my 

 calculations for the present to oxygen, hydrogen, and atmo- 

 spheric air*. 



(13.) The heat produced by compressing so much of a perfect 

 gas as wtmld occu])y unity of volume under the pressure unity, 

 at the temperature 0° Centigrade, from its actual volume 



nMV,= .pp into a volume which is less in a given ratio s (when 



K is neglected as compared with t), is expressed by the following 

 equation : — 



/iMQ' = - -|t /J*''^ • y = " "MV,y^ Prf.9, . (25) 



* For a comniirinon of the tlicory with the hitcr mid more aceiiratc ex{)e- 

 rimentH of M. Regnault, see the Philosophical Magazine for June 186.3. 



