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



being, in fact, equal to the mechanical power used in the com- 

 pression. When the temperature is maintained constant, this 

 becomes 



nMQ'(^)=-Jlog-,.^, (26) 



which is ob^dously independent of the nature of the gas. 



Hence equal volumes of all substances in the state of perfect gas, 

 at the same pressure and at equal and constant temperatures, being 

 compressed by the same amount, disengage equal quantities of heat ; 

 a law already deduced from experiment by Dulong. 



(14.) The determination of the fraction N affords the means 

 of calculating the mechanical or absolute value of specific heat, 

 as defined by equation 1, Section I. The data for atmospheric 

 air being taken as follows, 



N = 0-4, C = 274°'6 Centigrade, 



1 . ... 



-^ ■=■ height of an imaginary column of air of uniform density, 



at the temperature OP Cent., whose pressure by weight on a given 

 base is equal to its pressure by elasticity, 



= 7990 metres, 



=26214 feet : 

 the real specific heat of atmospheric air, or the depth of fall 

 equivalent to one Centigrade degree of temperature in that gas, 

 is found to be 



fe= r. Lat =72-74 metres = 238-66 feet. . . (27) 



The ratio of its real specific heat to the apparent specific heat of 

 water at 0° Centigrade is therefore 



fe _ 238-66 _ 



K;;~1389^-°^'^^' .... (28) 

 Kw being the mechanical value of the apparent specific heat of 

 liquid water, as determined by Joule. 



The apparent specific heat of air under constant pressui-e, as 

 compared with that of liquid water, is 

 K 



Kw 



=0-1717x1-4=0-2404. . . (28A) 



The value of this last quantity, according to the experiment of 

 De la Roche and Berard, is 



0-2669, 

 the discrepancy being about one-ninth of the value according to 

 Joule's equivalent*. 



* According to the experiments of M. Regnault, — ^ for air =02379, 



differing by about one-hundredth part from the result of theory. 



