Mr. W. J. M. Rankine on the Mechanical Action of Heat. 113 



Thus are obtained the following approximate results, for per- 

 fect "-ases, and gases which may without material error be treated 

 as perfect. 

 General value of the total apparent specific heat : — 

 1/1 _^rdY\_ d\ 



1 



/I T^\ 



Apparent specific heat at constant volume : — 



being equal to the real specific heat. 



Apparent specific heat under constant pressure: — 



Ratio of those two specific heats : — 



(20) 



(21) 



This ratio is the quantity called by Poisson 7, in his researches 

 on the propagation of sound. 



(11.) It is unnecessary to do more than to refer to the 

 researches of Poisson, and to those of Laplace, for the proof that 

 the effect of the production of heat by the compression of air is 

 the same as if the elasticity varied in proportion to that power 

 of the density whose index is the ratio of the two specific heats ; 

 so that the actual velocity of sound is greater than that which it 

 would have if there were no such development of heat, in the 

 proportion of the square root of that ratio*. 



The following is the value of the velocity of sound in a gas, 

 as given by Poisson in the second volume of his Traite de 

 Mecanique, 



«= ■yff-'y 



(l+ET)^', 



(22) 



where a denotes the velocity of sound, g the velocity generated 

 by gravity in unity of time, E the coefficient of increase of elas- 

 ticity with temperature, at the freezing-point of water, T the 



this result is subject to some uncertainty. The details of the calculation 

 arc given in the sixth section of this jwper, published in the Transactions 

 of the Iloval Society of Edinburgh, vol. xx. part 4. 



* This th(!orcui is proved for all substances whatsoever in a i)aj)er on the 

 Centrifugal Theory of Elasticity, published in the Transactions of the Royal 

 Society of Edinburgh, vol. xx. part 3. 



