484 Mr. W. J. M. Rankine on the Mechanical Theory of Heat. 



shown by Laplace and Poisson that the following formula is true 

 for perfect gases : 



•V(-^)-x/(-5fe)- • • ") 



And I have shown further (Trans. Roy. Soc. Edinb. vol. xx. 

 p. 440), that the same formula is applicable, not only to perfect 

 gases, but to all fluids whatsoever. 



In making use of this formula to calculate theoretically the 

 velocity of sound in gases, it is generally sufficiently correct for 

 practice to make 



which represents the height of an imaginary column of uniform 

 density equal to that of the gas, whose weight or unity of base 

 is equal to the pressure of the gas. 



To determine the ratio of the specific heats 



Kp 



Ky' 



we have in the first place the mechanical equivalent of Kp, which 

 is found by multiplying the specific heat of unity of weight of 

 the gas under constant pressure as compared with liquid water, 

 by the mechanical equivalent of the specific heat of liquid water. 

 In the second place, the difference between the mechanical 

 equivalents of the specific heats at constant pressure and at con- 

 stant volume (being the heat which is converted into expansive 

 power while the gas is heated one degree under constant pres- 

 sure), is to be calculated a priori by the following formula, de- 

 duced from the mechanical theory of heat, 



(-)' 

 Kp-Kv=<^(T).-^; .... (2) 



in which t is the absolute temperature, measured from the abso- 

 lute zero of a perfect gas thermometer, 274°* 6 below zero on the 

 Centigrade scale. 



According to the views of M. Clausius and Professor Thomson, 

 ^(t) is an unknown function, to be determined by experiment ; 

 according to the supposition of M. Mayer, it is simply the abso- 

 lute temperature itself; according to the hypothesis adopted in 

 my own researches, and which I shall here continue to follow, it 

 is of the form 



4>{r)=T-K', (a) 



K being the absolute temperature on the perfect gas-thermometer 



