394 Proceedings of the Royal Society of Edinburgh. [Sess. 
XXV. — Inversion Temperatures, and the Form of the Equation of 
State. By Prof. W. Peddie. 
(MS. received May 25, 1908. Read July 6, 1908.) 
1. Recent experiments by Olszewski on hydrogen (Phil. Mag., May 
1902), and on air and nitrogen (Phil. Mag., June 1907), have exhibited 
results which are not in accordance with theoretical deductions based upon 
Van der Waal’s equation of state (Dewar, Proc. Roy. Soc., March 1904 ; 
Porter, Phil. Mag., April 1906 ; Hamilton Dickson, Phil. Mag., January 
1908). An inversion temperature is not necessarily limited by the 
condition, which was satisfied in the porous-plug experiment of Joule and 
Kelvin, that the initial and final pressures should be nearly equal. In 
Olszewski’s experiments that condition was widely departed from. Taking 
account of large differences of pressure, Dickson shows that Van der Waal’s 
equation leads to the result that the inversion temperature must fall when 
the initial pressure increases, the final pressure being kept constant. 
Olszewski’s experimental results are opposed to this conclusion ; and 
Dickson suggests, as a possible cause of the discrepancy, an appreciable 
difference between the initial and final values of the kinetic energy. The 
following reasoning seems to indicate that such a difference would not 
alter the nature of the theoretical conclusion. 
2. Accented letters referring to the final state, the quantity 
Q = j pdv + pv - p'v - J + T' — T , . . . ( 1 ) 
V V 
where T is the kinetic energy of mass motion, represents the amount of 
heat given out in the passage of unit mass from the initial to the final 
state. Using Van der Waal’s equation 
(p+^y v - b )= m > ( 2 > 
and postulating 
T' -T = k(p -p) , (3) 
where k is a constant, the condition Q = 0 gives 
as an expression for the temperature of inversion. 
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