526 SCIENCE PROGRESS 



indicating by zero suffixes the values of the variables at 

 temperature T and at zero pressure, 



M Po v = KT</> (25) 



Hence, from (23) and (25), 



py _ <fr 



Po V o 0o 



Leduc assumes that (j> is sensibly equal to 1, i.e. at a common 

 temperature and under a common, indefinitely small pressure, 

 all gases have the same molecular volume. This is, of course, 

 the fundamental assumption of D. Berthelot's method. Hence, 



<p = pv/p o v 



Further, Leduc assumes that over the range of a few atmospheres 

 pressure, the compressibility of a gas may be represented by the 

 equation 



pv 

 E = 1 - — = mp + np 2 , 



ro o 



where m and n are small constants to be determined for each 

 gas. 1 Hence, 



(f> = 1 - mp - np 2 , 



Leduc measures p in cms. of mercury and p c in atmospheres 

 and denotes p/p c by e, so that 



cf> = 1 - mp c . e - np* . e 2 (27) 



The values of m and n are arrived at by an application of the 

 theorem of corresponding states. At the same "reduced" tem- 

 perature and u reduced" pressure, the molecular volumes of gases 

 are assumed to be equal. The " reduced " temperature and 

 "reduced" pressure of a substance are T/T c and p/p c respec- 

 tively, i.e. the temperature and pressure expressed as fractions 

 of the critical values. Accordingly, for the same value of the 

 " reduced " pressure (or e), different gases give the same values 

 for <f) when at the same " reduced " temperature. Hence, in 

 equation (27), the coefficients mp c and npc must be functions 

 of the " reduced " temperature only. Leduc calls the reciprocal 



1 If for <p and <£ 02 in equation (24) the values I — E and 1 — E 02 are inserted, it 

 will be immediately seen that the equation is identical with that derived from the 

 method of limiting densities. 



