5 o6 SCIENCE PROGRESS 



stood that pressures are expressed in atmospheres). Referring 

 to Fig. i (p. 509), it will be seen that 



A Pb i_ _ p v - pbVb 1 EB 



Pa PaVa Pb ~ Pa ~ p a V a EC 



Since the product pv is approximately constant, it therefore 

 follows that the coefficient Aj£ is (very nearly) proportional 

 to the slope of the chord BC of the curve ABCD joining the 

 joints B (p a , p a v a ) and C (p b , p b v b ). 



In accordance with this definition of APA we have 



PoV 



It has been assumed by Rayleigh and Berthelot (3) that, 

 under extremely small pressures, Avogadro's hypothesis loses 

 its approximate character ; in other words, it is supposed that 

 at a definite temperature and under a common, indefinitely 

 small pressure, the molecular volumes of all gases are equal, 

 an assumption which forms the basis of the method of limiting 

 densities. The calculation of exact molecular weights by this 

 process was given by D. Berthelot (3) in 1898 in the following 

 manner : 



Let the common molecular volume of two gases be v under 

 an indefinitely small pressure p and at the same temperature 

 T. When the pressure is increased to the finite value p, the 

 molecular volumes v and v' of the gases cease to be equal. 

 Applying equation 2 (p. 505), we have 



v = v Q - 



p 



[. - A'p> - P )] 



v .P° 



p 

 The ratio of the molecular volumes is given by 



v_ ' -AP > (p-Po) __ i-p.Ag 

 V ' i-A'P(p-po) i-p.A'P 



since p is indefinitely small. 



The molecular volumes of the gases at the temperature T 

 and under the pressure p are therefore proportional to 



1 - pA£ and 1 - pA'£ 



