DETERMINATION OF ATOMIC WEIGHTS 525 



i.e. one for which the laws of Boyle and Gay Lussac hold 

 exactly, are connected by the relationship 



pV= KT 



where K is a constant which, by Avogadro's theorem, has 

 the same value for all perfect gases. But no known gas is 

 perfect and if, at the temperature T and pressure p, the 

 molecular volume V of a gas be expressed by the equation 



P V = K'T (22) 



the value of K' is not identical with K. By division, 



K'/K = V'/V 



The ratio V'/V, i.e. the ratio of the molecular volume of a gas to 

 the molecular volume of a perfect gas at the same temperature 

 and pressure, will be called $. Since, then, </> is equal to K'/K, 

 equation (22) may be written 



P V = KT<£ 



or, if M be the molecular weight of the gas and v its specific 

 volume, 



Mpv = KT0 (23) 



which is Leduc's method of writing the equation. It must 

 be noted that, in this equation, <f> is a variable quantity. 

 For the particular case of oxygen, we may write 



32 pv 02 = KT0 



o 3 



whence the molecular weight of a gas is seen to be given by the 



equation 



M (ftv 02 



32 = <£o 2 V 



This in turn may be written 



M = A.A (24) 



32 0o 2 do 2 



In this equation d and d 02 denote the densities of the gas and 

 oxygen at the temperature T and pressure p, whilst tf> and O2 

 refer to the same temperature and pressure. 



It remains to indicate the manner in which Leduc arrives at 

 the values of <f> and <j> . t . Referring back to equation (23) and 



