DETERMINATION OF ATOMIC WEIGHTS 507 



Let the densities of the gases be L and L' respectively at the 

 same temperature and pressure T and p. Then the molecular 

 weights M and M' are proportional to 



(1 - pAP)L and (1 - pA'P)L' 



A simplification may be effected in these expressions if we recall 

 the fact that the densities are always measured at o° C. and 

 reduced to the values under normal pressure. By taking L 

 and L' to represent the weights of the normal litre (p. 505) and 

 measuring pressures in atmospheres, the previous expressions 

 are reduced to 



(1 - A:)L and (1 -A':)L' 



Hence, if the weights of the normal litre of gases are 

 L, L', L" . . . , their molecular weights M, M', M" ... are 

 related to these magnitudes by the equations 



M M' M" 



(i-a:) L -(i-a':)l' = (i-a":)l"- •• (3) 



in which A , A", A" . . . represent mean compressibility co- 

 efficients between zero and atmospheric pressures defined by 

 equation (2) on p. 505 and measured at o°C. 



Each of the fractions expressed in (3) above is equal to R, 

 the gramme-molecular volume of a perfect gas at normal tem- 

 perature and pressure. This is seen if it be assumed for the 

 moment that Ao is zero, in which case equation (3) gives 



M/L = R or M = LR 



for the supposed perfect gas of molecular weight M. Hence the 

 equalities (3) may be written 



M = RL(i - A;), M' = RL'(i - A^) (4) 



It follows, then, from the preceding calculations, that it is 

 possible, from measurements of the weights of the normal litre 

 of gases and observations of their compressibilities at o°C, to 

 deduce their molecular weights and also the gramme-molecular 

 volume of a perfect gas. 



Densities. — The densities actually required for the calculation 

 are densities referred to oxygen. Table I. gives these values at 

 N. T. P. and also the weights of the normal litre L (see p. 505) 

 and the critical data that will be required later on. 



A few remarks upon these figures are necessary. A number 



