DETERMINATION OF ATOMIC WEIGHTS 513 



to the points H or J, as the case may be, instead of to the point 

 A (fig. 2). It is necessary, therefore, to consider the theoretical 

 views that have been applied in making the requisite extra- 

 polations. 



In the first place, it must be understood that the true form 

 of the initial portion AB of the curve (fig. 2) is unknown. 

 If Boyle's Law were a true statement within the limit, the curve 

 would of course be initially horizontal, i.e. the tangent to the 

 curve at A would be horizontal. On this assumption, it is 

 easy to account for the fact that the molecular weights obtained 

 for easily liquefiable gases by the limiting density method 

 are usually low ; the values of A„ would have been over- 

 estimated in the extrapolation. There are no experimental 

 data from which accurate estimates can be made of the slopes 

 of the compressibility curves at exceedingly low pressures ; 

 but the assumption that all compressibility curves become 

 horizontal when p = o requires that, under very small pressures, 

 considerable changes in compressibility must occur in the 

 case of the difficultly liquefiable gases. The validity of Boyle's 

 Law as a " limit-law " is, however, not generally accepted ; the 

 slope of the compressibility curve at the origin is usually 

 regarded as being qualitatively in agreement with the observed 

 slope at atmospheric pressure. This is in accordance with 

 van der Waals' equation and it may be remarked that most 

 of the deductions from this equation are qualitatively correct, 

 even though quantitative agreement may be lacking. 



In calculating the values of Ao for liquefiable gases, Berthelot 

 (6, 13) adopts van der Waals' equation as a basis. Choosing 

 the units so that pressures are expressed in atmospheres and 

 the limiting value of pv when p = o is unity at o° C, the 

 compressibility of a gas at o° C. may, according to this equation, 

 be deduced in the following manner : 



(p+p)(T-b)-l (6) 



Neglecting the small term ab/v 2 , substituting for pb its 

 approximate value b/v and writing e for (a — b), this equation 

 may be written 



pv - 1 - 5 (7) 



i.e. the product pv is a linear function of the reciprocal of the 

 volume. 



