$i 4 SCIENCE PROGRESS 



Hence, 



Ao = i - PiV./poVo = I - (i - e/v t ) = e/v, 

 = e/(i - e/v,) =e/(i - e) 



with a sufficient approach to accuracy ; i.e. 



K = -£- (8) 



i - e 



Berthelot also gives equations deduced from van der Waals' 

 equation for other coefficients, viz. : 



5_ T^ ; A '~i _ 2 - 5 e ; A2 = (i-2e)(i- 3 e) W 



and from these he arrives at the following relationships : 



A ' A s A 1 , , 



A| - A 's - A ' - Aa (io) 



I + A-s i + i'5A'S i +4AJ 



by the use of which it is possible to obtain the value of Ao from 

 the results of compressibility measurements made at moderate 

 pressures (o'5 — 2 atmos.). 



Before applying these formulae to the experimental data for 

 other gases, their application to the case of hydrogen chloride 

 may be considered. The value of A* s already quoted (p. 512) 

 leads to the following result : 



A^ x ios for HCl at o° C, from equation = 840 



Actual value = 743 



In this case, therefore, the value of A Q is greatly over-esti- 

 mated by formula (10). It is also interesting to utilise Gray and 

 Burt's results to test equation (7). For this purpose, the writer has 

 calculated the values of i/v and plotted them against pv values. 

 The points do not lie on a straight line ; the graph has a 

 curvature similar to that of the compressibility curve but not 

 so pronounced. The high value of A afforded by equation (10) 

 is therefore explained. The results are interesting also from 

 another point of view ; had the measurements extended only 

 down to 425 mm., it might very reasonably have been concluded 

 that equation (7) was accurate, when a linear extrapolation 

 would have given A = 863 x io -5 (about), in agreement with 

 that deduced from equation (10) and much too high. This 

 brings out very clearly the danger attaching to extrapolation 

 over any considerable range of pressure ; in fact, linear extra- 

 polation of the results obtained between 158 and 265 mm. led 



