and the Isot hernials of Vapours. 449 



•secure the best value ; a likely value was " spotted," and 

 the resulting magnitudes of b and p worked out. It was 

 evident, in several cases, that slightly better agreement could 

 be obtained; but this was not worth the time it would have 

 taken, in view of the facts that the formula can be modified 

 and made somewhat less empirical (see the next section), 

 and that a systematic error exists which requires a re- 

 examination of the premises ; this has been done, and will 

 form the subject of a further paper. 



The new values of b determined as above have also been 

 applied to the recalculation of the isothermals of Table II. 

 Column 3 of this table shows the resulting pressures. Here 

 ;dso greatly improved agreement with experimental data is 

 found. At temperatures above the critical the agreement is 

 as good as at lower temperatures, whereas the former equation 

 broke down in these cases. 



§ 5. We have thus found that equation (1 a) for saturation 

 pressure, and equation (2 a) for the isothermal relation between 

 pressures and the corresponding volumes yield close agree- 

 ment with the results of experiment. In these equations, 

 however, is an adjustable constant, and 6, though it has a 

 physical interpretation, is not directly given by independent 

 data, whereas in the original equations (1) and (2) only 

 separately measurable quantities occurred, viz. temperatures 

 and densities. 



We may to some extent restore a physical meaning to C, 

 and thereby give it a determinate magnitude for eacli 

 substance. At the critical temperature equation (1 a) 

 becomes 



p T _ c 



-L^ 1 C T h -i 



)) ■=. P c u c 



^ b c 



1RT 



while equation (1) reduces top c = —j-°e~ 2 . 



Oc 



If, then, we identify these two values of p c , we have 



C = 2TA 2 , 

 and therefore 



RT _ 2 W RT __*£__ 

 P=-j-e lb ' = -r-e 2d e vm. . . . (lb) 



The equation of state similarly becomes 



4T,.A 2 T,. 



p(v-b) = liTe vbL =MV *°* bTv . . . (2 A) 



The values, calculated from (2 6), of the pressures along 

 thej various isothermals are given in column 4 of Table II. 



