100 Journal of the Mitchell Society. [June 



[14] fi = d J)/ -r. 



where T is the critical temperature and d is the critical den- 

 sity. We can now combine this value of fx with the value of 

 fx given in equation 13 and obtain, 



M ^/¥=^(^-.0,95SPV 



whence, 



run PYm 



[16] — = — = constant. 



P Vm 



We show the values of in Table 2 and it will be seen 



m 



that hexamethylene and carbon tetrachloride alone (the 



associated substances being- excepted) give a value more than 



three per cent, from the averag-e value 16293. 



.016014 Vm . ,. ,, .. , ^.. , , 



— * = is the theoretical critical density and equation 



16 is really the ratio of the theoretical, D c , to the actual crit- 

 ical density, d c , and can take the form, 



[17] -t^ = constant. 



The relation in this form has been fully discussed by Dr. 

 Young* 1 . It here appears as a necessary consequence of the 

 ideas that we have advanced thoug-h we did not foresee that 

 such would be the case, and hence are justified in considering- 

 the deduction of this relation as further evidence that those 

 fundamental ideas upon which this series of papers is based 

 are correct. 



It may seem unusual that we should have been able to 

 derive two different equations for n (equations 13 and 14) in 

 terms of the critical constants. This is due to the fact that 

 the critical temperature besides possessing- the property that 

 the molecular attraction just balances the kinetic energy of 

 the molecules — the relation upon which equation 14 is based 



Fkil. Mag., [5], 50, 291 (1900). 



