214 SCIENCE PROGRESS. 



its value, calculated from />^ and 4, mostly about f. 

 Again, the critical volume should be 2 '667 times less than 

 the volume calculated according to Boyle's law, while it has 

 been found to be 37 or 3*8 times smaller. Apparently 

 even at the critical point Van der Waals' equation does not 

 hold. It seems as if the changes in density on the isother- 

 mal are much more sudden than according to Van der 

 Waals' formula, and as if the process of transition from 

 vapour to liquid is connected with a more intimate combina- 

 tion of the particles. Attempts have been made to improve 

 upon Van der Waals' formula by starting from more general 

 suppositions about the molecular actions, both at a distance 

 and during collision. Formulae with more than two constants 

 are obtained that way which can be made to agree with 

 facts over a larger area of the diagram. Those formulae 

 are mostly half empirical and are nothing more than Van 

 der Waals' formula with a few more judiciously introduced 

 constants. Professor Tait arrives at a formula containing 

 four constants, the physical meanino- of which is well de- 

 fined ; but even this formula does not yield satisfactory 

 results. The value of the critical constants is derived 

 from the formula in the way originated by Van der Waals ; 

 but in order to make the formula agree with Amagat's 

 results for carbonic acid it appears necessary to calculate 

 two systems of constants based on two different values for 

 the critical volume, one set for the observations at higher 

 and the other set for observations at lower density. Even 

 then the agreement is not perfect. Professor Tait justifies 

 this doubling of his constants by the fact that experiments 

 show the critical volume to lie between two limits. But it 

 was shown above what this apparent range of critical 

 volumes was due to. viz., the action of gravitation. At the 

 same time, even if the critical isothermal was very nearly 

 horizontal and straight in the critical point, how can v^, the 

 volume in the summit of the border-curve, by the way in 

 which it is derived from the formula possibly have two 

 values or a range of values? It seems, therefore, that even 

 Professor Tait's formula with its four constants is not 

 •capable of describing the behaviour of carbonic acid. And 



