2i6 SCIENCE PROGRESS. 



critical constants, so that say e^^ may be found from/^ and 

 4 ; also that v^ should be in a constant ratio to the volume 

 as calculated by the laws of Boyle and Charles. These 

 two relations were mentioned above, and we saw how 

 they are confirmed by experiment. Another consequence 

 of the law is that the vapour-pressure expressed in 

 terms of the critical presence will be the same for all 

 substances at temperatures which are the same fractions of 

 the critical temperature. Similar relations regarding the 

 densities of vapour and liquid, and even quantities like the 

 capillary constants, co-efficients of viscosity, co-efficients of 

 expansion, etc., may be derived from the general law. It 

 is difficult within the scope of this article to give an idea 

 in how far experiment confirms these laws. Sometimes 

 the agreement is very close, in others it is less satisfactory, 

 but for most substances at least approximate even for 

 pretty high densities. Again, the acids, alcohols, water, 

 etc., the groups of bodies that were mentioned before as 

 disobeying other laws of liquids, form exceptions. It will 

 be better understood now what right we have to explain 

 the abnormal behaviour of those bodies by association of 

 molecules. If we assume that for the majority of sub- 

 stances no such association takes place, substances in which 

 it does cannot be regarded as dynamically similar, and for 

 them the law cannot therefore hold. 



These laws in so far as they are confirmed restrict 

 the number of isothermal equations that are possible. 

 When in the isothermal equation we introduce the critical 

 constants as far as possible, all constants like a and d in 

 Van der Waals' equation, in other words, everything 

 specific for the special substance, should disappear. An 

 equation in which that does not happen is in contradiction 

 to the law of corresponding states. On the other hand 

 the hypothesis on which the law may be based shows that 

 there are quite a number of equations to be imagined which 

 could be in agreement with the law. 



Finally, therefore, we are confronted with the fact, that 

 though important laws both empirical and semi-theoretical 

 have been discovered, a satisfactory equation between jZ^, v, T 



