CONDEXSATION AND CRITICAL PHENOMENA. 215 



though one or other of the formulse mentioned may occa- 

 sionally be used with success, the problem of a satisfactory 

 formula does not seem much nearer its solution than where it 

 was left by Van der Waals in 1873. There is one law, 

 however, essentially empirical, which has been found pretty 

 well confirmed where tested, vi2., that the pressure at con- 

 stant volume is a linear function of the temperature. The 

 accurate series of observations due to Amagat, Ramsay and 

 Young, etc., confirm this law, though the most recent results 

 obtained for isopentane and hexane by Young and Thomas, 

 and for a number of liquids by Barus and especially Ama- 

 gat, show slight but certain deviations. Van der Waals' 

 formula is in form a special case of this law, but theo- 

 retically there is nothing to say in favour of the general one. 

 While it is at present impossible to explain the behaviour 

 of a substance in detail on the kinetic theory, a remarkable 

 set of laws has been discovered which shows the existence 

 ot a o^reat resemblance between the behaviour of different 

 substances, the laws of corresponding states of matter. 

 The law was deduced by Van der Waals in 1880 from his 

 formula, but appears to hold in circumstances where the 

 formula itself would not be applicable at all. This is quite 

 intelligible, as the law would follow from a good many 

 equations different from Van der Waals' equation. In fact, 

 as was first pointed out by Kamerlingh Onnes in 188 1, it 

 follows from a general hypothesis, tji's., that the molecules 

 of different substances are similar bodies of constant dimen- 

 sions acting upon each other with attractive forces that can 

 be reduced to a surface pressure, or forces inversely pro- 

 portional to a certain power of the molecules. In both 

 cases by the application of Newton's principle of the 

 dynamical similarity the law of corresponding states of 

 matter is arrived at. The simplest way in which to put 

 the law is that if /, v and / are expressed in terms of their 

 values at the critical point, the relation between them is 

 the same for all substances. This law leads to numerous 

 consequences which may be used in testing it, a few im- 

 portant ones of which I will here mention. In the first 

 place, that there must be a relation between the three 



15 



