210 SCIENCE PROGRESS. 



will be discussed presently, and the theory of the associa- 

 tion of molecules to groups for those substances will then 

 appear a very probable one. But it must once more be 

 pointed out that an association of this kind would never be 

 able to explain a change in the vapour-pressure, as has 

 been attempted by Batelli and others. This was already 

 discussed above. 



The problem of the behaviour of molecules in the 

 different states of matter belongs to the kinetic theory of 

 matter, a theory which had been worked out for gases long be- 

 fore Andrews published his investigation on the condensation 

 and critical phenomena of CO._,. It was Van der Waals who 

 succeeded in drawing Andrews' results within the range of the 

 kinetic theory, and at the same time expanded the idea of 

 the continuity of the two states. It was suggested by James 

 Thomson that the isothermal does not really possess the 

 two sharp breaks at the beginning and at the end of the 

 condensation, but that the two parts of the curve outside the 

 border-curve are to be joined by a curve with a maximum 

 and a minimum like a wave-crest and a wave-trough. 

 Three of such curves are given in the diagram. The 

 reality of the phases between e and /> is shown by the 

 possibility of lowering the pressure of a liquid a good deal 

 below its vapour-pressure as long as no vapour is present.. 

 The phases on the crest part {d 9) have not been realised in 

 the same way. But both these and the phases between e 

 and /> occur where liquid and vapour are separated by a 

 curved surface. All this makes the existence of the rest of 

 the hypothetical curve more or less probable also. As early 

 as 1873, Van der Waals published his famous memoir in 

 which he proves that the kinetic theory leads to an equation 

 for the isothermal having the shape proposed by Thomson. 



The equation is (/ + -,We^ - ^) = R (i + « /). This result 



he obtains by assigning a finite size to the molecules and 

 attractive forces between them acting over distances large 

 compared with the distances of neighbouring molecules. 

 The term in d depends on the former, the term in a on 

 the latter sui)position. By increasing / in the formula 



