( 15 ) 



the peculiarities of the course of the PT-lines may easily be derived 

 by means of the foregoing. 



For the determination of tlie last mentioned locus, we start from 

 the equation: 



"V = 



P + ( ^)y, J ^'^' + (^^/)" . . . , (9) 



The factor of Vgf being naturally positive and. (es/)y being always 

 negative, Ws/ can only be equal to zero in a point x where Vsf is 



positive, so between the loci where Vsf=0 and ^r — = 0. 



Ovf 



Further it is now easy to understand that at the same time 

 with Vsf- the quantity W^f will become infinitely great, there where 



ö> 



^— - =i 0. In order to avoid this complication van der Waals has 



multiplied the quantity Wg/- by ^— ^ as equation (4) shows ; the 

 obtained product never becomes in finitely great now. 

 If we multiply equation (9) by t — - , we get : 





/. + il^ 



Vsf + T~{^sfh ■ . (10) 



öiyyyvjör/ dvf' 



Now we know that the locus for ;r — . Wsfz=zO will have to lie 



between that for ^ — . V^f =: and for ^ — = , as drawn in 

 dvf' ^ dvf^ 



fig. 1, which compels us to make ^^ — . Wsf^=0 and - — -. Vg/- := 



intersect on the line of the compound. 



That this must really be so, is easily seen, when we bear in mind, 



that on the line of the compound the locus where ^— ^ = coincides 



with that where ^;^ — . F^/- = , from which in connection with 



equation (10) it follows immediately that at the same point also 



- — . Wsf =z 0. In this way we arrive at the conclusion, that the three loci 

 dv;" -^ -^ 



^;^ — - = , - — . Vsf = and ^ — . Wgf =z will intersect on the Ime 



