( 150) 



V 



traced curve is an equilateral hyperbola. So a value of 7— larger 



v 

 than 3 is possible only when v lies between and 1. Thus — =4 



requires a value of m = l / % . 



Accordingly it is impossible to account for a minimum plaitpoint 

 temperature of substances for which m does not lie between and 1 . 



Now I have already repeatedly called attention to the equation : 



d*a fda\ 

 2a d^~[d~c) + 4 ( a i a ' _a >> )' 



which follows from the supposition that a is a quadratic form of#, 

 and already in my Molecular Theory for a binary mixture I pointed 

 out, realizing the desirability of a relation being found between a l9 

 and a, and a„ that the equation of the spinodal line for a binary 

 mixture might be very much simplified if we were justified in 

 assuming a Xi " = a x a s . I also pointed out other relations between 

 these quantities; but I have carefully refrained from even giving so 

 much as the slightest indication of the greater probability of one 

 relation. I have only repeatedly, then and later, assumed as relation 

 for mixtures with minimum plaitpoint temperature a, -j- a, ]> 2a lt , 

 and reversely, when also mixtures with maximum plaitpoint tempera- 

 ture might occur: a x -\- a, < 2a It . And I have repeatedly pointed 

 out that there is no reason whatever for putting e.g. a,, a = a x a 7 . 

 And to this the following considerations have chiefly led me. 



In the equation of state for a simple substance the two constants 

 b and a have not been introduced on equally sufficient grounds and 

 with the same certainty. To the existence of the quantity b we 

 conclude with perfect certainty if we believe that to occupy space 

 is an essential property of matter Even Maxwell, who would not 

 attribute a volume of their own to the molecules, but wanted to 

 consider them as so-called material points, understanding that colli- 

 sions could not take place between material points, could not but 

 attribute to them at least an apparent volume. By assuming a 

 repulsive force he had to account for their never meeting, and for 

 their behaviour as particles possessing impermeability on approaching 

 each other with reversal of motion. A hypothesis whose improbability 

 is not to be denied. The force would be a repulsive one, and pro- 

 bably in inverse ratio to the fifth power of the distance. How and 

 why the attraction at somewhat larger distance is converted into such 

 a repulsive force is a question that was probably never put by him, 



