( 56 ) 



family A, whose period is 77 = T' . Darwin's computations show 



that the value of' 7" for which the. families .1 and /< co-incide 

 must lie between 1.836 .-r and 1,97 .t. The point of co-incidence of 

 .1 and C is outside the region explored by Darwin, the corresponding 

 value of 7" must therefore I»' larger than 2.23 jr. 



It' in die equations (J) we lake account <>l' the square of e, the 

 right-hand member of die first must be multiplied by VI— i'. In 

 die second J," miisi lie replaced by 



.1, » -f ,"- (b^) ± {31 J, 3) + 24 ,1 ; (3) + li .L «J ) 



and 1 / i e*t must be added id the second member. Now it' we lake 

 T' = const, then r is constant and also o can be taken to be constant. 

 The second equation (1) then is of die form 



const. =fi{P-\- Qe*) (2) 



Now we have +' = e*, therefore (2) is approximately the equation 

 ij» (ft , g) = 0. For the family BB' /' and Q are of opposite signs, 

 for CO they have the same sign. Thus the form of these curves 

 as drawn in die figures 4ö and 4A is confirmed. ! 



Physics. - - "Contribution A» the theory of binary mixtures. I\." 

 1!\ Prof. .1. 1). van dek Waals. 



Continued, see p. 849 vol. IX. 

 The BINODAL CURVE. 



We might dunk thai for the determination of the binodal curve 

 we could follow the following course. It is required for coexistence 

 that besides the temperature three oilier quantities are equal, i.e. 

 ii, q and -l/j Mi- " W( ' nnn a ' so 'race the lines on which M 1 pi l , is 

 equal, we should have to seek in order to find a point of a binodal 

 curve, the points satisfying the condition thai the p. a and M l ;i, 

 lines passing through this point intersect in still another point of 

 the held. This search, however, being exceedingly difficult would 

 give moreover no clear survey of the results. We shall, therefore 

 nol follow this course. Still I shall make some prefatory remarks 

 mi the course of this third group of lines. For it is bv no means 

 devoid of interest to know in which phases of a binary system the 



') This last paragraph has been added in Hie English translation. 



