( 146 ) 



by a corresponding one in which the constant index i is given to 

 the coefficients a, b, c, so we have: 



G = 



— (a; a -{- bi p-\- a yf 

 L9 



= gi (ai a; 4- bi $ 4- a y/) 



from which results after division by gr the relation I was to prove. 

 Using this relation I find : 



u 2 



M£ = (1 — ai ai — bi ft — c t y ( ) — . 



9i 



If we call a a -\-bfi -\- cy = x, then f\/ — can be calculated 



out of each apparent error and the mean value of this system of 

 errors is equal to ;i, as that of the system of unknown errors is 

 h]/ g. It therefore seems to me not only permissible, but for a test 

 of the weights even useful, to make use of that system of errors 

 which allows the mean error of the unity of weight to be deduced 

 out of each definite part of these errors. The connection between 

 the quantities v. and the number h of the above formula applied by 

 me can be indicated by the relation Sx = k. 



Physics. - "Contribution to the theory of binary mixtures". VII. 

 By Prof. J. D. van der Waals. 



On the relation between the quantities a la and a 1 and a if which 



OCCUR IN THE THEORY OF A BINARY MIXTURE. 



I have already frequently traced the course of the thermodynamic 



curves for the case that for a binary system minimum plaitpoint 



a x 

 temperature occurs, and so also the quantity — has a minimum value 



b x 



for certain value of x. Both the course of the isobars and the course 



f dp \ /dp \ 



of the lines — 1 = and — ) = may be assumed as known 

 \dx J u \dv J x 



for that case. And experiment has shown that the shape of these 



lines predicted by theory it at least qualitatively accurate. 



I purpose to demonstrate in these pages that in the case mentioned 



the course of these lines (see among others tig. 1 page 626 Vol. IX 



of these Proceedings 1907) is not compatible with the supposition 



a ls 1 = a 1 a 3 . 



