535 
Ox 
sum of the factors by which 55 is multiplied is zero, and that the 
Pp 
same holds for each of the “unknowns”. The left hand side of the 
resultant equation is therefore shown to be zero. We have then as 
a result: 
Oz Qzx Ox Oy Qy dy 
5 Xe + Ve de kK 44+ 40,4 ..... ==, 
EL ror 
that is, equation (2) results. This is the equation which we set out 
to establish as an extension of Braun’s law. 
Note J. It is not necessary that the solvent should be a pure 
substance. It may be a mixture of different substances of which, 
however, none occurs in the solid state. With this assumption 
the above method of proof remains exactly the same, and the validity 
of the result is unaffected. The quantities Q, etc., have, of course 
in general different values when the “solvent” is differently 
constituted. 
Note [/J. In the above treatment we have nowhere made use ot 
any explicit relation connecting Z and the composition. It follows 
from this that the results are valid both for constant and for reacting 
components. The only assumption made was that the components 
were independent in the sense of the phase theory. 
Note III. For the general case we can give a demonstration on 
the lines of that given for the simple case of three components. It 
would then be seen that we must deal with a state of stable equi- 
librium. Since the proof is more involved than that given above we 
do not reproduce it here. In a later communication dealing with a 
more general problem another proof will be found. 
Katwijk a. d. Rijn, August 1919. 
