( 792 ) 
becomes infinite for exceedingly dilute solutions. For the (of course 
also very slight) changes to which the concentrations in an exceedingly 
dilute solution can be subjected we may, therefore, consider u, u’, 
ete. as invariable, independent of the concentrations, when we take 
the variations of 7’logn, ete. with the concentration into account. 
If we now substitute the value (5) for u,, and bring down the term 
RT log n, from the exponent, we get again: 
d 
== > = k, In, — k, In, (da) 
where: 
2u, + F, =u,+F 
RT RR : 
Le en k, =e ee 
may be considered as constants according to the above, as is required 
by the law of the mass-action. 
We conclude from this equation (4 and 4) that really equation (2) 
can properly account for a highly important property of the course 
of the reaction. This result was by no means to be considered as 
certain beforehand. For we have drawn up this equation by analogy, 
and drawn attention to the close agreement with the use of equation (1) 
in this and the preceding communication, but not to the existing 
differences. It is here the place to set forth these differences. It is 
true that in the ease of the ‘osmotic temperatures” the final state 
is no state of equilibrium, but each of the two homogeneous phases 
may yet be considered as in equilibrium, if we leave the immediate 
neighbourhood of the membrane out of consideration. So we are 
undoubtedly justified in speaking of quantities as temperature, entropy, 
thermodynamic potential in each of the phases, and there the formula 
was applied only to that final state “of equilibrium of mass exchange”. 
But not without justification it might be doubted whether the same 
thing is allowed for states in which the equilibrium of mass exchange 
has not yet set in, and a fortiori this holds for the case under 
consideration. For the homogeneous phase in which the reaction 
takes place, is not in equilibrium in itself; it is not certain that 
Maxwerr’s distribution of velocities holds there, and even if with 
BOLTZMANN we want to introduce a definition for the entropy of a 
state of non-equilibrium, it will, of course, in general have another 
value than the from equation (2). 
Now it appears from equation (4) that all the same these undoubt- 
edly weighty objections need not Jead to a rejection of equation (2). 
For the very extensive material of facts concerning the reaction 
