In the case of a fluid mixture, it is obvious that 
must depend upon the composition as as as 
and 
.
If we have a single dissolved constituent of mass S per unit
mass of fluid, then 
.
In extending the Kelvin hypothesis to a fluid mixture it is
natural to suppose that a modified form of Eqs. (V-3) is
applicable. The modification is simply
Furthermore, if more than one constituent is present then we
may replace S by 
where the latter symbol represents
any of of several constituents 
.
Eq. (V-4) represents the most general form of Kelvin's hypothesis
and is free of any restrictions regarding thermal gradients,
viscosity or diffusion. It is, in essence, the Gibbs extension
of the Kelvin hypothesis and is in itself a more far reaching
proposition. Like the Kelvin version, Eqs. (V-4) are more
than definitions since it is implied that all known empirical
data with regard to any fluid are consistent with these equations.