  The definition of the Soret coefficient of a binary mixture includes a
concentration prefactor, $x(1-x)$ when mol fraction $x$ is used, or $w(1-w)$
when mass fraction $w$ is used. In this paper the physical reasons behind this
choice are reviewed, emphasizing that the use of these prefactors makes the
Soret coefficient invariant upon change in the reference frame, either mass or
molar. Then, it is shown how this invariance property can be extended to
ternary mixtures by using an appropriate concentration prefactor in matrix
form. The work is completed with some considerations of general non-isothermal
diffusion fluxes, binary limits of the concentration triangle, selection of the
dependent concentration in a ternary mixture, use of molar concentrations and,
finally, extension to multi-component mixtures.
