  We analyze two representative systems containing a three-phase-contact line:
a liquid lens at a fluid--fluid interface and a liquid drop in contact with a
gas phase residing on a solid substrate. We discuss to which extent the
decomposition of the grand canonical free energy of such systems into volume,
surface, and line contributions is unique in spite of the freedom one has in
positioning the Gibbs dividing interfaces. In the case of a lens it is found
that the line tension is independent of arbitrary choices of the Gibbs dividing
interfaces. In the case of a drop, however, one arrives at two different
possible definitions of the line tension. One of them corresponds seamlessly to
that applicable to the lens. The line tension defined this way turns out to be
independent of choices of the Gibbs dividing interfaces. In the case of the
second definition,however, the line tension does depend on the choice of the
Gibbs dividing interfaces. We provide equations for the equilibrium contact
angles which are form-invariant with respect to notional shifts of dividing
interfaces which only change the description of the system. Conceptual
consistency requires to introduce additional stiffness constants attributed to
the line. We show how these constants transform as a function of the relative
displacements of the dividing interfaces. The dependences of the contact angles
on lens or drop volumes do not render the line tension alone but a combination
of the line tension, the Tolman length, and the stiffness constants of the
line.
