  Multipole expansions depend on the coordinate system, so that coefficients of
multipole moments can be set equal to zero by an appropriate choice of
coordinates. Therefore, it is meaningless to say that a physical system has a
nonvanishing quadrupole moment, say, without specifying which coordinate system
is used. (Except if this moment is the lowest non-vanishing one.) This result
is demonstrated for the case of two equal like electric charges. Specifically,
an adapted coordinate system in which the potential is given by a monopole term
only is explicitly found, the coefficients of all higher multipoles vanish
identically. It is suggested that this result can be generalized to other
potential problems, by making equal coordinate surfaces coincide with the
potential problem's equipotential surfaces.
