  The Feynman--Hellmann theorem is used to show that vector meson energy
eigenvalues are monotonically decreasing functions of the reduced masses of
their constituent quarks. The experimental meson masses are used to put
constraints on the values of quark masses and to predict the masses of some as
yet undiscovered mesons. The mass of the $B_c^*$ meson is predicted to be
$6320\pm 10$ MeV, and, with less precision, the masses of a number of excited
vector mesons are also predicted.
