  In a relativistic model of a neutron star, the star's mass is less than the
mass of the individual component baryons. This is due to the fact that the
star's negative binding energy makes a contribution to the star's total energy
and its mass. A consequence of this relativistic mass deficit is that a neutron
star that is accreting matter increases its mass at a rate which is slower than
the mass of a baryon times the rate that baryons are accreted. This difference
in the rate of change of the masses has a simple relation with the star's
gravitational redshift. We show that this effect has the potential to be
observed in binaries where the mass transfer is driven by angular momentum
losses from the gravitational radiation emitted by the binary motion.
