  In 1992, L.G. Levchuk noted that the asymmetries measured in M\o ller
scattering polarimeters could be significantly affected by the intrinsic
momenta of the target electrons. This effect is largest in devices with very
small acceptance or very high resolution in laboratory scattering angle. We use
a high resolution polarimeter in the linac of the polarized SLAC Linear
Collider to study this effect. We observe that the inclusion of the effect
alters the measured beam polarization by -14% of itself and produces a result
that is consistent with measurements from a Compton polarimeter. Additionally,
the inclusion of the effect is necessary to correctly simulate the observed
shape of the two-body elastic scattering peak.
