  The introduction of a longitudinal polarised positron beam in an $e^+e^-$
linear collider calls for its polarisation monitoring and measurement at low
energies near its production location. Here it is shown that a relatively
simple Bhabha scattering polarimeter allows, at energies below 5000 MeV, a more
than adequate positron beam longitudinal polarisation measurement by using only
the final state electrons. It is further shown that out of the three, 10, 250
or 5000 MeV positron beam energy locations, where the polarisationmeasurement
in the TESLA linear collider can be performed, the 250 MeV site is best suited
for this task.
