  Birmingham Solar Oscillations Network (BiSON) instruments use resonant
scattering spectrometers to make unresolved Doppler velocity observations of
the Sun. Unresolved measurements are not homogenous across the solar disc and
so the observed data do not represent a uniform average over the entire
surface. The influence on the inhomogeneity of the solar rotation and limb
darkening has been considered previously (Brookes et al. 1978a) and is well
understood. Here we consider a further effect that originates from the
instrumentation itself. The intensity of light observed from a particular
region on the solar disc is dependent on the distance between that region on
the image of the solar disc formed in the instrument and the detector. The
majority of BiSON instruments have two detectors positioned on opposite sides
of the image of the solar disc and the observations made by each detector are
weighted towards differing regions of the disc. Therefore the visibility and
amplitudes of the solar oscillations and the realization of the solar noise
observed by each detector will differ. We find that the modelled bias is
sensitive to many different parameters such as the width of solar absorption
lines, the strength of the magnetic field in the resonant scattering
spectrometer, the orientation of the Sun's rotation axis, the size of the image
observed by the instrument and the optical depth in the vapour cell. We find
that the modelled results best match the observations when the optical depth at
the centre of the vapour cell is 0.55. The inhomogeneous weighting means that a
`velocity offset' is introduced into unresolved Doppler velocity observations
of the Sun, which varies with time, and so has an impact on the long-term
stability of the observations.
