The GOLF instrument provides a stable and continuous measurement of the intensity of spatially integrated sunlight in one wing of the sodium D lines. Because the detected radiation results from atomic scattering, the GOLF signal can be traced to an atomic reference wavelength. The planned operations were to involve a form of relative photometry through the use of measurements on both the blue and red wings of the solar D lines of neutral sodium. However, due to the occasional malfunction of the polarization subsystem a ``one wing photometric mode" operational alternative has been selected in order to ensure achievement of a 100% duty cycle. In this case, the signal observed consists of two photometric measurements at only one wing of each line of the sodium doublet separated by gx0.43 picometers (pm). The sodium cell system in GOLF combines photons scattered at three different wavelengths: one at D_1 and two at D_2. This paper developes a formalism to describe this system in terms of the solar spectral line profiles. A method of converting the one wing data to an effective velocity scale is presented. The method is applied to the nearly continuous 804 day sequence received from the GOLF instrument prior to the loss of telecommunications with SOHO on 24-June-1998. The resulting time sequence is part of the GOLF archive and can be made available to investigators. This publication describes some properties of this time series.