  The resonant scattering solar spectrophotometer 'Mark-I', designed and build
at the University of Birmingham (UK) and located at the Observatorio del Teide
(Spain), has been continuously in operation for the past 38 years. During this
period of time, it has provided high precision measurements of the radial
velocity of the Sun as a star, which has enabled the study of the small
velocity fluctuations produced by the solar oscillations and the
characterization of their spectrum. So far, it has been one of the pioneer
experiments in the field of helioseismology and contributed to the development
of that area. Moreover, because of its high sensitivity and long term
instrumental stability, it also provides an accurate determination (to within a
few parts in $10^3$) of the absolute daily velocity offset, which contains the
so-called 'solar gravitational red-shift'. In the present paper, results of the
analysis of the measurements of this parameter over the whole period 1976--2013
are presented. The result of this series of measurements is 600.4 $\pm$ 0.8 m
s$^{-1}$ with an amplitude variation of $\pm$5 m s$^{-1}$, which is in
anticorrelation with the phase of the solar activity cycle. The 5\% difference
found respect to the value predicted by the equivalence principle is probably
due to the asymmetry of the solar spectral line used.
