  We look for a diurnal anisotropy in the cosmic ray flow, using the
Mexico-City Neutron Monitor (NM) detector, due to the Earth's orbital motion
and predicted by Compton-Getting (C-G) in 1935, as a first-order relativistic
effect. The Mexico-City NM's geographic latitude is not very high
($19.33^{\circ}$N), and it has a high cutoff geomagnetic rigidity (8.2 GV) and
mountain altitude (2274 m asl) favoring the observation of the C-G effect.
Furthermore, during the solar cycle minima, the galactic cosmic ray flux is
maxima, and the solar magnetic field gets weakened, with a dipolar pattern. Its
influence on cosmic rays reaching Earth is the smallest. Analysis of the
combined counting rate during two solar minima, 2008 and 2019, from Mexico-city
NM's data yields the C-G effect with an amplitude variation of (0.043$\pm$
0.019)\%, and phase of (6.15$\pm$ 1.71) LT. The expected amplitude variation is
0.044\%, and the phase of 6.00 LT.
