Foucault long pendulums, with spherical suspended mass, show Earth rotation by the constant velocity drift of their oscillation plane. Maurice Allais used a short, 84 centimeters pendulum, with a suspended bronze disc mass. He recorded its oscillation plane drift velocity, during solar eclipses, in 1954 and 1959. Both times, he noticed an anomalous drift of the oscillation plane. Several authors confirmed the effect, during next solar eclipses, with other types of pendulums. Then a group of Geophysicists, from the Science Academy of China, used an accurate digital gravimeter to measure Earth Gravity acceleration during March 09, 1997 solar eclipse. Their gravimeter recorded two drops of Earth Gravity acceleration (respectively 5.02 and 7.7 µ Gals) before and during first and last contacts of the Moon disc. However there was no acceleration drop during eclipse totality. Same phenomena were confirmed later, during next solar eclipses, with the same gravimeter. No classical causes for these facts were found, since modern gravimeters take care of temperature and atmospheric pressure variations. We analyse the effect of Moon rotation, and of solar Corona mass, in the frame of our Quantum model of Inertia and of Gravitation. The model predicts that Moon / Earth Gravity acceleration changes, when the Moon direction is close to the Sun one, as observed from the gravimeter place. That phenomenon should be tied to Quantum fluctuations dispersion by matter. Recorded measurements confirm that interpretation.