  The Total Solar Irradiance varies over a solar cycle of 11 years and maybe
over cycles with longer period. Is the solar diameter variable over time too?
We introduce a new method to perform high resolution astrometry of the solar
diameter from the ground, through the observations of eclipses by reconsidering
the definition of the solar edge. A discussion of the solar diameter and its
variations must be linked to the Limb Darkening Function (LDF) using the
luminosity evolution of a Baily's Bead and the profile of the lunar limb
available from satellite data. This approach unifies the definition of solar
edge with LDF inflection point for eclipses and drift-scan or heliometric
methods. The method proposed is applied for the videos of the eclipse in 15
January 2010 recorded in Uganda and in India. The result shows light at least
0.85 arcsec beyond the inflection point, and this suggests to reconsider the
evaluations of the historical eclipses made with naked eye.
