  We analyse the constraints obtained from new atomic clock data on the
possible time variation of the fine structure `constant' and the
electron-proton mass ratio and show how they are strengthened when the seasonal
variation of Sun's gravitational field at the Earth's surface is taken into
account. We compare these bounds with those obtainable from tests of the Weak
Equivalence Principle and high-redshift observations of quasar absorption
spectra consistent with time variations in the fine structure constant.
