A new experimental limit to the possible time variation of the proton
gyromagnetic ratio times the electron-to-proton mass ratio has been ob
tained from the frequency comparison data between Cs and Mg atomic bea
m standards. The measurements, made over a period of one year, lead to
an upper limit for the rate of change of g(p)(m(e)/m(p)) of 5.4 x 10(
-13)/yr. This result, based only on the validity of the quantum mechan
ical theory of the atomic spectra, together with astrophysical data re
garding analogous products of atomic fundamental constants, leads also
to a new limit for the time stability of the fine structure constant
a (2.7 x 10(-13)/yr).