  In 2003 we have measured the absolute frequency of the $(1S, F=1, m_F=\pm 1)
\leftrightarrow (2S, F'=1, m_F'=\pm 1)$ two-photon transition in atomic
hydrogen. We observed a variation of $(-29\pm 57)$ Hz over a 44 months interval
separating this measurement from the previous one performed in 1999. We have
combined this result with recently published results of optical transition
frequency measurement in the $^{199}$Hg$^+$ ion and and comparison between
clocks based on $^{87}$Rb and $^{133}$Cs. From this combination we deduce the
stringent limits for fractional time variation of the fine structure constant
$\partial/{\partial t}(\ln \alpha)=(-0.9\pm 4.2)\times 10^{-15}$ yr$^{-1}$ and
for the ratio of $^{87}$Rb and $^{133}$Cs spin magnetic moments
$\partial/{\partial t}(\ln[\mu_{\rm {Rb}}/\mu_{\rm {Cs}}])=(0.5\pm 2.1)\times
10^{-15}$ yr$^{-1}$. This is the first precise restriction for the fractional
time variation of $\alpha$ made without assumptions about the relative drifts
of the constants of electromagnetic, strong and weak interactions.
