  We have remeasured the absolute $1S$-$2S$ transition frequency $\nu_{\rm
{H}}$ in atomic hydrogen. A comparison with the result of the previous
measurement performed in 1999 sets a limit of $(-29\pm 57)$ Hz for the drift of
$\nu_{\rm {H}}$ with respect to the ground state hyperfine splitting $\nu_{{\rm
{Cs}}}$ in $^{133}$Cs. Combining this result with the recently published
optical transition frequency in $^{199}$Hg$^+$ against $\nu_{\rm {Cs}}$ and a
microwave $^{87}$Rb and $^{133}$Cs clock comparison, we deduce separate limits
on $\dot{\alpha}/\alpha = (-0.9\pm 2.9)\times 10^{-15}$ yr$^{-1}$ and the
fractional time variation of the ratio of Rb and Cs nuclear magnetic moments
$\mu_{\rm {Rb}}/\mu_{\rm {Cs}}$ equal to $(-0.5 \pm 1.7)\times 10^{-15}$
yr$^{-1}$. The latter provides information on the temporal behavior of the
constant of strong interaction.
