  We report a new measurement of the ratio $h/m_{\mathrm{Rb}}$ between the
Planck constant and the mass of $^{87}\mathrm{Rb}$ atom. A new value of the
fine structure constant is deduced, $\alpha^{-1}=137.035\,999\,037\,(91)$ with
a relative uncertainty of $6.6\times 10^{-10}$. Using this determination, we
obtain a theoretical value of the electron anomaly
$a_\mathrm{e}=0.001~159~652~181~13(84)$ which is in agreement with the
experimental measurement of Gabrielse
($a_\mathrm{e}=0.001~159~652~180~73(28)$). The comparison of these values
provides the most stringent test of the QED. Moreover, the precision is large
enough to verify for the first time the muonic and hadronic contributions to
this anomaly.
