  The first precise measurement of the Casimir force between dissimilar metals
is reported. The attractive force, between a Cu layer evaporated on a
microelectromechanical torsional oscillator, and an Au layer deposited on an
Al$_2$O$_3$ sphere, was measured dynamically with a noise level of 6
fN/$\sqrt{\rm{Hz}}$. Measurements were performed for separations in the 0.2-2
$\mu$m range. The results agree to better than 1% in the 0.2-0.5 $\mu$m range
with a theoretical model that takes into account the finite conductivity and
roughness of the two metals. The observed discrepancies, which are much larger
than the experimental precision, can be attributed to a lack of a complete
characterization of the optical properties of the specific samples used in the
experiment.
