  We report measurements of the resistivity in the ferromagnetic state of
epitaxial thin films of La_{1-x}Ca_{x}MnO_{3} and the low temperature specific
heat of a polycrystalline La_{0.8}Ca_{0.2}MnO_{3}. The resistivity below 100 K
can be well fitted by \rho - \rho_{o} = E \omega_{s}/sinh^{2}(\hbar
\omega_{s}/2k_{B}T) with \hbar \omega_{s}/k_{B} \simeq 100 K and E being a
constant. Such behavior is consistent with small-polaron coherent motion which
involves a relaxation due to a soft optical phonon mode. The specific heat data
also suggest the existence of such a phonon mode. The present results thus
provide evidence for small-polaron metallic conduction in the ferromagnetic
state of manganites.
