  We measure the branching ratios from the $y^8{\rm P}_{9/2}$ excited state to
six metastable states of europium through fluorescence spectroscopy of an
atomic beam. The sum of the six branching ratios is estimated to be
$1.05(2)\times 10^{-3}$. This research provides us with insightful information
to determine the feasibility of using the $a^8{\rm S}_{7/2} - y^8{\rm P}_{9/2}$
transition in order to implement the Zeeman slowing for europium atoms in the
ground state. Based on this result, we also propose a scheme for Zeeman slowing
and magneto-optical trapping, using a specific metastable state which has a
cyclic transition.
