  The average prompt-fission-neutron multiplicity $\bar{\nu}$ is of
significance in the areas of nuclear theory, nuclear nonproliferation, and
nuclear energy. In this work, the surrogate-reaction method has been used for
the first time to indirectly determine $\bar{\nu}$ for $^{239}$Pu($n$,$f$) via
$^{240}$Pu($\alpha$,$\alpha^{\prime}f$) reactions. A $^{240}$Pu target was
bombarded with a beam of 53.9-MeV $\alpha$ particles. Scattered $\alpha$
particles, fission products, and neutrons were measured with the NeutronSTARS
detector array. Values of $\bar{\nu}$ were obtained for a continuous range of
equivalent incident neutron energies between 0.25--26.25~MeV, and the results
agree well with direct neutron measurements.
