  Knowledge of the energy spectrum of $^8$B neutrinos is an important
ingredient for interpreting experiments that detect energetic neutrinos from
the Sun. The neutrino spectrum deviates from the allowed approximation because
of the broad alpha-unstable $^8$Be final state and recoil order corrections to
the beta decay. We have measured the total energy of the alpha particles
emitted following the beta decay of $^8$B. The measured spectrum is
inconsistent with some previous measurements, in particular with a recent
experiment of comparable precision. The beta decay strength function for the
transition from $^8$B to the accessible excitation energies in $^8$Be is fit to
the alpha energy spectrum using the R-matrix approach. Both the positron and
neutrino energy spectra, corrected for recoil order effects, are constructed
from the strength function. The positron spectrum is in good agreement with a
previous direct measurement. The neutrino spectrum disagrees with previous
experiments, particularly for neutrino energies above 12 MeV.
