  We calculate three jet cross sections in photoproduction using exact matrix
elements for the direct and resolved contributions. Numerical distributions are
presented in a generic, irreducible set of variables that allows to disentangle
the dynamics of partonic QCD subprocesses from each other and from pure phase
space distributions. The results are compared to preliminary data from the ZEUS
collaboration at HERA. It is found that the largest contribution comes from
photon-gluon fusion in the mass range 36 GeV $< M_{\rm 3-jet} <$ 80 GeV. The
measured leading jet scattering angle distribution is consistent with the
$t$-channel exchange of a massless fermion in $2\to 2$ scattering, where the
third parton is assumed to arise from soft bremsstrahlung. The data are
inconsistent with pure phase space and Rutherford scattering distributions.
