  Soft resonant x-ray Bragg diffraction (SRXD) at the Ho M$_{4,5}$ edges has
been used to study Ho $4f$ multipoles in the combined magnetic and orbitally
ordered phase of HoB$_2$C$_2$. A full description of the energy dependence for
both $\sigma$ and $\pi$ incident x-rays at two different azimuthal angles, as
well as the ratio $I_\sigma/I_\pi$ as a function of azimuthal angle for a
selection of energies, allows a determination of the higher order multipole
moments of rank 1 (dipole) to 6 (hexacontatetrapole). The Ho 4f multipole
moments have been estimated, indicating a dominant hexadecapole (rank 4) order
with an almost negligible influence from either the dipole or the octupole
magnetic terms. The analysis incorporates both the intra-atomic magnetic and
quadrupolar interactions between the 3d core and 4f valence shells as well as
the interference of contributions to the scattering that behave differently
under time reversal. Comparison of SRXD, neutron diffraction and non resonant
x-ray diffraction shows that the magnetic and quadrupolar order parameter are
distinct. The $(0 0 1/2)$ component of the magnetic order exhibits a Brillouin
type increase below the orbital ordering temperature T$_Q$, while the
quadrupolar order increases more sharply. We conclude the quadrupolar
interaction is strong, but quadrupolar order only occurs when the magnetic
order gives rise to a quasi doublet ground state, which results in a lock-in of
the orbitals at T$_Q$.
