Neutron diffraction experiments have been performed on single crystals of ${\mathrm{La}}_{2}$${\mathrm{NiO}}_{4}$. Above 70 K the structure is orthorhombic Bmab. At 70 K a first-order transition occurs to a crystal structure that we believe to be tetragonal P${4}_{2}$/ncm. With our resolution we see no splitting of the diffraction peaks that would indicate the lower-symmetry orthorhombic Pccn. A crystallographic refinement of 307 independent reflections from two different crystals gives an R factor of 6% for the P${4}_{2}$/ncm phase. The refinement also shows that our crystals are stoichiometric with an oxygen composition of 4.02\ifmmode\pm\else\textpm\fi{}0.03. The crystals are antiferromagnetic with a magnetic structure in which the propagation and spin directions are parallel to [100], in agreement with other studies. The antiferromagnetic ordered moment at T=10 K is (1.62\ifmmode\pm\else\textpm\fi{}0.05)${\ensuremath{\mu}}_{B}$ per Ni atom. According to susceptibility measurements ${T}_{N}$\ensuremath{\simeq}650 K on stoichiometric ${\mathrm{La}}_{2}$${\mathrm{NiO}}_{4}$, but we have not checked this in our neutron experiment. No change in the antiferromagnetic structure occurs at the 70-K transition, but we cannot exclude the formation of a 2k magnetic structure at this temperature that would give rise to the same diffraction pattern in the tetragonal phase. In the second part of our experiment the induced magnetic form factor (H=4.6 T, applied parallel to the [010] axis at 5 K) has been measured with polarized neutrons. Our object in this experiment was to search for covalency effects, in particular evidence orbital and the ${p}_{x}$, ${p}_{y}$ orbitals of the oxygens in the Ni-O plane.We have measured 18 reflections with three different neutron wavelengths. The induced moment is 7.9 m${\ensuremath{\mu}}_{B}$ per molecule, which is in good agreement with bulk susceptibility measurements. Surprisingly, we find no evidence for any spin transfer or asphericity in the Ni spin density in the Ni-O planes. Instead we find new effects along the long c axis. The ${\mathrm{La}}^{3+}$ atoms develop a positive susceptibility which we suggest comes from hybridization between the La 5d and O p bands.