A systematic study of the 10 GHz electron paramagnetic resonance spectra of the gadolinium ion (Gd³⁺;⁸S) in isomorphic diamagnetic lattices of hydrated rare earth double-nitrate single crystals is reported. These lattices are of the form M₂triple primeM₃double prime(NO₃)₁₂.24H₂O, where Mtriple prime is bismuth or lanthanum and Mdouble prime is zinc or magnesium. The ratio of Gd³⁺ to Mtriple prime ions was approximately 0·1%. The experimental data for temperatures of 290 °K and 77 °K are fitted to the phenomenological spin Hamiltonian for C_3i symmetry. The angular dependence of the spectra shows substantial variations from that predicted, which have not been reported previously. These variations are not inconsistent with C_3i symmetry but cannot be completely described by any spin Hamiltonian of the above form. This raises doubts as to the usefulness of the spin-Hamiltonian formalism because the intrinsic symmetry of the terms is too high to describe the variations.