  We derive a semiclassical quantization for a spin, study it for not too small
a spin quantum number (S>5), and compute the 2S+1 eigenvalues of a Hamiltonian
exhibiting resonant tunnelling as the magnetic field parallel to the anisotropy
axis is increased. Special attention is paid to the resonance condition. As a
corollary we prove that semiclassical quantization and quantum-mechanical
perturbation theory agree there where they should.
