The problem of a spin one Weiss molecular field Hamiltonian with uniaxial anisotropy is solved exactly. The free energy contains magnetocrystalline anisotropy terms of all even order Legendre polynomials. TheP2coefficient varies as the third power of the magnetization rather well even for fairly large anisotropy, and over the entire temperature range. The higher order terms can be of both signs, and all change sign as the temperature is increased.