A quantum-mechanical theory is given for the transition temperature and the nature of the ordered state for a system of spins interacting through general magnetic forces. The transition temperature and the ordered state below it are found to be, respectively, the lowest eigenvalue and the corresponding eigenvector of an Hermitian matrix derived quantum mechanically, within the framework of the molecular-field approximation. The method is then applied to the pure dipolar systems dysprosium ethyl sulphate and cerium magnesium nitrate.