The equilibrium properties of a system of N two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, are evaluated exactly by the 'thermodynamically equivalent Hamiltonian' method of Bogoliubov et at. (1957). The results are identical with those obtained by Hepp and Lieb (1973) and Wang and Hioe (1973). The thermodynamically equivalent Hamiltonian is shown to be equivalent to the mean field Hamiltonian of the Ising model, which indicates why the transition from the 'normal' to the 'superradiant' state of the Dicke model is similar to the transition from the disordered to the ordered state of the Ising model.