\infty $ with a continuous distribution of polydisperse parameters corresponds to *continuous polydispersity*). The present paper will consider discrete polydispersity of spherical colloidal particles, with their diameter being the only polydisperse attribute (size-polydispersity).

When polydispersity is not negligible, the phase behaviour becomes much richer, but the determination of phase transition boundaries requires a much more involved formalism, compared to the monodisperse counterpart. In fact, the coexistence condition in terms of intensive variables requires that all phases must have equal temperature, pressure and chemical potentials of the $%
M$ components. In the presence of polydispersity, one should thus solve a number of equations of the order of $M^{2}$, a task which is practically impossible for $M$ large or infinite.

However, the study of phase equilibria can conveniently start from the appropriate thermodynamic potential, which is the Helmholtz free energy $A$ when the experimentally controlled variables are temperature, volume and numbers of different colloidal species. In the one-component case, the coexistence condition of equal pressure and chemical potential has a simple geometrical interpretation in terms of free energy density $a$: the densities of two coexisting phases are determined by constructing a double-tangent to $a$ plotted versus particle density. This recipe leads to 