The "model of three densities" is a mathematical relationship between the densities of liquid and saturated vapor in the coexistence system and the critical density without the help of any other physical property. The model uses the same set of density data as the "law of the rectilinear diameter". It is based on two ratios : the reduced densities of liquid and saturated vapor, i.e., the reciprocals of the reduced liquid and vapor volumes, and a numerical factor called the "density number". The numerical factor is nearly constant between 7.98 and 8.02 over a temperature range of about 200 deg for elements, inorganic substances, and organic substances that are homogeneous throughout the liquid and vapor phases. This leads to empirical equations for the projection of the critical density.