It is argued that in a galaxy like ours a third integral of motion, a third independent argument in the distribution function, should exist if the potential function has to satisfy a third condition imposed on it, namely symmetry with respect to a plane. Orbit computations of single stars in a symmetric potential of the kind (Martinet and Hayli, 1971) indicate that a third integral seems to exist for Population I stars while it ceases to exist for Population II objects. This situation is explained by the author as follows. We state that a third integral should exist for all populations alike if the Boltzmann equation is interpreted within the statistical context for which it is valid. When applied to a complex system like the galaxy the third integral of the Boltzmann equation, which holds for an elementary volume in phase space, will also hold for a single particle if the latter is representative of the behavior of the element of volume as in Population I (coherent motion) whereas it will not necessarily hold for a single star of Population II; in the latter population the elementary volume, containing the same number of stars, does not represent the behavior of the element of volume during the motion of this in phase space.