AbstractPeriodic solutions may be characterized by the mean values and initial values of their orbital elements. Accordingly in Chapter I a method is developed for calculating the mean values and in Chapter II a method is given for calculating the initial values of the orbital elements in the case of SCHWARZSCHILD's periodic solutions. The methods are illustrated by numerical calculations for the commensurabilities 2:1, 3:1, 3:2, and 5:3 of the mean motions of the planetoid and Jupiter.