"With these introductory specifications in mind, let us assume any number of material particles to be restricted, by forces of some sort, to motion within limited space, and the system either withdrawn from outer influences or under such as are constant; let us, moreover, suppose the system undisturbed by the interference of psychic freedom, or the latter impossible. In such case, certain initial positions, velocities, and directions of the parts of the system being assumed, all following states will be determined by these. And now, if there are among these conditions, either present at the beginning, or attained in the course of the motion, any such as have for their result a return of the same states after a given time, then the motion, and so also the positions of the parts conceived as at first undergoing alteration in form and velocity, will, unless they contain the immediate condition of periodic recurrence, continue altering until those of all the possible states are reached which contain the condition of recurrence; until this point is attained, the system will, so to speak, know no rest. Has the recurrence once taken place within a given time, then it must always take place anew within the same time, because the same conditions are there to determine it. And since these conditions are determinative of the whole course of motion from one recurrence to the next, the same course must be repeated; that is, in every like phase of the period a like state of motion will exist. But this gives us full stability of the system, a change, a deviation from the attained stability being possible only through changes in outer influences, the assumed constancy of which rendered the attainment of stability possible. "This principle appears at first purely _a priori_; but the assumption should not be overlooked that there are among the conditions determining the motion such as lead to their own recurrence, and this is to be taken for granted, since it is necessary to assume that a system must continue to change until, but only until, the conditions of full stability are attained, in case it is attainable; and that this full stability, when once reached, cannot be again destroyed by the action of the system itself. The question presents itself as to how far calculation and experience permit us to lay down a more general principle.