THE ORBITS OF BINARY SYSTEMS. We have already seen (p. 47) how the two constituents of a binary system permanently describe closed elliptical orbits about one another, because neither can escape from the gravitational hold of its companion. Energy can reside in the orbital motion of these systems, as well as in their motion through space. And strict mathematical analysis shews that a long succession of gravitational pulls from passing stars must finally result in equipartition of energy, not only between the energies of motion of one system and another through space, but also between the various orbital motions of which each binary system is capable. When this final state of equipartition is ultimately reached, the orbits of the systems will not all be similar, but it can be shewn that their shapes will be distributed according to a quite simple statistical law[19]. As the orbits of actual systems are not found to conform to this law, it is clear that the stars have not yet lived long enough to attain equipartition of energy in respect of their orbital motions. It is impossible to discuss how far they have travelled along the road to equipartition without knowing the point, or points, from which they started. [19] The eccentricity of orbit _e_ is distributed in such a way that all values of _e_² from _e_² = 0 to _e_² = 1 are equally probable. The question of the origin of binary systems will be discussed more fully in the next chapter. For the moment it may be said that they appear to come into being in two distinct ways.