In the final state of equipartition of energy, the shapes of the orbits will, as we have seen, be distributed according to a definite statistical law. This law of distribution is the same for all sizes of orbit. On the other hand, the time needed for equipartition of energy to bring this law about is not the same for all sizes of orbit; it is far greater for the compact orbits of the spectroscopic binaries than for the more open orbits of the visual binaries. The reason for this is that changes in the shape of an orbit are caused merely by the _difference_ of the gravitational pulls of a passing star on the two components of the binary. If the two components are very close together, the passing star exerts practically the same forces on both. These forces affect the motions of the two components in precisely the same way, with the result that the motion of the binary system as a whole through space is changed, but the shape of orbit remains unaltered. The passing star gets a grip on the motion of the binary as a whole, but none on the orbits of the components. On the other hand, when the components are far apart, the gravitational forces acting on the two may be widely different, so that a substantial change in the shape of the orbit may result, even if the encounter is not a very close one. In visual binaries, in which the components are usually hundreds of millions of miles apart, the time necessary to establish the final distribution of the “eccentricities,” by which the shapes of elliptical orbits are measured, is once again found to be of the order of millions of millions of years, but it is something like a hundred times as great as this for the far more compact spectroscopic binaries. The following table, compiled from material given by Dr Aitken of Lick Observatory, shews the observed distribution of eccentricities in the orbits of those binaries for which accurate information is available: _The Approach to Equipartition of Energy in Binary Orbits_ +-------------+--------------+----------+---------------------+ | | Observed |Observed |Number to be expected| |Eccentricity | number of |number of | theoretically | | of Orbits |spectroscopic |visual | when the | | | binaries |binaries | final state is | | | | | attained | +-------------+--------------+----------+---------------------+ | 0 to 0·2 | 78 | 7 | 6 | | 0·2 ” 0·4 | 18 | 18 | 18 | | 0·4 ” 0·6 | 16 | 28 | 30 | | 0·6 ” 0·8 | 6 | 11 | 42 | | 0·8 ” 1·0 | 1 | 4 | 54 | +-------------+--------------+----------+---------------------+