230 RESULTS OF RECENT RESEARCHES ON THE 
the system revolves as a rigid body. This last condition cannot come about while the 
stars are still contracting and shining by their own light, and hence all visible systems 
are characterized by highly eccentric orbits. 
To leave no doubt that tidal friction is a sufficient cause to account for the elongation 
of the orbits of the double stars, I applied the theory to a special case, in which the 
masses, distances and velocities are known. Taking two spheroidal fluid masses each 
three times as large as the sun, expanded to fill the orbit of Jupiter, and set revolving in 
an orbit of 0.1 eccentricity at a mean distance of 30 astronomical units, I find that by 
tidal friction the major axis of the orbit will be increased to 48 astronomical units, while 
the eccentricity will rise to 0.57. In this problem the masses are set rotating at such a 
rate as will produce an oblateness of about 2, so that the equilibrium is stable. Different 
conditions will produce different results, but it is easy to see by this numerical example 
that tidal friction is a sufficient cause to account for the observed elongation of the 
orbits of double stars. 
Though it may be supposed that there could be little doubt of the generality 
of the law of the eccentricity which I inferred in 1888, yet the importance of this 
fundamental fact of the universe is so great that I did not feel satisfied till all the obser- 
vations of double stars had been examined anew and this conclusion touching the 
eccentricity established upon the most unshakable foundation. At length I have been 
enabled to show by the most exhaustive investigation of stellar orbits ever attempted, that 
the most probable eccentricity is 0.48; while on the other hand extremely eccentric and 
extremely circular orbits are equally rare, and must be referred to some unusual cireum- 
stances. Thus of the 40 orbits now well-known, it turns out that none lie between the 
eccentricities 0.0 and 0.1; two between 0.1 and 0.2; four between 0.2 and 0.3; eight 
between 0.5 and 0.4; nine between 0.4 and 0.5; nine between 0.5 and 0.6; two between 
0.6 and 0.7; four between 0.7 and 0.8; two between 0.8 and 0.9, and none between 0.9 
and 1.0. It follows therefore that by whatever process the stars developed, their orbits 
assumed a form which is about a mean between the nearly circular orbits of the planets 
and the extremely elongated orbits of the periodic comets. 
Now a double star can originate by but one of two processes: either such a system 
is the outgrowth of the breaking up of a common nebula, or it is made up of separate 
stars brought together in a manner analogous to that involved in the capture of a 
comet. That these systems are not the outgrowth of accidental approach of separate 
stars we may at once affirm; for if we suppose them to be so produced, there being 
no third disturbing body which acts like the sun in the capture of comets, the 
captured star would recede to a distance equal to that from whence it came. In that 
eyent we should observe stars moving in paths of very immense extent, and consequently 
