1921 .] 
Astronomical Notes. 
137 
To fix ideas let us consider approximately spherical systems each 
10,000 light-years in diameter and having each a mass 100 million times 
that of the sun. Their encounter begins with a relative velocity of over 
100 miles per second, which rises to over 140 miles per second if the 
centres approach within 10,000 light-years of one another. If fusion of the 
two systems does not ensue the encounter will be over in about 360 million 
years. If only the outskirts pass through one another the two main 
systems may pass on, leaving a globular cluster formed of the colliding 
stars. But if the collisions due to the interpenetration are sufficiently 
numerous the effect may be to wed the two systems into one. 
In every case, however, the destruction of momentum due to the collisions 
must (by diminishing the rate of separation) increase the gravitational 
pull on the outer portions of the systems, and diminish the eccentricity 
of the orbits of the stars round the centre of the combined system. The 
orbits of particular stars in various parts depend on the distribution 
of density within the united mass. We may take as extreme cases that, 
on the one hand, in which the concentration is so great centrally that the 
mass beyond a certain distance is negligible, and that, on the other hand, 
in which the density of the combined system is approximately uniform. 
Fig. 1 shows the form of the resulting spiral in an intermediate 
imaginary case in which the mass within any distance from the centre is 
proportional to that distance. In this case the orbits have the same 
eccentricity. Consider four stars, A, B, C, D, which have reached 
simultaneously positions whose distances from the centre O are as 
