518 
Proceedings of Royal Society of Edinburgh. [sess. 
An example may illustrate this simple reasoning. Suppose a 
swarm of meteors approaches the star 0 from A in hyperbolic 
orbits. The perihelion distance of the inner particles is assumed 
to he less than the star’s radius E. These particles must im- 
pinge upon the star’s surface, where their further career will he 
checked ; i.e. Y 2 , which 
was greater than 
R 
immediately before 
the impact, will he zero after the catastrophe, supposing that the 
whole orbital motion has been transformed into heat. On the 
other hand, the orbital velocities of particles grazing the sur- 
face, though impeded by surface friction, will undergo much 
A. 
smaller reductions, while bodies sufficiently removed from the 
star may pursue their hyperbolic paths practically undisturbed. 
Hence we notice a gradual transition in the values of Y from zero 
to hyperbolic velocities, so that the swarm, although arriving at 
the star with practically uniform velocity, exhibits after the impact 
the most heterogeneous motions of its individual members. These 
new motions determine the character of the orbits described by 
those particles which are at all capable of escaping the star after 
impact. Since Y may have all possible values, the new orbits 
contain all possible conic sections, from the circle to the hyperbola. 
The important point is, that many of these new orbits are closed, 
the particles becoming permanently attached to the system of the 
