which it may pass. Commonly the
action will be so slight as to have little influence on the orbit and
the time of revolution. But should the comet chance to pass the orbit of
Jupiter just in front of the planet, its motion would be retarded and
the orbit would be changed into one of shorter period. Should it pass
behind the planet, its motion would be accelerated and its period
lengthened. In such cases the orbit might be changed to a hyperbola, and
then the comet would never return. It follows that there is a tendency
towards a gradual but constant diminution in the total number of comets.
If we call [Delta]e the amount by which the eccentricity of a cometary
orbit is less than unity, [Delta]e will be an extremely minute fraction
in the case of the original orbits. If we call [+-][delta] the change which
the eccentricity 1 - [Delta]e undergoes by the action of the planets
during the passage of the comet through our system, it will leave the
system with the eccentricity 1 - [Delta]e [+-] [delta]. The possibilities
are even whether [delta] shall be positive or negative. If negative, the
eccentricity will be diminished and the period shortened. If positive,
and greater than [Delta]e, the eccentricity 1 - [Delta]e + [delta] will
be greater than 1, and then the comet will be thrown into a hyperbolic
orbit and become for ever a wanderer through the stellar spaces.

The nearer a comet passes to a planet, especially to Jupiter, the
greatest planet, the greater [delta] may be. If [delta] is a
considerable negative fraction, the eccentricity will be so reduced that
the comet will after the approach be one of short period. It follows
that, however long the period of a comet may be, there is a possibility
of its becoming one of short period if it approaches Jupiter. There have
been several cases of this during the past two centuries, the most
recent being that of Brooks's comet, 1889, V. Soon after its discovery
this body was found to have a period of only about seven years. The
question why it had not been observed at previous returns was settled
after the orbit had been determined by computing its motion in the past.
It was thus found that in October 1886 the comet had passed in the
immediate neighbourhood of Jupiter, the action of which had been such as
to change its orbit from one of long period to the short observed
period. A similar case was that of Lexel's comet, seen in 1770.
Originally moving in an unknown orbit, it encou