We may illustrate the matter by supposing the planet to be running
like a railway engine on a track which has been laid in a long
elliptic path. We may suppose that while the planet is coursing
along, the shape of the track is gradually altering. But this
alteration may be so slow, that it does not appreciably affect the
movement of the engine in a single revolution. We can also suppose
that the plane in which the rails have been laid has a slow
oscillation in level, and that the whole orbit is with more or less
uniformity moved slowly about in the plane.
In short periods of time the changes in the shapes and positions of
the planetary orbits, in consequence of their mutual attractions, are
of no great consequence. When, however, we bring thousands of years
into consideration, then the displacements of the planetary orbits
attain considerable dimensions, and have, in fact, produced a
profound effect on the system.
It is of the utmost interest to investigate the extent to which one
planet can affect another in virtue of their mutual attractions. Such
investigations demand the exercise of the highest mathematical
gifts. But not alone is intellectual ability necessary for success
in such inquiries. It must be united with a patient capacity for
calculations of an arduous type, protracted, as they frequently have
to be, through many years of labour.
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