Newton's method of calculating the precession of the equinoxes,
already referred to, is as beautiful as anything in the _Principia_.
He had already proved the regression of the nodes of a satellite
moving in an orbit inclined to the ecliptic. He now said that the
nodes of a ring of satellites revolving round the earth's equator
would consequently all regress. And if joined into a solid ring its
node would regress; and it would do so, only more slowly, if
encumbered by the spherical part of the earth's mass. Therefore the
axis of the equatorial belt of the earth must revolve round the pole
of the ecliptic. Then he set to work and found the amount due to the
moon and that due to the sun, and so he solved the mystery of 2,000
years.

When Newton applied his law of gravitation to an explanation of the
tides he started a new field for the application of mathematics to
physical problems; and there can be little doubt that, if he could
have been furnished with complete tidal observations from different
parts of the world, his extraordinary powers of analysis would have
enabled him to reach a satisfactory theory. He certainly opened up
many mines full of intellectual gems; and his successors have never
ceased in their explorations. This has led to improved mathematical
methods, which, combined with the greater accuracy of observation,
have rendered physical astronomy of to-day the most exact of the
sciences.

Laplace only expressed the universal opinion of posterity when he said
that to the _Principia_ is assured "a pre-eminence above all the
other productions of the human intellect."

The name of Flamsteed, First Astronomer Royal, must here be mentioned