lanetary Motion, which have
always been associated with the name of their discoverer. The profound
skill by which these laws were elicited from the mass of observations,
the intrinsic beauty of the laws themselves, their widespread
generality, and the bond of union which they have established between
the various members of the solar system, have given them quite an
exceptional position in astronomy.

As established by Kepler, these planetary laws were merely the results
of observation. It was found, as a matter of fact, that the planets did
move in ellipses, but Kepler assigned no reason why they should adopt
this curve rather than any other. Still less was he able to offer a
reason why these bodies should sweep over equal areas in equal times, or
why that third law was invariably obeyed. The laws as they came from
Kepler's hands stood out as three independent truths; thoroughly
established, no doubt, but unsupported by any arguments as to why these
movements rather than any others should be appropriate for the
revolutions of the planets.

It was the crowning triumph of the great law of universal gravitation to
remove this empirical character from Kepler's laws. Newton's grand
discovery bound together the three isolated laws of Kepler into one
beautiful doctrine. He showed not only that those laws are true, but he
showed why they must be true, and why no other laws could have been
true. He proved to demonstration in his immortal work, the "Principia,"
that the explanation of the famous planetary laws was to be sought in
the attraction of gravitation. Newton set forth that a power of
attraction resided in the sun, and as a necessary consequence of that
attraction every planet must revolve in an elliptic orbit round the sun,
having the sun as one focus; the radius of the planet's orbit must sweep
over equal areas in equal times; and in comparing the movements of two
planets, it was necessary to have the squares of the periodic times
proportional to the cubes of the mean distances.

As this is not a mathematical treatise, it will be impossible for us to
discuss the proofs which Newton has given, and which have commanded the
immediate and universal acquiescence of all who have taken the trouble
to understand them. We must here confine ourselves only to a very brief
and general survey of the subject, which will indicate the character of
the reasoning employed, without introducing details of a technical
character.

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