the ancient
geometry. Not until subsequently was the analytical method resorted to
and cultivated. This method possesses the inappreciable advantage of
relieving us from the mental strain which would otherwise oppress us. It
has been truly said that the symbols think for us. [Sidenote: The
"Principia;" its incomparable merit.] Mr. Whewell observes: "No one for
sixty years after the publication of the 'Principia,' and, with Newton's
methods, no one up to the present day, has added any thing of value to
his deductions. We know that he calculated all the principal lunar
inequalities; in many of the cases he has given us his processes, in
others only his results. But who has presented in his beautiful geometry
or deduced from his simple principles any of the inequalities which he
left untouched? The ponderous instrument of synthesis, so effective in
his hands, has never since been grasped by any one who could use it for
such purposes; and we gaze at it with admiring curiosity, as on some
gigantic implement of war which stands idle among the memorials of
ancient days, and makes us wonder what manner of man he was who could
wield as a weapon what we can hardly lift as a burden."

[Sidenote: Philosophical import of Newton's discoveries.] Such was the
physical meaning of Newton's discoveries; their philosophical meaning
was of even greater importance. The paramount truth was resistlessly
coming into prominence--that the government of the solar system is under
necessity, and that it is mathematically impossible for the laws
presiding over it to be other than they are.

Thus it appears that the law of gravitation holds good throughout our
solar system. But the heliocentric theory, in its most general
acceptation, considers every fixed star as being, like the sun, a
planetary centre. [Sidenote: Unity of idea in the construction of the
universe.] Hence, before it can be asserted that the theory of
gravitation is truly universal, it must be shown that it holds good in
the case of all other such systems. The evidence offered in proof of
this is altogether based upon the observations of the two Herschels on
the motions of the double stars. Among the stars there are some in such
close proximity to each other that Sir W. Herschel was led to suppose it
would be possible, from observations upon them, to ascertain the stellar
parallax. While engaged in these inquiries, which occupied him for many
years, he discovered that many of these st