to religion, and cultivate an incredulous
spirit,--such as would never for a moment listen, let us hope, to any
theory which proclaims this green earth and all the universe "such stuff
as dreams are made of," even though the doctrine be ecclesiastically
sustained and backed with abundant wealth of learning. Numerous were the
defenders, called out rather by the acknowledged metaphysical ability of
Bishop Berkeley than by any transcendent merit in these two tracts; and
among others came Maclaurin.

Taylor's Theorem, based upon that first published by Maclaurin, is the
foundation of the Calculus by La Grange, differing from the methods of
Leibnitz and Newton in the manner of deriving the auxiliaries employed,
proceeding upon analytical considerations throughout. Of his "Theorie
des Fonctions," and that noblest achievement of the pure reason, the
"Mecanique Analytique," we do not propose to speak, nor of the later
developments of the Calculus, so largely due to his genius and labors.
These are mysteries, known only to the initiated, yet capable of raising
their thoughts in as sublime emotion as arose from the view of the
elder, forgotten mysteries, which Cicero deemed the very source and
beginning of true life.

We have seen how, and through whose toil, this mightiest instrument of
human thought has reached its present perfection. Now, its vast powers
fully recognized, it has become interwoven with all Natural Philosophy.
On its sure basis rests that majestic structure, the "Mecanique Celeste"
of La Place. Its demonstration supports with undoubted proof many
doctrines of the great Newton. Discovery has succeeded discovery; but
its powers have never yet been fully tested. "It is that field of
mathematical investigation," says Davies, "where genius may exert its
highest powers and find its surest rewards." Looking back through the
long course of events leading to such a magnificent result, looking up
to that choral dance of wandering planets, all whose courses and seasons
are marked down for us in the yearly almanac, can we not find in these
manifestations something on the whole quite wonderful, worthy of very
deep thankfulness, heartfelt humility withal, and far-reaching hope?

In an age of many-colored absurdity, when extremes meet and
contradictions harmonize,--when men of gross, material aims give
implicit confidence to the wildest ravings of the supernatural, and
pure-minded men embrace French theories of social organi