worthy adversaries in a contest concerning his Calculus, but unfortunately failed.  Bishop Berkeley, too, author of the “Essay on Tar-Water,” devout disbeliever in the material universe, could not resist the Quixotic inclination to run a tilt against a science which promised so much aid in unveiling those starry splendors which he with strenuous asseveration denied.  He published, in 1754, “The Minute Philosopher,” and soon after, “The Analyst, or the Discourse of a Mathematician,” showing that the Mathematics are opposed 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?