The Calculus at first found its chief supporters on the Continent. James and John Bernouilli, Varignon, author of the "Theory of Variations," and the Marquis de l'Hôpital, were the first to appreciate it; but soon it attracted the attention of the scientific world to such a degree that the frivolous populace of Paris had even a well-known song with the burden, "Des infiniment petits." Neither were opponents wanting. Wrong-headed men and thick-headed men are unfortunately too numerous in all times and places. One Nieuwentiit, a dweller in intellectual fogbanks, who had distinguished himself by proving the existence of the Deity in one of his works, made about this time what he doubtless considered a second discovery. He found a flaw in the reasoning of Leibnitz, namely, that he (Nieuwentiit) could not conceive of quantities infinitely small! A certain Chever also performed sundry singular mathematical feats, such as squaring the circle, a problem which he reduced to the single question, Construere mundum divinae menti analogum, and showing that the parabola, the only conic section squared by ancient or modern geometers, could never be quadrated, to the eternal discomfiture and discredit of the shade of Archimedes. Leibnitz used every means in his power to engage these 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 "Théorie des Fonctions," and that noblest achievement of the pure reason, the "Mécanique 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 "Mécanique Céleste" 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 organization,—when crowds of dullards all aflame with unexpected imagination assemble in ascension-robes to await the apocalyptic trump, and Asiatic polygamy spreads unmolested along our Western rivers,—when the prediction is accomplished, "Old men dream dreams and young men see visions," and the most practical of the ages bids fair to glide ghostly into history as the most superstitious,—it is well, it can but be well, to contemplate reverently that Reason, which Coleridge, after Leighton, calls "an influence from the Glory of the Almighty." In the contemplation of the spirit of man (not your animula, by any means!) there is earnest of immortality which needs not that one rise from the dead to confirm it. In view of the Foresight which guides men, we may trust that all this tumultuous sense of inadequacy in present institutions, this blind notion of wrong, far enough from intelligent correction, is, after all, better than sluggish inaction.
BULLS AND BEARS.
[Concluded.]
CHAPTER XXX.
The suspension of specie payments brought instant relief to all really solvent mercantile houses; since those who had valuable assets of any kind could now obtain discounts sufficient to enable them to meet their liabilities. Among those who were at once relieved was the house of Lindsay and Company; they resumed payment and recommenced business.
Mr. Lindsay lost no time in finding his clerk Monroe, and reinstated him with an increased salary. Great was the sorrow in the ragged school at the loss of the teacher; and it was with some regret that he abandoned the place. He felt no especial vocation to the career of a missionary; but his duties had become less irksome than at the beginning, if not absolutely pleasant. His own position, however, was such that he could not afford to continue in his self-denying occupation. Easelmann was one of the first to congratulate him upon his improved prospects.
"Don't you feel sorry, my dear fellow? Now you get upon your treadmill of business, and you must keep going, or break your legs. Think, too, of the jolly little rascals you have left! The beggars are the only aristocracy we have,—the only people who enjoy their dolce far niente. Look on the Common: who are there amusing themselves on a fine day, unless it be your Duke Do-nothing, Earl Out-at-elbows, Duchess Draggle-tail, and others of that happy class? Meanwhile your Lawrences, Eliots, and the 'Merchant Princes' (a satirical dog that invented the title!) are going about with sharpened faces, looking as though they weren't sure of a dinner. Oh, business is a great matter, to be sure! but the idlers, artists, poets, and other lazzaroni, are the only people that enjoy life."