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crude paralogifms of a vitiated metaphyfics, fetting themselves in oppofition to the very poftulates of all geometry, the truth of which we recognize by intuition, may pretend, that motion is a principle foreign to the nature of the fubject; we are not to rank these fciolisms among the things which the rigour of the most exact reafoning requires. On this head we concur with D'Alembert, whofe authority there is a temporary propriety in recurring to, that "to arrive at an exact, we must not hunt after an imaginary rigour." We will fay of quantity, as he says of space; " that no regard is to be paid to fcholaftic notions and fubtilties relating to it." And that the modern geometrician, who could not permit himself to admit as an hypothefis or poftulate, that a right line can be conceived to be drawn on a plane from one point to another," is not to be called a rigorous but an abfurd reafoner. These considerations, however, form no part of Mr. H's own defence against the objection of the Monthly Reviewer, that "in the explanation of his own method, he fuppofes quantity to be generated by motion;" for he replies by declaring, that it is a mifconception on the part of his opponent; and he thereby admits. that affumption to be an exception to the demonftrations of the fluxionary method founded on it, the point above contendedagainft.

Let us, however, examine his own defence against this charge. "What I effectively fuppofe in my theory is, that every quantity varying in magnitude continually and fucceffively, ought to be regarded as having at every instant a tendency to change its ftate; and that its increments or decrements ought to be confidered as effects refulting from it:" he further obferves that his theory is effentially dependent on the relation of the parts of time," because "the idea of time, has a neceffary connection with that of fucceffion." And to this admiffion it must be added, that the idea of tendency has a neceffary connection with that of a power or force producing it. That theory, therefore, neceffarily includes the idea of time, and power, conftant, or variable, each equally as foreign to that of quantity, in the abftract, as that of motion, which he fo folicitoufly attempts to get rid of. And Mr. S. undoubtedly admits, that in the higher geometry, where the powers of nature and their effects are to be inveftigated; they may with geometrical rigour be represented by lines conftant or variable as the fubject requires.

But in the defence he had made against the objections to his analyfis, he seems to have fucceeded much better. Any algebraical expreffion of one or more terms, in all of which one variable quantity only is found, either without or com

bined with others that are conftant, is called a function of that variable quantity: every fuch quantity, may have an indefinite number of fuch functions. And Mr. Stockler derotes in general any function of by F: whence if w be augmented until it becomes +w, its correfponding function will be F(+): which converted into feries becomes F(+w) = F + P' w + P'' w2 + P!!! w3 &c. his cehfurer has objected to him," that he has not demonftrated that the functions P', P", P"" are independent of w, or derived from F; or that none but integer and pofitive powers of w can enter into the feries."

In answer to this he obferves that the quantity + w is a binomial; and affuming a proper feries to reprefent F, or the functions of generally, he obtains by the ufual methods of feries,

F(9+w)=FO+

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Here P, P, P" being respectively equal to

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, are derived from F and in

dependent of w the powers of which are true when the variable quantity involves no fractional power of w, and when the contrary is the cafe he fhows how it is to be gotten rid of out of the feries.

This theorem was difcovered by Dr. Brooke Taylor, and we admit with Mr. Stockler, that he has given a very elegant demonftration of it. We fhall add that it is to be found in the 2d cor. of the 7th propofition of his Methodus Incrementorum : and, in a paper in the Philofophical Transactions, he gives an account of the extenfive ufes of it, as furnishing excellent forms of approximation, not only for equations of the common form, but which are alfo applicable to expreffions in general, wherein any thing is propofed, as given which by any known method might be computed; if, vice verfa, the roots were confidered as given: fuch are all radical expreffions of Binomials, Trinomials, or any other nomial, which may be computed by the root given, or at least by Logarithms, what ever be the index of the power of that nomial; as likewife expreffions of Logarithms, of arches by the fines and tangents, of areas of curves by the abfciffas, or any other fluents, or roots of fluxional equations, &c. and this he has illuftrated with examples."

We have already confidered this fubject at much length,

but

but concur with Mr. Stockler, that the formula of La Grange as applied to finding the fluxions of powers, is nothing elfe than the Newtonian inveftigation of the fame thing, difguifed and rendered lefs clear, but not totally obfcured, because the covering has fufficient transparency. But we think his deduction of the fluxionary formulæ for drawing tangents to curves, finding their areas, and the other greater operations of that calculus, more complicated than those formerly in use. And here we cannot avoid noting that "he profeffedly confiders, in imitation of the ancient geometers, all lines formed by the motion of a point; to which he gives the name of the generating point," and again a superficies by the motion of a line, and a folid by that of a plane. As we have not his eloge of D'Alembert before us, we are unable to judge how far the critique upon it, which he remonftrates against is well or ill-founded. The general truth of the motto which he has taken for it, from D'Alembert himself, cannot be disputed: "that we ought to remember that the hiftory of celebrated literary men is that of their thoughts and of their writings only; and this part of an eloge on them, is the most effential and ufeful." And to this Mr. S. profeffes in his defence to have chiefly confined himself. But there was a fecond and still more important point of view, under which the character of Mr. D'Alembert ought to have been furveyed : that is as the founder and leader of that literary faction, which became a band of conspiration against focial order; whose crimes have produced the present diftraction and miferies of Europe. Accident had formerly drawn our attention to small parts of his works in that point of view, where we had there particularly noted many of thofe bad principles, the influence of which has produced all these calamitous effects fully develloped; fome left in half concealment only; or as germs, that the pernicious culture of others has reared into deadly poisons. By the fpirit with which Mr. S. writes in a foreign language, we are certain he could have done that juftice to this part of the character of D'Alembert in his own, which we doubt not but he has rendered to his literary abilities: but we perceive, by Mr. Stockler's account of the object of the eloge, he has not entered into this: had he made this his plan however, we cannot be certain that, if the execution had been a model of academical eloquence in conjunction with that of political morality, fome of the writers in the, journal he complains of, would have been disposed to treat it with the least abatement of afperity.

APPENDIX, VOL. VI.

PP

ART.

AMERICAN LITERATURE.

ART. XVI. Eulogium on General George Washington. By the Rev. Mr. Meffinger; delivered in the Meeting-Houfe of Old York.

1800.

WE

E have before had occafion (Vol. V. P. 547.) to cenfure the adulatory, the fulfome, the falfe and impious praifes beftowed on the late Prefident of the American States; but if we and our readers were difgufted at the prefumption, and fhocked at the impiety of Mr. JACKSON, whofe courfe of life' (he having been, it appears, an officer in the rebel army) might be an excufe for "his ignorance, and that ignorance fome apology for the irreverence of his language, what plea can be offered in extenuation of the daring profanity of the Reverend Mr. Meffinger. We fincerely lament the neceffity of making extracts from this Eulogium, but nothing that we can fay will convey an adequate idea of the matter, which we feel it our duty to reprobate.

"If our tongue," fays this Reverend Eulogift, "were an angel's it would faulter If our eyes were flints, they would fwell with tears-If our heart were marble, it would bleed-If our foul were Zembla, it would melt and mourn for Washington is no more!!!??

This hyperbolical rant, though intended for deception, we could treat with contempt. We could laugh at it, as we do at the harmlefs extravagance of Tilburina, or of Queen Dollolola. We could fee the "great and good Washington" expire in a farce, with as little anger as we behold the death of the "great and gallant Wifkerandos,"" or as we hear of the lamentable cataftrophe of the "great and mighty Tom Thumb ;" but, the fequel of Mr. Meffinger's ravings, we cannot liften to without indignation and horror.

"Happily," continues this Meeting-House orator, "Happily for the human race, his tranflation was not in a chariot of fire; nor by any vifible convoy of angels-but, by the secret power of diffolution, which filently fprinkles its daft on the body of manotherwife he might have been revered as a GOD. The globe might have bowed in the attitude of worship at the feet of his likeness ! ! ! ! !”

Yet is this not the worst." The fun is not darkened" [a folemu truth], "the foundations of the earth do not tremble" [another fo lemn truth],"rocks have not crumbled into duft" [another folemn truth], "the mountains have not melted away" [another folemn truth; but the veil of the temple of liberty is rent in twain" [a moft impious lie], "for the fons and daughters of liberty feaned on his bofom and called him ABBA FATHER"!!!!!!!! And thus winds up the bombaftical climax of blafphemy.

And fhall we, after this, be told of the high fpirit of republi cans?" Shall we, after this, be taunted with the charge of adulation to royalty? Where is the Prince, dead or living, of whom any culogift has dared to speak in the ftrain of this republican priest? Shocking

Shocking as are the fentiments which have been uttered on the life and death of Washington, they lofe half their depravity till the motive, from which they have been, and ftill are, promulgated, is perceived. Could we believe in the fincerity of the eulogift, we fhould think lefs of their profanity. That which would, as flowing from the transports of enthusiasm, excite our pity, roufes our indignation and abhorrence when we perceive it to be employed for the purpofes of deception; and we fcruple not to affert, that, from the official eulogy, decreed by the Congrefs, down to the most defpicable conventicle lamentation, the whole has been a féries of diffimulation, intended to amuse the populace of America, and to deceive the nations of Europe.

ART. XVII. An Oration upon the Death of Gen. George Wafbington, delivered in the State-Houfe, át Trenton. By the Rev. Samuel Stanhope Smith, D. D. 1800.

YEARY as we are of orations on this fubject, we cannot

appear, a Diffenting Clergyman of great weight in New Jersey, and a writer of no mean abilities.

Dr. Smith begins by obferving, that " other nations open their eulogiums of great men, by tracing their birth to fome royal houfe, or fome noble family," and this, he fays," is the praife of faves." He, of courfe, difdains to exhibit any fuch retrospect: had He not been fo faftidious on this point, we might probably have learnt from him, that the General's paternal eftate," the peaceful thade of Mount Vernon," was a donation. from the grandfather of that Sovereign, againt whom he had the ingratitude to

rebel.

From a reprobation of the praife 'beftowed on royal and noble families, the orator proceeds to enumerate the virtues and the gal lant exploits of his hero; and here he does not forget what was, indeed, the principal object of his, as of all the other orations on this beaten fubject: we mean, to awaken the prejudices, and revive, as far as poffible, the animofity of the people againft GreatBritain.

"It was," fays he," when America called him to the head of her armies, in the long and bloody war, which she was obliged to maintain, in defence of ber rights, and her existence, again that nation, become baughty and unjust, that he difplayed the full extent, and variety, of his genius. Britain [the Americans, we obferve, never fay Great Britain] had cherished her colonies in the new world merely as inftruments of commerce, 'till their growing profperity rendered them, at length, an object both of avarie and ambition. She had already, in imagination, fwallowed our treafures, divided our provinces among ber princes, our cities and fields among ber nobles, and destined our busbandmen to be tenants and labourers for ber." Falfhood more grofs, rancour more implacable, never were com

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