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crude paralogisms of a vitiated metaphysics, setting themselves in opposition to the very postulates of all geometry, the truth of which we recognize by intuition, may pretend, that motion is a principle foreign to the nature of the subject ; we are not to rank these sciolisms among the things which the rigour of the most exact reafuning requires. On this head we concur with D'Alembert, whose 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 say of quantity, as he says of space; “ that no regard is to be paid to scholastic notions and subtilties relating to it.” And that the modern geometrician, who could not permit himself to admit as an hypothesis 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 absurd reasoner. These considera-, tions, 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 supposes quantity to be generated by motion;" for he replies by declaring, that it is a misconception on the part of his opponent; and he thereby admits that assumption to be an exception to the demonstrations of the Auxionary method founded on it, the point above contendedagainst,
Let us, however, examine his own defence against this charge. “What I effectively suppose in my theory is, that every quantity varying in magnitude continually and succesfively, ought to be regarded as having at every instant a tendency to change its state; and that its increments or decrements ought to be considered as effects resulting from it:" he further observes " that his theory is essentially dependent on the relation of the parts of time," because " the idea of time, has a necessary connection with that of succeffion.” And to this admission it must be added, that the idea of tendency has a necessary connection with that of a power or force producing it. That theory, therefore, necessarily includes the idea of time, and power, constant, or variable, each equally as foreign to that of quantity, in the abstract, as that of motion, which he so solicitously 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 investigated ; they may with geometrical rigour be represented by lines constant or variable as the subject requires. · But in the defence he had made against the objections to his analysis, he seems to have succeeded much better. Any algebraical expression of one or more terms, in all of which one variable quantity only is found, either without or com
bined with others that are constant, is called a function of that variable quantity: every such quantity, may have an indefinite nuber of such functions. And Mr. Stockler de. rotus in general any function of ♡ by F O: whence if w be augmented until it becomes o tw, its corresponding function will be F (DO + w): which converted into series becomes F(@t-w)= FO + p'w + p'w? + P111.23 &c. his cenfurer has objected to him, " that he has not demonftrated that the functions P', p", P' are independent of w, or derived from FØ; or that none but integer and positive powers of w can enter into the series.”
In answer to this he observes that the quantity 0 + w is a binomial; and assuming a proper series to represent Fø, or the functions of generally, he obtains by the usual methods of feries,
dF® 20 dd F© 22 di F® 73 3. F($+w=F¢+ - + - - - .
do 1. do 2 1.2. dọ3 1.2.3 Here ľ, , ľ" being respectively equal to d FC dd FO (FCO . -
---, are derived from FQ and indo 1.2.002 1.2.3 do? dependent of w the powers of which are true when the variable quantity O involves no fractional power of w, and when the contrary is the case he shows how it is to be gotten rid of out of the series.
This theorem was discovered by Dr. Brooke Taylor, and we admit with Mr. Stockler, that he has given a very elegant demonstration of it. We shall add that it is to be found in the 2d cor, of the 7th proposition of his Methodus Incrementorum : and, in a paper in the Philofophicai Transactions, he gives an account of the extensive uses of it, as furnishing excellent forms of approximation, « not only for equations of the common form, but which are also applicable to expreslions in general, wherein any thing is proposed, as given which by any known method might be computed ; if; vice versa, the roots were considered as given : such are all radical expressions 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 likewise expresfions of Logarithms, of arches by the fines and tangents, of areas of curves by the abscissas, or any other fluents, òr roots of fluxional equations, &c. and this he has illustrated with examples.” We have already considered this subject at much length,
but concur with Mr. Stockler, that the formula of La Grange as applied to finding the fuxions of powers, is nothing elfe than the Newtonian investigation of the same thing, dira guised and rendered less clear, but not totally obscured, because the covering has sufficient 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 profefsedly considers, 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 solid 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 remonstrates againft 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 history 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 essential and useful.” And to this Mr. S. professes in his defence to have chiefly confined himself. But there was a second and still more important point of view, under which the character of Mr. D'Alembert ought to have been surveyed : that is as the founder and leader of that literary faction, which became a band of conspiration against social order; whose crimes have produced the present distraction and miseries 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 those bad principles, the influence of which has produced all these calamitous effects fully devel. loped; some left in half concealment only; of as germs, that. the pernicious culture of others has reared into deadly poisons, By the spirit with which Mr. S. writes in a foreign language, we are certain he could have done that justice 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 elogė, 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, some of the writers in the journal he complains of, would have been disposed to treat it with the least abatement of asperity,
urope. Ac produced the ration againta terary factiofur
ART. XVI. Eulogium on General George Washington. By the Rev. - Mr. Meslinger ; delivered in the Meeting-House of old York. . i 1800. T E have before had occafion (Vol. V. p. 547.) to censure the
VV ádulatory, the fulsome, the false and impious praises be. ftowed on the late President of the American States, but if 'we and our readers were disgusted at the presumption, and thócked at the impiety of Mr. JACKSON, whose course of life' (he having been, it appears, an officer in the rebel army) might be an excuse for "his ignorance, and that ignorance some apology for the irreverence of his language, what plea can be offered in extenuation of the daring profanity of the Reverend Mr. Mellinger. We sincerely lament the necessity of making extracts from this Eulogium, but nothing that we can say will convey an adequate idea of the matter, which we feel it our duty to reprobate. ." If our tongue,” says this Reverend Ealogift, “ were an angel's it would faulter. If our eyes were fints, they would fwell with tears--If our heart were marble, it would bleed. If our soul were Zembla, it would melt and mournfor 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 harm. less extravagance of Tilburina, or of Queen Dollolola. We could see the “ great and good Washington” expire in" a farće, with as fitde anger as we behold the death of the great and gallant Wikeråndos," or as we hear of the lamentable catastrophe of the '"great and mighty Tom Thumb ;', but, the fequel of Mr. Meflinger's ravings, 'we cannot liften to without indignation and horror."
- Happily," continues this Meeting House orator, « Happily * for the human race, his translation was not in a chariot of fire ; * nor by any visible convoy of angels---but, by the secret power of "diffolution, which filently fprinkles its dalt on the body of mant
otherwise 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 sun is not darkened” (a folema truth), « the foundations of the earth do not tremble" another folemn truth], « rocks have not crumbled into dust” (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 · most impious lie), “ 'for the sons and daughters of liberty leaned on
his bofom and called him 'ABBA FATHER”!!!!!!!! And thus
Shocking as are the sentiments which have been üttéted on the life, and death of Walhington, they lofe half their depravity till the mofive, from which they have been, and still are, promulgated, is per. ceived. Could we believe in the fincerity of the eulogist, we should think less of their profanity. That which would, as Aowing from the transports of enthufiafm, excite our piry, 'rouses our indignation and abhörrence when we perceive it to be employed for the purposes of deception, and we' scruple not to assert, that, from the official eulogy, decreed by the Congress, down to the most despicable 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 Washington, I delivered in the State-House, át Trenton. By the Rev. Samuel
Stanlope Smith, D.D. 1800, IT YEARY as we are of orations on this subject, we cannot
W Tefrain from noticing that of Dr. Smith, who is, it would appear, a Diflenting Clergyman óf 'great weight in New Jersey, and 'a' writer of no'meán abilities.
Dr. Smith begins by 'observing, that'", other nationis open their eulogiums of great mến, by 'tracing their birth to some royal
house, or some noble family, and this, he says, " is the praise of - Naves." He, of course, disdains to exhibit any such retrospect :
had he not been so 'faltidious 'on this point, we might probably have learnt from him, that 'the General's paternal estate, '“ 'the peaceful shade of Mount Vernon," was a donation from the grandfatber of tbát Sovèreign, again't whom he had the ingratitude to - jebel.
From a reprobation of the praise bestowed on royal and noble familles, the oratór proceeds to enumerate the virtues, and the-gala lant exploits of his héro; and here he does not forget what was, indeed, the, principal object of his, as of all the other orations on this beaten fubject : wé méan, to awaken the prejudices, and revive, as far as poflible, the animosity of the people against Great*Britain. :
It was," says he's 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 her, rights, and her existence, againīt that
nation, become baughty and unjust, that he displayed the full tex. i tent, and variety, of his genius. Britain (the Americaris, Webm serve, never say Great Britain] had cherished her colonies in the nèw world merely as instruments of commerce, 'till their growing pro-, sperity rendered them, at length, an object both of avorite and ambition. She had already, in imagination, swallowed our treasures, : divided our provinces among ber, princes, our cities and fields dmontg ber mobles, and destined our busandmen to be tenants and labourers ofor ber," : Falfhood more grofs, rancour more implacable, never wore com ..PpL