have given so unscientific a description of it. "The key-stone should be about or of the span, and the rest should increase in size all the way down to the impost; the more they increase the better." In the propositions, he considers the whole thickness at the vertex as so much wall standing upon a mathematical curve, in the same manner as Mr. Emerson does. Even in speaking of the arch of Blackfriars-bridge, he considers the whole thickness at the vertex as wall, and the arch, as he above defines it. The leading proposition of Emerson's theory, is thus: "The nature of a curve forming an arch being given, to find the nature of the curve, bounding the top of the wall supported by that arch, by the pressure or weight of which wall, all the parts of the arch are kept in equilibrio without falling." Here the arch is con. sidered as something given, not something to be discovered; it is true, if the arch is to be considered as of infinite thinness, it would be absurd for any useful purposes to attempt to determine its shape; but it would be mathematically proper to discover the infinitesimal increments from the vertex. If it is of some thickness, as practice requires, it is anomalous to set about determining what it shall bear, until it is itself determined; for its extrados is the curve upon which the Emerson theory proceeds to determine the wall to be placed upon it. As by this, or, rather as it may be sig. nificantly termed, the wall theory, the arch can have but an imaginary existence, it follows that in proportion as the arch is practically secure and stable by the increase, in consequence of the depth of the voussoirs, in that proportion it is insecure and unstable by the theory. What the wall is, as applied to bridges, which is to stand upon the arch, an architect would be at a loss to guess; but it is consistent that an imaginary wall should stand upon an imaginary arch. Were the wall theory the true theory, the propositions could have no applica tion in respect of bridges among scientific inen. The practice of arch-building from Michael Angelo at the Rialto, through the most enlightened architects on the Continent, to Mr. Labelye and Mr. Mylne, have been to increase each voussoir in depth, from the vertex to the springing: nor has there been wanting eminent mathematicians to confirm this principle, and the relative increase has not been a matter of guess; hence, if the arch have substance, the propositions of the wall theory must be framed anew to a novel series of curves; if the arch be spiritual, then the infinite ascension of the two points of the forked extradoses of the semicircular, elliptical, and cycloidal, arches, have properly intercourse with the aerial regions; or these, and the unicorn of the cissaid, might serve at Balniberbi, to prevent the descent of the flying island of Laputa. It is not difficult to conceive, that the mathematician who, in a mathematical work, could seriously give an account of an automaton which could play at chess, might have his risible faculties so organised as to be unsusceptible of the absurdities merely exemplified in the diagrams of this theory. But it is difficult to conceive that an enlightened philosopher should thus slander "most innocent Nature." "She, good cateress, means her provisions" for the uses of mankind : in the contemplation of a bridge, she could not have prescribed a form which would render it impassable; the bounty of Nature, in respect of bridges, has exceeded any other instance of her providence. What in other cases are impediments to perfection, in this instance are auxiliaries; what in other cases oppose the artist, and increase his errors, in this instance assist him, and are antidotes to his mistakes: could a semicircular or elliptical arch be built after the wall theory, cohesion and friction might prevent for a minute the ruin which, without their aid, must instantly ensue. The first proposition on which the whole of this theory depends, most certainly does not apply to the question of the equilibration of arches, and is not true in itself, as stated in the tracts in the support of this theory; it is still further from the truth than the proposition of the funicular polygon, acted upon in a vertical plane by weights in different points of the cord, when the weight of the cord itself is not taken into the account. In the question of an arch, it is all cord-all voussoirs. When the voussoirs balance each other, there is no wall but the parapet or fence-wall, which, it is hardly possible to believe, has been thought to be in the thickness the depth of the vault. The filling-in of the spandrels, is but another mode of balancing the voussoirs, or giving them the same perpendicular action, when from economy, or other causes, it has been judged expedient to give the arch-stones on the face the same depth. In this primary proposition, the tangential forces are neither neither opposite, nor are they equal; and those forces are assumed which are to be discovered, and that is to be found out which is given. In the question of the equilibration of arches, justly considered, some one force is given (generally that at the vertex, as there the perpendicular action is equal to its whole absolute gravity,) to find the two adjoining forces, or any others in the systein, which is precisely the question of the simple catenary, where there are no weights but those incorporated in the chain. The wall theory is a plagiary, garbled and misunderstood, from the familiar mechanical method of suspending from a chain bits of chain, their lower extremities forming a given line of roadway to determine the curve. This method is untrue, and could only be made to approximate to truth, as Dr. Robison has observed, by making the voussoirs bear the same proportion to the weight as the chain does to that of the bits of chain. The result from this operation is untrue, inasmuch as it differs from that of the simple catenaria. In the investigation of the catenaria, the powers considered were the absolute gravity of the particle, or link, “absolutam gravitatem particula Dd;" and that part of the gravity which acts per pendicularly, "gravitatis partem eam que normaliter in Dd agit:" now it is admitted by all, that the actions of the Voussoirs of an arch are similar to the links in a chain, and that the conclusion elicited from the one, that the action of gravity, perpendicularly exerted on the correspondent parts of the chain Dd, will be every where the same, "gravitatis actio in partes correspondentes catenæ Dd normaliter exerta etiam constans erit, sive ubique eadam," applies equally to the other. To produce an arch of equilibration, each voussoir, or the weight incorporated in each vous soir, requires to be increased, so that the Dr. Milner, in his answer to the Select Committee of the House of Commons, to questions submitted to him on this subject, most justly observes: "It is not from any error of computation, that erroneous practical inferences are apt to be made by the theorists; the errors almost always arise from the assumptions made at the setting out of the salution of the problem. Dr. Milner thinks he is within bounds in believing, that for one error in the fluxionary and algebraical part of calculations, a hundred have been made by discordant and unnatural hypotheses, respecting powers, forces, and modes of action." $ force exerted perpendicularly, may be every where the same; or that the same adjustment should be obtained by art in an arch which, in a chain suspended at its extremities, naturally appertains to it. The distinction between the weight and the chain is not real. A catenary may be formed of links of unequal weights, as well as of equal weights; though the curve would be different, the operation to discover that curve would be the same. Whatever the weight is, or wherever it is, it must be incorporated in the chain; and the perpendicular action of cach force, in a system of forces in equilibra tion solicited by gravity, whether an arch or chain, must be constant, or everywhere the same; and it is the constant force which must determine the other forces. Architects well acquainted with the facility to be derived on some occasions by the methods of investigation by algebra and fluxions, affect generally to disregard them as marks in their profession rather of speculative than real knowledge; but there would be no affectation in asserting, that they would as soon apply a theodolite to measure a cornice, as their knowledge of fluxions to the simple and plane theory of equili bration, and the easy proposition of describing the extrados of an arch of equilibration. There are mathematical hermits, as well as religious hermits; the common practices of mankind are mysteries to the one as well as to the other. There is also a superior order of learned men, who condescend to try their theoretical knowledge by the practice of the workmen, or their own experiments; in the praise of such men, the skilful builder will become an enthusiast; and from such men, he will be proud to acknowledge himself indebted for the best acquirements in his art. Mr. Thomas Simpson, in his answer to the three questions proposed by the Com mittee for building a bridge at Blackfriars, seems to reason on the subject not like a theorist, but an architect, notwithstanding that Emerson's notions had been published some time: indeed, throughout the papers published previ ously to the erection of Blackfriarsbridge, although Emerson volunteered his opinions to the public, they seem to have been wholly neglected; and they would have remained so to the present time, among other proposi tions, as the curious wanderings of a mathematician, had it not been for the doubly doubly-unfortunate dilapidations of the bridges on the river Tyne. Professor Robison certainly inserted the Emerson theory in the Encyclopædia Britannica, and at first held it in some esteem, out of respect to common opinion; for he really believed, from the mode in which it was introduced to the public, that it was the "common theory" of architects and builders. But from the article "Roof," to the article "Arch," in the Supplement, until we come to the conclusions of the latter, we perceive, in the gradual unravelling, how difficult it is long to deceive men who look beyond their own speculations and libraries for knowledge. Speaking of the fallacious ness of the theory, from the test of numerous experiments which he had been at the trouble and expense of making, he says, "But the clearest proof is, that arches very rarely fail, where their load differs most remarkably from that which this theory allows." And, again speak ing of those arches which have stood the test of ages, he says, "Here is a most remarkable deviation from the theory, for, as is already observed, the load is frequently not the fourth part of what the theory requires." The supporters of the wall theory say, and it is all which can be obtained in explanation of the theory, that they have "exploded" the wedge-theory, and that their theory is, "the true theory;" and that those who cannot "perceive the force of it, are ignorant and prejudiced." Permit me to recommend to your readers to peruse attentively the first proposition of Dr. David Gregory's paper on the catenaria; and to dwell on the second, and its corollaries; to turn in their mind Dr. Hooke's deduction, (decyphered) ut pendet continuum flexile, sic stabit contiguum rigidum inversum;" Dr. Johnson's three Letters; Mr. Simpson's Answer to the Committee for building Blackfriars Bridge; the Answer of the Monthly Review, (written, as Dr. Hutton states, by Mr. Woodhouse, now sufliciently eminent,) June, 1802; the Letters in Answer to your Review, and the Monthly Review, in the Monthly Magazine, August and October, 1802; they will then exclaim, in the words of the commencement of one of Dr. Johnson's Letters, “It is the common fate of erroneous positions, that they are betrayed by defence, and obscured by explanation; their authors deviate from the main question into incidental disquisitions, and raise a mist where they should let in light." If there were wanting any instances of the absurdities which great and eminent men have been led into by the modern analysis, when they have not been sufficiently attentive to deter mine the truth of the first proposition, depending merely on the principles of mechanics, Emerson's Extradoses of Arches, and especially of domes, would stand like the full and perfect warning which a wreck offers to the heedless mariner; his charts and books lying ne glected in his chest. Not even those on whom the authority of the Woolwich Academy has imposed Emerson's theory of arches, can contemplate with a serious countenance, the monstrosities of his conclusions in respect of domes. It is difficult for a mason to resist exclaiming, in this instance, "Multos se deliros senes sæpe vidisse, sed qui magis, quam Phormio, deliraret, vidisse neminem!” The methods by analysis and geometry, resemble the progress of a young and an old hound. The former, if he get a right scent, and keep it, will soon overtake the pursued; but, on a wrong scent, his ficetness but removes him further from the object: the old hound is oftener in at the death, and is always near the victim. Notwithstanding the importance which has been attached by mathematicians to the question of the equilibration of arches, it is a question of little worth to the builder, in comparison with that of the piers. On this part of arch-building little has been written, and still less understood, except by those who have been nursed in the practice. Should you think the above worth inserting in your Magazine, and hold of any value the theory which has in fact been, from the first arch which ever stood, the theory which has guided the builder, though unconscious of the extent of his knowledge, and which I have attempted to detail from Dr. Gregory's paper, and Dr. Hooke's conclusion; I shall, at my leisure, send you a paper on the subject of piers; shewing their properties involved, and dependent on the accurate reasoning of Gregory and Hooke, in which an extraordinary va riation between false theory and true practice, extracted from the second Report of the Committee of the House of Commons on the Holy-head Roads and Harbour, printed June, 1810, may further illustrate this subject. LAPICIDA. P.S. See letters on this subject, Monthly Magazine, Sept. 1809, Nov. 1809, Aug. 1810, and Nov. 1810. Το To the Editor of the Monthly Magazine. A SIR, MONG the curious productions of nature and art, lately deposited in the Hunterian Museum, at Glasgow, as mentioned in your last Number, page 161, are "specimens of the only two meteor-stones that are known to have fallen in Britain, viz. one in Yorkshire, 13th of December, 1795; another at Possil, near Glasgow, 5th of April, 1804." From the above information, I should suppose, that the instances of such stones being known to fall from the clouds are very rare, at least in our own country. It may be interesting to some of your readers, to hear of a third well-authenticated instance. On the 17th of May, 1806, as Mr. William Paice, of Basingstoke, Hants, was travelling with his cart a few miles from home, he met a person who enquired of him, whether he had seen a stream of fire descend from the air, like what is called a falling star; there having been some thunder just before. Mr. Paice had not observed it; but, going on a little farther, he found a large ball, or stone, on the middle of the road, which he took up while it was yet hot, threw it into his cart, and brought it home. Its external appearance resem bles a metallic substance, similar to those stones sometimes met with in the fields, and denominated thunder-stones. This ball weighs two pounds and a half, and is preserved for the inspection of the curious. The writer of this article is in possession of several others of the same kind. It may not be unknown to some of your philosophical readers, that the celebrated French philosopher, La Place, has given some reasons to show the probability of such stones being discharged from some great volcanoes in the moon, J. JEFFERSON. Basingstoke, March 5, 1811. To the Editor of the Monthly Magazine. SIR, HE remarks of the Enquirer, in THE your Magazine for February, page 5, respecting religious toleration, as far as they relate to its justice and political utility, are judicious; but the means by which he proposes to effect it, do not appear to me to be equally so. Nay, they seem not only inadequate to the attainment of the end the Enquirer has in view, but even subversive of it: for they seem calculated to subject the members of the established church to a species of intolerance equally novel and oppressive, without being likely to prove beneficial to dissenters of any description. To aid the cause of religious toleration, he proposes that the patron of a rectory should be at liberty to present a clergyman to it of the religion he himself professes; that a Goldsmid should present a rabbi; a duke of Grafton, a Unitarian; a lord Petre, a Catholic. I have yet to learn, how the right to present a rabbi to a rectory could, in any degree, promote the cause of toleration, unless the greater proportion of the parishioners professed the Jewish religion as well as the patron; which, whatever may be the aggregate number of Jews in England, is probably not the case in a single parish in the kingdom. Such a measure might gratify the pride of one individual, and increase the income and comforts of another; it might please the patron, and enrich the rabbi; but the object to be attained by the proposed measure, is of a widely different nature. The free and equal exercise of their religion, by persons of all persuasions, with the possession of an equal political importance, and a permanent support for their clergy, are the legitimate objects of toleration, and not the exaltation of one sect by the depression of another. Then let us ascertain if this end be likely to be attained, by the means the Enquirer proposes. There are many parishes, particularly in the country, in which not a single Jew resides. Suppose the living of such n parish were in the gift of a Jew, and he were to bestow it upon a rabbi, would this, in any shape whatever, promote the cause of toleration? Would it not rather have the very contrary effect? The parishioners must then either go to church, and join in the ceremonies of a strange religion, with the mysteries and language of which they are wholly unacquainted, or be altogether deprived of the means of attending divine worship. Thus, the most complete intolerance would be the result of the very means by which the Enquirer proposes to effect the contrary end. The same observations will, under similar circumstances, apply with equal force to the presentation to rectories of the clergyman of any other religion, except the established one. If a patron of a living, who is of a different religion from the established one, be desirous, by means of his patronage, of ameliorating the condition of the clergy of his own religion, the opportunity exists of doing so, without injuring the parishioners, or driving them from the church in which they have been accustomed to attend divine worship. Let him sell the advowson, or should he be reluctant wholly to part with it, let him sell the next presentation, which he may legally do; and with the money it produces, create an income for the sup port of a clergyman of the religion of which he is a member, to officiate either in his own immediate neighbourhood, or wherever else his religion may most prevail. This, he and his family may repeat on every ensuing presentation; and the money thus produced, may be employed to encrease the income of the clergyman already created; to found a fresh one; or in the erection and repair of chapels, for such clergymen to officiate in. H. February 17, 1811. To the Editor of the Monthly Magazine. I SIR, HAVE read with much satisfaction, in your last Number, the celt brated trial of William Penn and William Mead, and believe there are many of your readers who will agree with me, that at no time, from the æra of the glorious Revolution to the present awful crisis, a republication of it was more necessary. I am not alone in the opinion, that the violent and arbitrary conduct of the magis trates, who, at that juncture, sat on the bench, fully confirmed the well-known dictum of a celebrated author, that “summum jus est summa injuria,” After having made these few cursory remarks, it seems proper to add, that the gentleman who sent that article to your Magazine, has, through inadvertency or misinformation, been guilty of a mistake respecting the great William Penn. He was committed a prisoner to the Tower, not for writing No Cross No Crown, but for a publication entitled, “The Sandy Foundation Shaken," in which the commoniy-received doctrines of the Trinity were explained in a different manner from the creed of St. Athanasius and his adherents, though he explicitly owns the doctrine of the divinity of Christ." "With his prison hours he enriched the world;" for the well-known treatise, Penn's Letter to Dr. Arlington, in his I.ife. Select Works. page 5. "No Cross No Crown," was written during his confinement; a work which the learned and pious Dr. Henry More, in a letter to the author, says, he looks upon as a serious book, and very pious in the mein," though he differs from the author with regard to titles and ceremonies. He also acknowledges that "a soul well awakcued unto a sense of the best things, can scarcely want any external director or monitor; but the quaker's principle is the most safe and seasonable to keep close to the light within a man.”* It must give pleasure to a large circle of your readers, to be informed that a Life of the great William Penu, s prepa ring for the press, by a person well qualitied to do the subject justice; and as he will doubtless have recourse to a great number of letters and manuscript papers in different hands, and other original documents, much entertainment, as well as instruction, may be expected from the publication; and perhaps some of your a readers, who enjoy the friendship of the gentleman in question, may give us information whether the intended Life is in forwardness. BENEVOLUS. Murch 5, 1811. To the Editor of the Monthly Magazine. SIR, AVING lately had the pleasure of Canterbury, I was induced (as formerly) to attend divine service at some parishchurch in the week days: accordingly, I resolved to go to St. Margaret's on the Friday, at the usual time of prayers; but alas! the doors were shut. Upon inquiring the cause of it, I was informed that the week day's duty had been discontinued for many years. This was my first disappointment. On the Wednesday following, I was determined to pay a visit to the church of St. Alphage, where the late rector never omitted the weekly duty without sufficient grounds; and where the congregation used to be a very decent and respectable one. But here, alas! the doors were shut. On the Friday, I sallied forth to St. George's church, where, to my great comfort, I found the doors open, and a congregation devoutly assembled for the purpose of offering up their prayers and praises to Almighty God. This, I am sorry to find, is the only parish-church in the large and populous city of Canterbury, where the Life of Dr. Henry More. By R. Ward, A.M. page 247, page 310, London 1710. weekly |