change resulted, either from ascensive or descensive opinion, the chance would be in favor of increased harmony. Probably not many congregations would undertake or undergo any alteration at all. The Enquirer, however, attaches little value to a conformity of opinion between clergy and people. In his idea the teachers ought to be a wiser order of men, and to hold a purer creed than the multitude, and to be at liberty to say so. Angels of heaven, they should be constanly lifting the erring dupes of fanaticism out of the mire of 'superstition, and cleansing them for the serener region of truth. Be it left to sects to elect ministers down to their own narrow bigotries, and credulous articles of faith; but let the magis trate not impede the progress of in struction. The pursuers of uniformity, to have any prospect of success, must always prefer the average creed of the people to the creed of the enlightened class: knowing a better, they must choose a worse, religion; and, perpetually fire from a double battery at superior illumination, and at groping blindness. Happily uniformity is as impracticable as it is unnatural; and, wherever there is tolerance, different sects are found to arise suited to the various shades of insight and hues of temper prevalent among men. This is best for the public; the great awakener of intellect is controversy; where there is no discord, no competition, the stimulus to acquire learning and to display eloquence, is wanting. Spain, Portugal, Italy, have sunken in the rank of literary nations, for no other reason than because an universal consentaneity of religious profession was exacted by the guardians of the press. Water, if stagnant, putrifies; but, whether it ebbs or flows, it diffuses lustre and fertility. It is so with the tide of opinion. The true interest of the magistrate is to subdivide society into sects so numerous, that no one of them shall include a majority of the people, or be so powerful as a coalition of the rest. Toleration is in that case the permanent interest of all denominations of persuasion, and is likely to be inforced by the sovereign, with the concurrence of all religious parties. What method so conducive to this desirable multiplication of heresies, as a repeal of the Act of Uniformity? MONTHLY MAG, No. 213, com There is nothing in the historic origin of this act to render its stability honourable. In the year 1662 a bill was brought into the house of mons on the 14th of January, and carried by a majority of 186 to 180, which provides that all and singular ministers shall be bound to say and use the morning prayer, evening prayer, and all other common prayers, in such order and form as is mentioned in the Prayerbook; and that all such ministers as omit declaring on or before the following 24th August, being the feast of Saint Bartholomew, their unfeigned assent and consent to all and every thing contained in and prescribed by the book shall, ipso facto, be deprived of all their spiritual promotions." This law soon introduced a monotonous uniformity of worship throughout the parish churches of England. Seven months were found sufficient for the conversion of ninetenths of the clergy to the agreed for mulas. About two thousand priests were ejected from their benefices by the regulation. The act of uniformity was to have been a compromise between the epis copalian and the presbyterian clergy, who professed to be willing to accom modate one another, provided those intolerable sects, (as Baxter called them) the Papists and Socinians, could be effectually excluded. The terms of comprehension were for a long time dis cussed; but, as soon as the king had received his crown at the hands of the episcopalians, these conferences were closed. The king, in a declaration issued prior to his coronation, had expressly promised, that half of the chapter attached to each see, should be elected by the Presbyterians; but this introduction of the elective principle into the constitution of the legal hierar chy, which would have rendered the church more independent, was offered during the conferences at the Savoy. never The Calvinists waved every frivolous difficulty: they agreed to accept liturgic forms of worship; they agreed that the ecclesiastic superinten dents should be called bishops. But the Bucerists retracted the very promises made under the signature of their king; and scrupled not at having obtained the co-operation of a great party, by the offer and promise of concessions, no one of which was eventually to be realized, Preferment was offered with profuse profuse liberality to Baxter, Calamy, and others of the Presbyterian party; but they were in return expected to sell themselves entire to the sect which had so basely defrauded them, by violating engagements the most solemn. Their noble disinterest rejected all hushhire. The purest atonement which can now be made for the perfidy, is to repeal the act of uniformity, and to open the church to the defrauded sectaries. The most important feature of the Enquirer's plan is however not its ecclesiastic operation. An alert statesman would have perceived in it the only practicable way of enabling government to avail itself of those revenues of the church, which are in the gift of the crown, for purposes of civil patronage. Without any infringement of private property, with new indulgence to private judgment, it would enable the minister to give among Edinburgh and Quarterly Reviewers, the prebendal stalls and sinecure preferments of the church, and thus render needless many an increase of the pension-list. 1. Theorists consider "the whole thickness at the vertex as so much wall standing upon a mathematical curve." 2. Emerson's leading proposition is, to find the extrados from a given intrados. 3. This proposition is not true, nor does it apply to the question, because its result "differs from that of the simple' catenaria." 4. "The authority of the Woolwich Academy has imposed Emerson's Theory of Arches," but the true theory is that, which Lapicida" attempts to detail from Dr. Gregory's paper, and Dr. Hooke's conclusion." 5. Dr. Robison admitted the fallaciousness of the theory, and adduced, as the "clearest proof of it, that arches very rarely fail where their load differs most remarkably from that which this theory allows." 6. The theory of domes, founded upon the same principles of equilibration, stands "like the full and perfect warning which a wreck offers to the heedless mariner.” 7. The theory of piers "is a part on which little has been written, and still To the Editor of the Monthly Magazine. less understood, except by those who A SIR, LAS! Mr. Editor, how melancholy it is to trace the progress of poor Lapicida's disorder! A year and a half ago I administered some medicines, and pointed out a regimen, that I hoped would have proved salutary, and ultimately have restored the patient. But the equilibratio-phobia, under which he labours, having not yet been introduced into any of our modern systems of nosology, it is certainly difficult to know when to form a favourable prognosis. The disorder, however, seems now rapidly hastening to a crisis; but the cacoethes scribendi, with which the poor gentleman has been all along troubled, is a most unfavourable symptom. Like Gratiano, he talks an infinite deal of nothing, more than any man in all Venice. His reasons are as two grains of wheat, hid in two bushels of chaff; 'you shall seek all day ere you find them; and when you have them, they are not worth the search." I have gone through his last paper, which you have indulged with insertion in your Magazine for this month, (April) in order to pick out this grain or two, which he sets against the genuine theory of equilibration, and here they are. have been nursed in the practice." 8. "The methods by analysis and geometry, resemble the progress of a young and old hound." 9. "There are mathematical hermits," to whom "the common practices of mankind are mysteries." Now, in replying as briefly as possible to these, allow me to say, First. That in Gregory's Mechanics, page 141, vol. 1, there may be seen a demonstration of this proposition: "The force of a voussoir depending on the magnitude of the angle, formed by its sides, the impelling force, and the resistance to be overcome, is on the first account directly as the radius of curvature of the arch at that point; on the second, as the square of the sine of the angle, included between the tangent of the curve at the given point, and the vertical line passing through that point; and on the third, as the sine of the same angle." From this proposition the obvious corollary is deduced, that "if the height of the wall incumbent on any point of the intrados, is directly as the cube of the secant of the angle, formed by a tangent to the voussure at the given point with the horizon; and inversely as the radius of curvature; all the voussures will endeavour to split the arch with equal forces, and will be in perfect equilibrium with each other." Here the theorist does not consider, as Lapicida pretends, "an imaginary wall upon an imaginary arch," but a load upon voussoir; and yet the proposition corresponds accurately in its results with those of Dr. Hutton, in his book on Bridges, as Dr. Gregory proves immediately after. Secondly. Though Emerson left the theory imperfect, as he found it, Dr. Hutton does not. He gives a general proposition to determine the intrados from a proposed extrados, and illustrates it by some of the most useful examples. Thirdly and fourthly, the results of a theory differing "from that of the simple catenaria," are no proofs of its inaccuracy. Here both Lapicida's autho. rities are against him, though he is so lamentably ignorant of the subject as not to be aware of it; as I shewed at page 362 of your valuable Magazine for November, 1809; to which I now refer, in order to avoid repetition. But I must be permitted to remark, that if Lapicida's malady had not been of the most desperate kind, the wholesome dose I then administered, would have produced a perfect cure. Fifthly. The instances of failure adduced by Dr. Robison, have nothing to do with the question, as I shewed in the Magazine, and at the page just referred 10. But it is, on the contrary, perfectly in point to remark, that in semicircular arches with rectilinear extradosses, ei ther horizontal or sloping on both sides to meet over the vertex, it is constantly found that, after the centring of such arches is struck and removed, they settle at the crown and rise up at the flanks: for this is exactly what the true theory of equilibration, against which Lapicida so absurdly cavils, would lead us to expect. Sixthly. Dr. Robison, another of Lapicida's authorities, gives evidence directly in his teeth, on the subject of Domes. For, in the article ARCH, (Sup. Ency. Britan.) he applies exactly the same theory of equilibration, to investigate the properties of Domes; I say the same theory, though a few additional principles are called in: he shews to what extent a deviation from true equilibration may be allowed, and why; and illustrates his positions by references to some remarkable structures, such as the dome of St. Paul's, the Halle du Bled at Paris, &c. Seventhly. The theory of piers has been stated accurately by at least four authors; namely, Drs. Hutton and Gregory, M. M. Bossut and Prony. I will assert farther, that the most candid, skilful, and experienced of those who have been "nursed in the practice," are ready to acknowledge, that in general they give to the piers full twice the substance they apprehend may be necessary, because of their uncertainty as to what is actually required for stability. Eighthly. Whatever, in Lapicida's estimation," the methods by analysis and geometry" may resemble; the fact is, that the principles of equilibration are always deduced from a simple and very elementary application of geometry, to the composition and resolution of forces; and that the fluxionary processes only arise in the solutions of problems which cannot be touched in any other way, except by a gross approximation. "mathe Ninthly. With regard to matical hertnits," to whom "the common practices of mankind are myste rious," few of them seem to have meddled with the theory of arches. Dr. Hutton, the author against whom Lapicida levels his ill-directed fire, is notorious, for his having, for a series of years, united theory with practice, to an extent never exceeded, and perhaps never equalled by any other man since the time of Archimedes. We owe to him, to his judiciously blending theory with experiment, all extant that is worth knowing on the subject of gunnery: and he has done more, both as a man of science, an engineer, and an architect, to improve and confirm the only tenable theory of arches and piers, than any other philosopher. Whence theu ori ginates this incessant tendency on the part of men who are not able to read (and of course not to estimate) a tenth of his writings, to depreciate and despise them? His Essay on Bridges, though published as a hasty imperfect attempt, contains more valuable and correct propositions on the subject, than can be collected from the performances of all the mathematicians who have attended to it. I hope and trust he will extend his researches on this interesting branch of enquiry, in the edition of his Tracts now announced, (I perceive) as publishing; for I doubt not, the result of his enquiries for so many years, will place the subject in a flood of light, will shew in what points all various theories, sup. posed by infants in science to differ, in fact agree, in what points authors sup posed profuse liberality to Baxter, Calamy, and others of the Presbyterian party; but they were in return expected to sell themselves entire to the sect which had so basely defrauded them, by violating engagements the most solemn. Their noble disinterest rejected all hushhire. The purest atonement which can now be made for the perfidy, is to repeal the act of uniformity, and to open the church to the defrauded sectaries. The most important feature of the Enquirer's plan is however not its ecclesiastic operation. An alert statesman would have perceived in it the only practicable way of enabling government to avail itself of those revenues of the church, which are in the gift of the crown, for purposes of civil patronage. Without any infringement of private property, with new indulgence to private judgment, it would enable the ininister to give among Edinburgh and Quarterly Reviewers, the prebendal stalls and sinecure preferments of the church, and thus render needless many an increase of the pension-list. 1. Theorists consider "the whole thickness at the vertex as so much wail standing upon a mathematical curve.” 2. Emerson's leading proposition is, to find the extrados from a given intrados. 3. This proposition is not true, nor does it apply to the question, because its result "differs from that of the simple catenaria." 4. "The authority of the Woolwich Academy has imposed Emerson's Theory of Arches," but the true theory is that, which Lapicida "attempts to detail from Dr. Gregory's paper, and Dr. Hooke's conclusion." 5. Dr. Robison admitted the fallaciousness of the theory, and adduced, as the "clearest proof of it, that arches very rarely fail where their load differs most remarkably from that which this theory allows." 6. The theory of domes, founded upon the same principles of equilibration, stands "like the full and perfect warning which a wreck offers to the heedless mariner.” 7. The theory of piers "is a part on which little has been written, and still To the Editor of the Monthly Magazine. less understood, except by those who A SIR, LAS! Mr. Editor, how melancholy it is to trace the progress of poor Lapicida's disorder! A year and a half ago I administered some medicines, and pointed out a regimen, that I hoped would have proved salutary, and ultimately have restored the patient. But the equilibratio-phobia, under which he labours, having not yet been introduced into any of our modern systems of nosology, it is certainly difficult to know when to form a favourable prognosis. The disorder, however, seems now rapidly hastening to a crisis; but the cacoethes scribendi, with which the poor gentleman has been all along troubled, is a most unfavourable symptom. Like Gratiano, he "talks an infinite deal of nothing, more than any man in all Venice. His reasons are as two grains of wheat, hid in two bushels of chaff; 'you shall seek all day ere you find them; and when you have them, they are not worth the search." I have gone through his last paper, which you have indulged with insertion in your Magazine for this month, (April) in order to pick out this grain or two, which he sets against the genuine theory of equilibration, and here they are. have been nursed in the practice." 8. "The methods by analysis and geometry, resemble the progress of a young and old hound.” 9." There are mathematical hermits," to whom "the common practices of mankind are mysteries." Now, in replying as briefly as possible to these, allow me to say, First. That in Gregory's Mechanics, page 141, vol. 1, there may be seen a demonstration of this proposition: "The force of a voussoir depending on the magnitude of the angle, formed by its sides, the impelling force, and the resistance to be overcome, is on the first account directly as the radius of curvature of the arch at that point; on the second, as the square of the sine of the angle, included between the tangent of the curve at the given point, and the ver tical line passing through that point; and on the third, as the sine of the same angle." From this proposition the obvious corollary is deduced, that "if the height of the wall incumbent on any point of the intrados, is directly as the cube of the secant of the angle, formed by a tangent to the voussure at the given point with the horizon; and inversely as the radius of curvature; all the voussures been stated accurately by a cass Eighth geometry CRGI + the inv mertect, a te tart Fifthly. The instances of duced by Dr. Robison, have nemur 1 do with the question, as I stemer 1 Magazine, and at the page to. But it is, on the coctr in point to remark, that in sem for this is exactly war te te directly in 里 Domes. For, nr. Ency. Bra # same their o tigate the same theor prine pan what esta libracon m L 1 paved h off p on Doden each are usand ards ure of The thou ed on ck prehas not erefore, cely any ts. The furnished and now ted from Ise, pota re brought is now con tation is so lowers, and throughout a few small tuberances of lly belong to d there see the Dom. for the sake of h faces prone |