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preferred, if with greater strength it has greater beauty.

Those who are acquainted with the mathematical principles of architecture, are not many; and yet fewer are they who will, upon any single occasion, endure any laborious stretch of thought, or harass their minds with unaccustomed investigations. We shall therefore attempt to shew the weakness of the elliptical arch, by arguments which appeal simply to common reason, and which will yet stand the test of geometrical examination.

All arches have a certain degree of weakness. No hollow building can be equally strong with a solid mass, of which every upper part presses perpendi. cularly upon the lower. Any weight laid upon the top of an arch, has a tendency to force that top

into the vacuity below; and the arch thus loaded on the top, stands only because the stones that form it, being wider in the upper than in the lower parts, that part that fills a wider space cannot fall through a space less wide; but the force which laid upon a flat would press directly downwards, is dispersed each way in a lateral direction, as the parts of a beam are pushed out to the right and left by a wedge driven between them. In proportion as the stones are wider at the top than at the bottom, they can less easily be forced downwards, and as their lateral surfaces tend more from the centre to each side, to so much more is the pressure directed laterally towards the piers, and so much less perpendicularly towards the vacuity.

Upon this plain principle the semicircular arch may be demonstrated to excel in strength the elliptical arch, which approaching nearer to a

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straight line must be constructed with stones whose diminution downwards is very little, and of which the pressure is almost perpendicular.

It has yet been sometimes asserted by hardy ignorance, that the elliptical arch is stronger than the semicircular; or in other terms, that any mass is more strongly supported the less it rests

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supporters. If the elliptical arch be equally strong with the semicircular, that is, if an arch, by approaching to astraight line, loses none of its stability, it will follow, that all arcuation is useless, and that the bridge may at last, without any inconvenience, consist of stone laid in straight lines from pillar to pillar. But if a straight line will bear no weight, which is evident at the first view, it is plain likewise, that an ellipsis will bear very little ; and that as the arch is more curved, its strength is increased.

Having thus evinced the superiour strength of the semicircular arch, we have sufficiently proved, that it ought to be preferred; but to leave no objection unprevented, we think it proper likewise to observe, that the elliptical arch must always appear to want elevation and dignity; and that if beauty be to be determined by suffrages, the elliptical arch will have little to boast, since the only bridge of that kind has now stood two hundred years without imitation.

If in opposition to these arguments, and in defiance at once of right reason and general authority, the elliptical arch should at last be chosen, what will the world believe, than that some other motive than reason influenced the determination? And some degree of partiality cannot but be suspected by him, who has been told that one of the judges appointed to decide this question, is Mr.Mlr, who having by ignorance, or thoughtlessness, already preferred theelliptical arch,will probably think himselfobliged to maintain his own judgment, though his opinion will avail but little with the publick, when it is known that Mr. Srps--n declares it to be false.

He that in the list of the committee chosen for the superintendency of the bridge, reads many of the most illustrious names of this great city, will hope that the greater number will have more reverence for the opinion of posterity, than to disgrace themselves, and the metropolis of the kingdom, in compliance with any man, who, instead of voting, aspires to dictate, perhaps without any claim to such superiority, either by greatness of birth, dignity of employment, extent of knowledge, or largeness of fortune.

SIR,

LETTER II.

Dec. 8, 1759. In questions of general concern, there is no law of government, or rule of decency, that forbids open examination and publick discussion. I shall therefore not betray, by a mean apology, that right which no man has power, and, I suppose, no wise man has desire to refuse me; but shall consider the Letter published by you last Friday, in defence of Mr. M—'s* design for a new bridge. Mr. M- ,

proposes elliptical arches. It has been objected that elliptical arches are weak: and therefore improper for a bridge of commerce, in a country where greater weights are ordinarily carried

* Mr. Milne.

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by land than perhaps in any other part of the world. That there is an elliptical bridge at Florence is allowed, but the objectors maintain, that its stability is so much doubted, that carts are not permitted to pass over it.

To this no answer is made, but that it was built for coaches; and if it had been built for carts, it would have been made stronger: thus all the controvertists agree, that the bridge is too weak for carts; and it is of little importance, whether carts are pro. hibited because the bridge is weak, or whether the architect, knowing that carts were prohibited,voluntarily constructed a weak bridge. The instability of the elliptical arch has been sufficiently proved by argument, and Ammanuti's attempt has proved it by example.

The iron rail,whether gilt or varnished, appears to me unworthy of debate. I suppose every judicious eye

will discern it to be minute and trifling, equally unfit to make a part of a great design, whatever be its colour. I shall only observe how little the writer understands his own positions, when he recommends it tobecastin whole pieces from pierto pier. Thatiron forged is stronger than iron cast, every smith can inform him; and if it be cast in large pieces, the fracture of a single bar must be repaired by a new piece.

The abrupt rise, which is feared from firm circular arches, may be easily prevented, by a little extension of the abutment at each end, which will take away the objection, and add almost nothing to the expense.

The whole of the argumentin favour of Mr.M—-, is only that there is an elliptical bridge at Florence, and an iron balustrade at Rome ; the bridge is owned to be weak, and the iron balustrade we consider as mean; and are loth that our own country should unite two follies in a publick work.

The architrave of Perault, which has been pompously produced, bears nothing but its entablature; and is so far from owing its support to the artful section of the stone, that it is held together by cramps of iron; to which I am afraid Mr. M- must have recourse, if he persists in his ellipsis, or, to use the words of his vindicator, forms his arch of four seg. ments of circles drawn from four different centres.

That Mr. Mobtained the prize of the architecture at Rome, a few months ago, is willingly confessed; nor do his opponents doubt that he obtained it by deserving it. May he continue to obtain whatever he deserves; but let it not be presumed that a prize granted at Rome, implies an irresistible degree of skill. The competition is only between boys, and the prize given to excite laudable industry, not to reward consummate excellence. Nor will the suffrage of the Romans much advance any name among those who know, what no man of science will deny, that architecture has for some time degenerated at Rome to the lowest state, and that the Pantheon is now deformed by petty decorations.

I am, Sir,

Yours, &c.

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