In three letters, to the printer of the Gazetteer.
LETTER I.
Dec. 1, 1759.
SIR,
The plans which have been offered by different architects, of different reputation and abilities, for the construction of the bridge intended to be built at Blackfriars, are, by the rejection of the greater part, now reduced to a small number; in which small number, three are supposed to be much superiour to the rest; so that only three architects are now properly competitors for the honour of this great employment; by two of whom are proposed semicircular, and by the other elliptical arches.
The question is, therefore, whether an elliptical or semicircular arch is to be preferred?
The first excellence of a bridge, built for commerce, over a large river, is strength; for a bridge which cannot stand, however beautiful, will boast its beauty but a little while: the stronger arch is, therefore, to be preferred, and much more to be 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 show 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 perpendicularly 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 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 upon the supporters. If the elliptical arch be equally strong with the semicircular; that is, if an arch, by approaching to a straight 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. M--ll--r, who, having by ignorance, or thoughtlessness, already preferred the elliptical arch, will, probably, think himself obliged to maintain his own judgment, though his opinion will avail but little with the publick, when it is known that Mr. S--ps--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.
LETTER II.
Dec. 8, 1759.
SIR,
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[1] 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 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 prohibited, 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 to be cast in whole pieces from pier to pier. That iron 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 argument in 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 loath that our own country should unite two follies in a publick work.
The architrave of Perrault, 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 segments of circles drawn from four different centres.
That Mr. M---- obtained 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. [1]
Mr. Milne.
LETTER III.
Dec. 15, 1759.
Sir,
It is the common fate of erroneous positions, that they are betrayed by defence, and obscured by explanation; that their authors deviate from the main question into incidental disquisitions, and raise a mist where they should let in light.
Of all these concomitants of errours, the letter of Dec. 10, in favour of elliptical arches, has afforded examples. A great part of it is spent upon digressions. The writer allows, that the first excellence of a bridge is undoubtedly strength: but this concession affords him an opportunity of telling us, that strength, or provision against decay, has its limits; and of mentioning the monument and cupola, without any advance towards evidence or argument.
The first excellence of a bridge is now allowed to be strength; and it has been asserted, that a semi-ellipsis has less strength than a semicircle. To this he first answers, that granting this position for a moment, the semi-ellipsis may yet have strength sufficient for the purposes of commerce. This grant, which was made but for a moment, needed not to have been made at all; for, before he concludes his letter, he undertakes to prove, that the elliptical arch must, in all respects, be superiour in strength to the semicircle. For this daring assertion he made way by the intermediate paragraphs, in which he observes, that the convexity of a semi-ellipsis may be increased at will to any degree that strength may require; which is, that an elliptical arch may be made less elliptical, to be made less weak; or that an arch, which, by its elliptical form, is superiour in strength to the semicircle, may become almost as strong as a semicircle, by being made almost semicircular.
That the longer diameter of an ellipsis may be shortened, till it shall differ little from a circle, is indisputably true; but why should the writer forget the semicircle differs as little from such an ellipsis? It seems that the difference, whether small or great, is to the advantage of the semicircle; for he does not promise that the elliptical arch, with all the convexity that his imagination can confer, will stand without cramps of iron, and melted lead, and large stones, and a very thick arch; assistances which the semicircle does not require, and which can be yet less required by a semi-ellipsis, which is, in all respects, superiour in strength.
Of a man who loves opposition so well, as to be thus at variance with himself, little doubt can be made of his contrariety to others; nor do I think myself entitled to complain of disregard from one, with whom the performances of antiquity have so little weight; yet, in defiance of all this contemptuous superiority, I must again venture to declare, that a straight line will bear no weight; being convinced, that not even the science of Vasari can make that form strong which the laws of nature have condemned to weakness. By the position, that a straight line will bear nothing, is meant, that it receives no strength from straightness; for that many bodies, laid in straight lines, will support weight by the cohesion of their parts, every one has found, who has seen dishes on a shelf, or a thief upon the gallows. It is not denied, that stones may be so crushed together by enormous pressure on each side, that a heavy mass may safely be laid upon them; but the strength must be derived merely from the lateral resistance; and the line, so loaded, will be itself part of the load.
The semi-elliptical arch has one recommendation yet unexamined: we are told, that it is difficult of execution. Why difficulty should be chosen for its own sake, I am not able to discover; but it must not be forgotten, that, as the convexity is increased, the difficulty is lessened; and I know not well, whether this writer, who appears equally ambitious of difficulty, and studious of strength, will wish to increase the convexity for the gain of strength, or to lessen it for the love of difficulty.
The friend of Mr. M----, however he may be mistaken in some of his opinions, does not want the appearance of reason, when he prefers facts to theories; and that I may not dismiss the question without some appeal to facts, I will borrow an example, suggested by a great artist, and recommended to those who may still doubt which of the two arches is the stronger, to press an egg first on the ends, and then upon the sides.
I am, Sir, yours, &c.
[The end]
Samuel Johnson's essay: Considerations On The Plans Offered For The Construction Of Blackfriars Bridge