Of all these concomitants of errors, the Letter of Dec. 10, in favour of elliptical arches, has afforded examples.1 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,2 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 superior 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 encreased 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 superior 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 superior 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 strait line will bear no weight; being convinced, that not even the science of Vasari can make that form strong,3 which the laws of nature have condemned to weakness. By the position, that a strait line will bear nothing, is meant, that it receives no strength from straitness; for that many bodies, laid in strait 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 un-examined; 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 encreased, 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 encrease 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,4 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.