In three letters, to the printer of the Gazetteer.

LETTER I.

SIR, Dec. 1, 1759.

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.