height of the keystone in Table I. of bridges. Ifgranite be as strong as marble, may we not have abridge over the Thames something resembling theeconomy of figure and of material in this bridge,and not like the Egyptians, Greeks, and Romans,encumber the earth with a mass of stone largeenough, according to the best guess which can bemade to enclose the line of thrust, doubtful of itsdirection, and negligent of the expense of the struc-ture ? Ammanati was a countryman of Brunelleschi ,the architect of the vault of Santa Maria del Piore,of whom it has been said, “ La posterita gli ha resoi dovuti onori; poiehe in lui ha fissata l’epoca derisorgimento della buona architettura •” and both ofthem were employed in the Pitti palace . He was acountryman and contemporary of Michael Angelo and Galileo; in his time the investigations relatingto the construction of and the building itself, of thedome of Santa Maria, were fresh in memory, and thatof St. Peter was erected. In his time, the cycloidand the elastic and catenarian curves were invented,and the difficulty of investigating the properties ofthem may have driven, a few years afterwards, New-ton, the Bernoullies, and Leibnitz to that invention $which, in the licence of poetry, has placed them inthe same degree of approximation to angels as the apeis to man. The curve of the bridge of Ammanati ispointed, formed by the intersection of two arcs, pro-bably of an elongated cycloid or of an elastic, logarith-mic, or catenarian curve, the axis horizontal. Perronihas shown that the curve is not an arc of an ellipse norof a parabola, and, forgetting that the anse de panieris only an approximation to some other curve, andmay be made to approximate to any, concludes that