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In the Menai bridge, the chord of the arch is 560feet, the absciss, or versed sine, 37 feet; and thereare to be only 16 cables, or bearers, of wrought iron,in a width of SO feet, 4 inches diameter, weighingtogether 164 tons.

In Southwark bridge, the chord of the middlearch is only 240 feet, the versed sine 24 feet, andthere are eight ribs or bearers of cast iron, in 45feet, each 72 inches in height at the vertex, weigh-ing together 907 tons. The radius of the circle ofcurvature at the vertex of the proposed pendentbridge over the Strait of Menai, is 10654- feet; thatof the middle arch of the Southwark bridge, at thevertex, 312 feet.

Then, by reference to the cohesiveness of castiron in a state of compression, to wrought iron in astate of tension, to the radii of curvature at thevertices of the two bridges, it follows, that the onebridge is many hundred times too strong, or the othermany hundred times too weak, if either of them beof a due strength.

If the true principles of bridges had been elicited,mathematicians would not continue the enquiry afterthem, nor would they be clogged by the modificationsand conditions necessary to reconcile the discrepantresults of different enquirers, and they would be

Eobison, art. Strength of Mat. Encyc . Britt. 1797, says, that“ the strength will increase in a greater ratio than the area of thesection.” Muschenbroek and Euler suppose that the strength ofcolumns to be as the biquadrates of their diameters. Assumingthat 25 tons are required to tear asunder, in direct tension,wrought iron inch-square in section, and upon “ the well ascer-tained fact,’’ according to the Report 1819, 70 tons may betaken as necessary to crush an inch square of cast iron.