rib and solid-rib arches, however, the hinge should always be placed at mid-depth, so as to distribute properly the thrust over the two chords.

Fourth. Comparing the economics of solid-rib, braced-rib, and spandrel-braced arches, it was found that the first mentioned is always considerably heavier than either of the others; and, under normal conditions of the metal market, it is also more expensive. The spandrel-braced-arch requires for long spans a little more metal than the braced-rib arch; but,

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in case of cantilevering, this would generally be offset by the extra quantity of erection metal needed for the braced-rib structure. In short spans, the spandrel-braced arch is a trifle the lighter.

Fifth. Comparing three-hinged, two-hinged, and hingeless arches, it was found that the three-hinged is a little heavier than the two-hinged, but nearly always lighter than the hingeless. The variations in weight among the three types, however, are never great. In Fig. 26c are given ratios of weights of metal in hingeless arches as compared with three-hinged arches for both railway and highway bridges.