design and build arch bridges had been few and far between, and because the ratio of rise to span has a great effect upon the weight of metal in an arch. Of course, there is for any span length some economic value of that ratio; but it is not yet known, and it probably varies more or less not only with the span but also with the type of construction. The only practicable method of determining the original question would be to settle first that of the economic ratios of rise to span, design a few arch bridges with the said ratios, and make the comparison. This would have to be done for the solid-rib, the braced-rib, and the spandrel-braced types to make the job complete, adopting for the first set of curves the three-hinged type, and afterward modifying the results for the other three types of hinging. It is evident that the amount of work involved in such an investigation would be immense. It should be done by an experienced bridge designer, as the results would be worthless if obtained by any other investigator. The author suggests that one of his younger brother-specialists undertake the investigation."

The result of this appeal, as in all previous attempts, was absolutely nil; and in 1917, despairing of ever being able to induce anyone to assume the obligation, the author himself shouldered the burden by making, with the aid of one of his assistants, all the calculations needed to determine every desired point, and from the results thereof prepared a paper on "The Economics of Steel Arch Bridges," which he presented to the American Society of Civil Engineers. As soon as he learned of its acceptance by the Publication Committee, he sent a circular letter to all the bridge engineers in America whose addresses he could obtain, as well as to a number of prominent engineers abroad, inviting them to discuss the paper, and enclosing the following synopsis:

Up to the present time, nothing at all certain has been known concerning the economics of steel arch-bridges, the weights of metal required to build them, or how they compare in cost with the corresponding steel truss-bridges.

The objects of this paper and its anticipated discussions are to settle finally every important economic question that can arise in the designing of steel arches; to give formulae and diagrams for determining, with a fair amount of accuracy, the weights of metal in both arch-bridges as a whole and the arches themselves; and to indicate the relations between the weights and costs of arch-bridges in comparison with those of the corresponding truss-bridges.

There are eight economic problems set for solution; and all of them have been solved-the first two by employing certain formulas given in "Bridge Engineering," and the other six by means of a large number of special arch-designs and the resulting estimates of weights of metal. Incidentally, during the investigation there have arisen and been solved a few minor questions which may properly be termed side-issues. The computations have been made for both railway and highway arch-bridges; and the weights of metal are plotted for both carbon-steel and nickel-steel structures. Several diagrams are given to show the percentage effects of weight-increase due to departure from economic conditions.

The need for the special knowledge concerning arch-bridges presented in this paper has  been  recognized  during  the  last  three  decades  by American structural-steel- engineers; but the authors of books  on  bridges  (this  author  included)  have  hitherto