will demand special study, if the springings are located at different elevations; otherwise, the principles of aesthetics are likely to be violated.

The influence of earth-thrust on an arch abutment has already been mentioned. Where such thrust exists, it will favor the use of longer spans, in order that the larger arch-thrust may counterbalance the said earth-thrust. In a long bridge of many spans, the abutments will not cut much figure; but if only two or three spans are to be adopted, they may be of more importance than the intermediate piers. If there is no earth-thrust on the abutment, its cost will augment as the span-length increases; but if there is such a thrust, the cost may reduce when the span-length is made greater.

In many layouts the positions and even the sizes of certain piers are fixed, and specified clearances (both horizontal and vertical) must be maintained under certain of the spans. These conditions, of course, must be taken as a basis, and the layout adapted to suit them. Special governing conditions must often be observed, such as the character of the surroundings, the relative importance of aesthetics and cost, or the adoption of some special architectural treatment.

In a discussion of economic span-lengths of arch bridges it is impracticable to give exact figures, for there are too many variables concerned. Whenever there is any choice, it will be necessary to make preliminary designs for at least two span-lengths; and, if one of these proves to be somewhat cheaper than the other, a third length should be figured. There is no other way to ensure that the truly economic length has been selected, unless it happens that the figures can be compared with those for a very similar structure.

Comparison of Solid-Spandrel versus Open-Spandrel and Solid-
Barrel versus Ribbed Structures

Arch-spans can be divided into two general classes, solid-spandrel and open-spandrel. In the first form the arch-rib must be solid, while in the second it may be either solid or ribbed. Considering the two solid-barrel types, the filled-spandrel has no floor-system or cross walls, but instead an earth fill between the spandrel-walls: For very low rises the walls and filling are cheaper than the floor-system and columns; but for high rises the reverse is true. The great weight of the filling makes the piers expensive in the cases of pile foundations and bearings upon comparatively soft soil. The spandrel-filled arch is often used on railroads when it is not the most economic type, in order that the weight and inertia of the filling may absorb the impact of moving trains.

In highway structures, the open-spandrel type is generally preferred to the filled type, for various good and economic reasons, among which may be mentioned the fact that, with the latter type, it will be found desirable, for  the  sake  of  appearance,  to make the  ring  the full width of the