thousand pounds per lineal foot for short spans to eight thousand pounds per lineal foot for long spans; and the bridge is twenty per cent wider than in the case of the two five-hundred-foot spans just mentioned.

The greater the live load and the wider the bridge, the greater can the truss depth be made advantageously.

The little mathematical investigation given in this chapter can be applied with advantage to plate-girder bridges and to the floor systems of truss-bridges. If for ordinary cases, in designing plate girders, one will adopt such a depth as will make the total weight of the web with its splice-plates and stiffening angles about equal to the weight of the flanges, he will obtain an economically designed girder, and a deep and stiff one. For long spans, however, this arrangement would make the girders so deep as to become clumsy and expensive to handle; consequently when a span exceeds, say, forty feet, the amount of metal in the flanges should be a little greater than that in the web; and the more the span exceeds forty feet the greater should be the relative amount of metal in the flanges.

Concerning economic panel lengths, it is safe to make the following statement: "Within the limit set by good judgment and one's inherent sense of fitness, the longer the panel the greater the economy of material in the superstructure." Of course, when one goes to such an extent as to use a thirty-foot panel in an ordinary single-track bridge he exceeds the limits referred to, because the lateral diagonals become too long, and their inclination to the chords becomes too flat for rigidity. Again, an extremely long panel would often cause the truss diagonals to have an unsightly appearance, because of their small inclination to the horizontal.

There is another mathematical investigation which is of practical value. It relates to the economic lengths of spans, and was first demonstrated, in print, by the author some six years ago in Indian Engineering, although the principle was announced three years before then in the first edition of his General   Specifications   for   Highway   Bridges   of   Iron   and   Steel.    Strange  to   say,   many   engineers   failed   to   see   that  there