floor systems, will provide a check on the correctness of the old method of determining economic span-lengths. Let us take the case of a low-level, double-track-railway bridge founded on rock, find the cost per lineal foot of the trusses and laterals in the span of economic length, and check it against the cost per lineal foot for the substructure thereof. For a 50-foot depth of bed rock the economic span-length is 275 feet; and for that span (see "Bridge Engineering," pages 1239 and 1240) the weight of metal per lineal foot for trusses and laterals with Class 60 live load is 4,600 pounds, which at six cents per pound would be worth $276, while the cost per foot for the substructure given by the diagram is $270. This is not a bad check.

For a depth of 100 feet, the economic span-length is 325 feet, for which the weight of trusses and laterals is 5,860 pounds, which at six cents per pound would be worth $352. The diagram makes the cost per foot for the substructure $420—quite a discrepancy.

For low-level, single-track-railroad bridges with a foundation depth of 50 feet, the economic span-length given by diagram is 250 feet, for which the weight of trusses and laterals is 2,480 pounds, which at six cents per pound would be worth $149, while the said diagram gives the cost per foot for substructure at $175—not a close check.

For a depth of 100 feet, the economic span-length is 300 feet, for which the weight of trusses and laterals is 3,050 pounds, which at six cents per pound would be worth $183. The diagram makes the cost per foot for substructure $275—another large variation.

It is evident from the preceding comparisons of cost that the former rule for determining the economic span-length is not reliable, especially for foundations at great depths; hence its use should be discontinued.

There is a little economic, or more strictly speaking uneconomic, investigation concerning simple-truss spans the results of which are worth knowing and may sometimes prove valuable, especially in answering questions propounded by laymen, viz., "what are the relative weights of metal in equal-truss, three-span bridges and structures of the same kind, same total length, and same loading, but having the central span lengthened and the other two equally shortened?" The answer to this question is that the weight-ratios for the unequal-span layouts, as compared with those for equal spans, are greater for long structures than for short ones, and increase with the ratio of middle-span length to average-span length. The values of such ratios for three-span structures, varying in average span-length by one hundred feet from 200 feet to 500 feet, are given in Fig. 18i.

The curves for cost ratios are almost coincident with those for weight-ratios, because the pound prices erected for the metal in the various layouts are nearly alike. On the one hand, those for the equal-span layouts should be less because of a saving in cost of making working drawings and templets; but, on the other hand, the erection costs per pound are a trifle less for the layouts of unequal-span length because of their greater total weights of metal. C. W. Bryan,  Esq.,  Chief  Engineer  of  the  American