Fifth. The ratio of weights of metal in cantilever bridges of various types to those in simple-span bridges having the same number of spans.

Mr. Hedrick's method of determining the economic functions was to take the data on hand for the proposed Japanese cantilever bridges, exact weights of metal having been computed for structures of 320-ft., 400-ft., and 500-ft. openings, and, by varying the layouts so as to use longer and shorter suspended spans and longer and shorter anchor-arms, obtain, by actual designs and estimates, the weights of metal for a sufficient number of layouts to indicate the desired minima.

In determining the economic length of suspended span for a certain opening, the length for the anchor-arms was first assumed to be one fourth of said opening, then the total weight of metal in the entire bridge, including even the anchorages and pedestals, was figured for several cases; and the length of suspended span giving the least weight of metal for the whole Structure Was found to be about three eighths of the opening, although this length showed only one and a half per cent advantage over the case where the ratio was one half. Now, as the rigidity of the entire structure certainly increases with the length of the suspended span, it will often be found best to make the length of the latter about one half of the opening rather than three eighths or any smaller proportion. On the other hand, though, it has been found by trial that, with the three-eighths ratio, there results a more sightly layout than can be obtained with the one-half ratio.

Next Mr. Hedrick tabulated the various component truss and lateral weights of several of the typical cantilever bridges designed in the author's office, the leading dimensions for which are given in the following table.

From these weights be constructed the curves shown on Plate X, from which can be found the total weight of metal in the trusses and lateral systems of any three-span cantilever bridge, when the weight per lineal foot of the trusses and laterals in the suspended span is known. This weight, by the way, is, on the average, eight per cent greater than that  for an  ordinary  simple  span  of  the  same length, the extra metal