work, the ratio would be as unity to 0.8. These results were obtained by assuming average probable conditions; but the longer the simple spans and the greater the total length of structure, the less will be the variation in weights of cantilever and simple-span bridges, although it would require very long spans and a great total length of structure to change materially the ratios found.

It is therefore evident that, when economy in first cost is considered, as it always ought to be, there will seldom, if ever, be any need for considering the adoption of cantilever bridges with anchor-spans, because structures with simple spans are both cheaper and better. It is also evident that in many cases it is advisable, from considerations of both rigidity and economy, to adopt a bridge consisting of three simple spans, with the middle one cantilevered from the others, rather than the ordinary three-span cantilever bridge. When each of the side spans is as short as one-half of the middle span, or even shorter, there will be no difficulty experienced in the erection, and no great provision will be required for holding down the outer ends of the side spans during erection. Of course, the nearer to equality that the three span lengths are made, the greater will be the economy of metal, but a wide divergence in these lengths will not necessitate any such increase in weight as to alter the preceding conclusion regarding the great economy of simple-span bridges over ordinary cantilever structures.

The question sometimes arises as to how the total weight of metal in a three-span cantilever bridge varies with the length of the main opening. If the lengths of the anchor-arms vary proportionately to the main opening, the increase or decrease in the total weight of metal in the structure will vary about twice as rapidly as the increase or decrease in length. Fur instance, if the main opening and total length of bridge be increased ten per cent, the total weight of metal in the entire structure will be increased twenty per cent. This rule, which is merely an approximation, will apply fairly well for changes not exceeding twenty per cent and for spans of median length. For greater changes the ratio of increase or decrease gradually augments, and for very long spans it is slightly greater than two, while for very short ones it is slightly less.