properly designed cantilever bridge where the conditions call for such a structure. Compared with a suspension bridge, a cantilever bridge is rigidity itself. But, again, this is no reason for condemning in toto suspension bridges, which have their legitimate place in engineering construction, viz., where either an extremely long span is necessary, or where a cheap highway bridge over a wide river is required.

There is but one kind of steel structure in which the cantilever is more economical of metal than the simple span, viz., roofs supported on steel columns, as in train-sheds and workshops. The reason for this economy is the shortening of the spans and the ignoring of the effects of reversion of stress when proportioning members. The latter is legitimate within certain limits because of the infrequency or improbability of such reversion.

Cantilever bridges being of such an unusual type, and their use with very few exceptions dating back only about twenty years, but little effort has yet been made to systematize their designing or to investigate their economic features. The only paper of any real value on the subject, which has come to the author's notice, is one by Prof. Edgar Marburg, published in the Proceedings of the Engineers' Club of Philadelphia for July, 1896. This paper is an excellent one, but it really does not settle any important point concerning the economic relations of span lengths, for its mathematical investigations are rather crude approximations.

As the author has lately in his practice accumulated a mass of data concerning weights of metal in cantilever bridges, he has had his assistant engineer, Mr. Hedrick, extend his calculations not only so as to determine all the economic relations of cantilever bridges, but also so as to prepare percentage curves, by using which the total weight of metal in any cantilever bridge of any ordinary type can be found very quickly and with considerable accuracy.

Before proceeding to present these results, though, several other matters will receive consideration.

In no work on bridges, that the author has ever seen, has there been  given a statement of the various stresses for which