the other cases there are; and they must always receive due consideration in proportioning the members.

All things considered, the author prefers to adopt the three-hinged arch for railroad bridges, because the stresses can be determined as accurately as can those of an ordinary truss bridge, and because of the absence of temperature stresses; at the same time it must be admitted that an arch without hinges is more rigid than one with hinges, and that, theoretically, it is more economical of metal.

For highway bridges, in which the assumed live loads will seldom, if ever, be realized, it would be best, all things considered, to adopt the arch without hinges, so as to obtain the greatest possible rigidity, even at the expense of certainty in computing stresses.

For arched train-sheds, the two-hinged arch of crescent shape will generally be found the most satisfactory.

While the author was engaged on the preparation of this chapter he received a copy of Prof. Malverd A. Howe's new book, entitled "A Treatise on Arches." This work, which is entirely mathematical in character, is certainly the most complete book on arches that has ever been written, and appears to cover the entire subject of stresses in arches of all kinds in a most satisfactory manner, although, of course, the anthor cannot vouch for the correctness of Prof. Howe's figures without checking the mathematics from start to finish, a task which he feels is too great for both his spare time and his advancing years. It is probable, though, that the author will have the book checked some time by one of his assistant engineers, in case that he has to make another design for an arch. Meanwhile he is satisfied to assume that all of the mathematical work is correct, because of Prof. Howe's established reputation as both a mathematician and an engineer. Prof. Howe has tabulated the results of his computations in a very convenient form, so that his formulae can readily be applied in designing, especially for preliminary designs and estimates.   In  spite  of  its  discouragingly  mathematical  appearance, Prof.  Howe's   book   promises  to  prove  of  great   practical   value  to   designers   in   structural   steel;   and   its   author   is  certainly  to  be