factory results; but there is no hard-and-fast rule about this, and it is permissible to use any depth between the limits of one-eighth and one-tenth of the span. In the past the author had never tested the economics of this feature, having been content to accept the dictum of experience as recorded in engineering text books and hand books; but in connection with the special investigations prepared for this treatise and the late economic studies upon which it is so largely based, a number of estimates have been made which have enabled him to obtain some rough figures upon the effect of increasing the depth of catenary.

The result of these computations appears to indicate that the economic depth for cables was originally adjusted upon the basis of carrying the masonry piers all the way up to the cable carriages, as in the case of the first East River bridge known as the Brooklyn Bridge; because an assumed increase in the height for this type effected no economy. But in the case of a bridge with steel towers the result was quite different; for a saving of total cost was indicated when the depth was made one-seventh of the span-length. That is probably as great a depth as a proper consideration of appearance would permit.

The question of the best type of approaches to adopt is one that has to be settled at the outset. It is an economic one in most cases, but occasionally the local conditions or the matter of estheties will necessitate a departure from the economic layout. Briefly, it may be stated that the type of approach which costs the least is an ordinary trestle or viaduct entirely independent of the main structure. This may be either straight or built in spiral form, as there is but little difference in the construction costs of the two, the latter generally having the advantage of saving in expense for right-of-way and property damages. Suspending the floor-system or stiffening trusses from the backstays is not economic, if it be practicable to build a trestle approach; and even if it is not, it may be better to substitute short spans for the trestle, supporting them at intervals on either piers or rocker bents, the depth of the said spans, if through ones, being made the same as that of the stiffening trusses in the case of a wire cable structure, or of any convenient or economic depth in the case of an eye-bar-cable bridge.

The uneconomies of suspending the floor of the approaches from the backstays are as follows:

First. The far greater weight of metal required for stiffening trusses and hangers as compared with that for the trestle approach, the item of pedestals for the latter being generally a bagatelle.

Second. The far greater cost of the anchorages due to the large lever arm for the overturning moment, the cable pull being horizontal and applied near the elevation of the floor.

The only case in which it is economic to suspend the floor of the approaches from the backstays is when there is deep water beneath that is required for navigation purposes. If there be fairly deep water that is