points where the bending moment changes sign, and therefore the magnitude
and distribution of the stresses, generally prevents the adoption of
continuity. If, however, hinges or joints are introduced at the points of
contrary flexure, they become necessarily points where the bending moment
is zero and ambiguity as to the stresses vanishes. The exceptional local
conditions at the site of the Forth bridge led to the adoption there of the
cantilever system, till then little considered. Now it is well understood
that in many positions this system is the simplest and most economical
method of bridging. It is available for spans greater than those
practicable with independent girders; in fact, on this system the spans are
virtually reduced to smaller spans so far as the stresses are concerned.
There is another advantage which in many cases is of the highest
importance. The cantilevers can be built out from the piers, member by
member, without any temporary scaffolding below, so that navigation is not
interrupted, the cost of scaffolding is saved, and the difficulty of
building in deep water is obviated. The centre girder may be built on the
cantilevers and rolled into place or lifted from the water-level. Fig. 21
shows a typical cantilever bridge of American design. In this case the
shore ends of the cantilevers are anchored to the abutments. J.A.L. Waddell
has shown that, in some cases, it is convenient to erect simple independent
spans, by building them out as cantilevers and converting them into
independent girders after erection. Fig. 22 shows girders erected in this
way, the dotted lines being temporary members during erection, which are
removed afterwards. The side spans are erected first on staging and
anchored to the piers. From these, by the aid of the temporary members, the
centre span is built out from both sides. The most important cantilever
bridges so far erected or projected are as follows:--

[Illustration: FIG. 23.--Forth Bridge.]

(1) The Forth bridge (fig. 23). The original design was for a stiffened
suspension bridge, but after the fall of the Tay bridge in 1879 this was
abandoned. The bridge, which was begun in 1882 and completed in 1889, is at
the only narrowing of the Forth in a distance of 50 m., at a point where
the channel, about a mile in width, is divided by the island of Inchgarvie.
The length of the cantilever bridge is 5330 ft., made up thus: central
tower on Inchgarvie 260 ft.; Fife and Queensfe