struts are vertical and the ties inclined, and the lattice in
which both struts and ties are inclined at equal angles, usually 45 deg. with
the horizontal. The earliest published theoretical investigations of the
stresses in bracing bars were perhaps those in the paper by W.T. Doyne and
W.B. Blood (_Proc. Inst. C.E._, 1851, xi. p. 1), and the paper by J.
Barton, "On the economic distribution of material in the sides of wrought
iron beams" (_Proc. Inst. C.E._, 1855, xiv. p. 443).

[Illustration: FIG. 18.--Span of Saltash Bridge.]

The Boyne bridge, constructed by Barton in Ireland, in 1854-1855, was a
remarkable example of the confidence with which engineers began to apply
theory in design. It was a bridge for two lines of railway with lattice
girders continuous over three spans. The centre span was 264 ft., and the
side spans 138 ft. 8 in.; depth 22 ft. 6 in. Not only were the bracing bars
designed to calculated stresses, and the continuity of the girders taken
into account, but the validity of the calculations was tested by a
verification on the actual bridge of the position of the points of contrary
flexure of the centre span. At the calculated position of one of the points
of contrary flexure all the rivets of the top boom were cut out, and by
lowering the end of the girder over the side span one inch, the joint was
opened 1/32 in. Then the rivets were cut out similarly at the other point
of contrary flexure and the joint opened. The girder held its position with
both joints severed, proving that, as should be the case, there was no
stress in the boom where the bending moment changes sign.

[Illustration: FIG. 19.--Newark Dyke Bridge and Section of Newark Dyke
Bridge.]

By curving the top boom of a girder to form an arch and the bottom boom to
form a suspension chain, the need of web except for non-uniform loading is
obviated. I.K. Brunel adopted this principle for the Saltash bridge near
Plymouth, built soon after the Britannia bridge. It has two spans of 455
ft. and seventeen smaller spans, the roadway being 100 ft. above high
water. The top boom of each girder is an elliptical wrought iron tube 17
ft. wide by 12 ft. deep. The lower boom is a pair of chains, of
wrought-iron links, 14 in each chain, of 7 in. by 1 in. section, the links
being connected by pins. The suspending rods and cross bracing are very
light. The depth of the girder at the centre is about one-eighth of the
span.

[Illustration: FIG. 20.--Fin