limits of working stress in public and railway bridges are
prescribed by law. The development of theory has advanced _pari passu_ with
the demand for bridges of greater strength and span and of more complex
design, and there is now little uncertainty in calculating the stresses in
any of the types of structure now adopted. In the modern metal bridge every
member has a definite function and is subjected to a calculated straining
action. Theory has been the guide in the development of bridge design, and
its trustworthiness is completely recognized. The margin of uncertainty
which must be met by empirical allowances on the side of safety has been
steadily diminished.

The larger the bridge, the more important is economy of material, not only
because the total expenditure is more serious, but because as the span
increases the dead weight of the structure becomes a greater fraction of
the whole load to be supported. In fact, as the span increases a point is
reached at which the dead weight of the superstructure becomes so large
that a limit is imposed to any further increase of span.

[Illustration: FIG. 2.--Bridge of Alcantara.]

HISTORY OF BRIDGE BUILDING

[Illustration: FIG. 3.--Ponte Salario.]

4. _Roman Bridges_.--The first bridge known to have been constructed at
Rome over the Tiber was the timber Pons Sublicius, the bridge defended by
Horatius. The Pons Milvius, now Ponte Molle, was reconstructed in stone by
M. Aemilius Scaurus in 109 B.C., and some portions of the old bridge are
believed to exist in the present structure. The arches vary from 51 to 79
ft. span. The Pons Fabricius (mod. Ponte dei Quattro Capi), of about 62
B.C., is practically intact; and the Pons Cestius, built probably in 46
B.C., retains much of the original masonry. The Pons Aelius, built by
Hadrian A.D. 134 and repaired by Pope Nicholas II. and Clement IX., is now
the bridge of St Angelo. It had eight arches, the greatest span being 62
ft.[1] Dio Cassius mentions a bridge, possibly 3000 to 4000 ft. in length,
built by Trajan over the Danube in A.D. 104. Some piers are said still to
exist. A bas-relief on the Trajan column shows this bridge with masonry
piers and timber arches, but the representation is probably conventional
(fig. 1). Trajan also constructed the bridge of Alcantara in Spain (fig.
2), of a total length of 670 ft., at 210 ft. above the stream. This had six
arches and was built of stone blocks without cement. The bridge of Narses