der bridge
with one large span and several small spans; and the arch with small
girder spans on each side. The suspension bridge was left out of question
as inadmissible. A girder bridge with small independent spans on rocker
piers would probably have been the most economical, even taking into
account the great height of the piers near the middle of the ravine, but
there would have been some difficulty in holding those piers in position
until they could be secured to the girders at the top; and, moreover, such
a structure would have been strikingly out of harmony with the character
of the site. On the other hand, a cantilever or continuous girder bridge
in three spans--although such structures have been erected in similar
localities--could not enter into comparison of simple economy of material,
because such a design would entirely disregard the anomaly that the
greater part of the structure, viz., the side spans, being necessarily
constructed to carry across a large space, would be too near the ground to
justify the omission of further supports. The question was, therefore,
narrowed to a comparison between the present arch and a central
independent girder of the same span, including the piers on which it
rests. The small side spans could obviously be left out in each case. The
comparison was made with a view not only to arrive at a decision in this
particular case, but also of answering the question of the economy of the
arch more generally. The following table contains the weights of
geometrically similar structures of three different spans, of which the
second is the one here described. The so-called theoretical weight is that
which the structure would have if no part required stiffening, leaving out
also all connections and all wind bracing. The moving load is taken at one
ton per foot lineal, and the strain on the iron at an average of four tons
per square inch. The proportion of the girder is taken at 1 in 8.

--------------+-----------------------+------------------------+
| Theoretical Weight. | Total Weight. |
Span in Feet. +-----------------------+------------------------|
| Arch. | Girder. | Arch. | Girder. |
--------------+---------+-------------+------------+-----------|
100 | 0.0724 | 0.1663 | 0.1866 | 0.2443 |
220 | 0.1659 | 0.4109 | 0.4476 | 0.7462 |
300 | 0.2414 | 0.6445 | 0.6464 | 1.25