hese rods unassailable end anchorages; every
detail would be amply cared for. If loose methods are good enough for
proportioning loose stirrups, and no literature is needed to show why or
how they can be, why analyze a chimney so accurately and apply
assumptions which cannot possibly be realized anywhere but on paper and
in books?

It is not rule-of-thumb to find the tension in plain concrete and then
embed steel in that concrete to take that tension. Moreover, it is safer
than the so-called rational formula, which allows compression on slender
rods in concrete.

Mr. Thacher says, "No arch designed by the elastic theory was ever known
to fail, unless on account of insecure foundations." Is this the correct
way to reach correct methods of design? Should engineers use a certain
method until failures show that something is wrong? It is doubtful if
any one on earth has statistics sufficient to state with any authority
what is quoted in the opening sentence of this paragraph. Many arches
are failures by reason of cracks, and these cracks are not always due to
insecure foundations. If Mr. Thacher means by insecure foundations,
those which settle, his assertion, assuming it to be true, has but
little weight. It is not always possible to found an arch on rock. Some
settlement may be anticipated in almost every foundation. As commonly
applied, the elastic theory is based on the absolute fixity of the
abutments, and the arch ring is made more slender because of this
fixity. The ordinary "row-of-blocks" method gives a stiffer arch ring
and, consequently, greater security against settlement of foundations.

In 1904, two arches failed in Germany. They were three-hinged masonry
arches with metal hinges. They appear to have gone down under the weight
of theory. If they had been made of stone blocks in the old-fashioned
way, and had been calculated in the old-fashioned row-of-blocks method,
a large amount of money would have been saved. There is no good reason
why an arch cannot be calculated as hinged ended and built with the arch
ring anchored into the abutments. The method of the equilibrium polygon
is a safe, sane, and sound way to calculate an arch. The monolithic
method is a safe, sane, and sound way to build one. People who spend
money for arches do not care whether or not the fancy and fancied
stresses of the mathematician are realized; they want a safe and lasting
structure.

Of course, calculations can be made for shrinka