om
or the designer's office. The most serious feature of such theories is
not merely the approximate and erroneous results which they give, but
the extreme confidence and faith in their certainty which they beget in
their users, enabling them to cut down factors of safety with no regard
whatever for the enormous factor of ignorance which is an essential
accompaniment to the theory itself.

Mr. Mensch says, "The elastic theory enables one to calculate arches
much more quickly than any graphical or guess method yet proposed." The
method given by the writer[Z] enables one to calculate an arch in about
the time it would take to work out a few of the many coefficients
necessary in the involved method of the elastic theory. It is not a
graphic method, but it is safe and sound, and it does not assume
conditions which have absolutely no existence.

Mr. Mensch says that the writer brings up some erratic column tests and
seems to have no confidence in reinforced concrete columns. In relation
to this matter Sanford E. Thompson, M. Am. Soc. C. E., in a paper
recently read before the National Association of Cement Users, takes the
same sets of tests referred to in the paper, and attempts to show that
longitudinal reinforcement adds much strength to a concrete column. Mr.
Thompson goes about it by means of averages. It is not safe to average
tests where the differences in individual tests are so great that those
of one class overlap those of the other. He includes the writer's
"erratic" tests and some others which are "erratic" the other way. It is
manifestly impossible for him to prove that longitudinal rods add any
strength to a concrete column if, on one pair of columns, identically
made as far as practicable, the plain concrete column is stronger than
that with longitudinal rods in it, unless the weak column is defective.
It is just as manifest that it is shown by this and other tests that the
supposedly reinforced concrete column may be weaker.

The averaging of results to show that longitudinal rods add strength, in
the case of the tests reported by Mr. Withey, includes a square plain
concrete column which naturally would show less compressive strength in
concrete than a round column, because of the spalling off at the
corners. This weak test on a square column is one of the slender props
on which is based the conclusion that longitudinal rods add to the
strength of a concrete column; but the weakness of the square concrete