the paper, he should not have attempted to criticize it. What the writer
presented for consideration was more than his opinion of the matter. In
fact, no opinion at all was presented. What was presented was tests
which prove absolutely that longitudinal rods without hoops may actually
reduce the strength of a column, and that a column containing
longitudinal rods and "hoops which are not close enough to stiffen the
rods" may be of less strength than a plain concrete column. A properly
hooped column was not mentioned, except by inference, in the quotation
given in the foregoing sentence. The column tests which Mr. Turner
presents have no bearing whatever on the paper, for they relate to
columns with bands and close spirals. Columns are sometimes built like
these, but there is a vast amount of work in which hooping and bands are
omitted or are reduced to a practical nullity by being spaced a foot or
so apart.

A steel column made up of several pieces latticed together derives a
large part of its stiffness and ability to carry compressive stresses
from the latticing, which should be of a strength commensurate with the
size of the column. If it were weak, the column would suffer in
strength. The latticing might be very much stronger than necessary, but
it would not add anything to the strength of the column to resist
compression. A formula for the compressive strength of a column could
not include an element varying with the size of the lattice. If the
lattice is weak, the column is simply deficient; so a formula for a
hooped column is incorrect if it shows that the strength of the column
varies with the section of the hoops, and, on this account, the common
formula is incorrect. The hoops might be ever so strong, beyond a
certain limit, and yet not an iota would be added to the compressive
strength of the column, for the concrete between the hoops might crush
long before their full strength was brought into play. Also, the hoops
might be too far apart to be of much or any benefit, just as the lattice
in a steel column might be too widely spaced. There is no element of
personal opinion in these matters. They are simply incontrovertible
facts. The strength of a hooped column, disregarding for the time the
longitudinal steel, is dependent on the fact that thin discs of concrete
are capable of carrying much more load than shafts or cubes. The hoops
divide the column into thin discs, if they are closely spaced; widely
spaced h