is justified, because designing engineers do not carry
the theory to its logical conclusion nor take into account the actual
stresses which may be expected from slight changes of span, settlements
of abutments, and unexpected amounts of shrinkage in the arch ring or
ribs. Where conditions indicate that such changes are likely to take
place, as is almost invariably the case unless the foundations are upon
good rock and the arch ring has been concreted in relatively short
sections, with ample time and device to allow for initial shrinkage; or
unless the design is arranged and the structure erected so that hinges
are provided at the abutments to act during the striking of the
falsework, which hinges are afterward wedged or grouted so as to produce
fixation of the arch ends--unless all these points are carefully
considered in the design and erection, it is the speaker's opinion that
the elastic theory is rarely properly applicable, and the use of the
equilibrium polygon recommended by the author is much preferable and
actually more accurate. But there must be consistency in its use, as
well, that is, consistency between methods of design and erection.

The author's fourteenth point--the determination of temperature stresses
in a reinforced concrete arch--is to be considered in the same light as
that described under the foregoing points, but it seems a little amusing
that the author should finally advocate a design of concrete arch which
actually has no hinges, namely, one consisting of practically rigid
blocks, after he has condemned so heartily the use of the elastic
theory.

A careful analysis of the data already available with regard to the heat
conductivity of concrete, applied to reinforced concrete structures like
arches, dams, retaining walls, etc., in accordance with the well-known
but somewhat intricate mathematical formulas covering the laws of heat
conductivity and radiation so clearly enunciated by Fourier, has
convinced the speaker that it is well within the bounds of engineering
practice to predict and care for the stresses which will be produced in
structures of the simplest forms, at least as far as they are affected
by temperature changes.

The speaker concurs with the author in his criticism, contained in the
fifteenth point, with regard to the design of the steel reinforcement in
columns and other compression members. While there may be some question
as to the falsity or truth of the theory underlying