nding moment at the end of the arch, which is found
by the elastic theory (on paper), has merely to overturn this block of
concrete, and it is aided very materially in this by the thrust of the
arch. The deformation of the abutment, due to deficiency in its moment
of inertia, is a theoretical trifle which might very aptly be minutely
considered by the elastic arch theorist. He appears to have settled all
fears on that score among his votaries. The settlement of the abutment
both vertically and horizontally, a thing of tremendously more magnitude
and importance, he has totally ignored.

Most soils are more or less compressible. The resultant thrust on an
arch abutment is usually in a direction cutting about the edge of the
middle third. The effect of this force is to tend to cause more
settlement of the abutment at the outer, than at the inner, edge, or, in
other words, it would cause the abutment to rotate. In addition to this
the same force tends to spread the abutments apart. Both these efforts
put an initial bending moment in the arch ring at the springing; a
moment not calculated, and impossible to calculate.

Messrs. Taylor and Thompson, in their book, give much space to the
elastic theory of the reinforced concrete arch. Little of that space,
however, is taken up with the abutment, and the case they give has
abutments in solid rock with a slope about normal to the thrust of the
arch ring. They recommend that the thrust be made to strike as near the
middle of the base of the abutment as possible.

Malverd A. Howe, M. Am. Soc. C. E., in a recent issue of _Engineering
News_, shows how to find the stresses and moments in an elastic arch;
but he does not say anything about how to take care of the large bending
moments which he finds at the springing.

Specialists in arch construction state that when the centering is
struck, every arch increases in span by settlement. Is this one fact not
enough to make the elastic theory a nullity, for that theory assumes
immovable abutments?

Professor Howe made some recent tests on checking up the elastic
behavior of arches. He reports[X] that "a very slight change at the
support does seriously affect the values of _H_ and _M_." The arch
tested was of 20-ft. span, and built between two heavy stone walls out
of all proportion to the magnitude of the arch, as measured by
comparison with an ordinary arch and its abutment. To make the arch
fixed ended, a large heavily reinforced hea