work, both mathematical and logical, is emphatically questioned.

The writer believes that, in the design of permanent structures,
consideration of arch action should not be included, at least, not until
much more information has been obtained. He also believes that the
design of temporary structures with this inclusion is actually dangerous
in some instances, and takes the liberty of citing the following
statement by the author, with regard to his first experiment:

"About an hour after the superimposed load had been removed, the
writer jostled the box with his foot sufficiently to dislodge some
of the exposed sand, when the arch at once collapsed and the bottom
fell to the ground."

The writer emphatically questions the author's ideas as to "the
thickness of key" which "should be allowed" over tunnels, believing that
conditions within an earth mass, except in very rare instances, are
such that true arch action will seldom take place to any definite
extent, through any considerable depths. Furthermore, the author's
reason for bisecting the angle between the vertical and the angle of
repose of the material, when he undertakes to determine the thickness of
key, is not obvious. This assumption is shown to be absurd when carried
to either limit, for when the angle of repose equals zero, as is the
case with water, this, method would give a definite thickness of key,
while there can be absolutely no arch action possible in such a case;
and, when the angle of repose is 90°, as may be assumed in the case of
rock, this method would give an infinite thickness of key, which is
again seen to be absurd. It would seem as if altogether too many
unknowable conditions had been assumed. In any case, no arch action can
be brought into play until a certain amount of settlement has taken