estions 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 deg., 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
place so as to bring the particles into closer contact, and in such a
way that the internal stresses are practically those only of
compression, and the shearing stresses are within the limits possible
for the material in question.

The author has repeatedly made assumptions which are not borne out by
the application of his mathematical formulas to actual extreme
conditions. This method of application to limiting conditions is
concededly sometimes faulty; but the writer believes that no earth
pressure theory, or one concerning arch action, can be considered as
satisfactory which does not apply equally well to hydraulic pressure
problems when the proper assumptions are made as to the factors for
friction, cohesion, etc. For example, when the angle of repose is
considered as zero, in the author's first formula for _W_{1}_, the value
becomes 1/2 _W_{1}_, whereas it should depend solely on the depth, which
does not enter the formula, and not at all on the width of opening, _l_,
which is thus included.

The author has given no experiments to prove his statement that "the
arch thrust is greater in dryer sand," and the accuracy of the statement
is questioned. Again, no reason is apparent for assuming the direction
of the "rakers" in Fig. 3 as that of the angle of repose. The writer
cannot see why that particular angle is repeatedly used, when almost any
other woul