putting the water into the box, he can do this without bringing about
the collapse of the arch; the only essential condition is that the
bottom shall be keyed up tightly, so as not to allow the escape of any
sand. He is also referred to the two photographs, Plate XXIV,
illustrating the writer's first experiment, showing how increases in the
loading resulted in compacting the material of the arch and in the
consequent lowering of the false bottom. As long as the exposed sand
above this false bottom had cohesion enough to prevent the collapse of
the "centering," this arch could have been loaded with safety up to the
limits of the compressive strength of the sand.

To quote again from Mr. Goodrich:

"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."

Mr. Goodrich assumes that water or liquid has an angle of repose equal
to zero, which is true, but the writer's assumptions applied only to
solid material, and the liquid gives an essentially different condition
of pressure, as shown by a careful reading of the paper. In solid rock
Mr. Goodrich assumes an angle of repose equal to 90°, for which there is
no authority; that is, solid rock has no known angle of repose. In order