to carry these assumptions to a definite conclusion, we must assume for
that material with an angle of repose of 90° some solid material which
has weight but no thrust, such as blocks of ice piled vertically. In
this case Mr. Goodrich can readily see that there will be no arching
action over the structure, and that the required thickness of key would
be infinite. As to the other case, it is somewhat difficult to conceive
of a solid with an angle of repose of zero; aqueous material does not
fulfill this condition, as it is either a liquid or a combination of
water and solid material. The best illustration, perhaps, would be to
assume a material composed of iron filings, into which had been driven a
powerful magnet, so that the iron filings would be drawn horizontally in
one direction. It is easy to conceive, then, that in tunneling through
this material there would be no necessity for holding up the roof; the
definite thickness of key given, as being at the point of intersection
of two 45° angles, would be merely a precautionary measure, and would
not be required in practice.

It is thus seen that both these conditions can be fulfilled with
practical illustrations; that is, for an angle of repose of 90°, that
material which has weight and no thrust, and for an angle of repose of
zero, that solid material which has thrust but no weight.

Mr. Goodrich says the author has given no experiments to prove his
statement that the arch thrust is greater in dryer sand. If Mr. Goodrich
will make the experiment partially described as Experiment No. 3, with
absolutely dry sand, and with moist sand, and on a scale large enough
to eliminate cohesion, he will probably find enough to convince him that
in this assumption the writer is correct. At the same time, the writer
has based his theory in this regard on facts which are not entirely
conclusive, and his mind is open as to what future experiments on a