bottom settled 2 in. more, or nearly 4 in. in all, due to the further
compression of the sand arch. 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.

Referring to Fig. 2, if, instead of being ordinary sand, the block
comprised within the area, _A U J V X_, had been frozen sand, there can
be no reason to suppose that it would not have sustained itself, forming
a perfect arch, with all material removed below the line, _V E J_, in
fact, the freezing process of tunneling in soft ground is based on this
well-known principle.

[Illustration: FIG. 2.]

[Illustration: FIG. 3.]

If, then, instead of removing the mass, _J E V_, it is allowed to remain
and is supported from the mass above, one must concede to this mass in
its normal state the same arching properties it would have had if
frozen, excepting, of course, that a greater thickness of key should be
allowed, to offset a greater tendency to compression in moist and dry as
against frozen sand, where both are measured in a confined area.

If, in Fig. 2, _E V J_ = [phi] = the angle of repose, and it be assumed
that _A J_, the line bisecting the angle between that of repose and the
perpendicular, measures at its intersection with the middle vertical
(_A_, Fig. 2) the height which is necessary to give a sufficient
thickness of key, it may be concluded that this sand arch will be
self-sustaining. That is, it is assumed that the arching effect is taken