ion 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
up virtually within the limits of the area, _A N_{1} V E J N A_, thus
relieving the structure below of the stresses due to the weight or
thrust of any of the material above; and that the portion of the
material below _V E J_ is probably dead weight on any structure
underneath, and when sustained from below forms a natural "centering"
for the natural arch above. It is also probably true that the material
in the areas, _X N_{1} A_ and _A N U_, does not add to the arching
strength, more especially in those materials where cohesion may not be
counted on as a factor. This is borne out by the fact that, in the
experiment noted, a well-defined crack developed on the surface of the
sand at about the point _U_{1}_, and extended apparently a considerable
depth, assumed to be at _N_, where the haunch line is intersected by the
slope line from _A_.

[Illustration: PLATE XXIV, FIG. 1.--INITIAL SETTLEMENT IN 3-FT. SAND
ARCH, DUE TO COMPRESSION OF MATERIAL ON REMOVING SUPPORTS FROM
BOTTOM.]

[Illustration: PLATE XXIV, FIG. 2.--FINAL SETTLEMENT OF SAND ARCH,
DUE TO COMPRESSION IN EXCESS LOADING.]

In this experiment the sand was good and sharp, containing some gravel,
and was taken directly from the adjoining excavation. When thrown
loosely in a heap, it assumed an angle of repose of about 45 degrees. It
should be noted that this material when tested was not compacted as
much, nor did it possess the same cohesion, as sand in its normal
undisturbed condition in a bank, and for this reason it is believed that
the depth of key given here is absolutely safe for all except
extraordinary conditions, such as non-homogeneous material and others
which may require special consideration.

Referring again to the area, _A N_{1} V J N A_, Fig. 2, it is probable
that, while self-sustaining, some at least of the lower portion must
derive its initial support from the "centering" below, and the writer
has made the arbitrary assumption that the lower