As soon as the blocking was removed the bottom settled nearly 2 in., as noted in Fig. 1, Plate XXIV, due to the initial compacting of the sand under the arching stresses.  A measurement was taken from the bottom of the washers to the top of the false bottom, and it was noted as 41 in.  (Fig. 1).  After some three or four hours, as the arch had not been broken, it was decided to test it under greater loading, and four men were placed on it, four others standing on the haunches, as shown in Fig. 2, Plate XXIV.  Under this additional loading of about 600 lb. the 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 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.