_h_ 2
then _P_ = _h_ × ----- (tan. [beta]) × _W_ × --- _h_ =
2 3
1
--- _h^{3}_ _W_ tan. [beta].
3

When the angle of repose, [phi], is less than 45°, this result must be
reduced by dividing by tan. [phi]; that is,

1
_h_ = --- _h^{3}_ tan. [beta] ÷ tan. [phi].
3

Figs. 1 and 2, Plate XXV, show recently excavated banks of gravel and
sand, which, standing at a general angle of 45°, were in process of
"working," that is, there was continual slipping down of particles of
the sand, and it may be well to note that in time, under exposure to
weather conditions, these banks would finally assume a slope of about 33
degrees. They are typical, however, as showing the normal slope of
freshly excavated sandy material, and a slope which may be used in
ordinary calculations. The steps seen in Plate XXV show the different
characteristics of ground in close proximity. In Fig. 2, Plate XXVI,[D]
may be seen a typical bank of gravel and sand; it shows the well-defined
slope of sand adjacent to and in connection with the cohesive properties
of gravel.

The next points to be considered are the more difficult problems
concerning subaqueous or saturated earths. The writer has made some