angle divides this area into two, in one of which the
weight resolves itself wholly into thrust, the other being an area of no
thrust, or wholly of weight bearing on the plane of repose. Calling this
line, _B O_, the haunch line, the thrust in the area, _A O B_, is
measured by its weight divided by the tangent of the angle,
_P Q R_ = [phi], which is the angle of repose; that is, the thrust at
any given point, _R_ = _R Q_ / tan. [phi].

The writer suggests that, in those materials which have steeper angles
of repose than 45 deg., the area of pressure may be calculated as above, the
thrust being computed, however, as for an angle of 45 degrees.

In calculating the bending moment against a wall or bracing, there is
the weight of the mass multiplied by the distance of its center of
gravity vertically above the toe, or, approximately:

2
Area, _A O B_ x weight per unit x --- height,
3

where _h_ = height,

_W_ = weight per cubic foot of material = 90 lb.,

90 deg. - [phi]
and [beta] = -------------
2

_P_ = pressure per linear foot (vertically),

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

When the angle of repose, [phi], is less than 45 deg., 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 deg., 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