that is:

_l_ / 90° - [phi] \
_D_{X}_ = ----- ( tan. { ------------- } + [phi] ) =
2 \ 2 /

_l_ [phi]
----- tan. (45° + ------- ),
2 2

where [phi] = angle of repose,
and _D_{W}_ > _D_{E}_ > _D_{X}_.

Then the pressure on any square foot of roof, as _V_{P}_ as at the base of
any vertical ordinate, as 9 in Fig. 2, = _V_{O}_,

_W_{E}_ = weight per cubic foot of earth (90 lb.),
_W_{W}_ = " " " " " water (62½ lb.), we have

_V_{P}_ = _V_{O}_ × _W_{E}_ + _D_{W}_ × _W_{W}_ × 0.40 =

1
_V_{O}_ × 90 + _D_{W}_ × 62--- × 0.4 = _V_{O}_ 90 + _D_{W}_ × 25.
2

And for horizontal pressure:

_P_{h}_ = the horizontal pressure at any abscissa (10), Fig. 2, = _A_{10}_
at depth of water _D_{W1}_ is