edly drained the ground above them, thus accounting for the
standing of the ground-water in planes practically parallel with
the surface.

_Third._--Weight of buildings back of wall neglected, as that of the
present type will about equal the cellars filled with material at
100 lb. per cu. ft., and if large buildings are erected in the
future they will undoubtedly be carried to rock.

_Fourth._--Reaction from superstructure, live and dead load, 20,000
lb. per lin. ft. of wall.

_Fifth._--Weight of materials below the 12-ft. line, 124 lb. per
cu. ft., ascertained as follows: The material was considered as
weighing 165 lb. per cu. ft. in the solid, and having 40% of voids
filled with water at 62.5 lb. per cu. ft., the resulting weight
being (165 x 60/100) + (62.5 x 40/100) = 124 lb. per cu. ft.

Various angles of repose were used for this material in the
investigation, and it was finally decided that 30 deg. was the greatest
angle that could be expected, whereas the worst condition that could be
anticipated was that the sand and water would act separately and give a
pressure as follows:

Hydraulic pressure from liquid weighing 62.5 lb. per cu. ft. plus
pressure from sand with angle of repose at 30 deg. and weight as follows:

Weight of 1 cu. ft. in air = 165 x 60/100 = 99 lb.

Weight of water displaced by 1 cu. ft. = 60/100 x 62.5 lb. = 37.5 lb.

Weight in water, therefore = 61.5 lb. per cu. ft.

These combined weights, of course, are equal to the weight of the
combined material in the previous assumption.

_Sixth._--The usual requirement that the resultant of both horizontal
and vertical forces should, at all points, fall within the middle
third of the wall, or, in other words, that there should be no
tension in the concrete.

[Illustration:
Plate LIV.
Diagram Showing Widths of Base of Retaining Wall Required
for Different Batters and Pressures, Pennsylvania Station]

With these assumptions, investigation was made of walls with various
batters and differently designed backs. This investigation developed the
fact that the reaction from the superstructure was so great that, for
economy, both in first cost and space occupied, the batter must be
sufficient to cause that reaction to fall within or very close to the
middle third. Nothing could have been gained by having that reaction
fall back of the front of the middle third, as the wall was req