or its equivalent, _B D_{1} G B_) of the weight
of this is assumed to be carried by the structure, the upper half being
self-sustaining, as shown by the line, _B_{III} D_{IV}_ (or, for
absolute safety, the curved line), and therefore, if rods could be run
from sheeting inside the tunnel area to a point outside the line, _F
B_{1}_, as indicated by the lines, 5, 6, 7, 8, 11, 12, 13, etc., that
the internal bracing of this tunnel could be omitted, or that the tunnel
itself would be relieved of all loading, whereas these rods would be
carrying some large portion at least of the weight within the area
circumscribed by the curve, _D_{II} I T G_, and further, that a tunnel
structure of the approximate dimensions shown would carry its maximum
load with the surface of the ground between _D_{IV}_ and _F_, beyond
which point the pressure would remain the same for all depths.

In calculating pressures on circular arches, the arched area should
first be graphically resolved into a rectangular equivalent, as in the
right half of Fig. 4, proceeding subsequently as noted.

The following instances are given as partial evidence that in ordinary
ground, not submerged, the pressures do not exceed in any instance those
found by the above methods, and it is very probable that similar
instances or experiences have been met by every engineer engaged in
soft-ground tunneling:

In building the Bay Ridge tunnel sewer, in 62d and 64th Streets,
Brooklyn, the arch timber bracing shown in Fig. 1, Plate XXVI, was used
for more than 4,000 ft., or for two-thirds of the whole 5,800 ft. called
for in the contract. The external width of opening, measured at the
wall-plate, averaged about 19 ft. for the 141/2-ft. circular sewer and 191/2
ft. for the 15-ft. sewer. The arch timber segments in the cross-section
were 10 by 12-in. North Carolina pine of good grade, with 2 in. off the
butt for a bearing to take up the thrust. They were set 5 ft. apart on
centers, and rested on 6 by 12-in. wall-plates of the same material as
noted above. The ultimate strength of this material, across the grain,
when dry and in good condition, as given by the United States Forestry
Department tests is about 1,000 lb. in compression. Some tests[C] made
in 1907 by Mr. E.F. Sherman for the Charles River Dam in Boston, Mass.,
show that in yellow pine, which had been water-soaked for two years,
checks began to open at from 388 to 581 lb. per sq. in., and that yields
of 1/4 in. were no