independent, and finally an
interdependent arch.

If Mr. Goodrich's experience has led him to examine any large number of
tunnel arches or brick sewers, he will have noted in many of them
longitudinal cracks at the soffits of the arches and perhaps elsewhere.
These result from three causes:

_First._--In tunneling, there is more or less loss of material, while,
in back-filling, the material does not at first reach its final
compactness. Therefore, in adjusting itself to normal conditions, this
material causes impact loads to come upon the green arch, and these tend
to crack it.

_Second._--No matter how tightly a brick or other arch is keyed in,
there must always be some slight subsidence when the "centers" are
struck. This, again, results in a shock, or impact loading, to the
detriment of the arch.

_Third._--The most prolific cause, however, is that in tunneling, as
well as in back-filling open cuts, the material backing up the haunches
is more or less loosened and therefore is not at first compact enough to
prevent the spreading of the haunches when the load comes on the arch.
This causes cracking, but, as soon as the haunches have been pressed out
against the solid material, the cracking usually ceases, unless the
pressure has been sufficiently heavy to cause collapse.

An interesting example of this was noted in the Joralemon Street branch
of the Rapid Transit Tunnel, in Brooklyn, in which a great many of the
cast-iron rings were cracked under the crown of the arch, during
construction; but, in spite of this, they sustained, for more than two
years, a loading which, according to Mr. Goodrich, was continually
increasing. In other words, the cracked arch sustained a greater loading
than that which cracked the plates during construction, according to his
theory, as noted in the following quotation:

"But it should be equally conceded by the advocates of the
existence of such action that changes in humidity, due to moving
water, vibration, and appreciable viscosity, etc., will invariably
destroy this action in time."

As to the correctness of this theory Mr. Goodrich would probably have
great difficulty in convincing naturalists, who are aware that many
animals live in enlarged burrows the stability of which is dependent on
the arching action of the earth; in fact, many of these burrows have
entrances under water. He would also have some difficulty in convincing
those experienced miners who