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, after a cave-in, always wait until the ground has settled and compacted itself before tunneling, usually with apparent safety, over the scene of the cave-in.

The writer quotes as follows from Mr. Goodrich’s discussion: 

“In any case, no arch action can be brought into play until a certain amount of settlement has taken place so as to bring the particles into closer contact, and in such a way that the internal stresses are practically those only of compression, and the shearing stresses are within the limits possible for the material in question.”

Further: 

     “Consequently, an almost infinitesimal settlement of the
     ‘centering’ may cause the complete destruction of an arch of
     earth.”

And further: 

“On the other hand, it is believed that the author’s statement, as to the ‘tendency of marbles to arch,’ * * * should be qualified by the addition of the words, ’only when a certain amount of deflection has taken place so as to bring the arch into action.’”

In a large measure the writer agrees with the first and last quotations, but sees no reason to endorse the second, as it is impossible to consider any arch being built which does not settle slightly, at least, when the “centers” are struck.