Page:Great Neapolitan Earthquake of 1857.djvu/188

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FRACTURE AT BASE—NORMAL WAVE.

the continuous beds of the masonry, or through homogeneous bodies, such as stone shafts of columns, &c.—to none of which the same uncertainty of coefficient applies—

First. Let the wave-path be normal (the force horizontal).

If any prismatic or cylindrical (Fig. 103) solid structure be broken off, by an horizontal fracture at its base, from its own material below that base, and by a normal wave, neither turning over, nor being displaced, but tending to overturn, upon the axis of $\mathrm {A}$ , by the first semiphase, and upon that of $\mathrm {B}$ , by the second semiphase of the wave.

The condition for its fracture thus, without overthrow, is that the overturning moment, shall be equal to the moment of cohesion of the fractured surface of the base.

The fracturing force may be considered as applied at the centre of gravity of the mass detached; and the moment of cohesion at half the radius of oscillation of the plane of fracture, at the base, viewed as surface about to vibrate round the axis $\mathrm {A}$ or $\mathrm {B}$ , as a compound pendulum.^[1]

↑ It has been remarked that "this involves the assumptions, (1) that the body will begin to revolve as if it were absolutely rigid, and (2) that the force of adhesion, on any element of the plane of fracture, will vary, cæteris paribus, as its distance from the axis $\scriptstyle {\mathrm {A} }$ , as if the force were not impulsive, but the mass had extensibility; and it is asked, is there any experimental law which sanctions this conclusion for impulsive as well as continuous forces? If the mass has extensibility in its elements perpendicular to the plane of severance, it must, in like manner, have compressibility; and in such case the mass will not tend to turn round the axis through $\scriptstyle {\mathrm {A} }$ , but round some axis parallel to it, on one side of which, there will be compression, and on the other

[page_140-1] It has been remarked that "this involves the assumptions, (1) that the body will begin to revolve as if it were absolutely rigid, and (2) that the force of adhesion, on any element of the plane of fracture, will vary, cæteris paribus, as its distance from the axis $\scriptstyle {\mathrm {A} }$ , as if the force were not impulsive, but the mass had extensibility; and it is asked, is there any experimental law which sanctions this conclusion for impulsive as well as continuous forces? If the mass has extensibility in its elements perpendicular to the plane of severance, it must, in like manner, have compressibility; and in such case the mass will not tend to turn round the axis through $\scriptstyle {\mathrm {A} }$ , but round some axis parallel to it, on one side of which, there will be compression, and on the other

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