Earthquakes and other earth movements

by John Milne

Thus, for instance, if the stones in the Yokohama cemetery, at the time of the earthquake of 1880, had been twisted in consequence of the cause suggested by Mallet, we should most certainly have found that some stones had turned in one direction whilst others had been twisted in another. By a careful examination of the rotated stones, I found that every stone—the stones being in parallel lines—had revolved in the same direction, namely in a direction opposite to that of the hands of a watch.

As it would seem highly improbable that the centre of greatest friction in all these stones of different sizes and shapes should have been at the same side of their centres of gravity, an effect like this could only be explained by the conjoint action of two successive shocks, the direction of one being transverse to the other.

Although fully recognising the sufficiency of two transverse shocks to produce the effects which have been observed in Yokohama, I will offer what appears to me to be the true explanation of this phenomenon: it was first suggested by my colleague, Mr. Gray, and appears to be simpler than any with which I am acquainted.

Fig. 30.

If any columnar-like object, for example a prism which the basal section is represented by a b c d (see fig. 30), receives a shock at right angles to b c, there will be a tendency for the inertia of the body to cause it to overturn on the edge b c. If the shock were at right angles to d c, the tendency would be to overturn on the edge d c. If the shock were in the direction of the diagonal c a, the tendency would be to overturn on the point c. Let us, however, now suppose the impulse to be in some direction like e g, where g is the centre of gravity of the body. For simplicity we may imagine the overturning effect to be an impulse given through g in an opposite direction—that is, in the direction g e. This force will tend to tip or make the body bear heavily on c, and at the same time to whirl round c as an axis, the direction of turn being in the direction of the hands of a watch. If, however, the direction of impulse had been e′ g, then, although the turning would still have been round c, the direction would have been opposite to that of the hands of a watch.

To put these statements in another form, imagine g e′ to be resolved into two components, one of them along g c and the other at right angles, g f. Here the component of the direction g c tends to make the body tip on c, whilst the other component along g f causes revolution. Similarly g e may be resolved into its two components g c and g f′, the latter being the one tending to cause revolution.

From this we see that if a body has a rectangular section, so long as it is acted upon by a shock which is parallel to its sides or to its diagonals, there ought not to be any revolution. If we divide our section a b c d up into eight divisions by lines through these directions, we shall see that any shock the direction of which passes through any of the octants which are shaded will cause a positive revolution in the body—that is to say, a revolution corresponding in its direction to that of the movements of the hands of a watch; whilst if its direction passes through any of the remaining octants the revolution will be negative, or opposite to that of the hands of a watch. From the direction in which any given stone has turned, we can therefore give two sets of limits between one of which the shock must have come.

Further, it will be observed that the tendency of the turning is to bring a stone, like the one we are discussing, broadside on to the shock; therefore, if a stone with a rectangular cross section has turned sufficiently, the direction of a shock will be parallel to one of its faces, but if it has not turned sufficiently it will be more nearly parallel to its faces in their new position than it was to its faces when in their original position.

If a stone receives a shock nearly parallel with its diagonal, on account of its instability it may turn either positively or negatively according as the friction on its base or some irregularity of surface bearing most influence. Similarly, if a stone receives a shock parallel to one of its faces, the twisting may be either positive or negative, but the probability is that it would only turn slightly; whereas in the former case, where the shock was nearly parallel to a diagonal, the turning would probably be great.