normal, the transverse, and the surface waves, are seldom seen though they are more or less felt. The fourth kind are both seen and felt, and are often the most conspicuous and terrifying. They are also the most destructive. They occur only in the epifocal districts of the great earthquakes, and never far outside of them.

In most of the greater or very destructive quakes the ground is seen to be traversed with swiftly moving waves. Their outward forms as described by eye-witnesses exactly resemble flat waves on the water. They move with a speed which to the observer seems no doubt very swift, though in reality it cannot be more than a small fraction of the speed of the waves already mentioned. But they are seen to tilt buildings, to raise and lower the pavements of streets, to swing and lash trees and telegraph poles, to hurl down in ruins brick or stone walls, to sway or even snap off tall chimneys. The ground has been seen to open in cracks in the crests of the waves and close together in the troughs, squeezing out water thick with sand and mud, which is spurted upwards or which forms little craters around the vent holes. The ground if soft and unconsolidated is often permanently distorted by these waves. Railroad tracks and road-beds partake of this distortion, which is often extreme. Excessive distortion was suffered by the road-bed and rails of the South Carolina railway where it crossed the epicentral trail of the Charleston quake. Similarly the Japanese railway in the Mino-Owari quake, and the Assam railway in the great convulsion of 1897, were so distorted that entire reconstruction was necessary.

It is these waves which produce cracks in the soil and

unconsolidated alluvia, which remain after the shaking is past. They also cause landslips by forcibly shaking the materials with aid of gravity down the slopes of the bed rock. It is a frequent occurrence for the alluvial banks of rivers to crowd during the vibrations towards the middle of the stream, opening long, wide cracks on the banks. The

FIG. 50. Locomotive Derailed while Running near Epicentre of Charleston Quake. This and the Preceding Disasters from Figs. 42 to 49

sliding alluvia carry the abutments of bridges with them, crushing up the spans or trusses as if they were wax.

For a long time these motions of the ground were questioned by seismologists, who could hardly believe that such waves could be visible. But the testimony of hosts of credible witnesses at length reached such force and volume, was so concordant and circumstantial, and was so universal in all great earthquakes that it overwhelmed all doubt or

dispute about the fact and left as the only questions the nature and causes of these waves.

The three preceding classes of waves (normal, transverse, and surface waves) all have as their potential energy of motion the elasticity of the materials composing the earthmass. There is abundant reason for inferring that these epifocal waves are of a very different nature and have no relation to elasticity. Their lengths are too small, their amplitudes too great, and their speeds of propagation too slow to be dependent upon elasticity. Their lengths indeed are not known exactly, but the inference from the accounts given of them is that their wave-lengths range between ten and fifty metres and their heights between five and thirty centimetres. Their speeds of propagation are even more uncertain, but are almost surely less than one hundred metres per second. These quantities do not fall within the possible range of elastic wave-motion in any such material as the rocks or soil.

That they are the results of deeper waves passing from a highly elastic to a feebly elastic medium is obvious, and the result must be to diminish the speed of propagation and also the wave-lengths through the yielding and deformation of materials thus invaded. That a greatly increased amplitude should result from the much lower elasticity might also be expected. Probably the deeper transverse waves are the principal agents of this motion. They may be conceived of as flinging the loose, discontinuous surface layers right and left with resistless energy, finding here and there a spot which can be made to oscillate with a period which is some small multiple of their own.

CHAPTER VIII

AMPLITUDES AND PERIODS

Meaning of Amplitude-Illustrations of it Especially Near an EpicentreAmplitude of Vertical Motion-Professor Sekiya's Investigations of Vertical Amplitudes and Periods-Lengthening Out of Periods as Distance Increases-Illustrated in Charleston Quake-Increase of WaveLength with Distance-Effects of Variable Ground upon Amplitudes and Periods-Milne's Results in Observing them at Great Distances from their Origins - Omori's Investigation - His Subdivision of the Phases-Long Distances and their Effects on these Elements-Omori's Conclusion Respecting the Effect of the Free Period of the Ground— Duration of Quakes and its Variation with Distance

BY

Y amplitude is meant the distance which a vibrating particle moves from its mean position of rest. It should not be confounded with double amplitude, or the sum of the distances on both sides of its mean position to which it may move. Thus the amplitude of a water wave is the height either above or below the mean water-level to which a particle rises or falls, and the height from crest to trough is the double amplitude. It is impracticable, or at least inconsequential, to consider amplitude apart from period, which is the time required to complete an oscillation. For wave-motion is a matter of energy in which time is an inseparable element. The energy of the quake is proportional to the square of the velocity of the earth particle and this velocity is in turn proportional to the amplitude directly

ΙΟ

and the time of its excursion, or period, inversely. With equal amplitudes the effects are inversely proportional to the square of the period. Or with equal periods they are proportional to the squares of the amplitudes.

In an ordinary earthquake we have, near the epicentrum, a wide range of both amplitudes and periods, from the smallest quivers to the longest swings. The smallest period which any seismograph can register is not far from the twentieth of a second, though in most instruments the records seldom show a smaller interval than a tenth of a second. This is not because there are no quicker tremors, but simply because the structure of most instruments does not admit of any legible response to quicker ones.

As regards the greatest amplitudes of earthquakes they are never recorded. They are sufficient to destroy or overthrow the instrument and thus prevent its record. It is certain, however, that in some cases it is as great as a foot and possibly in extreme cases a little more. But such an amplitude occurs only on soft ground near the epicentre of a quake of the highest order of energy. Even in such a quake the amplitude on firm rock is probably never more than two inches. An amplitude of .5 mm. and a period of .2 second is quite sensible to the feeling. An amplitude of 10 mm. and .5 second period is a decidedly forcible quake, sufficient to crack walls badly, while 20 mm. and .5 second is a destructive one.

Generally the amplitudes and periods both increase together near an epicentrum, but the former increases more than the latter, thus giving a greater acceleration for the larger swings and consequently greater destructiveness.