610 EARTHQUAKE permanent elevation. That elevation has been frequently observed after an earthquake is a fact beyond question ; thus, Captain Fitzroy found, after the South American earthquake of 1835, that a part of the isle of Santa Maria, in the Bay of Coucepcion, had been raised upwards of 10 feet, and, although this elevation was followed by a slow subsidence, it is believed that the land was permanently left considerably higher than its level before the occurrence of the catastrophe. Mr Mallet, however, would refer such alteration of level to the action of elevatory forces accom panying the earthquake, but not to the direct transit of the earth-wave. From the density and the modulus of elasticity of a given rock, it is possible to calculate the velocity with which a vibration would travel through such a medium. But the rate deduced by calculation usually exceeds very greatly that actually observed in an earthquake. To determine the rate of transit through various rocks, Mr Mallet and his son Dr J. W. Mallet conducted many years ago a series of experiments, at the instance of the British Association. A mile was carefully levelled and measured on sand in Killiney Bay, near Dublin, and by explosion of gunpowder the velocity of transmission through this damp sand was observed. This sand was selected as a medium likely to give a minimum velocity, whilst an assumed maximum velocity was observed by experiments on the granite of Killiney Hill. The velocity in sand was about 825 feet, and in solid granite 1665 feet per second. These figures are much lower than those obtained from theoretical con siderations, and it is believed that the difference is due to loss of speed occasioned by the discontinuity of the rock, even the solid granite being always more or less affected by joints. The velocity deduced from these experiments accords tolerably well, however, with that observed during earthquake-shocks. Thus the velocity of shock during the Lisbon earthquake of 1755 is computed to have been about 20 miles per minute, or 1760 feet per second. This velocity of the vibration, or wave of shock, is of course to be carefully distinguished from the velocity of the oscillat ing particles. The mischief of the shock depends in fact on the rate at which the earth-molecules are moving, and this is vastly inferior to that of the wave. Thus Mr Mallet calculated from his observations in Naples that the shock of the great earthquake of 1857 had a mean velocity at the surface of 788 feet per second, whilst the greatest velocity of the wave-particles was never more than 15 feet per second, and in many places was very much less. Yet this low velocity is quite sufficient to produce effects of the most disastrous kind upon solid objects exposed to the shock. If the earth were a homogeneous solid, perfectly isotropic that is to say, possessing equal elasticity in all directions the waves of alternate compression and expansion would take the form of a series of concentric spherical shells around the seismic focus as a common centre. As a matter of fact, however, the crust of the earth is made up of rocks varying greatly in physical properties, each having its own density and elasticity, whilst the rocks themselves are fissured in all directions. Symmetry of wave-surface is therefore hardly to be expected ; for the waves will neces sarily have greater velocity in one direction than in another, whilst the transit of the wave may be interrupted by breach of continuity in the transmitting medium. The points at which a wave-shell reaches the surface form a curve which is conveniently called a coseismal line. It is obviously the line along which an earthquake shock will be simultane ously felt, and where the waves will emerge at the same angle. Since the wave-shells are not concentric spheres, the coseismal curves cannot be concentric circles. It may readily be supposed that the greatest effect of an earthquake, at least in shaking a building up and down, will be felt at that point of the surface which is situated vertically over the centre of impulse. A line joining this point with the earthquake-focus is termed the seismic vertical, and the wave travelling to the surface along this vertical has a shorter path than that of a wave emerging at any other point. Just as the seismic focus is, in nature, not a single point, but a considerable space, so the seismic vertical is not a single line, but rather a succession of parallel lines drawn vertically from every point of the focal area to the surface. The mean of these lines may be taken as the seismic vertical. In the neighbourhood of this line the waves emerge at very steep angles, and indeed for a considerable area may be regarded as practically vertical in direction. As the distance from the seismic vertical increases, the angle of emergence becomes less and less ; but it is evident that since the focus is seated beneath the surface, the path of an emergent wave can never be perfectly horizontal, unless indeed it be that of a reflected wave. Almost any object which has been overthrown or projected by an earthquake-shock may afford direct information as to the path of the wave along the surface. For when the vibration is trans mitted to such a solid body as an upright column, the particles are pushed together and then pulled apart in the line of wave-transit. It is clear too that half the excursion of each particle is executed in the same direction as that _in which the wave is travelling, and half in the opposite direction. Each particle of the object when first disturbed moves with the wave, and its velocity increases from zero to the maximum, this maximum being reached at one quarter of the total vibration ; then the velocity diminishes from the maximum to zero, which it attains at the end of half the oscillation. During this first semi-phase, therefore, the vibration has been in the direction in which the wave moves. After the first half oscillation has been executed, movement begins afresh, but this time in the contrary direction, attaining its maximum at the end of the third quarter, and then falling again to zero when the vibration is completed. Hence during the first semi-phase, the motion of the particles is in the same sense or direction as that of the wave, and during the second semi-phase in the opposite direc tion. But in consequence of the inertia of the body its apparent movement if free, will be in a direction contrary to that of the wave during the first semi-phase. Whatever the direction of overthrow, however, it will always be in the line of wave-transit. Hence the azimuthal direction of the wave is easily found. Whenever any two wave-paths, not in the same right line, can be thus traced on the surface, the position of the seismic vertical may be immediately determined. For this line must pass through the point of their in tersection. If, for example, it is found by observation on bodies displaced by the shock that one wave moved in the direction AB (fig. 1), whilst another had a path along CD, it is only necessary to mark on the surface the point 0, at which these azimuths meet, and the seismic focus will be vertically be neath such a point. The point indicates, in fact, the centre on the surface from which the waves radiated. Practically it is found that the several wave-paths of an earthquake do not diverge from a single point, for reasons already indicated; but intersections of the paths are crowded together in the neighbourhood of the mean vertical. It is easy to understand that the greatest amount of mechanical damage is not to be expected immediately above the focus, although this is the point nearest to the origin of impulse. It is true, the shock passing directly upwards along the seismic vertical might destroy the roof or floor of a building, but it would not tend directly to overturn the walls or produce lateral disturbance. In fact, the side-thrust will be greatest in waves which reach the surface at small angles, and are therefore necessarily at great dis tances from the seismic vertical. But the energy of the wave diminishes as the square of the distance along the normal increases. Hence there must be some definite position upon the surface beyond which advantage of direction is counterbalanced by loss of energy. Indeed it is generally possible after an earthquake to trace a zone of maximum disturbance, where the damage to the shaken country has been greatest. The line indicating this maximum is termed the meizoseismic curve, whilst lines along which the overthrow of objects may be regarded as practically the same are known as isoseismic curves. After what has been already said, it is hardly necessary to remark that these lines are not true circles, iior indeed
are they in all cases regular closed curves.