Accounts of earthquakes are to be found scattered through the writings of many ancient authors, but they are, for the most part, of little value to the seismologist. There is a natural tendency to exaggeration in describing such phenomena, sometimes indeed to the extent of importing a supernatural element iuto the description. It is true that attempts were made by some ancient writers on natural philosophy to offer a rational explanation of earthquake phenomena, but the hypotheses which their explanations involved are, as a rule, too fanciful to be worth reproducing at the present day. It is therefore unnecessary to dwell upon the references to seismic phenomena which have come down to us in the writings of such historians and philosophers as Thucydides, Aristotle, and Strabo, Seneca, Livy, and Pliny. Nor is much to be gleaned from the pages of mediaeval and later writers on earthquakes, of whom the most notable are Fromondi (1527), Maggio (1571), and Travagini (1679). In this country, the earliest work worthy of mention is Dr Robert Hooke’s Discourse on Earthquakes, written in 1668, and read at a later date before the Royal Society. This discourse, though containing many passages of considerable merit, tended but little to a correct interpretation of the phenomena in question. Equally unsatisfactory were the attempts of Priestley and some other scientific writers of the last century to connect the cause of earthquakes with electrical phenomena. The great earthquake of Lisbon in 1755 led the Rev. John ΛIichell, professor of mineralogy at Cambridge, to turn his attention to the subject; and in 1760 he published in the Philosophical Transactions a remarkable essay on the Cause and Phenomena of Earthquakes. Regarding the earth as having a liquid interior covered by a comparatively thin crust, he conceived that waves might be generated in this subterranean liquid, and that such waves by shaking the flexible crust would produce the shocks of an earthquake.

Hie illustration of the movement of the ground is that of a loose carpet thrown into undulations by being shaken at one corner. Although Michell’s hypothesis is still accepted, in a modified form, by some geologists, it should be remembered that many arguments of considerable weight have been urged by modern physicists against the doctrine of a liquid nucleus and a thin crust. Whatever the merits of Michell’s theory, he failed to understand the true nature of wave-motion, and the way in which it is transmitted during an earthquake shock. Modern seismologists believe that an earthquake is a vibratory motion propagated through the solid materials of the earth, much in the same way that sound is propagated by vibrations in the atmosphere. It appears that this view was first suggested by Dr Thomas Young in his Lectures on Natural Philosophy, published in 1807. The development of this view, especially in its quantitative results, lies at the very base of seismology. In 1846 Mr Mallet communicated to the Royal Irish Academy his first paper “On the Dynamics of Earthquakes;” and in the following year the late Mr Hopkins, of Cambridge, presented to the British Association a valuable report in which earthquake-phenomena are discussed in some detail. Since that date the great advances in this country have been made by Mr Mallet, assisted occasionally by the Rev. Professor Haughton and other mathematicians.

Even at the present day, after all that has been written on the subject, but little is really known as to the origin of earthquakes. Probably several distinct causes should be recognized, for it is hardly to be supposed that all subterranean disturbances, differing as they do so widely in intensity and in duration, should be referable to one common mechanism. Any great concussion, even upon the surface, is competent to produce tremors which may be regarded as diminutive earthquakes; thus the great landslip at the Rossberg in Switzerland in 1806 was accompanied by a local quaking of the ground. Volger and Mohr have suggested that some of the small earthquakes which have been felt in Germany may be referred to the falling-in of the roof of enormous subterranean cavities formed by the long-continued solvent action of water on deposits of rocksalt, limestone, and gypsum. Such causes, however, can have given rise to only very petty shocks, and must be quite subordinate to subterranean disturbances of a more general character. The late Mr Poulett Scrope was led to refer most earthquakes to “the snap and jar occasioned by the sudden and violent rupture of solid rock-masses, and perhaps the instantaneous injection into them of intumescent molten matter from beneath.” He believed that the rupture of the rocks was due to expansion of deeply seated masses of mineral matter, consequent upon either increased temperature or diminished temperature. It is argued, however, by Mr Mallet, on mechanical principles, that such fractures could produce only very weak impulses; but he believes that some earthquakes, especially those marked by long continued tremors, may be due to the movement and crushing of rock masses by tangential pressures produced by secular cooling of the earth. Steam has always been a favourite agent with seismologists, since it is clearly competent to produce great effects by its sudden generation or by its sudden condensation. It has been suggested that water, finding its way through fissures in the earth’s crust, might reach highly-heated rocks and remain quietly, in the spheroidal condition, until a local reduction of temperature suddenly caused it to flash into steam. After all, the origin of earthquakes is probably to be regarded as part only of a much wider question. Whatever causes are competent to produce volcanic action are, in all likelihood, equally competent to produce the ordinary manifestations of seismic energy. A relation is clearly traceable between the geographical distribution of volcanoes and the chief earthquake-areas; and although it is not for a moment to be supposed that the volcano and the earthquake stand to each other in the relation of cause and effect, it is nevertheless highly probable that they represent merely different expressions of the same subterranean forces.

Whatever may be the real origin of the earthquake shock, it is convenient to regard its effects as proceeding from a concussion or sudden blow delivered underground at some definite centre. This centre of impulse is called the seismic focus. It must be borne in mind, however, that such a centre, so far from being anything like a mathematical point, is in nature a subterranean region, which in many cases is no doubt of very large dimensions, measuring perhaps some miles in diameter.

From the seismic centre waves are propagated in all directions through the solid materials of the earth’s crust; and if the focus be situated beneath the sea, the vibrations of the ground will be accompanied by undulations of the water. Those waves which pass through the elastic materials of the earth consist, for the most part, of longitudinal vibrations, like those of atmospheric sound-waves, and consequently not like ordinary water-waves. In the sound-wave the air is alternately condensed and rarefied, the molecules advancing and retreating in the line of direc tion in which the wave is travelling. In a water-wave, on the contrary, the molecules of liquid rise and fall, or rather describe closed curves in planes which are transverse to the direction in which the undulation or wave-form advances. According to Mr Hopkins, both orders of vibration—longitudinal and transversal—coexist in the earth quake-wave, and call for investigation. When, for example, the molecules of an iron bar are disturbed by a blow delivered at one end, both kinds of vibration are generally excited, and hence two waves are sent through the bar,— the longitudinal, however, having a much greater velocity than the transversal wave. But it may be doubted whether the seismologist need concern himself with any but longitudinal vibrations. For, admitting that small transversal vibrations are generated at the seismic focus, it is probable that they would be cut off to a great extent during transmission from stratum to stratum. Indeed, the planes of junction between the several beds in stratified deposits would hinder the transmission of transversal vibrations travelling in a direction normal to the strata. Hence Mr Mallet maintains, that in studying the effects of an earthquake, attention may be restricted, without danger of error, to the longitudinal or normal vibrations, the transversal or tangential vibrations being neglected.

Around the seismic centre, or mean focal point, the molecules of the rock will first be squeezed together by the concussion, and then separated by virtue of the elasticity of the solid medium; the onward motion is then rapidly taken up by the next set of molecules, which in like manner are pushed against each other, and then spring apart. In this way the pulse, or form of the wave, may be propagated to an enormous distance, whilst the excursions of the individual particles are confined within very narrow limits. It is therefore of great importance to distinguish between the transit of the wave and the movement of the material particles. Each molecule may move only through a few inches, but the undulation may travel for hundreds of miles. The distance through which the individual particles oscillate is called the amplitude of the wave. After the Neapolitan earthquake of 1857 Mr Mallet found from actual observation at a place called Polla, situated nearly above the seismic centre, that the amplitude of a wave which caused certain fractures in masonry could not have been more than 2∣ inches. He is thus led to believe, contrary to the opinion of most geologists, that earthquakes are not great agents of 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 Concepcion, 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 accompanying 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 considerations, 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 oscillating 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 necessarily 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 simultaneously 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 transmitted 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 jn 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 direction. 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 intersection. 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 beneath 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 distances 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 meizoseismie curve, whilst lines along which the overthrow of objects may be regarded as practically the same are known as Vioseismw curves. After what has been already said, it is hardly necessary to remark that these lines are not true circles, nor indeed are they in all cases regular closed curves.

Fractures and fissures in walls which have been rent by an earthquake, are of great value to the seismologist, since they often indicate the direction in which the waves emerge at the surface. The interpretation of such phenomena, in some cases very complicated, has been ably discussed by Mr Mallet, who applied the results with excellent effect to his observations on the Neapolitan earthquake. If it is possible to find, from such indications, the direction in which any two waves emerged at the surface, the depth of the seismic focus is easily determined. For since the waves radiate from this focus, any two wave-paths when produced backwards will meet at the seismic centre. It has already been shown how easily the vertical is found, and when this is known the determination of the focus is simplified, for as the vertical itself represents one-wave path it is necessary to find only one other. Let 0 (fig. 2) be the seismic focus, and OA the seismic vertical; if a wave, OB, emerge at the surface B, at an angle 0, it is evident that

AO = AB . tan 0.

To find the depth of the focus, it is consequently only necessary to know the angle of emergence of a wave at a given station, and the distance of this station from the seismic vertical. As the stations A and B are comparatively near each other, the earth’s sphericity may be neglected, and the surface between the two regarded as practically a horizontal plane.

Where several wave-paths are known, several values of AO will be obtained, and as the seismic centre is not a point, like 0, but a cavity of determinate magnitude, the average of these different values must be taken to represent the mean focal depth. After the great Neapolitan earthquake of 1857, Mr Mallet, aided by the Éoyal Society, spent some months...