Result of Feelings.—As the result of our experiences, and by observations upon the movements produced in various bodies, we can say that an ordinary earthquake consists of a number of backward and forward motions of the ground following each other in quick succession. Sometimes these commence and die out so gently that those who have endeavoured to time the duration of an earthquake have found it difficult to say when the shock commenced and when it ended. This was a difficulty which Mr. James Bissett in Yokohama, and the author in Tokio, had to contend against when, in 1878, they commenced to time shocks between these two places.

Sometimes these motions gradually increase to a maximum and then die out as gradually as they commenced.

Sometimes the maximum comes suddenly, and at other times during an earthquake our feelings distinctly tell us that there are several maxima.

These have been the experiences of many observers, and have been recorded by writers since the earliest times. Mallet devotes a chapter to a consideration of the tremulous motion that precedes and follows a shock, and he tells us that a single shock is an absolute impossibility. In speaking of earthquakes, he says: ‘The almost universal succession of phenomena recorded in earthquakes is, first a trembling, then a severe shock, or several in quick succession, and then a trembling gradually but rapidly becoming insensible.’

A quantitative and exact knowledge of the nature of earthquake motion has only been attained of late years. The chief results which investigators have aimed at have been the measurement of the amplitude, the period, the direction, and the duration of the motions which constitute an earthquake. Attention has also been given to the velocity with which a disturbance is propagated.

The Direction of Motion.—One of the most ordinary observations which are made about an earthquake is its direction. If we were to ask the inhabitants of a town which had been shaken by an earthquake the direction of the motion they experienced, it is not unlikely that their replies would include all the points of the compass. Many, in consequence of their alarm, have not been able to make accurate observations. Others have been deceived by the motion of the building in which they were situated. Some tell us that the motion had been north and south, whilst others say that it was east and west. A certain number have recognised several motions, and amongst the rest there will be a few who have felt a wriggling or twisting. Leaving out exceptional cases, the general result obtained from personal observation as to the direction of an earthquake of moderate intensity is extremely indefinite, and the only satisfactory information to be obtained is that derived from instruments or from the effects of the earthquake exhibited in shattered buildings and bodies which had been overturned or projected.

By the direction in which walls, columns, and other objects had been overthrown or fractured, Mallet was enabled to determine the position of the origin of the Neapolitan earthquake. Similar phenomena have many times been taken advantage of by other investigators of earthquake phenomena. Effects produced upon structures are, however, only to be observed as the results of a destructive earthquake, at which time cities may be regarded as collections of seismometers. (See chapter on Effects in Buildings.)

To determine the direction of movement during a small earthquake, the most satisfactory method appears to be an appeal to instruments.

Instruments as Indicators of Direction.—The relative values of different kinds of instruments, such as columns, pendulums, and the like, as indicators of direction have already been discussed.

By the use of pendulum seismographs it has been shown that during an earthquake the ground may move in one, two, or several directions (see p. 21); and it is, generally speaking, only in those cases where we experience a decided shock in the disturbance that we can determine with any confidence the direction in which the motion has been propagated. Such directions are usually indicated by the major axis of certain more or less elliptical figures which have been drawn, which in themselves appear to indicate the combination of two rectilinear movements.

Results similar to those indicated by the records of pendulum seismographs have also been obtained upon moving plates with a double bracket seismograph. Thus, in the earthquake which shook Tokio at 6 a.m. on July 5, 1881, there were indications of the following motions:—

Near the commencement of the shock the motion was N. 112° E. One and a half second after this, the direction of motion appears to have been N. 50° E. In three-fourths of a second more it gradually changed to a direction N. 145° E., and after a similar interval to N. 62° E. Half a second after this it was N. 132° E., and four seconds later the motion was again in the original direction—namely, N. 112° E.

These particular directions of motion have been selected because they were so definitely indicated.

The commonest type of earthquake which is experienced in Japan, and probably also in other earthquake-shaken districts, is the compound or diastrophic form.

That earthquakes often have motions compounded of two sets of vibrations, has also been proved by the analysis of the records obtained from two component seismographs. From an analysis of a record of this description, Professor Ewing has shown that in the earthquake felt in Tokio on March 11, 1881, there were approximate circular (somewhat spiral) movements.

This leads us to the consideration of the twisting and wriggling motions which are said to be experienced by some observers. Motions like these, which by the Italians and Mexicans are called vorticosi, are usually supposed to be the cause of objects like chimneys and gravestones being rotated. These phenomena, it will be seen from what is said in the chapter upon the effects produced in buildings, can be more easily explained upon the supposition of a simple rectilinear movement.

That at the time of an earthquake there may be motion in more than one direction has been recognised since the time of Aristotle; and it is possible that two sets of rectilinear motion, as, for instance, the normal and transverse movements, may have led observers to imagine that there has been a twisting motion taking place, and this especially when the two sets of movements have quickly succeeded each other.

Persons inside flexible buildings may possibly have experienced more or less of a rotatory motion, although the shock was rectilinear; the building assuming such a motion in consequence of its construction and its position with regard to the direction of the shock.

In the case of destructive earthquakes, especially at points situated practically above the origin, the universal testimony, Mallet tells us, is that a twisting, wriggling motion in different planes, attended by an up-and-down movement of greater range, is experienced. To such disturbances the word sussultatore is sometimes applied. Mallet has given many elliptical and other closed curves to illustrate the nature of such motions.

Duration of an Earthquake.—When reading accounts of earthquakes it is often difficult to determine the length of time a shaking was continuous. In Japan, in a.d. 745, there was a shaking which is said to have lasted sixty hours; and in a.d. 977 there were a series of shakings lasting 300 days. Often we meet with records of disturbances which have lasted from twenty to seventy days.

At San Salvador, in 1879, more than 600 shocks were felt within ten days; in 1850, at Honduras, there were 108 shocks in a week; in 1746, at Lima, 200 shocks were felt in twenty-four hours; at the island of St. Thomas, in 1868, 283 shocks were felt during about ten hours.

Disturbances like these, which succeed each other with sufficient rapidity to cause an almost continual trembling in the ground, may be regarded as collectively forming one great seismic effort which may last a minute, an hour, a day, a week, or even several years. Strictly speaking, they are a series of separate earthquakes, the resultant vibrations of which more or less overlap. Whenever a large earthquake occurs it is generally succeeded by a large number of smaller shocks.

The seismic disturbance as regards time is, as Mallet remarks, very often ‘like an occasional cannonade during a continuous but irregular rattle of musketry.’ In the New Zealand earthquake of 1848, shocks continued for nearly five weeks, and during a large portion of the time there were at least 1,000 shocks per day.[12]

The earthquake of Lisbon, which in five minutes destroyed the whole town, was followed by a series of disturbances lasting over several months. After Basle had, on October 18, 1356, been laid in ruins, it is stated shocks followed each other for a period of a year. The Calabrian earthquake was continued with considerable strength for a year, and it is said that the earth did not come completely to rest for ten years. During this cannonade the heavy shocks announced, as they do in most earthquake countries at the present day, a series of weaker disturbances. In certain exceptional cases this order of events has been inverted, and slight shocks have announced the coming of heavy ones. Fuchs gives an example of this in the earthquake of Broussa, when the first shock was on February 28, 1855. On March 9 and 23 there were heavier shocks, but the heaviest did not arrive until March 28.

Under certain conditions it is possible to have a sensible vibration produced in the ground which is practically of unlimited duration; thus, for instance, it has been noticed that the falling of water at certain large waterfalls, by its continuous rhythmical impact on the rocks, produces in them tremors which are to be observed at great distances. Of this the author convinced himself at the Falls of Niagara, where he observed the reflected and ever-moving image of the sun in a pool of water. Under favourable circumstances almost continual condensation of steam might take place in volcanic foci, each condensation giving rise to a blow sufficiently powerful to produce vibrations in the surrounding ground. Those who have stood near a large geyser, like the one in Iceland, when it makes an ineffectual effort to erupt, will recognise how powerful such a cause might be. Humboldt has remarked shocks on Vesuvius and Pichincha which were periodic, occurring twenty to thirty seconds before each ejection of vapour and ashes.

Earthquakes like these may be of vast extent, gradually spreading further and further outwards. This spreading of earth vibrations may be observed at a large factory containing heavy machinery or a steam hammer. After the machinery comes to rest, it is probably some time before the ground returns to rest. Examples of disturbances of this nature are spoken of under the head of Earth Tremors.

The record of the duration of an ordinary earthquake as observed at a given point is dependent upon the sensibility of our instruments.

Continuous motions perceptible to our senses without the aid of instruments usually last from thirty seconds to about two or three minutes. In Japan the shocks, as timed by watches, usually last from twenty to forty seconds. Occasionally a continuous shaking is felt for more than one and a half minutes, and cases have been recorded where the motion has continued for as much as four minutes and thirty-three seconds.

Seismometers having a multiplication of 6 to 12 usually indicate that motion continues longer than is perceptible to the senses.

Period of Vibration.—When an earthquake contains several prominent vibrations which might be called the shocks of the disturbance, our feelings tell us that these have occurred at unequal intervals.

About the time which is taken for the complete backward and forward oscillation of the ground which constitutes the shock a little has already been said. This was deduced from the records of disturbances as drawn by seismographs. From the same sources we can readily obtain the period of all the prominent vibrations in a disturbance.

In any given earthquake there are irregularities in period, and different earthquakes differ from each other. About the early attempts to determine the period of earth vibrations something has been said in the chapter on Earthquake Instruments.

In the earthquake of March 11 (referred to on p. 70) we find that both components commenced with a series of small vibrations, about five or six to the second; next came the shock, consisting of two complete vibrations executed in two seconds. In this it is to be observed that the motion eastwards was performed much more quickly than the motion westwards. Next, by reference to the east and west component, it is seen that there are a number of large vibrations, about one per second, on which a number of smaller motions are superposed. As the motion proceeds, these become less and less definitely pronounced and more irregular in their intervals, until finally the motion dies away.

This earthquake, as recorded at the author’s house in Tokio, lasted about one and a half minute.

The same earthquake, as recorded by Professor Ewing at a station situated about one and a half mile distant, but on flat ground, appears to have lasted four and a half minutes. The largest wave had a period of 0·7 second.

In the earthquake of March 8, 1881, there were on an average 1·4 vibrations per second. These vibrations were executed in a direction transverse to the line joining the observing station and the locality from which the disturbance must have originated as determined by time observations. It can, therefore, be assumed that these vibrations, having so slow a period, were transverse motions, this slowness or sluggishness being due to the fact that the modulus for distortion is less than the modulus which governs the propagation of normal vibrations.

The Amplitude of Earth Movements.—In making estimates of the distances through which we are moved backward and forward at the time of an earthquake, if we judge by our feelings, we may often be misled. If a person is out of doors and walking, an earthquake may take place sufficiently strong to cause chimneys to fall and unroof houses, which, so far as the actual shaking of the ground is concerned, will be passed by unnoticed. On the other hand, to persons indoors, especially on an upper story, it is impossible even for a tremor to pass by without creating considerable alarm by the angular movement that has been taken up by the building.

Many observers have endeavoured to make actual measurements of the maximum extent through which the earth moves at the time of an earthquake. Among the reports of the British Association for 1841 is the report of a committee which had been appointed ‘for obtaining instruments and registers to record shocks of earthquakes in Scotland and Ireland’. We read that in one earthquake which had been measured the displacement of the ground had been half an inch, and in another it had been less than half an inch. The instruments used to make these observations depended upon the inertia of pendulums which at the time of the disturbance were supposed to remain at rest. Observations similar to these have been made in Japan. One long series were made by Mr. E. Knipping for Dr. Gr. Wagener. They extended from November 1878 to April 1880, and were as follows:—

With his apparatus for vertical motion Dr. Wagener also made observations on the absolute vertical motion. This seldom reached ·02 mm. The greatest value was that observed for the destructive shock of Feb. 22, 1880, which was ·56 mm.

By means of a number of instruments distributed at various localities round Tokio, the chief of which were pendulums with friction pointers to render them ‘dead beat,’ and with magnifying apparatus to show the actual motion of the ground, the author arrived at results similar to those obtained by Dr. Wagener—namely, that the earth’s maximum horizontal motion at the time of a small earthquake was usually only the fraction of a millimetre, and it seldom exceeded three or four millimetres. When we get a motion of five or six millimetres, we usually find that brick and stone chimneys have been shattered.

The results obtained for vertical motion were also very small. In Tokio it is seldom that vertical motion can be detected, and when it is recorded it is seldom more than a millimetre.

These results, which were put forward some years ago, have since received confirmation by the use of a variety of instruments in the hands of different observers.

Mallet, in his account of the Neapolitan earthquake of 1857, approximated to the amplitude of an earth particle by observing the width, at the level of the centre of gravity, of fissures formed through and remaining in great masses of very inelastic masonry.

Taking stations situated on or very nearly on the same line passing through the seismic vertical (epicentrum), Mallet observed the amplitude increased as some function of the distance, as will be seen from the following table:—

The possibility of a law such as this having an existence for places at a distance from the seismic vertical comparable with the vertical depth of the centrum will be shown farther on.

With regard to the maximum displacement of an earth particle. Mallet was of opinion that there was evidence to show that it had in some cases been over one foot. M. Abella, in an earthquake which occurred in the Philippines in 1881, made a rough observation of the motion of the earth to a distance of about two metres. This, as might be expected, was beyond the elastic limits of the material, and caused fissures to be formed, which were seen to open and shut.

Intensity of Earthquakes.—In speaking of the strength of an earthquake, we usually employ terms like ‘weak,’ ‘strong,’ ‘violent,’ &c. Although these expressions, accompanied by illustration of the effects which an earth quake has produced, convey a general idea of the strength of a shock as felt at some particular locality, our ideas nevertheless wanting in definiteness; and if we endeavour to compare one shock with another, as a whole, our want of exactness is augmented. We have seen that Palmieri’s seismograph indicates intensity by a certain number of degrees, which, to a certain extent, is a measure of the violence of the motion as indicated at a particular locality. The degrees, as before stated, refer to the height to which in consequence of the shaking, a certain quantity of mercury was washed in a tube, which is a function of the depth of mercury in the tube, and also of the duration of the disturbance.

From this it seems possible that a very slow motion of small amplitude, continuing over a sufficient period of time, might, if it agreed with the period of the mercury, indicate an earthquake of many degrees of intensity, whilst residents in the neighbourhood might not have noticed the disturbance; and, on the other hand, a short but intense shock creating considerable destruction might have been recorded as of only a few degrees of intensity.

Although objections like these might be raised to such a method of recording intensity, in practice it would appear that such results are not pronounced, and the indications of the instrument usually give us approximate indications of relative intensity.

In writing about the Neapolitan earthquake of 1857, Mallet says that ‘area alone affords no test of seismic energy.’

The area over which a shock is felt will depend not only upon the initial force of the disturbance, but also upon the focal depth of a shock, the form and position of that focus, the duration of the disturbance, and the nature and arrangement of the materials which are shaken.

From observations in Japan, it is clearly shown that massive mountain ranges exert a considerable influence upon the extension of seismal disturbances. On one side of a large range of mountains large cities might be laid in ruins, whilst on the other side the disturbance creating this destruction might not be noticed.

Velocity and Acceleration of an Earth Particle.—We now pass on to methods of determining the intensity of an earthquake which are less arbitrary than those which have just been discussed. These methods have already been discussed when speaking of artificial disturbances, where it was shown that the intensity of an earthquake as measured by its destructive effects greatly depended upon the suddenness with which the backward and forward motions of the ground were commenced or ended.

Amongst the earlier investigators of seismic phenomena who observed that there existed a connection between the distance to which bodies had been projected during an earthquake and the suddenness or initial velocity with which the ground had been moved beneath them, was Professor Wenthrop of Cambridge, Massachusetts, who noted that bricks from his chimneys had, by the New England earthquake of 1755, been thrown thirty feet. From this and the known height of the chimney, he calculates that the bricks had been projected with an initial velocity of twenty-one feet per second.[13]

The calculations made by Mallet respecting the maximum velocity of an earth particle at the time of the Neapolitan earthquake in 1857 depended upon the overthrow, projection, and fracture of bodies.

The principles which guided him in making the calculations will be understood from the following illustration.

If a column, a b c d, receive a shock or be suddenly moved in the direction of the arrow, the centre of gravity, g, of this column will revolve round the edge, and tend to describe the path g o. If it passes o, the column will fall. The work done in such a case as this is equal to lifting the column through the height o h.

If g a = a, the angle g a h = ϕ, and the weight of the body = w, then the above work equals

wa (1 − cos ϕ).

This must equal the work acquired—that is to say, the kinetic energy of rotation of the body, or

Where w is the angular velocity of the body at starting, k the radius of gyration round a, and g the velocity acquired by a falling body in one second. Whence

but w, the angular velocity, is equal to the statical couple applied, divided by the moment of inertia, or,

squaring and substituting

and since the length of the corresponding pendulum is l =  ^k2/_a,

To apply this to any given case we must find the value of l or of  ^k2/_a.

Mallet finds these values for the cube, solid and hollow rectangular parallelopipeds, solid and hollow cylinders, &c. In these formulæ we have a direct connection between the dimensions and form of a body and the velocity with which the ground must move beneath it to cause its overthrow.

Not only is the case discussed for horizontal forces, but also for forces acting obliquely. Similar reasonings are applied to the productions of fractures in walls, but as there is uncertainty in our knowledge of the co-efficient of force necessary to produce fracture through joints across beds of masonry, the deductions ought not to be applied as the measures of velocity. Where the fractures occur at the base or in horizontal planes, or in those of the continuous beds of the masonry, or through homogeneous bodies, the uncertainty is not so great, and for cases like these Mallet gives several illustrations. The distance to which bodies had been projected, as, for example, ornaments from the tops of pedestals, coping-stones from the edges of roofs, were also used as means of determining the angle at which the shock had emerged, or, if this be known, for determining the velocity.

Thus by a shock in the direction o c, a ball, a, on the top of a pedestal would describe a trajectory to the point c. Let the angle which o c makes with the horizon be e, the vertical height through which the ball has fallen be b, and the horizontal distance of projection be a; then

h being the height due to the velocity of projection. Whence

For the back motion or subnormal wave in the direction c o,

A serious error which may enter into calculations of this description when practically applied has been pointed out when speaking of columns as seismometers. It was then shown that such bodies before being overthrown may often be caused to rock, and therefore that their final overthrow may not have any direct connection with the impulse of the succeeding shock.

Another point to which attention must be drawn respecting the above calculations is that if there was no friction or adherence between the projected body and its pedestal, in consequence of its inertia it would be left behind by the forward motion of the shock, and simply drop at the foot of its support. In the case of frictional adherence it would be carried forward by the velocity acquired before this adherence was broken, and thrown in a direction opposite to that given in the figure—that is to say, in the direction of the shock.[14]

The Absolute Intensity of the Force exerted by an Earthquake.—No doubt it has occurred to many who have experienced an earthquake that the power which gave birth to such a disturbance must have been enormously great. The estimates which we shall make of the absolute amount of energy represented by an earthquake cannot, on account of the nature of the factors with which we deal, be regarded as accurate. They may, however, be of assistance in forming estimates of quantities about which we have at present no conception. One method of obtaining the result we seek is that which was employed by Mallet in his calculations respecting the Neapolitan earthquake. Although disbelieving in the general increment of temperature as we descend in the earth at an average rate of 1° F. for every fifty or sixty feet of descent, for want of better means. Mallet assumes this law to be true, and, knowing from a variety of observations the depth of various parts of the cavity from which the disturbance sprang, he calculates the temperatures of this cavity in various parts as due to its depth beneath the surface. Next, it is assumed that steam was suddenly admitted into this cavity, which might exert the greatest possible pressure due to the maximum temperature. This was calculated as being about 684 atmospheres.

Next, he determined the column of limestone necessary to balance such a pressure, which is about 8,550 feet in height. As the least thickness of strata above this cavity was 16,700 feet, the pressure of 684 atmospheres was not sufficient to blow away its cover, but if suddenly admitted or generated in the cavity it might have produced the wave of impulse by the sudden compression of the walls of the cavity.

The pressure of 684 atmospheres is equivalent to about 4·58 tons on the square inch, and, as the total area of the walls of the cavity is calculated at twenty-seven square miles, the total accumulated pressure would be more than 640,528 millions of tons. Mallet, however, shows that it is probable that the temperature of the focal cavity was much greater than that due to the hypogeal increment, and that therefore the pressure may have been greater.

The capability of producing the earthquake impulse, however, depends on the suddenness with which the steam is flashed off. According to the experiments of Boutigny and others, Mallet tells us that the most sudden production of steam would take place at a temperature of 500°-550° C., which is but a few degrees below that calculated for the mean focal depth.

Assuming the above calculated pressure to be true, and knowing the co-efficient of compression of the materials on which it acted, the volume of the wave at a given moment near the instant of starting—that is, at the focus—can be calculated, and from this the wave amplitude on reaching the surface may be deduced.

Proceeding backwards, if we have observed the wave amplitude, calculated the depth of the focus, and know the co-efficient of expansion, then the total compression may be calculated and the temperature due to the pressure producing this may be arrived at. In this way earthquakes may be used as a means of calculating subterranean temperature at depths that can never be attained experimentally.

A method of proceeding which is probably more definite than that adopted by Mallet would be the application of the method indicated when speaking of the intensity of artificial disturbances.

If for a given earthquake the origin of which is known we have determined by seismographs the mean acceleration of an earth particle at two or more stations at different distances from that origin, we are enabled to construct a curve of intensity the area between which and its asymptotes was shown to be a measure of the total intensity of the shock. Comparing this area with that of a unit disturbance produced, say, by the explosion of a pound of dynamite, one may approximately calculate in terms of this unit the initial intensity of the earthquake.

Radiation of an Earthquake.—The tremors preceding the more violent movements of an earthquake may be due, as Mallet has suggested,[15] to the free surface waves reaching a distant point before the direct vibrations.

The fact that earth vibrations produced by striking a blow on or near the surface of the ground are wholly obliterated in reaching a cutting or valley, there being no underground waves of distortion to crop up on the opposite side of the valley, indicates that the disturbance is one that travels on the surface; the same fact is illustrated when we endeavour to transmit vibrations through the side of a hill into a tunnel.

In the tunnel, although the distance may be small, no sensible effects are produced, whilst the same disturbance may be recorded at a long distance from its origin on the surface of the ground outside the tunnel.

Lastly, we may refer to the experiences of miners underground.

Occasionally it has happened that miners when deep underground, as in the Marienberg in the Saxon Erzgebirge, have felt shocks which have not been noticed on the surface. These observations are rare, and it is possible that they may be explained by the caving in of subterranean excavations.

The usual experience is, that if a shock is felt underground it is also felt on the surface, as for example in the lead mines in Derbyshire at the time of the Lisbon disturbance (1755).

The most frequent observation, however, is that a shock may be felt on the surface while it is not remarked by the miners beneath the surface, as at Fahlun and Presburg in November, 1823.

At the Comstock Lode in Colorado about twelve years ago many earthquakes were felt. On one particular day twenty-four were counted. Superintendent Charles Foreman told the author when he visited Virginia City in 1882, that special observations were made to determine whether these shocks were felt as severely deep down in the mines as on the surface, where they were on the verge of being destructive. The universal testimony of many observers was that in most cases they were not felt at all underground, and when a shock was felt it was extremely feeble. At Takashima Colliery, in Japan, it is seldom that shocks are felt underground.

The explanation of these latter observations appears to be either that, in consequence of a smaller amplitude of motion in the solid rocks beneath the surface as compared with the extent of motion on the surface, the disturbances are passed by unnoticed, or else the disturbance is, at a distance from its origin, practically confined to the surface.

Velocity of Propagation of an Earthquake.—Although many have written upon earthquakes and have endeavoured to give to us the velocity with which they were propagated, the subject is one about which we have as yet but little exact information.

The importance of this branch of investigation is undoubtedly great. By knowing the velocity with which an earthquake has travelled in various directions we are assisted in determining the locality of its origin; we may possibly make important deductions respecting the nature of the medium through which it has passed; perhaps also we may learn something regarding the intensity of the disturbance which created the earthquake. In the Report of the British Association for 1851 Mallet gives the table on next page, in which are placed together the approximate rates of transit of shocks of several earthquakes which he discusses. Some of these, it will be observed, are records of disturbances which must have passed through or across the bed of the ocean.

In Mallet’s British Association Report for 1858, he gives data compiled by Mr. David Milne[16] respecting the Lisbon earthquakes of 1755 and 1761, from which data the tables of velocities (p. 89) have been calculated, omitting those which Mr. Mallet has marked as uncertain.

The distances are marked in degrees of seventy English miles each, and the time is reduced to Lisbon time.

The Lisbon Earthquake on November 1, 1755.

The Lisbon Earthquake of March 31, 1761.[17]

These tables, owing to the nature of the materials which Mallet had at his disposal, are but rude approximations to the truth. Two interesting facts are, however, observable: the first being that the velocities for the earthquake of 1761 are much higher than those obtained for the earthquake of 1755; and, secondly, that in both cases the velocities as determined from the observations of ships at sea closely approximate to each other, in all cases being nearly the same as that with which a sound wave would travel through water.

The great differences in transit velocity obtained for different earthquakes is a point worthy of attention.

Seebach’s velocity is a true transit velocity, and its determination is dependent on the assumption that the shock radiated from the centrum and not from the epicentrum, Seebach’s method is explained when speaking about the determination of origins.

Some interesting observations on the velocity with which the earthquake of October 7, 1874, was propagated, are given by M. S. di Rossi.[18]

One assumption is that the disturbance radiated from an origin to surrounding points of observation, whilst another is that the disturbance followed natural fractures, the direction of which is derived from the crest of certain mountain ranges. These velocities are as follows, Maradi being at or near the origin of the disturbance:—

Another set of interesting results are those of P. Serpieri on the earthquake of March 12, 1873. The curious manner in which this shock radiated is described in the chapter on the Geographical Distribution of Earthquakes (see p. 231). Two large areas appear to have been almost simultaneously struck, so that, there being no time for elastic yielding, the velocities calculated between places situated on either of the areas are exceedingly great.[19]

The following are examples of approximate earthquake velocities which have been determined in Japan.

The Tokio Earthquake of October 25, 1881.—From records respecting this earthquake it appears to have been felt over the whole of Yezo and the northern and eastern coast of Nipon, a little farther south than Tokio. It was severest at Nemuro and Hakodate, and at the former place a little damage was done. From these facts, together with the indications of instruments recording direction of movement and a general inspection of the time records, it seems that the disturbance must have originated beneath the sea on the east coast of Yezo at a very long distance to the north-east of Tokio, from which place it passed in a practically direct line on to Yokohama.

As the disturbance was felt at Yokohama twenty-one seconds later than at Tokio, and the distances between these two places is about sixteen geographical miles, for this portion of its course the disturbance must have travelled at a rate of at least 4,300 feet per second. If we assume that the shock, after having reached Hakodate, travelled on at the same rate as it did between Tokio and Yokohama in order to reach Saporo, where the shaking was felt eighteen seconds after Hakodate, it must have had about thirteen geographical miles to travel after Hakodate was shaken before Saporo felt its effect.

Drawing from Hakodate a tangent to the eastern side of a circle of thirteen miles radius described round Saporo, the origin of the disturbance must be on the line bisecting this tangent at right angles. As it also lies on a line drawn through Tokio and Yokohama, it lies in a position about 41 N. lat. and 144° 15′ E. long., which is a position somewhat nearer to Nemuro than Hakodate, as we should anticipate. If this be taken as approximately indicating the origin, then the shock, after reaching Hakodate from the Hakodate homoseist, travelled about 218 miles to reach Tokio in 128 seconds, which gives a velocity of 10,219 feet per second.

The method here followed is equivalent to that of the hyperbola and one direction (see p. 204). The hyperbola is described on the assumption that the velocity deduced from the time taken to travel between Tokio and Yokohama is correct, and also that the earth waves travelled with approximately the same velocity in the vicinity of Saporo as near Tokio. The probability, however, is that they travelled more quickly. If this be so, then the origin is thrown somewhat to the south-east and the velocity between the Hakodate homoseist and Tokio reduced. Thus, if the velocity in the Saporo district be double that observed in the Tokio district, the origin is shifted about twenty-eight miles to the south-west, and the last-mentioned velocity is reduced to about 9,000 feet per second.

If we work by the method of circles, and assume the velocity to have been constant in all directions, then this velocity must have been about 6,000 feet per second. If we assume that the indications of direction obtained from seismographs and other sources give to us by this intersection a proper origin, the velocity in some directions may have been as much as 17,000 feet per second.

An origin thus determined, or even if determined by the method of circles, is in discord with the fact that places like Nemuro, in the north-east of Yezo, were nearer to the origin than any of the other places which have been mentioned.

The conclusion which we are therefore led to with regard to this shock, assuming of course that the time observations are tolerably correct, is that the velocity of propagation was variable, being greater when measured between points near to the origin than between points at a distance. The velocities estimated vary between 4,000 and 9,000 feet per second.

In the case of the earthquake which has just been discussed, we have an example of a disturbance which must have passed between Tokio and Yokohama in what was almost a straight line from the origin. As this direction ought to give the maximum time of transit if all earthquakes are propagated with the same velocity, the following table is given of the interval between the time of observation of several shocks at these two stations:—

As these are observations which have been made with the assistance of a telegraphic signal daily employed to correct and rate the clocks from which the observations were obtained, they may be regarded as being tolerably, correct.

The disturbance of February 6, the two shocks of March 1, appear, like that of October 25, to have passed in almost a direct line from an origin in the N.N.E, through Tokio on to Yokohama. Their velocities of propagation as calculated from the above intervals are approximately 3,900, 1,900, and 1,400 feet per second. The shock of February 16 appears to have had its origin near to a point in Yedo Bay about eight miles east of Yokohama. Assuming this to be the case, the shock between the Yokohama homoseist and Tokio travelled at the rate of 2,454 feet per second, but between the Tokio homoseist and Chiba at the rate of 750 feet per second; that is to say, the velocity of propagation rapidly decreased as the disturbance spread outwards.

At Yokohama it was recorded at 5.31.54, at Tokio at 5.32.16, and at Chiba at 5.33.48. These times are given in Tokio mean time.

The shock of March 11, which was recorded at Tokio at 7.51.22 p.m. and at Yokohama at 7.51.33 p.m., appears, from the indications of instruments which were exceptionally definite in their records, to have originated in the N.E. corner of Yedo Bay, about nineteen miles S.S.W. from Chiba. This shock was rather severe, fracturing several chimneys. From the Tokio homoseist it appears to have travelled on to Yokohama at the rate of about 2,200 feet per second. Assuming these observations to be approximately accurate, if we take them with the records of previous observers they lead us to the following conclusions:—

1. Different earthquakes, although they may travel across the same country, have very variable velocities, varying between several hundreds and several thousands of feet per second.

2. The same earthquake travels more quickly across districts near to its origin than it does across districts which are far removed.

3. The greater the intensity of the shock the greater is the velocity.