THE INTERNATIONAL SCIENTIFIC SERIES
VOLUME LV

THE INTERNATIONAL SCIENTIFIC SERIES

EARTHQUAKES
AND
OTHER EARTH MOVEMENTS

BY
JOHN MILNE
PROFESSOR OF MINING AND GEOLOGY IN THE IMPERIAL COLLEGE OF ENGINEERING,
TOKIO, JAPAN

WITH THIRTY-EIGHT FIGURES

NEW YORK
D. APPLETON AND COMPANY
1, 3, and 5 BOND STREET
1886

PREFACE

In the following pages it has been my object to give a systematic account of various Earth Movements.

These comprise Earthquakes, or the sudden violent movements of the ground; Earth Tremors, or minute movements which escape our attention by the smallness of their amplitude; Earth Pulsations, or movements which are overlooked on account of the length of their period; and lastly, Earth Oscillations, or movements of long period and large amplitude which attract so much attention from their geological importance.

It is difficult to separate these Earth Movements from each other, because they are phenomena which only differ in degree, and which are intimately associated in their occurrence and in their origin.

Because Earthquakes are phenomena which have attracted a universal attention since the earliest times, and about them so many observations have been made, they are treated of at considerable length.

As very much of what might be said about the other Earth Movements is common to what is said about Earthquakes, it has been possible to make the description of these phenomena comparatively short.

The scheme which has been adopted will be understood from the following table:—

In some instances the grouping of phenomena according to the above scheme may be found inaccurate, as, for example, in the chapters referring to the effects and causes of Earthquakes.

This arises from the fact that the relationship between Earthquakes and other Earth phenomena are not well understood. Thus the sudden elevation of a coast line and an accompanying earthquake may be related, either as effect and cause, or vice versâ, or they may both be the effect of a third phenomenon.

Much of what is said respecting Earthquake motion will show how little accurate knowledge we have about these disturbances. Had I been writing in England, and, therefore, been in a position to make references to libraries and persons who are authorities on subjects connected with Seismology, the following pages might have been made more complete, and inaccuracies avoided. A large proportion of the material embodied in the following pages is founded on experiments and observations made during an eight years’ residence in Japan, where I have had the opportunity of recording an earthquake every week.

The writer to whom I am chiefly indebted is Mr. Robert Mallet. Not being in a position to refer to original memoirs, I have drawn many illustrations from the works of Professor Karl Fuchs and M. S. di Rossi. These, and other writers to whom reference has been made, are given in an appendix.

For seeing these pages through the press, my thanks are due to Mr. Thomas Gray, who, when residing in Japan, did so much for the advancement of observational Seismology.

For advice and assistance in devising experiments, I tender my thanks to my colleagues, Professor T. Alexander, Mr. T. Fujioka, and to my late colleague. Professor John Perry.

For assistance in the actual observation of Earthquakes, I have to thank my friends in various parts of Japan, especially Mr. J. Bissett and Mr. T. Talbot, of Yokohama. For assistance in obtaining information from Italian sources I have to thank Dr. F. Du Bois, from German sources Professor C. Netto, and from Japanese sources Mr. B. H. Chamberlain. For help in carrying out experiments, I am indebted to the liberality of the British Association, the Geological Society of London, the Meteorological and Telegraph departments of Japan, and to the officers of my own institution, the Imperial College of Engineering.

And, lastly, I offer my sincere thanks to those gentlemen who have taken part in the establishment and working of the Seismological Society of Japan, and to my publishers, whose liberality has enabled me to place the labours of residents in the Far East before the European public.

John Milne.

Tokio, Japan; June 30, 1883

CONTENTS.

EARTHQUAKES.

CHAPTER I.
INTRODUCTION.

Relationship of man to nature—The aspect of a country is dependent on geological phenomena—Earthquakes an important geological phenomenon—Relationship of seismology to the sciences and arts—Earth movements other than earthquakes—Seismological literature—(Writings of Perrey, Mallet, Eastern writings, the Philosophical Transactions of the Royal Society, the ‘Gentleman’s Magazine,’ the Bible, Herodotus, Pliny, Hopkins, Von Hoff, Humboldt, Schmidt, Seebach, Lasaulx, Fuchs, Palmieri, Bertelli, Seismological Society of Japan)—Seismological terminology.

In bygone superstitious times lightning and thunder were regarded as supernatural visitations. But as these phenomena became better understood, and men learned how to avoid their destructive power, the superstition was gradually dispelled. Thus it is with Earthquakes: the more clearly they are understood, the more confident in the universality of law will man become, and the more will his mental condition be advanced.

In his ‘History of Civilisation in England,’ Buckle has laid considerable stress upon the manner in which earthquakes, volcanoes, and other of the more terrible forms in which the workings of nature reveal themselves to us, have exerted an influence upon the imagination and understanding; and just as a sudden fright may affect the nerves of a child for the remainder of its life, we have in the annals of seismology records which indicate that earthquakes have not been without a serious influence upon the mental condition of whole communities.

To a geologist there are perhaps no phenomena in nature more interesting than earthquakes, the study of which is called Seismology. Coming, as shocks often will, from a region of volcanoes, the study of these disturbances may enable us to understand something about the nature and working of a volcano. As an earthquake wave travels along from strata to strata, if we study its reflections and changing velocity in transit, we may often be led to the discovery of certain rocky structures buried deep beneath our view, about which, without the help of such waves, it would be hopeless ever to attain any knowledge.

By studying the propagation of earthquake waves the physicist is enabled to confirm his speculations respecting the transmission of disturbances in elastic media. For the physicist earthquakes are gigantic experiments which tell him the elastic moduli of rocks as they exist in nature, and when properly interpreted may lead him to the proper comprehension of many ill-understood phenomena. It is not impossible that seismological investigation may teach us something about the earth’s magnetism, and the connection between earthquakes and the ‘earth currents’ which appear in our telegraph wires. These and numerous other kindred problems fall within the domain of the physicist.

It is of interest to the meteorologist to know the connections which probably exist between earthquakes and the fluctuations of the barometer, the changes of the thermometer, the quantity of rainfall, and like phenomena to which he devotes his attention.

Next we may turn to the more practical aims of seismology and ask ourselves what are the effects of earthquakes upon buildings, and how, in earthquake-shaken countries, the buildings are to be made to withstand them. Here we are face to face with problems which demand the attention of engineers and builders. To attain what we desire, observation, common sense, and subtle reasoning must be brought to bear upon this subject.

In the investigation of the principle on which earthquake instruments make their records, in the analysis of the results they give, in problems connected with astronomy, with physics, and with construction, seismology offers to the mathematician new fields for investigation.

A study of the effects which earthquakes produce on the lower animals will not fail to interest the student of natural history.

A study like seismology, which leads us to a more complete knowledge of earth-heat and its workings, is to be regarded as one of the corner-stones of geology. The science of seismology invites the co-operation of workers and thinkers in almost every department of natural science.

We have already referred to the influence exerted by earthquakes over the human mind. How to predict earthquakes, and how to escape from their dangers, are problems which, if they can be solved, are of extreme interest to the world at large.

In addition to the sudden and violent movements which we call earthquakes, the seismologist has to investigate the smaller motions which we call earth tremors. From observations which have been made of late years, it would appear that the ground on which we dwell is incessantly in a state of tremulous motion.

A further subject of investigation which is before the seismologist is the experimental verification of the existence of what may be called ‘earth-pulsations.’ These are motions which mathematical physicists affirmed the existence of, but which, in consequence of the slowness of their period, have hitherto escaped observation.

The oscillations, or slow changes in the relative positions of land and sea, might also be included; but this has already been taken up as a separate branch of geology.

These four classes of movements are no doubt interdependent, and seismology in the widest sense might conveniently be employed to include them all. In succeeding chapters we will endeavour to indicate how far the first three of these branches have been prosecuted, and to point out that which remains to be accomplished. It is difficult, however, to form a just estimate of the amount of seismological work which has been done, in consequence of the scattered and uncertain nature of many of the records. Seismology, as a science, originated late, chiefly owing to the facts that centres of civilisation are seldom in the most disturbed regions, and that earthquake-shaken countries are widely separated from each other.

As every portion of the habitable globe appears to have been shaken more or less by earthquakes, and as these phenomena are so terrible in their nature, we can readily understand why seismological literature is extensive. In the annals of almost every country which has a written history, references are made to seismic disturbances.

An idea of the attention which earthquakes have received may be gathered from the fact that Professor Alexis Perrey, of Dijon, who has published some sixty memoirs on this subject, gave, in 1856, a catalogue of 1,837 works devoted to seismology.[1] In 1858 Mr. Robert Mallet published in the Reports of the British Association a list of several hundred works relating to earthquakes. Sixty-five of these works are to be found in the British Museum. So far as literature is concerned, earthquakes have received as much attention in the East as in the West. In China there are many works treating on earthquakes, and the attention which these phenomena received may be judged of from the fact that in a.d. 136 the Government appointed a commission to inquire into the subject. Even the isolated empire of Japan can boast of at least sixty-five works on earthquakes, seven of which are earthquake calendars, and twenty-three earthquake monographs.[2] Besides those treating especially of earthquakes, there are innumerable references to such disturbances in various histories, in the transactions of learned societies, and in periodicals. To attempt to give a complete catalogue of even the books which have been written would be to enter on a work of compilation which would occupy many years, and could never be satisfactorily finished.

In the ‘Philosophical Transactions of the Royal Society,’ which were issued in the eighteenth century, there are about one hundred and eighty separate communications on earthquakes; and in the ‘Gentleman’s Magazine’ for 1755 there are no less than fifty notes and articles on the same subject. The great interest shown in earthquakes about the years 1750–60 in England, was chiefly due to the terrible calamity which overtook Lisbon in 1755, and to the fact that about this time several shocks were experienced in various parts of the British Islands. In 1750, which may be described as the earthquake year of Britain, ‘a shock was felt in Surrey on March 14; on the 18th of the same month the whole of the south-west of England was disturbed. On April 2, Chester was shaken; on June 7, Norwich was disturbed; on August 23, the inhabitants of Lancashire were alarmed; and on September 30 ludicrous and alarming scenes occurred in consequence of a shock having been felt during the hours of Divine service, causing the congregations to hurry into the open air.’[3] As might be expected, these occurrences gave rise to many articles and notes directing attention to the subject of earthquakes.

Seismic literature has not, however, at all times been a measure of seismic activity: thus, in Japan, the earthquake records for the twelfth and sixteenth centuries scarcely mention any shocks. At first sight it might be imagined that this was owing to an absence of earthquakes; but it is sufficiently accounted for by the fact that at that time the country was torn with civil war, and matters more urgent than the recording of natural phenomena engaged the attention of the inhabitants. Professor Rockwood, who has given so much attention to seismic disturbances in America, tells us that during the recent contest between Chili and Peru a similar intermission is observable. We see, therefore, that an absence of records does not necessarily imply an absence of the phenomena to be recorded.

Perhaps the earliest existing records of earthquakes are those which occur in the Bible. The first of these, which we are told occurred in Palestine, was in the reign of Ahab (b.c. 918–897).[4] One of the most terrible earthquakes mentioned in the Bible is that which took place in the days of Uzziah, king of Judah (b.c. 811–759), which shook the ground and rent the Temple. The awful character of this, and the deep impression produced on men’s minds, may be learned from the fact that the time of its occurrence was subsequently used as an epoch from which to reckon dates.

The writings of Herodotus, Pliny, Livy, &c., &c., show the interest which earthquakes attracted in early ages. These writers chiefly devoted themselves to references and descriptions of disastrous shocks, and to theories respecting the cause of earthquakes.

The greater portion of the Japanese notices of earthquakes is simply a series of anecdotes of events which took place at the time of these disasters. We also find references to superstitious beliefs, curious occurrences, and the apparent connection between earthquake disturbances and other natural phenomena. In these respects the literature of the East closely resembles that of the West. The earthquake calendars of the East, however, form a class of books which can hardly be said to find their parallel in Europe;[5] while, on the other hand, the latter possesses types of books and pamphlets which do not appear to have a parallel elsewhere. These are the more or less theological works—‘Moral Reflections on Earthquakes,’ ‘Sermons’ which have been preached on earthquakes, ‘Prayers’ which have been appointed to be read.[6]

Speaking generally, it may be said that the writings of the ancients, and those of the Middle Ages, down to the commencement of the nineteenth century, tended to the propagation of superstition and to theories based on speculations with few and imperfect facts for their foundation.

Among the efforts which have been made in modern times to raise seismology to a higher level, is that of Professor Perrey, of Dijon, who commenced in 1840 a series of extensive catalogues embracing the earthquakes of the world. These catalogues enabled Perrey, and subsequently Mallet in his reports to the British Association, to discuss the periodicity of earthquakes, with reference to the seasons and to other phenomena, in a more general manner than it had been possible for previous workers to accomplish. The facts thus accumulated also enabled Mallet to discuss earthquakes in general, and the various phenomena which they present were sifted and classified for inspection. Another great impetus which observational seismology received was Mr. Mallet’s report upon the Neapolitan earthquake of 1857, in which new methods of seismic investigation were put forth. These have formed the working tools of many subsequent observers, and by them, as well as by his experiments on artificially produced disturbances, Mallet finally drew the study of earthquakes from the realms of speculation by showing that they, like other natural phenomena, were capable of being understood and investigated.

In addition to Perrey and Mallet, the nineteenth century has produced many writers who have taken a considerable share in the advancement of seismology. There are the catalogues of Von Hoff, the observations of Humboldt, the theoretical investigations of Hopkins, the monographs of Schmidt, Seebach, Lasaulx, and others; the books of Fuchs, Credner, Vogt, Volger; the records and observations of Palmieri, Bertelli, Rossi, and other Italian observers. To these, which are only a few out of a long list of names, may be added the publications of the Commission appointed for the observation of earthquakes by the Natural History Society of Switzerland, and the volumes which have been published by the Seismological Society of Japan.

Before concluding this chapter it will be well to define a few of the more ordinary terms which are used in describing earthquake phenomena. It may be observed that the English word earthquake, the German erdbeben, the French tremblement de terre, the Spanish terremoto, the Japanese jishin &c., all mean, when literally translated, earth-shaking, and are popularly understood to mean a sudden and more or less violent disturbance.

Seismology (σειμός an earthquake, λόγος a discourse) in its simplest sense means the study of earthquakes. To be consistent with a Greek basis for seismological terminology, some writers have thrown aside the familiar expression ‘earthquake,’ and substituted the awkward word ‘seism.’

The source from which an earthquake originates is called the ‘origin,’ ‘focal cavity,’ or ‘centrum.’

The point or area on the surface of the ground above the origin is called the ‘epicentrum.’ The line joining the centrum and epicentrum is called the ‘seismic vertical.’

The radial lines along which an earthquake may be propagated from the centrum are called ‘wave paths.’

The angle which a wave path, where it reaches the surface of the earth, makes with that surface is called the ‘angle of emergence’ of the wave. This angle is usually denoted by the letter e.

As the result of a simple explosion at a point in a homogeneous medium, we ought, theoretically, to obtain at points on the surface of the medium equidistant from the epicentrum, equal mechanical effects. These points will lie on circles called ‘isoseismic’ or ‘coseismic’ circles. The area included between two such circles is an ‘isoseismic area.’ In nature, however, isoseismic lines are seldom circles. Elliptical or irregular curves are the common forms.

The isoseismic area in which the greatest disturbance has taken place is called the ‘meizoseismic area.’ Seebach calls the lines enclosing this area ‘pleistoseists.’

These last-mentioned lines are wholly due to Mallet and Seebach.

Many words are used to distinguish different kinds of earthquakes from each other. All of these appear to be very indefinite and to depend upon the observer’s feelings, which, in turn, depend upon his nervous temperament and his situation.

In South America small earthquakes, consisting of a series of rapidly recurring vibratory movements not sufficiently powerful to create damage, are spoken of as trembelores.

The terremotos of South America are earthquakes of a destructive nature, in which distinct shocks are perceptible. It may be observed that shocks which at one place would be described as terremoto would at another and more distant place probably be described as trembelores.

The succussatore are the shocks where there is considerable vertical motion. The terrible shock of Riobamba (February 4, 1797), which is said to have thrown corpses from their graves to a height of 100 feet, was an earthquake of this order.

The vorticosi are shocks which have a twisting or rotatory motion.

Another method of describing earthquakes would be to refer to instrumental records. When the vibrations of the ground have only been along the line joining the observer and the epicentrum, the disturbance might be called ‘euthutropic.’ A disturbance in which the prominent movements are transverse to the above direction might be called ‘diagonic.’ If motions in both of these directions occur in the records, the shock might be said to be ‘diastrophic.’ If there be much vertical movement, the shock might be said to be ‘anaseismic.’ Some disturbances could only be described by using two or three of these terms.

CHAPTER II.
SEISMOMETRY.

Nature of earthquake vibrations—Many instruments called seismometers only seismoscopes—Eastern seismoscopes, columns, projection seismometers—Vessels filled with liquid—Palmieri’s mercury tubes—The ship seismoscope—The cacciatore—Pendulum instruments of Kreil, Wagner, Ewing, and Gray—Bracket seismographs—West’s parallel motion instrument—Gray’s conical pendulums, rolling spheres, and cylinders—Verbeck’s ball and plate seismograph—The principle of Perry and Ayrton—Vertical motion instruments—Record receivers—Time-recording apparatus—The Gray and Milne seismograph.

Before we discuss the nature of earthquake motion, the determination of which has been the aim of modern seismological investigation, the reader will naturally look for an account of the various instruments which have been employed for recording such disturbances. A description of the earthquake machines which have been used even in Japan would form a bulky volume. All that we can do, therefore, is to describe briefly the more prominent features of a few of the more important of these instruments. In order that the relative merits of these may be better understood, we may state generally that modern research has shown a typical earthquake to consist of a series of small tremors succeeded by a shock, or series of shocks, separated by more or less irregular vibrations of the ground. The vibrations are often both irregular in period and in amplitude, and they have a duration of from a few seconds to several minutes. We will illustrate the records of actual earthquakes in a future chapter, but in the meantime the idea that an earthquake consists of a single shock must be dismissed from the imagination.

To construct an instrument which at the time of an earthquake shall move and leave a record of its motion, there is but little difficulty. Contrivances of this order are called seismoscopes. If, however, we wish to know the period, extent, and direction of each of the vibrations which constitutes an earthquake, we have considerable difficulty. Instruments which will in this way measure or write down the earth’s motions are called seismometers or seismographs.

Many of the elaborate instruments supplemented with electro-magnetic and clockwork arrangements are, when we examine them, nothing more than elaborate seismoscopes which have been erroneously termed seismographs.

The only approximations to true seismographs which have yet been invented are without doubt those which during the past few years have been used in Japan. It would be a somewhat arbitrary proceeding, however, to classify the different instruments as seismoscopes, seismometers, and seismographs, as the character of the record given by certain instruments is sometimes only seismoscopic, whilst at other times it is seismometric, depending on the nature of the disturbance. Many instruments, for instance, would record with considerable accuracy a single sudden movement, but would give no reliable information regarding a continued shaking.

Eastern Seismoscopes.—The earliest seismoscope of which we find any historical record is one which owes its origin to a Chinese called Chôko. It was invented in the year a.d. 136. A description is given in the Chinese history called ‘Gokanjo,’ and the translation of this description runs as follows:—

Fig. 1.

‘In the first year of Yōka, a.d. 136, a Chinese called Chôko invented the seismometer shown in the accompanying drawing. This instrument consists of a spherically formed copper vessel, the diameter of which is eight feet. It is covered at its top, and in form resembles a wine-bottle. Its outer part is ornamented by the figures of different kinds of birds and animals, and old peculiar-looking letters. In the inner part of this instrument a column is so suspended that it can move in eight directions. Also, in the inside of the bottle, there is an arrangement by which some record of an earthquake is made according to the movement of the pillar. On the outside of the bottle there are eight dragon heads, each of which holds a ball in its mouth. Underneath these heads there are eight frogs so placed that they appear to watch the dragon’s face, so that they are ready to receive the ball if it should be dropped. All the arrangements which cause the pillar to knock the ball out of the dragon’s mouth are well hidden in the bottle.’

‘When an earthquake occurs, and the bottle is shaken, the dragon instantly drops the ball, and the frog which receives it vibrates vigorously; any one watching this instrument can easily observe earthquakes.’

With this arrangement, although one dragon may drop a ball, it is not necessary for the other seven dragons to drop their balls unless the movement has been in all directions; thus we can easily tell the direction of an earthquake.

‘Once upon a time a dragon dropped its ball without any earthquake being observed, and the people therefore thought the instrument of no use, but after two or three days a notice came saying that an earthquake had taken place at Rōsei. Hearing of this, those who doubted the use of this instrument began to believe in it again. After this ingenious instrument had been invented by Chōko, the Chinese Government wisely appointed a secretary to make observations on earthquakes.’

Not only is this instrument of interest on account of its antiquity, but it is also of interest on account of the close resemblance it bears to many of the instruments of modern times.

Another earthquake instrument also of Eastern origin is the magnetic seismoscope of Japan.

On the night of the destructive earthquake of 1855, which devastated a great portion of Tokio, the owner of a spectacle shop in Asakusa observed that a magnet dropped some old iron nails and keys which had been attached to it. From this occurrence the owner thought that the magnet had, in consequence of its age, lost its powers. About two hours afterwards, however, the great earthquake took place, after which the magnet was observed to have regained its powers. This occurrence led to the construction of the seismoscope, which is illustrated in a book called the ‘Ansei-Kembun-Roku,’ or a description of the earthquake of 1855, and examples of the instrument are still to be seen in Tokio. These instruments consist of a piece of magnetic iron ore, which holds up a piece of iron like a nail. This nail is connected, by means of a string, with a train of clockwork communicating with an alarm. If the nail falls a catch is released and the clockwork set in motion, and warning given by the ringing of a bell. It does not appear that this instrument has ever acted with success.

Columns.—One of the commonest forms of seismoscope, and one which has been very widely used, consists of a round column of wood, metal, or other suitable material, placed, with its axis vertical, on a level plane, and surrounded by some soft material such as loose sand to prevent it rolling should it be overturned. The fall of such a column indicates that a shaking or shock has taken place. Attempts have been made by using a number of columns of different sizes to make these indications seismometric, but they seldom give reliable information either as to intensity or direction of shock. The indications as to intensity are vitiated by the fact that a long-continued gentle shaking may overturn a column which would stand a very considerable sudden shock, while the directions in which a number of columns fall seldom agree owing to the rotational motion imparted to them by the shaking. Besides, the direction of motion of the earthquake seldom remains in the same azimuth throughout the whole disturbance.

An extremely delicate, and at the same time simple form of seismoscope may be made by propping up strips of glass, pins, or other easily overturned bodies against suitably placed supports. In this way bodies may be arranged, which, although they can only fall in one direction, nevertheless fall with far less motion than is necessary to overturn any column which will stand without lateral support.

Projection Seismometers.—Closely related to the seismoscopes and seismometers which depend on the overturning of bodies. Mallet has described two sets of apparatus whose indications depend on the distance to which a body is projected. In one of these, which consisted of two similar parts arranged at right angles, two metal balls rest one on each side of a stop at the lower part of two inclined

like troughs. In this position each of the balls completes an electric circuit. By a shock the balls are projected or rolled up the troughs, and the height to which they rise is recorded by a corresponding interval in the break of the circuits. The vertical component of the motion is measured by the compression of a spring which carries the table on which this arrangement rests. In the second apparatus two balls are successively projected, one by the forward swing, and the other by the backward swing of the shock. Attached to them are loose wires forming terminals of the circuits. They are caught in a bed of wet sand in a metal trough forming the other end of the circuit. The throw of the balls as measured in the sand, and the difference of time between their successive projections as indicated by special contrivances connected with the closing of the circuits, enables the observer to calculate the direction of the wave of shock, its velocity, and other elements connected with the disturbance. It will be observed that the design of this apparatus assumes the earthquake to consist of a distinct isolated shock.

Oldham, at the end of his account of the Cachar earthquake of 1869, recommends the use of an instrument based on similar principles. In his instrument four balls like bullets are placed in notches cut in the corners of the upper end of a square stake driven into the ground.

Vessels filled with liquid.—Another form of simple seismoscope is made by partially filling a vessel with liquid. The height to which the liquid is washed up the side of the vessel is taken as an indication of the intensity of the shock, and the line joining the points on which maximum motion is indicated, is taken as the direction of the shock. If earthquakes all lasted for the same length of time, and consisted of vibrations of the same period, such instruments might be of service. These instruments have, however, been in use from an early date. In 1742 we find that bowls of water were used to measure the earthquakes which in that year alarmed the inhabitants of Leghorn. About the same time the Rev. S. Chandler, writing about the shock at Lisbon, tells us that earthquakes may be measured by means of a spherical bowl about three or four feet in diameter, the inside of which, after being dusted over with Barber’s puff, is filled very gently with water. Mallet, Babbage, and De la Bêche have recommended the same sort of contrivance, but, notwithstanding, it has justly been criticised as ‘ridiculous and utterly impracticable.’[7]

An important portion of Palmieri’s well-known instrument consists of horizontal tubes turned up at the ends and partially filled with mercury. To magnify the motion of the mercury, small floats of iron rest on its surface. These are attached by means of threads to a pulley provided with indices which move in front of a scale of degrees. We thus read off the intensity of an earthquake as so many degrees, which means so many millimetres of washing up and down of mercury in a tube. The direction of movement is determined by the azimuth of the tube which gives the maximum indication, several tubes being placed in different azimuths.

This form of instrument appears to have been suggested by Mallet, who gives an account of the same in 1846. Inasmuch as the rise and fall of the mercury in such tubes depend on its depth and on the period of the earthquake together with its duration, we see that although the results obtained from a given instrument may give us means of making approximate comparisons as to the relative intensity of various earthquakes, it is very far from yielding any absolute measurement.

Another method which has been employed to magnify and register the motions of liquid in a vessel has been to float upon its surface a raft or ship from which a tall mast projected. By a slight motion of the raft, the top of the mast vibrated through a considerable range. This motion of the mast as to direction and extent was then recorded by suitable contrivances attached to the top of the mast.

A very simple form of liquid seismoscope consists of a circular trough of wood with notches cut round its side. This is filled with mercury to the level of the notches. At the time of an earthquake the maximum quantity of mercury runs over the notches in the direction of greatest motion. This instrument, which has long been used in Italy, is known as a Cacciatore, being named after its inventor. It is a prominent feature in the collection of apparatus forming the well-known seismograph of Palmieri.

Pendulum instruments.—Mallet speaks of pendulum seismoscopes and seismographs as ‘the oldest probably of seismometers long set up in Italy and southern Europe.’ In 1841 we find these being used to record the earthquake disturbances at Comrie in Scotland.

These instruments may be divided into two classes: first, those which at the time of the shock are intended to swing, and thus record the direction of movement; and second, those which are supposed to remain at rest and thus provide ‘steady points.’

To obtain an absolutely ‘steady point’ at the time of an earthquake, has been one of the chief aims of all recent seismological investigations.

With a style or pointer projecting down from the steady point to a surface which is being moved backward and forward by the earth, such a surface has written upon it by its own motions a record of the ground to which it is attached. Conversely, a point projecting upwards from the moving earth might be caused to write a record on the body providing the steady point, which in the class of instruments now to be referred to is supposed to be the bob of a pendulum. It is not difficult to get a pendulum which will swing at the time of a moderately strong earthquake, but it is somewhat difficult to obtain one which will not swing at such a time. During the past few years, pendulums varying between forty feet in length and carrying bobs of eighty pounds in weight, and one-eighth of an inch in length, and carrying a gun-shot, have been experimented with under a great variety of circumstances. Sometimes the supports of these pendulums have been as rigid as it is possible to make a structure from brick and mortar, and at other times they have intentionally been made loose and flexible. The indices which wrote the motions of these pendulums have been as various as the pendulums themselves. A small needle sliding vertically through two small holes, and resting its lower end on a surface of smoked glass, has on account of its small amount of friction been perhaps one of the favourite forms of recording pointers.

The free pendulums which have been employed, and which were intended to swing, have been used for two purposes: first, to determine the direction of motion from the direction of swing, and second, to see if an approximation to the period of the earth’s motion could be obtained by discovering the pendulum amongst a series of different lengths which was set in most violent motion, this probably being the one which had its natural period of swing the most nearly approximating to the period of the earthquake oscillations.

Inasmuch as all pendulums when swinging have a tendency to change the plane of their oscillation, and also as we now know that the direction of motion during an earthquake is not always constant, the results usually obtained with these instruments respecting the direction of the earth’s motion have been unsatisfactory. The results which were obtained by series of pendulums of different lengths were, for various reasons, also unsatisfactory.

Of pendulums intended to provide a steady point, from which the relative motion of a point on the earth’s surface could be recorded, there has been a great variety. One of the oldest forms consisted of a pendulum with a style projecting downwards from the bob so as to touch a bed of sand. Sometimes a concave surface was placed beneath the pendulum, on which the record was traced by means of a pencil. Probably the best form was that in which a needle, capable of sliding freely up and down, marked the relative horizontal motion of the earth and the pendulum bob on a smoked glass plate.

It generally happens that at the time of a moderately severe earthquake the whole of these forms of apparatus are set in motion, due partly to the motion of the point of support of the pendulum, and partly to the friction of the writing point on the plate.

Among these pendulums may be mentioned those of Cavallieri, Faura, Palmieri, Rossi, and numerous others. It is possible that the originators of some of these pendulums may have intended that they should record by swinging. If this is so, then so far as the determination of the actual nature of earthquake motion is concerned, they belong to a lower grade of apparatus than that in which they are here included.

A great improvement in pendulum apparatus is due to Mr. Thomas Gray of Glasgow, who suggested applying so much frictional resistance to the free swing of a pendulum that for small displacements it became ‘dead beat.’ By carrying out this suggestion, pendulum instruments were raised to the position of seismographs. The manner of applying the friction will be understood from the following description of a pendulum instrument which is also provided with an index which gives a magnification of the motion of the earth.

b b b b is a box 113 cm. high and 30 cm. by 18 cm. square. Inside this box a lead ring r, 17 cm. in diameter and 3 cm. thick, is suspended as a pendulum from the screw s. This screw passes through a small brass plate p p, which can be moved horizontally over a hole in the top of the box. These motions in the point of suspension allow the pendulum to be adjusted.

Fig. 2.

Projecting over the top of the pendulum there is a wooden arm w carrying two sliding pointers h h, resting on a glass plate placed on the top of the pendulum. These pointers are for the purpose of giving the frictional resistance before referred to. If this friction plate is smoked, the friction pointers will write upon it records of large earthquakes independently of the records given by the proper index, which only gives satisfactory records in the case of shocks of ordinary intensity. Crossing the inside of the pendulum r there is a brass bar perforated with a small conical hole at m. A stiff wire passes through m and forms the upper portion of the index i, the lower portion of which is a thin piece of bamboo. Fixed upon the wire there is a small brass ball which rests on the upper side of a second brass plate also perforated with a conical hole, which plate is fixed on the bar o o crossing the box.

If at the time of an earthquake the upper part of the index i remains steady at m, then by the motion at o, the lower end of the index which carries a sliding needle at g, will magnify the motion of the earth in the ratios m o : o g. In this instrument o g is about 17 cm.

The needle g works upon a piece of smoked glass. In order to bring the glass into contact with the needle without disturbance, the glass is carried on a strip of wood k, hinged at the back of the box, and propped up in front by a loose block of wood y. When y is removed the glass drops down with k out of contact with the needle. The box is carried on bars of wood c c, which are fixed to the ground by the stakes a a.

The great advantage of a pendulum seismograph working on a stationary plate is, that the record shows at once whether the direction of motion has been constant, or whether it has been variable. The maximum extent of motion in various directions is also easily obtained.

The disadvantage of the instrument is, that at the time of a large earthquake, owing perhaps to a slight swing in the pendulum, the records may be unduly magnified.

On such occasions, however, fairly good records may be obtained from the friction pointers, provided that the plates on which they work have been previously smoked. It might perhaps be well to use two of these instruments, one having a comparatively high frictional resistance, and hence ‘dead beat’ for large displacements.

Many attempts have been made to use a pendulum seismograph in conjunction with a record-receiving surface, which at the time of the earthquake should be kept in motion by clockwork. In this way it was hoped to separate the various vibrations of the earthquake, and thus avoid the greater or less confusion which occurs when the index of the pendulum writes its backward and forward motion on a stationary plate. Hitherto all attempts in this direction, in which a single multiplying index was used, have been unsuccessful because of the moving plate dragging the index in the direction of its motion for a short distance, and then allowing it to fall back towards its normal position.

In connection with this subject we may mention the pendulum seismographs of Kreil, Wagener, Ewing, and Gray.

In the bob of Kreil’s pendulum there was clockwork, which caused a disc on the axis of the pendulum to continuously rotate. On this continually revolving surface a style fixed to the earth traced an unbroken circle. At the time of an earthquake, by the motion of the style, the circle was to be broken and lines drawn. The number and length of these lines were to indicate the length and intensity of the disturbance.

Gray’s pendulum consisted of a flat heavy disc carrying on its upper surface a smoked glass plate. This, which formed the bob of the pendulum, was supported by a pianoforte steel wire. When set ready to receive an earthquake, the wire was twisted and the bob held by a catch so arranged that at the time of the earthquake the catch was released, and the bob of the pendulum allowed to turn slowly by the untwisting of the supporting wire. Resting on the surface of this rotating disc were two multiplying indices arranged to write the earth’s motions as two components.

In the instruments of Wagener and Ewing, the clockwork and moving surface do not form part of the pendulum, but rest independently on a support rigidly attached to the earth. In Wagener’s instrument one index only is used, while in Ewing’s two are used for writing the record of the motion.

A difficulty which is apparent in all pendulum machines is that when the bob of such a pendulum is deflected it tends to fall back to its normal position. To make a pendulum perfect it therefore requires some compensating arrangement, so that the pendulum, for small displacements, shall be in neutral equilibrium, and the errors due to swinging shall be avoided.

Several methods have been suggested for making the bob of an ordinary pendulum astatic for small displacements. One method proposed by Gray consists in fixing in the bob of a pendulum a circular trough of liquid, the curvature of this trough having a proper form. Another method which was suggested, was to attach a vertical spiral spring to a point in the axis of the pendulum a little below the point of suspension, and to a fixed point above it, so that when the pendulum is deflected it would introduce a couple.

Professor Ewing has suggested an arrangement so that the bob of the pendulum shall be partly suspended by a stretched spiral spring, and at the same time shall be partly held up from below by a vertically placed strut, the weight carried by the strut being to the weight carried by the spring in the ratio of their respective lengths. As to how these arrangements will act when carried into practice yet remains to be seen.

Another important class of instruments are inverted pendulums. These are vertical springs made of metal or wood loaded at their upper end with a heavy mass of metal. An arrangement of this sort, provided at its upper end with a pencil to write on a concave surface, was employed in 1841 to register the earthquakes at Comrie in Scotland. In Japan they were largely employed in series, each member of a series having a different period of vibration. The object of these arrangements was to determine which of the pendulums, with a given earthquake, recorded the greatest motion, it being assumed that the one which was thrown into the most violent oscillation would be the one most nearly approximating with the period of the earthquake. The result of these experiments showed that it was usually those with a slow period of vibration which were the most disturbed.

Bracket Seismographs.—A group of instruments of recent origin which have done good work, are the bracket seismographs. These instruments appear to have been independently invented by several investigators: the germ from which they originated probably being the well-known horizontal pendulum of Professor Zöllner. In Japan they were first employed by Professor W. S. Chaplin. Subsequently they were used by Professor Ewing and Mr. Gray. They consist essentially of a heavy weight supported at the extremity of a horizontal bracket which is free to turn on a vertical axis at its other end. When the frame carrying this axis is moved in any direction excepting parallel to the length of the gate-like bracket, the weight causes the bracket to turn round a line known as the instantaneous axis of the bracket corresponding to this motion of the fixed axis. Any point in this line may therefore be taken as a steady point for motions at right angles to the length of the supporting bracket. Two of these instruments placed at right angles to each other have to be employed in conjunction, and the motion of the ground is written down as two rectangular components. In Professor Ewing’s form of the instrument, light prolongations of the brackets form indices which give magnified representations of the motion, and the weights are pivoted round a vertical axis through their centre.

In the accompanying sketch b is a heavy weight pivoted at the end of a small bracket c a k, which bracket is free to turn on a knife-edge, k, above, and a pivot a, below, in the stand s. At the time of an earthquake b remains steady, and the index p, forming a continuation of the bracket, magnifies the motion of the stand, in the ratio of a c : c n.

Fig. 3.

In an instrument called a double-bracket seismograph, invented by Mr. Gray, we have two brackets hinged to each other, and one of them to a fixed frame. The planes of the two brackets are placed at right angles, so as to give to a heavy mass supported at the end of the outer bracket two degrees of horizontal freedom.

In all bracket machines, especially those which carry a pivoted weight, it is doubtful whether the weight provides a truly steady point relatively to the plate on which the record is written for motion parallel to the direction of the arm.

Fig. 4.

Parallel motion Instrument.—A machine which writes its record as two components, and which promises great stability, is one suggested by Professor C. D. West. Like the bracket machines it consists of two similar parts placed at right angles to each other, and is as follows: A bar of iron a is suspended from both sides on pivots at c c by a system of light arms hinging with each other at the black dots, between the upper and lower parts of the rigid frame b c. The arms are of such a length that for small displacements parallel to the length of the bar, c c practically move in a straight line, and the bar is in neutral equilibrium. A light prolongation of the bar d works the upper end of the light index e, passing as a universal joint through the rigid support f. A second index e′ from the bar at right angles also passes through f. The multiplying ends of these indices are coupled together to write a resultant motion on a smoked glass plate s.

Conical Pendulums.—Another group of instruments which have also yielded valuable records are the conical pendulum seismographs. The idea of using the bob of a conical pendulum to give a steady point in an earthquake machine was first suggested and carried into practice by Mr. Gray. The seismograph as employed consists of a pair of conical pendulums hung in planes at right angles to each other. The bob of each of these pendulums is fixed a short distance from the end of a light lever, which forms the writing index, the short end resting as a strut against the side of a post fixed in the earth. The weight is carried by a thin wire or thread, the upper end of which is attached to a point vertically above the fixed end of the lever.

Rolling Spheres and Cylinders.—After the conical pendulum seismographs, which claim several important advantages over the bracket machines, we come to a group of instruments known as rolling sphere seismographs. Here, again, we have a class of instruments for the various forms of which we are indebted to the ingenuity of Mr. Gray.

The general arrangement and principle of one of these instruments will be readily understood from the accompanying figure. s is a segment of a large sphere with a centre near c. Slightly below this centre a heavy weight b, which may be a lead ring, is pivoted. At the time of an earthquake c is steady, and the earth’s motions are magnified by the pointer c a n in the proportion of c a : a n. The working of this pointer or index is similar to that of the pointer in the pendulum.

Fig. 5.

Closely connected with the rolling sphere seismographs, are Gray’s rolling cylinder seismographs.

These are two cylinders resting on a surface plate with their axes at right angles to each other. Near to the highest point in each of these cylinders, this point remaining nearly steady when the surface plate is moved backwards and forwards, there is attached the end of a light index. These indices are again pivoted a short distance from their ends on axes connected with the surface plate. In order that the two indices may be brought parallel, one is cranked at the second pivot.

Ball and Plate Seismograph.—Another form of seismograph, which is closely related to the two forms of apparatus just described, is Verbeck’s ball and plate seismograph. This consists of a surface plate resting on three hard spheres, which in turn rests upon a second surface plate. When the lower plate is moved, the upper one tends to remain at rest, and thus may be used as a steady mass to move an index.

The Principle of Perry and Ayrton.—An instrument which is of interest from the scientific principle it involves is a seismograph suggested by Professors Perry and Ayrton, who propose to support a heavy ball on three springs, which shall be sufficiently stiff to have an exceedingly quick period of vibration. By means of pencils attached to the ball by levers, the motions of the ball are to be recorded on a moving band of paper. The result would be a record compounded of the small vibrations of the springs superimposed on the larger, slower, wave-like motions of the earthquake, and, knowing the former of these, the latter might be separated by analysis. Although our present knowledge of earthquake motion indicates that the analysis of such a record would often present us with insuperable difficulties, this instrument is worthy of notice on account of the novelty of the principle it involves, which, the authors truly remark, has in seismometry been a ‘neglected’ one.

Instruments to record Vertical Motion.—The instruments which have been devised to record vertical motion are almost as numerous as those which have been devised to record horizontal motion. The earliest form of instrument employed for this purpose was a spiral spring stretched by weight, which, on account of its inertia, was supposed at the time of a shock to remain steady. No satisfactory results have ever been obtained from such instruments, chiefly on account of the inconvenience in making a spring sufficiently long to allow of enough elongation to give a long period of vibration. Similar remarks may be applied to the horizontally placed elastic rods, one end of which is fixed to a wall, whilst the opposite end is loaded with a weight. Such contrivances, furnished with pencil on the weight to write a record upon a vertical surface, were used in 1842 at Comrie, and we see the same principle applied in a portion of Palmieri’s apparatus. Contrivances like these neither give us the true amplitude of the vertical motion, insomuch as they are readily set in a state of oscillation; nor do they indicate the duration of a disturbance, for, being once set in motion, they continue that motion in virtue of their inertia long after the actual earthquake has ceased. They can only be regarded as seismoscopes.

Fig. 6.

The most satisfactory instrument which has yet been devised for recording vertical motion is Gray’s horizontal lever spring seismograph.

This instrument will be better understood from the accompanying sketch. A vertical spring s is fixed at its upper end by means of a nut n, which rests on the top of the frame f, and serves to raise or lower the spring through a short distance as a last adjustment for the position of the cross-arm a. The arm a rests at one end on two sharp points, p, one resting in a conical hole and the other in a v-slot; it is supported at b by the spring s, and is weighted at c with a lead ring r. Over a pin at the point c a stirrup of thread is placed which supports a small trough, t. The trough t is pivoted at a, has attached to it the index i (which is hinged by means of a strip of tough paper at h, and rests through a fine pin on the glass plate g), and is partly filled with mercury.

Another method of obtaining a steady point for vertical motion is that of Dr. Wagener, who employs a buoy partly immersed in a vessel of water. This was considerably improved upon by Mr. Gray, who suggested the use of a buoy, which, with the exception of a long thin style, was completely sunk.

Among the other forms of apparatus used to record vertical motion may be mentioned vessels provided with india-rubber or other flexible bottoms, and partially filled with water or some other liquid. As the vessel is moved up and down, the bottom tends to remain behind and provides a more or less steady point. Pivoted to this is a light index, which is again pivoted to a rigid frame in connection with the earth. Instruments of this description have yielded good records.

Record Receivers.—A large number of earthquake machines having been referred to, it now remains to consider the apparatus on which they write their motions. The earlier forms of seismographs, as has already been indicated, recorded their movements in a bed of sand; others wrote their records by means of pencils on sheets of paper. Where we have seismographs which magnify the motion of the earth, it will be observed that methods like the above would involve great frictional resistances, tending to cause motion in the assumed steady points of the seismographs. One of the most perfect instruments would be obtained by registering photographically the motions of the recording index by the reflection of a ray of light. Such an instrument would, however, be difficult to construct and difficult to manipulate. One of the best practical forms of registering apparatus is one in which the record is written on a surface of smoked glass. This can afterwards be covered with a coat of photographer’s varnish, and subsequently photographed by the ‘blue process’ so well known to engineers.

To obtain a record of all the vibrations of an earthquake it is necessary that the surface on which the seismograph writes should at the time of an earthquake be in motion. Of record-receiving machines there are three types. First, there are those which move continuously. The common form of these is a circular glass plate like an old form of chronograph, driven continuously by clockwork. On this the pointers of the seismograph rest and trace over and over again the same circles. At the time of an earthquake they move back and forth across the circles, which are theoretically fine lines, and leave a record of the earthquake. Instead of a circular plate, a drum covered with smoked paper may be used, which, after the earthquake, possesses the advantage, after unrolling, of presenting the record in a straight line, instead of a record written round the periphery of a circle, as is the case with the circular glass plates. Such records are easily preserved, but they are more difficult to photograph.

The second form of apparatus is one which is set in motion at the time of a shock. This may be a contrivance like one of those just described, or a straight smoked glass plate on a carriage. By means of an electrical or a mechanical contrivance called a ‘starter,’ of which many forms have been contrived, the earthquake is caused to release a detent and thus set in motion the mechanism which moves the record receiver.

The great advantage of continuously-moving machines is that the beginning and end of the shock can usually be got with certainty, while all the uncertainty as to the action of the ‘starter’ is avoided. Self-starting machines have, of course, the advantage of simplicity and cheapness, while there is no danger of the record getting obliterated by the subsequent motion of the plate under the index.

Time-recording Apparatus.—Of equal importance with the instruments which record the motion of the ground, are those instruments which record the time at which such motion took place. The great value of time records, when determining the origin from which an earthquake originates, will be shown farther on. The most important result which is required in connection with time observations, is to determine the interval of time taken by a disturbance in travelling from one point to another. On account of the great velocity with which these disturbances sometimes travel, it is necessary that these observations should be made with considerable accuracy. The old methods of adapting an apparatus to a clock which, when shaken, shall cause the clock to stop, are of little value unless the stations at which the observations are made are at considerable distances apart. This will be appreciated when we remember that the disturbance may possibly travel at the rate of a mile per second, that its duration at any station may often extend over a minute, and that one set of apparatus at one station may stop, perhaps, at the commencement of the disturbance, and the other near the end. A satisfactory time-taking apparatus will therefore require, not only the means for stopping a clock, but also a contrivance which, at the same instant that the clock is stopped, shall make a mark on a record which is being drawn by a seismograph. In this way we find out at which portion of the shock the time was taken.

Fig. 7.

Palmieri stops a clock in his seismograph by closing an electric circuit. Mallet proposes to stop a clock by the falling of a column which is attached by a string to the pendulum of the clock. So long as the column is standing the string is loose and the pendulum is free to move; but when the column falls, the string is tightened and the pendulum is arrested. The difficulty which arises is to obtain a column that will fall with a slight disturbance. The best form of contrivance for causing a column to fall, and one which may also be used in drawing out a catch to relieve the machinery of a record receiver, is shown in the accompanying sketch.

s is the segment of a sphere about 4·5 cm. radius, with a centre slightly above c. l is a disc of lead about 7 cm. in diameter resting upon the segment. Above this there is a light pointer, p, about 30 cm. long. On the top of the pointer a small cylinder of iron, w, is balanced, and connected by a string with the catch to be relieved. When the table on which w p s rests is shaken, rotation takes place near to c, the motion of the base s is magnified at the upper end of the pointer, and the weight overturned. This catch may be used to relieve a toothed bar axled at one end, and held up above a pin projecting from the face of the pendulum bob. When this falls it catches the projecting pin and holds the pendulum.

Another way of relieving the toothed bar is to hold up the opposite end to that at which it is axled by resting it on the extremity of a horizontal wire fixed to the bob of a conical pendulum—for example, one of the indices of a conical pendulum seismograph. The whole of this apparatus, which may be constructed at the cost of a few pence, can be made small enough to go inside an ordinary clock case.

The difficulty which arises with all these clock-stopping arrangements is that it is difficult for observers situated at distant stations to re-start their clocks so that their difference in time shall be accurately known. Even if each observer is provided with a well-regulated chronometer, with which he can make comparisons, the rating of these instruments is for all ordinary persons an extremely troublesome operation.

In order to avoid this difficulty the author has of late years used a method of obtaining the time without stopping the clock. To do this a clock with a central seconds hand is taken, and the hour and minute hands are prolonged and bent out slightly at their extremities at right angles to the face, the hour hand being slightly the longest. Each hand is then tipped with a piece of soft material like cork, which is smeared with a glycerine ink. A light flat ring, with divisions in it corresponding to those on the face of the clock, is so arranged that at the time of a shock it can be quickly advanced to touch the inked pads on the hands of the clock and then withdrawn. This is accomplished by suitable machinery, which is relieved either by an electro-magnet or some other contrivance which will withdraw a catch. In this way an impression in the form of three dots is received on the disc, and the time known without either stopping or sensibly retarding the clock.

For ordinary observers, if a time-taker is not used in conjunction with a record receiver, as good results as those obtained by ordinary clock-stopping apparatus are obtainable by glancing at an ordinary watch. Subsequently the watch by which the observation was made should be compared with some good time-keeper, and the local time at which the shock took place is then approximately known.

From what has now been said it will be seen that for a complete seismograph we require three distinct sets of apparatus—an apparatus to record horizontal motion, an apparatus to record vertical motion, and an apparatus to record time. The horizontal and vertical motions must be written on the same receiver, and if possible side by side, whilst the instant at which the time record is made a mark must be made on the edge of the diagram which is being drawn by the seismograph. Such a seismograph has been constructed and is now erected in Japan. It is illustrated in the accompanying diagram.

The Gray and Milne Seismograph.—In this apparatus two mutually rectangular components of the horizontal motion of the earth are recorded on a sheet of smoked paper wound round a drum, d, kept continuously in motion by clockwork, w, by means of two conical pendulum seismographs, c. The vertical motion is recorded on the same sheet of paper by means of a compensated-spring seismograph, s l m b.

The time of occurrence of an earthquake is determined by causing the circuit of two electro-magnets to be closed by the shaking. One of these magnets relieves a mechanism, forming part of a time-keeper, which causes the dial of the timepiece to come suddenly forwards on the hands and then move back to its original position. The hands are provided with ink-pads, which mark their positions on the dial, thus indicating the hour, minute, and second when the circuit was closed. The second electro-magnet causes a pointer to make a mark on the paper receiving the record of the motion. This mark indicates the part of the earthquake at which the circuit was closed.

Fig. 8.

The duration of the earthquake is estimated from the length of the record on the smoked paper and the rate of motion of the drum. The nature and period of the different movements are obtained from the curves drawn on the paper.

Mr. Gray has since greatly modified this apparatus, notably by the introduction of a band of paper sufficiently long to take a record for twenty-four hours without repetition. The record is written in ink by means of fine siphons. In this way the instrument, which is extremely sensitive to change of level, can be made to show not only earthquakes, but the pulsations of long period which have recently occupied so much attention.

CHAPTER III.
EARTHQUAKE MOTION DISCUSSED THEORETICALLY.

Ideas of the ancients (the views of Travagini, Hooke, Woodward, Stukeley, Mitchell, Young, Mallet)—Nature of elastic waves and vibrations—Possible causes of disturbance in the Earth’s crust—The time of vibration of an earth particle—Velocity and acceleration of a particle—Propagation of a disturbance as determined by experiments upon the elastic moduli of rocks—The intensity of an earthquake—Area of greatest overturning moment—Earthquake waves—Reflexion, refraction, and interference of waves—Radiation of a disturbance.

Ideas of Early Writers.—One of the first accounts of the varieties of motion which may be experienced at the time of an earthquake is to be found in the classification of earthquakes given by Aristotle.[8] It is as follows:—

1. Epiclintæ, or earthquakes which move the ground obliquely.

2. Brastæ, with an upward vertical motion like boiling water.

3. Chasmatiæ, which cause the ground to sink and form hollows.

4. Rhectæ, which raise the ground and make fissures.

5. Ostæ, which overthrow with one thrust.

6. Palmatiæ, which shake from side to side with a sort of tremor.

From the sixth group in this classification we see that this early writer did not regard earthquakes as necessarily isolated events, but that some of them consisted of a succession of backward and forward vibratory motions. He also distinguishes between the total duration of an earthquake and the length of, and intervals between, a series of shocks. Aristotle had, in fact, some idea of what modern writers upon ordinary earthquakes would term ‘modality.’

The earliest writer who had the idea that an earthquake was a pulse-like motion propagated through solid ground appears to have been Francisci Travagini, who, in 1679, wrote upon an earthquake which in 1667 had overthrown Ragusa. The method in which the pulses were propagated he illustrated by experiments.

Hooke, who, in 1690, delivered discourses on earthquakes before the Royal Society, divides these phenomena according to the geological effects they have produced; thus there is a genus producing elevations, a genus producing sinkings, a genus producing conversions and transportations, and a genus which produces what, in modern language, we should term metamorphic action.

Woodward, in his ‘Natural History,’ written in 1695, speaks of earthquakes as being agitations and concussions produced by water in the interior of the earth coming in contact with internal fires.

Stukeley observed that an earthquake was ‘a tremor of the earth,’ to be explained as a vibration in a solid. The Rev. John Mitchell, writing in 1760, says that the motion of the earth in earthquakes is partly tremulous and partly propagated by waves.

From these few examples, to which might be added many more, it will be seen that an earthquake disturbance has usually been regarded as a concussion, vibration, trembling, or undulatory movement. Further, it can be seen in narratives of earthquakes that it had been often observed that these tremblings and shakings continued over a certain period of time. Although it had been noticed that large areas were almost simultaneously affected by these disturbances, no definite idea appears to have existed as to how earthquake motion was propagated. Usually it was assumed that the disturbance spread through subterranean channels.

The first true conception of earthquake motion and the manner of its propagation is due to Dr. Thomas Young, who suggested that earthquake motion was vibratory, and it might be ‘propagated through the earth nearly in the same manner as a noise is conveyed through the air.’ The same idea was moulded into a more definite form by Gay Lussac.

The first accurate definition of an earthquake is due to Mr. Robert Mallet, who, after collecting and examining many facts connected with earthquake phenomena, and reasoning on these, with the help of known laws connected with the production and propagation of waves of various descriptions, formulated his views as follows:—

An earthquake is ‘the transit of a wave or waves of elastic compression in any direction from vertically upwards to horizontally, in any azimuth, through the crust and surface of the earth, from any centre of impulse or from more than one, and which may be attended with sound and tidal waves, dependent upon the impulse and upon circumstances of position as to sea and land.’

In brief, so far as motion in the earth is concerned. Mallet defined an earthquake as being a motion due to the transit of waves of elastic compression. In many cases it is possible that this is strictly true, but in succeeding pages it will be shown that earthquake motion may also be due to the transit of waves of elastic distortion.

To obtain a true idea of earthquake motion is a matter of cardinal importance, as it forms the key-stone of many investigations.

If we know the nature of the motion produced by an earthquake, we are aided in tracking it to its origin, and in reasoning as to how it was produced. If our knowledge of the nature of the motion of an earthquake is incorrect, it will be impossible for us intelligently to construct buildings to withstand the effects of these disturbances. We have thus to consider, in this portion of seismology, a point of great scientific importance, and shall deal with it at some length.

Nature of Elastic Waves and Vibrations.—When it is stated that an earthquake consists of elastic waves of compression and distortion, the student of physics has a clear idea of what is meant and a knowledge of the mechanical laws which govern such disturbances. The ordinary reader, however, and the majority of the inhabitants of earthquake countries, who of all people have the greatest interest in this matter, may not have so clear a conception, and it will, therefore, not be out of place to give some general explanation on this point.

The ordinary idea of a wave is that it is a disturbance similar to that which we often see in water. Waves like these must not, however, be confounded with elastic waves. A disturbance produced in water, say, for instance, by dropping a stone into a pond, is propagated outwards by the action of gravity. First, a ridge of water is raised up by the stone passing beneath the surface. As this ridge falls towards its normal position in virtue of its weight, it raises a second ridge. This second ridge raises a third ridge, and so on. The water moves vertically up and down, whilst the wave itself is propagated horizontally.

To understand what is meant by elastic waves, it is first necessary to understand what is meant by the term elastic. In popular language the term elastic is confined to substances like india-rubber, and but seldom to rock-like materials, through which earthquake waves are propagated. India-rubber is called elastic because after we remove a compressive force it has a tendency to spring back to its original shape. The elastic force of the india-rubber is in this case the force which causes it to resist a change of form. Now, a piece of rock may, up to a certain point, like the india-rubber, be compressed, and when the compressing force is removed it will also tend to resume its original form. However, as the rock offers more resistance to the compressing force than the india-rubber offers, we say that it is the more elastic. It may be here observed that a substance like granite offers great resistance, not only to compression or a change of volume, but also to a change of form or shape; whereas a substance like air, which is also elastic, only offers resistance to compression, but not to a change of shape.

With these ideas before us we will now proceed to consider how, after a body has been suddenly compressed or distorted, this disturbance is propagated through the mass. For the elastic body let us take a long spiral spring hung from the ceiling of a room and kept slightly stretched by a weight. If we give this weight an upward tap from below, say with a hammer, we shall observe a pulse-like wave which runs up the spring until it reaches the ceiling of the room. Here it will, so to speak, rebound, like a billiard ball from the end of a table, and run towards the weight from which it started. Whilst this is going on we may also observe that the weight is moving up and down.

Here, then, we have two distinct things to observe—one being the transmission of motion up to the ceiling, which we may liken to the transmission of an earthquake wave between two distant localities on the earth’s surface, and the other being the up and down motion of our weight, which we may compare to the backward and forward swinging which we experience at the time of an earthquake.

These two motions—namely, the pulse-like wave produced by the transmission of motion, and the backward and forward oscillation of the weight or of any point on the spring—must be carefully distinguished from each other.

First, we will consider the backward and forward motion of the weight. The distance through which the weight moves depends upon the force of the blow. The number of up and down oscillations it makes, say in a second, depends upon the stiffness of the spring. The weight, supposing it to be always the same, will move more quickly at the end of a stiff spring than at the end of a flaccid one; that is to say, its velocity is quicker. As in any given spring the number of up and down oscillations are always the same in a given interval of time, if these oscillations are of great extent, the weight must move more quickly with large than with small oscillations.

At the time of an earthquake the manner in which we are moved backward and forward is very similar to the manner in which the weight is moved. If we stand on a hard rock-like granite, we are to a great extent placed as if we were attached to a stiff quickly-vibrating spring. If, however, we are on a soft rock, it is more like being on a loose flaccid spring.

All that has thus far been considered has been a backward and forward kind of motion, where there is a rectilinear compression and extension amongst the particles on which we stand.

We might, however, imagine our rock, which for the moment we will consider to be a square column, to be twisted, and thus have its shape altered. When the twisting force is taken off it seems evident that the column would endeavour to untwist itself or regain its original form. Now the force which a body offers against a change of volume may be very different from that which it offers against a change of form.

In disturbances which take place in the rocky crust of our earth, it would seem possible that we may have vibrations set up which are either compressions and extensions or twistings and distortions. These may take place separately or simultaneously, or we may have resultant motions due to their combination.

The following are examples of possible causes which might give rise to these different orders of disturbance:—

1. Imagine a large area stretched by elevation until it reaches the limit of its elasticity and cracks. After cracking, in consequence of its elasticity, it will fly back over the whole area like a broken spring, and each point in the area will oscillate round its new position of equilibrium. In this case there will be no waves of distortion excepting near the end of the crack, where waves are transmitted in a direction parallel to the fissure.

2. The ground is broken and slips either up, down, or sideways, as we see to have taken place in the production of faults. Here we get distortion in the direction of the movement, and waves are produced by the elastic force of the rock, causing it to spring back from its distorted form. In a case like this the production of a fissure running north and south might give rise to north and south vibrations, which would be propagated end on towards the north and south, but broadside on towards the east and west. With disturbances of this kind, on account of the want of homogeneousness in the materials in which they are produced, we should expect to find waves of compression and extension.

3. A truly spherical cavity is suddenly formed by the explosion of steam in the midst of an elastic medium. In this case all the waves will be those of compression, each particle moving backward and forward along a radius.

Should the cavity, instead of being truly spherical, be irregular, it is evident that, in addition to the normal vibration of compression, transverse waves of distortion will be more or less pronounced, depending upon the nature of the cavity.

The combination of these two sets of vibrations may cause a point in the earth to move in a circle, an ellipse, the form of a figure eight, and in other curves similar to these, which are produced by apparatus designed to show the combination of harmonic motion. From these examples it will be seen that we have therefore to consider two kinds of vibrations—one produced by compression or the alteration of volume, and the other produced by an alteration in shape.

Now the resistance which a body offers, either to a change in its volume or in its shape, is called its elasticity, and the law which governs the backward and forward motion of a particle under the influence of this elasticity may be expressed as follows:

If t be the time of vibration, or the time taken by a particle to make one complete backward and forward swing, d the density of the material of which this particle forms a part, and e the proper modulus of elasticity of the material, then,

t = 2π √^d/_e

From this formula, t = 2π √^d/_e, we see that the time of vibration of the earth during an earthquake, or the rate at which we are shaken backwards and forwards, varies directly as the square root of the density of the material on which we stand, and inversely as the square root of a number proportional to its elasticity.

Velocity and Acceleration of an Earth Particle.—Another important point, which the practical seismologist has often brought to his notice, is the question of the velocity with which an earth particle moves. According to the formula, t = 2π √^d/_e, we should expect that a particle would make each semi-vibration in an equal time, and from a knowledge of the density and elastic moduli of a body this time might be calculated. Although the time of a semi-oscillation may be constant, we must bear in mind that, like the bob of a pendulum during each of its swings, the particle starts from rest, increases in velocity until it reaches the middle portion of its half swing, from which it gradually decreases in speed until it reaches zero, when it again commences a similar motion in the opposite direction.

These pendulum-like vibrations are sometimes spoken of as simple harmonic motions. If we know the distance through which an earthquake moves in making a single swing, and the time taken in making this swing, on the assumption that the motion is simple harmonic we can easily calculate the maximum velocity with which the particle moves.

Thus, if an earth particle takes one second to complete a semi-oscillation, half of which, or the amplitude of the motion, equals a, the maximum velocity equals π × a.

Again, assuming the earth vibrations to be simple harmonic, the maximum acceleration or rate of change in velocity will come about at the ends of each semi-oscillation; and if v be the maximum velocity of the particle, and a the amplitude or half semi-oscillation, then the maximum acceleration equals ^v2/_a.

Later on it will be shown, as the result of experiment, that certain of the more important earth oscillations in an earthquake are not simple harmonic motion. Nevertheless the above remarks will be of assistance in showing how the velocity and other elements connected with the motion of an earth particle, which are required by the practical seismologist, may be calculated, irrespective of assumptions as to the nature of the motion.

Propagation of a Disturbance.—We may next consider the manner in which a disturbance, in which there are both vibrations of compression and of distortion, is propagated. The first or normal set of vibrations are propagated in a manner similar to that in which sound vibrations are propagated. From a centre of disturbance these movements approach an observer at a distant station, so to speak, end on. The other vibrations have a direction of motion similar to that which we believe to exist in a ray of light. These would approach the observer broadside on.

If the disturbance passed through a formation like a series of perfectly laminated slates, each of these two sets of vibration might be subdivided, and we should then obtain what Mallet has termed ordinary and extraordinary normal and transverse vibrations.

In consequence of the difference in the elastic forces on which the propagation of these two kinds of vibration depends, the normal vibrations are transmitted faster than the transversal ones—that is to say, if an earthquake originated from a blow, the first thing that would be felt at a point distant from the origin of the shock would be a backward and forward motion in the direction to and from the origin, and then, a short interval afterwards, a motion transversal, or at right angles to this, would be experienced.

From the mathematical theory of vibratory motions it is possible to calculate the velocity with which a disturbance is propagated. As the result of these investigations it has been shown that normal vibrations travel more quickly than transverse vibrations.

Deductions from experiments on small specimens are, however, invalidated by the fact that the specimens used for experiments are, of course, nearly homogeneous, whilst the earthquake passes through a mass which is heterogeneous and more or less fissured. Mallet, by experiments ‘on the compressibility of solid cubes of these rocks, obtained the mean modulus of elasticity,’ with the result that ‘nearly seven-eighths of the full velocity of wave-transit due to the material, if solid and continuous, is lost by reason of the heterogeneity and discontinuity of the rocky masses as they are found piled together in nature.’ The full velocities of wave-transit, as calculated by Mallet from a theorem given by Poisson, were—

For slate and quartz transverse to lamination, 9,691 feet per second.
„ „ in line of lamination, 5,415 „ „

This more rapid transmission in a direction transverse to the lamination, Mr. Mallet observes, may be more than counterbalanced by the discontinuity of the mass transverse to the same direction.

The Intensity of an Earthquake.—The intensity of an earthquake is best estimated by the intensity of the forces which are brought to bear on bodies placed on the earth’s surface. These forces are evidently proportional to the rate of change of velocity in the body, and, as the destructive effect will be proportional to the maximum forces, we may consistently indicate the intensity of an earthquake by giving the maximum acceleration to which bodies were subject during the disturbance. On the assumption that the motion of a point on the earth’s surface is simple harmonic, the maximum acceleration is directly as the maximum velocity and inversely as the amplitude of motion, or as ^v2/_a where v indicates velocity and a amplitude.

The next question of importance is to determine the manner in which earthquake energy becomes dissipated—that is, to compare together the intensity of an earthquake as recorded at two or more points at different distances from the origin. First let us imagine the origin of our earthquake to be surrounded by concentric shells, each of which is the breadth of the vibration of a particle. Going outwards from the centre, each successive shell will contain a greater number of particles, this number increasing directly as the square of the distance from the origin. Let the blow have its origin at the centre, and give a vibratory movement to the particles in one of the shells near the centre.

This shell may be supposed to possess a certain amount of energy, which will be measured by its mass and the square of the velocity of its particles. In transferring this energy to the neighbouring shell which surrounds it, because it has to set in motion a greater number of particles than it contains itself, the energy in any one particle of the second layer will be less than the energy in any one particle in the first layer; the total energy in the second shell, however, will be equal to the total energy in the first shell. Neglecting the energy lost during the transfer, if the energy in a particle of the first shell at any particular phase of the motion be k₁, and the energy in a particle of the second shell k₂, these quantities are to each other inversely as the masses of the shells—that is, inversely as the squares of the mean radii of the shells.

In symbols, ^k₂/_k1 = ^r₁2/_r2² (1)

Assuming that energy is dissipated,

^k₂/_k1 > ^r₁2/_r2² = f ^r₁2/_r2² (2)

where f < 1 is the rate of dissipation of energy which is assumed to be constant.

Area of greatest Overturning Moment.—Although the rate of dissipation of the impulsive effects of an earthquake may follow a law like that just enumerated, it must be remembered that if the depth of the origin is comparable with the radius of the area which is shaken, the maximum impulsive effect as exhibited by the actual destruction on the surface may not be immediately above the origin where buildings have simply been lifted vertically up and down, but at some distance from this point, where the impulsive effort has been more oblique.

At the epicentrum we have the maximum of the true intensity as measured by the acceleration of a particle, or the height to which a body might be projected, but it will be at some distance from this where we shall have the maximum intensity as exhibited by an overturning effort.

This will be rendered clear by the following diagram.

In the accompanying diagram let o be the origin of a shock, and o c the seismic vertical equal to r. Let the direct or normal shock emerge at c, c₁, c₂, and at the angles θ₁, θ₂, &c.

Assuming that the displacement of an earth particle at c equals c b, and at c₁ equals c₁ b₁, and at c₂ equals c₂ b₂, &c., and let these displacements c b, c₁ b₁, c₂ b₂, &c., for the sake of argument, vary inversely as r, r₁, r₂, &c.

Fig. 9.

The question is to determine where the horizontal component c a of these normal motions is a maximum.

First observe that the triangle o c c is similar to a, b, c.

Also r = ^h/_{sin θ}, and therefore the normal component c₁ b₁ at c₁ is equal to c ^{sin θ}/_h.

Also c₁ a₁ = c₁ b₁, cos θ.

∴ c₁ a = c ^{sin θ cos θ}/_h = ^c/_h ∙ ^{sin 2θ}/₂,

and sin 2θ is greatest when 2θ = 90° or θ = 45°.

That is to say, the horizontal component reaches a maximum where the angle of emergence equals 45°.

This question has been discussed on the assumption that the amplitude of an earth particle varies inversely as its distance from the origin of the shock. Should we, however, assume that this amplitude varies inversely as the square of the distance from the origin, we are led to the result that the area of greatest disturbance is nearer to the point where the angle of emergence is 55° 44′ 9″. Both of these methods are referred to by Mallet, but the first is considered as probably the more correct.

Earthquake Waves.—Hitherto we have chiefly considered earthquake vibrations; now we will say a few words about earthquake waves. If we strike a long iron rod at one end, we can imagine that, as in the long spring, a pulse-like motion is transmitted. If the rod be struck quickly, the pulses will rapidly succeed each other, and if struck slowly the pulses will be at longer intervals. Each individual pulse, however, will travel along the rod at the same rate, and hence the distance between any two will remain constant; but that distance will depend on the interval between the blows producing these pulses being equal to the distance travelled by one pulse before the next blow is struck.

From this we see that an irregular disturbance will produce an irregular succession of motions; some will be like long undulations in a wide deep ocean, whilst others will be like ripples in a shallow bay. Again, consider the bar to be struck one blow only, and then left to itself. The bar will propagate a series of pulses along its length, due to the out and in vibration of its end. These will succeed each other at regular intervals, and will be mixed up with the pulses we have previously considered.

From this we see that in an earthquake, if it be produced by one blow, the motion will be isochronous in its character; but if it be due to a succession of blows at regular intervals, the motion will be the resultant of a series of isochronous motions, and will be periodical. If the impulses are irregular, you have a motion which is the resultant of a number of isochronous motions due to each impulse, but these compounded together in a different manner at each instant during the earthquake, and giving as a result a motion which is in no sense isochronous. This approaches more nearly to the actual motions we feel as earthquakes.

If we can imagine the ground shaken by an earthquake, made of a transparent material which transmitted less light when compressed, and we could look down upon a long extent of this at the time of an earthquake, we should see a series of dark bands indicating strips of country which were compressed. The distances between these bands might be irregular. Keeping our attention on one particular band, this would be seen to travel forward in a direction from the source. If we kept our eye on one particular point, it would appear to open and shut, becoming light and dark alternately.

As to the existence of these elastic waves in actual earthquakes we have no direct experimental evidence. The only kind of wave with which we are familiar is a true surface undulation, which, although having the appearance of a water-wave, may nevertheless represent a district of compression.

CHAPTER IV.
EARTHQUAKE MOTION AS DEDUCED FROM EXPERIMENT.

Experiments with falling weights—Experiments with explosives—Results obtained from experiments—Relative motion of two adjacent points—The effect of hills and excavations upon the propagation of vibrations—The intensity of artificial disturbances—Velocity with which earth vibrations are propagated—Experiments of Mallet—Experiments of Abbot—Experiments in Japan—Mallet’s results—Abbot’s results—Results obtained in Japan.

Experiments with Falling Weights.—A series of experiments, as the nature of the disturbance produced in the surface of the earth when a heavy weight is allowed to fall on it, was begun in November 1880 by Mr. T. Gray and the author. These experiments were carried out at the Akabane Engineering Works in Tokio. The weight used was a ball of iron weighing about a ton, which in the different experiments was allowed to fall from heights varying between ten and thirty-five feet. The position of the place where the ball was allowed to fall was such that in one direction the vibrations were transmitted up the side of a steep hill, in another direction across a pond with perpendicular sides, and in another direction across a level plain the material of which consisted for the most part of hardened mud extending to a very considerable depth. The vibrations produced by the fall of the ball were transmitted through this hard mud with considerable intensity to a distance of between 300 and 400 feet.

The object of the experiment was to find the nature of the vibrations produced in the crust of the earth by such a blow, the velocity of transmission through this comparatively soft material, the effect of hills and excavations in cutting off such disturbances, and the law according to which the amplitude of the vibrations diminishes with the distance from the source.

A considerable variety of apparatus was used during these experiments, but the most reliable results were obtained from the records of a rolling sphere seismograph, which wrote the vibrations on a stationary plate, and from the records of two bracket seismographs, similar to Professor Ewing’s horizontal lever seismographs, which gave a record of the vibrations as two rectangular components on a moving plate of smoked glass.

Fig. 10.

The general result as to the nature of the disturbance was that two distinct sets of vibrations were set up by the blow. In one set the direction of motion was along a line joining the point of observation with the point from which the disturbance emanated; in the other set the direction of motion was at right angles to that line. The nature of the resultant motion will be gathered from fig. 10, which is taken from the records drawn by the rolling sphere seismograph at a distance of 50 feet, 100 feet, and 200 feet respectively from the point where the ball struck the ground. The direct or normal vibrations reached the instrument first, and were followed at an interval depending on the distance of the instrument from the origin by the transverse vibrations. From the records of these two sets of vibrations as separated by the bracket seismographs, combined with the known rate of motion of the glass plate, the velocity of transmission was found to be, for normal vibrations 446–438 feet per second, and for transverse vibrations 357–353 feet per second.

The effect of the hill in cutting off the disturbance seemed to be slight, but the direction of the vibrations which ascended the side was mostly transverse. The pond, on the other hand, seemed completely to cut off the disturbance, which, however, gradually crept round the side, so that only a comparatively small triangular area was in shadow.

The amplitude of the vibrations diminished directly as the distance increased for some distance from the origin, but at greater distance the rate of diminution seemed to be slower. The transverse vibration seemed to die out less quickly than the normal vibrations.[9]

These experiments were afterwards very considerably extended by the author. In these later experiments charges of from one to two pounds of dynamite were placed in bore-holes of various depths and exploded by means of electricity. The results obtained confirmed the conclusions already arrived at from the former experiments. The experiments on velocity, however, seemed to indicate that the higher the initial impulse the greater was the velocity. The velocity of propagation of the transverse vibrations seemed to approach more and more to that of the directed vibrations as the distance from the origin of disturbance increased. Fig. 11 shows the nature of the record obtained from the explosion of two pounds of dynamite at the bottom of a bore-hole eight feet deep. These records show the interval of time which elapsed between the arrival of the normal and the transverse vibrations at points distant 100, 250, and 400 feet from the bore-hole. In the case of the 100-feet station it will be observed that the motion towards the origin is greater than that from the origin. It is also to be noticed that the period of vibration becomes greater as the distance from the origin increases.

Fig. 11.—Records obtained at three stations of the motion of the ground produced by the explosion of 2 lbs. of dynamite.

The Intensity of Artificial Disturbances.—The data which we have at our disposal for determining the intensity of an earth particle which has been caused to vibrate by the explosion of a charge of dynamite are a series of records similar to that given on [p. 60]. These disturbances are practically surface movements, and may be compared with the movements of an earthquake which spreads over an area the radius of which is great as compared with its depth.

To find the mean acceleration of an earth particle, which quantity has been taken to represent intensity, during any simple backward or forward motion of the earth, it will be first necessary to determine the amplitude of this motion and its maximum velocity, the mean acceleration being equal to ^v2/_2a.

Fig. 12.

The second and third movements in a shock invariably exhibited the greatest intensity, and to a distance of 400 feet from the origin, where about three pounds of dynamite had been exploded in a bore-hole about six feet deep, these intensities decreased directly as the distance from the origin. The less intense movements also decreased directly as the distance from the origin to a certain point, but after that they decreased more slowly. A mean result of the more prominent vibrations in four sets of experiments is shown in the curve, fig. 12, where the horizontal measurements represent distance from the origin in feet, and the vertical measurements mean acceleration in thousands of millimetres per second.

This curve approximates to an equi-angular hyperbola. The area between the curve and its asymptotes is proportional to the whole energy of the shock. The area of the diagram is proportional to the energy given up to the ground by the explosion of three pounds of dynamite. If we call the unit shock the effect produced by the explosion of one pound of dynamite, the above artificial earthquake had an intensity equal to three.

The only other investigations which have been made in this interesting branch of observational seismology are those by Mr. Robert Mallet,[10] and those by General Henry L. Abbot.[11]

Mallet’s Results.—The velocity with which earth vibrations were transmitted as deduced by Mr. Mallet were as follows:—

A striking result which was obtained by Mallet in his experiments at Holyhead was that the transit velocity increases with an increase in the intensity of the initial shock. Thus with a charge of 12,000 pounds of powder the transit rate was 1,373 feet per second, whilst with 2,100 pounds the transit rate was 1,099 feet per second. In these experiments tremors were observed as preceding and following the main shock.

Abbot’s Results.—The important results obtained by General Abbot are contained in the following table:—

A seismometer of type A means that the telescope used in observing the tremor produced on the surface of a vessel of mercury by the passage of the shock had a magnification of 6, whilst a telescope of the type B had a magnification of 12.

The mean velocity given by six observations with type A is 4,225 feet per second, while that given by the same number with type B is 7,475 feet per second.

Fig. 13.

If we assume that the first tremor observed in the mercury is to determine the true rate of transmission, General Abbot tells us that we must reject all observations made with type A, inasmuch as they do not reveal the velocity of the leading tremor. However, he also tells us that a still higher power above 12 might have detected still earlier tremors.

When gunpowder was the explosive, the observers noted that the disturbance observed in the mercury took a much longer time to reach a maximum than it did when dynamite was employed.

It was also observed that explosions fired beneath deep water gave a higher velocity than similar explosions which took place beneath shallow water. In the latter case much of the energy was probably expended in throwing a jet of water into the air.

Another point which was observed appears to have been that the rate varied with the initial shock. Thus:—

Also it is probable that the rate of a wave diminished with its advance. For,

General Abbot’s general conclusions are:—

1. A high magnifying power of telescope is essential in seismometric observations.

2. The more violent the initial shock the higher is the velocity of transmission.

3. This velocity diminishes as the general wave advances.

4. The movements of the earth’s crust are complex, consisting of many short waves first, increasing and then decreasing in amplitude; and with a detonating explosive the interval between the first wave and the maximum wave, at any station, is shorter than with a slow burning explosive.

Results obtained in Japan.—From some experiments made by the author in the grounds of the Meteorological Department in Tokio, the following results were obtained:—

The general results to be deduced from the above appear to be:—

1. For vertical motion.

(a) For the first 200 feet. The velocity depends upon the initial force—the greater the charge of dynamite the greater the velocity.

(b) For the second 200 feet. The above law only appears in experiments IV. and V., but it must be remembered that the origins of I. and III. were farther removed from A than IV. and V.

The speed of the wave during the second 200 feet is always less than during the first 200 feet.

2. For normal vibrations.

Here the speed between A and C is all that was measured, but we again see that the greater the initial force, or the nearer we are to the origin of the disturbance, the greater is the velocity. This velocity is greater than the velocity of the vertical or transverse vibrations.

3. For transverse vibrations.

If we assume that the vertical vibrations are a component of the transverse motions we see the same law as before—namely, that the nearer we are to the origin of the disturbance the greater is the speed with which that disturbance is propagated.

It will be observed that the chief law here enunciated respecting the decrease in speed of earth vibrations is the same as that pointed out by General Abbot, from which it only differs by its being in all cases proved without the introduction of personal errors, for the same explosion, along the same line of ground and for different kinds of vibrations.

CHAPTER V.
EARTHQUAKE MOTION AS DEDUCED FROM OBSERVATION ON EARTHQUAKES.

Result of feelings—The direction of motion—Instruments as indicators of direction—Duration of an earthquake—Period of vibration—The amplitude of earth movements—Side of greatest motion—Intensity of earthquakes—Velocity and acceleration of an earth particle—Absolute intensity of an earthquake—Radiation of an earthquake—Velocity of propagation.

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.

Fig. 14.

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

wa (1 − cos ϕ) = ^ww2k2 /_{2 g}.

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

w² k² = 2 ga (1 − cos ϕ),

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

w = ^{va cos ϕ} /_k²,

squaring and substituting

v² = 2g × ^k2/_a × ^{1 − cos ϕ}/_{cos² ϕ},

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

v² = 2gl × ^{1 − cos ϕ} /_{cos² ϕ},

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.

Fig. 15.

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

b = a tan e + ^a2 /_{4h cos² e},

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

Tan e = ^{2h ± √4h(h + b) − a2} /_a

v² = ^{a2 g} /_{2 cos² e (b − a tan e)}.

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

Tan e = ^{2h ± √4h(h + b) − a2} /_a

v² = ^{a2 g} /_{2 cos² e (b + a tan e)}.

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.

CHAPTER VI.
EFFECTS PRODUCED BY EARTHQUAKES UPON BUILDINGS.

The destruction of buildings is not irregular—Cracks in buildings—Buildings in Tokio—Relation of destruction to earthquake motion—Measurement of relative motion of parts of a building shaken by an earthquake—Prevention of cracks—Direction of cracks—The pitch of roofs—Relative position of openings in a wall—The last house in a row—The swing of buildings—Principle of relative vibrational periods.

The subject of this chapter is, from a practical point of view, one of the most important with which a seismologist has to deal. We cannot prevent the occurrence of earthquakes, and unless we avoid earthquake-shaken regions, we have not the means of escaping from them. What we can do, however, is in some degree to protect ourselves. By studying the effects produced by earthquakes upon buildings of different construction and variously situated, we are taught how to avoid or at least to mitigate calamities which, in certain regions of the world, are continually repeated. The subject is an extensive one, and what is here said about it must be regarded only as a contribution to the work of future writers who may give it the attention it deservedly requires.

The Destruction produced by Earthquakes is not irregular.—If we were suddenly placed amongst the ruins of a large city which had been shattered by an earthquake, it is doubtful whether we should at once recognise any law as to the relative position of the masses of débris and the general destruction with which we are surrounded. The results of observation have, however, shown us that, amongst the apparently chaotic ruin produced by earthquakes, there is in many cases more or less law governing the position of bodies which have fallen, the direction and position of cracks in walls, and the various other phenomena which result from such destructive disturbances.

Mallet, at the commencement of his first volume, describing the Neapolitan earthquake of 1857, discusses the general effect produced by various shocks upon differently constructed buildings. First he shows that, if we have a rectangular building, the walls at right angles to the shock will be more likely to be overthrown than those which are parallel to it. Experience teaches a similar lesson. Thus Darwin, when speaking of the earthquake at Concepcion in 1835,[20] tells us that the town was built in the usual Spanish fashion, with all the streets running at right angles to each other. One set ranged S.W. by W. and N.E. by E. and the other N.W. by N. and S.E. by S. The walls in the former direction certainly stood better than those in the latter. The undulations came from the S.W.

In Caraccas it is said that every house has its laga securo, or safe side, where the inhabitants place their fragile property. This laga securo is the north side, and it was chosen because about two out of every three destructive shocks traversed the city from west to east, so that the walls in these sides of a building have been stricken broadside on.[21]

Cracks in Buildings.—Results like the above come from destructive earthquakes rather than from movements such as those we have to deal with ordinarily. When a building is subjected to a slight movement it is assumed that the walls at right angles to the direction of the shock move backwards and forwards as a whole, and there is little or no tendency for them to be fractured at their weaker parts, these weaker parts being those over the various openings. The walls, however, which are parallel to the direction of the movement are, so to speak, extended and contracted along their length, and in consequence they may be expected to give way over the various openings. This tendency for extension and contraction of a wall along its length may be supposed, for instance, to be due to the different portions of a wall, owing to differences in dimensions and elasticity, having different periods of natural vibration, or possibly for two portions of a long line of wall to be simultaneously affected by portions of waves in different phases.

As an illustration of the giving way of a building in the manner here suggested we may take the case of a large brick structure which was recently being erected in Tokio. This building, at the time of the earthquake, was only some fourteen or fifteen feet above the surface of the ground. The length of the building stretched from N.W. to S.E., and it was intersected by many walls at right angles to this direction. Through all the walls of this building there were many arched openings. In the central part of the transverse walls, which walls were fully five feet in thickness, the arches which joined them together were 4 feet 4 inches in thickness. The arches therefore formed a comparatively lightly constructed link between heavy masses of brickwork.

On March 3, 1879, at 4.43 p.m., an earthquake was felt throughout Tokio, the strength of which, as judged by our feelings, was above that of an average shock. As registered by one of Palmieri’s instruments, it had a direction S.S.W. to N.N.E. and an intensity of 11°. On the same day there were several smaller shocks having the same direction, and these were succeeded by others on the 9th of the month.

Immediately after these shakings it was discovered that almost every arch in the internal walls of the building here referred to had been cracked across the crown in a direction about N. 40° W. All the other arches of the building, of which there were a great number in walls at right angles to the direction of the shock, were found not to have sustained any injury. To this statement, however, there was one exception, which was subsequently proved to have been due to a settlement taking place.

After examining these cracks the only cause to which they could be attributed was the series of shakings which they had just experienced. It seemed as if the heavy walls right and left of the arches had been in vibration without synchronism in their periods, and as a consequence the arches which connected them had been torn asunder.

Although the time at which the cracks were formed and the peculiar positions in which they were only to be found pointed distinctly to their origin, to be certain that they were not due to settlement of the foundations, horizontal lines were ruled upon the brickwork and from time to time subsequently observed.

The points to which the various cracks extended were also marked and observed. Beneath the walls as foundations there were beds of concrete about three feet thick and about ten feet in width. These had been under the pressure of the partially built walls for two years before the arches had been put in. As these foundations were unusually strong, being intended to carry so very much greater weight than that to which they had been subjected, if any settlement had been detected it would have been a matter of surprise.

Some weeks after the formation of these cracks it was observed that they gradually closed. This was probably due to the gradual falling inwards of the two broken portions of the arch, their position when open being one of instability.

Fig. 16.—Cracks in a corner house,
Belluno, June 29, 1873 (Bittner).

Had this building been more complete at the time of the shock, and the heavy walls been tied together at higher points, although the archways would have been points of weakness, it is quite possible that fracture would not have taken place. This illustration shows us that when a building is shaken in a definite direction there will be some rule as to the positions in which fractures occur. As another example, we may take the observations of Alexander Bittner upon the buildings of Belluno after the shock of June 29, 1873 (see Beiträge zur Kenntniss des Erdbebens von Belluno am 29 Juni, 1873, p. 40. Von Alexander Bittner. Aus dem LXIX. Bande der Sitzungsb. der K. Akad. der Wissensch., II. Abth., April-Heft. Jahrg. 1874).

Speaking generally, he remarks that ‘Houses similarly situated have suffered in corresponding walls and corners in a similar manner. In Belluno there is a certain kind of damage which is repeated everywhere, making a peculiar system of splits in the S.W. and N.E. corners of the houses.’ This is well shown in the accompanying sketch, which evidently illustrates the effect of a shock oblique to the direction of two walls at right angles to each other.

Fig. 17.—Brick buildings
in Tokio, showing fractures.

Buildings in Tokio.—For the purpose of finding out what has been the effect produced by earthquakes upon the buildings of Tokio, and at the same time for ascertaining whether blocks of buildings ranging in different directions suffered to the same extent, the author examined, in company with Mr. Josiah Conder, a large number of foreign-built houses in the district of the Ginza. The chief reason for choosing this was because it was the only district where a large number of similar buildings could be found. By examining houses or buildings of different constructions, the effects produced upon them by earthquakes are very often likely to show so many differences that it becomes almost an impossibility to determine what the general effect has been—unsymmetrical construction involving unsymmetrical ruin.

A number of similarly constructed buildings in one locality may be regarded as a number of seismographs, the effect upon any one of them being judged of by the average of the general effect which has been produced upon the whole. The general form of two of these houses which were examined is shown in fig. 17. In this figure the general character of the fractures which have been produced can also be seen. The houses are built of brick, and are in many cases faced with a thin coat of white plaster. Projecting from the level of the upper floor there is a balcony fronted by a low balustrade. This is supported by small beams which at their outer extremity are carried on a row of cylindrical columns. This forms a covered way in front of each row of houses. The roofs are covered with thick tiles. It will be observed that the arches of the upper windows spring sharply from their abutments, and at their crown they carry a heavy key-stone. The lower openings, which have a span of 9 feet, have evidently been constructed in imitation of the open front of an ordinary Japanese house. These archways curve out gently from their abutments. The outside walls have a thickness of 13½ inches.

The results obtained from a careful examination of 174 houses in streets running N.E. and 156 houses in streets running N.W., all of these houses being similar, were as follows:—

1. In the upper windows nearly all the cracks ran from the springing, which formed an angle with the abutment.

2. In the lower arches, which curved into the abutments, not a single crack was observed at the springway. The cracks in these arches were near the crown, where beams projected to carry the balcony. In many instances the cracks proceeded from such beams, even if there were no arch beneath. That cracks should occur in peculiar positions, as is here indicated, is shown in the illustrations which accompany the accounts of many earthquakes.

3. The houses which were most cracked were in the streets running parallel to the direction in which the greater number and most powerful set of shocks cross the city.

The results showed that, in order to avoid the effects of small shocks, all walls containing principal openings should be placed as nearly as possible at right angles to the direction in which the shocks of the districts usually travel. The blank walls, or those containing unimportant openings, would then be parallel to the direction of the shocks—that is, presuming our building to be made up of two sets of walls at right angles to each other.

Another point of importance would be to build archways curving into the supporting buttresses; the archways over doors and windows which we find in earthquake countries do not appear to be in any way different from those which are built in countries free from earthquakes. In the one country these structures have simply to withstand vertical pressures applied statically; in the other, they have to withstand more or less horizontal stresses, applied suddenly.

Relation of Destruction to Earthquake Motion.—The relations which exist between the overturning and projection of bodies and the motion of the ground have already been discussed. It may be interesting to call attention to the fact that in the formulæ showing three relationships, it was the shape rather than the weight of a body which determined whether it should be overturned or projected by a motion at its base.

As an interesting proof that light bodies may be overturned as easily as heavy ones. Mallet refers to the overturning of several large haystacks as one of the results of the Neapolitan earthquake.

If masses of material are displaced or fractured, then Mallet remarks that the maximum velocity will exceed √2gh, where h is the amplitude of the wave. Should the maximum velocity be less than this quantity, the masses which are acted upon will be simply raised and lowered, and there will be no relative displacements even if the emergence of the wave be nearly or quite vertical.

When we get a vertical wave acting upon an irregular mass of masonry, the heavier portions of the masonry, by their inertia, tend to descend relatively to the remaining portions, and in this way vertical fissures will be produced. For this reason it would not be advisable to use heavy materials above archways, heavy roofs, or heavy floors. The vertical fissures, Mallet remarks, would have their widest opening at the base.

In considering cases of fracture produced by earthquake motion, it must be remembered that these are due to stresses applied suddenly, and that if the same amount of stress had been slowly applied to a building, fractures might not have occurred.

If a disturbance is horizontal, and has a direction parallel to the length of a wall, the wall is carried forward at its foundations. This motion is opposed by the inertia of the upper portion of the wall and the various loads it carries. The wall being elastic, distortion takes place, and cracks, which are widest at the top, will be formed. In a uniform wall the two most prominent fissures ought to be near the ends.

If the horizontal backward and forward movement has a direction oblique to the plane of the wall, the wall will be either overthrown, fractured, or have a triangular fragment thrown off towards the origin from the end last reached.

Should the wave emerge steeply, diagonal fissures at right angles to the direction of transit will be formed, or else triangular pieces will be projected.

The accompanying figures are reduced from Mallet’s ‘Account of the Neapolitan Earthquake of 1857.’

Fig. 18.—Cathedral Church, Potenza (Mallet).

Taking a b as the general direction of the fractures in fig. 18, then c d will represent the direction in which the shock emerged, which is at an angle of 23°·20′ to the horizon. It might be argued that the direction of these fractures was due to the direction in which surface undulations had travelled, or to the relative strengths and proportions of different portions of the building. The directions of cracks in a building are undoubtedly due to a complexity of causes, but for buildings situated in the region of shock the impulsive effect of the shock is probably the most important function to be considered. The method of applying the directions of emergence, deduced from observations on fractures, to determine the origin of a disturbance will be referred to in Chapter X.

Fig. 19.—The Cathedral, Paterno (Mallet). Neapolitan Earthquake of 1857.

Mallet observed that, although two ends of a building might be nearly the same, the fissures and joints do not occur at equal distances from the ends, nor are they equally opened.

The end where the joints are the most opened is that which was first acted upon, and this phenomenon may be sufficiently well pronounced to indicate the direction in which we must look to find the origin of a disturbance. Amongst possible explanations for this disposition of fractures in a wall. Mallet suggests that they may be due to real differences in the two semiphases of the wave of shock, the second semiphase being described with a somewhat slower velocity than the first. This, it will be observed, is contrary to the indications of seismographs.

Fig. 19, of the cathedral at Paterno, shows the effect of a subnormal shock striking a wall obliquely and projecting one of its corners.

MEASUREMENTS OF THE RELATIVE MOTION OF PARTS OF A BUILDING AT THE TIME OF AN EARTHQUAKE.

In 1880 a series of observations was made in Tokio to determine whether at the time of an earthquake the various parts of the arched openings which we see in many buildings synchronised in their vibrations, or, for want of synchronism, were caused to approach and recede from each other. The arches experimented on were heavy brick arches forming the two corridors of the Imperial College of Engineering. The direction of one set of these corridors is N. 40° E. and that of the other N. 50° W.

The thickness of the walls in which these arches are placed is 1 ft. 11 in. They are built of Japanese bricks bound together with ordinary lime. The span of the arches is 8 ft. 3 in., and the height of the arch from the springing-line to the crown 4 ft. 1 in. The height of the abutments is 7 ft. 1½ in. The voussoirs of the arch are formed of a light grey soft volcanic rock, and on their faces show a depth of 12 inches. The width of the intermediate columns between the arches is 4 ft. 6⅞ in.

To determine whether at the time of an earthquake there was any variation in the dimensions of these arches, a light stiff deal rod, about 2 in. by ½ in. in cross section, was placed across the springing-line of the arch. One end of this was firmly fixed to the top of one abutment by means of a spike; on the other end, which was to indicate any horizontal movement if the abutments approached each other, there was fixed a pointer made out of a piece of steel wire. This rested on a piece of smoked glass fixed to the ledge on which the loose end of the rod was resting. If the abutments approached or receded from each other a line would be drawn measuring the extent of the motion. As a further indication of motion, a second smoked glass plate was fixed on the transverse rod, which plate was marked on by a pointer attached to a vertical rod hanging down from the crown of the arch.

As a general result of these experiments it may be said that the portions of the building which were examined usually either did not move at all, or else they practically synchronised in their movements. When they did move, the extent of motion was small, and the small differences in movement which were observed were in every probability far within the elastic limits of the structure.

Observations on Cracks.—To determine whether the walls of a building which have once been cracked, when subjected to a series of shocks, similar to those which they experienced before being cracked, still continued to give way, the extremities of a considerable number of cracks in the N.E. end of the museum buildings of the Engineering College were marked with pencil. Although since the time of marking there had been many severe shocks, these cracks did not visibly extend. These marks were made on the outside wall of the building. On the inside, one of these same cracks showed itself as a fissure about ¼ inch in width. Across this crack a horizontal steel wire pointer was placed. One end of this wire was fixed in the wall; the other end, which was pointed, rested on the surface of a smoked glass plate placed on the other side of the crack. After small earthquakes there was no indication of motion having taken place, but after a shock on February 21, as indicated by a line upon the smoked glass plate, it was seen that the sides of the crack had approached and receded from each other through a distance of about ¹/₁₆ inch.

By similar contrivances placed on cracks in a neighbouring building exactly similar results were obtained, namely, that during small earthquakes the two sides of the crack had retained their relative positions, but at the time of a large shock this position had been changed.

In this building it was also observed that the cracks in many instances increased their length.

By attaching levers to the end of the pointers to multiply any motion that might take place, no doubt the indications would be more frequent and more definite. It would also be easier to note the relative distances of motion in two directions, namely, how far the cracks had closed and how far they had opened. As to whether motion would occur or not, much would no doubt depend upon the direction of the earthquake.

Prevention of Fractures.—One conclusion which may perhaps be drawn from these observations is, that a cracked building at the time of an earthquake shows a certain amount of flexibility. Whether a building which had been designed with cracks or joints between those parts which were likely to have different periods of vibration would be more stable, so far as earthquake shakings are concerned, than a similar building put up in an ordinary manner, is a matter to be decided by experiment. Certainly some of the cracks which have been examined indicate that if they had not existed, the strain upon the portion of the building where they occur would have been extremely great.

Direction of Cracks.—In looking at the cracks produced by small earthquakes it is interesting to note the manner of their extension. The basements of the buildings which have been most carefully examined are, for a height of two or three feet, built of large rectangular blocks of a greyish-coloured volcanic rock. In these parts the cracks pass in and out between the joints of the stone, indicating that the stones have evidently been stronger than the mortar which bound them together, and as a consequence the latter had to give way. Above this basement when the cracks enter the brickwork, they no longer exclusively confine themselves to the joints, but run in an irregular line through all they meet with, sometimes across the bricks and sometimes through the mortar joints. In places where they have traversed the brickwork, we can say that the mortar has been stronger than the bricks. This traversing of the bricks rather than the joints is, I think, the general rule for the direction of the cracks in the brickwork of Tokio buildings.

The Pitch of Roofs.—From observation of the effects produced by earthquakes, it appears to us that the houses which lost the greater number of tiles appear to be those with the steepest pitch, and those where the tiles were simply laid upon the roof and not in any manner fastened down. It would seem that destruction of this sort might to a great extent be obviated by giving the roofs a less inclination and fixing the tiles with nails. It was also noticed that the greatest disturbance amongst the tiles was upon the ridges of the roofs. Destruction of this sort might be overcome by giving especial attention to these portions during the construction of the roof.

Fig. 20. Fig. 21.

Relative Position of Openings in Walls.—From what has been said about the fractures in the buildings of Tokio it will have been seen that, with but few exceptions, they have all taken place above openings like doorways and windows. If architecture demands that openings like arches should be placed one above another in heavy walls of this kind, as in fig. 17, there will be lines of weakness running through the openings parallel to the dotted lines. As arches are only intended to resist vertical thrusts, special construction must be adopted to make them strong enough to resist horizontal pulls. For instance, a flat arch would offer more resistance to horizontal pulls than an arch put together with ordinary voussoirs, there being in the former case more friction to prevent the component parts sliding over each other. Or again, above each arch an iron girder or wooden lintel might be inserted in the brick or stone arch. It was suggested to me by my colleague, Mr. Perry, that the best form calculated to give a wall uniform strength, would be to build it so that the openings of each tier would occupy alternate positions, that is to say, along lines parallel to the struts and ties of a girder. In this way we should have our materials so arranged that they would offer the same resistance to horizontal as to vertical movements. Such a wall is shown in fig. 20: the dotted lines running through the openings, and all similar lines parallel to the former, representing lines of weakness. If we compare this with fig. 21, we shall see that in the case of a horizontal movement a b or of a vertical movement c d, we should rather expect to find fractures in a house built like fig. 21 than in one built like fig. 20. If, however, these two buildings were shaken by a shock which had an angle of emergence of about 45° in the direction e f, the effects might be reversed. Usually, however, and always in a town like Tokio which is visited by shocks originating at a distance, the movements are practically horizontal ones, and, therefore, buildings erected on the principles illustrated by fig. 20 should be much superior, so far as resisting earthquakes is concerned, to buildings constructed in the ordinary manner, as in fig. 21. Fractures following a vertical line of weakness are shown in the accompanying drawing, fig. 22, of the Church of St. Augustin, at Manilla, shattered by the earthquakes of 1880.

The last House in a Row.—When an earthquake shock enters a line of buildings, and proceeds in a direction coincident with that of the buildings, we should expect that the last of these houses, being unsupported on one side, would be in the position of the last person in Tyndall’s row of boys. From this it would seem that the end house in a row would show the greatest tendency to fly away from its neighbours. If the last house stood upon the edge of a deep canal or a cliff, there would be a layer of ground, equal in thickness to the depth of the canal or to the height of the cliff, as the case may be, which would also be in a position to be thrown forward. The effect which is sometimes produced upon an end building is shown in fig. 23, which is taken from the photograph of a house shattered in 1868 at San Francisco.

Fig. 22.—Church of St. Augustin, Manilla. Earthquakes of July 18–20, 1880.

The Swing of Buildings.—The distance through which buildings are moved at the time of an earthquake depends partly on their construction and partly on the extent, nature, and duration of the movement communicated to them at their foundations. By violent shocks buildings may be completely overthrown. In the case of small earthquakes, the upper portion of a house may frequently move through a much greater distance than the ground at its foundation. For instance, during the Yokohama earthquake of February, 1880, when the maximum amplitude of the earth’s motion was probably under ¾ of an inch, from the slow swing of long Japanese pictures, from three to six feet in length, which oscillated backwards and forwards on the wall, it is very probable that the extent through which the upper portion of houses moved was very considerable. In some instances these pictures seem to have swung as much as two feet, and from the manner in which they swung they evidently synchronised with the natural swing of the house.

Fig. 23.—Webber House, San Francisco. Oct. 21, 1868.

From this it would seem that such a house must have rocked from side to side one foot out of its normal perpendicular position. That the motion was great is testified by nearly all who tried to stand at the time of the shock, it having been impossible to walk steadily across the floor of a room in an upper story. The houses here referred to are either those which are purely Japanese, or else those which are framed of wood and built on European models, a class of building which is very common in Tokio and Yokohama.

Perry and Ayrton calculated the period of a complete natural vibration of different structures. For a square house whose outer and inner sections were respectively 30 and 26 feet, and whose height was 30 feet, the period calculated would be about ·06 second.

At the time of the above earthquake many houses seem to have moved like inverted pendulums. On the morning after the shock my neighbour, who was living upstairs in a tall wooden house with a tile roof, told me that he endeavoured to count the vibrations, and was of the impression that to make a complete swing it took about 2 seconds.

Assuming now that the distance through which the top of a wooden house moved was about 1 foot, and the number of vibrations which it made per second was about ·5, then the greatest velocity of a point on the top of such a house must have been about 6 feet per second.

Mallet, who made observations upon the vibrations of various structures, tells us that Salisbury spire moves to and fro in a gale more than 3 inches. A well-constructed brick and mortar wall, 40 feet high and 1 foot 6 inches thick, was observed to vibrate in a gale 2 feet transversely before it fell.

An octagonal chimney with a heavy granite capping, 160 feet high, was observed instrumentally to vibrate at the top nearly 5 inches.[22]

At the time of a severe earthquake it does not seem impossible but that a building may be swung completely over. The accompanying illustration, fig. 24, taken from a photograph,[23] apparently indicates a movement of description.

Fig. 24.—Stud Mill at Haywards, California. Oct. 21, 1868.

Principle of relative Vibrational Period.—If a lath or thin pole loaded at one end with a weight fixed to the ground, so as to stand vertically, be shaken by an earthquake it will be caused to rock to and fro like an inverted pendulum. The period of its swing will be chiefly dependent on its dimensions, its elasticity, and its load. In a building we have to consider the vibration of a number of parts, the periods of which, if they were independent of each other, would be different. On account of this difference in period, whilst one portion of a building is endeavouring to move towards the right, another is pulling towards the left, and, in consequence, either the bonds which join them or else they themselves are strained or broken. This was strikingly illustrated by many of the chimneys in the houses at Yokohama, which by the earthquake of February 20, 1880, were shorn off just above the roof. The chimneys were shafts of brick, and probably had a slower period of vibration than the roof through which they passed, this latter vibrating with the main portion of the house, which was framed of wood.

A particularly instructive example of this kind which came under my notice is roughly sketched in fig. 25.

Fig. 25.

This is a chimney standing alone, which, for the sake of support, was strapped by an iron band to an adjoining building. It would seem that at the time of the shock, the building moving one way and the chimney another, the swing of the heavy building gave the chimney a sharp jerk and cut it off. The upper portion, being then loose upon the lower part, rotated under the influence of the oscillations in manner similar to that in which gravestones are rotated.

Mallet made observations similar to these in Italy. He tells us that a buttress may often not have time to transmit its stability to a wall. The wall and the buttress have different periods of vibration, and therefore they exert impulsive actions on each other. Effects like these were strikingly observable in many of the rural Italian churches where the belfry tower is built into one of the quoins of the main rectangular building.

Not only have we to consider the relative vibrations of the various parts of a building amongst themselves, but we have to consider the relation of the natural vibrations of any one of them or the vibration of the building as a whole, with regard to the earth, the vibrations of which it must be remembered are not strictly periodic.

Some of the more important results dependent upon the principle of ‘relative vibrational periods’ may be understood from the following experiments:—

Fig. 26.

In fig. 26 a, b, and c are three flat springs made out of strips of bamboo, and loaded at the top with pieces of lead. At the bottom they are fixed into a piece of board d e, and the whole rests on a table f g. The legs of this table being slightly loose, by placing the fingers on the top of it, a quick short backward and forward movement can be produced. The weights on a and b are the same, but they are larger than the weight on c. Consequently the periods of a and b are the same, but different to the period of c. The dimensions of these springs are as follows: height, 18 inches; a and b each carry weights equal to 320 grammes, and they make one vibration per second; c has a weight of 199 grammes, and makes 0·75 vibrations per second.

First Experiment.—It will be found that by giving the table a gentle backward and forward movement, the extent of which movement may be so small that it will be difficult to detect it with the eye, either a and b may be made to oscillate violently whilst c remains still; or vice versâ, c may be caused to oscillate whilst a and b remain still. In the one case the period of shaking will have been synchronous with the natural period of a and b, whilst in the latter it will have been synchronous with that of c. This would seem to show us that if the natural period of vibration of a house, or of parts of it, at any time agree with the period of the shock, it may be readily thrown into a state of oscillation which will be dangerous for its safety.

Second Experiment.—Bind a and b together with a strip of paper pasted between them. (The paper used was three-eighths of an inch broad and would carry a weight of nearly three pounds.) If the table be now shaken as before, a and b will always have similar movements, and tend to remain at the same distance apart, and as a consequence the strip of paper will not be broken. From this experiment it would seem that so long as the different portions of a building have almost the same periods of vibration, there will be little or no strain upon the tie-rods or whatever contrivance may be used in connecting the different parts.

Third Experiment.—Join a and c, or b and c with a strip of paper in a manner similar to the last experiment. If the table be now shaken with a period approximating either to that of a and b, or with that of c, the paper will be suddenly snapped.

This indicates that if we have different portions of a building of such heights and thicknesses that their natural periods of vibration are different, the strain upon the portions which connect such parts is enormous, and it would seem, as a consequence, that either the vibrators themselves, or else their connections, must, of a necessity, give way. This was very forcibly illustrated in the Yokohama earthquake of February 1880 by the knocking over of chimneys. The particular case of the chimneys is, however, better illustrated by the next experiment.

Fourth Experiment.—Take a little block of wood three-quarters of an inch square and about one inch high, and place it on the top of a, b, or c. It will be found that, although the spring on which it stands is caused to swing backwards and forwards through a distance of three inches, the little block will retain its position.

This little block we may regard as the upper part of a chimney standing on a vibrating stack, and we see that, so long as this upper portion is light, it has no tendency to fall.

Fifth Experiment.—Repeat the fourth experiment, having first placed a small leaden cap on the top of the block representing the chimney. (The cap used only weighed a few grammes.) When vibration commences it will be found that the block quickly falls. This would seem to indicate that chimneys with heavy tops are more likely to fall than light ones.

Sixth Experiment.—Bind a and b together with a strip of paper and stand the little block upon the top of either. It will be found that the block will stand as in the fourth experiment.

Seventh Experiment.—Bind a and c, or b and c together, and place the block upon the top of either of them. When vibration commences, although the paper may not be broken, the little block will quickly fall.

Eighth Experiment.—Take two pencils or pieces of glass tube and place them under the board d e. If the table F G be now shaken in the direction d e, it will be found that the springs will not vibrate.

In a similar manner if a house or portion of a house were carried on balls or rollers, as has already been suggested, it would seem that the house might be saved from much vibration.

Ninth Experiment.—Set any of the springs in violent vibration by gently shaking d e instead of the table, and then suddenly cease the actuating motion. It will be observed that at the moment of cessation the board and the springs will have a sudden and very decided motion of translation in the same direction as that in which the springs were last moving, and although the springs were at the time swinging through a considerable arc, all motion will suddenly cease.

This shows, that if a house is in a state of vibration the strain at the foundations must be very great.

It would not be difficult to devise other experiments to illustrate other phenomena connected with the principle of relative vibrational periods, but these may perhaps be sufficient to show to those who have not considered this matter its great importance in the construction of buildings. Perhaps the greater portion of what is here said may by many be regarded as self-evident truisms hardly worth the trouble of demonstration. Their importance, however, seems to be so great that I hope that their discussion has not been altogether out of place.

I may remark that in the rebuilding of chimneys in Yokohama the principles here enunciated were taken advantage of by allowing the chimneys to pass freely through the roofs without coming in contact with any of the main timbers.

In putting up buildings to resist the effects of an earthquake, besides the idea of making everything strong because the earthquake is strong, there are several principles which, like the one just enunciated, might advantageously be followed which as yet appear to have received but little attention.

CHAPTER VII.
EFFECTS PRODUCED UPON BUILDINGS (continued).

Types of buildings used in earthquake countries—In Japan, in Italy, in South America, in Caraccas—Typical houses for earthquake countries—Destruction due to the nature of underlying rocks—The swing of mountains—Want of support on the face of hills—Earthquake shadows—Destruction due to the interference of waves—Earthquake bridges—Examples of earthquake effects—Protection of buildings—General conclusions.

Types of buildings used in earthquake countries.—In Japan there are excellent opportunities of studying various types of buildings. The Japanese types, of course, form the majority of the buildings. The ordinary Japanese house consists of a light framework of 4 or 5 inch scantling, built together without struts or ties, all the timbers crossing each other at right angles. The spaces are filled in with wattle-work of bamboo, and this is plastered over with mud. This construction stands on the top of a row of boulders or of square stones, driven into the surface soil to a distance varying from a few inches to a foot. The whole arrangement is so light that it is not an uncommon thing to see a large house rolled along from one position to another on wooden rollers. In buildings such as these after a series of small earthquake shocks, we could hardly expect to find more fractures than in a wicker basket.

The larger buildings, such as temples and pagodas, are also built of timber. These are built up of such a multitude of pieces and framed together in such an intricate manner that they also are capable of yielding in all directions. The European buildings are, of course, made of brick and stone with mortar joints. Some of these, as the buildings of the Ginza in Tokio, are not designed for great strength. On the other hand, others have thick and massive walls and are equal in strength to those we find in Europe.

The third type of buildings are those which are built in blocks; and these blocks being bound together with iron rods traversing the walls in various directions are especially designed to withstand earthquakes. A system somewhat similar to this has been patented in America, and examples of these so-called earthquake-proof buildings are to be found in San Francisco.

Speaking of Japanese buildings, Mr. R. H. Brunton, who has devoted especial attention to them says that,[24] ‘to imagine that slight buildings, such as are seen here (i.e. in Japan), are the best calculated to withstand an earthquake shock is an error of the most palpable kind.’ After describing the construction of a Japanese house in pretty much the same terms as we have used, he says ‘that with its unnecessarily heavy roof and weak framework it is a structure of all others the worst adapted to withstand a heavy shock.’ He tells us, further, that these views are sustained by the truest principles of mechanics. In order to render buildings to some extent proof against earthquakes, some of the heavy roofs in Tokio have been so constructed that they are capable of sliding on the walls. Mr. Brunton mentions a design for a house, the upper part of which is to rest on balls, which roll on inverted cups fixed on the lower part of the building, which is to be firmly embedded in the earth. A similar design was, at the suggestion of Mallet, used to support the tables carrying the apparatus of some of the lighthouses erected in Japan by Mr. Brunton. The very existence of these designs seems to indicate that the ordinary European house, however solidly and strongly it may be built, is not sufficient to meet the conditions imposed upon it. What is required, is something that will give way—an approximation to the timber frame of a Japanese house, so strongly condemned by Mr. Brunton and others. The crucial test of the value of the Japanese structure, as compared with the modern buildings of brick and stone, is undoubtedly to be found by an appeal to the buildings themselves. So far as my own experience has gone, I must say that I have never seen any signs in the Japanese timber buildings which could be attributed to the effects of earthquakes, and His Excellency Yamao Yozo, Vice Minister of Public Works, who has made the study of the buildings of Japan a speciality, told me that none of the temples and palaces, although many of them are several centuries old, and although they have been shaken by small earthquakes and also by many severe ones, show any signs of having suffered. The greatest damage wrought by large earthquakes appears to have resulted from the influx of large waves or from fires. In every case where an earthquake has been accompanied by great destruction, by consulting the books describing the same, it can be seen, from the illustrations in these books portraying conflagrations, that this destruction was chiefly due to fire. When we remember that nearly all Japanese houses are constructed of materials that are readily inflammable, it is not hard to imagine how destruction of this kind has come about. To a Japanese, living as he does in a house which has been compared to a tinder-box, fire is one of his greatest enemies, and in a city like Tokio it is not at all uncommon to see during the winter months many fires which sweep away from 100 to 500 houses. In one winter I was a spectator of three fires, each of which was said to have destroyed upwards of 10,000 houses.

Although it would appear that the smaller earthquakes of Japan produce no visible effect upon the native buildings, it is nevertheless probable that small effects may have been produced, the observation of which is rendered difficult by the nature of the structure. If we look at buildings of foreign construction, by which are meant buildings of brick and stone, the picture before us is quite different, and everywhere the effects of earthquakes are palpable even to the most casual observer. Of these effects numerous examples have already been given. Not only are these buildings damaged by the cracking of walls and the overturning of chimneys, but they also appear to be affected internally. For instance, in the timbers of the roof of the museum attached to the Imperial College of Engineering in Tokio, there are a number of diagonal faces acting as struts or ties intended to prevent more or less horizontal movements taking place. Those which are rigidly joined together with bolts and angle irons have apparently suffered from their rigidity, being twisted and bent into various forms. The buildings in Tokio, which are strongly put together, being especially designed to withstand earthquakes, appear to have suffered but little. I know only one example which at the time of the severe shock of 1880 had several of its chimneys damaged.

The ordinary houses in Italy, though built of stone and mortar, are but poorly put together, and, as Mallet has remarked, are in no way adapted to withstand the frightful shakings to which they are subjected from time to time.

In the large towns, like Naples, Rome, and Florence, where happily earthquakes are of rare occurrence, although the building may be better than that found in the country, the height of the houses and the narrowness of the streets are sufficient to create a shudder, when we think of the possibility of the occurrence of a moderately severe earthquake.

In South America, although many buildings are built with brick and stone, the ordinary houses, and even the larger edifices, are specially built to withstand earthquakes. In Mr. James Douglas’s account of a ‘Journey Along the West Coast of South America,’ we read the following[25]: ‘The characteristic building material of Guayaquil is bamboo, which grows to many inches in thickness, and which, when cut partially through longitudinally at distances of an inch or so, and once quite through, can be opened out into fine elastic boards of serviceable width. Houses, and even churches, of a certain primitive beauty are built of such reeds, so bound together with cords that few nails enter into the construction, and which, therefore, yield so readily to the contortions of the earth during an earthquake as to be comparatively safe.’

Here we have a house, which, so far as earthquakes are concerned, is an exaggerated example of the principles which are followed in the construction of an ordinary Japanese dwelling.

Another plan adopted in South America can be gathered from the same author’s writings upon Lima, about which he says, ‘To build high houses would be to erect structures for the first earthquake to make sport of, and, therefore, in order to obtain space, safety, and comfort, the houses of the wealthy surround court after court, filled with flowers, and cooled with fountains, connected one with another with wide passages which give a vista from garden to garden.’

History would indicate that houses of this type have been arrived at as the results of experience, for it is said that when the inhabitants of South America first saw the Spaniards building tall houses, they told them they were building their own sepulchres.[26]

In Jamaica, we find that even as early as 1692 experience had taught the Spaniards to construct low houses, which withstood shakings better than the tall ones.[27]

In Caraccas, which has been called the city of earthquakes, it is said that the earthquakes cause an average yearly damage amounting to the equivalent of a per capita tax of four dollars. To reduce this impost to a minimum much attention is paid to construction. ‘Projecting basement corners (giving the house a slightly pyramidal appearance) have been found better than absolutely perpendicular walls; mortised corner-stones and roof beams have saved many lives when the central walls have split from top to bottom; vaults and key-stone arches, no matter how massive, are more perilous than common wooden lintels, and there are not many isolated buildings in the city. In many streets broad iron girders, riveted to the wall, about a foot above the house door, run from house to house along the front of an entire square. Turret-like brick chimneys, with iron top ornaments, would expose the architect to the vengeance of an excited mob; the roofs are flat, or flat terraced; the chimney flues terminate near the eaves in a perforated lid.’[28]

Typical houses for earthquake countries.—From what has now been said about the different buildings found in earthquake countries, it will be seen that if we wish to put up a building able to withstand a severe shaking, we have before us structures of two types. One of these types may be compared with a steel box, which, even were it rolled down a high mountain, would suffer but little damage; and the other, with a wicker basket, which would equally withstand so severe a test. Both of these types may be, to some extent, protected by placing them upon a loose foundation, so that but little momentum enters them at their base. One suggestion is to place a building upon iron balls. Another method would be to place them upon two sets of rollers, one set resting upon the other set at right angles. The Japanese, we have seen, place their houses on round stones. The solid type of building is expensive, and can only be approached partially, whilst the latter is cheap, and can be approached closely. In the case of a solid building it would be a more difficult matter to support it upon a movable foundation than in the case of a light framework. Such a building is usually firmly fixed on the ground, and consequently at the time of an earthquake, as has already been shown by experiment, must be subjected to stresses which are very great. In consequence also of the greater weight of the solid structure, more momentum will enter it at its base than in the case of the light structure. Also, we must remember that the rigidity favours the transmission of momentum, and with rigid walls we are likely to have ornaments, coping-stones, and the comparatively freer portions forming the upper part of a building displaced; whilst, with flexible walls absorbing momentum in the friction of their various parts, such disturbances would not be so likely. Mr. T. Ronaldson, referring to this, says, that in 1868, at San Francisco, the ornamental stone work in stone and cement buildings was thrown from its position, whilst similar ornaments in neighbouring brick buildings stood.

To reduce the top weight of a building, hollow bricks might be employed. To render a building more homogeneous and elastic, the thickness of bricks might be reduced. Inasmuch as the elasticity of brick and timber are so different, the two ought to be employed separately. For internal decorations plaster mouldings might be replaced by papier mâché and carton-pierre, the elastic yielding of which is comparatively great.[29] Houses, whether of brick and stone, or of timber, ought to be broad and low, and the streets three or four times as wide as the houses. The flatter the roofs the better.

One of the safest houses for an earthquake country would probably be a one-storied strongly framed timber house, with a light flattish roof made of shingles or sheet-iron, the whole resting on a quantity of small cast-iron balls carried on flat plates bedded in the foundations. The chimneys might be made of sheet-iron carried through holes free of the roof. The ornamentation ought to be of light materials.

At the time of severe earthquakes many persons seek refuge from their houses by leaving them. In this case accidents frequently happen from the falling of bricks and tiles. Others rush to the doorways and stand beneath the lintels. Persons with whom the author has conversed have suggested that strongly constructed tables and bedsteads in their rooms would give protection. To see persons darting beneath tables and bedsteads would undoubtedly give rise to humiliating and ludicrous exhibitions. This latter idea is not without a value, and most certainly, if applied in houses of the type described, would be valuable.

The great danger of fire may partially be obviated by: the use of ‘earthquake lamps,’ which are so constructed that before they overturn they are extinguished. It is said that in South America some of the inhabitants are ready at any moment to seek refuge in the streets, and they have coats prepared, stocked with provisions and; other necessaries, which, if occasion demands, will enable them to spend the night in the open air. These coats, called ‘earthquake coats,’ might also, with properly constructed houses, be rendered unnecessary.

Destruction due to the nature of the underlying rocks.—That the nature of the ground on which a building stands is intimately related with the severity of the blow it receives is a fact which has often been demonstrated.

One cause of destruction is due to placing a building on foundations which are capable of receiving the full effects of a shock, and transmitting it to the buildings standing on them.

For instance, the reason why a soft bed might possibly make a good foundation, is, as has been pointed out by Messrs. Perry and Ayrton, because the time of transmission of momentum is increased; in fact, the soft bed is very like a piece of wood interposed between a nail and the blows of a hammer—it lengthens the duration of impact. For this reason we are told that a quaking bog will make a good foundation. When a shock enters loose materials its waves will be more crowded, and it is possible that a line of buildings may rest on more than one wave during a shock. There are many examples on record of the stability of buildings which rested on beds of particular material at the time of destructive earthquakes. As the observations which have been made by various writers on this subject appear to point in a contrary direction, I give the following examples:—

In the great Jamaica earthquake of 1692, the portions of Port Royal which remained standing were situated on a compact limestone foundation; whilst those on sand and gravel were destroyed (‘Geological Observer,’ p. 426). Again, on p. 148 of the same work, we read, ‘According to the observations made at Lisbon, in 1737, by Mr. Sharpe, the destroying effects of this earthquake were confined to the tertiary strata, and were most violent on the blue clay, on which the lower part of the city is constructed. Not a building on the secondary limestone or on the basalt was injured.’

In the great earthquakes of Messina, those portions of the town situated on alluvium, near the sea, were destroyed, whilst the high parts of the town, on granite, did not suffer so much. Similar observations were made in Calabria, when districts consisting of gravel, sand, and clay became, by the shaking, almost unrecognisable, whilst the surrounding hills of slate and granite were but little altered. At San Francisco, in 1868, the chief destruction was in the alluvium and made ground.

At Talcahuano, in 1835, the only houses which escaped were the buildings standing on rocky ground; all those resting on sandy soil were destroyed.

From the results of observations like these, it would seem the harder rocks form better foundations than the softer ones. The explanation of this, in many cases, appears to lie in the fact that the soft strata were in a state of unstable equilibrium, and by shaking, they were caused to settle. Observations like the following, however, point out another reason why soft strata may sometimes afford a bad foundation.

‘Humboldt observed that the Cordilleras, composed of gneiss and mica-slate, and the country immediately at their foot, were more shaken than the plains.’[30]

‘Some writers have asserted that the wave-like movements (of the Calabrian earthquake in 1783) which were propagated through recent strata from west to east, became very violent when they reached the point of junction with the granite, as if a reaction was produced when the undulatory movement of the soft strata was suddenly arrested by the more solid rocks.’

Dolomieu when speaking of this earthquake says, the usual effect ‘was to disconnect from the sides of the Apennines all those masses (of sand and clay) which either had not sufficient bases for their bulk, or which were supported only by lateral adherence.’

These intensified actions taking place at and near to lines of junction between dissimilar strata is probably due to the phenomena of reflection and refraction.

When referring to the question as to whether buildings situated on loose materials suffered more or less than those on solid rocks, Mallet, in his description of the Neapolitan earthquake of 1857, remarks: ‘We have in this earthquake, towns such as Saponara and Viggiano, situated upon solid limestone, totally prostrated; and we have others such as Montemarro, to a great extent based upon loose clays, totally levelled. We have examples of almost complete immunity in places on plains of deep clay as that of Viscolione, and in places on solid limestone, like Castelluccio, or perched on mountain tops like Petina.’[31]

After reading the above, we see that the probable reason why, in several cases, beds of soft materials have not made good foundations, consists in the fact that they have either been of small extent or else have been observed only in the neighbourhood of lines which divided them from other formations, which lines are always those of great disturbances.

At the end of his description of the Neapolitan earthquake of 1857, Mallet says that more buildings were destroyed on the rock than on the loose clay. This, however, he remarks, is hardly a fact from which we can draw any valuable deductions, because it so happened that more buildings were constructed on the hills than on the loose ground.[32]

Professor D. S. Martin, writing on the earthquake of New England in 1874, remarks that in Long Island the shock was felt where there was gneiss between the drift. Around portions to the east the observations were few and far between. He also remarks that generally the shocks were felt more strongly and frequently on rocky than on soft ground.[33]

From these examples, it would appear that the hard ground, which usually means the hills, forms a better foundation than the softer ground, which is usually to be found in the valleys and plains. Other examples, however, point to a different conclusion. For instance, a civil engineer, writing about the New Zealand earthquake of 1855, when all the brick buildings in Wellington were overthrown, says that ‘it was most violent on the sides of the hills at those places, and least so in the centre of the alluvial plains.’[34]

In this example it must be noticed that the soft alluvium here referred to was of large extent, and not loose material resting on the flanks of rocks, from which it was likely to be shaken down, as in most of the previous examples.

The results of my own observations on this subject point as much in one direction as in the other. In Tokio, from instrumental observations upon the slopes and tops of hills, the disturbance appears to be very much less than it is in the plains. Thus, at my house, situated on the slope of a hill about 100 feet in height, for the earthquake of March 11, 1882, I obtained a maximum amplitude of motion of from three to four millimètres only, whilst Professor Ewing, with a similar instrument, situated on the level ground at about a mile distant, found a motion of fully seven millimètres. This calculation has been confirmed by observations on other earthquakes. Thus, for instance, in the destructive earthquake of 1855, when a large portion of Tokio was devastated, it was a fact, remarked by many, that the disturbance was most severe on the low ground and in the valleys, whilst on the hills the shock had been comparatively weak. As another illustration, I may mention that within three-quarters of a mile from my house in Tokio there is a prince’s residence which has so great a reputation for the severity of the shakings it receives that its marketable value has been considerably depreciated, and it is now untenanted.

In Hakodadi, which is a town situated very similarly to Gibraltar, partly built on the slope of a high rocky mountain and partly on a level plain, from which the mountain rises, the rule is similar to that for Tokio, namely, that the low, flat ground is shaken more severely than the high ground. At Yokohama, sixteen miles south-west from Tokio, the rule is reversed, as was very clearly demonstrated by the earthquake of February 1880, when almost every house upon the high ground lost its chimney, whilst on the low ground there was scarcely any damage done; the only places on the low ground which suffered were those near to the base of the hills. The evidence as to the relative value of hard ground as compared with soft ground, for the foundation of a building, is very conflicting. Sometimes the hard ground has proved the better foundation and sometimes the softer, and the superiority of one over the other depends, no doubt, upon a variety of local circumstances.

These latter observations open up the inquiry as to the extent to which the intensity of an earthquake may be modified by the topography of the disturbed area.

The swing of mountains.—If an earthquake wave is passing through ground the surface of which is level, so long as this ground is homogeneous, as the wave travels further and further we should expect its energy to become less and less, until, finally, it would insensibly die out. If, however, we have standing upon this plain a mountain, judging from Mallet’s remarks, this mountain would be set in a state of vibration much in the same way as a house is set in vibration, and it would tend to oscillate backward and forward with a period of vibration dependent upon the nature of its materials, size, and form. The upper portion of this mountain would, in consequence, swing through a greater arc than the lower portion, and buildings situated on the top of it would swing to and fro through a greater arc than those which were situated near its foot. This explanation why buildings situated on the top of a mountain should suffer more than those situated on a plain, is one which was offered by Mallet when writing of the Neapolitan earthquake. He tells us that towns on hills are ‘rocked as on the top of masts,’ and if we accept this explanation it would, in fact, be one reason why the houses situated on the Bluff at Yokohama suffered more than those situated in the settlement. This explanation is given on account of the great authority it claims as a consequence of its source. It is not clear how the statement can be supported, as different portions of the mountain receive momentum in opposite directions at the same time.

Want of support on the faces of hills.—When a wave of elastic compression is propagated through a medium, we see that the energy of motion is being continually transmitted from particle to particle of that medium. A particle, in moving forwards, meets with an elastic resistance of the particles towards which it moves, but, overcoming these resistances, it causes these latter particles to move, and in turn to transmit the energy to others further on. So long as the medium in which this transfer of energy is continuous, each particle has a limit to its extent of motion, dependent on the nature of the medium. When, however, the medium, which we will suppose to be the earth, is not continuous, but suddenly terminates with a cliff or scarp, the particles adjacent to this cliff or scarp, having no resistance offered to their forward motion, are shot forward, and, consequently, the ground here is subjected to more extensive vibrations than at those places where it was continuous. This may be illustrated by a row of marbles lying in a horizontal groove; a single marble rolled against one end of this row will give a concussion which will run through the chain, like the bumping of an engine against a row of railway cars, and as a result, the marble at the opposite end of the row, being without support, will fly off. Tyndall illustrates the same thing with his well known row of boys, each one standing with his arms stretched out and his hands resting upon the shoulders of the boy before him. A push being given to the boy at the back, the effect is to transmit a push to the first boy, who, being unsupported, flies forward.

In the case of some earthquakes, most disastrous results have occurred which seem only to admit of an explanation such as this. A remarkable instance of this kind occurred when the great earthquake of 1857 ‘swept along the Alps from Geneva to the east-north-east, and its crest reached the edge of the deep glen between Zermatt and Visp. Then the upper part of the wave-movement, a thousand or two thousand feet in depth from the surface, came to an end; the forward pulsation acted like the breaker of the sea, and heavy falls of rock encumbered the western side of the valley.’

Earthquake shadows.—If a mountain stands upon a plain through which an elastic wave is passing, which is almost horizontal, the mountain is, so to speak, in the shadow of such a wave. If we only consider the normal motion of this wave, we see that the only motion which the mountain can obtain will be a wave of elastic distortion produced by a shearing force along the plain of the base. Should, however, the wave approach the mountain from below, and emerge into it at a certain angle, only the portion of the mountain on the side from which the wave advanced could remain in shadow, whilst the portion on the opposite side would be thrown into a state of compression and extension. Portions in shadow, however, would be subject to waves of elastic distortion. In a manner similar to this we may imagine that certain portions of the bluff, so far as the advancing wave was concerned, were in shadow, and thus saved from the immediate influence of the direct shock. A hypothetical case of such a shadow is shown in the accompanying section, illustrating the contour of the ground at Yokohama. The situation which might be in the shadow of one shock, however, it is quite possible might not be in that of another. We must also remember that a place in shadow for a direct shock might be affected by reflected waves, and also by the transverse vibrations of the direct shock. These effects are over and above the effects produced by the waves of elastic distortion just referred to. It might be asked whether whole countries, like England, which are but seldom shaken, are in shadow.

Fig. 27.—Hypothetical section at Yokohama.

Destruction due to the interference of waves.—Referring to the section of the ground at Yokohama (Fig. 27), it will be seen that both the settlement and the bluff stand upon beds of gravel capping horizontal beds of grey tuff. The gravel of that portion of the settlement on the seaboard originally formed the line of a shingle beach. That portion of the settlement back from the sea stands upon ground which was originally marshy. In the central portions of the settlement this bed of gravel is very thick, perhaps 100 feet or so, but as you near the edge of the bluff it probably becomes thinner, until it finally dies out upon the flanks of the scarps.

On the top of the bluff, the beds of gravel will, in every probability, be generally thinner than they are upon the lower level. The beds of tuff, which is a soft grey-coloured clay-like rock, produced by the solidification of volcanic mud, appear, when walking on the seaboard, to be horizontally stratified. If there is a dip inland, it is in all probability very slight. Here and there the beds slightly faulted. Taken as a whole we may consider these beds as being tolerably homogeneous, and an earthquake in passing through them would meet with but little reflection or refraction. At the junction of these beds with the overlying gravels, both reflection and refraction would comparatively be very great.

On entering the gravel, as the wave would be passing into a less elastic medium, the direction of the wave would be bent towards the perpendicular to the line of junction, and the angle of emergence at the surface would consequently be augmented. At the surface certain reflection would also take place, but the chief reflections would be those at the junction of the tuff and the alluvium.

Under the settlement it is probable that all the reflections which took place would be single. Thus wave fronts like a₁ advancing in a direction parallel to the line a₁; would be reflected in a direction a₂ and give rise to a series of reflected waves a₂. These are shown by thicker lines. Similarly all the neighbouring waves to the right and left of a₁ would give rise to a series of reflected waves. If the lines drawn representing wave fronts are districts of compression, then, where two of the lines cross each other, there would be double energy in producing compression. Similarly, districts of rarefaction might accord, and, again, compression of one wave might meet with the rarefaction of another and a neutralisation of effect take place. A diagram illustrating concurrence and interference of this description is given in Le Conte’s ‘Elements of Geology,’ p. 115. The interference which has been spoken of, however, is not the greatest which would occur. The greatest would probably be beneath the bluff and the scarps which run down to join the level ground below. This would be the case because it is a probability that there might not only be cases of interference of single reflected waves, but also of waves which had been not only twice but perhaps thrice reflected. For example, a wave like b₁ (which is parallel to a₁ of the first supposition), advancing in a direction parallel to b₁ might be reflected along the line b₂ giving rise to waves like b₂, which in turn might be reflected along b₃ giving rise to waves like b₃. The number of districts where there would be concurrence and interference would, in consequence of the number of times waves might be reflected, be augmented. Here the violence of the shock would, at certain points, be considerably increased, but as a general result energy must be lost, so that even if some of the reflected waves found their way into the portion we have regarded as being in shadow, their intensity would not be so great as if they had entered it directly.

The shaking down of loose materials from the sides of hills may be partially explained on the assumption of an increased disturbance due to interference.

Earthquake bridges.—In certain parts of South America there appear to exist tracts of ground which are practically exempt from earthquake shocks, whilst the whole country around is sometimes violently shaken. It would seem as if the shock passes beneath such a district as water passes beneath a bridge, and for this reason these districts have been christened ‘bridges.’

This phenomenon appears to depend upon the nature of the underlying soil. When an elastic wave passes from one bed of rock to another of a different character, a certain portion of the wave is reflected, while the remainder of it is transmitted and refracted, and ‘bridges’ we may conceive of as occurring where the phenomenon of total reflection occurs.

In the instances given of soft materials having proved good foundations, it was assumed that they had chiefly acted as absorbers of momentum. They have also acted as reflecting surfaces, and where no effects have been felt by those residing on them, this may have been the result of total reflection, and the soft beds thus have played the part of bridges.

Fuchs gives an example taken from the records of the Syrian earthquake of 1837, where not only neighbouring villages suffered differently, but even neighbouring houses. In one case a house was entirely destroyed, whilst in the next house nothing was felt.

In Japan, at a place called Choshi, about 55 miles east of the capital, earthquakes are but seldom felt, although the surrounding districts may be severely shaken.

From descriptions of this place it would appear that there is a large basaltic boss rising in the midst of alluvial strata. The immunity from earthquakes in this district has probably given rise to the myth of the Kanam rock, which is a stone supposed to rest upon the head of a monstrous catfish (Namadzu), which by its writhings causes the shakings so often felt in this part of the world.[35]

Prof. D. S. Martin, writing on the earthquake of New England in 1874, says that it was felt at four points; it was felt in the heart of Brooklyn all within a circle of half a mile across; ‘and this fact would suggest that a ridge of rock perhaps approaches the surface at that point, though none is known to appear.’[36]

The subject of special districts, which are more or less protected from severe shakings, will be again referred to, and it will be seen that after a seismic survey has been made even of a country like Japan, where there are on the average at least two earthquakes per day, it is possible to choose a place to build in as free from earthquakes as Great Britain.

General examples of earthquake effects.—The following examples of earthquake effects are drawn from Mallet’s account of the Neapolitan earthquake of 1857.

At a town called Polla there was great destruction. Judging from the fissures in the parts that remained standing it seemed that the emergence of the shock had been more vertical in the upper part of the town than in the lower, proving that whatever had been the angle below, the hill had itself vibrated, which, being horizontal, had modified the angle of the fissures.

Diano suffered but little, partly because it was well built, and partly on account of its situation, which was such that before the shock reached it the disturbance had to pass from beds of clay into nearly vertically placed beds of limestone. Also a great portion of the shock was cut off by the Vallone del Raccio to the north and north-west of the town. Here the effects of the partial extinction of the wave on the ‘free outlaying stratum’ were visible in the masses of projected rock.

Castellucio did not suffer because its well buttressed knoll was end on to the direction of shock, and on account of a barrier of vertical breccia beds protecting it upon the east.

Pertosa stands on a mound. The destruction was least in the southern part of the town. From the relation of the beds of breccia on which the town stands, and the direction of the wave-path, it is evident that the southern part of the town received the force of the shock through a greater thickness of the breccia beds than the other parts did.

Petina, standing on a level limestone spur jutting out from a mountain slope, suffered nothing, whilst Anletta five miles to the south-west, and Pertosa six miles distant, were in great part prostrated. (1) The terrace did not vibrate, and (2) between Petina and Anletta there is almost 6,000 feet of piled up limestone, so that any shock emergent at a steep angle had to pass up transversely through these beds.

Protection of buildings.—In addition to giving proper construction to our buildings, choosing proper foundations and positions for them, something might possibly be done to ward off the destructive effects of an earthquake. We read that the Temple of Diana at Ephesus was built on the edge of a marsh, in order to ward off the effect of earthquakes. Pliny tells us that the Capitol of Rome was saved by the Catacombs, and Elisée Reclus[37] says that the Romans and Hellenes found out that caverns, wells, and quarries retarded the disturbance of the earth, and protected edifices in their neighbourhood. The tower of Capua was saved by its numerous wells. Vivenzis asserts that in building the Capitol the Romans sunk wells to weaken the effects of terrestrial oscillations. Humboldt relates the same of the inhabitants of San Domingo.

Quito is said to receive protection from the numerous cañons in the neighbourhood, whilst Lactacunga, fifteen miles distant, has often been destroyed.

Similarly, it is extremely probable that many portions of Tokio have from time to time been protected more or less from the severe shocks of earthquakes by the numerous moats and deep canals which intersect it.

Although we are not prepared to say how far artificial openings of this description are effectual in warding off the shocks of earthquakes, from theoretical considerations, and from the fact that their use has been discovered by persons who, in all probability, were without the means of making theoretical deductions, the suggestions which they offer are worthy of attention.

General conclusions.—The following are a few of the more important results which may be drawn from the preceding chapter:—

1. In choosing a site for a house find out by the experience of others or experimental investigation the localities which are least disturbed. In some cases this will be upon the hills, in others in the valleys and on the plains.

2. A wide open plain is less likely to be disturbed than a position on a hill.

3. Avoid loose materials resting on harder strata.

4. If the shakings are definite in direction, place the blank walls parallel to such directions, and the walls with many openings in them at right angles to such directions.

5. Avoid the edges of scarps or bluffs, both above and below.

6. So arrange the openings in a wall, that for horizontal stresses the wall shall be of equal strength for all sections at right angles.

7. Place lintels over flat arches of brick or stone.

8. To withstand destructive shocks either rigidly follow one or other of the two systems of constructing an earthquake-proof building. The light building on loose foundations is the cheaper and probably the better.

9. Let all portions of a building have their natural periods of vibration nearly equal.

10. If it is a necessity that one portion of a building should have a very different period of vibration to the remainder, as for instance a brick chimney in a wooden house, it would seem advisable either to let these two portions be sufficiently free to have an independent motion, or else they must be bound together with great strength.

11. Avoid heavy topped roofs and chimneys. If the foundations were free the roof might be heavy.

12. In brick or stone work use good cement.

13. Let archways curve into their abutments.

14. Let roofs have a low pitch, and the tiles, especially those upon the ridges, be well secured.

CHAPTER VIII.
EFFECTS OF EARTHQUAKES ON LAND.

1. Cracks and fissures—Materials discharged from fissures—Explanation of fissure phenomena. 2. Disturbances in lakes, rivers, springs, wells, fumaroles, &c.—Explanation of these latter phenomena. 3. Permanent displacement of ground—On coast lines—Level tracts—Among mountains—Explanation of these movements.

Cracks and fissures formed in the ground.—Almost all large earthquakes have produced cracks in the ground. The cracks which were found in the ground at Yokohama (February 22, 1880) were about two or three inches wide, and from twenty to forty yards in length. They could be best seen as lines along a road running near the upper edge of some cliffs which overlook the sea at that place. The reason that cracks should have occurred in such a position rather than in others was probably owing to the greater motion at such a place, due to the face of the cliff being unsupported, and there being no resistance opposed to its forward motion. It often happens that earthquake cracks are many feet in width. At the Calabrian earthquake of 1783, one or two of the crevasses which were formed were more than 100 feet in width and 200 feet in depth. Their lengths varied from half a mile to a mile.[38] Besides these large cracks, many smaller ones of one or two feet in breadth and of great length were formed. In the large fissures many houses were engulfed. Subsequent excavations showed that by the closing of the fissures these had been jammed together to form one compact mass. These cracks are usually more or less parallel, and at the same time parallel to some topographical feature, like a range of mountains. For example, the cracks which were formed by the Mississippi earthquake of 1812 ran from north-east to south-west parallel to the Alleghanies. By succeeding shocks these crevasses are sometimes closed and sometimes opened still wider. Their permanency will also depend upon the nature of the materials in which they are made.

During an earthquake large cracks may suddenly open and shut.

During the convulsions of 1692 which destroyed Port Royal, it is said that many of the fissures which were formed, opened and shut. In some of these, people were entirely swallowed up and buried. In others they were trapped by the middle, and even by the neck, where if not killed instantaneously they perished slowly. Subsequently their projecting parts formed food for dogs.[39]

The earthquake which, July 18, 1880, shook the Philippines caused many fissures to be found, which in some places were so numerous that the ground was broken up into steps. Near to the village of San Antonio the soil was so disturbed that the surface of a field of sugar-canes was so altered that in some cases the top of one row of full grown plants was on a level with the roots of the next. Into one such fissure a boat disappeared, and into another, a child.

Subsequently the child was excavated, and its body, which was found a short distance below the surface, was completely crushed.[40]

At the time of the Riobamba earthquake, not only were men engulfed, but animals, like mules, also sank into the fissures which were formed.

The fissures which were formed at the time of the Owen’s Valley earthquake in 1872 extended for miles nearly parallel to the neighbouring Sierras. In some places the ground between the fissures sank twenty or thirty feet, and at one place about three miles east of Independence, a portion of the road was carried eighteen feet to the south by a fissure.[41]

Speaking generally, it may be said that all large earthquakes are accompanied by the formation of fissures. The Japanese have a saying that at the time of a large earthquake persons must run to a bamboo grove.

The object of this is to escape the danger of being engulfed in fissures, the ground beneath a bamboo grove being so netted together with fine roots that it is almost impossible for it to be rent open.

Materials discharged from fissures.—Together with the opening of cracks in the earth it often has happened that water, mud, vapours, gases, and other materials, have been ejected.

At the time of the Mississippi earthquake water, mixed with sand and mud, was thrown out with such violence that it spurted above the tops of the highest trees. In Italy such phenomena have often been repeated.

From the fissures which were formed in 1692 at the time of the earthquakes in Sicily, water issued which in some instances was salt.[42]

By the Cachar earthquake (January 10, 1869) numerous fissures were formed parallel to the banks of a river, from this water and mud were ejected. Dr. Oldham, who describes this earthquake, says that the first shot of dry mud or sand was mistaken for smoke or steam. The water was foul, and hotter than surface water at the time, but only slightly so; and the sulphurous smell was nothing more than you would perceive in stirring up the mud at the bottom of any stagnant pool which had lain undisturbed for some time.[43]

In 1755, when Tauris was destroyed, boiling water issued from the cracks which were formed. Similar phenomena were witnessed at a place eight miles from La Banca in Mexico, in the year 1820. Part of this hot water was pure and part was muddy.

Sometimes the water which has been ejected has been so muddy that the mud has been collected to form small hills. This was the case at the time of the Riobamba earthquake. The mud in this case consisted partly of coal, fragments of augite, and shells of infusoria.

At the time of the Jamaica earthquake men who had fallen into crevices were in some cases thrown out again by issuing water.

Sometimes, as has already been mentioned, vapour, gases, and even flames issue from fissures. Vapour of sulphur appears to be exceedingly common. Kluge says that many fish were killed in consequence of the sulphurous vapours which rose in the sea near to the coast of New Zealand in 1855.

On December 14, 1797, an insupportable smell of sulphur was observed to have accompanied the earthquake which at that time shook Cumana, which was greatest when the disturbance was greatest.

Sulphurous fumes which were combustible were belched out of the earth at the time of the Jamaica earthquake in 1692. The smell which accompanied this was so powerful that it caused a general sickness which swept away about 3,000 persons.[44]

From the fissures formed at Concepcion in 1835, water, which was black and fœtid, issued.[45]

The earthquakes of New England in 1727 were accompanied by the formation of fissures, from which sand and water boiled out in sufficient quantity to form a quagmire. In some places ash and sulphur are said to have been ejected.

At one house the stink of sulphur accompanying the earthquake was so great that the family could not bear to remain in doors.[46]

Emanations of gas sometimes appear to have burst out from submarine sources.

Thus the earthquake at Lima, in March, 1865, was accompanied with great agitation of the water and an odour of sulphuretted and carburetted hydrogen. This former gas was developed to such an extent that the white paint of the U.S. ship ‘Lancaster’ was blackened.[47] With the smell, flames have sometimes been observed, as, for instance, at the time of the Lisbon earthquake.

At the time of the earthquakes of 1811 and 1813, in the Mississippi valley, steam and smoke issued from some of the fissures which were formed.

Instances are recorded where stones have been shot up from fissures unaccompanied by water, as, for instance, at the earthquake of Pasto (January, 1834). It is imagined that the propelling power must have been the sudden expansion of escaping gases.

It has been suggested that flames seen above fissures might perhaps be due to the burning of materials like sulphur. Mr. D. Forbes, who examined the effects of the earthquakes of Mendoza, which were felt for a distance of 1,200 miles, says that where the hard rock came to the surface there were no traces of fissures, these being entirely confined to the alluvium. The rumours of fire and smoke having appeared at some of the fissures were without foundation, the presumed smoke being nothing but dust.[48]

In addition to flames lights appear often to have been observed, the origin of which cannot be easily explained.

The earthquake of November 22, 1751, at Genoa is said to have been accompanied by a light like that of a prodigious fire which seemed to arise out of the ground.[49]

Explanation of fissure phenomena.—The manner in which fissures are formed has already been explained when referring to the want of support in the face of hills (page 136).

Similar remarks may be applied to the banks of rivers and all depressions, whether natural or artificial, which have a steep slope. At such places the wave of shock emerges on a free surface, which, being unsupported in the direction of its motion, tends to tear itself away from the material behind, and form a fissure parallel to the face of the free surface. The distance of the fissure from the face of the free surface will, theoretically, be equal to half the amplitude of the wave of motion, one half tending to move forwards, and the other half backwards. The reason that water and other materials rush forth from fissures has been explained by Schüler as being due to cracks having been opened through impervious strata, which, before the earthquake, by their continuity prevented the rising of subterranean water under hydrostatic pressure.[50]

Kluge explains the coming up of the waters as being due to the same causes which he considers may be the origin of disturbances in the sea.

The most reasonable explanations of the eruption of water, mud, sand, and gas through fissures are those given by Oldham and Mallet in their account of the Cachar earthquake.

In the case of a horizontal shock passing through a bed of ooze or water-bearing strata, the elastic wave will tend to pack up the water during the forward motion to such an extent that it will flow or spout up through any aperture communicating with the surface. By the repetition of these movements causing ejections, sand or mud cones, like those produced by a volcanic eruption, may be formed, and by a similar action water may be shot violently up out of wells, as was the case in Jamaica in 1692.

If an emergent wave acts through a water-bearing bed upon a superincumbent layer of impervious material, this upper layer is, during the upward motion, by its inertia suddenly pressed down upon the latter.

This pressure is equal to that which would raise the upper layer to a height equal to the amplitude of the motion of an earth particle, and with a velocity at least equal to the mean velocity of the earth particle resolved in the vertical direction.

For a moment the water-bearing strata receive an enormous squeeze, and the water or mud starts up through any crevice which may be formed leading to the surface.

From this we see that liquids may rise far beyond the level due to hydrostatic pressure.[51]

Volger has attributed the origin of lights or flames appearing above fissures to the friction which must take place between various rocky materials at the time when the fissures are opened. As confirmatory of this he refers to instances where similar phenomena have been observed at the time of landslips. At the time of these landslips the heat developed by friction has been sufficiently intense to convert water into steam, the tension of which threw mud and earth into the air like the explosion of a mine.[52]

The gas eruptions which occasionally take place with earthquakes are probably due to the opening of fissures communicating with reservoirs or strata charged with products of natural distillation, or chemical action, which previously had accumulated beneath impervious strata. Of the existence of such gases we have abundant evidence. In coal mines we have fire damp which escapes in increased quantities with a lowering of the barometrical pressure. In volcanic regions we have many examples of natural springs of carbon dioxide.

These various gases sometimes escape in quantity, or erupt without the occurrence of earthquakes. Rossi mentions an instance where a few years ago quantities of fish were killed by the eruption of gas in the Tiber, near Rome. Another instance is one which occurred at Follonica on April 6, 1874. On the morning of that day many of the streets and roads were covered with the dead bodies of rats and mice. It seemed as if it had rained rats. From the facts that the bodies of the creatures seemed healthy, that the destruction had happened suddenly, and not come on gradually like an epidemic, it was supposed that they had been destroyed by an emanation of carbon dioxide. The fact that many of them lay in long lines suggested the idea that they had been endeavouring to escape at the time of the eruption.[53] If we can suppose sudden developments of gas like this to have occasionally accompanied earthquakes, we may sometimes have the means of accounting for the sickness which has been felt.

Disturbances in lakes.—It has often been observed that, at the time of large earthquakes, lakes have been thrown into violent agitation, and their waters have been raised or lowered. At the time of the great Lisbon earthquake, not only were the waters of European lakes thrown into a state of oscillation, but similar effects were produced in the great lakes of North America. In some instances, as in the case of small ponds, these movements may be produced by the horizontal backward and forward motion of the ground. At other times they are probably due to an actual tipping of a portion of their basins. Movements like these latter will be again referred to in the chapter on Earth Pulsations. On January 27, 1856, there was a shock of earthquake at Bailyborough, Ireland, which occasioned an adjacent lough to overflow its banks and rush into the town with great impetuosity. In returning it swept away two men, leaving behind a great quantity of pike and eels of a prodigious growth.[54]

Disturbances in rivers.—Just as lakes have been disturbed, so also have there been sudden disturbances in rivers. Sometimes these have overflowed their banks, whilst at other times they have been suddenly dried up. In certain cases the reason that a portion of a river should have become dry has been very apparent, as, for instance, at the time of the Zenkoji earthquake in Japan in 1847, when the Shikuma-gawa became partly dry in consequence of the large masses of earth which had been shaken down from overhanging cliffs damming a portion of its course, and thus forming, first, lakes, and subsequently, new water-courses. As another example, out of the many which might be quoted, may be mentioned the sudden drying up of the river Aboat, a tributary of the Magat, in the Philippine Islands, on July 27, 1881, shortly after a severe shock of earthquake. The water of this river ceased to flow for two hours, after which it reappeared with considerable increase of volume and of a reddish colour. Signor E. A. Casariego, who describes this, remarks that the phenomenon could easily be explained through the slipping down of the steep banks in narrow parts of its upper valley, by which means its flow had been obstructed until the water had time to accumulate and pass over or demolish the obstruction.

After the earthquake of Belluno (June 29, 1873), the torrent Tesa, which is ordinarily limpid, became very muddy.[55] Similar phenomena have been observed even in Britain, as, for instance, in 1787, when, at the time of a shock which was felt in Glasgow, there was a temporary stoppage in the waters of the Clyde. Again, in 1110, there was a dreadful earthquake at Shrewsbury and Nottingham, and the Trent became so low at Nottingham that people walked over it.

The earthquake of 1158, which was felt in many parts of England, was accompanied by the drying up of the Thames, which was so low that it could be crossed on foot even at London.[56]

Facts analogous to these are mentioned in the accounts of many large earthquakes. Sometimes rivers only come muddy or change their colour. In an account of the Lisbon earthquake we read that some of the rivers near Neufchâtel suddenly became muddy.[57]

At other times large waves are formed. Thus the earthquake of Kansas (April 24, 1867) apparently created a disturbance in the rivers at Manhattan, which rolled in a heavy wave from the north to the south bank.[58]

Sometimes curious phenomena have happened with regard to rivers without the occurrence of earthquakes. Thus, for instance, on November 27, 1838, there was a simultaneous stoppage of the Teviot, Clyde, and Nith.

In these rivers similar phenomena have been observed in previous years.

Again, on January 1, 1755, there was a sudden sinking of the river Frooyd, near Pontypool. This appears to have been due to the water sinking into chasms which were suddenly opened.[59]

Effects produced in springs, wells, fumaroles, &c.—Springs also are often affected by earthquakes. Sometimes the character of their waters change; those which were pure become muddy, whilst those which were hot have their temperature altered.

Sometimes springs have been dried up, whilst at other times new springs have been formed.

This latter was the case in New England (October 27, 1727). In some places springs were formed, whilst at other places they were either entirely or partly dried up.[60]

At and near Lisbon, in 1755, some fountains became muddy, others decreased, others increased, and others dried up. At Montreux, Aigle, and other places, springs became turbid.

The baths at Toplitz, in Bohemia, which were discovered in a.d. 762, were seriously affected by the same earthquake. Previous to the earthquake it is said that they had always given a constant supply of hot water. At this time, however, the chief spring sent up vast quantities of water and ran over. One hour before this it had grown turbid and flowed muddy. After this it stopped for about one minute, but recommenced to flow with prodigious violence, driving before it considerable quantities of reddish ochre. Finally, it settled back to its original clear state and flowed as before.[61]

In 1855, at the earthquake of Wallis, many new springs burst forth, and some of these in Nicolai Thale were so rich in iron that they quickly formed a deposit of ochre.

At the time of the Belluno earthquake (June 29, 1873), a hot spring, La Vena d’Oro, suddenly became red.[62]

The following examples of like changes are taken from the writings of Fuchs.[63]

In 1738 the hot springs of St. Euphema rose considerably in their temperature.

During the earthquake of October, 1848, the hot springs of Ardebil, which usually had a temperature of from 44° to 46° C., rose so high that their temperature was sufficient to cause scalding.

At the time of the earthquake of Wallis, in 1855, the temperature of hot springs rose 7°, and the quantity of water increased three times.

During the earthquake of 1835 in Chili, the springs of Cauquenes fell from 118° to 92° F. Subsequently, however, they again rose.

Fumaroles are similarly disturbed. Thus, at the time of the earthquakes of Martinique (September, 1875), the fumaroles there showed an abnormal activity.[64]

Wells often appear to be acted upon in the same manner as springs.

At the time of the California earthquake (April, 1855), the level of the water in certain wells was raised ten to twelve feet.

A consequence of the earthquake at Neufchâtel, in 1749, was to fill some of the wells with mud.[65] At Constantinople, on September 2, 1754, wells became dry.[66]

Explanation of the above phenomena.—That the water in springs and wells should be caused to rise at the time of an earthquake, admits of explanation on the supposition of compressions taking place similar to those which cause the rise of water in fissures. That the water in wells and springs should be rendered turbid, is partly explained on the supposition of more or less dislocation taking place in the earthy or rocky cavities in which they are contained or through which they flow.

At the time of a large earthquake it is extremely probable that there is a general disturbance in the lines of circulation of subterranean waters and gases throughout the shaken area. By these disturbances, new waters may be brought to the surface, two or more lines of circulation may be united, and the flow of a spring or supply of a well be augmented. Fissures, through which waters reached the surface, may be closed, wells may become dry, or springs may cease to flow, hot springs may have their temperature lowered by the additions of cold water from another source, and, in a similar manner, waters may be altered in their mineralisation. An important point to be remembered in this consideration is the mutual dependence of various underground water supplies, and the area over which any given supply may circulate. A well in the higher part of Lincoln Heath is said to be governed by the river Trent, which is ten miles distant; when the river rises the well rises in proportion, and when the river falls the water in the well falls.[67]

The change which is usually observed in hot springs is, that before or with earthquakes they increase in temperature, but afterwards sink back to their normal state. This increase in temperature may possibly be due to communication being opened with new or deeper centres of volcanic activity, or a temporarily increased rate of flow.

That the water issuing from newly formed fissures or springs should be hot, might be explained on the supposition of its arising from a considerable depth, or from some volcanic centre. It might also be attributed to the heat developed by friction at the opening of the fissures. These changes which earthquakes produce upon the underground circulation of waters are phenomena deserving especial attention. Although we know much about the circulation of surface water, it is but little that we yet know about the movement of the streams hidden from view, from which these surface waters have their sources. Earthquakes may be regarded as gigantic experiments on the circulatory system of the earth, which, if properly interpreted, may yield information of scientific and utilitarian value.

The sudden elevations, depressions, or lateral shifting of large tracts of country at the time of destructive earthquakes are phenomena with which all students of geology are familiar. In most cases these displacements have been permanent; and evidences of many of the movements which occurred within the memory of man, remain as witnesses of the terrible convulsions with which they were accompanied.

Movements on coast lines and level tracts.—At the time of the great earthquake of Concepcion, on February 20, 1835, much of the neighbouring coast line was suddenly elevated four or five feet above sea level. This, however, subsequently sank until it was only two feet. A rocky flat, off the island of Santa Maria, was lifted above high-water mark, and left covered with ‘gaping and putrefying mussel-shells, still attached to the bed on which they had lived.’ The northern end of the island itself was raised ten feet and the southern extremity eight feet.[68]

By the earthquake of 1839, the island of Lemus, in the Chonos Archipelago, was suddenly elevated eight feet.[69]

Of movements like these, especially along the western shores of South America, Darwin, who paid so much attention to this subject, has given many examples. In 1822, the shore near Valparaiso was suddenly lifted up, and Darwin tells us that he heard it confidently asserted ‘that a sentinel on duty, immediately after the shock, saw a part of a fort which previously was not within the line of his vision, and this would indicate that the uplifting was not vertical.’[70] That the large areas of land should be shifted permanently in horizontal directions, as well as vertically, we should anticipate from the observations which we are able to make upon large fissures which are caused by earthquakes.

Another remarkable example of sudden movement in the rocky crust is that which took place during the earthquakes of 1811–12 in the valley of the Mississippi, near to the mouth of the Ohio, which was convulsed to such a degree, that lakes, twenty miles in extent, were formed in the course of an hour. This country, which is called the ‘sunk country,’ extends some seventy to eighty miles north and south, and thirty miles east and west.[71]

In the ‘Gentleman’s Magazine’ we read of the little territory of Causa Nova, in Calabria, being sunk twenty-nine feet into the earth by an earthquake, without throwing down a house. The inhabitants, being warned by a noise, escaped into the fields, and only five were killed.[72]

Other examples of these permanent dislocations of strata are to be found in almost every text-book on geology.

Geological changes produced.—Passing over the accounts of earth movements which are more or less fictitious, and confining our attention to the well authenticated facts, we see at once the important part which earthquakes have played as agents working geological changes. Even in the nineteenth century long tracts of coast, as in Chili and New Zealand, have been raised, whilst other areas, like the Delta of the Indus, have been sunk. Sir H. Bartle Frere, speaking about the disturbance which took place in his latter region in 1819, remarks that all the canals drawn from the Fullalee River ceased to run for about three days, probably indicating a general upheaval of the lower part of the canal. In consequence of the earthquakes in former times it is not unlikely that water-courses have ceased to flow, water has decreased in wells, and districts have been depopulated.[73]

Sometimes these changes have taken place gradually and sometimes with violence. Mountains have been toppled over, valleys have been filled, cities have been submerged or buried.

With the records of these convulsions before us, we see that seismic energy yet exhibits a terrible activity in changing the features of the globe.

Reason of these movements.—To formulate a single reason for these catastrophes would be difficult. Where they are of the nature of landslips, or materials have been dislodged from mountain sides, the cause is evidently the sudden movement of this ground acting upon strata not held together in a sufficiently stable condition. A similar explanation may be given for the sudden elevations or depressions of strata in a district removed from the centre where the disturbance had its origin. The seismic effort exhibits itself in a certain area round its origin as a sudden push, and by this push, strata are fractured and caused to move relatively to each other.

At or near to the origin of an earthquake it might be argued that it was the sudden falling of rocky strata towards a position of stable equilibrium that caused the shaking, and in such a case the movements referred to may be regarded as the cause rather than the effect of an earthquake.

A subject closely connected with the sudden dislocation of strata, is the production of secondary or consequent earthquakes, due to the disturbance of ground in a critical state (see p. 248).

CHAPTER IX.
DISTURBANCES IN THE OCEAN.

Sea vibrations—Cause of vibratory blows—Sea waves: Preceding earthquakes; Succeeding earthquakes—Magnitude of waves—Waves as recorded in countries distant from the origin—Records on tide gauges—Waves without earthquakes—Cause of waves—Phenomena difficult of explanation—Velocity of propagation—Depth of the ocean—Examples of calculations—Comparison of velocities of earthquake waves with velocities which ought to exist from the known depth of the ocean.

Sea vibrations.—Whilst residing in Japan I have had many opportunities of conversing with persons who had experienced earthquakes when on board ships, and it has often happened that these same earthquakes have been recorded on the shore. For example, at the time of every moderately severe earthquake which has shaken Yokohama, the same disturbance has been felt on board the ships lying in the adjoining harbour. In some cases the effect had been as if the ship was grounding; in others, as if a number of sharp jerks were being given to the cable. The effect produced upon a man-of-war lying in the Yokohama harbour on the evening of March 11, 1881, was described to me as a ‘violent irresistible shaking.’ Vessels eighty miles at sea have recorded and timed shocks which were felt like sudden blows. These were accompanied by a noise described as a ‘dull rattle like thunder.’

In none of the cases here quoted was any disturbance of the water observed.

The great earthquake of Lisbon was felt by vessels on the Atlantic, fifty miles away from shore.

On February 10, 1716, the vessels in the harbour of New Pisco were so violently shaken that both ropes and masts were broken, and yet no motion in the water was observed. Some have described these shocks like those which would be produced by the sudden dropping of large masses of ballast in the hold of the vessel. Other cases are known where rigging was damaged, and even cannon have been jerked up and down from the decks on which they rested.

Cause of vibratory blows.—From the rattling sound which has accompanied some of these submarine shocks, many of which, it may be remarked, have never been recorded as earthquakes upon neighbouring shores, it does not seem improbable that they may have been the result of the sudden condensation of volumes of steam produced by submarine volcanic eruptions.

As confirmatory of this supposition we have the fact, that many of the marine disturbances which might be called ‘sea-quakes,’ have been observed in places which are close to, or in the line of, volcanic vents. Thus, M. Daussy, who has paid special attention to this subject, has collected evidence to show that a large number of shocks have been felt by vessels in that portion of the Atlantic between Cape Palamas, on the west coast of Africa, and Cape St. Roque, on the east coast of South America.[74]

Some of the vessels only felt shocks and tremblings, but others saw smoke, and some even collected floating ashes. In considering the submarine shocks of this particular area, we must bear in mind that it lies in the line of Iceland, the west coast of Scotland, the Azores, Canaries, Cape de Verd Islands, St. Helena, and other places, all of which, if not at present in volcanic activity, shew evidence of having been so within recent times. The connection between volcanic action and earthquakes will be again referred to.

Sea waves.—Although in the above-mentioned instances sea waves have not been noticed, it is by no means uncommon to find that destructive earthquakes have been accompanied by waves of an enormous size, which, if the earthquake has originated beneath the sea, have, subsequently to the shaking, rolled in upon the land, to create more devastation than the actual earthquake. It may, however, be mentioned that a few exceptional cases exist when it is said that the sea wave has preceded the earthquake, as, for example, at Smyrna, on September 8, 1852.

Again, at the earthquake in St. Thomas, in 1868, it is said that the water receded shortly before the first shock. When it returned, after the second shock, it was sufficient to throw the U.S. ship ‘Monagahela’ high and dry.[75]

Another American ship, the ‘Wateree,’ was also lost in 1868 by being swept a quarter of a mile inland by the sea wave which inundated Arequippa.

Much of the great destruction which occurred at the time of the great Lisbon earthquake was due to a series of great sea waves, thirty to sixty feet higher than the highest tide, which swamped the town. These came in about an hour after the town had been shattered by the motion of the ground.

The first motion in the waters was their withdrawal, which was sufficient to completely uncover the bar at the mouth of the Tagus. At Cadiz, the first wave, which was the greatest, is said to have been sixty feet in height. Fortunately the devastating effect which this would have produced was partially warded off by cliffs.

At the time of the Jamaica earthquake (1692) the sea drew back for a distance of a mile.

In South America sea waves are common accompaniments of large earthquakes, and they are regarded with more fear than the actual earthquakes.

On October 28, 1724, Lima was destroyed, and on the evening of that day the sea rose in a wave eighty feet over Callao. Out of twenty-three ships in the harbour, nineteen were sunk, and four others were carried far inland. The first movement which is usually observed is a drawing back of the waters, and this is so well known to precede the inrush of large waves, that many of the inhabitants in South America have used it as a timely warning to escape towards the hills, and save themselves from the terrible reaction which, on more than one occasion, has so quickly followed.

At Caldera, near to Copiapo, on May 9, 1877, which was the time when Iquique was devastated, the first motion which was observed in the sea was that it silently drew back for over 200 feet, after which it rose as a wave over five feet high. At some places the water came in as waves from twenty to eighty feet in height.

At Talcahuano, on the coast of Chili, in 1835, there was a repetition of the phenomena which accompanied the destruction of Penco in 1730 and 1751. About forty minutes after the first shock, the sea suddenly retired. Soon afterwards, however, it returned in a wave twenty feet high, the reflex of which swept everything towards the sea. These phenomena were repeated three times.[76]

When Callao and Lima were destroyed, in 1746, the sea first drew back, then came in as waves, four or five minutes after the earthquake. Altogether, between October 28 and February 24, 451 shocks were counted. At one time the sea came in eighty feet above its usual level. One account says that the large waves came in forty-one and a half hours after the first shock, and seventeen and a half hours after comparative tranquillity had prevailed.[77]

At the eruption of Monte Nuovo, near Naples, in September 27, 1538, the water drew back forty feet, so that the whole gulf of Baja became dry.

In 1696, at the time of the Catanian earthquake, the sea is said to have gone back 2,000 fathoms. Instances are recorded where the sea has receded several miles.

The time taken for the flowing back of the sea is usually very different. Sometimes it has only been five or six minutes, whilst at other times over half an hour, and there are records where the time is said to have been still longer.

Thus, at the earthquake of Santa (June 17, 1678), the sea is stated to have gone as far back as the eye could reach, and did not rise again for twenty-four hours, when it flooded everything.

In 1690 at Pisco the sea went back two miles, and did not return for three hours. When it returns it does so with violence, and examples of the heights to which it may reach have been given. The greatest sea wave yet recorded, according to Fuchs, is one which, on October 6, 1737, broke on the coast of Lupatka, 210 feet in height.

There are, however, cases known where the sea has returned as gradually as it went out. Thus, on December 4, 1854, when Acapulco was destroyed, the sea is said to have returned as gently as it went out.

When sea waves have travelled long distances from their origin, as, for instance, whenever a South American wave crosses the Pacific to Japan, the phenomena which are observed are like those which were observed at Acapulco; the sea falls and rises, at intervals of from ten minutes to half an hour, to heights of from six to ten feet, without the slightest appearance of a wave. Its phenomenon is like that of an unusually high tide, which repeats itself several times per hour. Even if we watch distant rocks with a telescope, although the surface of the ocean may be as smooth as the surface of a mirror, there is not the slightest visible evidence of what is popularly called a wave. The sea being once set in motion it continues to move as waves of oscillation for a considerable time. In 1877, as observed in Japan, the motion continued for nearly a whole day. The period and amplitude of the rise and fall were variable, usually it quickly reached a maximum, and then died out gradually. As observed in a self-recording tide gauge at San Francisco, the disturbance lasted for about four days. A diagram of this is here given. In its general appearance it is very similar to the records of other earthquake waves. The large waves represent the usual six hours rise and fall of the tides; usually these are fairly smooth curves. Superimposed on the large waves are the smaller zigzag curves of the earthquake disturbance, lasting with greater or less intensity for several days. As these curves are drawn to scale—horizontally for hours, and vertically one fifth inch to the foot, to show the extent of the rise and fall—they will be easily understood.

Sometimes, as in the present example, the first movement in the waters is that of an incoming wave. In many instances, however, this observation may be due to the slow and more gentle phenomena of the previous drawing out of the water, which in a steep waste, or when the water is rough, would be difficult to observe, not having been remarked.

The distance to which these sea waves have extended has usually been exceedingly great.

Fig. 28.—Record of Tide Gauge at Port Point, San Francisco. Showing Earthquake Waves of May 1877.

The sea wave of the Iquique earthquake of May 9, 1877, like many of its predecessors, was felt across the basin of the whole Pacific, from New Zealand in the south, to Japan and Kamschatka in the north. And but for the intervention of the Eurasian and American continents would have made itself appreciable over the surface of the whole of our globe. At places on the South American coast, it has been stated that the height of the waves varied from twenty to eighty feet. At the Samoa Islands the heights varied from six to twelve feet. In New Zealand the sea rose and fell from three to twenty feet. In Australia the heights to which the water oscillated were similar to those observed in New Zealand. In Japan it rose and fell from five to ten feet. In this latter country, the phenomena of sea waves which follow a destructive earthquake on the South American coast are so well known that old residents have written to the local papers announcing the probability of such occurrences having taken place some twenty-five hours previously in South America. In this way news of great calamities has been anticipated, details of which only arrived some weeks subsequently. Just as the destructive earthquakes of South America have announced themselves in Japan, in a like manner the destructive earthquakes of Japan have announced themselves upon the tide gauges of California. Similarly, but not so frequently, disturbances shake the other oceans of the world.

For example, the great earthquake of Lisbon propagated waves to the coasts of America, taking on their journey nine and a half hours.

Sea waves without earthquakes.—Sometimes we get great sea waves like abnormal tides occurring without any account of contemporaneous earthquakes. Although earthquakes have not been recorded, these ill understood phenomena are usually attributed to such movements.

Several examples of these are given by Mallet. Thus, at 10 a.m. on March 2, 1856, the sea rose and fell for a considerable distance at many places on the coast of Yorkshire. At Whitby, the tide was described ebbing and flowing six times per hour, and this to such a distance that a vessel entering the harbour was alternately afloat and aground.

In 1761, on July 17, a similar phenomena was observed at the same place.

A like occurrence took place at Kilmore, in the county of Wexford, on September 16, 1864, when the water ebbed and flowed seven times in the course of two hours and a half. These tides, which appear to have taken about five minutes to rise and five minutes to fall, were seen by an observer approaching from the west as six distinct ridges of water. The general character of the phenomena appears to have been very similar to that which was produced at the same place by the Lisbon earthquake of 1755; and the opinion of those who saw and wrote about their occurrence was that it was due to an earthquake disturbance. Such phenomena are not uncommon on the Wexford coast, where they are popularly known as ‘death waves,’ probably in consequence of the lives which have been lost by these sudden inundations.

They have also been observed in other parts of Ireland, the north-east coast of England, and in many parts of the globe. They will be again referred to under the head of earth pulsations.

Cause of sea waves.—Mallet, who in his report to the British Association in 1858, writes upon this last-mentioned occurrence at considerable length, whilst admitting that many may have originated from earthquakes, he thinks it scarcely probable that an earthquake blow, sufficiently powerful to have produced waves like those observed at Kilmore, should not have been felt generally throughout the south of Ireland. He, therefore, suggests that sometimes waves like the above might be produced by an underwater slippage of the material forming the face of a submarine bank, the slope of which by degradation and deposition, produced by currents, had reached an angle beyond the limits of repose of the material of which it was formed. Mallet does not insist upon the existence of these submarine landslips, but only suggests their existence as a means of explaining certain abnormal sea waves which do not appear to have been accompanied by earthquakes.

In the generality of cases sea waves are accompanied by earthquakes, but it may often happen that the connection between the two is difficult to clearly establish. One simple explanation for the origin of waves occurring with earthquakes, is, that in consequence of the earthquake a large volume of water suddenly finds its way into cavities which have been opened, the disturbance produced by the inrush giving rise to waves.

A second explanation is, that the land along a shore is caused by an earthquake to oscillate upwards, the water running off to regain its level. A supposition like this is negatived by the fact that these disturbances are felt far away from the chief disturbance, on small islands. Also, it may be added, that the whole disturbance appears to approach the land from the sea, and not in the opposite direction. Thus, in the earthquake of Oahu (February 18, 1871), it was remarked that the shock was first felt by the ships farthest from the land.[78]

Another suggestion is that the waves are due to a sudden heaving up of the bottom of the ocean. If this lifting took place slowly, then the first result would be that the water situated over the centres of disturbance would flow away radially in all directions from above the area of disturbance.

If, however, the submarine upheaval took place with great rapidity, say by the sudden evolution of a large volume of steam developed by the entry of water into a volcanic vent, as the water was heaped above the disturbed area, water might run in radially towards this spot.

Supposing a primary wave to be formed in the ocean by any such causes, then the falling of this will cause a second wave to be formed, existing as a ring round the first one. The combined action of the first and second wave will form a third one, and so the disturbance, starting from a point, will radiate in broadening circles. During the up and down motion of these waves, the energy which is imparted to any particle of water will, on account of the work which it has to do in displacing its neighbours, by frictional resistance, gradually grow less and less, until it finally dies away. The waves which are the result of this motion will also grow less and less.

If a series of sea waves were produced by a single disturbance, we see that these will be of unequal magnitude. Now, for small waves, the velocity with which they travel depends upon the square root of their lengths; but with large waves, like earthquake waves, the velocity depends upon the square root of the depth of water, and these latter travel more quickly than the former.

If, therefore, we have a series of disturbances of unequal magnitude producing sea waves, which, from the series of shocks which have been felt upon shores subsequently invaded by waves, seems in all probability often to have been the case, it is not unlikely that the waves of an early disturbance may be overtaken and interfered with by a series which followed.

These considerations help us to understand the appearance of the records on our tide gauges, and also the phenomena observed by those who have recorded tidal waves as they swept inwards upon the land. For instance, we understand the reason why sea waves, as observed at places at different distances from the origin of a disturbance, should be of different heights. We also see an explanation for the fact that small waves should sometimes appear to be interpolated between large ones, and that these should occur at varying intervals.

The fact that whenever a wave is produced, a certain quantity of water must be drawn from the level which surrounds it, in order that it should be formed, explains the phenomena that the sea is often observed first to draw back. Out in the open ocean it is drawn from the hollow between two waves. As has been pointed out by Darwin, it is like the drawing of the water from the shore of a river by a passing steamer.

The difference in the height of waves, as observed at places lying close to each other, is probably due to the configuration of the coast, the interference of outlying islands, reefs, &c.—causes which would produce similar effects in the height of tide.

As a wave approaches shallow water it gradually increases in height, its front slope becomes steep, and its rear slope gentle, until finally it topples over and breaks. This increasing in height of waves is no doubt connected with the destruction of Talcahuano and Callao, which are situated at the head of shallow bays. Valparaiso, which is on the edge of deep water, has never been overwhelmed.[79] Another case tending to produce anomalies in the character of waves would be their reflection and mutual interference, the reflections due to the configuration of the ocean bed and coast lines.

The complete phenomena which may accompany a violent submarine disturbance are as follows:—

By the initial impulse of explosion or lifting of the ground, a ‘great sea wave’ is generated, which travels shorewards with a velocity dependent upon its size and the depth of the ocean. At the same instant, a ‘sound wave’ may be produced in the air, which travels at a quicker rate than the ‘great sea wave.’ A third wave which is produced, is an ‘earth wave,’ which will reach the shore with a velocity dependent on the intensity of the impulse and the elasticity of the rocks through which it is propagated. This latter, which travels the fastest, may carry on its back a small ‘forced sea wave.’ On reaching the shore and passing inland, this ‘earth wave’ will cause a slight recession of the water as the ‘forced sea wave’ slips from its back.

As these ‘forced sea waves’ travel they will give blows to ships beneath which they may pass, being transmitted from the bottom of the ocean to the bottom of the ships like sound waves in water. At the time of small earthquakes, produced, for example, by the explosion of small quantities of water entering volcanic fissures, or by the sudden condensation of steam from such a fissure entering the ocean, aqueous sound waves are produced, which cause the rattling and vibrating jars so often noticed on board ships.

Phenomena difficult of explanation.—Although we can in this way explain the origin and phenomena of sea waves, we must remember, as Kluge has pointed out, that it is not the simple backward and forward movement of the ground which produces sea waves, and that the majority of earthquakes which have occurred in volcanic coasts have been unaccompanied by such phenomena. Out of 15,000 earthquakes observed on coast lines, only 124 were accompanied by sea waves.[80] Out of 1,098 earthquakes catalogued by Perrey for the west coast of South America, only nineteen are said to have been accompanied by movements in the waters. According to the ‘Geographical Magazine’ (August 1877, p. 207), it would seem that out of seventy-one severe earthquakes which have occurred since the year 1500 upon the South American coast many have been accompanied by sea waves. Darwin also remarks, when speaking of South America, that almost every large earthquake has been accompanied by considerable agitation in the neighbouring sea.[81]

On April 2, 1851, when many towns in Chili were destroyed, the sea was not disturbed. At the time of the great earthquake of New Zealand (June 23, 1855), although all the shocks came from the sea, yet there was no flood. The small shock of February 14, however, was accompanied by a motion in the sea.

To these examples, which have been chiefly drawn from the writings of Fuchs, must be added the fact that the greater number of disturbances which are felt in the north-eastern part of Japan, although they emanate from beneath the sea, do not produce any visible sea waves. They are, however, sufficient to cause a vibratory motion on board ships situated near their origin.

Another point referred to by Fuchs, as difficult of explanation, is, that the water, when it draws back, often does so with extreme slowness, and farther, in some instances, it has not returned to its original level. That the sea might be drawn back for a period of fifteen or thirty minutes is intelligible, when we consider the great length of the waves which are formed. Cases where it has retired for several hours or days, and when its original level is altered, appear only to be explicable on the assumption of more or less permanent changes in the levels of the ground. For example, in the earthquake of 1855 which shook New Zealand, the whole southern portion of the northern island was raised several feet.

These sudden alterations in the levels of coast lines have already been referred to.

Other points which are difficult to understand are the occurrence of disturbances in the sea at the time of feeble earthquakes, and with earthquakes occurring in distant places. As examples of such occurrences, Fuchs quotes the following: ‘On May 16, 1850, at 4.28 a.m., an earthquake took place in Pesth, and at 7.30 a motion was observed in the sea at Livorno. Again, at the time of the earthquake of December 19, 1850, which shook Heliopolis, a flood suddenly came in upon Cherbourg.’ May not these phenomena be the result of an earth pulsation, which produced an earthquake at one point, and a sea wave at another?

Equally difficult to understand are the observations when the disturbance in the sea has occurred several hours after an earthquake; as, for instance, at Batavia, in 1852, when there was an interval of two hours; and to this must be added the observations where the motion of the sea has preceded that of the earthquake—as, for instance, in 1852, at Smyrna. Whilst recognising the fact that it is possible to suggest explanations for many of these anomalies, we must also bear in mind that they are, generally speaking, exceptional, and, in some instances, may possibly be due to errors in observations.

Velocity of propagation of sea waves, and depth of the ocean.—It has long been known to physical science that the velocity with which a given wave is propagated along a trough of uniform depth, holds a relation to the depth of the trough.

If v is the velocity of the wave, and h the depth of the trough, this relation may be expressed as follows:—

h = ^v2/_g or h = (^v/_k)²

Where g = 32·19 and k = 5·671.

It will be observed that these two formulæ (the first of which is known as Russell’s formula, and the second as Airy’s) are practically identical.

The apparent difference is in the average value assigned to the constant.

For large waves such as we have to deal with, it would be necessary, if we were desirous of great accuracy, to increase the value of h by some small fraction of itself. We might also make allowance for the different values of g, according to our position on the earth’s surface. With these formulæ at our disposal it is an easy matter, after having determined the velocity with which a wave was propagated, to determine the average depth of the area over which it was transmitted.

In making certain earthquake investigations the reverse problem is sometimes useful—namely, determining the velocity with which a sea wave has advanced upon a shown line, from a knowledge of the depth of the water in which it has been propagated.

Calculations of the average depths of the Pacific, dependent on the velocity with which earthquake waves have been propagated, have been made by many investigators.

In most cases, however, in consequence of having assumed the wave to have originated on a coast line, when the evidence clearly showed it to have originated some distance out at sea, the calculations which have been made are open to criticism. The average depths which I obtained for various lines across the Pacific appear to be somewhat less than the average depth as given by actual soundings. We must, however, remember that the common error in actual soundings is that they are usually too great, it being difficult in deep-sea sounding to determine when the lead actually reaches the bottom. Until oceans have been more thoroughly surveyed with the improved forms of sounding apparatus, we shall not be able to verify the truth of the results which have been given to us by earthquake waves.

Examples of Calculations on Sea Waves.

1. The wave of 1854.—This wave originated near Japan, and it was recorded on tide gauges at San Francisco, San Diego, and Astoria.

On December 23, at 9.15. a.m., a strong shock was felt at Simoda in Japan, which, at 10 o’clock, was followed by a large wave thirty feet in height. The rising and falling of the water continued until noon. Half an hour after, the movement became more violent than before. At 2.15 p.m. this agitation decreased, and at 3 p.m. it was comparatively slow. Altogether there were five large waves.

On December 23 and 25, unusual waves were recorded upon the self-registering tide gauges at San Francisco, San Diego, and Astoria.

At San Francisco three sets of waves were observed. The average time of oscillation of one of the first set was thirty-five minutes, whilst one of the second and third sets was almost thirty-one minutes.

At San Diego three series of waves were also shown, but with average times of oscillation of from four to two minutes shorter than the waves at San Francisco.

The San Francisco waves appear to indicate a recurrence of the same phenomena.

The record at San Diego shows what was probably the effect of a series of impulses, the heights increasing to the third wave, then diminishing, then once more renewed, after which it died away.

The result of calculations based on these data were:—

The difference for the depths in the San Francisco path depends whether the length of the waves is reckoned at 210 or 217 miles. The length of the waves on the San Diego path were 186 or 192 miles.[82]

The wave of 1868.—On August 11, 1868, a sea wave ruined many cities on the South American coast, and 25,000 lives were lost. This wave, like all the others, travelled the length and breadth of the Pacific.

In Japan, at Hakodate, it was observed by Captain T. Blakiston, R.A., who very kindly gave me the following account:

On August 15, at 10.30 a.m., a series of bores or tidal waves commenced, and lasted until 3 p.m. In ten minutes there was a difference in the sea level of ten feet, the water rising above high water and falling below low water mark with great rapidity. The ordinary tide is only two and a half to three feet. The disturbance producing these waves originated between Iquique and Arica, in about lat. 18.28 S. at about 5 p.m. on August 13. In Greenwich time this would be about 13h. 9m. 40s. August 13. The arrival of the wave at Hakodate in Greenwich time would be about 14h. 7m. 6s. August 14: that is to say, the wave took about 24h. 57m. to travel about 8,700 miles, which gives us an average rate of about 511 feet per second. These waves were felt all over the Pacific. At the Chatham Islands they rushed in with such violence that whole settlements were destroyed. At the Sandwich Islands the sea oscillated at intervals of ten minutes for three days.

Comparing this wave with the one of 1877 we see that one reached Hakodate with a velocity of 511 feet per second, whilst the other travelled the same distance at 512 feet per second.

An account of this earthquake wave has been given by F. von Hochstetter (‘Über das Erdbeben in Peru am 13. August 1868 und die dadurch veranlassten Fluthwellen im Pacifischen Ocean,’ Sitzungsberichte der Kaiserl. Akademie der Wissenschaften, Wien 58. Bd., 2. Abth. 1868). From an epitome of this paper given in ‘Petermann’s Geograph. Mittheil.’ 1869, p. 222, I have drawn up the following table of the more important results obtained by F. von Hochstetter.

The wave is assumed to have originated near Arica.

Calculations on the same disturbance are also given by J. E. Hilgard.[83]

Assuming the origin of the wave to have been at Arica, his results are as follows:

The wave of 1877.—Two sets of calculations have been made upon the wave of 1877 by Dr. E. Geinitz of Rostock.[84]

The following table is taken from Dr. Geinitz’s second paper, in which there are several modifications of his first results. The origin of the disturbance is assumed to have been near Iquique.

The mean depths represent a mean of two sets of calculations, one made with the aid of Airy’s formula, and the other by Scott-Russell’s formula. The result of my own investigation about this disturbance, the origin of which, by several methods of calculation, is shown to have been beneath the ocean, near 71° 5′ west long., and 21° 22′ south lat., are given on next page.

Dr. Geinitz considers that his calculated depths of the ocean and those obtained by actual soundings are in accordance, a result which is diametrically opposed to that which I have obtained.

This difference between my calculations and those of Dr. Geinitz, Hochstetter, and others, chiefly rests on the origin we have assigned for the sea waves. Dr. Geinitz, for instance, although he says that the origin of the 1877 earthquake was not on the continent but to the west in the ocean, bases all his calculations on the assumption that the centrum was at or near to Iquique, and the time at which that city was disturbed was the time at which the waves commenced to spread across the ocean. This time is 8.25 p.m. At this time, however, it appears that the waves must have been more than double the distance between the true origin and Iquique, from Iquique on their way towards the opposite side of the Pacific. Introducing this element into the various calculations which have been made respecting the depth of the Pacific Ocean as derived from observations on earthquake waves—which element, insomuch as the waves appear to have come in to inundate the land some time after the shock, needs to be introduced—we reduce the velocity of transit of the earthquake wave and, consequently, the resultant depths of the ocean.

In Dr. Geinitz’s paper there are also some slight differences in the times at which the earthquake phenomena were observed at various localities. These, however, are but of minor importance. At the end of the paper by Dr. Geinitz two interesting tide gauge records are introduced, one from Sydney and the other from Newcastle. These appear to show a marked difference in the periods of the sea waves at these two places.[85]

Comparison of velocities of wave-transit which have been actually observed, with velocities which ought to exist from what we know of the depth of the Pacific by actual soundings.—From a chart given in ‘Petermann’s Geograph. Mittheilungen,’ Band xxiii. p. 164, 1877, it is possible to draw approximate sections on lines in various directions across the bed of the Pacific.

From the origin of the shock to Japan (Kameishi) the line would be as follows:—

On account of the Tuscarora and Belkap Deeps this would be the most irregular line over which the wave had to travel.

From the origin to New Zealand (Wellington) the line would be

From the origin to Samoa the line would be

From the origin to the Sandwich Islands (Honolulu) the line would be

By Scott-Russell’s rule, or, what is almost identically the same, by Airy’s general formula, we can calculate how long it would take such waves as we have been speaking about to travel over the different portions of each of these lines, and by adding these times together we obtain the time taken to travel across any one line. I have made these calculations, but as I get in every case answers which are too small, I think it unnecessary to give them.

The actual times taken to travel the distances just referred to were,

From San Francisco to Simoda the line is almost 3,567 miles, 3,000 fathoms deep, 840 miles, 2,500 fathoms deep, and 120 miles 1,000 fathoms deep. This gives an average depth of about 2,854 fathoms. Bache calculated the depth at 2,500 fathoms.

If we are to consider that, because the sea wave at Simoda came in some time after the land shock had been felt, the origin of this earthquake, instead of being at Simoda, was some distance out at sea, this calculated depth would be reduced.

CHAPTER X.
DETERMINATION OF EARTHQUAKE ORIGINS.

Approximate determination of an Origin—Earthquake-hunting in Japan—Determinations by direction of motion—Direction indicated by destruction of buildings—Direction determined by rotation—Cause of rotation—The use of time observations—Errors in such observations—Origin determined by the method of straight lines—The method of circles, the method of hyperbolas, the method of co-ordinates—Haughton’s method—Difference in time between sound, earth, and water waves—Method of Seebach.

One of the most practical problems which can be suggested to the seismologist is the determination of the district or districts in any given country from which earthquake disturbances originate. With a map of a country before us, shaded with tints of different intensity to indicate the relative frequency of seismic disturbance in various districts, we at once see the localities where we might dwell with the least disturbance, and those we should seek if we wish to make observational seismology a study. Before erecting observatories for the systematic investigation of earthquakes in a country, it would be necessary for us, in some way or other, to examine the proposed country to find out the most suitable district. The special problem of determining approximately the origin or origins of a set of earthquakes would be given to us. Having made this preliminary investigation, the next point is, by means of observatories so arranged that they could always work in conjunction with each other, to determine the origins more accurately. By knowing the origin from which a set of shocks spring we know the general direction in which we may expect the most violent disturbances, and we can arrange our seismometers accordingly.

Approximate determination of origins.—In 1880 I obtained a tolerably fair idea of the distribution of seismic energy throughout Japan, by compiling the facts obtained from some hundreds of communications received from various parts of the country respecting the number of earthquakes that had been felt.

The communications were replies to letters sent to various residents in the country and to a large number of public officers. By taking these records, in conjunction with the records made by instruments, it was ascertained that in Japan alone there were certainly 1,200 shocks felt during the year, that is to say, three or four shocks per day. The greater number of these shocks were felt along the eastern coast, commencing at Tokio, in the south, and going northwards to the end of the main island. These shocks were seldom felt on the west coast. It appeared as if the central range of mountains formed a barrier to their progress. Similarly, ranges of mountains to the south-west of Tokio prevented the shocks from travelling southwards. Proceeding in this way the conclusion was arrived at that the west coast, the southern part of Japan, and the islands of Shikoku and Kiushiu, had their own local earthquakes.

Earthquake-hunting.—These preliminary enquiries having shown that the northern part of Japan was a better district for seismological observations than the southern half, the next step was to subject the northern half to a closer analysis. This analysis was commenced by sending to all the important towns, from thirty to one hundred miles distant from Tokio, bundles of postcards. These were entrusted to the local government offices with a request that each week one of these cards would be returned to Tokio stating the number of shocks felt. In this way it was quickly discovered that the majority of shakings emanated from the north and east, and seldom, if ever, passed a heavy range of mountains to the south. The barricade of postcards was then extended farther northwards, with the result of surrounding the origin of certain shocks amongst the mountains, whilst others were traced to the sea shore. By systematically pursuing earthquakes it was seen that many shocks had their origin beneath the sea—they shook all the places on the north-east coast, but it was seldom that they crossed through the mountains, forming the backbone of the island, to disturb the places on the west coast.

The actual results obtained in three months by this method of working are shown in the accompanying map, which embraces the northern half of the main island of Nipon and part of Yezo. The shaded portion of the map indicates the mountainous districts, which are traversed by ranges varying in height from about 2,000 and 7,000 feet. The dotted lines show the boundaries of the more important groups of earthquakes which were recorded.

I. is the western boundary of earthquakes, which at places to the eastward are usually felt somewhat severely. Some of these have been felt the most severely at or near Hakodadi, whilst farther south their effects have been weak. Occasionally the greatest effect has been near to Kameishi. Sometimes these earthquakes terminate along the western boundaries of III. or IV., not being able to pass the high range of mountains which separate the plain of Musashi from Kofu.

Fig. 29.—Northern Japan. Mountainous districts shaded with oblique lines.

II. is the boundary of a shock confined to the plain which surrounds Kofu. These earthquakes are evidently quite local. Many of the disturbances have evidently originated beneath the ocean, having come in upon the land in the direction of the arrows a or b.

III. This line indicates the boundary of a group of shocks which are often experienced in Tokio. These may come in the directions d, e, or f. It is probable that some of them originate to the eastward of Yokohama, on or near to the opposite peninsula.

IV. V. and VI. The earthquakes bounded by these lines probably originate in the directions c or d.

VII. The earthquakes bounded by this line probably come from the direction e.

VIII. This line gives us the boundary of earthquakes which may come from the direction b.

The above boundaries sometimes do not extend so far to the westward as they are shown. At other times, groups like V. and VI. extend farther to the south-west. These earthquake boundaries, which so clearly show the effects of high mountains in preventing the extension of motion, have been drawn up, not from single earthquakes, but from a large series of earthquakes which have been plotted upon blank maps, and are now bound together to form an atlas. To give an idea of the material upon which I have been working, I may state that between March 1 and March 10, 1882, I received records of no less than thirty-four distinct shocks felt in districts between Hakodate and Tokio, and for each of these it is quite possible to draw a map. In addition to the boundaries of disturbances given in the accompanying map, other boundaries might be drawn for shocks which were more local in their character. The groups which contained the greatest number of shocks are III., IV., V., VI., and VII. By work of this description it was found that a very important group of earthquakes might be studied by a line of stations commencing at Saporo in the north, passing through Hakodate, down the east coast of the main island, to Tokio or Yokohama in the south. A further aid to the study of this group, together with the study of an important local group, might be effected with the help of a few additional stations properly distributed on the plain of Musashi, which surrounds Tokio. With this example before us it will be recognised that the choice of sites for a connected set of seismological observatories will often be more or less a special problem. If earthquake stations were to be placed in different directions around Tokio without preliminary investigation, it is quite possible that some of them might be so situated that they would seldom if ever work in conjunction with the remaining observatories, and therefore be of but little value. And this remark must equally apply to districts in other portions of the globe. The method is crude, and, so far as actual earthquake origins are concerned, it only yields results which are approximate. The crudeness and the want of absoluteness in the results is, however, more than counterbalanced by the certainty with which we are enabled to express ourselves with regard to such results as are obtained. Even when working with the best instruments we have at our command, unless we are employing some elaborate system, this method of working gives a most valuable check upon our instrumental records, and enables us to interpret them with greater confidence.

Determination of earthquake origins from the direction of motion.—If we assume that an earthquake is propagated from a centre as a series of waves, in which normal vibrations are conspicuous, and obtain at two localities, not in the same straight line with the origin, and sufficiently far separated from each other, the direction of movement of these normal motions, by drawing lines parallel to these directions through our two stations, the lines would intersect at a point above the required origin. If instead of two points we had three, or, better still, a large number, the results we should obtain ought to be still more certain. Unfortunately, it seems that earthquakes seldom originate from a given point, and, further, normal motions are not always (sufficiently) prominent. Sometimes, as has already been shown in the chapters on earthquake motion, they may be non-existent. It is probable, however, that difficulties of this sort are more usually associated with non-destructive earthquakes. Mallet regards the destructive effects of an earthquake as almost solely due to normal motions. If this be true, for destructive earthquakes, the problem is shorn of many of its difficulties. In cases where normal vibrations are not prominent, where we have only transverse vibrations, motions due to the interference of normal or transverse motions, or directions of motions due to the topographical or geological nature through which the disturbance has passed, the determination of the origin of an earthquake by observations on the direction in which the ground has been moving appears to be a problem which is practically without a solution. We will, therefore, only consider the determination of the origin of those earthquakes which have predominating directions in their movements, which directions we will consider as normal ones. The question which is, then, before us, is the determination of the direction of these normal movements. First of all we may take the evidence of our senses. In exceptional cases these have given results which closely approximate to the truth, but in the majority of cases such results are not to be relied upon, as the inhabitants of a town will, for the same shock, give directions corresponding to all points of the compass. Much, no doubt, depends upon the situation of the observer, and much, perhaps, upon his temperament. If he is sitting in a room alone, and is accustomed to making observations on an earthquake, on feeling the earthquake, if he concentrates his attention on the direction in which he is being moved, his observations may be of value. If, however, he is not so situated, and his attention is not thus concentrated, his opinions, unless the motion has been very decided in its character, are usually of but little worth.

Direction determined from destruction of buildings.—When an observer first sees a town that has been partially shattered by an earthquake, all appears to be confusion, and it is difficult to imagine that in such apparent chaos we are able to discover laws. If, however, we take a general view of this destruction and compare together similarly built buildings, it is possible to discover that similar and similarly situated structures have suffered in a similar manner. By carefully analysing the destruction we are enabled to infer the direction in which the destroying forces have acted. It was chiefly by observing the cracks in buildings, and the direction in which bodies were overthrown or projected, that Mallet determined the origin of the Neapolitan earthquake. From the observations given in Chapter VII. it would appear that, with destructive earthquakes, walls which are transverse to the direction of motion are most likely to be overturned, whilst, with small earthquakes, these walls are the least liable to be fractured.

From a critical examination of the general nature of the damage done on the buildings of a town, earthquake observers have shown that the direction of a shock may often be approximately determined. The direction in which a body having a regular form like a prismatic gravestone or a cylindrical column is overturned sometimes gives the means by which we can determine the direction from which a movement came.

The rotation of bodies.—It has often been observed that almost all large earthquakes have caused objects like tombstones, obelisks, chimneys, &c., to rotate.

One of the most natural and at the same time most simple explanations is to suppose that during the shock there had been a twisting, or backward and forward screw-like motion in the ground. Amongst the Italians and the Mexicans earthquakes producing an effect like this are spoken of as ‘vorticosi.’ In the Calabrian earthquake, not only were bodies like obelisks twisted on their bases, but straight rows of trees seem to have been left in interrupted zigzags. These latter phenomena have been explained upon the assumption of the interference of direct waves and reflected waves, the consequence of which being that points in close proximity might be caused to move in opposite directions. Reflections such as these would be most likely to occur near to the junction of strata of different elasticity, and it may be remarked that it is often near such places that much twisting has been observed.

Another way in which it is possible for twisting to have taken place would be by the interference of the normal and transverse waves which probably always exist in an earthquake shock, or by the meeting of the parts of the normal wave itself, one having travelled in a direct line from the origin, whilst the other, travelling through variable material, has had its direction changed.

Mallet, however, has shown that the rotation may have been in many cases brought about without the supposition of any actual twisting motion of the earth—a simple backward and forward motion being quite sufficient. If one block of stone rests upon another, and the two are shaken backwards and forwards in a straight line, and if the vertical through the centre of gravity of the upper block does not coincide with the point where there is the greatest friction between the blocks, rotation must take place. If the vertical through the centre of gravity falls on one side of the centre of friction, the rotation would be in one direction, whilst, if on the other side, the rotation would be in the opposite direction.

Although the above explanation is simple, and also in many cases probably true, it hardly appears sufficient to account for all the phenomena which have been observed.

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.

Determination of direction from instruments.—When speaking about earthquakes it was shown, as the result of many observations, that the same earthquake in the space of a few seconds, although it may sometimes have only one direction of motion, very often has many directions of motion. In certain cases, therefore, our records, if we assume the most permanent motions to be normal ones, give definite and valuable results. In other cases it is necessary to carefully analyse the records, comparing those taken at one station with those taken at another.

One remarkable fact which has been pointed out in reference to artificial earthquakes produced by exploding charges of gunpowder or dynamite, and also with regard to certain earthquakes, is that the greatest motion of the ground is inwards, towards the point from which the disturbance originated. Should this prove the rule, it gives a means of determining, not only the direction of earthquake, but the side from which it came.

Determination of earthquake origins by time observations.—The times at which an earthquake was felt at a number of stations are among the most important observations which can be made for the determination of an earthquake origin. The methods of making time observations, and the difficulties which have to be overcome, have already been described. When determining the direction from which a shock has originated, or determining the origin of the shock by means of time observations, it has been usual to assume that the velocity of propagation of the shock has been uniform from the origin. The errors involved in this assumption appear to as follows:—

1. We know from observations on artificial earthquakes that the velocity of propagation is greater between stations near to the origin of the shock than it is between more remote stations; and also the velocity of propagation varies with the initial force which produced the disturbance. If our points of observation are sufficiently close together as compared with their distance from the origin of the disturbance, it is probable that errors of this description are small and will not make material differences in the general results.

2. We have reasons for believing that the transit velocity of an earthquake is dependent on the nature of the rocks through which it is propagated. Errors which arise from causes of this description will, however, be practically eliminated if our observation points are situated on an area sufficiently large, so that the distribution of the causes tending to alter the velocity of a shock balance each other. It must be remarked, that causes of this description may also produce an alteration in the direction of our shock.

Other errors which may sometimes enter into our results, when determining the origin of shocks by means of observations on velocities, are the assumptions that the disturbance has travelled along the surface from the epicentrum and not in a direct line from the centrum. Again, it is assumed that the origin is a point, whereas it may possibly be a cavity or a fissure. Lastly, if we desire extreme accuracy, we must make due allowance for the sphericity of the earth and the differences of elevation of the observing stations.

I. The method of straight lines.—Given a number of pairs of points a₀, a₁, b₀, b₁, c₀, c₁, &c., at each of which the shock was felt simultaneously, to determine the origin.

Theoretically if we bisect the line which joins a₀ and a₁ by a line at right angles to a₀, a₁, and similarly bisect the lines b₀, b₁, c₀, c₁, all these bisecting lines a₀, a₁, b₀, b₁, c₀, c₁, &c., ought to intersect in a point, which point will be the epicentrum or the point above the origin.

This method will fail, first, if a₀, a₁, b₀, b₀, c₀, c₁ form a continuous straight line, or if they form a series of parallel lines.

Hopkins gives a method based on a principle similar to the one which is here employed—namely, given that a shock arrives simultaneously at three points to determine, the centre. In this case, the relative positions of the three points, where the time of arrival was simultaneous, must be accurately known, and these three points must not lie in a straight line, or the method will fail. For practical application the problem must be restricted to the case of three points which do not lie nearly in the same straight line.

II. The method of circles.—Given the times t₀, t₁, t₂, &c., at which a shock arrived at a number of places a₀, a₁, a₂, &c., to determine the position from which the shock originated.

Suppose a₀ to be the place which the shock reached first, and that it reached a₁, a₂, a₃, &c., successively afterwards.

Let t₁ - t₀ = a
t₂ - t₀ = b
t₃ - t₀ = c, &c.

With a₁, a₂, a₃, &c. as centres, describe circles with radii proportional to the known qualities a, b, c, &c., and also a circle which passes through a₀ and touches these circles. The centre of the last circle will be the epicentrum. The radii proportional to a, b, c, &c. may be represented by the quantities ax, bx, cx, &c., where x is the velocity of propagation of the shock.

It will be observed that the times at which the shock arrived at three places might alone be sufficient. If, instead of taking the times of arrival of a shock, the arrival of a sea wave be taken, the result would be a closer approximate to the absolute truth.

It will be observed that this method is not a direct one, but is one of trial. If, however, an imaginary case be taken, and three given points of observation, a₀, a₁, a₂, be plotted on a piece of paper, it will be found that it is not a difficult matter to determine two numbers proportional to a and b which will allow you to draw two circles so that they may be touched by a third circle drawn through a₀. This problem has practically been applied in the case of the arrival of a sea wave at a number of places on the South American coast, at the time of the earthquake of May 9, 1877. This is illustrated as follows. The places which were chosen were Huanillos, Tocopilla, Cobija, Iquique, Mejillones.

In the following table the first column gives the times at which the sea wave arrived at each of these places in Iquique time; in the second column the difference between these times and the time at which it reached Huanillos is given; in the third column the distances through which a sea wave, propagated at the rate of 350 feet per second, could travel during the intervals noted in the second column is given.

The distances marked in the third column are used as radii of the circles drawn round the places to which they respectively refer.

The centre of the circle drawn to touch the circles of the first column, and at the same time to pass through Huanillos, is marked c.

The position from which the shock originated appears therefore to have occurred very near to a place lying in Long. 7° 15′ W. and Lat. 21° 22′ S.

Fig. 31.

The actual operations which were gone through in making the accompanying map were as follows. First, the places with which we had to deal were represented on a map in orthographical projection, the centre of projection being near to the centre of the map. This was done so that the measurements which were made upon the map might be more correct than those we should obtain from an ordinary chart where this portion of the world was not the centre of projection. Next, a number was taken as equal to the velocity with which the sea wave had travelled. The first velocity taken was about 400 feet per second—this being about the velocity with which, theoretically, it must have travelled in an ocean having a depth equal to that indicated upon the charts—also it seemed to have travelled at this rate from the various times of arrival as recorded at places along the coast. Circles were then drawn round Tocopilla, Cobija, Iquique, and Mejillones with radii equal to 2, 8, 10, and 15, each multiplied by (60 × 400). It was then seen by trial that it was impossible to draw a single circle which should touch four circles and also pass through Huanillos. These four circles were, in fact, too large. Four new but smaller circles, which are shown in the map, were next drawn, their radii being respectively equal to the numbers 2, 8, 10, and 16, each multiplied by (60 × 350), and it was found that a circle, with a centre c, could be drawn which would practically touch the four circles, and at the same time would pass through Huanillos.

III. The method of hyperbolas.—The method which I call that of hyperbolas is only another form of the method of circles. It is, however, useful in special cases, as, for instance, where we have the times of arrival of earthquakes at only two stations. Between Tokio and Yokohama, at which places I frequently obtain tolerably accurate time records, the method has been applied on several occasions with advantage. In the preceding example let us suppose that the only time records which we had were for Huanillos and Mejillones, and that the wave was felt at the latter place sixteen minutes or 960 seconds after it was experienced at the former. Calling these places h and m respectively, round m draw a circle equal to the 960 multiplied by the velocity with which the wave was propagated. It is then evident that the origin of this disturbance must be the centre of a circle which passes through h and touches the circle drawn round m. Join h m, cutting the circle round m in y. Bisect y h in v. It is evident that v is one possible origin for the disturbance. Next, from m, in the direction of h, draw any line m z p; join z h; bisect z h at right angles by the line o p n. Because ph = pz, it is evident that p is a second possible origin. Proceeding in this way a series of points lying to the right and left of v on the curve r v t may be found, and we may therefore say that the origin lies somewhere in the curve r v t. By increasing or decreasing our velocity we vary the position of the curve r v t, and, instead of a line on which our origin may be, we obtain a band. As the assumed velocity increases, the circle round m becomes larger, and has its limit when it passes through h, where the two arms of the curve r v t will close together and form a prolongation of the line m y h as the assumed velocity diminishes. The circle round m becomes smaller until it coincides with the point m. At such a moment the curve r v t opens out to form a straight line bisecting m h at right angles. The curve r v t is a hyperbola with a vertex v and foci h and m. Inasmuch as pm - ph = a constant quantity. If we have the time given at which the shock or wave arrived at a third station as at Iquique, it is evident that a second hyperbola r′ v′ t′ might be drawn with Iquique and Huanillos as foci, and that the mutual intersection of these two hyperbolas with a third hyperbola, having for its foci Iquique and Mejillones, would give the origin of the wave. The obtaining of a mutual intersection would depend on the assumed velocity, and the accuracy of the result, like that of the method of circles, would depend upon the trials we made. The method here enunciated may be carried farther by describing hyperboloids instead of hyperbolas, the mutual intersection of which surfaces would, in the case of an earth wave, give the actual origin or centrum rather than the point above the origin or epicentrum.

IV. The method of co-ordinates.—Given the times at which a shock arrived at five or more places, the position of which we have marked upon a map, or chart, to determine the position on the map of the centre of the shock, its depth, and the velocity of propagation.

Commencing with the place which was last reached by the shock, call these places p, p₁, p₂, p₃, and p₄, and let the times taken to reach these places from the origin be respectively t, t₁, t₂, t₃, and t₄.

Through p draw rectangular co-ordinates, and with a scale measure the co-ordinates of p₁, p₂, p₃, and p₄, and let these respectively be a₁, b₁; a₂, b₂; a₃, b₃; a₄, b₄. Then if x, y, and z be the co-ordinates of the origin of the shock, d, d₁, d₂, d₃, and d₄, the respective distances of p, p₁, p₂, p₃, and p₄ from this origin, and v the velocity of the shock, we have

1. x² + y² + z² = d² = v² t²
2. (a₁ - x)² + (b₁ - y)² + z² = v² t₁²
3. (a₂ - x)² + (b₂ - y)² + z² = v² t₂²
4. (a₃ - x)² + (b₃ - y)² + z² = v² t₃²
5. (a₄ - x)² + (b₄ - y)² + z² = v² t₄²

Because we know the actual times at which the waves arrived at the places p, p₁, p₂, p₃, p₄, we know the values t—t₁, t—t₂, t—t₃, t—t₄. Call these respectively m, p, q, and r. Suppose t known, then

• t₁ = t - m
• t₂ = t - p
• t₃ = t - q
• t₄ = t - r.

Subtracting equation No. 1 from each of the equations 2, 3, 4, and 5, we obtain,

• a₁² + b₁² - 2a₁ x - 2b₁ y = v² (t₁² - t²) = v² (m² - 2t m)
• a₂² + b₂² - 2a₂ x - 2b₂ y = v² (t₂² - t²) = v² (p² - 2t p)
• a₃² + b₃² - 2a₃ x - 2b₃ y = v² (t₃² - t²) = v² (q² - 2t q)
• a₄² + b₄² - 2a₄ x - 2b₄ y = v² (t₄² - t²) = v² (r² - 2t r)

Now let v² = u, and 2v² t = w.

Then

1. 2a₁ x + 2b₁ y + u m² - n m = a₁² + b₁²
2. 2a₂ x + 2b₂ y + u p² - n p = a₂² + b₂²
3. 2a₃ x + 2b₃ y + u q² - n q = a₃² + b₃²
4. 2a₄ x + 2b₄ y + u r² - n r = a₄² + b₄²

We have here four simple equations containing the four unknown quantities x, y, u, and w.

x and y determine the origin of the shock. The absolute velocity v equals √ u. From v and w we obtain t. Substituting x, y, v, and t in the first equation we obtain z.

We have here assumed that the points of observation have all about the same elevation above sea level.

If it is thought necessary to take these elevations into account, a sixth equation may be introduced.

If the propagation of the wave is considered as a horizontal one, as would be done when calculating the position of the epicentrum or point above the origin, by means of the times of arrival of a sea wave, the ordinate z of the first five equations would be omitted. Working in this way the resulting four equations, viz.

2a₁ x + 2b₁ y + um² - wm² = a₁² + b₁²
&c. &c. &c.

remained unchanged.

Applying this method to the same example as that used as illustration for the two previous methods, we obtain for the co-ordinates of Mejillones, Iquique, Cobija, Tocopilla, and Huanillos, measured in geographical miles, and the times in Iquique time at which the wave reached each, as given in the following table; ox and oy being, drawn through Mejillones.

From this data we find the co-ordinates x and y of this origin to be 85·8 and 56·7; whilst the velocity of propagation = 45 feet per second.

Measuring these ordinates upon the map, we obtain a centre lying very near Long. 71° 5′ W. and Lat. 21° 22′ S., a position which is very near to that which has already been obtained by other methods.

If instead of Huanillos we substitute the ordinates and time of arrival of the sea wave for Pabalon de Pica, another point for the origin will be obtained lying farther out at sea. To obtain the best result, the method to be taken will evidently be, first to reject those places at which it seems likely that some mistake has been made with the time observations, and then with the remaining places to form as many equations as possible, and from these to obtain a mean value. This is a long and tedious process, and as the time observations of this particular earthquake are probably one and all more or less inaccurate, it is hardly worth while to follow the investigation farther.

In this example, as in the preceding ones, it will be observed that it has been sea waves that have been dealt with, rather than earth vibrations. It is evident, however, that these latter vibrations may be dealt with in a similar manner.

In these determinations it will also have been observed that it is assumed that the disturbance has radiated from a centre, and, therefore, approached the various stations in different directions. If we assume that we have three stations very near to each other as compared with their distances from the origin, so that we can assume that the wave fronts at the various stations were parallel, the determination of the direction in which the wave advanced appears to be much simplified. The determination of the direction in which a wave has passed across three stations was first given by Professor Haughton.

Haughton’s method.—Given, the time of an earthquake shock at three places, to determine its horizontal velocity and coseismal line.

The solution of this is contained in the formula

tan ϕ = ^{a (t₂ - t₁) sin β}/_{c (t3 - t2) + a (t2 - t1) cos β}.

When a, b, and c are three stations at which a shock is observed at the times t₁, t₂, and t₃; a, b, and c are the distances between a, b, and c, and ϕ is the angle made by the coseismal lines x a x, y b y, and the line a b, which are assumed to be parallel.

This I applied in the case of the Iquique earthquake, but owing to the smallness of the angles between the three stations a, b, and c, the result was unsatisfactory. The problem ought to be restricted, first, to places which are a long distance away from a centre, and, secondly, to places which are not nearly in a straight line. This problem may be solved more readily by geometrical methods. Plot the three stations a, b, and c on a map, join the two stations between which there was the greatest difference in the time observation. Let these, for example, be a and c. Divide the line a c at point d, so that a d : d c as the interval between the shock felt at a and b is to the interval between the shock felt at b and c. The line b d will be parallel to the direction in which the wave advanced.

The difference in time of the arrival of two disturbances.—In the various calculations which have been made to determine an origin based on the assumption of a known or of a constant velocity, we have only dealt with a single wave, which may have been a disturbance in the earth or in the water. A factor which has not yet been employed in this investigation is the difference in time between the arrival of two disturbances; one propagated, for instance, through the earth, and the other, for example, through the ocean. The difference in the times of the arrival of two waves of this description is a quantity which is so often recorded that it is well not to pass it by unnoticed. To the waves mentioned we might also add sound waves, which so frequently accompany destructive earthquakes, and, in some localities, as, for instance, in Kameishi, in North Japan, are also commonly associated with earthquakes of but small intensity. It was by observing the difference in time between the shaking and the sound in different localities that Signor Abella was enabled to come to definite conclusions regarding the origin of the disturbances which affected the province of Neuva Viscoya in the Philippines, in 1881; the places where the interval of time was short, or the places where the two phenomena were almost simultaneous, being, in all probability, nearer to the origin than when the intervals were comparatively large. I myself applied the method with considerable success when seeking for the origin of the Iquique earthquake of 1877. The assumptions made in that particular instance were, first, that the velocity of the disturbance through the earth was known, and, secondly, that the velocity with which a sea wave was propagated was also known.

A method similar to the above was first suggested by Hopkins. It depended on the differences of velocity with which normal and transversal waves are propagated.[86]

Seebach’s method.—To determine the true velocity of an earthquake, the time of the first shock, and the depth of the centre.

Fig. 32.

Let the straight line m, m₁, m₂, m₃ represent the surface of the earth shaken by an earthquake. For small earthquakes, to consider the surface of the earth as a plane will not lead to serious errors.

If an earthquake originates at c, then to reach the surface at m it traverses a distance h in the time t. To reach the surface at m₁ it traverses a distance h + x₁ in a time t₂. If v equals the velocity of propagation,

then t = ^h/_v, t₁ = ^{h + x₁}/_v,

t₂ = ^{h + x₂}/_v, &c.

Seebach now says that if we have given the position of m or epicentrum of the shock, and draw through it rectangular axes like m m₃ and m t₃, and lay down on m m₃ in miles the distances from M of the various stations which have been shaken, and in equal divisions for minutes lay down on m t₃ the differences of time at which m, m₁, m₂, &c. were shaken, then m₁ t₁, m₂ t₂, &c. are the co-ordinates of points on an hyperbola. The degree of exactness with which this hyperbola is in any given case constructed is a check upon the accuracy of the time observations and the position of the epicentrum. The apex of the hyperbola is the epicentrum.

The intersection of the asymptote with the ordinate axis is the time point of the first shock, which, because the scale for time and for space were taken as equal, gives the absolute position of the centrum. This intersection is shown by dotted lines. Knowing the position of the centrum, we can directly read from our diagram how far the disturbance has been propagated in a given time.

CHAPTER XI.
THE DEPTH OF AN EARTHQUAKE CENTRUM.

The depth of an earthquake centrum—Greatest possible depth of an earthquake—Form of the focal cavity.

Depth of centrum.—The first calculations of the depth at which an earthquake originated were those made by Mallet for the Neapolitan earthquake of 1857. These were made on the assumption that the earth wave radiated in straight lines from the origin, and, therefore, at points at different distances from the epicentrum it had different angles of emergence. These angles of emergence were chiefly calculated from the inclination of fissures produced in certain buildings, which were assumed to be at right angles to the direction of the normal motion. If we have determined the epicentrum of an earthquake and the muzoseismal circle, and make either the assumption that the angle of emergence in this circle has been 45° or 54° 44′ 9″ (see page 54), it is evidently an easy matter by geometrical construction to determine the depth of the centrum. Höfer followed this method when investigating the earthquake of Belluno.

Other methods of calculation which have been employed are based on time observations, as, for instance, the method of Seebach, the method of co-ordinates, the method of hyperboloids or spheres (see pages 200–212).

By means of a number of lines parallel to twenty-six angles of emergence, drawn in towards the seismic vertical, Mallet found that twenty-three of these intersected at a depth of 7⅛ geographical miles. The maximum depth was 8⅛ geographical miles, and the minimum depth 2¾ geographical miles.

The mean depth was taken at a depth of 5¾ geographical miles where, within a range of 12,000 feet, eighteen of the wave paths intersected the seismic vertical.

The point where these wave paths start thickest is at a depth not greater than three geographical miles, and this is considered to be the vertical depth of the focal cavity itself.

For the Yokohama earthquake of 1880, from the indications of seismometers, and by other means, certain angles of emergence were obtained, leading to the conclusion that the depth of origin of that earthquake might be between 1½ and 5 miles.

Possibly, perhaps, the earthquake may have originated from a fissure the vertical dimensions of which was comprised between these depths.

A source of error in a calculation of this description is that the vertical motions may have been a component of transverse motions or perhaps due to the slope of surface waves.

The following table of the depths at which certain earthquakes have originated has been compiled from the writings of several observers.

A table similar to this has been compiled by Lasaulx.[87]

With the exception of the determination for the two last disturbances these calculations have been made with the assistance of the method of Seebach, which depends, amongst other things, on the assumptions of exact time determinations, direct transmission of waves from the centrum, and a constant velocity of propagation.

Admitting that our observations of time are practically accurate, it appears that the other assumptions may often lead to errors of such magnitude that our results may be of but little value.

From what has been said respecting the velocity with which earth disturbances are propagated, it seems that these velocities may vary between large limits, being greatest nearest to the origin.

If we refer to Seebach’s method, we shall see that a condition of this kind would tend to make the differences in time between various places, as we recede from the epicentrum, greater than that required for the construction of the hyperbola. The curve which is obtained would, in consequence, have branches steeper than that of the hyperbola, and the resultant depth, obtained by the intersection of the asymptotes of this curve with the seismic vertical, indicates an origin which may be much too great.

Another point worthy of attention, which is common to the method of Mallet as well as to that of Seebach, is the question whether the shock radiates directly from the origin, or is propagated from the origin more or less vertically to the surface, and then spreads horizontally. We know that earthquakes, both natural and artificial, may be propagated as undulations on the surface of the ground, and that the vertical motion of the latter, as testified by the records of well-constructed instruments, has no practical connection with the depth from which the disturbance originated.

In cases like these, the direction of cracks in buildings, and other phenomena usually accredited to a normal radiation, may in reality be due to changes in inclination of the surface on which the disturbed objects rested. When our points of observation are at a distance from the epicentrum of the disturbance which, as compared with the depth of the same, is not great, calculations or observations based on the assumption of a direct radiation of the disturbance may possibly lead to results which are tolerably correct. The calculations of Mallet for the Neapolitan earthquake appear to have been made under such conditions.

For smaller earthquakes, and for places at a distance from the seismic vertical of a destructive earthquake, the results which are deduced from the observations on shattered buildings, and all observations based upon the assumption of direct radiation, we must accept with caution.

Another error which may enter into calculations of this description is one which has been discussed by Mallet at some length. This is the effect which the form and the position of the focal cavity may have upon the transmission of waves.

Should the impulse originate from a point or spherical cavity, then we might, in a homogeneous medium perhaps, regard the isoseismals as concentric circles, and expect to find that equal effects had been produced at equal distances from the epicentrum. Should, however, this cavity be a fissure, it is evident that even in a homogeneous medium the inclination of the plane of such a cavity will have considerable effect upon the form of the waves which would radiate from its two walls.

For example, let it be assumed that the first impulse of an earthquake is due to the sudden formation of a fissure, rent open from its centre, and that the waves leave the walls at all points normal to its surface. Then, as Mallet points out, it is evident that the disturbance will spread out in ellipsoidal waves, the greatest axis of which will be perpendicular to the plane of the fissure.

By taking a number of cases of fissures lying in various directions and drawing the ellipsoidal waves which would result from an elastic pressure, like that of steam suddenly admitted into such cavities, the differences in effect which would be simultaneously produced by these waves on reaching the surface can be readily understood. The following example of an investigation on this subject will serve as an example to illustrate the general nature of the many other cases which might be taken.

Fig. 33.

Let a disturbance simultaneously originate from all points of the fissure f f. This will spread outwards in ellipsoidal shells to the surface of the earth e e. The major axis of these ellipsoidal shells will be the direction of greatest effect. In the direction c d the waves will plunge into the earth, and places to the right side of the fissure will, to use an expression due to Stokes, when speaking of analogous phenomena connected with sound, be in earthquake shadow. The same expression has been employed, somewhat differently, when speaking of the effects produced on buildings.

For places, like s and p, situated at equal distances from the seismic vertical, it is evident that the intensity of the shock will be different, and also its time of arrival. It will also be observed that the isoseismals will take the form of ovals or distorted ellipses, the larger or fuller end of which being to the left of the fissure.

Other cases, like those just given, which are discussed by Mallet in his account of the Neapolitan earthquake, are where the fissure forms the division between materials of different elasticities. In the hard and more elastic material the waves will be more crowded, the velocity of a wave particle will be greater, and the transit will be quicker than in the less elastic medium.

The result is that the distance of equal effect from the seismic vertical will be greatest in the direction of the more compressible material.

Unless these considerations are kept carefully before the mind when investigating the depth and, we may add, the position and form of the centrum of an earthquake, serious errors may arise.

Greatest depth of an earthquake origin.—A curious but instructive calculation which Mallet made was a determination of the greatest possible depth at which an earthquake may occur. This calculation is based upon the idea that the impulsive effect of an earthquake has an intimate relationship with the height of neighbouring volcanoes, the column of lava supported on a volcanic cone being a measure of the internal pressure tending to rupture the adjacent crust of the earth.

Mitchell, in 1700, virtually propounded this idea, when he suggested that the velocity of propagation of an earthquake was related to the height of such a column.[88]

Mallet showed that there was probably considerable truth in such a supposition by appealing to the results of actual observation. The pressure gauge of the Neapolitan district would be Vesuvius, the height of which has in round numbers varied between 3,500 to 4,000 feet. One of the most destructive earthquakes in this district—namely, the one of 1857—projected bodies with an initial velocity of about fifteen feet per second. The Riobamba earthquake, which projected bodies with an initial velocity of eighty feet per second, appears to have been the most violent earthquake, so far as its impulsive effort is concerned, of which we have any record. It occurred amongst the Andes, where there are volcanoes from 16,000 to 21,000 feet in height.

Comparing these two earthquakes together, we see that the Riobamba shock had a destructive power 5·33 times that of the Neapolitan shock, and we also see that the Riobamba volcanoes were about 5·33 times higher than Vesuvius. The accordance in these quantities is certainly interesting, and tends to substantiate the idea that volcanoes are barometrical-like pressure gauges of a district.

Carrying the argument still further. Mallet says that if the depth of origin of earthquakes were the same, then the area of disturbance would, for like formations and configuration of surface, be a measure of the earthquake effort, and also some function of the velocity of the wave. From this we may generally infer ‘that earthquakes, like that of Lisbon, which have a very great area of sensible disturbance, have also a very deep seismal focus, and also the greatest depth of seismal focus within our planet is probably not greater than that ascertained for this Neapolitan earthquake, multiplied by the ratio that the velocity of the Riobamba wave bears to that of its wave, or, what is the same thing, by the ratio of the altitudes of the volcanoes of the Andes to that of Vesuvius.’

Now, as the depth of the Neapolitan shock may be taken at 34,930 feet, the greatest probable depth of origin of any earthquake impulse occurring in our planet is limited to 5·333 × 4,930 feet, or 30·64 geographical miles.

Ingenious as this argument is, we can hardly admit it without certain qualifications.

First, we are called upon to admit the identity of the originating cause of the volcano and the earthquake—as to what may be the originating cause of earthquakes we have yet to refer, but certainly in the case of particular earthquakes, as, for instance, those which occur in countries like Scotland, Scandinavia, and portions of Siberia, the direct connection between these phenomena are not at first sight very apparent.

Secondly, even if we admit the identity of the origin of these phenomena, it is not difficult to imagine that the fluid pressure brought to bear upon certain portions of the crust of the earth may possibly in many instances be infinitely greater than that indicated by the height of the column of liquid lava in the throat of a volcano, the true height of which we are unable to obtain. Further, in certain instances such a column only appears to be a measure of the pressure upon the crust of the earth in the immediate vicinity of the cone.

Thus, in the Sandwich Islands, we have lava standing in the throat of the volcano of Mauna Loa 10,000 feet higher than it stands in the crater Kilauea, only twenty miles distant. That these columns should be measures of the same pressure, originating in a general subterranean liquid layer with which they are connected, is a supposition difficult to satisfactorily substantiate.

Another measure of the impulsive efforts which subterranean terranean forces may exert upon the crust above them is evidently the height to which volcanoes eject materials. Cotopaxi is said to have hurled a 200-ton block of stone nine miles. Sir W. Hamilton tells us that in 1779 Vesuvius shot up a column of ashes 10,000 feet in height; and Judd tells us that this same mountain in 1872 threw up vapours and rock fragments to the enormous height of 20,000 feet. This would indicate an initial velocity of 1,131 feet per second.

Notwithstanding Mallet’s calculation that thirty miles is the limiting depth for the origin of an earthquake, the origin of the Owen’s Valley earthquake of March 1872 was estimated as being at least fifty miles.[89]

Form of the focal cavity.—Among the various problems which are put before those who study the physics of the interior of our earth it would at first sight appear that there was none more difficult than the attempt to determine the form of the cavity, if it be a cavity, from which an earthquake originates. Almost all investigators of seismology have recognised that the birthplace of an earthquake is not a point, and have made suggestions about its general nature. The ordinary supposition is that the earthquake originates from a fissure, and if the focus of a disturbance could be laid bare to us it would have the appearance of a fault such as we so often see exposed on the faces of cliffs.

A strong argument, tending to demonstrate that some of the shakings which are felt in Japan are due to the production of such fissures, is the fact that the vibrations which are recorded are transverse to a line joining the point of observation and the district from which, by time observations, we know the shock to have originated. The most probable explanation of this phenomena appears to be that one mass of rock has been sliding across another mass, giving rise to shearing strains, and producing waves of distortion.

The first seismologist who attacked the problem of finding out the dimensions and position of such a fissure was Mallet, when working on the Neapolitan earthquake of 1857. The reasons that the origin should, in the first place, have been a fissure, rather than any other form of cavity, was that such a supposition seemed to be a priori the most probable, and, further, that it afforded a better explanation of the various phenomena which were observed, than that obtained from any other assumption.

The method on which Mallet worked to determine the form and position of the assumed fissure, which method was subsequently more or less closely followed by other investigators, was as follows:—

From an observation of the various phenomena produced upon the surface of the disturbed area, a map of isoseismals was constructed. These were seen, as has been the case with many earthquakes, not to distribute themselves in circles round the epicentrum, but as distorted oval or elliptical figures, the major axes of which roughly coincided with each other. Further, the epicentrum, did not lie in the centre of these ovals, but was near to the narrow end where they converged.

This at once showed, if the reasoning respecting the manner in which waves are propagated from an inclined fissure be correct, that the fissure was at right angles to the major axis of the curves, dipping from their narrow end downwards, in the direction of their larger widespread ends.

The next weapon which Mallet employed to attack this problem was the sound which was heard at different points round about the focus. These sounds appear to have been of the nature of sudden explosive reports accompanied by rushing, rolling sounds. The form of the area in which these sounds were heard was closely similar to that of the first two isoseismals. Except in the central area of great disturbance, no sound was heard to accompany the shock.

Those at the northern and southern extremity of the sound area all described what they heard as a ‘low, grating, heavy, sighing rush, of twenty to sixty seconds’ duration.’ Those in the middle and towards the east and west boundaries of this area described a sound of the same tone, but shorter and more abrupt, and accompanied with more rumbling.

The nature of the arguments which were followed in discussing the sound observations will be found in the chapter relating to these phenomena.

A portion of the argument which it is difficult to follow relates to the maximum rate at which it can be supposed possible for a fissure to be rent in rocks, which rate depends on the density and elasticity of these rocks and other constant factors.