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.

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.

_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 √2_gh_, 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.’

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.

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.

_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.

_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.

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.

_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.

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:—

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.