motion pendulum horizontal fixed earth ground vertical plane method earthquake
SEISMOMETER. This name was originally given to instruments designed to measure the movement of the ground during earthquakes. Recent observations have shown that, in addition to the comparatively great and sudden displacements which occur in earthquakes, the ground is subject to other movements. Some of these, which may be called " earth-tremors," resemble earthquakes in the rapidity with which they occur, but differ from earthquakes in being imperceptible (owing to the smallness of the motion) until instrumental means are used to detect them. Others, which may be called " earth-tiltings," show themselves by a slow bending and unbending of the surface, so that a post stuck in the ground, vertical to begin with, does not remain vertical, but inclines now to one side and now to another, the plane of the ground in which it stands shifting relatively to the horizon. No sharp distinction can be drawn between these classes one another, and in almost every earthquake there is some tilting of the surface. The term " seismometer " may conveniently be extended (and will here be understood) to cover all instruments which are designed to measure movements of the ground.
Measurements of earth-movements are of two distinct types. In one type, which is applicable to ordinary earthquakes and earth-tremors, the thing measured is the displacement of a point in the earth's crust. In the second type, which is applicable to slow tiltings, the thing measured is any change in the plane of the earth's surface relatively to the vertical. Under EARTHQUAKE mention is made of instruments designed by Palmieri and others to register the occurrence of earthquakes, and in some cases to give a general idea of their severity. While some of those instruments act well as seismoscopes, none of them serve to determine with precision the character or the magnitude of the motion. In this article notice will be taken only of instruments intended for exact measurement.
Earthquake displacements are in general vertical as well as horizontal. For the purpose of measurement it is convenient to treat the vertical component separately, and in some cases to resolve the horizontal motion into two components at right angles to each other.
Inerli2 Method. - In the first type of measurements what may be called the " inertia " method is followed. A mass is suspended with freedom to move in the direction of that component of the earth's motion which is to be measured. When an impulse occurs the supports move, but the mass is prevented by its inertia from accompanying them. It supplies a steady point, to be used as a standard of reference in determining the extent through which the ground has moved in the direction in question. But, in order that the suspended mass shall not acquire motion when its supports move, one essential condition must be satisfied. Its equilibrium must be neutral, or nearly so, in order that, when the supports are displaced, little or no force may be brought into operation tending to bring the mass into the same position relative to the supports as it occupied before disturbance. This can bo made plain by considering the case of a common pendulum hung from a support which is rigidly fixed to the ground. When the ground moves in any horizontal direction the pendulum's inertia causes a certain point in it (the centre of percussion) to remain for the instant at rest. But this contrivance does not yield a steady point, because the stability of the pendulum makes the bob swing down to recover its place directly under the support ; and in fact, if a succession of oscillations of the ground occur, the bob acquires a motion often much greater than the motion of the sup- port itself. This tend- ency may be corrected, and the pendulum made fit to act as a seismometer, by any contrivance which (without introducing friction) else it would be unmanageable ; but its period of free oscillation must be much greater than that of the earthquake-motions which it is employed to measure. Even a simple pendulum can have its stability reduced sufficiently to fit it for seismometric work by making it very long. The same result is, however, much more conveniently achieved by combining a common pendulum with an inverted pendulum placed just beneath it. The common pendulum being stable and the inverted pendulum unstable, if the bobs are jointed so that they must move together, the combination can be made as nearly astatic as may be desired.' Figs. 1 and 2 illustrate how this combination is applied in seismometry. The stable bob cc, hung from a fixed support above by three parallel wires, is connected with the inverted pendulum b by a ball-and-tube joint. A lever c, carried by a gimbal joint in the fixed bracket d, is geared also by a ball-and-tube joint to the upper bob. Its long arm carries a jointed index e, which projects out and touches a smoked-glass plate f, held on a fixed -shelf. Any horizontal motion of the ground acts on the lever by the bracket d, and causes the index to trace a magnified record on the smoked-glass plate. Fig. 1 is taken from a photograph of an instrument of this kind, constructed to give a much magnified record of small movements. When large earthquakes are to be recorded the multiplying lever is dispensed with, and the index is attached directly to one of the bobs. Observations with instruments of this class exhibit well the very complicated motion which the earth's surface undergoes during an earthquake. In small earthquakes (such as are only slightly or not at all destructive) the greatest amplitude of motion is often less than a millimetre, and rarely more than a centimetre ; the disturbance nevertheless consists of a multitude of successive movements, quite irregular in amplitude, period, and direction. Fig. 3 is a facsimile of the record given by a duplex pendulum seismograph during one of the earthquakes which occur frequently in the plain of Yedo, Japan. The record, as engraved, is three and a half times the earth's actual motion. Instead of two pendulums, a single inverted pendulum has been used, with a spring stretched between it and a fixed support above. By adjusting the spring so that a proper proportion of the weight is borne by it and the remainder by the rigid stem of the pendulum, an approach to neutral equilibrium can be made." In Forbes's inverted pendulum seismometers a somewhat similar plan was adopted : the foot of the pendulum was attached to an elastic wire which tended to restore it to its normal vertical position when displaced.
Another group of instruments designed to furnish two degrees of freedom for the purpose of recording all motions in a horizontal plane, but much less satisfactory on account of their friction, is that in which a rolling sphere either itself supplies inertia or forms a support for a second inertia-giving mass. Probably the earliest was one used in Japan by Dr G. F. Verbeck in 1876 (see fig. 4).
On a marble table, ground plane and carefully levelled, four balls of rock-crystal were placed, carrying a massive block of hard wood. A pencil, sliding in a hole in the block, registered the relative motion of the table and the block on a sheet of paper fixed below. The motion regis tered is (or would be, if there were no friction) somewhat larger than the true motion of the table, for the system is kinetically equivalent to four upright pieces whose centres of percussion lie in a plane nearly, but not quite, as high as the tops of the balls. This forms what may be called the steady plane ; its position depends on the relative masses of block and balls, and is easily calculated. When the ground moves in any direction the block moves through a short distance in the opposite direction, and the record is magnified in a fixed ratio. Various forms of rolling-sphere seismometers have been proposed by Dlr. T. Gray,' Mr. C. A. Stevenson,a and others. Prob-ably the best form would be that of a light spherical segment rolling on a level plane base and carrying a heavy bob fixed to it. To give some stability the bob should be placed so as to bring the centre of gravity a little nnder the centre of curvature. The centre of percussion, somewhat higher than this, would of course be the steady point, and a multiplying pointer might take the motion either from it or from any other convenient part of the rolling piece. All rolling seismometers - including rolling cylinders, which have been proposed by 3fr Gray. as single-freedom instruments, to register one component of horizontal motion - fail to act well, partly because of the comparatively great frictional or quasi-fric-tional resistance which is presented to the motion of the free mass, and partly because, owing to imperfections in the construc-tion and want of perfect rigidity m the materials, the ball or cylinder takes up a position in which there is an objectionably great stability as regards very small displacements. These objections make the use of rolling seismometers unadvisable, except perhaps for the rough measurement of violent earthquakes.
The seismonaphs which have been described draw a horizontal plan of the pabth pursued during an earthquake by a point on the earth's surface. They take no note of tbe relation of the displace-ment to time, - an element which is required if we are to form any estimate of the violence of an earthquake from the recorcL With this view a different method of registration is also followed. The whole movement is resolved into rectilinear components, and these are separately recorded (by single-freedom seismometers) on a plate or drum which is kept in continuous movement, so that the record of each component takes the form of an undulating line, from which the number, succession, amplitude, velocity, and acceleration of the component movements can be deduced and the resultant motion determined. A single steady mass with two degrees of freedom inay still be employed to record, separately, two components of horizontal motion ; but it is generally preferable to provide two distinct masses, each with one degree of freedom. The principal instrument of this class is the horizontal pendulum seismograph,3 which has been used to record Japanese earthquakes since 1880. It consists of two horizontal pendulums, set at right angles to each other, each supplying a steady point with respect to horizontal motions transverse to its own length. Each pendulum is pivoted about two points, on an axis which is nearly vertical, but in-clined slightly forwards to give a suitable degree of stability. In some forms of the instrument the pivoted frame of the pendulum is light, and the inertia is practically all furnished by a second piece or bob pivoted on the frame about a vertical axis through the centre of percussion of the frame. This construction has the advantage of compactness and of making the position of the steady point at once determinate. But a simpler construction is to at-tach the bob rigidly to the frame. This shifts the steady point a little way outwards from the position it would have if the bob were pivoted. In either construction a prolongation of the pendu-lum beyond the bob forms a convenient multiplying index. Fig.
or be started into motion by an electric seismoscope when the earliest indications of an earthquake are felt. The former plan is practicable only 'when the instrument can receive careful attend-ance and where earthquakes occur often. It has the drawback that the circle which is drawn by each pointer as the plate revolves below it gradually broadens, partly because of warping and tempera-ture changes in the supports and partly because of actual tilting of the ground. As an earthquake generally begins with comparatively insignificant movements, there is not much to object to in having the plate at rest to begin with, provided a sufficiently sensitive starting seismoscope be used. A suitable arrangement for this pur-pose is one due to Pahnieri: a short pendulum hangs over a cup of mercury, in the centre of which a depression is formed by an iron pin, whose top is a little lower than the surface of the mercury. The pendulum ends in a platinum point, which stands clear in the centre of this depression, but touches the edge whenever a horizontal movement of the ground takes place, thereby closing the circuit of an electro -magnet, which starts the clock. In the most recent form of the horizontal pendulum seismograph the bobs are fixed to the pivoted frames, and the pointers are arranged to trace their records side by side. Records with instniments of tbis class, besides giving much additional information, agree with those of the duplex pendulum in show-ing that earthquake motion is a tangle of waves in all azi-muths. This will be seen by reference to fig. 6,which shows a small portion of an earthquake re-gistered by a pair of horizontal pendulums. Contemporary parts of the two records are shown together, the straight radial lines marking seconds of time. The phases of the two components are con-tinually changing, and when the two are compounded the result is a path having the same characteristics as those of the diagram In fig. 3. Fig. 7 gives the result of compoundine the records of fig. 6 during three seconds, while the range of move-ment was a maximum.
To register the vertical com-ponent of earthquake motions we require to suspend a ma.ss with vertical freedom. Most , ways of doing this give too ' much stability, as, for instance, vertical motion seis-mometer which wa.Q used by the British Association Commit-tee at Comrie in 1842. Another form, me-chanically equivalent to this, is a weighted I horizontal bar, pivot- I ed on a fixed hori- I zontal fulcrum, and held up by a spiral I spring, stretched ' from a point near the fulcrum to a fixed support above. This mode of suspen-sion is still too stable, though less so than if the spring were directly loaded. To make it nearly atel.114.1t, .1111 1 • ,-31 - upulell LIM 1.I.G of a tube containing mercury, connected with the bar in such a manner that when the bar goes down the mercury, running to-wards one end of the tube, has the effect of increasing the weight, and when the bar goes up an opposite effect occurs. This plan is open to the objection that the mercury is disturbed by horizontal movements of the ground. A simpler plan is shown in fig. 3.5 There the pull of the spring is applied at a short distance v below the plane of the bar. Ilence when the weight goes down the spring, which then pulls with more force, pulls with a smaller leverage, and it is easy to adjust the distance v so that the moment of the pull of the spring remains sensibly equal to the moment of the weight, - the condition necessary to make the bar astatic. This is secured when v = - 1' h being the horizontal distance from the fulcrum to the point at which the spring acts, and / the length by which the spring is stretched when the bar is undeflected. Stability is siven by maktn,g v somewhat less than this. A vertical-motion seismograph, constructed on the principle which fig. 8 illustrates diagrammatically, is arranged to trace its record on a revolving glass plate. This, along with a pair of horizontal pendulums recording on the same plate, completes a three-component seismograph.
An interesting mode of suspension, by which a mass is hung in neutral or nearly neutral equilibrium. with one dearee of horizontal freedom, is shown in fig. 9. It is based on the approximate straight linkwork of Tchebicheff. 1Vben a bar is hung from fixed supports by crossed ties, at a distance below the supports equal to the distance between the supports, the length of the bar being equal to half that distance, its middle point moves in very nearly a straight line. By fix-ing a weight at the centre of the bar and adding a suitable recording apparatus, we have a very friction-less form of one- component hori-zontal seismometer.' When a displacement of the ground occurs in the line of the bar, the bar is tilted through an angle which is proportional to the linear displace-ment, and the centre of the bar consequently shares, in a small and definite proportion, the motion of the ground, - a fact which is to be borne in mind in estimating the degree of multiplication given by the recording apparatus.
The instruments which have been described afford complete and satisfactory means of determining the motion which a point of the ground undergoes during any disturbance which would be recog-nized as an earthquake. For minute earth-tremors, however, a larger multiplication is necessary, and the absence of friction is of even more importance than in the measurement of earthquakes proper. Optical methods of magnifying the motion are accordingly resorted to. In the "normal tromometer" of Bertelli, used in Italy to detect earth-tremors, the bob of a pendulum, suspended by a fine wire from a fixed support, is viewed through a reflecting prism and its motion in any azimuth measured by a micrometer microscope. The great stability of the pendulum, which is only metres long, prevents it from behaving as a steady-point seismometer ; and, if successive earth-movements were by chance to occur with a period equal or nearly equal to its own free period, its acquired swing would altogether mask the legitimate indications. This kind of action has, in fact, been turned to account as a means of detecting very minute earth - tremors by Rossi, who has devised a micro-soismoscope, consist-ing of a number of pendu-lums of various lengths, one or other of which is likely to be set swinging when the ground shakes to and fro re-peatedly, through even the minutest range. To measure tremors, however, the instill-ments of Bertelli and Rossi are inappropriate ; for that purpose, just as for the pur-pose of measuring larger motions, the suspended mass must be in nearly neutral equiliblium. To find a mode of suspension which is at once astatic and extremely fric-tionless is a matter of some difficulty ; the crossed-link suspension, which has been already described, is probably the most satisfactory moans ' hitherto suggested. It has been adopted in the micro-seismometer sketched in section in fig. 10. Two bobs are separately suspended, in the manner shown by fig. -9, at right angles to each other, one above the other, in a cast-iron case. A microscope, fixed to the top of the case and furnished with a micrometer eye-piece, is focused on a hair, which is stretched transversely across a vertical tube in the upper bob a.. This serves to measure horizontal motion in the plane of the droning. Motion at right angles to this is shown by the lower bob e (drawn in section), which carries a similar transverse hair. A fixed lens b between the bobs gives an image of the lower hair in the plane of the upper hair, so that both appear crossed in the field of the microscope, thereby allowing both components of horizontal motion to be observed together.
Equilibrium illethod. - In observing slow earth-tiltings an entirely different process is followed. The problem then is, not to measure displacements by aid of the inertia of a body which tends to pre-serve its original position, but to compare the direction of a line or plane fixed to the earth with the direction of the vertical. The earliest observations of earth-tiltings were made by the aid of spirit-levels. If a level be set on a table fixed to the rock, its bubble, watched through a microscope, will be seen to move slowly 1101V tO one side and now to another. The movements are so slow that the inertia of the fluid is unimportant. Observations with pairs of levels, set at right angles to each other, have been carried on systematically for some years by M. P. Plantamour.2 This is the simplest method of measunng earth-tiltings, but it is liable to errors which are not easily excluded. Another method of investigating changes in the direction of the vertical was initiated in 1868 by M. A. d'Abbadie,3 who had before that observed the movements of level-bubbles. Light from a fixed source is made to fall on a reflect-ing basin of mercury about 10 metres below it Above the basin is a large lens of long focus, which brings the rays into parallelism dur-ing their passage to the mercury, and causes them to converge after reflexiou, so that an image of the source is formed at a convenient distance from it, and in the same horizontal plane. The interval between tho source and the image is measured (in amount and azimuth) at least twice a day by a micrometer microscope. The accuracy of the method dopends on the fixity of the source of light relatively to the lens and to the surface of the ground, and to secure this M. d'Abbadie built a massive hollow cone of concrete for the support of his apparatus. His observations have shown that the earth's surface undergoes almost incessant slow tilting through angles which, in the courso of a year, have been found to range over four seconds. He has also noticed the occurrence of earth-tremors by the occasional blurring of the image through agitation of the mercury. An improvement on his annaratus sug gested by II. Wolf 4 IS shown in fig. 11. The light, instead of being all reflected from the free surface of merciury (a), is partly reflected from that and partly from a plane mirror (b) fixed to the rock. Two images are therefore formed, whose rela-tive position measures the tilting of the surface. The advantage of this is that the position of the source of light need no longer be fixed, and the accuracy of the method depends only on the fixity of the mirror b with respect to the rock. Further, to avoid having the source and image at a great height above the surface, M. Wolf allows the light to reach and ' leave the apparatus horizontally, in the manner indicated in the sketch, by using a plane mirror inclined at 45° to the horizon. Still another mode of investigating slow changes of the vertical was followed (at the suggestion of Sir William Thomson) by Messrs G. H. and H. Darwin, in observations made by them with the view of measuring the lunar disturbance of gravity. The Reports of the British Association for 1881 and 1882 contain a full account of their appamtus, as well as noticag of the work of other observers and a discussion of the cause of earth-tiltings. Their in-strument was a short pendulum hung in a viscous fluid, from a fixed support, by two wires arranged V-wise to leave the pendulum only one degree of freedom. Below the bob was a small mirror hung by two threads, one of which was attached to the pendulum bob and the other to a fixed support The pendulum was free to swing It right angles to the plane of the threads, and any movement of this kind caused the mirror to rotate through an angle which was measured in the usual way by a telescope and scale. The method is susceptible of very great delicacy, but Messrs Darwin found that when the instrument was adjusted to be specially sensitive its manipulation became extremely difficult Wolfs modification of D'Abbadie's method appears to furnish, on the whole, the most promising apparatus for measurements of this type. The ap-paratus represented in fig. 10 is also applicable. The method of measurement employed in the case of s/ow finings may be called the equilibrium method in contradistinction to the inertia method, which is used to measure comparatively Wdden displacements. The two methods are applicable to two widely different classes of movements. It is at least possible that between these classes there maybe other modes of motion, - displacements which are too slow for the inertia method, and which give rise to too little change of slope for the equilibrium method. How to measure them is, and must apparently remain, an unsolved problem in seismomctry.
References. - The Report of the British Association for 1858 contains an account by Mallet of some of the older and now obsolete funs of seismometers (see also EARTI1QVAKE). For accounts of modern instruments of the inertia class, see the Transactions of the Seismological Society of Japan from ISSO, also Prof. Ewing's Memoir on Earthquake Measunntent, published by the university of Tokio (1855). References to papers on the equilibrium method or measure- ment have been made in the text (J. A. E.)