SECOND SERIES

Aet. L—Theory of EarUiquakes ; by Professer Alexis Perret,

of Dijon, France.* ^

Earthquakes are a complex phenomenon. It is difficult to refer thetn to one cause alone. The shocks or séries of shocks in a given région may hâve a spécial or local cause. We may distinguish a numberof such spécial causes acting independently of tbe principal cause whose gênerai action they modify. Moreover, tnese secondary causes may be modified in their action by the principal cause, the latter manifesting itself on]y through a dififerential resuit.

Among the phcnomena, it is diiiicult to distinguish those which are the eSects of the principal cause from those of spécial or local causes. The first aim of investigation should oe to détermine that difierential resuit in which the preponderating influence of the principal cause shall become manifest. For this

Eurpose the comparison of a great number of facts is requisite. >efore such a comparison, the local or anomalous influences disappear; or, in other words, the influence of the principal cause is brought into strong relief, the differential action making it manifest.

There is a periodicity as to times of occurrence in earthquakes, as in other cosmical and meteorological phenomena. When

^ Trenslnted for thîa Journal from n memoir communicated by the author entitlod PropoHtionê ntr Um Tremblemêntê de terre et Ut Voleanê ; formtdéei par M. Alxzii Pbkeet, Profeueur à la Faculté dei Seieneei de jDyon, adressées à M. LAMi. Membre de r Institut; 86 pp. 8vo. Paris, 1868. Mallet-Bachelicr, Quai des Augustins, 66.

Ooly tbe part on Earthquakes is hère reproduced.

Ax. JeuB. Sci.~S8COND SsBiKS, Vol. XXXVII, No. 109.— Jait., 1864.

s Alexis Perrey on Earthquàkes.

earthquakes, througb a long period, are grouped with référence to the moon's âge, two maxima and two minima of frequency may be distinguished in each lanar month, tbe maxima following immediately the syzygies, and tbe minima corresponding to tbe quadratures. Wben, again, they are grouped witb référence to tne passage of the rooou over the meridian, tbere are two analogous maxima and two minima, tbe maxima corresponding to tbe passage of the superior and inferior meridian, and tbe minima to the intermediate times.

Thèse laws, based, one on a comparison of more than 6000 days of earthquakes, and the otber on a thousand of earthquake shocks, show that there is a relation between tbe frequency of earthquakes and the rotation of tbe moon. Is tliis relation one of cause and eflFect? I believe so, after a careful study of tbe subject, and propose to présent the évidence.

Suppose the globe to bave a fluid nucleus, incandescent, and either liquid or viscous, with a solid crust. Suppose, aiso, tbe thickness of the crust to be such that tbe outer limit of the interior mass be a spheroidal surface, similar to that of the exterior of the sphère. The moon will exert attraction on the central nucleus, and tend to give it an elongated form; and tbe opposite protubérant parts, formed under the lunar action, will tend to lollow the Une which connects the centre of the moon with the centre of the earth, as this line changes its position witb référence to any fixed point on the earth.

Let us consiaer, first, the movement of the moon alone, leasing out of view the earth's orbital motion and rotation. The §reater axis of the elongated central nucleus would then be irected constantly towards the moon. The two opposite protubérances would exert pressure against the interior surface of the crust, and would tend to change its form ; and if the crust had but little thickness and were sufficiently elastic, it would at each instant take the form of the elongated nucleus. Thèse successive changes of form in the solid crust could not take place without causing vibrations which should occur periodically, like their cause, nor without altering, at each place, the direction of the plumb-line which would pass periodically througb tbe same positions. Thèse two periodical phenomena bave not yet been shown certainly to occur. Still a séries of observation, made througb several years by Mr. Airy, give us some reason to believe in their existence.

Suppose now the envelop or crust to bave so great thickness and such elasticity that it cannot take at once the form of tbe central nucleus. Pressure and tension in the crust of a greater or less amount will be the resuit, which will be a cause of fractures. Thèse fractures will be the starting point of molecular vibrations which znay be propagated in the crust to its surface

Alexis Perrey on Earthquakes. 8

and hâve tbe character of trae earthquakes. Such is the first or principal cause of the phenomenon.

Tho two opposite protubérances of the central nucleus together constitute, in their movement of rotation, what we call tbe great or primary earthquake or seismic wave. The greater the lunar influence, the greater will be the protubérances and the higher the seismic wave.

The sun should produce an analogous effect during tbe progress of tbe earth in its orbit. From this, a second seismic wave should resuit, which, in the case supposed, would also cause, when its crests pass under the points of least résistance, the same kind of subterninean movement

It is easy to conceive tbat in their simultaneous progress, thèse two seismic waves should add to, or diminish, one another, or coalesce in one wave, as with oceanic tidal waves. They will therefore manifest themselves at the surface onlj by their difTerential or their résultant efTects ; and their union will form the great luni-solar wave. Its effect will therefore be the greatest possible at the syzygies ; and hence the ruptures of the earth, conséquent thereupon, should be most fréquent at thèse two epochs in the lunar period.

Let us now take note of the diurnal motion of the earth. We now bave two new seismic waves; a lunar, the crests of which will change place under the meridian with the motion of our satellite, and a solar which will follow the course of the sun. Their effects on the inner surface of the earth's crust will bo similar to those of the first two waves mentioned above; and the resulting diurnal wave may be regarded under the same points of view as the luni-solar wave depending solely on the motion of the moon in its orbit.

In their progress, thèse différent waves are similar, or, at least, analogous, to those of the oceanic tides. They may be represented, in their movement, by a periodical function whose maxima and minima correspond to the maxima and minima of près* sure on the earth 's crust, which, supposing it homogcneous, will expérience at thèse points maxima and minima in change of ibrm, and consequcntly in frequency of fractures; and therefore maxima and minima in vibrations of the crust, or earthquakes.

Into thèse periodical functions of the seismic waves (or analytical expressions of the physical laws of the phenomenon) will enter necessarily the distances of tbe sun and moon from the earth. But the action beinç in the inverse ratio of the squares of the distances, the effect sliould be, under this point of view, great(ïr at the périgée than at the apogée. In accordance with this, I hâve found, tbat, relatively to the lunar motion, earthquakes are more fréquent at the périgée than at the apogée ; and

4 Alexis Perrey on Eiarihquaku.

relatively to the eartVs orbital motion, they are more fréquent at the winter solstice ihan at the summer, that is, at the périhelioD than at the aphelion.

Ail thèse waves are, physically, not single waves, bat are

g'oups of successive undulations, like the tidal in the océan, ence there must be a succession of "pressures and tensions in the passage of a seismic wave over a given point. Henoe, also, a possible, and probable, succession in the vibrations of the crust fience, also, an undulatory character in the earthquake shocks, with aJtemations of intensity during their passage.

Thus far, we hâve regarded the crust as having interiorly an ellipsoidal surface, and the central nucleos as liquid or viscous. Let us now suppose the nucleus the same, but the inner surfitoe of the crust as having irregularities like the outer, — ^that % xnountain élévations projectingânward, and immersed in the âuid xnass, and valleys whose dépressions are excavated in the crust Such an internai orographie system would modify the progreas of the seismic waves. A wave would rise and increase its velocity and, consequently, its active force, between two raountains or élévations that obstruct its passage; it would spread and lose velocity over a plain or in a valley where it could expand and •develop itself ; and would beat against the declivities or projections encountered. Hence a new kind of compression, and, therefore, of molecular vibrations, which should propagate themselves to the earth's surface, and anpear as earthquakes. Hence also, beyond question, some partial displacements in the walls of the vaulted crust, and ruptures causing vibrations more or less intense. Hence, also, fissures in the vault, of greater or less extent, and more or less abrupt.

An introduction of the incandescent liquid from the earthquake-wave into thèse fissures could hardly take place without ahocks or vibrations more or less apparent. But it is a question whether such vibrations would reach the earth's surface. This would dépend on their intensity; and also on the thickness and elasticity of the crust, which would necessarily hâve an important influence.

Thèse displacements and ruptures could not take place without Sound.

Whether the ruptures be a resuit of the altération of the form of the crust, under the pressure of a passing seismic wave, or of the shock of a wave against an internai protubérance, or of the contraction of the liquid material on its cooling after it bas entered a fissure, or of any other cause, they must always be accompanied by vibrations ; and thèse vibrations would propagate tbemselves to a greater or less distance, according to the condition and nature of the région.

Alexis Perrey on Earthquakes. 5

But are thèse fractures, as bas been said, tbe only cause of the souods wbicb so ofleu précède, accompany, or folio w, earthquakes ? It is dii&cult to believe it. We ackuowledge tbat we are not ready.to explain tbe sounds tbat so often précède eartbquakes. In the case of earthquake sbocks wbicb are continued for a lengtb of time, thèse sounds are oflen repeated : And bow does tbe sound-vibration differ from tbe dynamical vibration wbicb immediately follows it? Moreover, in sucb eartbquakeshocks, continued for a lengtb of time, botb aërial and subterra* nean détonations are frequently repeated without any sensible xnovement of tbe ground. Many instances of tbis kina occurred in tbe valley of Yisp in 1855 and 1856.' Tbe sounds are, in fact^ one of tbe most obscure éléments connected witb eartbquakes.

But to proceed, tbe ruptures wbicb take place at certain points in tbe crust shake tbe neigbboring parts, wbicb, in tbeir turn, under tbe action of successive earthquake waves, lead to other like fractures. Sucb catastrophes may again and again follow. We thus account for tbe sbocks wbicb are repeated ibr a greater or less time ailer every great earthquake.

The fractures openêd at any point will become prolonged in the direction of the line of least résistance. Hence cornes tbe change in the centre or focus of principal disturbance, wbicb is oflen noticed in the course of a long séries of sbocks.

Tbe introduction of the liquid material of the earth's centre into the fissures is not always efiected instantaneously. It may require more or less time ; and the vibrations thus caused may ^ take place after tbe passage of the earthquake*wave. Hence corne perturbations in the periodicity of the phenomenon,

It follows from thèse views, tbat eartbquakes should bave tbeir greatest regularity of march and greatest frcquency in a certain equatorial zone more or less wide ; and outside of tbis zone, similar efiects should be produced, proportioned in intensity to tbe différent eartbquake-waves, derived or reâected. But it is seen tbat tbe waves that are propagated laterally arrive later, rclatively to the passage of the moon over tbe meridian, at tbe places wbere the derivative currents go.

Wben thèse derivative or reflected waves, in any case, produce fractures, folio wed by vibrations wbicb continue for a lengtb of time, we should bave a prolonged shaking of a région in wbicb, otherwise, tbe phenomenon is of rare occurrence. Examples of tbis kind are the sbocks on the Mississippi in 1811 ; those of Maurienne in 1838 ; those of Scotland in 1842 and 1848.

* The détonations în tbo vàUej of Yisp continued to occur at intervais even tiU May, 1861. Tbe Inter roonths of tbe year do not appear to bave been marked by any répétition of tbe phenomena of 1866.— (Letters and Journal of M. Tscbeineo, curate at Gracben.)— Kote added August 26tb, 1662.

6 Alexis Perrey on Earthquakes.

The periodîcitj of the phenomenon may tnanifest itself again in the renewal of the sbocks. But the maxima and minima of frequency will not correspond with the passage of the principal seismic waves. The order may even be wholly reversed. It is a phenomenon analogous to the '* establishment of the port" in the oceanic tides.

The physical law, that earthquakes are more numerons at the syzygies than at the quadratures, is one that is ver iiied by simply counting the days of earthquakes during a sufficiently large number of j'ears. This I hâve done for a period of 50 years, from 1801 to 1850,' and alsoforeach ha]f of this period. Again, dividing tbese 50 years into 10 periods of 5 years each, I hâve detected two maxima and tvvo minima in nine of thèse partial periods. In seven, the maxima has occurred at the syzygies and the mioima at the quadratures; in two the reverse has taken place. The principal, above pointed out, of the establishment of the port is alone sufficient to explain this apparent anomaly. In thèse two 5-year periods, there was a séries of local shocks in a région where earthquakes are unfrequent.

The quinquennial period from 1810 to 1815 affords no sensible maxima and minima. But the facts on record are few. During the unhappy years of 1814, 1815, the journals took little note of subterranean commotions.

' Prof. Porrej bas made out, from the facts which he hoa collected. for tha first half of the présent century (from ISOl to 1850), that there were 63S8 lunar days on tehich eartliquakos occurred ; or, counting as 60 manv separato days, vhere S or 8 or nuire earthquakes occur oo the same day, but in distant countriea aod wbolly independent, (the most correct mctbod for his calculations,) 6596 lunar days. In order to refer thèse days to Ihe syzygies and quadrature», he divides the mean luna* lion of 29*53 dnyn intu 8 equal ]mrtR, and thcn groups thèse iuto 4, by uniling the Ist and 8th and 4th and 5 th. for the new and full moon or syzygies, and the 2nd and Sd and 6th and 7th for the quadratures.

Arranging thusthe phenomena, he obtained for the 5388 days, — 2761-48 at the syzygies and 2626 52 at the quadratures, leaving a différence in favor of the syzygies of 134-96.

For the 6596 days, he obtained 3434*64 at the syzygies and 8161*86 at the quadratures, leaving 273**28 in favor of the syzygies.

In a similar manner, fur the lialf century preceding, or from 1751 to 1800, he obtained 1901*18 earthquake days at the syzygies, and 1753*82 at the quadratures, the différence io favor of the syzygies being 147*86.

Counting the earthquake days during the years 1761 to 1800, vhich oocur within the periud of five days, from the second day before the apogée and périgée to tha second day after inclusive, he found 526 earthquake days at the perigec and 4654- Bt the apogée, leaving a différence of 60^ in favor of (he périgée ; or leaving off the outer two of the five days, the resuit was 318^ at the périgée and 278^ at tbe apogée, or an cxcess of 85 at the perigec.

Taking the earthquakes of Reggio in Calabria as given for the years 1836 to 1858 (18 yeani) in a Journal kept by M. S. Arcovito, be ânds 487 eartliquake shocln at the syzygies and 349 at the quadratures, or an ezcess of 88 at the syzygies. He also obtains, for the number of shocks when the moon was less than 45^ from the meridian 413, when more than 45^, 847, leaving 66 shocks in favor of the former.— 8ee for a fuller statement of thèse results, aod additioool facta, Oomptet Rendue, lu, 146-161, Jao. 28, 1861.

Alexis Perrey on Earthquakes. 7

We hâve above supposed the central nuclens of the eartli to be in an incandescent statc, eitlier liquid or viscous. But can this be without the existence of intense chemical action proportional to the bigh température of incandescence ? Under such circumstances woald tbere uot be electro-magnetic currents? May it not be tbat, through the influence of such currents, which Dr. Ami Boue makes the first cause of eartbquakes, and also under that of the various chemical actions going on, gnses M'ould be developed so as to form a more or less continuous atmosphère between tne central nucleus and the crust? And should not the présence of thèse gases modify in somo way, the dynamic action of the eartihquake waves ? Is not their sudden explosion, the cause, at times, of transient disturbances in the central mass ? And, consequently, are there not thence sensible reactions against the inner surface of the crust, causing strong vibrations that are propagated to the outer surface ?

This idea, which I bave elsewbere brought forward,* is remarked upon as follows by the learned author of the Histoire des Progrès de la Otohgie. **As to thèse immense tempests which the autlior raises at the surface of the incandescent âuid, whose waves of fire beat against the âanks of the mountains which project downward like gigantic stalactites, they appear to us to be a little remote from the domain of science and to pertain rather^o that of the imagination."

But, without taxing too much the imagination, can we not see that thèse chemical actions, which others bave made the sole cause of earthquakes, may produce some perturbations, or modifications, in earthquake movements which shall obscure at times the periodicity ?

Formerly, especially during the last century, the existence of numerous vast caverns in the eartb, for the propagation of earthquakes, was admitted. We do not deny the existence of such caverns; but, in our view, instead of their favoring earthquake vibrations they would arrest, or at least impede, them. The simplest break will modify the rate and direction of the undulations. But such caverns should also cause, in some cases, molecular vibrations which, on being propagated to the eartb 's surface, would not differ from ordinary earthquakes. The liquid matter, in entering the cavities, would also cause shocks of a similar kind. Hence may corne some of those facts registered in earthquake tables, which interfère with the exhibition of the periodicity.

We pass by other causes to which earthquakes bave been attributed. Several, although less gênerai than they bave been supposed to be, may be admitted among spécial or secondary causes.

* Memoir on the earthquakes of the Scandinavian peninsula, Voyage$ de la ComnuaUm SeunHfi^ue du Nord en Scandinavie, en Laponie, etc., Paria, 1846.

8 Akxis Perrey on Earthquakes,

It cannot be too offcen repeated, tbat earthquakes are not of one single kind, identically the ^ame. They are varions both in causes and efifects; I aim simply to bring ont in relief the principal cause. I seek to establish its truth, by the differential influence manifested in its march as regards time.

As to the geographical relations of earthquakes, I say only, that no région is secure from subterranean movements; and that no geological formation is exempt; but that the mountain Systems of the surface appear to exercise a great influence at leaat on their propagation if not on their frequency. The vibrations are usually propagated along the main axis of a cbain; as bas been observed in the Pyrénées and the Andes. In the great valleys occapied by rivers, the mean direction, as calculated by Lambert, appears to be that of the course of the dépression. I hâve shown this to be the fact with the basins of the Bhone and the Rhine, where the direction is nearly méridional, and the basin of the Danube, which bas a transverse course, or from west to east.

In France, the departments most subject to earthquakes appear to be those about the raouths of the large rivers. The départment of the Isère, where the dépression of the valley of the Rhône forms a kind of node with that of the Saône, is the only one which can compare with the kind just mentioned in number of earthquakes.

It is a question whether or not a double orthogonal curvature in the outer surface indicates an analogous structure through tbe whole thickness of the crust ; and whether or not a structure of this kind présents less résistance to the propagation of shocks.

Whatever may be the cause of the molecular vibration at any given point in the crust, vibrations will be propagated in the form of waves ; and in a homogeneous médium, the waves will be spherical and concentric. How will it then be in a médium which is not homogeneous, or is of unequal density ? This cannot be decided without investigation.

In the case of the propagation of a séries of waves which succeed one another through each point in the sphère of undulation and make successive shocks at the earth's surface, tbe shocks directly over the centre or focus of the vibrations will be vertical: and the obliquity, or variation from verticality, will be greater the more remote the place of émergence at the surface îs from the centre of vibration alluded to; or, the locality being fixed, the nearer this centre is to the surface.

There can be no^rotary shocks ; the cases of apparent rotation we bave explained elsewhere. But does the direction of a shock indicate the point from which it actually comes? I believe not The différence in the rocks encountered should produce dérivative and reflected undulations, as in the case of waves of soand.

Alexis Perrey on Earihquakes. 9

Breaks in the rocks, as the oayeras referred to, mast raodify their propagation, vary their direction and weaken their intensitjr, and may extinguish tbem; and this may account for the simultaneoos shaking of two régions while an intermediate locality is undisturbed — a phenomenon of so fréquent occurrence in certain parts of America that the people speak of it under the expression of the earth being bindged wùhin^ or siispended.

BoQssingault recognized, as the principal cause of the earthquakes of the Andes, the continuai and progressive siiding of tne dislo<^ted rocks of which they consist ; and he oonsidered the phenomenon as incessant in South America, an earthquoke taking place, in his view, somewhere in the Andes at every instant of time.

Thèse views are not at variance with my own. Any slidings due to gravity will be caused, or favored, by the daily vibrations vhose cfiTects and causes hâve been considered.

Calculation demonstrntes the existence of two kinds of waves moving with différent velocities around a centre of vibration ; I admit readily, with Mr. Wertheim, the coexistence of thèse two kinds of waves. If then there are several successive sets of vibrations at a given point, each will propsgate the double System of waves. It will be the same, also, if there are simulta* neous disturbances at a number of neighboring points. The waves t>î greatest velocity of one set will overtase and pass by those of least velocity in the preceding set, and at an interval of distance depending on the interval of time between the successive vibrations.

The ingénions idea that two species of waves or undulations pertaining to two successive sets of vibrations ma^ produce at the surface of the earth one vibration of combined intensity, bas nothing in it to which I can object. It is analogous to the interférence of waves of light. We also admit, with Mr. Wertheim, that two such combined waves may occasion greater violence of disturbance than the passage of two successive waves. In this case, the surface of the earth under vibration, if perfectlv homogeneous, should présent concentric zones in whicn the disturbance will be alternately more and less great. I would say, however, that I do not beliève that such an alternation of effects from earthquakes has ever been observed. For such results, not only would a uniformity in the earth's crust be required, but also tne structures on the surface to be upset or damaged should hâve fn identity of construction and of position with référence to the points of compass which cannot be looked for.

At some future time, I propose to consider, from this point of view, the occurrence of the first shock more or less light which précèdes often the ccreat shakings, and of the harmless vibrations which separate the disastrous shocks ; and also the short interval

▲m. Joub. Soi.— 43BCOND Ssbixs, Vol. XXXVII, No. 109.— Jav., 1864.

of relative repose or simple tremulousness wUch séparâtes iwo consécutive snocks of moderate inteosity.

As to the velocitj of the propagation of sliocks, we make no definite statement. NotwitnstaDding the trials of Dr. Julius Schmidt, we hâve no confidence in the résulta derived from bis calculations, believing that they are based ou too uncertain data.

The methods proposed by Mr. R. Mallet, will we doubt not^ if carried out, give an exact détermination of this élément in the phenomena of earthquakes. We recognize the importance of the problem. But even if the meana of noting time should be much better than at présent, and in more gênerai use, it may be doubted whether numerical results will be obtained of mnch value to science.

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