THE

AMERICAN

JOURNAL OF SCIENCE AND ARTS.

[SECOND SERIES.]

ART. I.—Theory of Earthquakes; by Professor ALEXIS PERREY, of Dijon, France.'

EARTHQUAKES are a complex phenomenon. It is difficult to refer them to one cause alone. The shocks or series of shocks in a given region may have a special or local cause. We may distinguish a number of such special causes acting independently of the principal cause whose general action they modify. Moreover, these secondary causes may be modified in their action by the principal cause, the latter manifesting itself only through a differential result.

Among the phenomena, it is difficult to distinguish those which are the effects of the principal cause from those of special or local causes. The first aim of investigation should be to determine that differential result in which the preponderating influence of the principal cause shall become manifest. For this purpose the comparison of a great number of facts is requisite. Before 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

1 Translated for this Journal from a memoir communicated by the author entitled Propositions sur les Tremblements de terre et les Volcans; formulées par M. ALEXIS PERREY, Professeur à la Faculté des Sciences de Dijon, adressées à M. LAMÉ, Membre de l'Institut; 36 pp. 8vo. Paris, 1863. Mallet-Bachelier, Quai des Augustins, 55. Only the part on Earthquakes is here reproduced.

AM. JOUR. SCI.-SECOND SERIES, VOL. XXXVII, No. 109.-JAN., 1864.

earthquakes, through a long period, are grouped with reference to the moon's age, two maxima and two minima of frequency may be distinguished in each lunar month, the maxima following immediately the syzygies, and the minima corresponding to the quadratures. When, again, they are grouped with reference to the passage of the moon over the meridian, there are two analogous maxima and two minima, the maxima corresponding to the passage of the superior and inferior meridian, and the minima to the intermediate times.

These laws, based, one on a comparison of more than 6000 days of earthquakes, and the other on a thousand of earthquake shocks, show that there is a relation between the frequency of earthquakes and the rotation of the moon. Is this relation one of cause and effect? I believe so, after a careful study of the subject, and propose to present the evidence.

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

Let us consider, first, the movement of the moon alone, leaving out of view the earth's orbital motion and rotation. The greater axis of the elongated central nucleus would then be directed constantly towards the moon. The two opposite protuberances 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. These 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 through the same positions. These two periodical phenomena have not yet been shown certainly to occur. Still a series of observation, made through several years by Mr. Airy, give us some reason to believe in their existence.

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

and have the character of true earthquakes. Such is the first or principal cause of the phenomenon.

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

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

It is easy to conceive that in their simultaneous progress, these 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 only by their differential or their resultant effects; 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, consequent thereupon, should be most frequent at these two epochs in the lunar period.

Let us now take note of the diurnal motion of the earth. We now have 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 be 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, these different waves are similar, or, at least, analogous, to those of the oceanic tides. They may be repre sented, in their movement, by a periodical function whose maxima and minima correspond to the maxima and minima of pressure on the earth's crust, which, supposing it homogeneous, will experience at these points maxima and minima in change of form, and consequently in frequency of fractures; and therefore maxima and minima in vibrations of the crust, or earthquakes.

Into these periodical functions of the seismic waves (or analyt ical expressions of the physical laws of the phenomenon) will enter necessarily the distances of the sun and moon from the earth. But the action being in the inverse ratio of the squares of the distances, the effect should be, under this point of view, greater at the perigee than at the apogee. In accordance with this, I have found, that, relatively to the lunar motion, earth. quakes are more frequent at the perigee than at the apogee; and

relatively to the earth's orbital motion, they are more frequent at the winter solstice than at the summer, that is, at the perihelion than at the aphelion.

All these waves are, physically, not single waves, but are groups of successive undulations, like the tidal in the ocean. Hence there must be a succession of pressures and tensions in the passage of a seismic wave over a given point. Hence, also, a possible, and probable, succession in the vibrations of the crust. Hence, also, an undulatory character in the earthquake shocks, with alternations of intensity during their passage.

Thus far, we have regarded the crust as having interiorly an ellipsoidal surface, and the central nucleus as liquid or viscous. Let us now suppose the nucleus the same, but the inner surface of the crust as having irregularities like the outer, that is, mountain elevations projecting inward, and immersed in the fluid mass, and valleys whose depressions are excavated in the crust. Such an internal orographic system would modify the progress of the seismic waves. A wave would rise and increase its velocity and, consequently, its active force, between two mountains. or elevations 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 appear 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 these fissures could hardly take place without shocks or vibrations more or less apparent. But it is a question whether such vibrations would reach the earth's surface. would depend on their intensity; and also on the thickness and elasticity of the crust, which would necessarily have an important influence.

This

These displacements and ruptures could not take place without sound.

Whether the ruptures be a result of the alteration of the form of the crust, under the pressure of a passing seismic wave, or of the shock of a wave against an internal protuberance, or of the contraction of the liquid material on its cooling after it has entered a fissure, or of any other cause, they must always be accompanied by vibrations; and these vibrations would propagate themselves to a greater or less distance, according to the condition and nature of the region.

But are these fractures, as has been said, the only cause of the sounds which so often precede, accompany, or follow, earthquakes? It is difficult to believe it. We acknowledge that we are not ready to explain the sounds that so often precede earthquakes. In the case of earthquake shocks which are continued for a length of time, these sounds are often repeated: And how does the sound-vibration differ from the dynamical vibration which immediately follows it? Moreover, in such earthquakeshocks, continued for a length of time, both aërial and subterranean detonations are frequently repeated without any sensible movement of the ground. Many instances of this kind occurred in the valley of Visp in 1855 and 1856. The sounds are, in fact, one of the most obscure elements connected with earthquakes.

But to proceed, the ruptures which take place at certain points in the crust shake the neighboring parts, which, in their turn, under the action of successive earthquake waves, lead to other like fractures. Such catastrophes may again and again follow. We thus account for the shocks which are repeated for a greater or less time after every great earthquake.

The fractures opened at any point will become prolonged in the direction of the line of least resistance. Hence comes the change in the centre or focus of principal disturbance, which is often noticed in the course of a long series of shocks.

The introduction of the liquid material of the earth's centre into the fissures is not always effected instantaneously. It may require more or less time; and the vibrations thus caused may take place after the passage of the earthquake-wave. Hence come perturbations in the periodicity of the phenomenon.

It follows from these views, that earthquakes should have their greatest regularity of march and greatest frequency in a certain equatorial zone more or less wide; and outside of this zone, similar effects should be produced, proportioned in intensity to the different earthquake-waves, derived or reflected. But it is seen that the waves that are propagated laterally arrive later, relatively to the passage of the moon over the meridian, at the places where the derivative currents go.

When these derivative or reflected waves, in any case, produce fractures, followed by vibrations which continue for a length of time, we should have a prolonged shaking of a region in which, otherwise, the phenomenon is of rare occurrence. Examples of this kind are the shocks on the Mississippi in 1811; those of Maurienne in 1838; those of Scotland in 1842 and 1843.

* The detonations in the valley of Visp continued to occur at intervals even till May, 1861. The later months of the year do not appear to have been marked by any repetition of the phenomena of 1855.-(Letters and Journal of M. Tscheinen, curate at Græchen.)-Note added August 26th, 1862.