The tendency of this mass would be to produce a subsidence of the surface on which the original deposition took place, and on which the whole sedimentary mass reposed. If the solid crust of the earth were sufficiently thick, the depression would probably be insensible; but if the weight of the sedi mentary mass acted on a solid crust of large area, but not of a thickness greater than what we have already shown (art. 29.) to have been the probable thickness of those portions which have been subjected to great angular displacements, we easily perceive that slow but considerable subsidence would, under simple and probable conditions, be the necessary consequence. This reasoning would lead us to the conclusion that, in any proposed area, periods of great sedimentary deposition had been periods of gradual subsidence. Now that such has been actually the case, we have, I conceive, the most conclusive and independent evidence. The admirable researches of Professor E. Forbes seem to establish beyond doubt, that comparatively few species of marine animals are capable of existing in the full exercise of their animal functions at depths exceeding 1000 or 1200 feet. Consequently we may conclude that during the deposition of a mass of fossiliferous beds, having a thickness greater than 1000 or 1200 feet, there must have been a subsidence equal at least to the difference between the actual thickness of the stratified mass and that just mentioned; and if the stratification be conformable throughout, we may also conclude that the depression must have taken place, not by any paroxysmal movement, but by slow and gradual subsidence, a conclusion in exact accordance with that above enunciated.

Sir John Herschel was the first, I think, to direct attention distinctly to the possible effect of a great mass of sedimentary deposits, in depressing the portion of the earth's crust on which it rested. He also suggested the possible influence of the depression of one portion of the crust in producing an elevation of a neighbouring portion; and, in fact, if both portions were superincumbent on the same continuous mass of fluid or semifluid matter, such elevation would probably be the necessary consequence of the neighbouring depression. I am not aware however how far geological observations afford evidence of the synchronism of such opposite movements in adjoining areas.

Another consequence of sedimentary deposition was suggested, I believe contemporaneously and independently, by Sir John Herschel and Mr. Babbage. The temperature of sedimentary matter at the period of its deposition must be approximately that of the superficial temperature of the earth at the place of deposition, but the effect will be to increase the temperature of the mass beneath, by causing the rise of the internal isothermal surfaces. Any subjacent fluid mass would thus receive an accession of temperature which might again give to its expansive force sufficient energy to elevate and dislocate the superincumbent mass. The effectiveness of this cause in producing elevation, as well as the weight of sedimentary matter in producing subsidence, would manifestly be increased where the thickness of the crust should be comparatively small.

Mr. Babbage has deduced from this rise of the isothermal surfaces, an explanation of the slow upheaval of large areas, by referring it to the columnar expansion that must result from the augmentation of temperature in the subjacent rocks. This deduction however appears to me inadmissible. In the first place, if this theory were true, a period of great sedimentary deposition in any assigned area would be a period of elevation, instead of being (as we have above shown it must have been) a period of depression, since the rise in the isothermal surfaces would necessarily be contemporaneous with the process of deposition; and in the second place, the rate

of deposition must generally have been so exceedingly slow when considered with reference to extensive areas, as to leave little or no doubt, I think, that the positions of the isothermal surfaces at any proposed time during the process of deposition would approximate extremely near to that limit beyond which they could not have passed had the deposition ceased at that time. In such case, the ascent of the isothermal surfaces and the consequent columnar expansion would necessarily cease soon after the deposition of the whole sedimentary mass was completed, and could never be effective in raising the surface of the mass above the level of the sea. The theory would therefore fail to account for the elevation of the surfaces of whole continents to considerable heights above that level, the only great phænomenon of elevation, perhaps, which we could profess to account for by columnar expansion.

Section II. Vibratory Motions of the Earth's Crust produced by Subterranean Forces-Earthquakes.

33. In the preceding articles I have considered the mechanical effects of subterranean forces in elevating and dislocating the portions of the solid crust of the earth immediately superincumbent on the fluid matter, in which the elevatory forces have been supposed to originate. Other mechanical effects would also result from these sudden dislocations and the explosive action which would doubtless accompany them. The effects I allude to are the vibratory motions which would be excited in the solid or fluid masses in the immediate vicinity of the disturbed district, and propagated with great rapidity to others more remote. In those great disruptions which we have heretofore contemplated, these vibrations would be of great intensity near the regions where they originated, and it is possible that they might extend, in such cases, to very extensive portions of the globe, before their intensity should become sufficiently weakened to be no longer sensible. These secondary effects of the great elevating forces which have left so many phæ nomena as records of their primary effects, not being calculated to produce any permanent modification of character in the rocks through which the vibrations were transmitted, are matters of little interest to geologists as regards their existence at remote epochs; but they become, on the contrary, of especial interest when considered with reference to modern earthquakes. Many persons have regarded these phænomena as due in a great measure to vibrations like those just mentioned, and the subject has lately been brought under our notice in a memoir by Mr. Mallet, Ön the Dynamics of Earthquakes't, in which he has treated it in a more determinate manner, and in more detail than any preceding writer. I now proceed to consider the manner in which vibratory motions may be generated and propagated through a mass constituted like the crust of the globe. It will probably contribute to make the subject more easily understood if I begin by explaining the more simple cases of the propagation of such motions.

§ Explanation of different cases of the Propagation of Vibratory Motion. 34. The explanations of this subject become much simplified when the space through which the original disturbance producing the vibrations extends, is small compared with that into which they are subsequently propa

* "When the agitation produced by an earthquake extends further than there is any reason to suspect a subterraneous communication, it is probably propagated through the earth nearly in the same manner as a noise is conveyed through the air."-Young's Lectures on Natural Philosophy, vol. i. p. 717, 1807.

† Proceedings of the Royal Irish Academy, vol. xxi. part 1.

gated. I shall therefore commence the following explanations with this hypothesis. It should also be understood that the results deduced from the mathematical investigation of the problem depend on the assumption that the displacement of each vibrating particle from its place of rest, is very small, an assumption which may be considered as true to a sufficient degree of approximation in such vibratory motions as those frequently experienced in modern earthquakes, except at points so near the focus from which they proceed as to render the exception of little importance.

35. Propagation of Vibrations along a Cylindrical Tube.—The vibrations transmitted through fluids are more simple than those transmitted through solids. I shall therefore begin with the former case, and the explanations will perhaps be still further simplified if we conceive the fluid to be an elastic one, as atmospheric air. I shall also first take the case in which the vibrations are propagated along a cylindrical tube. Let us then suppose the tube AB of indefinite length to be filled with atmospheric air, and conceive a small disturbance of any kind instantaneously communicated in any manner to the portion of the fluid occupying the space pq bounded by transverse sections perpendicular to the axis of the tube, and then suppose the fluid to be left entirely to itself. In a very short time the vibratory Fig. 10.

motion will be entirely transferred from the particles originally disturbed, to others on the right and left, the particles first disturbed being left completely at rest. Let p'q' and pq, be the portions in a state of vibration at any time t. Each of these spaces may be termed a wave*, and each will have the same properties, the one being propagated to the right and the other to the left. Generally they will be of the same length. The particles beyond q' and p, respectively will not have begun their vibrations, and all those between p' and q, will have performed their vibrations and returned

to a state of rest.

(1.) The length p'q' (=l) of the wave will be constant.

(2.) The velocity (V) with which the wave will pass from one point to another (the velocity of propagation) is constant, and depends on the elasticity of the air.

(3.) Each particle will vibrate in succession exactly in the same manner. The time during which it will continue in motion, or that required for the 7 wave to pass over it, and is the same for each particle in succession. V'

=

(4.) The extent through which each particle moves in its vibration (the amplitude of vibration) is by hypothesis extremely small compared with the length of the wave; it will depend on the original disturbance. The direction of vibration will, at a sufficient distance from the original place of disturbance, be parallel to the axis of the tube, or perpendicular to the anterior and posterior bounding surfaces of the waves, those bounding surfaces being transverse sections of the tube perpendicular to its axis.

Waves of a more complicated character have properties, as we shall see, *This term has usually a more restricted and determinate meaning with reference to vibratory motions of this kind, but in our immediate application of the theory of vibrations to the subject before us, the term will be generally used in the sense defined in the text. We shall have little concern with that succession of vibrations of a peculiar type with which we are principally occupied in acoustics.

analogous to the above. It must be observed that these properties belong to the wave in its uninterrupted progress along the tube, and before it has been modified by reaching the extremity. We are not immediately concerned with the modification which will there take place.

In the propagation of these waves of vibratory motion, the particles of fluid are necessarily either condensed or rarefied, or they may be subject to alternate condensation and rarefaction during the period in which the wave is passing through them. They may therefore be termed waves of condensation or rarefaction. All substances, gaseous, fluid or solid, have some degree of compressibility, and are therefore capable of transmitting more or less perfectly waves of this nature. If the tube AB, for instance, were filled with water, a wave of this kind might be propagated along it, having properties exactly similar to those above stated for an aërial wave; but since the compressibility of water is so much less than that of air, the amplitudes of vibration will usually be much smaller. The velocity of propagation is also about four times as great in water as in air. It depends on the ratio of the elastic force of water to its density.

36. Propagation of Waves along the surface of Water in a uniform Canal. -In the transmission of vibratory motion through water as above described, the tube has been supposed to be completely filled with the fluid, so that no displacement of a particle from its place of rest could take place without condensation or rarefaction. If the fluid however exist in an open canal instead of a closed tube, it may transmit a wave of an entirely different character. For the greater simplicity, suppose the canal to be of uniform depth and width. Conceive a portion of the fluid occupying a part pq of the canal (fig. 11) to be disturbed, for example, by the sudden small elevation of the bottom of that part of the canal. The surface of the superincumbent fluid will be elevated in nearly the same degree, and being then left to itself Fig. 11.

will attempt to restore the horizontality of the fluid surface in obedience to the law of gravity, and will thus generate two waves p'q' and pq, which will be transmitted in opposite directions along the surface of the fluid. A wave of this kind will have the following properties, assuming the perfect fluidity of the fluid and the absence of friction along the sides of the canal. The depth is also supposed much less than the length of the wave.

(1.) The length (1) of the wave (not necessarily equal to pq) will be con

stant.

(2.) The velocity of propagation will depend on the square root of the depth of the canal nearly, that depth being much greater than the height

of the crest of the wave*.

(3.) Particles of the fluid situated in the same vertical section perpendicular to the axis of the tube, will have the same motion at the same instant. Every such section of particles will be carried in the direction of propa gation through a certain space, during the passage of the wave, and will then be left at rest. Consequently a wave of this kind will be attended by a current, the velocity of which will depend on the height of the crest of the wave and the depth of the canal.

(4.) The elevation of the bottom pq being sudden, as we have supposed,

* See Mr. Scott Russell's Experiments on Waves.

the front of the wave will be steep, the descent from the crest to the posterior boundary being a gradual slope.

The total difference in the characters of these two waves will be at once apparent. In the first case the waves depend entirely on the compressibility and elastic force of the fluid, the motions being independent of gravitation; the latter the motion depends on gravitation, and is independent of the compressibility and elasticity. In ordinary cases the velocity of propagation is very much greater in the former than in the latter kind of waves. In the larger disturbance which is necessary to produce the superficial wave of sensible magnitude, the disturbing force does not necessarily act with sufficient intensity at any instant to produce much compression, or therefore to cause a vibratory wave of the first kind of considerable intensity. When produced simultaneously, they will, in ordinary cases, separate very rapidly, on account of the great difference between the velocities with which they are propagated.

37. Waves propagated in Fluids in all directions from a centre.-The waves here contemplated are what I have termed waves of compression or dilatation. Let us suppose the original disturbance to take place in the interior of a fluid mass, perfectly or imperfectly elastic, the disturbance being restricted within a space which is small compared with that into which the wave subsequently diverges. The disturbing force being assumed, as in the preceding cases, to act only instantaneously, or for a very small space of time, the vibratory motion will be rapidly communicated to the neighbouring particles, leaving those originally disturbed at perfect rest. The space within which the vibratory motion will exist at any instant (i. e. the wave itself), will be comprised between two concentric spheres whose common centre is the centre of disturbance. At a sufficient distance from the origin the vibratory motion will be in a certain degree independent of the particular form of the original disturbance, and the wave will have the following properties.

(1.) The breadth (1) of the wave (which corresponds to what I have termed its length when propagated along a tube), measured by the difference of the radii of its exterior and interior surfaces, will depend on the time during which the cause exciting the vibrations continues to act. It will remain constant during the progression of the wave.

(2.) The velocity (V) with which the wave will be propagated along any radius will be constant.

(3.) The time during which each particle will vibrate will

(4.) The amplitude of the vibrations will decrease as the space through which the wave has expanded increases, being inversely as the distance of the vibrating particle from the centre of disturbance, when that distance is sufficiently great.

(5.) The direction in which a particle vibrates approximates more nearly to a line joining the particle and centre of disturbance, as the particle is further removed from the centre; and for a particle whose distance is sufficiently great, the direction of vibration sensibly coincides with that line*.

It is by waves of this kind that sound is propagated through the atmosphere or through water, the velocity in the former case being nearly 1200, and in the latter about 4800 feet per second.

Poisson's memoir, 'Sur la Théorie du Son,' Journal Polytechnique, Cahier 14. Also a memoir by the same author, Sur le Mouvement de deux Fluides superposées,' in the 'Mémoires de l'Institût,' vol. x.