Hence, then, we may conclude that the extension of the physical line ACB, under the circumstances supposed, will be at least equal, and generally greater, than that of any similar line in the higher portions of the uplifted mass. It seems also probable, that in cases occurring in nature the extensibility will be less in the lower portion of the elevated mass (at least to a certain depth) than in that which constitutes its upper surface. Now the tendency of any horizontal portion of the mass to separate, so as to form a vertical fissure, will vary directly as the extension, and inversely as the extensibility. We may therefore safely conclude, that when a mass has been elevated as above supposed, the greatest tendency to rupture will not be in its upper portion; and consequently, that if any fissure be produced, whether by a gradual increase of the horizontal tension, or by any more sudden impulsive action on the mass in its state of tension, such fissure will not commence at the surface, but at some lower part of the mass. 37. It appears, from what has been proved in the previous Section, that if we suppose the fissure produced solely by the tensions to which the mass is subjected, the plane in which it will lie will be perpendicular to the direction of the single system of tensions which, in this case, act upon the mass, and will consequently decline as much from a vertical plane as that direction deviates from horizontality. According to the hypothesis we have made, however, of the force acting on the elevated mass through the medium of an elastic vapour, this vapour will necessarily ascend into the fissure, and exert a fluid pressure on its sides, in a direction perpendicular to them, and of which the intensity may bear a considerable ratio to that of the tension. To form a rough estimate of this intensity, let r be the radius of the circle which shall most nearly coincide with the curve ACB (Fig. p. 41), p the pressure of the fluid on a unit of surface, T the intensity of the tension (supposed uniform) of the elevated mass estimated as in the previous section, and b the thickness of the mass. Then the whole tension exerted on a portion of the mass included between two vertical planes perpendicular to the axis of elevation, at a distance unity from each other, will bT, and we shall therefore have The value of r, according to the same rough approximation, will be AD nearly = 2 CD' which will always be very large; but as b also is probably large, p may bear a very considerable ratio to T Here then we have the case which has been anticipated in the investigation of Art. 20; and it appears that the action of this force p will greatly tend to increase the effect of any local causes in producing partial deviations in the plane of the fissure from a vertical plane, but that it will not alter generally its position when considered with reference to its whole extent. 38. Again, with respect to the comparative width of the fissure at different depths, it is manifest, taking the case of the Fig. p. 41, where the extension of each lamina is the same, that if the mass, when relieved from its tension by the rupture, return to its original horizontal length, the width of the fissure will be the same throughout its whole depth; and in the case of the Fig. p. 42, the same conclusion might be considered as very approximately true under the same hypothesis. If, however, the different laminæ, which I have supposed to have different powers of cohesion, have also different degrees of elasticity, this difference may materially affect any approximation to this uniformity of width. It seems probable, however, that the mean width (at least within certain limits) will rather increase than decrease with the depth. 39. Any number of these fissures might thus be formed simultaneously, (Art. 30.); and this simultaneous formation would be very much facilitated by the action of the pressure p in the interior of the fissure. If it be supposed, however, that partial causes prevent the commencement of the formation of each fissure at the same instant, exactly equal forces will not be exerted in the production of each, and consequently they will not be propagated with the same velocity. Some therefore will reach the exterior surface sooner than others; and when a certain number have thus been formed from the lower to the upper surface of the mass, the tension of it may become so far relaxed that the further formation of the others shall cease. We may therefore suppose it highly probable that the number of fissures formed in the inferior parts of the elevated mass, will be considerably greater than the number which reach the surface. 40. The phenomena, then, to which our investigation at present extends, may be represented as in the annexed diagram, a few of the fissures being complete ones, or running up to the external surface of the mass, and the others being incomplete ones, or rising to different heights, without reaching the surface. 41. If we recur to what has been previously advanced respecting the depths of veins, (Introd. II. p.), we shall see the importance of the fact established above, that the formation of fissures produced by the causes we have supposed must necessarily begin in some lower portion, and not at the upper surface of the mass, where it might perhaps at first sight be supposed more probable that they would begin. 42. We may also see, in what has been above stated, one cause of the inclination or hade of a fissure. (See Introd. II. x.) §. Formation of Transverse Fissures-Fissures of a Conical ElevationModification in the Position of Longitudinal Fissures. 43. In the case we have been considering, the whole tendency of the elevatory force, acting with perfect uniformity, will be, as we have before remarked, to produce longitudinal fissures; and a vertical section of the elevated mass parallel to the general axis of elevation, will be bounded above and below by straight horizontal lines. If, however, we now conceive this force to act with greater intensity at particular points along the general line of elevation, the section just mentioned will present such an appearance as represented in the annexed diagram, in which the line ABC, previously to the elevation, was horizontal. In such case we shall have longitudinal extension, (equal to the difference between the line ABC and the dotted line AC), which, if sufficiently great, will necessarily produce transverse fissures, similar to the longitudinal ones already described, and such as represented in the above section. 44. We may represent to ourselves this more intense action at particular points, by conceiving an additional force superimposed on uniform force producing the general elevation independently of the irregularities resulting from this partial action. It is manifest therefore that the tension perpendicular to the line of elevation will result from the sum of these forces, while the longitudinal tension will be produced by the superimposed force alone. The former will therefore, when the partial force is not great, be much the greatest; and we may consequently conclude, that the longitudinal fissures may in such case be formed first, during the continuous though rapid increase of intensity in the elevatory forces, according to the assumption we have made respecting them, (Art. 12.); and when this system is once formed (the fissures in it not being remote from each other), the transverse system must necessarily be approximately perpendicular to it, whether it be formed at the next instant, or at any succeeding epoch, and notwithstanding any irregularity in the forces producing it, provided they do not act impulsively. In this manner it is easy to understand the formation of a transverse system of fissures approximating to the law of parallelism, though resulting from forces which, acting partially, and under other circumstances, would produce the most irregular phenomena. 45. If however this more intense action at particular points be sufficiently great, and exactly simultaneous with that of the general elevatory force, it may modify materially the position of the longitudinal fissures. To determine the nature of this modification, we must consider the directions of the tensions which would be produced by an elevatory force, acting solely in the vicinity of any proposed point of a point of a mass; because such tensions superimposed upon those produced by a force acting uniformly along the whole range, will be very nearly equivalent to the tensions produced by the simultaneous action of two forces such as those just mentioned. 46. For the greater simplicity, we may take a cone as the approximate type of the partial elevation we have to consider. Let A'C'B' represent this cone, C'D its axis. Then if we assume the physical line A'pC' to be equally extended, and AD to be its original length, we have The original length of A'p: A'p: A'D: A'C', and therefore, A'D The original length of A'p = A'p. A'C' = A'm, |