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alluded to, (Introd. II. o, T,) presenting apparent horizontal displacements of the mass on one side of the unbroken veins, is not at first sight so easily accounted for, since it can hardly be regarded perhaps as physically possible that any horizontal pressure can have acted on the mass with sufficient intensity to produce an absolute displacement equal in many instances to the apparent one. A very ingenious mode has, however, been suggested” of explaining phenomena of this kind, by referring them to relative vertical movements of the masses in which the fissures have been formed. It will not be difficult to convey an idea of the manner in which this may be effected.

62. Let the annexed figure (1) represent a horizontal section at the

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surface, of two veins which intersect, both being somewhat inclined to vertical planes through AB, ED respectively. Now suppose the portion of the mass bounded by the horizontal surface MN, and the nearly vertical plane ABC" (Fig. 2.)+ of the vein AB, to be elevated (or the opposite portion to subside), so that the surface M'N' may be at a lower level than MN. If this change be effected by a movement parallel to the plane ABC' of the vein AB, CE (Fig. 1.) will assume the position C"E (Fig. 2.); and if EFG be a plane parallel to ABC", and intersecting the vein DCE (Fig. 1.) in EG (Fig. 2.) CEG will be the plane of the vein in the subsided mass, and it will no longer coincide with the plane DCC", the original plane of the fissure DCE. If we now conceive the higher portion of the mass to be removed by denudation, the general surface will coincide D. - d

* By the late M. Smidt. t The same letters denote the same points of the mass in the diagrams (1), (2), (3), (4).

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with M'N', and the broken plane of the vein will no longer intersect it in a continuous line, but as represented in (Fig. 3), along the broken

A. 4. B (3)

re line EC"C"D; thus producing the appearance of a horizontal movement of the mass on one side of the vein AB, relatively to that on the other.

63. That these phenomena cannot, in some cases, have been pro

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duced by actual horizontal movements, appears to admit of the most demonstrative proof; for it is sometimes found that when two veins

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intersect a third, both are apparently shifted horizontally, but in opposite directions, presenting the appearance represented in the preceding diagram (4), (a horizontal section), where C"D and c"d" are apparently so shifted, though it is manifestly impossible that they should be so heaved by any horizontal displacement of the mass containing them.

This case admits, however, of a perfectly simple explanation on the hypothesis of a vertical motion, provided the two veins, which are apparently shifted, hade or underlie in different directions. This will be immediately seen by a reference to the diagram (2), where dec" represents the plane of the second vein intersected by AB in the higher portion of the mass, and c'eg in the lower. The line ce' being parallel to CC", it is manifest that when C" coincided with C, c' would coincide with c; and consequently, after the denudation above supposed, the intersections of these veins with the exterior surface will present the appearance represented in (Fig. 4).

64. The case just described is admirably calculated to afford a decisive test, as to whether these phenomena have, or have not been produced by vertical movements, or rather by upward movements parallel to the plane of the unbroken rein. It is manifest that the explanation above given depends on the fact of the veins CD, cd, inclining in opposite directions, or more correctly, upon their intersecting the plane of the vein AB, in lines inclining towards each other from the parallel lines CC, cc respectively. Consequently, it may be stated in general terms, that if the two shifted veins incline in the same direction, the above explanation is inadmissible; but if, on the contrary, it be found that these displacements in opposite directions occur only in veins which hade in opposite directions, the truth of the explanation can no longer admit of a reasonable doubt.

65. Other cases also of the apparent displacement of a single vein, may afford most valuable evidence respecting the fact of the kind of elevation of which we have spoken. It is manifest, that whatever the case of displacement may be, the horizontal extent of it must depend on the following quantities: the inclinations of the planes of the broken and unbroken veins to the horizon (the complement of the angles which

measure the hades), the angle DCB (Fig. 1.) between their intersections with the horizontal surface, and the length of the line CC", which evidently measures the throw of the unbroken vein AB, produced by the supposed movement. To express the horizontal displacement of the vein in terms of these quantities, suppose a sphere described with center C in the previous diagram (2), or in the following one in which the same letters denote the same points as in (2)}, and any radius so as to

form the spherical triangle abc, by its intersections with the planes of the veins and the horizontal plane. Let

a = angle bac, the inclination of the plane DCC" of the broken vein to the horizon.

B = abc, the inclination of the unbroken vein to the horizon.

3 = ab = DCB the angle between the intersections of the veins with

the horizon.
bc = angle BCC",

h = CC", the throw of the unbroken vein.

Then shall we have cot 9 = cota. sin B cosec. 3 + cos 3. cot 8: and the apparent horizontal displacement C"C" = h . cot 6 = h {cot a . sin (3 cosec. 3 + cos 3 cot 3.

The quantities C"C", a, 3 and 3 can generally be obtained with very considerable accuracy, as may h also, when the mass in which the veins

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are formed is distinctly stratified. In such cases therefore, by comparing our observed and computed values of C'C'", we might obtain very accurate tests of the truth of the explanation which has been given of these phenomena.

66. The value of the explanation which has been given above of the phenomena we are now considering, consists in the substitution of vertical for horizontal movements, and therefore depends on the approximate verticality of the unbroken vein, parallel to the plane of which the motion is assumed to take place. It not unfrequently happens, however, that a horizontal displacement of a vertical vein takes place at the thin horizontal beds of moist clay, of which so considerable a number is found interstratified with the mountain limestone. The slimy nature of these beds undoubtedly affords a great facility for a relative movement of the masses respectively above and below them; and therefore where the displacement is small, there seems no difficulty in accounting for it on the supposition of this relative motion. In other cases a more probable cause may be found in the following considerations.

67. In the annexed figure let cd represent a thin stratum of clay,

of such a nature as to give a considerable facility to a relative horizontal motion of the masses above and below it, and suppose a fissure to have been propagated upwards by the action of horizontal tensions, from D to C. If there were no cohesion whatever between the upper and lower divisions of the mass, it is manifest that the position of DC would not in any degree influence the position of a fissure CE, which might be produced in the same manner and at the same time in the upper portion of the mass, and consequently the point C" would then

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