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V. Transverse Valleys.

Deep valleys are sometimes found of which the directions are nearly at right angles to that of the general elevation*.

a.

VI. Dykes or Veins, and Horizontal Beds of Trap.

The dykes are usually found in nearly vertical planes, and, when they occur in the vicinity of each other, with a general tendency to parallelism.

B Extensive beds of trap are found apparently interstratified with the stratified rocks.

VII. Granite Veins.

The form of a vein of this kind is frequently very different from that of mineral or trap-veins, as above described, inasmuch as a section of it does not generally approximate in the same degree to rectilinearity †.

These approximations to general laws have been, I believe, very generally recognized by geologists, and more especially in faults and mineral veins, in almost all cases in which these phenomena exist throughout districts of considerable extent; and this appears unquestionably to justify the notion, that they are not to be referred to partial causes, but to some cause general at least with reference to the district throughout which the same laws are observed to hold without breach of continuity. Local and accidental causes may in some cases act with sufficient energy to obliterate all traces of general laws in phenomena such as those above mentioned; but still this will manifestly not invalidate our inference with respect to those districts in which such laws have been clearly recognized. We may moreover

* These valleys may frequently be due in great measure to the effects of erosion. In some instances, however, they appear to have been obviously formed by the elevation of the strata on either side of them. The valley of the Wye, in Derbyshire, offers a beautiful example of this kind of formation.

+ Trap veins sometimes assume the tortuous form of a granite vein. See M'Culloch's Description of the Western Islands of Scotland. Vol. III. Pl. xxxiii.

observe, that the law of approximate parallelism which equally characterizes the phenomena of anticlinal lines, faults, and mineral veins, affords, à priori, a strong probability that they are all assignable to the same general cause. We may also further remark, that if, with the previous conviction that the stratified beds have been deposited from water, and with a knowledge of the physical impossibility of beds of uniform thickness being so deposited except on planes but little inclined to the horizon,—if, I say, under these circumstances, we examine many of the phenomena above mentioned, it seems impossible not to be struck with the idea of their being referrible to the action of some powerful elevatory force acting beneath the superficial crust of the globe, and thus producing those elevations and dislocations which we now witness. And, accordingly, such is the almost universal impression on the minds of geologists.

It appears, then, that we are arrived at that stage of geological science in which we are able to recognize certain well defined geological phenomena, distinctly approximating to geometrical laws; and we have also a distinct mechanical cause to which geologists, with almost one consent, have agreed in considering them to be assignable. The next step we are therefore called upon to take is obvious—it is to institute an investigation, founded on mechanical and physical principles, of the necessary relations which may exist between our observed phenomena and the general cause to which we attribute them. This investigation I have attempted, and now beg to lay it before the Society. I hope the nature of it will be deemed a justification of my introduction of a new term into the science, that of Physical Geology.

I have conducted the investigation by the methods supplied by mathematical analysis. I am aware, however, that to some persons the application of these methods to geological problems may appear like an affectation of an accuracy which the nature of the subject may not be conceived to admit of; but from this opinion I dissent entirely. We have, as I have before remarked, observed phenomena approximating to well-defined laws, and which we are prepared to regard as the effects of an assigned and definite cause; and to shew that this hypothetical

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cause is the true one, we must shew that, supposing all local and partial causes with which we are acquainted to be removed, it would produce effects strictly in harmony with those laws to which the actual phenomena are observed to approximate. The most obvious cause of deviation in our phenomena from strict geometrical laws, is irregularity in the intensity of the elevatory forces, and in the constitution of the masses on which they are supposed to act. Abstracting these sources of uncertainty, we have before us a definite problem, viz., to determine the nature of the effects produced by a general elevatory force acting at any assigned depth on extended portions of the superficial crust of the earth, and with sufficient intensity to produce in it dislocations and sensible elevations. To this simple and definite form the problem may be reduced; and at least a correctly approximate solution of it must necessarily be obtained by some means or other, before we can pronounce on the adequacy of the assigned cause to produce the observed effects. The complete solution of the problem presents many difficulties, which, however, are avoided by restricting ourselves to a first approximation, which will amply suffice for all practical applications of our results. This approximate solution

is what I have now to offer; and I may be allowed to observe, that those who may object to the mathematical resources of which I have availed myself, are at least bound to offer a solution equally conclusive and available by some method more adapted to the general reader. A slight examination however of the problem will suffice to shew that it can admit of no accurate solution independently of reasoning too intricate to be clearly embodied in any language but that of mathematical analysis.

The hypotheses from which I set out, with respect to the action of the elevatory force, are, I conceive, as simple as the nature of the subject can admit of. I assume this force to act under portions of the earth's crust of considerable extent at any assignable depth, either with uniform intensity at every point, or in some cases with a somewhat greater intensity at particular points; as for instance, at points along the line of maximum elevation of an elevated range, or at other points where the actual phenomena seem to indicate a more than ordinary energy of this subterranean action. I suppose this elevatory force, whatever may be its origin, to act upon the lower surface of the uplifted

mass through the medium of some fluid, which may be conceived to be an elastic vapour, or in other cases a mass of matter in a state of fusion from heat. Every geologist, I conceive, who admits the action of elevatory forces at all, will be disposed to admit the legitimacy of these assumptions.

The first effect of our elevatory force, will of course be to raise the mass under which it acts, and to place it in a state of extension, and consequently of tension. The increase of intensity in the elevatory force might be so rapid as to give it the character of an impulsive force, in which case it would be impossible to calculate the dislocating effects of it. This intensity and that of the consequent tensions will therefore be always assumed to increase continuously, till the tension becomes sufficient to rupture the mass, thus producing fissures and dislocations, the nature and position of which it will be the first object of our investigation to determine. These will depend partly on the elevatory force, and partly on the resistance opposed to its action by the cohesive power of the mass. Our hypotheses respecting the constitution of the elevated mass, are by no means restricted to that of perfect homogeneity; on the contrary, it will be seen that its cohesive power may vary in general, according to any continuous law; and moreover, that this power, in descending along any vertical line, may vary according to any discontinuous law, so that the truth of our general results will be independent, for example, of any want of cohesion between contiguous horizontal beds of a stratified portion of the mass. Vertical or nearly vertical planes, however, along which the cohesion is much less than in the mass immediately on either side of them, may produce considerable modifications in the phenomena resulting from the action of an elevatory force. The existence of joints for instance, or planes of cleavage in the elevated mass, supposing the regularly jointed or slaty structure to prevail in it previously to its elevation, might affect in a most important degree, the character of these phenomena. To a mass thus constituted, these investigations must not be considered as generally applicable. Vertical or highly inclined planes of less resistance, will only be assumed to exist partially and irregularly in the elevated

mass.

With these hypotheses then respecting the nature of the elevatory force, and the constitution of the elevated mass, I shall proceed in the next section to investigate the directions in which fissures will be formed in it when subjected to given internal tensions sufficiently great to overcome the cohesive power which binds together its component particles. These tensions, so far as this investigation is concerned, may either be supposed to be produced by external forces causing an extension of the mass, or by such as prevent that contraction of it which might be conceived to result from the loss of moisture or of temperature. It must be understood however that these internal forces are quite distinct from that sort of molecular action on which any kind of laminated or crystalline arrangement of the component particles may depend.

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