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Volume 6, 1873
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Art. XLVII.—On the Formation of Mountains; a Reply to the Rev. O. Fisher.

[Read before the Wellington Philosophical Society, 1st September, 1873.]

Having, at the last meeting, been requested by the President to lay before the Society my reply to the Rev. O. Fisher's critique, which appeared in the June number of the Geological Magazine, on my previous lecture on the formation of mountains, * I have now the honour to do so.

I have, in the first place, to thank Mr. Fisher for recalculating—more correctly, no doubt, than I have done—my table of the altitude of domes, and also for explaining several points which I had not clearly conceived before. Nevertheless, I think that I shall be able to show that his arguments against the theory that I have advocated are not well founded.

For the sake of conciseness I will, in what follows, call the theory that Mr. Fisher advocates the “contraction theory,” meaning thereby the theory of the formation of mountains by the secular cooling and contraction of the earth; while I will call the theory that I advocate the “deposition theory,” by which I mean the theory of the formation of mountains by the removal of matter from one portion of the earth and its deposition on another portion. In my lecture I called this latter the “Herschel-Babbage” theory, but I have since ascertained that Mr. Scrope was the first to suggest it, and it has therefore no right to the name that I applied to it.

(a.) The first argument that Mr. Fisher adduces against the deposition theory is, that any lateral pressure of expansion must be taken as strictly horizontal, and could not cause an upward rising. But the pressure relied on by Mr. Fisher to produce mountains is just as horizontal as the pressure produced by expansion, and if a cube foot of rock would be simply compressed by the horizontal pressure caused by expansion, why should not the effect be the same if the horizontal pressure was produced by the contraction of the nucleus? Practically we know that a perfectly horizontal sheet of dry paper stretched on a board will wrinkle when its dimensions are increased by damping; and the crust of the earth must do the same unless it crushes. From observation we know that anticlinal curves have been formed, and that the crust therefore does not always crush up.

Mr, Fisher also says that “we have no right to consider the crust rigid when regarded in proportions of sufficient dimensions to admit of these lateral pressures being otherwise than sensibly in the same straight line, but in opposite directions.” In his first paper, however, on the formation of mountains (Trans, Camb. Phil. Soc., 1869), he not only says that the portion of the

[Footnote] * See Trans. N.Z. Inst., Vol. V., App., p. xxv.

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“rigid” spherical shell that he is examining is kept in equilibrium by its attraction towards the centre (i.e., its weight), and by the pressures tangential to great circles round the circumference of the shell (i.e., the lateral thrust of the arch or dome), but he calculates the amount of the latter, and shows that it is independent of the size of the shell, except so far as the size alters the weight; and I really fail to see the difference between this and stating, as I did, that each portion of the rigid crust is partly supported by the lateral thrust of the arch.

(b.) Mr. Fisher explains very clearly that the interior could not rise higher than the surface by its own pressure, but it does not necessarily follow from this that “any abnormal elevation of a portion of such crust must be owing to lateral pressure,” because it might be owing to an increased upward pressure caused by the sinking of some adjoining area. This shows that the anticlinals could seldom attain the full amount of elevation shown in my table, for the abutments must sink; but the table shows an ample margin for such depressions.

(c.) Mr. Fisher says that the rocks would crush, and not rise up in anticlinals. But in order to crush there must be some space to crush into, and, by the deposition theory, it is the lower beds that are undergoing compression, while the upper are not; and, in order to relieve the compression, the upper beds must be forced up, either by fractures being formed and certain parts only raised, or else altogether, into one or more dome-shaped elevations. The last requires much the least work, and is therefore the way in which the pressure would be relieved. On the other hand, by the contraction theory, the upper beds are subject to the greatest compression, and, having no weight upon them, they would undoubtedly crush.

(d.) Mr. Fisher says that the specific gravity of the disturbed rocks ought to be less than it was before. This would be the case with the rocks causing the movement only while they were heated, and even then the difference would be too small to detect. When the rocks cooled they would go back to their original length by faulting, and the specific gravity would be the same as before.

These are all the arguments that Mr. Fisher can find against the deposition theory, and they virtually resolve themselves into this question: When rocks are expanded by heat do they, or do they not, crush up? The best answer is found by examining the rocks themselves, where we find that rocks which have been deeply buried, and which therefore must have been considerably heated, are not crushed but thrown into anticlinal and synclinal curves; and that the deeper they have been buried the more they have been folded, except when the burying occurred so long ago that the former more rapid conduction of heat outwards appreciably affected the result.

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Mr. Fisher then proceeds to attack my illustration of the theory from the Weald. But the Weald was not “adduced to give verisimilitude to this theory” as Mr. Fisher supposes, neither did I “pretend” to any precise measurements, as any unprejudiced reader will see, but it was given as an example of the way in which the theory might be tested in the field.

I have not access to any precise data as to the thickness of the beds, or the height or breadth of the anticlinal, and exact measurements would have been quite useless unless we also knew exactly the rate of expansion. In geological enquiries mathematical investigation can only be used as a check to our speculations, and as giving us a limit beyond which we cannot go. The average thickness of the cretaceous rocks was taken from Jukes' “Manual” (1862, p. 602), and the height of the hills in the Weald from Lyell's “Elements of Geology.” If the true thickness was under-estimated, by so much would my example tell against myself. The rocks below the wealden were not taken into consideration because they were the old surface, and had nothing to do with raising the temperature. Neither did I ever regard the wealden area as an isolated dome-shaped elevation, but the other elevated areas have, by the deposition theory, nothing to do with the amount of elevation of the Weald.

With regard to the latter part of the paragraph, it is, I believe, uncertain whether the tertiary rocks ever extended over the chalk or not; at any rate the fresh-water beds, as well as the vegetable remains of the London clay, show that land was then in the neighbourhood, which land must have been elevated since the deposition of the chalk in a deep sea. The depression succeeding the Woolwich beds no doubt took place after the dome of the Weald was formed; but I must leave these questions to be worked out by those geologists who have an intimate local knowledge of the district.

Hitherto I have confined myself to urging the claims of the deposition theory, but as Mr. Fisher says that he has “not had the good fortune to hear of the many arguments which have been urged against” the theory that he advocates, I will briefly state the reasons that have led me to reject the contraction theory as giving a sufficient explanation of the formation of mountains. I do so with the less reluctance, because nearly all rival theories in natural science must ultimately be weighed by the balance of probabilities, and it is therefore just as important to argue against a theory as to argue in favour of it. (Appendix.)

My reasons for rejecting the contraction theory are:—

1. Contraction of the earth could not produce any tangential pressures except in solid rock, so that the lateral compression must be confined to the rigid crust; consequently the more rapid contraction of the lower beds could only cause the upper beds to rise into anticlinals by one solid portion slipping horizontally over another

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solid portion. This is mechanically impossible, because the resistance to sheering would be far greater than the resistance to crushing when the area exposed to the compression was small compared to the area of the surface over which sliding has to take place. Neither in nature do we find any of these horizontal faults, which ought to be numerous and of considerable amount if the contraction theory be true. In the example, for instance, given by Mr. Fisher (Trans. Cam. Phil. Soc., 1869, p. 15, fig. 3), the central portion must have been faulted over the lower contracting beds for nearly half a mile. In this way utter confusion would reign in stratigraphical geology—palæozoic rocks would have slipped for miles over mesozoic rocks, granite over stratified beds, etc. It is quite certain that nothing of the kind has taken place in any portion of the earth's crust that has yet been examined. It is, however, accepted as probable by Professor Shaler (Geological Mag., V., p. 511); and Mr. Fisher also, when advocating the contraction theory, appears to see no difficulty in the thrust being extended through 50 miles of rock, although, when criticising the deposition theory, he says that the thrust can only be supposed to extend to an infinitesimal distance.

2. From the absence of any weight on the compressed rocks; from the impossibility of one part slipping horizontally over another; and from the absence of any support if any part should rise up into an anticlinal, we may, I think, confidently assert that the crust of the earth would simply crush up from the effect of contraction, and would rise uniformly over the whole surface. Mr. Fisher's formula, therefore, for the elevation should be h = ke instead of h=2 k m e.

3. If, however, it be granted—for the sake of argument—that the strata did not crush, but rose up on the lines of least resistance, it seems to me that these lines would take radiating directions from an area of depression; and that when these lines were once established, whatever their direction might be, elevation should be continuous on them. The theory, therefore, by itself appears to offer no explanation of oscillations in level. Professor Dana, however, seems to see no difficulty from this cause (Geology, 1863, p. 718, etc.), but he gives no explanation of it.

4. The same being granted as before: as the upper beds must undergo the greatest compression, the foldings would commence at the surface and would be propagated downwards in decreasing amount, and, as all sedimentary beds must once have occupied the surface, it follows that all strata should be more or less folded in proportion to their age, because the older they are the larger must have been the proportional area originally occupied by each. But we know that there are large districts in Russia and North America formed of undisturbed palæozoic rocks, while in Switzerland and Northern India tertiary beds are highly contorted.

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5.The theory also entirely fails to account for strata being elevated without disturbance, unless we suppose such an amount of horizontal slipping of one bed over another as is manifestly impossible.

6. If, however, as appears to me certain, the rocks must crush and rise tolerably uniformly, it is evident that the theory is quite inadequate to account for mountains; for, the contraction being universal, and the sea occupying the outer surface of the earth, the sea would rise more than the land, and the result would be that after the contraction the sea would stand higher above the land than it did before. In other words, the land would be said to have been depressed instead of having been elevated. If, therefore, we consider the earth when the crust was first formed, and it was surrounded by a universal ocean, we see that no land could rise above the water from contraction, but that, on the contrary, the ocean would gradually deepen. It was these considerations that led me to suppose that the first deposits were of organic origin, and that it was these deposits that first raised land above the water.

7. Mr. Fisher assumes, without giving any reasons, that since the date of the present surface features of the earth, a shell, 500 miles in thickness, has contracted as much as rock would do in passing from a fused to a devitrified state. But is this a reasonable assumption? I think not. It is certainly quite as reasonable to suppose, with Sir W. Thomson, that it is 100 millions of years since the crust of the earth cooled; and if we suppose that the oldest Laurentian rocks date from this period (which is the most favourable supposition that can be made for Mr. Fisher), then the Cambrian period will probably date about 50 millions of years ago; and, taking the thickness of formations as our guide, it is as reasonable a supposition as can be made that of the other 50 millions of years 39 were occupied by the rest of the palæozoic era, 9 by the mesozoic era, and 2 by the cainozoic era. So that, if we suppose the present features of the earth to have originated in the triassic period, it follows that 11 millions of years is the oldest date than can be assigned to any of them. This, by Fourrier's calculations of the rate of cooling of the earth— allowing for the slight increase of radiation in former times—is only sufficient to allow it to decrease 4° F. in temperature; and if we suppose that the whole of this heat was abstracted from the shell 500 miles in thickness underlying the crust, its temperature would be reduced by only 12° F., which is not nearly enough to give the amount of contraction supposed by Mr. Fisher.

8. We can look at this question in another way. If the surface of the earth has contracted, as Mr. Fisher supposes, one mile in a hundred since the present surface features originated, and the circumference is now 24,856 miles, it must at the time supposed have been 25,104 miles in circumference, and the radius, which is now 3,956 miles, must then have been 3,995 miles, so that it must have shrunk 39 miles. This in 11 millions of years would be

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11.9 yards in 2,000 years, the time during which we have astronomical observations, or 1 inch in 4 ½ years.

9. If, however, for the sake of argument, we allow Mr. Fisher all he asks, namely, that a mountain half a mile high might be formed on every 100 miles since the present surface features originated, we then find that, taking the date as before, Mr. Fisher's mountain has taken 11 millions of years to rise 2,640 feet, or it has risen only 1 foot in 4,166 years, which is slower than the ascertained rate of denudation.

Mr. Fisher, therefore, is in this dilemma: either the contraction of the earth's radius has been so rapid that astronomers ought to have detected it; or else elevation has been so slow that no land could rise above the sea level.

10. Another important objection to the contraction theory, is that mountains have always been formed in those places where deposits have been heaviest; while, by that theory, those areas should never rise at all. Mr. Fisher says that “the local pressure caused by a fresh deposit * * will originate a line of elevation along its shore line or boundary,” and again, “the thickness of the rigid crust being increased by the new deposit, it would offer an impediment to the elevation of ridges beneath it, and throw the whole disturbance into the region just outside its boundary.” This is exactly opposite to what we see in nature.

11. In my previous papers on this subject I have pointed out that mountains are formed on two different plans, the one being associated with volcanic rocks, the other with the crystalline schists; but the contraction theory supposes that all mountain chains are identically formed.

12. My last objection is, that this theory makes no provision for tension in rocks—everything is done by compression; while faults prove tension just as surely as contortions prove compression.

I am therefore of opinion that the effect on the crust caused by contraction has been very small, and that it has been totally obliterated by the much larger effects caused by deposition.

In conclusion, I wish to explain that I do not consider it necessary that the whole of an area must have been under water in order that it may be raised by the deposition of limestone; but that, owing to the lateral conduction of heat, one or more mountain ranges might project out of it as islands. Indeed, I believe that all high mountain ranges are the result of several subsidences and elevations, during which they may never have totally disappeared under the ocean.

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Extract from the Rev. O. Fisher's Paper “On the Elevation of Mountains by Lateral Pressure.” (Trans. Cambridge Philosophical Society, XI., 1869)

Let us call t the thickness of the crust, which has been thorwn into corrugations by the contraction of the subjacent stratum; and, for the sake of illustration, let us suppose one chain of mountains to be formed across every hundred miles of a great circle.

Let A B D C, fig. 1, be a vertical section of such a portion of the crust before the contraction of the stratum below it.

A B= 101 miles. A C = t. E B = 1 mile.

Then, owing to the contraction of the stratum below, A B D C will assume some such form as A M B D C, fig. 2, or fig. 3, where A B = 100 miles, and it is clear that the section of the elevated mass M being due to the shortening of the base of the rectangle A D by one mile (if we neglect compression), must be equal to the rectangle E D, i.e., to t square miles.

If then, as supposed, the crust be 25 miles thick, and, for simplicity's sake, we take an isosceles triangle for the profile of the upraised mountain mass, we shall get an isosceles triangle of 25 square miles on a base of 100 miles, which would give a range of mountains half a mile high. If only 50 miles out of the 100 were disturbed, as in fig. 3, the range would be a mile high, and so on. Such ratios would be rather greater than occur in nature, even allowing for subsequent denudation, so that the theory seems to be at any rate not deficient in its capability for producing the results attributed to it.