Having satisfied himself that weight is the most eligible source of stability, the next step of the Engineer is to inquire what quantity of matter is necessary to produce stability, and what is the most advantageous form for its arrangement in a tower. The first question, which respects the mass to be employed, is, as already stated, one of the utmost difficulty, and can be solved by experience alone, directed by that natural sagacity which Smeaton, in his account of his own thoughts on the subject, with much naïveté, terms ‘feelings,’ in contradistinction to that more accurate process of deduction which he calls ‘calculation.’ It is very difficult, for example, to conceive that the waves could displace a cylindric block of granite, 25 feet in diameter and 10 feet high, which would contain about 380 tons, and we almost feel that they could not do so. If, in order to test the soundness of this expectation, we appeal to such experience as we possess, and apply to the largest vertical section of such a solid, the greatest force yet indicated by my brother’s Marine Dynamometer, which, as already stated, is 4335 lb. per square foot, we shall obtain a pressure of 484 tons, which, being reduced by one-half[8] for the loss of force occasioned by the convexity of the opposing cylindric surface, gives 242 tons, as the greatest force of the waves tending to displace the cylinder. But in the extreme case we have now supposed the solid will be entirely immersed in the water, and its efficient weight will thus be reduced by 140 tons, or the weight of an equal bulk of sea-water; and the remaining weight of 240 tons, by which it will resist the force of the waves, will be almost exactly equal to the pressure which they exert. This imaginary cylinder may, however, be regarded as still within the limits of safety, because the waves could not overturn it, unless their pressure exceeded the weight of the block in a ratio greater than that of its diameter to its height, which in this case is that of 25 to 10, or 2¹⁄₂ times. In order, therefore, to endanger the stability of the solid by overturning it, the pressure, instead of being 240 tons, must be 600 tons.[9] We have thus seen, that the cylinder is secure from the chance of being overturned; but we have yet to consider how far it is exempt from the risk of being displaced by the pressure of the waves, causing it to slide along the surface of the Rock, owing to deficiency of friction between the two surfaces in contact. The block, for our present purposes, may be regarded as monolithic, either being really so or as a mass composed of parts so united by joggles, treenails and mortar, as to be free from any tendency to disintegration by the force of the waves; and in this case the stability of the cylinder will depend upon the amount of friction opposing the pressure of the waves which tends to produce a sliding movement. It appears, by some experiments of M. Rondelet,[10] that the friction of a block of stone sliding on a chiselled floor of rock is equal to ⁷⁄₁₀ths of its own weight; and we should thus obtain in the present instance 168 tons, as the amount of friction tending to resist the pressure of the waves, which would therefore exert a power superior to that resistance by 74 tons.[11] But this excess of force would be easily neutralized by the adhesion of the mortar and the abutment of the block against the sides of the foundation pit into which Lighthouse Towers in such exposed places are generally sunk in the solid rock. When, in addition to these considerations, we learn that the solid frustum, or lower part of the Eddystone Tower, which has weathered so many storms for the last ninety years, does not greatly exceed in mass the imaginary cylindric block which I have spoken of, our confidence in the stability of the cylinder is greatly increased. Our belief receives a still farther confirmation from the fact, that the strongest instance recorded of the power of the waves, falls considerably short of the case which we have just imagined. The instance alluded to is given in Mr Lyell’s Geology, on the authority of the Reverend George Low, of Fetlar, in Zetland, who mentions, that a block, whose dimensions seem to give us reason to estimate its weight at nearly 300 tons (or about one-fifth less than that of the cylinder), was moved over a point, and thrown into the sea; and it must be remembered, that the form of this block, which was only 5 feet thick and about 40 feet long, rendered it very susceptible of a sliding motion, and must have greatly aided its transport. We may therefore not unreasonably conclude, that, in designing such a tower, it is safe to assume a mass which our own judgment and recorded facts seem to concur in pronouncing beyond the power of the greatest waves, as fixing the lowest limit to which the contents of the proposed edifice may be reduced.
[ [8] This reduction seems to be warranted by the results of some experiments of Bossut.
[ [9] This is the product of 240 tons, by the ratio of 2·5.
[10] L’art de bâtir.
[11] The number 168 is ⁷⁄₁₀ths of 240, which is the weight of the cylinder, reduced by the weight of an equal bulk of salt water; and 74 is the excess of 242 tons, the pressure of the waves, above 168, the amount of friction.
There are several circumstances, however, which tend to increase or diminish the stability of the same mass exposed to the same forces. Of these a very prominent one is the form of the mass, which may be so modified as to offer more or less resistance to the forces which assault the building. Thus a parallelopiped would be a much less suitable form for a sea tower than a cylinder, and so proportionally of all the polygonal prisms which may occur between these two extremes. I remember having heard it proposed, in the course of conversation, by a non-professional friend, that Lighthouse Towers might be formed in such a manner, that each horizontal section should be a wedge with its narrow end directed to the greatest assaulting force. This notion is in itself not destitute of ingenuity; for, if the circumstances to which it is to be adapted were constant, we should thereby present the form of least resistance, and, at the same time, the greatest depth and strength of the building to the line of greatest impulse. But the notion is wholly impracticable, because the direction of the winds and waves is so variable, as to render it almost certain that a Tower so constructed would, on some occasion, be assaulted in the line of its thinnest section; and thus, what might in one case be an advantage, would, in the event of such a change in the point of attack, become a great source of weakness, as the flat side of the wedge would then be opposed to the force, thereby presenting to the direct assault of the waves the largest surface, with, at the same time, the most disadvantageous disposition of the resisting matter. There seems little reason, therefore, for any doubt as to the circular section being practically the most suitable for a Tower exposed in every direction to the force of the waves.
Next to this, and hardly to be separated from it, inasmuch as it involves the question regarding the form of the Tower, is the position of the centre of gravity. The stability of any solid will, in general, greatly depend upon its centre of gravity being placed as low as possible; and the general sectional form which this notion of stability indicates is that of a triangle. This figure revolving on its vertical axis, must, of course, generate a cone as the solid, which has its centre of gravity most advantageously placed, while its rounded contour would oppose the least resistance which is attainable in every direction. Whether, therefore, we make strength or weight the source of stability, the conic frustum seems, abstractly speaking, the most advantageous form for a high Tower. But there are various considerations which concur to modify this general conclusion, and, in practice, to render the conical form less eligible than might at first be imagined. Of these considerations, the most prominent theoretically, although, I must confess, not the most influential in guiding our practice, is, that the base of the cone must in many cases meet the foundation on which the Tower is to stand, in such a manner, as to form an angular space in which the waves may break with violence. The second objection is more considerable in practice, and is founded on the disadvantageous arrangement of the materials, which would take place in a conic frustum carried to the great height which Lighthouse Towers must generally attain, in order to render them useful as sea-marks. Towards its top, the Tower cannot be assaulted with so great a force as at the base, or, rather, its top is entirely above the shock of heavy waves; and, as the conoidal solid should be prolate in proportion to the intensity of the shock which it must resist, it follows that, if the base be constructed as a frustum of a given cone, the top part ought to be formed of successive frusta of other cones, gradually less prolate than that of the base. But it is obvious, that the union of frusta of different cones, independently of the objection which might be urged against the sudden change of direction at their junction, as affording the waves a point for advantageous assault, would form a figure of inharmonious and unpleasing contour, circumstances which necessarily lead to the adoption of a curve osculating the outline of the successive frusta composing the Tower; and hence, we can hardly doubt, has really arisen in the mind of Smeaton the beautiful form which his genius invented for the Lighthouse Tower of the Eddystone, and which subsequent Engineers have contented themselves to copy, as the general outline which meets all the conditions of the problem which they have to solve. And here I cannot help observing, as an interesting, and by no means unusual, psychological fact, that men sometimes appear to be conducted to a right conclusion by an erroneous train of reasoning; and such, from his “Narrative,” we are led to believe, must have been the case with Smeaton in his own conception of the form most suitable for his great work. In that “Narrative” (§ 81), he seems to imply, that the trunk of an oak was the counterpart or antitype of that form which his (§ 246) “feelings, rather than calculations,” led him to prefer. Now, there is no analogy between the case of the tree and that of the Lighthouse, the tree being assaulted at the top, and the Lighthouse at the base; and although Smeaton goes on, in the course of the paragraph above alluded to, to suppose the branches to be cut off, and water to wash round the base of the oak, it is to be feared the analogy is not thereby strengthened; as the materials composing the tree and the tower are so different, that it is impossible to imagine that the same opposing forces can be resisted by similar properties in both. It is obvious, indeed, that Smeaton has unconsciously contrived to obscure his own clear conceptions in his attempt to connect them with a fancied natural analogy between a tree which is shaken by the wind acting on its bushy top, and which resists its enemy by the strength of its fibrous texture and wide-spreading ligamentous roots, and a tower of masonry, whose weight and friction alone enable it to meet the assault of the waves which wash round its base; and it is very singular, that, throughout his reasonings on this subject, he does not appear to have regarded those properties of the tree which he has most fitly characterized as “its elasticity,” and the “coherence of its parts.” One is tempted to conclude that Smeaton had, in the first place, reasoned quite soundly, and arrived by a perfectly legitimate process at his true conclusion; and that it was only in the vain attempt to justify these conclusions to others, and convey to them conceptions which a large class of minds can never receive, that he has misrepresented his own mode of reasoning. In the paragraph preceding that which refers to the tree (§ 80), he has, in point of fact, clearly developed the true views of the subject; and, with the single exception of the allusion to the oak, he has discussed the question throughout in a masterly style.
In a word, then, the sum of our knowledge appears to be contained in this proposition—That, as the stability of a sea-tower depends, cæteris paribus, on the lowness of its centre of gravity, the general notion of its form is that of a cone; but that, as the forces to which its several horizontal sections are opposed decrease towards its top in a rapid ratio, the solid should be generated by the revolution of some curve line convex to the axis of the tower, and gradually approaching to parallelism with it. And this is, in fact, a general description of the Eddystone Tower devised by Smeaton.
No. 1.
