chapter I

purpose, in the first place, to make a few observations regarding the construction of Lighthouse Towers in situations which are exposed to the assault of the waves, and afterwards to give a short notice of the design which I adopted for the Tower on the Skerryvore Rock. In making a design for a Lighthouse Tower in an exposed situation, numerous considerations at once present themselves to the Engineer; and it is difficult to assign to any one of them a priority in the train of thought which eventually conducts him to the formation of his plan. These considerations, however, may be conveniently divided into two classes:--_1st_, Those which refer to elements common to Lighthouses in all situations, and differ only in amount, such as the height of the Tower necessary for commanding a given visible horizon, and the accommodation required for the Lightkeepers and the Stores; and, _2d_, Those which are peculiar to Towers in exposed situations, and which refer solely to their fitness to resist the force of the waves which tend to destroy them. The first class of considerations is so extremely simple, as to require few remarks in this place. The distance at which it is desirable that a light should be visible being ascertained, with reference to the nature of the surrounding seas and the extent to which any dangerous or foul ground lies seaward of the proposed Lighthouse, the height of the Tower is at once determined by means of the known relations which subsist between the spheroidicity of the earth, the effects of atmospheric refraction, and the height required for an object which is to be seen from a given distance. The question regarding the space to be provided in the interior of the Tower, can only be properly answered by a person who has a minute practical acquaintance with the peculiar wants and the internal economy of Lighthouses. The accommodation required for Lighthouses in exposed situations must, in a considerable degree, depend upon the greater or less facility of access to them, and the opportunities for replenishing the stores of all kinds which are in daily consumption. In such places, also, the risk of accidents naturally leads to the precaution of retaining additional Lightkeepers, and of having duplicates or even triplets of those parts of the apparatus that are liable to be injured. Of such circumstances, corresponding extension of the space devoted to the reception of Stores and the accommodation of the Lightkeepers, is the necessary consequence. In the long nights of a Scotch winter, when the lamps are kept burning for about seventeen hours, during which time they are never left for a moment without the superintendence of at least one Keeper, the care of the light, even in the most favourable situations, necessarily occupies at least two persons; but in places like the Eddystone, the Bell Rock, and the Skerryvore, where it sometimes happens that six or eight weeks elapse without its being possible to effect a landing, it has been thought necessary that there should never be fewer than three Keepers on duty. This addition to the ordinary establishment of a Lighthouse calls for a greater number of sleeping-cabins, and, at the same time, involves a corresponding increase in the supply of water, fuel and other provisions, requiring much additional stowage. So far, therefore, a Light Tower in an exposed situation, differs from one on shore only in the extent of its internal accommodation.

The second class of considerations, which must guide the Engineer in framing a design for a Light Tower which is exposed to the force of the waves, refers solely to the stability of the building.

The first observation which must occur to any one who considers the subject is, that we know little of the nature, amount and modifications of the forces, on the proper investigation of which the application of the principle which regulates the construction must be based. When it is recollected, that, so far from possessing any accurate information regarding the momentum of the waves, we have little more than conjecture to guide us, it will be obvious, that we are not in a situation to estimate the power or intensity of those shocks to which Sea Towers are subject; and much less can we pretend to deal with the variations of these forces which shoals and obstructing rocks produce, or to determine the power of the waves as destructive agents. No systematic or intelligible attempt has been made practically to measure the force of the waves, so as to furnish the Engineer with a _constant_ to guide him in his attempts to oppose the inroads of the ocean. The only experiments, indeed, on the subject, with which I am acquainted, are those of Mr Thomas Stevenson, Civil-Engineer, who had long entertained the idea of registering the force of the impulse of the waves, and lately contrived an instrument for the purpose, which he has applied at various parts of the coast. I therefore gladly avail myself of the present opportunity, to give a brief statement of the results indicated by it, as contained in a paper by the inventor, which appeared in the Transactions of the Royal Society of Edinburgh of 20th January 1845, and of which a digest will be found in the Appendix, as any attempt to throw light upon this most obscure, but highly important subject, cannot fail to be interesting, not merely to the philosopher, but to the Marine Architect. It would naturally be expected, that the force of the waves should vary according to the season of the year, and the nature of the exposure, and this expectation is fully justified by the indications of the Marine Dynamometer. Thus it appears, that during five summer months of 1843 and 1844, the average indications registered at different places near Tyree and Skerryvore, gave 611 lb. of pressure per square foot of surface exposed to the waves; while the average for the winter months for the same places during those two years, gave 2086 lb. per square foot, or upwards of _three times_ that of the summer months. It also appears, that the greatest result as yet obtained at Skerryvore Rock was 4335 lb. per square foot; while that observed on the Bell Rock was 3013 lb., or _one-fourth part_ less than that of Skerryvore. But these experiments have not been continued long enough as yet to render them available for the Engineer. In the present state of our information, therefore, we cannot be said to possess the elements of exact investigation, and must consequently be guided chiefly by the results of those numerous cases which observation collects, and which reason arranges, in the form which constitutes what is called _professional experience_. This kind of experience can only be acquired by long habit in carefully observing the appearance and effects of waves in different situations, and under various circumstances. We must attend to their magnitude and velocity, their level in regard to the rocks on which they break, the height of the spray caused by their collision against the shore, the masses of rock which they have been able to move, and those which have successfully resisted their assault; as also, where such exist, the slopes of the shores produced by the waves, viewed in connection with the nature of the materials composing the beach, with many other transient features which an experienced eye seizes and fixes in the mind as elements of primary importance in determining the power of the sea to produce certain effects. Such phenomena, with all their features and circumstances, we may carry in our recollection; and by comparing them with what has been observed at places where we know that artificial works have resisted the shocks of the waves, we may in some cases successfully arrive at a conclusion as to what works will, at all events, be within the bounds of safety. We must not, however, in any case, venture to approach too near the limit of stability, so long as we continue to labour under our present disadvantages of defective information on some of the most important elements in the inquiry. If it be asked, therefore, how the size and form of buildings exposed to the shock of the waves are to be determined, the answer must be, that, in any given case, the problem is to be solved chiefly by the union of an extensive knowledge of what the sea has done against man, and how, and to what extent, man has succeeded in controlling the sea; together with a cautious comparison of the circumstances which modify and affect _any given case_ which has not been the object of direct experience; nor does it seem possible as yet to found the art of Engineering, in so far as it refers to this class of works, upon any more exact basis. The uncertainty which must ever attend such reasoning can only, it is obvious, be dispelled by actual experience of the result; and time only can test the success of our schemes in cases of difficulty.

* * * * *

A primary inquiry, in regard to Towers in an exposed situation, is the question, whether their stability should depend upon their _strength_ or their _weight_; or, in other words, on their _cohesion_, or their _inertia_? In preferring _weight_ to _strength_, we more closely follow the course pointed out by the analogy of nature; and this must not be regarded as a mere notional advantage, for the more close the analogy between nature and our works, the less difficulty we shall experience in passing from nature to art, and the more directly will our observations on natural phenomena bear upon the artificial project. If, for example, we make a series of observations on the force of the sea, as exerted on masses of rock, and endeavour to draw from these observations some conclusions as to the amount and direction of that force, as exhibited by the masses of rock which resist it successfully and the forms which these masses assume, we shall pass naturally to the determination of the _mass_ and _form_ of a building which may be capable of opposing similar forces, as we conclude, with some reason, that the mass and form of the natural rock are exponents of the amount and direction of the forces they have so long continued to resist. It will readily be perceived, that we are in a very different and less advantageous position when we attempt, from such observations of natural phenomena, in which _weight_ is solely concerned, to deduce the _strength_ of an artificial fabric capable of resisting the same forces; for we must at once pass from one category to another, and endeavour to determine the _strength_ of a comparatively _light_ object which shall be able to sustain the same shock, which we know, by direct experience, may be resisted by a given _weight_. Another very obvious reason why we should prefer _mass_ and _weight_ to _strength_, as a source of stability, is, that the effect of mere _inertia_ is constant and unchangeable in its nature; while the _strength_ which results, even from the most judiciously disposed and well executed fixtures of a comparatively light fabric, is constantly subject to be impaired by the loosening of such fixtures, occasioned by the almost incessant tremor to which structures of this kind must be subject, from the beating of the waves.[7] Mass, therefore, seems to be a source of stability, the effect of which is at once apprehended by the mind, as more in harmony with the conservative principles of nature, and unquestionably less liable to be deteriorated than the _strength_, which depends upon the careful proportion and adjustment of parts.

[7] It was chiefly on these grounds that the Commissioners of Northern Lights, after consulting a Committee of the Royal Society of Edinburgh, and Messrs Cubitt and Rennie, Civil Engineers, rejected the design of Captain Sir Samuel Brown, R. N., who volunteered a proposal to build an Iron Pillar at the time that the erection of the Skerryvore Lighthouse was determined on in 1835.

* * * * *

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.

* * * * *

[Illustration: No. 1.]

It is deserving of notice, as one of the many proofs which the records of antiquity afford of the similarity of the results of human thought in all ages, and of the truth of the Wise Man’s saying, that “there is nothing new under the sun,” that the ancient Egyptians appear to have had the same conceptions of the solid of stability that were present to the mind of the modern Engineer of the Eddystone Lighthouse. In the admirable work recently published by Sir J. Gardner Wilkinson on the Manners and Customs of the Ancient Egyptians, he gives, in the first volume of his second series, at page 253, a wood-cut, shewing the figure of the deity Pthah, under the symbol of stability, according to Egyptian conceptions. This symbol so closely and strikingly resembles the general appearance of the Eddystone, that I willingly give it a place in the text, (No. 1) denuded, however, of the arms and head-dress of the deity whom it shrouds.

* * * * *

In applying these general notions to the design of a Tower for the Skerryvore Rock, I was, of course, guided by numerous circumstances, which modified my views and produced the individual form of Tower which I have adopted. Since the days of Smeaton, when his magnificent Tower was lighted by common candles, the application of optical apparatus to Lighthouses has greatly altered the state of the case; and the improvement of the system in modern times has, in most instances, rendered a greater altitude of Tower desirable, in order to extend, as much as possible, the benefit of a system capable of illuminating the visible horizon of any Tower which human art can reasonably hope to construct. In the particular case of the Skerryvore, also, the great distance of the outlying rocks (some of which, as will be seen from the chart, are 3 miles right seaward of the Lighthouse) concurs with the improvement of the Lights, in making it desirable that the Tower should be of considerable height, and that the light should command an extensive range. It was, therefore, from the first consideration of the subject, determined that the Light should be elevated about 150 feet above high water of spring tides, so as to illuminate a visible horizon of not less than 18 miles of radius; and, after much deliberation, and a full consideration of the infrequency of communication with the proposed Lighthouse from the great difficulty of landing on the Rock, and the consequent uncertainty of keeping up the supplies, I found that, for the convenient accommodation of the Lightkeepers and the suitable stowage of the stores, a void space of about 13,000 cubic feet would be required. These elements being fixed, the general proportions of the Tower came next to be considered.

* * * * *

In the Eddystone the radius of the base, at the level of high water of spring tides, is somewhat less than _one-fifth_ of the height of the Tower above that level; while in the Bell Rock, at the same level, it is little more than _one-seventh_ of the height. If, again, we suppose the curve of the Eddystone to be continued downwards to the level of low water, the radius (in so far as we may judge from sketching the continuation of a curve undefined by any geometrical property) would be rather more than _one-fourth_ of the whole height above that level; while in the Bell Rock the proportion, in reference to the same level, is a little more than _one-fifth_. Viewing the whole height of the Skerryvore Tower above _high water_ of spring tides as equal to 142 feet, and finding that, in the cases of the Eddystone and the Bell Rock, the radius of the horizontal section at that level is respectively _one-fifth_ and _one-seventh_ of the whole height; and again, viewing the extreme height of the Skerryvore Tower above _low water_ of spring tides as equal to about 155 feet, and considering the proportionate radii of the Bell Rock and Eddystone (in so far as the latter is ascertainable) as respectively _one-fifth_ and _one-fourth_ of the heights of the top of the masonry above the level of low water, I finally decided upon giving the Tower at the Skerryvore such dimensions as would not be widely discordant with these general proportions. In this view, I determined that the radius of the base should not exceed 22 feet, on the level of about 4 feet above the high water mark, where I expected to obtain a solid foundation--a base which bears to the whole height of the Tower a proportion somewhat _less_ than that of the Bell Rock, which is _one-fifth_. It so happens, that the diameter adopted is nearly the greatest which the Rock affords; for, although a glance at the accompanying plan of the Rock at high water (Plate, No. III.) would lead one to suppose that a more extended base might have been obtained, I found, after many careful examinations of the gullies and fissures which intersect it, that some of the concealed fissures run much farther into the Rock than might at first be imagined. The adoption of a much larger base, even had it been otherwise advisable, would therefore have involved some risk of the external ring of stones of the lowest course giving way by the yielding of an unsound part of the outer portion of the Rock to the pressure of the superincumbent mass, and might eventually have led to the destruction of the Tower.

[Illustration: No. 2.]

The height of the Pillar having been finally fixed at 138·5 feet, and the radius of the base, at the level of about 4 feet above high water, at 21 feet, I next proceeded to consider the details of its proportions. Of the whole height of 138·5 feet, 18 were to be absorbed in a suitable capital for the Pillar, consisting of a parapet for the Lantern, an abacus, a cavetto, and a belt separating these from the shaft. The internal void I determined should be 12 feet in diameter, as the size most suitable for the reception of the lantern and apparatus; and this, combined with the choice of about 13,000 cubic feet of void already mentioned, fixed the height of the solid frustum at the base of the Tower at about 26 feet above the foundation. Having farther decided that the thinnest part of the walls, immediately under the belt-course which separates the capital from the shaft, should not be less than 2 feet thick, as necessary to give due solidity and strength to the walls, and prevent, by the breadth of the joints, the percolation through the walls of the water which might be furiously dashed against them in storms, I had nothing farther to do but to determine the nature of the line which should connect the extremities of the top and bottom radii of the Pillar. As I had already concluded that this line must, as in the Eddystone and Bell Rock, be a curve line, concave to the sea, I next proceeded to try the effects of various curves traced between these points, in giving a convenient and advantageous disposition of the materials, with regard to both the thickness of the walls and the mass of the solid frustum at the base of the Tower. These two points, as will be better understood by means of the accompanying diagram (No. 2), are separated from each other vertically 120·25 feet, and are horizontally distant from each other 13 feet, which is the excess of the bottom radius over that of the top of the shaft, or the consequent amount of what may be called the _aggregate slope_ of the wall. The solid generated by the revolution of some curve line about the vertical axis of the building then becomes the shaft of the pillar. For this purpose I tried four different curves, the Parabola, Logarithmic, Hyperbola, and Conchoid, figures of which, upon the same scale, will be found in Plate, No. IV., with the position of the centre of gravity, which was carefully calculated, marked on each. The logarithmic curve I at once rejected, from its too near approach to a conic frustum, and the excessive thickness of the walls which such a figure would produce, where the hollow cylindric space for the internal accommodation commences at the level of 26 feet above the base. The parabolic form displeased my eye by the too rapid change of its slope near the base; and I had some difficulty in reconciling myself to the condition of the exterior ring of stones at the base, too much of the outer portion of each stone being left without the advantage of direct pressure from the superincumbent mass of the wall above. The two remaining pillars, derived from the hyperbolic and conchoidal[12] frusta, are nearly identical in form; and of these two curves I preferred the former, which gives the most advantageous arrangement of materials, in regard to stability, of all the four forms. This quality of advantageous proportion exists in these forms, in the ratio of the numbers in the last column of the following table:[13] which shews a slight superiority of the Hyperbolic over any of the other forms.

+------------+------+-----------+--------+---------+-----+----------+ | | | | Volume | Distance| | | | |Height| Diameter | of | of | | | | |of the| | | solid |centre of| | Economic | | | Tower| at | at | Tower | Gravity | |Advantage.| | | in | Base| Top |in cubic| from | H | G·M. | |Hypothetical| feet.| in | in | feet. | Base. | - | ------ | | Towers. | (H.)|feet.|feet.| M. | G. | G | G′·M′. | +------------+------+-----+-----+--------+---------+-----+----------+ |Hyperbolic, | 120 | 42 | 16 | 62,915 | 41·227 |2·911| 1·00000 | |Conchoidal, | 120 | 42 | 16 | 62,984 | 41·336 |2·903| 0·99627 | |Parabolic, | 120 | 42 | 16 | 63,605 | 43·400 |2·765| 0·93963 | |Logarithmic,| 120 | 42 | 16 | 74,742 | 42·460 |2·826| 0·81608 | |Conical, | 120 | 42 | 16 | 84,737 | 43·280 |2·773| 0·70725 | +------------+------+-----+-----+--------+---------+-----+----------+

[12] The solid, in this case, would have been formed by the revolution of the interior conchoid of Nicomedes about its directrix; and its co-ordinates were kindly calculated for me by my late revered preceptor, Dr WALLACE, Professor of Mathematics in the University of Edinburgh, who employed so many hours of his latter years in labours of kindness among his friends. This act of the Professor was the result of a conversation I had with him on the subject. Before I received his friendly communication, however, I had resolved to adopt the rectangular hyperbola, whose co-ordinates I had myself determined with this view some time before; and when I found that the conchoid and the hyperbola, traced between the two fixed points by means of the calculated co-ordinates, were so nearly coincident, that it was difficult to prevent their running into each other, even when drawn out on a large scale, I determined to adhere to my original purpose of adopting the latter curve as my guide.

[13] The last column of this table is derived as follows:--Assuming that the economic advantage of any proposed tower of given height and diameter at base and top, is _inversely_ as the mass and the height of the centre of gravity above the base, and denoting these quantities by M and G respectively, the fraction

1 --- G·M

may be taken as an indication of the economic advantage of the proposed tower. Let

1 ----- G′·M′

express the economic advantage of another tower; then the advantage of the second tower, compared to that of the first, taken as unity, will be

G·M -----, G′·M′

by which expression, the last column in the table was calculated.

The shaft of the Skerryvore Pillar, accordingly, is a solid, generated by the revolution of a rectangular hyperbola about its asymptote as a vertical axis. Its exact height is 120·25 feet, and its diameter at the base 42 feet, and at the top 16 feet. The ordinates of the curve, at every foot of the height of the column, were carefully determined in feet to three places of decimals; and the Appendix contains a tabular view of the co-ordinates from which the working drawings were made at full size. The first 26 feet of height is a solid frustum, containing about 27,110 cubic feet, and weighing about 1990 tons.[14] Immediately above this level the walls are 9·58 feet thick, whence they gradually decrease throughout the whole height of the shaft, until at the belt they are reduced to 2 feet in thickness. Above the shaft rests a cylindric belt 18 inches deep; and this is surmounted by a cavetto 6 feet high, and having 3 feet of projection. The contour of this cavetto is that resulting from a quadrant of an ellipse revolving about the centre of the tower, with a radius of 8 feet on the level of its transverse axis; and the moulds for this curve were drawn at full size from co-ordinates calculated for the purpose. The cavetto supports an abacus 3 feet deep, the upper surface of which forms the balcony of the tower, and above it rest the parapet-wall and lantern.

[14] At the rate of 13·62 cubic feet of granite to a ton.

It may, perhaps, be not uninteresting to the reader to examine the woodcuts (No. 3), which shew, on one scale, the elevations of the Lighthouses of the Eddystone, the Bell Rock, and the Skerryvore, and exhibit the level of their foundations in relation to high water. They will also serve to give some idea of the proportionate masses of the three buildings. The position of the centre of gravity, as calculated from measurements of the solids, is also marked by a round black dot on each tower; and in the table following, I have given the cubic contents of each of these towers, the height of the centre of gravity above the base and the ratio of that quantity to the height of the tower.

[Illustration: No. 3.

EDDYSTONE.

SKERRYVORE.

BELL ROCK.]

+-----------+-------+--------+----------+----------+----+ | | Height| | | | | | | of | | | Distance | | | | Tower | | | of | | | | above | | |centre of | | | | first | | | gravity | | | | entire|Contents| Diameter | in feet | H | | |course.| of | at | at |from Base.| - | |Lighthouse.| (H) | Tower. |Base.|Top.| (G) | G | +-----------+-------+--------+-----+----+----------+----+ |Eddystone, | 68 | 13,343 | 26 | 15 | 15·92 |4·27| |Bell Rock, | 100 | 28,530 | 42 | 15 | 23·59 |4·24| |Skerryvore,| 138·5 | 58,580 | 42 | 16 | 34·95 |3·96| +-----------+-------+--------+-----+----+----------+----+

I come now to notice the few subordinate points in which the design of the Skerryvore Tower may be regarded as differing from those of the Eddystone and the Bell Rock. In glancing at the contrasted figures of the three buildings, it will be at once observed that the outline of the Skerryvore approaches more nearly to that of a conic frustum than the other two. To the adoption of this form, various considerations induced me; and these I shall very briefly detail. In the first place, it seemed to me that, in both the Bell Rock and the Eddystone, the thickness of the walls had been reduced to the lowest limits of safety towards the top; and the effects of the sea and wind acting upon a heavy cornice, cause a degree of tremor which I felt satisfied would not occur in a building with thicker walls. The effect of thickening the walls at the top, is, of course, _cæteris paribus_, to diminish the projection of the base, and thus to produce less concavity of figure, and consequently a nearer approximation to the contour of a conic frustum. I have already stated, that this excess of the bottom radius over that of the top, is in the Skerryvore Tower 13 feet, and that the height of the shaft is 120·25 feet. The quotient resulting from the division of the height by the excess of bottom radius over that at the top is 9·27; and, if the figure had been conical, this number would have given a measure of the slope of the walls throughout. There can be little doubt that the more nearly we approach to the perpendicular, the more fully do the stones at the base receive the effect of the pressure of the superincumbent mass as a means of retaining them in their places, and the more perfectly does this pressure act as a bond of union among the parts of the Tower. This consideration materially weighed with me in making a more near approach to the conic frustum, which, next to the perpendicular wall, must, other circumstances being equal, possess the property of pressing the mass below with a greater weight, and in a more advantageous manner, than a curved outline in which the stones at the base are necessarily farther removed from the line of the vertical pressure of the mass at the top.[15] This vertical pressure operates in preventing any stone being withdrawn from the wall in a manner which, to my mind, is much more satisfactory than an excessive refinement in _dovetailing_ and _joggling_, which I consider as chiefly useful in the early stages of the progress of a work, when it is exposed to storms, and before the superstructure is raised to such a height as to prevent seas from breaking right over it.

[15] It is most satisfactory to find that the views expressed above, regarding the eligibility of the conical form, seem to have the sanction of the late Dr Thomas Young, who appears to have connected his preference of this form with its greater efficiency as a source of friction among the parts of a building. In his syllabus of Lectures, under the section “Architecture,” he thus speaks: “For a Lighthouse where a great force of wind and water was to be resisted, Mr Smeaton chose a curve convex to the axis. In such a case, the strength depends more on weight than on cohesion, and also in a considerable degree on the friction which is the effect of that weight. Perhaps a cone would be an eligible form.”

If these views be substantially correct, it may not, perhaps, be altogether inadmissible (without, however, venturing to enunciate any general law) to conclude, that, in the three Lighthouses of the Eddystone, the Bell Rock, and the Skerryvore, this source of union among the outer stones of the lower courses must bear some proportion to the numbers 753, 659, and 927, which are the quotients of the height of the column, divided by the difference of the top and bottom radii of the shaft in each case respectively. This consideration seems too important to be entirely overlooked; and I conceive that, by following out this view, I have been enabled to depart with perfect safety from the intricate and elaborate work required for the connection of the materials by means of dovetailing and joggling, which the adoption of a more concave outline (in which the vertical pressure could not have been so advantageously transmitted to the outer stones of the base), would perhaps have rendered advisable. In the case of the Bell Rock, however, whose construction, in regard to this property, is the least advantageous of the three buildings, it must be borne in mind that the Tower is covered to the depth of 15 feet at spring tides, and that this principle of vertical pressure could not have been safely appealed to during the whole time which intervened between the commencement of the building and the attainment of a height sufficient to render it available, which, in a Tower having so great a part submerged, was of necessity much prolonged. The stones were thus exposed to the full effect of heavy seas, at all levels, during two entire winters, and could not therefore have been safely left, without being kept together by numerous ties and dovetails. It also seemed important, in designing that Tower, with reference to the rise of tide, to give its lower part a sloping form, as the least likely to obstruct the free passage of the waves. The outer stones of the lower courses were also selected of unusual length _inwards_, so as to bring them more under the influence of the vertical pressure of the upper wall.

Before leaving this subject, I may remark, that it is quite possible to construct a Tower of a curved form, in such a manner, that the pressure of the upper part of the pillar shall be distributed to the greatest advantage on every stone, by building the outer walls as inverted arches, so that the section of each stone shall be that of a voussoir, with joints perpendicular to the successive tangents of the curve. This arrangement of the stones is, in fact, practised in sea walls of various kinds, and has even been recommended for circular Towers in an ingenious paper in the Transactions of the Royal Scottish Society of Arts. But in many situations, and at Skerryvore in particular, this mode of transmitting the pressure, so as to throw it perpendicular to the beds of the stones, is inadmissible, as conducing to or involving a greater evil. The evil has already been noticed, and consists in the thrust of the lowest stone (which is of course inclined to the horizon) having a tendency to push out the sides of the Rock on which the Tower is built. This fear, where the Towers are to be placed on small steep rocks or pinnacles, and more especially when these Rocks are traversed by veins nearly vertical, is by no means visionary; and there is good reason to apprehend, that the pressure thus resulting in a line considerably inclined to the plane of _cleavage_, might throw outwards a thin portion of rock, which, under the more conservative influence of a vertical pressure, might continue to retain its connection with the rest of the Rock unimpaired for ages.

Another method of, in some degree, increasing the resistance of a Sea Tower to a horizontal thrust, if such aid be required, is to give the line of courses a continuous spiral form, instead of building them in successive horizontal layers. Were there reason to fear that the entire dislocation of the building might take place in a plane nearly horizontal, this method seems more calculated to counteract the danger than the use of dowels or joggles passing from the course below to the course above; but, as this is one of the accidents least to be apprehended, there does not seem any good ground for resorting to a mode of structure which would lead to considerable intricacy of workmanship, and would, in practice, be attended with difficulty in obtaining a proper vertical bond or union among the several stones.

The only remaining point, in which the example furnished by the Eddystone and Bell Rock Lighthouses has been at all materially departed from, is (as has already been hinted at by an unavoidable anticipation) the mode of uniting the different parts of the masonry together. In both these Towers the stones were dovetailed throughout the buildings, chiefly (at least in the case of the Bell Rock where the foundation was so much below the tide) with the view of preventing the sea from washing away the courses which might be left exposed to the winter storms before the weight of the superstructure had been brought to bear upon them. In the upper part of the Bell Rock my father also introduced a kind of band joggle, which consists of a flat ribband of stone raised upon the upper bed of one course, and fitting into a corresponding groove cut in the under bed of the course above; and this system of tying the adjoining courses together also forms a chief feature in his design for a Lighthouse on the Wolf Rock.[16] When the great pressure of the superstructure of these Towers, however, and the effect of the mortar are considered, there seems little probability of one course being dislocated, in defiance of the friction resulting from the weight of the column. An impulse sufficient to produce such an effect would tend to overset the whole superstructure from mere deficiency in weight, and in this case the joggle would have little effect. But if joggles be thought necessary for this purpose, the ribband form certainly produces a better arrangement than that of the cubic joggles employed by Smeaton for connecting the adjoining courses of his building together, as the sectional strength of these scattered square joggles is very small compared to the effect of a shock which could be supposed capable of moving the whole mass of a Tower. In the lower parts of the Skerryvore Tower, I entirely dispensed with dovetailing and _joggles between the courses_, and thus avoided much expensive dressing of materials. The stones were retained in their places during the early progress of the work, chiefly by common diamond joggles, and the courses were temporarily united to each other by wooden treenails, like those used in the Eddystone and Bell Rock. These treenails had split ends, with small wedges of hardwood loosely inserted, which being forced against the bottom of the holes in the course below, into which the treenails were driven, expanded their lower ends until they pressed against the sides of the holes; while their tops were made tight by similar wedges driven into them with a mallet. I have, however, adopted the ribband-joggle in the higher part of the Tower, where the walls begin to get thin in the very same manner as at the Bell Rock, where it was used, partly that it might counteract any tendency to a _spreading_ outwards of the stones, and partly that it might operate as a kind of _false joint_ to exclude the water which, when pressed with great violence against the Tower, is apt to be forced through a straight or plain joint. The stones in the higher courses throughout each ring are also connected at the ends by double dovetailed joggles, which unite the two adjoining stones; and the walls are, besides, tied together at various points by means of the floor stones, which are all connected by dovetails let into large circular stones which form the centres of the floors. I also ventured to leave out the metallic ties at the cornice, which consisted, at the Eddystone, of chains, and, at the Bell Rock, of copper rings. The reasons which induced me to adopt this change I need not here enlarge upon. It is sufficient to state, that I believe I have nearly balanced the forces which would have tended to throw the cornice outwards, had a greater disproportion existed in the weight of the outer and inner parts of the cavetto, and to point out (Plate VII.) that the Lightroom or highest floor occurs, at such a level, as of itself to answer all the ends which metallic ties could have served.

[16] Account of the Bell Rock Lighthouse, Plate XXI.

##