CHAPTER IV.

PROGRESS IN THE SCIENCE OF SHIPBUILDING.

The appreciation and employment of scientific method and analysis in designing and building ships have at no previous time been greater than they are at present. This is already yielding benefits and ensuring successes which only a few years ago would have remained ungathered and unachieved, or at best would only have been attained after wasteful expenditure of money, time, and skill, if not the sacrifice of human life. Not so long ago endeavours were seldom made to extract lessons of general value from particular occurrences, there being a disposition prevalent to accept facts without accounting for them—“to rejoice in a success and regard a failure as irreparable”—the outcome, it may at once be said, of indifference, false ideas of economy, and of a limited conception of the part scientific methods should play in successful shipbuilding.

Particular occurrences within recent years have without doubt played a large part in bringing about this more general and intelligent appreciation of such matters. Some maintain, indeed, that it is only under pressure of circumstances that anything like proper regard for fundamental principles has obtained hold among mercantile shipbuilders. This remissness, even admitting it to be true, is the more natural and excusable in private commercial concerns, when it is considered that the bulk of progress made, even in Admiralty quarters—where ships take several years each to build, and there is more time for scientific investigation and experiment than is possible in mercantile work—is more attributable to the awakenings which have followed upon great disasters than to the natural improvement of ordinary practice. The terrible loss of the _Captain_ in September, 1870, for example, by which 500 lives were sacrificed, led to a fuller recognition of the necessity for exact experiment and calculation to determine thoroughly the conditions of stability for war vessels; and many war-ships then under construction at the dockyards—particularly those of the low freeboard type—were altered in consequence, for the purpose of adding to their safety. The capsizing of the _Eurydice_ off the Isle of Wight in March, 1878; the mysterious and mournful loss of her sister ship the _Atalanta_ in 1880; the explosion on board the _Thunderer_ in 1876, by which 45 lives were lost, and the still more calamitous case of the _Doterel_ in April, 1881, by which the ship and 148 lives were destroyed, are all instances of calamity, the causes of which have formed the subject of official inquiry, all in their turn teaching important lessons and yielding subsequent benefits not easily calculable.

Recent occurrences of a very calamitous nature in connection with merchant ships—some of which will be more explicitly referred to further on—have been attended with similarly mournful, but, it may be added, with similarly beneficial results. These disasters and the resulting inquiries have shown pretty conclusively that the knowledge of a vessel’s stability and other vital qualities possessed by ship’s officers is often meagre and erroneous; and that far too little attention is usually paid to a vessel’s technical qualities by shipowners or their advisers. They have also tended to prove that exact knowledge of the principles of ship design, and observance of scientific method in their construction, are not yet sufficiently prevalent or thorough in mercantile shipyards.

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Progress in the pure science of naval architecture, as distinguished from the practical application of scientific rules and principles to shipbuilding, is a great and complex subject, and one which it would be impossible to do full justice to here. Before attempting to treat upon these matters as concerned with the period covered by this review, it may be instructive to trace briefly the progress made in the past, and take note of the agencies through which such progress has been effected. In this undertaking, concerned as it is with matters relating to a period prior to that with which the present work chiefly deals, the author has availed himself to some extent of already published works traversing the same ground. As having afforded the needful assistance in this connection, and as being a source to which readers may turn for fuller information, reference may here be made to an article in the _Westminster Review_ of January, 1881, on “The Progress of Shipbuilding in England.” This article, though unsigned, is from the pen of Mr W. H. White, late Chief Constructor of the Navy, and author of the well known “Manual of Naval Architecture.” It furnishes an appreciative and concise account of the literature and the educational agencies connected with the theory of naval architecture, and sketches the influence of science on practice, and _vice versa_ in the profession since the beginning of the present century.

As has already been indicated, the period during which scientific knowledge and methods have had any considerable place in merchant shipbuilding, does not extend back over very many years. In connection with the Royal Navy, however, the study of scientific naval architecture has been fostered and promoted under Government auspices almost from the commencement of the present century; not, however—it must be added—without alternating periods of regard and neglect, nor irrespective of pressure from extraneous sources.

Although progress in this matter has not been solely due to Government agencies, it may be maintained that a large part of the positive and accurate scientific knowledge which now exists has grown out of the exigencies of the naval service, and has come from sources more or less supported by or connected with Government institutions. It will of course be understood that the science of naval architecture is a field in which many besides shipbuilders, and indeed many besides professional naval architects, have laboured with signal success. The fund of knowledge has been enriched, and the practice of shipbuilding improved, by men whose association with the shipyard has been of an indirect and amateur kind, and—it must be added—whose valuable labours the shipyard has often but scantily recognised. Mathematicians—“mere theorists,” as they have been called—have made original investigations and scientific analyses which have upset many previously received practical notions, and established principles, the appreciation of which alone, has led to subsequent progress in actual practice. The part taken by merchant shipbuilders has consisted in the experimental verification, and sometimes the practical correction of principles thus evolved, but even to this extent the service done has been largely incidental. Those considerations which form the economic basis of every commercial concern have naturally circumscribed such service, and only a few notable firms have been able to break through the common restrictions.

The systematic study of scientific naval architecture may be said only to have begun in Britain in 1811, in which year, as the outcome of recommendations made by a Government Commission appointed to inquire into naval construction in 1806, the first School of Naval Architecture was established at Portsmouth, under the direction of Dr Inman, a distinguished member of the University of Cambridge. All the great advances which had been made previously in the science of naval architecture were chiefly due to foreigners, and any one wishing to acquaint himself at first hand with all that was then most advanced would have to consult the learned treatises of such distinguished Frenchmen as Bouguer, Dupin, Euler, D’Alembert, and the Abbé Bossut, of the distinguished Spaniard Don Juan d’Ulloa, and of Chapman, the celebrated constructor of the Swedish Navy. One or two English writers, between 1750 and 1800, had published translations of some of these foreign treatises, but the only original work of any importance was by Atwood, who contributed a “Disquisition on the Stability of Ships” to the proceedings of the Royal Society (1796-98). This contribution was both a criticism and an extension of flotation and stability investigations by Bouguer, and as an example of scientific method applied to exact calculations of the qualities of ships it is still well worthy of study. In 1791 a “Society for the Improvement of Naval Architecture” had been formed, the membership being both numerous and influential, and in 1806 the growing sense of need for improved scientific methods culminated in the appointment of the Commission above mentioned, and in the establishment five years later of the first School of Naval Architecture. This institution existed for over twenty years, over forty students were trained, and the science of naval architecture was greatly promoted through its agency. Almost as a body the students of this school, with their able teacher, deserve the honour of being regarded as the founders of an English literature of naval architecture. Nevertheless, the recognition of Dr Inman’s services, and his pupils’ capabilities as designers, by the naval authorities was of a cold and disappointing nature. Ultimately, however, many of them attained positions wherein their talents found worthy exercise.

After the abolition of the School of Naval Architecture, under Dr Inman, in 1832, no agency for higher education existed until 1848, when the urgent necessity for a steam re-construction of the Navy forced attention to the want of trained men, and resulted in the establishment of a second school at Portsmouth. The principal of this school was Dr Woolley, an eminent graduate of the University of Cambridge. From 1848 on to the present time, Dr Woolley has held a prominent place amongst the promoters of naval science, and the pupils produced by the institution under his directorship have given in various ways good practical evidence of his capability as a teacher. After five or six years of useful work, this second school was done away with, and a third was established in London in 1864, after pressure had been brought to bear upon the Government of the day by the Institution of Naval Architects—an association which was founded in 1860, and which has since had so flourishing an existence.

The new school was placed for a time under the control of the Science and Art Department at South Kensington, Dr Woolley being Inspector-General, and the late Mr C. W. Merrifield, F.R.S., Principal. This school, unlike its predecessors, was not nominally a mere Admiralty establishment, but offered admission to private naval architects and engineers, and did not exclude foreigners. It remained in operation at South Kensington until 1873, when the Admiralty decided to establish the Royal Naval College at Greenwich, and to train their students of naval architecture and marine engineering there. Since 1873, therefore, what may be regarded as a continuation of the third school has been at work at Greenwich, the Admiralty granting facilities for the entry of private and foreign students, much as was done at South Kensington.

The small extent to which this institution has been taken advantage of by private students, or by those whose aim is to equip themselves for service in merchant shipbuilding, notwithstanding the inducements existing in the shape of substantial scholarships, has often been subject of comment. Various reasons have been adduced for this state of matters, but the true cause would seem to be largely concerned with the character of the entrance examinations and with the course of study provided. The subject is well worthy of consideration, and fuller reference will be made to it further on when some educational agencies which have been recently established are under consideration.

At such important junctures in the history of shipbuilding as the introduction of steam power for propulsion in place of sails, and the employment of iron in place of wood for the hulls, precedent and experience lost much of their value under the new conditions. The association of civil and mechanical engineers with shipbuilding at these crises was of immense advantage. Such men as Fairbairn and Brunel, who had previously gained high reputations in other branches, were enabled by their scientific skill in designing bridges and other structures in wrought-iron, to achieve much, and to take the lead in ship design and construction. “To men of this class,” says Mr W. H. White, in the article already alluded to, “careful preliminary investigation and calculation naturally formed part of the work of designing ships; ‘rule of thumb’ was not likely to find favour, even if it had been applicable, which it was not, under the circumstances. At first, much was done on imperfect methods, comparatively in the dark; failures were not rare; yet progress was made, and gradually greater precision was attained, in the attempt to design steamers capable of proceeding at certain assigned speeds when laden to a given draught. In fact, the construction of steamers rendered imperative a careful study of the laws of fluid resistance, and of the cognate investigation of the mechanical theory of propulsion—both of which subjects lay practically outside the field of the designers of sailing ships. The speed of a sailing ship is obviously dependent upon the force and direction of the wind; her designer, therefore, chooses forms and proportions which will enable a good spread of canvas to be carried, on a handy stable vessel. Questions of resistance to the progress of the ship were therefore subordinated to sail-carrying power and handiness in sailing ships; whereas in steamers designed for a certain speed the question of resistance occupies a primary place, seeing that the engine power must be proportioned to the resistance. Consequently, while keeping in view stability, handiness, and structural strength, the designer of a steamer has a more difficult task than the designer of a sailing ship, and the difficulty can only be met if faced intelligently by scientific analysis. Hence it happened, as was previously remarked, that a more general appreciation of the value of scientific methods accompanied the development of steam navigation and iron shipbuilding in the British mercantile marine.”

Another name that must be linked with those already mentioned in connection with the change from wood to iron in shipbuilding, and with the new conditions imposed by the transition from sail to steam, is that of the late Mr John Scott Russell, already referred to at the beginning of this work. In the fields of inquiry so largely opened up at the period referred to, Mr Russell was a most distinguished worker. His advocacy and adoption in practice of special structural principles, as illustrated not only in the _Great Eastern_ but in other vessels, has influenced subsequent practice incalculably, and by his persevering investigations upon the resistance of vessels, and the “wave-line” theory he advanced, as well as by his inquiry into the characteristics of wave motion, he laid designers of that period and subsequent investigators under great indebtedness. His contributions to the literature of the profession—notably his _magnum opus_, entitled “Modern System of Naval Architecture”—and the large share he subsequently took in the deliberations of the Institution of Naval Architects, and of other societies concerned with shipbuilding and engineering, enhance that indebtedness and remain as permanent records of his skill and originality.

Approaching the period with which this review is more particularly concerned, reference must now be made to the valuable labours of two eminent men, whose loss the profession has had to mourn within recent years. These are the late Professor Macquorn Rankine and the late Mr William Froude, neither of whom was by profession a naval architect, yet both of whom were led by love of the subject to give their matured experience as civil engineers and mathematical experts to the promotion of knowledge in this domain.

Rankine appears to have become specially interested in the problems connected with ship design, after he became Professor of Civil Engineering at Glasgow University in 1855. Conjointly with Mr Isaac Watts, late Chief Constructor of the Navy, and formerly a student of the first School of Naval Architecture; Mr F. K. Barnes, now Surveyor of Dockyards, and Chief Constructor of the Navy, and a distinguished student of the second school; and the late Mr J. R. Napier, a member of the famous Clyde shipbuilding firm, Prof. Rankine produced in 1866 “Shipbuilding: Theoretical and Practical.” This valuable treatise was edited, and for the most part written, by Prof. Rankine, and provides a complete system of information on all branches of shipbuilding and marine engineering, although subsequent progress in certain departments of naval science has made a new edition desirable. The work is also distinguished for its enunciation of several theories connected with the resistance and propulsion of vessels by Prof. Rankine, which have become the accepted basis of modern practice. Of these the mechanical theory of the action of propellers, and the stream-line theory of resistance, are the best known. His investigations and writings on the latter subject were most ably supplemented and confirmed by Mr Froude, whose beautifully-contrived model experiments, coupled with his discovery of the law by which such experiments can be made to afford reliable data for the resistance of full-sized vessels, have laid the profession under even a heavier load of indebtedness.

This, however, was not the only work of investigation and experiment with which Mr Froude actively and inseparably identified himself. Taking up a subject which many authorities before him had studied and written upon with but little success—that of the phenomena of wave motion and the oscillation of ships in a seaway—he propounded and demonstrated at the Institution of Naval Architects in 1861, after much careful thought and experiment, a theory with respect to it which at that time was entirely new and striking, but which has since been firmly established as the sound one.

At first, authorities in the science of naval architecture, like Moseley and Dr Woolley, regarded the new theory with suspicion and disapproval; Rankine, on the contrary, warmly supported it, and helped to develop it and to answer various objections urged against the hypothesis on which it was based. For nearly twenty years Mr Froude steadily pursued the inquiry, adding one mathematical investigation to another, carrying out numerous experiments, and making voyages for the purpose of studying the behaviour of ships. Broadly speaking, it may be said that whereas earlier investigations gave to the naval architect the power of making estimates of the buoyancy and stability of ships floating in smooth water, they gave up as altogether hopeless the attempt to predict the behaviour of ships at sea, or to determine the causes which produce heavy rolling. On the other hand, thanks to Mr Froude, the designer of a ship now knows what precautions to take in order to promote steadiness and good behaviour at sea.

Although the propositions enunciated by Mr Froude were accepted as laws in a wonderfully short time—considering their startling nature—their influence on practice, and especially the practical application of the methods of comparison by which they had been established, have not even yet been brought to anything like their full issue. The work is being continued upon the lines laid down by Mr Froude, amongst others by men whose closer intimacy with the actual affairs of the shipbuilding yard may be expected to yield results which will be more immediately reflected in actual practice.

Passing allusion has already been made to the founding of the Institution of Naval Architects, but an association which has gathered into its membership so largely of all sections of men concerned with shipbuilding and shipping, and absorbs so much of the knowledge and talent in these domains, must have fuller reference made to it. Regarding its foundation, in 1860, Mr White, in his article in the _Westminster Review_, says:

“The scheme of the Institution was happily conceived and well executed. Amongst its earliest members were found the trained naval architects of the first and second Schools, the leading private shipbuilders and marine engineers, the principal shipbuilding officers of the Dockyards, men of science specially interested in naval architecture, shipowners, merchants, and others connected with shipping; while a considerable number of sailors from the Royal Navy and Mercantile Marine showed their appreciation of the value of naval science by becoming Associates. The list of names is eminently representative. Sir John Pakington (afterwards Lord Hampton), then only recently retired from the office of First Lord of the Admiralty, was the first President. Many experienced naval officers supported him. There were men like Watts, Read, and Moorsom, who had been pupils of Dr Inman half a century before; others, like Fairbairn, Laird, and Grantham, who had been conversant with iron shipbuilding from its commencement; marine engineering was worthily represented by veterans like Penn, Maudslay, and Lloyd; mathematicians and men of science like Canon Moseley, Dr Woolley, Professor Airy, and Mr Froude appear on the list. Private shipbuilders and naval architects like Scott Russell, Samuda, Napier, and White, joined in the movement, so did the surveying staff of Lloyd’s Register. In fact, there was a general appreciation of the endeavour to establish an association which should enable all classes interested in shipping to interchange ideas and experience with a view to general improvement. Mr Reed was the first Secretary, retaining that post until he was appointed Chief Constructor of the Navy, and in that position did much to aid the progress of the Institution.”

While it is true that the membership list of the Institution in its early days was of the representative character above indicated, it should be pointed out that the actual proceedings of the Institution were not shared in by anything like the variety of talent which the list comprised, or which now distinguishes its annual meetings. For many years it was almost the exclusive conference of Admiralty authorities and members of those shipbuilding and engineering firms who undertook Government work, and the transactions for a long time were very largely confined to purely naval matters. The scientific value of the earlier volumes of the transactions would certainly have suffered considerably if the papers by Mr Froude and Prof. Rankine had not formed contributions, and the prosperity and development of the Institution would have been equally lessened had there not been general infusion of “new blood” from the mercantile marine in all parts of the country. This has been going on during the past twelve years or more, and the scope and utility of the Institution’s proceedings have increased with the change. Of the later development of the Institution, the authority already quoted says:—

“Owing to the rapid advances constantly being made in both the science and the practice of the profession, the ‘Transactions’ have come to be the chief text-books available. Members and Associates have joined from all the great maritime nations. Members of the professional corps of naval architects and engineers of France, Austria, Italy, Germany, the United States, Russia, Sweden, Norway, Denmark, Holland, are proud to be numbered with their English professional brethren, and not a few of these foreign members have contributed valuable Papers. The meetings of the Institution afford exceptional opportunities for the discussion of questions having general interest, as well as others having more special value to professional men. Different views of the same subject find capable exponents, and lead to valuable discussions. The latest systems of construction and most recent changes in _materiel_ are described by competent authorities. Valuable _data_ are put on record relating to the designs and performances of war-ships and merchant-ships. Inventions of various kinds are described and examined. Abstruse theoretical investigations are by no means rare; and, in many cases, the contribution of one such Paper by an original thinker has given a start to others and led to important extensions of knowledge. In fact, the Institution of Naval Architects has admirably fulfilled the intentions of its founders, acting as a centre where valuable information could be collected, and whence it could be distributed for the general benefit of the profession. Before it was founded naval science had no home in England; its treasures lay scattered far and wide in occasional Memoirs and Papers; but now everything worth preservation naturally finds its way to the ‘Transactions.’ Any movement affecting shipping also leaves its record there in Papers and Discussions which will hereafter have a high historical value.”

As evidencing the change which has latterly come over the Institution with respect to its annual proceedings, it may be noted that whereas in the early years there were at some meetings no papers—leaving out of account those by Froude and Rankine—except by Admiralty members and others concerned with Government work, there was not a single paper by an Admiralty man during the meetings of the present year.

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With the general reference already made to Mr Froude’s invaluable labours in connection with the resistance of vessels the brief statement of the agencies through which progress has been made during the present century may be considered as brought down to the period coming within the scope of the term “Modern,” as used in this work. The more difficult task of chronicling the progress made during the period in question, both in the science of naval architecture purely, and in the application of science to practice, must now be attempted. The plan upon which it is proposed to accomplish this is to show wherein and to what extent scientific methods in designing and observing the behaviour of ships have been regarded, and indicating generally where still further improvement may be looked for. To accomplish this in such a way as to take appreciative account of the most salient features, and yet to avoid difficult technical terms and unnecessary elaboration, may involve some omissions and slight inaccuracies, important enough from a strictly scientific point of view, yet which do not materially affect the faithfulness of the record.[5]

As preparing the way for references to those more special points in connection with which scientific progress has taken place during recent years, the following general and elementary outlines of the principal scientific problems in ship design and construction may be helpful to many readers:—

DISPLACEMENT AND CARRYING CAPABILITY.

A vessel floating at rest displaces a volume of water whose weight equals her own total weight.

For vessels floating in sea water the number of cubic feet of water displaced per ton of weight is, as nearly as possible, thirty-five. For vessels in fresh water—_i.e._, lakes or rivers—the cubic feet per ton of weight is thirty-six.

By calculating the volume of under-water portion of the vessel’s hull, the number of cubic feet displaced by the vessel when floating at any given draught is obtained. This result, divided by 35 or 36, according as the water is salt or fresh, gives the number of tons weight displaced, and consequently the total weight of the vessel.

Calculations being made of the volume of the vessel’s hull to intermediate distances between the keel and the maximum load line, it is thus possible to construct a “curve of displacement” from which the actual amount of displacement at any intermediate draught can be obtained.

From this curve a set of scales—usually set up alongside a vertical scale of feet and inches, representing the vessel’s draught-marks—are constructed, showing—1st, the tons “displacement” at any draught; 2nd, the tons of “dead-weight” capability—_i.e._, the tons displacement due to the weight of cargo, coal, ballast, stores, fresh water, spare gear, &c.—at any draught above the vessel’s light-draught: “light-draught” being that at which the vessel floats with holds clean-swept, bilges dry, water in boilers, and with such spare gear on board as is required by Board of Trade; and 3rd, the amount of “freeboard”—_i.e._, the distance in feet and inches from any particular draught line to the top of the deck amidships.

BUOYANCY AND STABILITY.

A ship floating upright and at rest in still water must fulfil two conditions—1st, as stated above, she must displace, a weight of water equal to her own weight; 2nd, her centre of gravity must lie in the same vertical line with the centre of gravity of the volume of displacement or “centre of buoyancy.”

The whole weight of the ship may be supposed to be concentrated at her centre of gravity, and to act vertically downwards, and the resultant vertical pressure of the surrounding water in the same way to act upwards through the centre of buoyancy.

When the ship has been inclined from the upright position, by any force, the downward and the upward forces—weight and buoyancy respectively—act through two separate but parallel vertical lines, and form what is technically known as a “couple.” The perpendicular distance between the vertical lines usually varies with the inclination, and is called the “arm” of the couple. This arm measures the leverage with which the weight and buoyancy of the ship tend either to force her back into the upright position, or to incline her still further, and, it may be, to capsize her. The former effect would be the result of what is known as a “righting couple,” the latter the result of an “upsetting couple.”

This may be made clearer by illustration. On Figs. 14 and 15, which show in outline a vessel’s midship section, the vessel being inclined to a small angle, =G= represents the centre of gravity of vessel, and =B= the centre of buoyancy. The water line =W.L.= corresponding to the upright position, in the inclined position becomes =W_{1}.L_{1}.=, and the centre of buoyancy =B= shifts out on the immersed side of the vessel to =B_{1}=. Assuming in the case of Fig. 14 that some external force not involving any shifting of the centre of gravity has produced the inclination, then the weight of the vessel acts downwards through =G=, and the buoyancy of her displacement acts upwards through =B_{1}=, as indicated by the arrows passing through these points. The combined effect of these forces, in this case, is to rotate the vessel towards the upright, _i.e._, it forms a “righting couple.” Fig. 15 illustrates a case of the opposite kind. The angle of inclination may be supposed to be greater than in Fig. 14, and the centre of gravity =G= is much higher in the vessel. The vertical through =B_{1}= is to the left instead of to the right of the vertical through =G=. The effect of the forces in this case is to rotate the vessel in the direction of inclining her still further, and to capsize her—_i.e._, it forms an “upsetting couple.” A line at =G=, therefore (Fig. 14), taken at right angles to the new vertical line, gives the distance which corresponds to the righting arm (=G= =Z=). A similar line at =G= (Fig. 15) represents the upsetting arm. The lengths of these arms when multiplied into the displacement, gives the “moments” at the respective degrees of inclination. The “curve of stability” for a vessel is simply a graphic representation of these arms or moments. When calculated for the various degrees of inclination, they are set off as ordinates along a base line—the righting arms or moments above, and the upsetting arms or moments below, the line—at distances corresponding to the number of degrees in the respective inclinations. A curve drawn through the extremities of these ordinates is the curve of stability.

The two points above named whose relative positions are vitally concerned with this subject—_i.e._, centre of buoyancy and centre of gravity—are determined by shipbuilders for many of their vessels, although the stability may not be calculated to its full extent. The position of the centre of buoyancy is easily ascertained from, and in fact usually forms part of, the displacement calculation. While the position of centre of gravity may be found by means of calculation alone, _i.e._—by the process of estimating the position of the centre of gravity of each of the component parts, and from this deducing the common centre of gravity of the whole ship—the work is so laborious, complex, and so liable to error, that it is scarcely ever adopted at the present day by mercantile shipbuilders. The position can be ascertained with comparative ease and greater accuracy by means of “inclining” experiments with the finished vessel, or closely estimated before-hand by means of data obtained in the manner alluded to from previous vessels of similar type.[6]

Another point concerned with stability is that termed the “metacentre,” which is found by calculation from the lines of the vessel. Referring to Fig. 14, a vertical line drawn through the centre of buoyancy =B_{1}= cuts the original vertical line at =M=. The intersection =M=, when the vessel is inclined to an indefinitely small angle, is the “metacentre.” It is approximately the same in all ordinary vessels for inclinations less than say 10°, but varies with greater inclinations. The corresponding intersections of the consecutive vertical lines for all degrees of inclination are embraced in the term “metacentrique.” These features in stability investigations were originated by Bouguer, to whom reference has already been made. The manner in which they are concerned with stability will be indicated further on. (See also footnote on preceding page.)

RESISTANCE POWER AND SPEED.

A ship, in moving through the water, experiences resistance due to a combination of causes, which combination, according to modern accepted theory, is made up of three principal elements.

1st—“Frictional” or “skin friction” resistance, due to the particles of water rubbing against the ship’s hull;

2nd—“Eddy-making” resistance, due to local disturbances or eddies amongst the particles of water—almost wholly at stern of ship;

3rd—Surface disturbance of the water by the passage of the ship, resulting in the creation and maintenance of waves: known as “wave-making” resistance.

The conditions which govern each of these elements, and their relative importance, may be generally indicated.

Surface-friction resistance, especially for vessels moving at moderate or slow speeds, is much greater than the resistance due to other causes—that is if the hull is ordinarily well formed. Its amount depends upon the area of the immersed surface, upon its length, upon its degree of roughness, and upon the velocity with which the water glides over it—_i.e._, upon the speed of the vessel.

Eddy-making resistance only acquires importance in exceptional cases, _e.g._, in ships having unusually full sterns. In ordinary well-formed ships it is of small amount, and is caused mainly by blunt projections such as shaft tubes, propeller brackets, and stern-posts.

Wave-making resistance is much more variable than surface-friction resistance. Its amount depends on the form and proportions of vessels, and on the speed at which they move: being greatest, of course, in ships of full form and in those moving at high speeds.

The sum of these three main elements of resistance constitutes the total resistance experienced by a vessel if “towed” through the water, that is, the resistance considered apart from the action or influence of the propelling instrument. In the case of a steamship, however, propelled by a screw or paddle-wheels, the resistance is augmented, more or less considerably, according to the form, surface, and disposition of the propelling instrument.

By the employment of various formulæ deduced by scientific authorities from theory and experiment, an approximation can be made before-hand to the total resistance of a proposed vessel, and from this an estimate of the power required to drive her at a certain speed. Moreover, through the law of comparison propounded by Mr Froude, the resistance of a ship can at all times be deduced with fair accuracy from the resistance of her model, certain corrections well determined by experiment having to be made.

The power of marine engines is expressed either in “nominal” or “indicated” horse-power. Nominal horse-power is a term practically obsolete so far as being a measure of the efficiency of engines, and only exists as a conventional method of commercially measuring the sizes of engines. Indicated horse-power measures the work done by the steam in the cylinders during a unit of time, and 33,000 units of work per minute, or 550 units of work per second, constitute one horse-power. The effective mean pressure of the steam is ascertained from diagrams drawn by means of the instrument known as the “Steam Engine Indicator,” and hence the term “indicated” horse-power.

The development by a vessel’s engines of the power requisite to drive her at a certain speed is always very considerably more than the power required simply to overcome her total resistance at that speed. This excess of power developed over power usefully employed in overcoming resistance is known as “waste work.” It amounts in many cases to as much as from 50 to 60 per cent. of the gross indicated power, and it is absorbed mainly as follows:—In overcoming frictional and other resistances of the engines and shafting, working air pumps, &c., and in overcoming the frictional and edgeways resistance of the propeller. The residue of power usefully employed is known as the ‘effective’ horse-power. The respective causes of ‘waste’ and their relative amounts are problems constantly demanding solution. Progressive speed trials with actual vessels and experiments with small scale models are daily contributing to their solution, and to some extent to their reduction.

STRUCTURAL STRENGTH.

Considering a ship as floating in a state of rest in still water, the volume of displacement represents a weight of water equal to the weight of the ship. This equality, however, does not exist evenly throughout the length of the vessel, or for individual portions: thus, amidships the weight of water displaced by a given length—in other words, the buoyancy—is usually considerably in excess of the weight of that portion of the vessel and her contents. Similarly at the extremities the ‘weight’ of a certain length exceeds the ‘buoyancy.’ Between the part or parts of the vessel in which there is excess of buoyancy over weight, and the part or parts in which the weight exceeds the buoyancy, there must obviously be sections of the ship at which the two are equal, and these are termed “water borne” sections. A ship circumstanced as described is in a condition similar to that of a beam supported at the middle and loaded at each end. Such a beam tends to become curved, the ends dropping relatively to the middle, and the ends of the ship tend to drop similarly, the change of form being called “hogging.” On the other hand, if the excess of buoyancy occurred at the extremities and that of weight amidship, the ship would resemble a beam supported at the ends and loaded at the middle. In such a condition the middle would tend to drop relatively to the ends: a change of form called “sagging.”

These general principles are much more readily and safely applicable to ships while floating in ‘still water’ than to ships when at sea—the strains experienced then being necessarily the results of far more complex and severe influences. The existence of waves and their rapid motions relatively to that of the vessel, and the pitching, heaving, and other movements thus caused, increase the inequality of distribution of weight and buoyancy and affect more materially the strains brought upon vessels. Consideration of the problem, therefore, involves a study of waves, both as to their formation and action, and necessarily leads to a mode of treatment which cannot have accurate regard for particular cases. Variable influences of immense importance are also constituted by the state of loading in vessels for merchant service. For a uniform basis of comparison in these calculations such vessels are usually assumed as loaded with homogeneous cargo—_i.e._, cargoes of equal density throughout.

This fundamental element of relative ‘weight’ and ‘buoyancy’ having been indicated, the chief strains to which a ship is subjected may now be stated. This may be done with sufficient regard to general accuracy, under four heads:—[7]

(1) Strains tending to produce longitudinal bending—“hogging” or “sagging”—in the structure considered as a whole.

(2) Strains tending to alter the transverse form of a ship, _i.e._, to change the form of athwartship sections.

(3) Strains incidental to propulsion by steam or sails.

(4) Strains affecting particular parts of a ship, or “local strains”—tending to produce local damage or change of form independently of changes in the structure considered as a whole.

To these might be added various other strains, which, however, are of less practical importance, and are not felt in any great degree—except in very special cases and under unusual circumstances—apart from the strains which affect the structure considered as a whole. The provisions made for the latter are, under ordinary circumstances, sufficient to cover the demands of the former, but particular cases may have to be provided for on their merits, apart from the treatment generally applicable.

The manner of ascertaining the strength of a ship to resist strains tending to produce longitudinal bending, is to compute the effective sectional area of all the longitudinal items in the structure which are brought under compressive or tensile strain, and from this to calculate the strength in the same manner as for a girder having an aggregate sectional area and a disposition of material equivalent to that of the ship.

To ascertain the accurate maximum strains tending to produce longitudinal bending, or, in excessive cases, to break the ship across at the transverse section where the strains reach their maximum, involves a careful and most laborious consideration of the relative weight and buoyancy of individual sections throughout the length, and is a task not generally undertaken in mercantile shipyards.[8]

References to the nature of the transverse and other strains above enumerated and the extent to which they have been investigated will be made further on.

With regard to such fundamental properties of vessels as displacement, weight, and carrying capability, nothing new has for a long period been added to the fund of scientific knowledge. One of the conditions now most commonly laid down by the owners of a proposed ship is that which provides for a certain carrying capability on a given draught of water and at a certain speed, the principal dimensions of the vessel also being stipulated. The problem of determining what total displacement will be required, involves consideration and an estimate of—1st, The total weight of hull having regard to structural strength; 2nd, the total weight of machinery having regard to speed required. By using “co-efficients” deduced from the weights of vessels of similar type already built,[9] these are determined; and adding them to the carrying capability or dead-weight stipulated, the required displacement can be closely approximated to. For vessels of abnormal proportions or of very unusual construction careful and detailed calculations of the weight of materials are undertaken previous to tendering for them. In some yards, indeed, a like degree of care is observed in ordinary cases: methods of approximation involving the use of co-efficients such as that based on cubic capacity being distrusted.

The further problem of determining what form of hull will give the required displacement is the essential and all-embracing feature of the work of design, as it involves consideration of almost all other properties. The methods of designing ships are various, and a very common method, at one time more followed than it now is, consists in shaping a block model direct, and from it taking the necessary measurements for displacement, and for full-size delineation in the moulding loft. The disadvantages pertaining to this somewhat antiquated method are becoming more recognised as shortened and exact methods of linear or “draught plan” design are put forward.

Unless the plan of lines of a similar vessel of nearly the same dimensions is at hand, the design of a new vessel is in many instances done without previous calculation being made to ensure at once obtaining the desired displacement. Special methods of quickly arriving at this result are, however, not uncommon in mercantile shipyards, and generally speaking the chief draughtsmen in the employ of large firms doing a varied class of work have rules derived from long experience, though not perhaps definitely systematised, by which they are guided.[10] Irrespective of all such special methods, however, the work of designing is now greatly shortened and simplified by means of Amsler’s “planimeter,” an ingenious instrument for measuring areas now becoming well known.[11] By employing the instrument in question, the draughtsman need not too laboriously strive after the exact displacement at first, as the time occupied in ascertaining what displacement any set of lines gives, and in the consequent fining or filling out, is very considerably less than by the ordinary methods.

* * * * *

The question of stability, which has next to be considered, is one of great difficulty and intricacy, and it was not till the middle of last century that some of the principles upon which it depends began to be understood. Bouguer showed in 1746 that the position of the “metacentre” limits the height to which the centre of gravity of a floating body may be raised without making it unstable, and that the righting moments at small angles of inclination from a position of stable equilibrium are proportional to the height of the metacentre above the centre of gravity. As the position of the metacentre for any given draught of water is easily determinable when once the volume of displacement and the centre of buoyancy at that draught have been ascertained, it has been the practice for a very long time to construct a curve representing the height of the metacentre at all draughts, and to use it for showing the limits above which the centre of gravity cannot be raised with due regard to the stability required for the practical working of vessels and for purposes of safety: By the method of “inclining” vessels, already described (see outline of fundamental principles, page 98), the determination of the precise position of the centre of gravity is rendered comparatively simple.[12]

While the vertical distance between the centre of gravity and the metacentre—commonly termed the “metacentric height”—forms a measure of the “initial stability,” or the stability at very small angles of inclination, it is imperfect by itself, and may be very misleading as regards the stability at larger angles. This was conclusively demonstrated by Atwood in his papers read before the Royal Society in 1796 and 1798, while other grounds for discrediting the standard of stability furnished by mere metacentric height were discovered subsequently, and have been signally emphasised, with additional reasons, by recent occurrences. Atwood, in the papers referred to, laid down a general theorem for determining the righting moments at any required angles of inclination possessed by a ship having a given draught of water and a fixed height of centre of gravity, the principle of which involved the use of the moments of the volumes of the “Wedges,” _i.e._, those parts of a vessel (see =W O W_{1}=, =L_{1} O L=, fig. 15), which become immersed and emerged as she is inclined. Several methods of simplifying Atwood’s calculations had been devised previous to 1861,[13] but in that year Mr F. K. Barnes, in a paper read before the Institution of Naval Architects, described a method of accomplishing this which until within recent years has been the one ordinarily adopted in computing the stability of a vessel at various angles of inclination.[14]

Owing to questions having arisen at the Admiralty in 1867 respecting the stability of some low freeboard monitors at very large angles of inclination, Sir E. J. Reed, then Chief Constructor, directed the matter to be investigated. The work was placed in the hands of Mr William John, who embodied for the first time the results of the calculations in the form of a curve of stability, which exhibited the variations of righting moments with angles of inclination up to the particular angle at which stability vanished. The entire range of a vessel’s stability was thus made evident, and in such a form as enabled the general problem to be far more comprehensively and accurately treated than before. The results of Mr John’s labours were described in a paper read by Sir E. J. Reed before the Institution of Naval Architects in 1868, and a further paper, containing an improved method of applying Atwood’s theorem to the calculation of stability upon this extended scale, was read before the same Institution by Messrs John and W. H. White in 1871. The loss of H.M.S. _Captain_, in 1870, as already pointed out near the beginning of this chapter, occasioned an immediate and serious regard for the stability of war vessels. This disaster, with other losses at sea from instability, also forcibly directed the attention of mercantile naval architects to the subject, and investigations on the same complete scale as those undertaken in the Admiralty have for some years been adopted in a few leading mercantile shipyards.

In this way the peculiar dangers attaching to low freeboard, especially when associated with a high centre of gravity, have been pretty fully made known, but the character of the stability which is often to be found associated with very light draught appears to have escaped the attention it demands. Light draught is often as unfavourable to stability as low freeboard, and in some cases more so.

These truths were forced into prominence at the inquiry held by Sir E. J. Reed on behalf of the Government into the disaster which befell the _Daphne_, a screw-steamer of 460 tons gross register, which capsized in the middle of the Clyde immediately on being launched from the yard of the builders, Messrs Alexander Stephen & Sons, Linthouse, on July 3rd, 1883. Sir E. J. Reed, in his exhaustive report, published in August, 1883, emphasised the lessons adduced at the inquiry as to the peculiar dangers attaching to light-draught stability; and Mr Francis Elgar, (now Professor of Naval Architecture in Glasgow University), who was employed to make investigations respecting the stability possessed by the _Daphne_ at the time of the disaster, did much to guide consideration of the subject into this channel. In a letter to the _Times_ on 1st September, 1883, Mr Elgar, by way of explaining portions of his evidence at the inquiry, called attention to the relation which exists between the righting moments at deep and light draughts in certain elementary forms of floating bodies, his communication throwing further light on the subject of light-draught stability. It appears that the fundamental proposition which underlies the variations in the stability of a floating body with draught of water had never before been demonstrated or enunciated.

It will be readily understood that a curve of stability for a given draught of water and position of centre of gravity ceases to be applicable if changes are made in the weight and consequent draught of water of a ship or the position of the centre of gravity, or in both. Now in mercantile steamers, from the extremely light condition in which they are launched to the uncertain loaded condition of their daily service as cargo-carriers, the variation of draught is very considerable, and imports into the subject considerations which do not obtain to any great extent in war ships.

To complete the representation of stability as it should be known for merchant ships, it is now recognised that curves showing the stability at every possible draught of water and for different positions of centre of gravity should be constructed. By means of “cross-curves” of stability, or curves representing the variation of righting moment, with draught of water at fixed angles of inclination, this comprehensive want can be met with something like the necessary expedition. From such curves it is a simple operation, involving no calculation save measurement, to construct curves of the ordinary description, showing the righting moment at all angles for any fixed draught of water and position of centre of gravity. Professor Elgar was the first to publicly direct attention to this valuable development of stability investigation of merchant ships, doing so in an able paper “On the Variation of Stability with Draught of Water in Ships,” read before the Royal Society on March 13th of the present year. Simultaneously with Prof. Elgar’s employment of such curves in actual practice their use had been independently instituted by Mr William Denny in his firm’s drawing office, and the mode in which they were worked out in this case was communicated in a paper read by Mr Denny in April of the present year before the Institution of Naval Architects.[15] Several important improvements with respect to simplifying and shortening calculation distinguish the method employed by Mr Denny, and that gentleman, in the paper referred to, accords individual credit to members of the scientific staff in his firm’s employ, who, on being entrusted with the work of calculation, brought considerable originality to bear upon their labours. The cross-curves described by Prof. Elgar were constructed from a series of curves of stability calculated in the ordinary way. This, however (as pointed out in an after-note to that gentleman’s Royal Society paper), is less simple and very much less expeditious than the method carried out under Mr Denny, which consists in calculating the cross-curves directly by applying Amsler’s mechanical integrator[16] to the under-water portion of the ship instead of to the wedges of immersion and emersion, thus determining at once the positions of the vertical lines through the centres of buoyancy at the required angles of inclination. As thus carried out a complete set of cross-curves can be produced with about one-third the labour involved in employing the older method. The ease and rapidity with which ordinary curves for separate draughts can be taken from cross-curves has already been commented upon.

Many other investigators besides those already mentioned have recently been working at the subject of stability, and a considerable number have read papers, dealing with the extension and simplification of stability calculations, before one or other of the scientific societies concerned with naval architecture, most of the methods put forward being well worthy of study.[17] To very many shipbuilders, however, and to others besides them responsible for the stability of ships, processes of arithmetical calculation—even allowing for all the simplification which mathematical skill has recently effected—appear still to be too intricate, or to absorb too much time for their being entirely followed. As a simple means of readily, although approximately, arriving at the results attained more elaborately and reliably by calculation, attention has recently been directed to an experimental process by which a complete curve of stability may be constructed almost without the use of a single figure! The method was first brought forward in 1873 by Capt. H. A. Blom, chief constructor of the Norwegian Navy, formerly a student of the South Kensington School of Naval Architecture, who described it to the United Service Institution. The method has been employed by shipbuilding firms on the Tyne and Clyde when a curve of stability had to be produced in a very limited time, and when extreme accuracy was not a desideratum. As practised by the firms in question, the _modus operandi_ differs in some slight respects from that described by Captain Blom, but the changes in no way affect the principles as first laid down by him. The modern mode of procedure may be briefly described:—

From the body plan of the ship, _i.e._, that portion of the draught plan representing the vessel’s form by a series of equidistant transverse sections—any convenient number of sections lip to the load water-line are pricked upon and then cut out of a sheet of drawing paper of uniform thickness. These sections are then gummed together in their correct relative positions, care being taken to spread the gum thinly and evenly. This paper model—greatly foreshortened, of course—represents the immersed portion of the ship (in other words, the displacement) when she is floating upright. By suspending this model from two different points, and taking the intersection of two vertical lines through the points of suspension—or better still, by balancing it horizontally on a pin and fixing the point when the model is in equilibrium—the centre of gravity of the model, or in other words, the actual centre of buoyancy is obtained.

Water lines at various angles of inclination are then drawn on the body plan, all intersecting the water line for the upright condition at the centre line of ship. The displacement represented by the inclined water lines thus drawn, generally not being equal to that for the upright position, a correcting layer has to be added or subtracted for each inclination, in order to obtain this end. By employing the planimeter the necessary thickness of this layer can be most readily ascertained. Where a planimeter is not available the actual floating line may be obtained, after the model has been made, by cutting off layers, allowance having been made for this purpose. The same number of sections as before are then cut out to each of the inclined corrected water-lines, the paper model prepared and the centre of buoyancy obtained as already described.

Through this new centre of buoyancy a line is drawn perpendicular to the inclined water line, and the distance between this line and the centre of gravity of the ship, already obtained, is the righting arm. If this process is repeated for each angle of inclination, it is thus seen a complete curve of stability may be approximately obtained.

A further method of arriving at results by experiment, involving principles not unlike those of the “paper section” method just described, has recently come under the author’s notice, and through the courtesy of its inventor—Mr John H. Heck, of Lloyd’s surveying staff at Newcastle—the following general description of the apparatus and fundamental principles is made public for the first time:—

By means of a “stability balance,” roughly illustrated by Figs 16 and 17, in conjunction with either an outside or inside model of the vessel, the moments of stability can be practically determined. In practice, an inside model has been found the most convenient to employ. This consists of a number of rectangular pieces of yellow pine of any uniform thickness, out of which a portion has been cut, respectively to the form of the vessel at equidistant intervals of say 15 feet. These pieces, together with two end pieces, are kept together by four or six bolts, thus forming a contracted model, the inside of which is of a similar form to that of the vessel. If this model is filled with water to a height corresponding to any draught, it will represent a volume of water having the same form, and proportional to the displacement of the vessel at that draught.

The stability balance consists of a frame =A= attached to a steel bar =Z=, having knife edges working upon the support =C=; a table =D= attached to a spindle working freely in the bearings =E=, and capable of being turned through any angle; a sliding weight =F= to balance the weight of the model when empty; a sliding weight =H= to balance and measure the weight of the water contained in inside or displaced by outside models; a sliding balance weight =K= which by adjustment will locate the centre of gravity of the combined weights of the table =D=, the model and the weight =K= in the axis of the table =D=, so that the model will remain when empty in any inclined position, and be balanced by the weight =F=.

In order to determine the moments of stability, the model is first fixed on the table =D=, and the weights =F= and =K= so adjusted that =F= will balance the model at all inclinations. The table is then brought into the upright position, and water is poured into the model to the height corresponding to the desired draught of water, and the weight =H= shifted until the whole is balanced. The weight of water in the model will evidently be = weight =H= × its distance from the fulcrum ÷ distance centre of model is from fulcrum.

If the table with the model is now turned through any angle, the distance the centre of gravity of the water has moved from the axis =E= of the table can easily be determined by shifting the weight =H= until the whole is balanced, then evidently from the principles of the lever, =H= × by its distance from fulcrum = weight of water in model × by the distance the centre of gravity of the water in the model is from fulcrum. Since the weight of =H= × its distance from fulcrum ÷ the weight of water in model is known, the distance that the centre of gravity of the water has shifted from centre line is easily ascertained and the righting lever determined.

From a lengthened series of experiments, conducted by Mr Heck—latterly in Messrs Denny’s Works where an apparatus from a special design by Mr Heck has been constructed for the firm’s use—the method gives promise of taking a firm place as an extremely simple and approximately accurate means of arriving at the stability of vessels.[18]

While a vessel’s qualities with respect to stability may be determined with great precision by the naval architect, his investigations are only directly applicable to the ship while empty or when in certain assumed conditions of loading which may or may not often occur in actual service. He cannot for obvious reasons estimate, far less control, the amounts and positions of centre of gravity of the various items of weight that may make up the loading.[19] This aspect of the subject has received attention at the hands of naval architects for a considerable time, but the forcible way in which it has been brought under view by recent experience has resulted in special efforts being made to practically meet the necessities of the case. In 1877 Mr William John read a paper before the Institution of Naval Architects, in which he dealt with the effect of stowage on the stability of vessels, and since that time such authorities as Martell, White, and Denny have given valuable papers or made suggestive comments bearing on this important matter. Much has also been done by several builders in the way of devising diagrams useful for regulating stowage and manipulating ballast with regard to initial stability. At the last meeting of the Institution, Professor Elgar read a paper on “The Use of Stability Calculations in Regulating the Loading of Steamers,” distinguished by its eminently practical character, and forming an important contribution to the solution of this problem. The author disapproved of curves of stability being supplied with vessels, as had been advised and was then becoming the practice. General notes, giving in a simple form easily applied in daily practice, particulars respecting the character of a ship’s stability in different conditions, are what the author recommended and had found through actual experience to meet the case most effectually. In the discussion which followed it was intimated by Mr William Denny that his firm had already resolved to furnish every new steamer produced by them with a volume containing general and special notes and diagrams dealing not only with stability but with several other important technical properties (see footnote, page 59). After consultation with Professor Elgar, however, he had abandoned his intention of supplying stability curves.

An arrangement designed to readily find the position of the centre of gravity experimentally by inclining, and to indicate at once the stability of loaded vessels as represented by metacentric height, has been devised and introduced on board several ships by Mr Alexander Taylor, of Newcastle—already referred to in connection with the triple expansion principle in marine engines. The instrument and apparatus, which he appropriately names the “Stability Indicator,” was described in a paper read by him before the Institution of Naval Architects at its last meeting. When once an inclining operation has been made, the degree of inclination is read from a glass gauge and the position of centre of gravity and corresponding metacentric height from a previously prepared scale set up alongside the gauge, or from tabulated figures.

* * * * *

The advance made within recent years in connection with steam propulsion comprises many matters necessarily left unconsidered in the chapter on speed and power of modern steamships. Scientific methods have undoubtedly contributed in no small degree to the realization of the remarkable results therein outlined. The achievement of one triumph after another as demonstrated in the actual performances of new vessels, and especially the confidence with which pledges of certain results are given and received long before actual trials are entered upon—and that sometimes with regard to ships embodying very novel features—are evidences of the truth of this.

The oldest method of approximating to the horse-power required to propel a proposed vessel at a given speed is to compare the new ship with ships already built by the use of formulæ known as “co-efficients of performance” deduced from the results of their speed trials. Two such co-efficients have been deduced from Admiralty practice, the one involving displacement, the other area of mid-section, with speed as the variable in both cases. Another method which has been largely used, consists in first determining the ratio of the indicated horse-power to the amount of “wetted surface,” or immersed portion of the vessel’s skin, in the exemplar ship, and then estimating from this ratio the probable value of the corresponding ratio for the proposed ship at her assigned speed. Inasmuch as these methods of procedure do not take account of the _forms_ of the hulls, and consequently of that factor in the total resistance due to _wave-making_, they cannot be used with any degree of confidence, or without large corrections, except in connection with vessels whose speeds are moderate in proportion to their dimensions: those in fact in which the resistance varies nearly as the square of the speed. A further method, somewhat resembling the one based upon the relation between indicated horse-power and the “wetted surface,” was proposed by the late Prof. Rankine, but has never been extensively employed. Apart from the unreliable nature of the results which an application of it gives—except for certain speeds—it is open to several serious objections in practice.

A method of analysis and prediction, meeting with considerable acceptance from shipbuilders on the Clyde and elsewhere, has been introduced within recent years by Mr A. C. Kirk, of Messrs R. Napier & Sons.[20] The method consists in reducing all vessels to a definite and simple form, such as readily admits of comparison being made between their immersed surface, length of entrance and angle of entrance and their indicated horse-power, and from this judging of the form and proportions best suited to a given speed or power in proposed vessels. The form in question consists of a block model, having a rectangular midship section, parallel middle body, and wedge-shaped ends; its length being proportioned to that of the ship, its depth to the mean draught of water, its girth of mid-section to the girth of immersed mid-section of the ship, and the surface of its sides, bottom and ends, to the immersed surface of the ship. By finding from one or more exemplar ships—the selection of which is obviously governed by the conditions of analysis—the rate of indicated horse-power required per unit of wetted surface at the speed assigned for the proposed vessel, the appropriate rate for the latter may easily be determined.

The data afforded by the modern system of progressive speed trials, especially when taken in conjunction with that of experiment with models as systematised by Mr Froude, supplies in a reliable way much of what is most lacking in the older methods of comparison and prediction. Progressive speed trials on the measured mile were first systematically instituted by Mr William Denny about nine years ago, since which it has been the practice of his firm to make such trials with all their vessels. The practice has been followed by other firms on the Clyde and elsewhere, and there is every probability it will be still more widely adopted in the future. The system consists in trying the vessel at various speeds, ranging from the highest to about the lowest of which she is capable. The several speeds are the mean of two runs—one run with the tide and one against, the object being to eliminate the tide’s influence from the results.[21]

Essentially noteworthy in connection with the system is the manner in which the data obtained from the trials is recorded for future use. This consists of a series of curves, representing the chief properties of ship, engines, and propeller—_e.g._, “speed and power,” “revolutions” and “slip”—which show to the eye, more easily and clearly than bare figures, the whole course and value of a steamer’s performances. For that of speed and power the various speeds made at the trials are set off to convenient scale as horizontal distances, and the indicated horse-power corresponding to those speeds are set off to scale as vertical distances. The intersection of the offsets so made, give spots for the curve. The other curves alluded to are similarly constructed, the requisite data being the direct or deduced results of the measured mile trials.

From the accumulation of trial results thus graphically recorded the designer of new ships can proceed to estimate with greater assurance of attaining satisfactory results than by employing the older methods. If, for example, a ship is to be built of virtually similar dimensions and form to one for which such information is available, but of less speed, the task is simply one of measurement from the curves, with some allowance for probable differences in the constant friction of the engines. If the speed is to be greater than that of the exemplar ship, but still within the limits when wave-making resistance assumes relative importance, the case is also one of simple reading from the curves, with slight corrections. When both the speed and size are different, but the form is approximately the same, the case is more difficult, but it can be dealt with approximately by employing the “law of comparison” or of “corresponding speeds” enunciated by Mr Froude. Formulæ based upon this law—which will be more fully referred to presently—have been devised by one or two designers, and applied by them to problems of the latter class as they occurred in the course of their professional work. Mr John Inglis, junr., described a method of analysis he had adopted, involving the use of Mr Froude’s law, in a paper read before the Institution of Naval Architects in 1877.

When unusual speeds are aimed at, or when novel types of vessels have to be dealt with, the only available method of making a trustworthy estimate of the power required lies in the use of direct or deduced results from model experiments. Mr Froude began the work of speed experiments with ships’ models on behalf of the Admiralty at the Experimental Tank in Torquay about 1872, carrying it on uninterruptedly until his death in May, 1879. Since that lamented event the work has been continued with most gratifying results by his son, Mr R. E. Froude. Experiments had, of course, been made by many other investigators previous to Mr Froude, but none before or since have made model experiments so practically useful and reliable. Since the value of the work carried on at Torquay has become appreciated, several experimental establishments of a similar character have been instituted. The Dutch Government, in 1874, formed one at Amsterdam, which, up till his death in 1883, was under the superintendence of Dr Tideman, whose labours in this direction were second only to those of the late Mr Froude. It is now superintended by Mr A. J. H. Beeloo, Chief Constructor, and under him by Mr H. Cop. It was here, it may be remembered, that experiments were made with a model of the Czar of Russia’s yacht _Livadia_, previous to the construction of that extraordinary vessel being begun by Messrs Elder & Co. On the strength of the data so obtained, together with the results of the trials made on Loch Lomond with a miniature of the actual vessel, those responsible for her stipulated speed were satisfied that it could be attained. The actual results as to the speed of the novel vessel amply justified the reliance put upon such experiments. In 1877 the French naval authorities established an experimental tank in the dockyard at Brest, and the Italian Government have formed one in the naval dockyard at Castellamare. The only experimental tank hitherto established by a private mercantile firm is that in the shipyard of Messrs Denny, Dumbarton. This establishment is on a scale of completeness not surpassed elsewhere, and is fitted with every appliance which the latest experience in such experiments shows to be advantageous. A special staff of experimentalists, forming a branch of the general scientific body, are engaged conducting experiments and accumulating data, which, besides being of service in their present daily practice, must ultimately yield fruit of a very special kind to this enterprising firm.[22]

From mathematical reasoning, and by means of an extended series of experiments with models and actual ships, Mr Froude determined that for two vessels of similar form—for instance a ship and her model—the “corresponding speeds” of ship and model are to one another as the square roots of the similar dimensions, and at corresponding speeds the resistance of ship and of model are to one another as the cubes of the similar dimensions—subject to a correction concerned with skin friction necessitated by the difference in the lengths of ship and model.[23] Having obtained the resistance of a model, and from it, by an application of the above law, deduced the resistance of the full-sized vessel, the effective horse-power is found by multiplying the resistance by the speed of the vessel in feet per minute, and dividing by 33,000. From the effective horse-power an estimate of the indicated horse-power required can be made by using ratios which the one bore to the other in former ships, as obtained from a comparison of their model experiments with their measured mile trial results.

The value of progressive speed trials and of experiments with models as affording convenient means whereby analysis may be made of the several sources of expenditure of power in propelling vessels can scarcely be over-estimated.

From a study of the graphic records of progressive trials, and from model experiment results, Mr Froude discovered a method whereby the power expended in overcoming the frictional resistance of the engines could be determined, and estimates made of the amount of power absorbed by other elements. The method in question was communicated in full in a paper read before the Institution of Naval Architects in 1876, and has since been extensively used. Methods of analysis resulting from a simultaneous study of this subject, were also proposed by Mr Robert Mansel, a prominent Clyde shipbuilder and noted investigator, but they failed in meeting with the acceptance which was at once accorded to Mr Froude’s propositions.[24]

Although the results obtained by an application of Mr Froude’s analysis to the trials of a large number of merchant vessels have undoubtedly thrown considerable light on the relative efficiency of hull and engines, and of various types of engines, still, for several reasons adduced by extended experience—most of which, indeed, were foreseen and perfectly appreciated by Mr Froude himself—the need has been felt for some means of directly measuring the power actually delivered to the propellers by the engines when working at different speeds. One of Mr Froude’s latest inventions, the perfecting of which was not accomplished until after his death, consisted of a dynamometric apparatus designed to accomplish this important end.[25] The construction of the instrument was undertaken for the Admiralty, and trials were made with it on H.M.S. _Conquest_ in the early part of 1880. The results of these experiments have not yet in any form been recorded, but there can be no question as to the benefit that would accrue to the profession if the Admiralty could be induced to publish these, as well as the results of other experiments with this instrument.

Experiments with actual vessels to determine directly the relative efficiency of hull, engines, and propellers have on several occasions been undertaken. A series of trials of this nature were made in 1874 by Chief-Engineer Isherwood, U.S. Navy on a steam launch, the results of which may be found detailed in the Report of the Secretary of U.S. Navy for 1875. Similar trials have been made recently on the United States steamer _Albatros_, an interesting account of which appeared in _Engineering_ of October 17 of the present year. These experiments are referred to as notable examples of what might be carried out with great advantage on other and larger vessels, although they are such, perhaps, as few single firms can well be expected to follow extensively.

The economies which may be obtained by changes in the propellers fitted to ships, and the great value of progressive speed trials as a means of measuring the effects of such changes, received most remarkable illustration in the results of the trials of H.M.S. _Iris_, carried out for the Admiralty in 1880. These showed that by simply varying the propellers—all other conditions remaining practically unchanged—the speed of the ship was increased from 16½ to 18½ knots per hour. Scarcely less striking improvements in the performances of vessels due to changed propellers might be found from the records of trials made with merchant vessels within recent years.

Inasmuch as measured mile trials are usually carried out when vessels are in the light or partially loaded condition, the results are far from being so valuable as they might be made; alike for the purposes of the naval architect, the shipowner, and ships’ officers; if they were undertaken with vessels in the completely laden condition. The information obtained from the trials of incompletely laden vessels does not yield that knowledge of a vessel’s qualities under the conditions necessarily imposed by actual service, which, if possessed by naval architects, would doubtless prove of immense value, nor does it furnish that standard of comparison for performances at sea which owners and captains should possess. In the interests of all concerned, it is to be hoped the practice of trying loaded vessels may become more common.

Amongst the earliest and most notable investigations involving the application of principle to the calculation of the longitudinal strength of iron vessels were those by Sir William Fairbairn, who contributed an elaborate statement of his views and methods to the first meeting of the Institute of Naval Architects in 1860. Investigation up till about this period, almost wholly concerned itself with vessels considered as girders, and in assumed conditions of fixed support, such as being pivoted on rocks. Later investigations have shown these conditions to be altogether too extreme and severe when compared with the known and estimated strains which vessels are called upon to bear in ordinary service. In 1861 Mr J. G. Lawrie, of Glasgow, in an able paper on Lloyd’s rules, read before the Scottish Shipbuilders’ Association,[26] reasoning from wave phenomenon and the probable effects attending motion in a seaway, endeavoured to deduce limits or absolute values for the extreme strains experienced by a vessel in the circumstances, the results obtained by Mr Lawrie bearing very closely on those deduced by later investigations. The late Professor Rankine made investigations involving consideration of strains in a seaway, and formulated several valuable rules which to some extent are still accepted, although giving results which are not likely to be exceeded in any case of ordinary service.[27]

For the most recent advances made in this important branch of the science of naval architecture, the profession lies under indebtedness chiefly to one or two naval architects of eminent ability, whose professional province for a time has lain more especially in the way of a full consideration of the subject. Sir E. J. Reed, while Chief Constructor of the Navy, and under him several Government-trained naval architects subsequently acquiring high positions, achieved much in accurate investigation of iron-clad vessels of war. In 1870 the authority named read an elaborate paper before the Royal Society dealing at length with such work.[28] In 1874 Mr William John, formerly under Sir E. J. Reed, but at that time Assistant Chief Surveyor to Lloyd’s Register, read a valuable paper before the Institution of Naval Architects, in which he gave the results of investigations of specific cases, and of long and careful study of the general problem as concerned with merchant vessels. In this paper, Mr John advanced the proposition that the maximum bending moment likely to be experienced on a wave crest may be taken approximately as one thirty-fifth of the product of the weight of the ship into her length. Proceeding on this assumption Mr John’s paper further gave valuable results of calculations made into the strength of a series of vessels representing large numbers of mercantile steamers then afloat.[29] Of this paper and the conclusions it pointed to, Mr John, in a later paper on “Transverse and other Strains of Ships,” said:—

“The investigations showed unmistakably that as ships increased in size a marked diminution occurred in their longitudinal strength, and the results caused some surprise at the time, although they might perhaps have been easily inferred from the writings of others published at an earlier period. Those results, in spite of their approximate character, impressed two conclusions strongly on my mind: firstly, that there was cause for anxiety as to the longitudinal strength of some very large iron steamers then afloat, and that the longitudinal strength of large ships needed on all hands the most careful vigilance and attention; and secondly, that in small vessels, and even vessels of moderate dimensions, the longitudinal strength need cause but little anxiety, because it is amply provided for by the scantlings found necessary to fulfil the other requirements of a sea-going trade.”

Using the formula as to the maximum bending moment advanced by Mr John many investigations have been made subsequently into the longitudinal strength of vessels, and this increased interest in the subject has not been without its effect on subsequent structural practice.

Mr John followed up his investigations on the longitudinal strength of merchant vessels viewed as girders by an inquiry into the transverse and other strains of ships, and in 1877 gave a valuable paper on the subject, from which a quotation has already been made, before the Institution of Naval Architects. The results of Mr John’s inquiry were such as demonstrated the need for systematic and thorough investigation of the subtle and intricate questions involved. This subject has been matter of study at Lloyd’s Register for several years, and in March, 1882, the results of inquiries conducted by Mr T. C. Bead and Mr P. Jenkins, members of the staff in London, and former students of the Royal Naval College, Greenwich, were communicated in an able paper by these gentlemen, read to the Institution of Naval Architects.

It will of course be understood that many investigations of strength are instituted not necessarily out of fear that maximum strains may not be adequately allowed for, but because the dual quality of strength-with-lightness may possibly be better attained by modifications in the arrangements of material or sufficiently met by reduced scantling. The functions and influence of the Registration Societies, already commented upon (see footnote, page 103), are such as to obviate the need for strength investigations generally, or at least are such as to discourage shipbuilders from independently instituting them. Nevertheless, some well-known shipbuilders, who are also notable investigators, amongst whom may be named Inglis, Mansel, Denny, and Wigham Richardson, have done much valuable work in this connection. Mr Denny, in particular, has vigorously devoted himself to strength analysis on the basis of Lloyd’s methods of fixing scantling, and read several papers on the subject, in which strong exception is taken to present practice. The healthy criticism which such labours have enabled those making them to offer regarding the Registry systems of scantlings has not doubtless failed in influencing the legislation of the Registries.

* * * * *

Reverting to the subject of agencies for education in naval architecture, a few remarks are due relative to Government institutions as having hitherto failed in being of immediate service to the mercantile marine. The training given to naval architects and marine engineers at the Admiralty Schools is admirably adapted for creating a staff of war-ship designers and expert mathematicians, such as are employed in the various departments of the Admiralty service. The course of instruction has been framed expressly with a view to this, and a very high standard of mathematical knowledge is necessary before students can enter upon it. The principle of requiring one to become a first-class mathematician before attempting to teach him much of the science of naval architecture and its application in practice, is of questionable merit: at any rate it cannot be carried out in the mercantile marine. Again; economy of time and of cost of production are conditions which largely govern the methods followed in mercantile practice. Short methods of calculation, or of tentative approximation, for the purpose of enabling tenders to be made for proposed vessels, and of quickly proceeding with the work when secured, form no inconsiderable feature in the training required by mercantile naval architects. These, however, do not as a rule enter to any extent into Admiralty modes of procedure.

The want of satisfactory means for obtaining a sound scientific and practical training in mercantile naval architecture has for some time been felt to be very pressing. The evening classes conducted in most of the shipbuilding centres under the auspices of the Science and Art Department, South Kensington, are fitted to supply a part of this want so far as elementary teaching is concerned. Until recently the antiquated character of the questions set for examination was subject of general complaint, both on the part of students and teachers. In August, 1881, Mr William Denny read a paper on “Local Education in Naval Architecture” before the Institution of Naval Architects, in which adequate expression was given to these complaints, and at the same time proposed amendments offered. As a consequence of this paper, and of the steps taken by the Institution in appointing a deputation to wait upon the Government, the questions have been considerably improved, and are now so framed as to form a fairly crucial test of a young student’s knowledge of the science and practice of modern shipbuilding.

During the past three years efforts have been made by the Council of the Institution of Engineers and Shipbuilders in Scotland[30] to supply more adequate means of advanced education. In 1880, the Council had before them a project, promoted, for most part independently, by Mr Robert Duncan and others, to establish a Lectureship of Naval Architecture and Marine Engineering. It was proposed to collect funds sufficient to endow the lectureship under the auspices of the University, and promises of substantial aid were obtained from several members. Mr J. G. Lawrie volunteered to give the first course of lectures and did so, according to arrangement, during the winter months of 1881-82 before a considerable number of students, the lectures being delivered in the University of Glasgow during the day, and repeated in the Institution rooms in the evening. These praiseworthy efforts were still being carried on when, in November, 1883, the gratifying announcement was made of a gift of £12,500 by Mrs John Elder, widow of the late eminent engineer, for the endowment of a Chair of Naval Architecture in the University. The founding of this chair, and the subsequent election by the University Court of Mr Francis Elgar to the Professorship, have thus doubtless obviated the need for further efforts to found the lectureship, but there are many commendable objects connected with the University Chair to which the continued efforts of the gentlemen who supported the lecture project might fittingly be directed. Many students who can afford it will doubtless study the higher branches of naval architecture at Glasgow University, and if a few small University scholarships were established, for which all classes of workers in the shipyards and drawing offices might compete, the highest professional training would then be within the reach of the poorest of lads.

Evidences have recently been given of a strong desire on the part of many engaged in the shipbuilding and engineering industries of the Tyne and Wear for the founding of a Chair of Naval Architecture in some educational institution in that district. Along with this movement a desire has been shown for the establishment of an Institution of Engineers and Shipbuilders such as has been so long carried on successfully in the Clyde district. Definite steps are about to be taken for the realisation of these important objects, and doubtless no great time will elapse before they are accomplished.

List of papers and lectures dealing with scientific problems in shipbuilding, to which readers desiring fuller acquaintance with the _technique_ and details of the subjects are referred:—

THE PROGRESS OF SHIPBUILDING IN ENGLAND: _Westminster Review_, January, 1881.

HISTORY OF NAVAL ARCHITECTURE. Lecture delivered by Mr Wm. John at Barrow-in-Furness: _Iron_, Dec. 8th, 1882.

DISPLACEMENT AND CARRYING CAPABILITY.

ON A METHOD OF OBTAINING THE DESIRED DISPLACEMENT IN DESIGNING SHIPS, by Mr R. Zimmerman: Trans. Inst. N.A., vol. xxiv, 1883.

ON FREEBOARD, by Mr Benjamin Martell: Trans. Inst. N.A., vol. xv., 1874.

ON THE LOAD DRAUGHT OF STEAMERS, by Mr W. W. Rundell: Trans. Inst. N.A., vol. xv., 1873: vol. xv., 1874; and vol. xvi., 1875.

ON THE LOAD LINE OF STEAMERS, by Mr John Wigham Richardson: Trans. Inst. N.A., vol. xix., 1878.

ON THE BASIS FOR FIXING SUITABLE LOAD LINES FOR MERCHANT STEAMERS AND SAILING SHIPS, by Mr Benjamin Martell: Trans. Inst. N.A., vol. xxiii., 1882.

ON THE ASSESSMENT OF DECK ERECTIONS IN RELATION TO FREEBOARD, by Mr H. H. West, vol. xxiv., 1883.

TONNAGE MEASUREMENT, MOULDED DEPTH, AND THE OFFICIAL REGISTER IN RELATION TO THE FREEBOARD OF IRON VESSELS, by Mr W. W. Rundell: Trans. Inst. N.A., vol. xxiv., 1883.

STABILITY.

ON THE CALCULATION OF THE STABILITY OF SHIPS AND SOME MATTERS OF INTEREST CONNECTED THEREWITH, by Mr W. H. White and Mr W. John: Trans. Inst. vol. xii., 1871.

ON THE RELATIVE INFLUENCE OF BREADTH OF BEAM AND HEIGHT OF FREEBOARD IN LENGTHENING OUT THE CURVES OF STABILITY, by Mr Nathaniel Barnaby: Trans. Inst. N.A., vol. xii., 1871.

ON THE LIMITS OF SAFETY OF SHIPS AS REGARDS CAPSIZING, by Mr C. W. Merrifield: _The Annual_ of the Royal School of Naval Architecture and Marine Engineering, No. 1, 1871; London, H. Sotheran & Co.

ON CURVES OF BUOYANCY AND METACENTRES FOR VERTICAL DISPLACEMENTS, by Mr George Stanbury: _The Annual_ of the Royal School of Naval Architecture and Marine Engineering, No. 2, 1872, London, H. Sotheran & Co.

THE GEOMETRICAL THEORY OF STABILITY FOR SHIPS AND OTHER FLOATING BODIES: _Naval Science_, vol. iii., 1874, and vol. iv., 1875 (Three Articles).

ON THE METACENTRE AND METACENTRIC CURVES: _Naval Science_, vol. iii., 1874.

ON POLAR DIAGRAMS OF STABILITY, by Mr J. MacFarlane Gray: Trans. Inst. N.A., vol. xvi., 1875.

ON THE STABILITY OF SHIPS, by Mr Wm. John: Trans. Inst. N.A., vol. xviii., 1877.

ON THE GEOMETRY OF METACENTRIC DIAGRAMS, by Mr W. H. White: Trans. Inst. N.A., vol. xix., 1878.

ON THE STABILITY OF CERTAIN MERCHANT SHIPS, by Mr W. H. White: Trans. Inst. N.A., vol. xxii., 1881.

ON CURVES OF STABILITY OF SOME MAIL STEAMERS, by Mr J. H. Biles: Trans. Inst. N.A., vol. xxiii., 1882.

ON THE REDUCTION OF TRANSVERSE AND LONGITUDINAL METACENTRIC CURVES TO RATIO CURVES, by Mr Wm. Denny: Trans. Inst. N.A., vol. xxiii., 1882.

ON THE ADVANTAGES OF INCREASED PROPORTION OF BEAM TO LENGTH IN STEAMSHIPS, by Mr J. H. Biles: Trans. Inst. N.A. vol. xxiv., 1883.

ON THE STABILITY OF SHIPS AT LAUNCHING, by Mr J. H. Biles: Trans. Inst. Eng. and Ship., vol. xxvii., 1883-84.

ON APPROXIMATION TO CURVES OF STABILITY FROM DATA FOR KNOWN SHIPS, by Mr F. P. Purvis & Mr B. Kindermann: Trans. Inst. E. and S., vol. xxvii., 1883-84.

ON CROSS-CURVES OF STABILITY, THEIR USES, AND A METHOD OF CONSTRUCTING THEM, OBVIATING THE NECESSITY FOR THE USUAL CORRECTION FOR THE DIFFERENCES OF THE WEDGES OF IMMERSION AND EMERSION, by Mr William Denny: Trans. Inst., N.A., vol. xxv., 1884.

ON A NEW METHOD OF CALCULATING AND SOME NEW CURVES FOR MEASURING THE STABILITY OF SHIPS AT ALL ANGLES OF INCLINATION, by M. V. Daymard: Trans. Inst., N.A., vol. xxv., 1884.

THE USES OF STABILITY CALCULATIONS IN REGULATING THE LOADING OF STEAMERS, by Professor F. Elgar: Trans. Inst., N.A., vol. xxv., 1884.

ON SOME POINTS OF INTEREST IN CONNECTION WITH THE CONSTRUCTION OF METACENTRIC DIAGRAMS AND THE INITIAL STABILITY OF VESSELS, by Mr P. Jenkins: Trans. Inst., N.A., vol. xxv., 1884.

ON THE USES OF J. AMSLER’S INTEGRATOR IN NAVAL ARCHITECTURE, by Dr A. Amsler: Trans. Inst., N.A., vol. xxv., 1884.

CONTRIBUTIONS TO THE SOLUTION OF THE PROBLEM OF STABILITY, by Mr L. Benjamin: Trans. Inst., N.A., vol. xxv., 1884.

THE GRAPHIC CALCULATION OF THE DATA DEPENDING ON THE FORM OF SHIPS REQUIRED FOR DETERMINING THEIR STABILITY, by Mr J. C. Spence: Trans. Inst., N.A., vol xxv., 1884.

DESCRIPTION OF ALEXANDER TAYLOR’S STABILITY INDICATOR FOR SHOWING THE INITIAL STABILITY AND STOWAGE OF SHIPS AT ANY DISPLACEMENT, by Mr Alex. Taylor: Trans. Inst., N.A., vol. xxv., 1884.

ROLLING.

CONSIDERATIONS RESPECTING THE EFFECTIVE WAVE SLOPE IN THE ROLLING OF SHIPS AT SEA, by Mr William Froude: Trans. Inst., N.A., vol. xiv., 1873.

ON AN INSTRUMENT FOR AUTOMATICALLY RECORDING THE ROLLING OF SHIPS, by Mr Wm. Froude: Trans. Inst. N.A., vol. xiv., 1873.

ON THE GRAPHIC INTEGRATION ON THE EQUATION OF A SHIP’S ROLLING, by Mr Wm. Froude: Trans. Inst. N.A., vol. xv., 1874.

ON THE ROLLING OF SAILING SHIPS, by Mr W. H. White: Trans. Inst. N.A., vol. xxii., 1881.

ON A METHOD OF REDUCING THE ROLLING OF SHIPS AT SEA, by Mr P. Watts: Trans. Inst. N.A., vol. xxiv., 1883.

RESISTANCE, SPEED, AND POWER.

ON STREAM LINE SURFACES, by Prof. W. J. Macquorn Rankine: Trans. Inst. N.A., vol. xi., 1870.

ON EXPERIMENTS WITH H.M.S. GREYHOUND, by Mr William Froude: Trans. Inst. N.A., vol. xv., 1874.

ON THE DIFFICULTIES OF SPEED CALCULATION, by Mr Wm. Denny: Trans. Inst. Eng. and Ship. in Scotland, vol. xvii., 1874-75.

ON THE RATIO OF INDICATED TO EFFECTIVE HORSE POWER AS ELUCIDATED BY MR DENNY’S MEASURED MILE TRIALS AT VARIED SPEEDS, by Mr Wm. Froude: Trans. Inst. N.A., vol. xvii., 1876.

ON THE COMPARATIVE RESISTANCES OF LONG SHIPS OF SEVERAL TYPES, by Mr Wm. Froude: Trans. Inst. N.A., vol. xvii., 1876.

ON EXPERIMENTS UPON THE EFFECT PRODUCED ON THE WAVE-MAKING RESISTANCE OF SHIPS BY LENGTH OF PARALLEL MIDDLE BODY, by Mr Wm. Froude: Trans. Inst. N.A., vol. xviii., 1877.

ON STEAMSHIP EFFICIENCY, by Mr Robert Mansel: Trans. Inst. Eng. and Ship. in Scotland, vol. xxii., 1878-79.

ON THE TRUE NATURE OF THE WAVE OF TRANSLATION AND THE PART IT PLAYS IN REMOVING THE WATER OUT OF THE WAY OF A SHIP WITH LEAST RESISTANCE, by Mr J. Scott Russell: Trans. Inst. N.A., vol. xx., 1879.

ON THE LEADING PHENOMENA OF THE WAVE-MAKING RESISTANCE OF SHIPS, by Mr R. E. Froude: Trans. Inst. N.A., vol xxii., 1881.

MR FROUDE’S EXPERIMENTS ON RESISTANCE AND ROLLING: _Naval Science_, vol. i., 1872, and vol. iv., 1875.

MR FROUDE’S RESISTANCE EXPERIMENTS ON H.M.S. GREYHOUND: _Naval Science_, vol. iii., 1874.

ON A METHOD OF RECORDING AND COMPARING THE PERFORMANCES OF STEAMSHIPS, by Mr John Inglis, jun.: Trans. Inst. N.A., vol. xviii., 1877.

ON A METHOD OF ANALYSING THE FORMS OF SHIPS AND DETERMINING THE MEAN ANGLE OF ENTRANCE, by Mr Alex. C. Kirk: Trans. Inst. N.A., vol. xxi., 1880.

ON SOME RESULTS DEDUCED FROM CURVES OF RESISTANCE AND PROGRESSIVE M M SPEED CURVES, by Mr J. H. Biles: Trans. Inst. N.A., vol. xxii., 1881.

ON PROGRESSIVE SPEED TRIALS, by Mr J. H. Biles: Trans. Inst. N.A., vol. xxiii., 1882.

STRUCTURAL STRENGTH.

THE DISTRIBUTION OF WEIGHT AND BUOYANCY IN SHIPS: _Naval Science_, vol. i., 1872.

THE STRAINS OF SHIPS IN STILL WATER: _Naval Science_, vol. i., 1872.

THE STRAINS OF SHIPS IN EXCEPTIONAL POSITIONS ON SHORE: _Naval Science_, vol. ii., 1873.

THE STRAINS OF SHIPS AT SEA: _Naval Science_, vol. ii., 1873.

ON THE STRENGTH AND STRAINS OF IRON SHIPS: _Naval Science_, vol. iii., 1874.

ON THE STRENGTH OF IRON SHIPS, by Mr William John: Trans. Inst. N.A., vol. xv., 1874.

ON USEFUL DISPLACEMENT AS LIMITED BY WEIGHT OF STRUCTURE AND OF PROPULSIVE POWER, by Mr Wm. Froude: Trans. Inst. N.A., vol. xv., 1874.

ON THE MODULUS FOR STRENGTH OF SHIPS, by Mr J. MacFarlane Gray: Trans. Inst. N.A., vol. xvi., 1875.

ON THE STRAINS AND STRENGTH OF SHIPS, by Mr John Wigham Richardson: Trans. Inst. N.A., vol. xvi., 1875.

ON TRANSVERSE AND OTHER STRAINS OF SHIPS, by Mr William John: Trans. Inst. N.A., vol. xviii., 1877.

ON THE STRAINS OF IRON SHIPS, by Mr William John: Trans. Inst. N.A., vol. xviii., 1877.

ON LLOYD’S NUMERALS, by Mr William Denny: Trans. Inst. N.A., vol. 1877.

ON LIGHTENED SCANTLINGS, by Mr Wm. Denny: Trans. Inst. N.A., vol. xix., 1878.

ON THE EFFECT OF DEPTH UPON THE STRENGTH OF A GIRDER TO RESIST BENDING STRAINS, by Mr Frank P. Purvis: Trans. Inst. N.A., vol. xix., 1878.

ON AN APPLICATION OF THE DECIMAL SYSTEM OF MEASUREMENT IN PRACTICAL SHIPBUILDING, by Mr Henry H. West: Trans. Inst. N.A., vol. xix., 1878.

ON LONGITUDINAL SEA STRAINS IN VESSELS AS INDICATED BY LLOYD’S EXPERIENCE, by Mr Robert Mansel: Trans. Inst. Eng. and Ship, in Scotland, vol. xxi., 1877-78.

ON THE STRENGTH OF IRON VESSELS, by Mr Geo. Arnison, jun.: Trans. Inst. Eng. and Ship., vol. xxii., 1878-79.

FREEBOARD AND DISPLACEMENT IN RELATION TO STRAINS IN SHIPS AMONG WAVES, by Mr W. W. Rundell: Trans. Inst. N.A., vol. xxii., 1881.

ON THE TRANSVERSE STRAINS OF IRON MERCHANT VESSELS, by Mr P. Jenkins and T. C. Read: Trans. Inst. N.A., vol. xxiii., 1882.

ON HOGGING AND SAGGING STRAINS IN A SEAWAY AS INFLUENCED BY WAVE STRUCTURE, by Mr W. E. Smith: Trans. Inst. N.A., vol xxiv., 1883.

EDUCATION IN NAVAL ARCHITECTURE.

ON THE COURSE OF STUDY IN THE ROYAL NAVAL COLLEGE, GREENWICH, by Mr W. H. White: Trans. Inst. N.A., vol. xviii., 1877.

ON THE ROYAL NAVAL COLLEGE AND THE MERCANTILE MARINE, by Mr Wm. John: Trans. Inst. N.A., vol. xix., 1878.

ON LOCAL EDUCATION IN NAVAL ARCHITECTURE, by Mr William Denny: Trans. Inst. N.A., vol. xxii., 1881.