necessary to apply to their designs such stability calculations as had been rendered possible by the researches of mathematicians. These were, for the most part, embalmed in abstruse treatises, but had been, in the years 1860, 1861, and 1868, made the subject of papers read before the Institution of Naval Architects in London by Mr. F. K. Barnes, Dr. Woolley, and Mr. E. J. Reed. The paper read by the latter gentleman, then Chief Constructor of the Navy, in 1868, was “on the stability of monitors under canvas,” and in it he showed the danger of carrying canvas on low-sided vessels. A proposal had been made to cut down some of our old wooden walls, to add armour-plating to their sides, and to rig them for sea-service. The “Captain” was projected by a naval officer as a rigged sea-going vessel to carry guns in round turrets above a low freeboard. Mr. Reed opposed both proposals; but so little value was attached to his calculations that the Admiralty devoted the money for Captain Cowper Coles to go to a private firm and get his vessel built. Controversy is probably dead now as to the personal details, and I allude to them not for the purpose of reviving them, but in order to emphasize the danger of ignoring the warnings of science.

In 1871 Mr. Barnaby, President of the Council of Construction to the Admiralty, read a paper in which the following paragraph occurs: “It is just three years since curves of stability were first introduced to public notice in a paper read here by the late Chief Constructor of the Navy. Few of us supposed then that they would receive such a melancholy notoriety as has since befallen them, and no one attached enough importance to them to calculate them for an actual ship until last August, when, unhappily, the curve only served to show clearly why the ship was lost, instead of preventing the calamity.”

The above quotation refers to the initiation of curves of stability. It had been up to this time the practice at the Admiralty to calculate the stability at 7° and 10° inclination, and if satisfactory at these small angles the design was passed. To construct the curve referred to by Mr. Barnaby it was necessary to calculate the stability at several other and larger angles of inclination. When the stability had been thus ascertained the results were plotted upon a scale, and the line drawn through the spots formed a “curve of stability” from which could be read off the stability at any other desired angle within the limits for which it had been calculated. It will be seen that this development of the practice in 1868 was a most important one, and that had it been applied to the case of the “Captain” the peculiar danger to which she was subject would have been observed, and a modification of the design would probably have followed.

The sad fatalities alluded to have greatly increased the number of those who have studied the principles governing the stability of ships, and scarcely a year of the last ten has passed without one or more papers being read before the Institution of Naval Architects. The principal value of these has been that they have introduced various methods by which the calculations can be greatly shortened, and their application thus rendered more generally possible. My object in reading this paper is not to explain the detailed calculations, but to endeavour to popularise a knowledge of the principles of stability by stripping the subject of its technicalities, and by making free use of simple and familiar models and diagrams.

As a preliminary to these explanations it will be desirable to distinguish between two terms—“steadiness” and “stability”—which are sometimes confounded. A ship which rolls considerably is an unsteady ship; but it does not follow that she possesses a small amount of stability. Quite the contrary may be the case, and, if her rolling is short and quick, it is very probably caused by having too much. The explanation of this apparent contradiction is that a stable vessel does not endeavour to stand upright, but to place herself at right angles to the surface of the water in which she is for the moment floating. If she happens to be amongst waves this tendency leads to a continual change of position; if she is in smooth water, and acted upon by a beam wind, she endeavours for the same reason to place herself at right angles to the surface of the water, which, being horizontal in this case, would be the upright position. Seafaring men know well that quick rolling is promoted by the stowage of heavy weights low down in the hold, but they will readily see that this operation, by lowering the centre of gravity, has increased the stability. On the other hand, very long rolling with slow recovery probably indicates a deficiency of stability. “Steadiness” is the quality of resistance in a ship to the tendency of waves to make her roll from side to side, while stability is the quality of resistance to the force of the wind (or of some force outside of and above the water) which tends to make her incline to one side, or, as sailors term it, to “take a list.” Steadiness is most desirable in a war-ship, to enable her to take good aim with her guns; and in a passenger-vessel adds greatly to the comfort of passengers. At the same time, all vessels should, for the sake of safety, not only possess a fair amount of stability at small angles, but should have a power of recovery from the very considerable inclination produced by sudden squalls. This quality also stands them in good stead when their cargoes have been badly shifted by stress of weather.

As another preliminary it will be necessary to define “the law of flotation.” It may be stated thus: Any floating body

displaces exactly its own weight of water. This means that it occupies a space from which it has expelled as much water as would weigh exactly the same as itself. It is therefore only necessary to calculate the bulk of that portion of the floating body which is below the surface of the water, and then to ascertain the weight of an equal bulk of water, in order to find out what must be the total weight of the body when immersed to the given draught.

We may vary the statement of this principle as follows: A ship placed in water will descend until she reaches a state of equilibrium, or to such a point that the downward pressure of her weight is exactly balanced by the upward pressure of the water. This fact is entirely unaffected by the depth of the water in which she floats or by the extent of surface around the ship.

The pressure of the water is constant at every point which, is at an equal distance below the surface, and it increases in the same ratio as the depth increases. That the extent of surface has nothing to do with the pressure may be seen by the case of a vessel lying at one side of a dock with, say, 1ft. of water between herself and the wall, while there are 500ft. on the off side. She has no tendency to fall towards the quay. Of the increasing density of water as the depth increases, and of the friction upon the surface of a ship when moving, I intend to take no notice, but shall consider the water as exerting an equal pressure at every point of the ship's surface below the water-line, and in direction at right angles to every point of such surface. It will always be assumed that we are dealing with still water.

To be able to deal with the effects of this pressure we must find out a point through which it acts, or at which it all culminates, and then we shall be able to examine its action in giving stability to bodies floating therein.

At this stage, then, we begin to deal with the stability problem. And in the first place let us consider a contrast and an analogy between a body out of water and the same body floating.

On land, or on any fixed and solid surface, it is the base upon which the body rests which affords it stability. The law of its stability is that a perpendicular from the centre of gravity must fall within the base. The further it falls within, the greater the stability. Consequently, an increase in the area of the base all round the perpendicular adds to the stability. But a knowledge of the latter fact often leads to misconception as to the stability of a ship, it being frequently asserted that “such a ship will be stiff enough because she has a good flat bottom to stand upon.” There could be nothing more erroneous than this idea. If there is any part of

a ship which may be considered at all analogous to a base it is the water-level section, and an increase of its area adds to stability. The form of the bottom, it is true, has its influence on stability, but flatness of bottom in a sea-going vessel tends to reduce it. The method of a ship when floating is in this respect entirely in contrast with that of a body resting on the ground.

The analogy appears when we consider the case of the body out of water when suspended from a point. The law of its stability in these circumstances is that its centre of gravity will hang perpendicularly below the point of suspension. Let us make use of a model to illustrate this analogy. It will be observed that I have in anticipation found its centre of gravity, and have screwed opposite to the spot a small eye by which to hang it up. A short definition of the term “centre of gravity” may be given as follows: It is that point from which if the body be conceived to be suspended it will remain in equilibrium in any position. This model cannot be hung from the actual point, because it is within its own substance; but by the law of suspension the centre of gravity must be somewhere in the vertical line below the eye. The model hangs horizontally lengthwise, and the deck hangs vertically, so that the centre of gravity must be at the point at which the perpendicular would cut the half-breadth line. This experiment serves to show that we can by this means identify the point in the fore-and-aft, vertical, and athwartship directions. That the model freely chooses its present position is shown by its prompt return to it if disturbed. I will now place it in the water and you will see that it descends, as before stated, until it arrives at a position of equilibrium. If I depress it at either end it rises again directly the pressure is removed. The analogy consists in the fact that the body has a preference for this exact position just as it had for another when suspended. Why is this? May it not be reasonably inferred that when floating there is an invisible but equally definite point of suspension to that which was provided by the hook upon which I placed it just now? Is it not equally reasonable to suppose that it obeys the same law, and will not remain at rest until its centre of gravity falls into a vertical line passing downwards from this invisible point of suspension? This is the fact of the case, and the point of support is that at which the upward pressure of the water culminates. If this is not quite evident let us demonstrate it by supposing that these two points are not so situated, but that the upward pressure is acting perpendicularly a little way from the centre of gravity. It will follow from this supposition that we have the weight pressing down in one line and the buoyancy up through another, not in the same lateral position. Under these circumstances

there can be no equilibrium, and the body, therefore, cannot remain at rest. This being so, the weight of the body must force it to descend in the water at one end until a sufficient movement has been made to change the buoyancy conditions enough to bring the two pressures into the same line. From the fact that no such movement did take place it is evident that the two forces were already in opposition, and had established an equilibrium. This proves that our two suppositions were correct, and that the body obeys the same law in water as when suspended.

It can be shown, however, by experiment. If a small weight is placed on one end of the model it at once sinks a little deeper at that end. By sinking deeper it has gained a little more buoyancy there, and evidently just enough to counterbalance the additional weight placed upon it, seeing that it soon comes to rest in the new position It did this because its centre of gravity had been disturbed, and therefore the perpendicular from it fell a little outside the former line of upward pressure. The result of this gain of buoyancy at one end was to cause the culminating point of upward pressure to follow in the same direction until the two forces were again directly opposed to each other vertically. This culminating point will hereafter bespoken of as the “metacentre.”

Before leaving this portion of the subject it may be as well to say a few words upon the meaning of the term “centre of gravity.” The words mean centre of weight, but they must be understood to stand for centre of moment of weight. The term would be complete if we had to deal with a plain bar of metal, or a plank of the same sectional area throughout. The centre of gravity of such bodies would be at the half-length, and if they were divided at this point the two halves would be equal in weight. In addition to being of the same sectional area throughout they are homogeneous in substance. But a ship possesses neither of these peculiarities, and it is found that neither is her centre of gravity at the centre of her length, nor would her two parts, supposing her to be divided at this point, equal each other in weight. Supposing that this model was made quite solid and of a homogeneous piece of wood, and that it was sawn across at its centre of gravity, it is not at all likely that the two portions would be equal in weight. The reason is that she is not equal in sectional area throughout her length. I think you will see this clearly if you consider the case of a ship lying at the wharf loaded. Let her centre of gravity in the fore-and-aft direction be ascertained and marked on her side. Let it be assumed, if she was divided at this point, that the two parts would be equal in weight, on the supposition that the centre of weight must be at the centre of gravity. In order to show that this need not

be the case I will undertake to shift the centre of gravity without removing any cargo from the forward portion into the after one. I will simply take 20 tons of cargo out of the midship end of the forward part and stow it in the forecastle. Common experience tells us that the result would be to trim the vessel a little more by the head. At the same time, it would not add to the total weight of the forward portion of the ship. But it would give the same weight a greater power of leverage upon the after part. This increased power, which is not due to added weight but to redistribution of what weight was already there, is known as an increase of moment. It has clearly moved the centre of gravity nearer to the bow, and therefore away from the point which had been assumed to be the dividing-line of equal weights. It can no longer be contended, therefore, that the centre of gravity in a ship is the dividing-point of equal weights. Her case is the sameas that of a steelyard, by means of which we can weigh large and small packages by moving a small weight along a graduated arm. It is the “moment” of the small weight acting at different parts of a long lever which enables it to balance at one time the small and at another the large package; and no one would contend that if the steelyard and its respective loads were separated at the fulcrum, which is the common centre of gravity of the whole, the two portions would be equal in weight.

I have dealt rather fully with this question of moment, because a true appreciation of it is necessary at every point in the consideration of stability.

It will now be desirable to treat of a similar point to the centre of gravity in connection with the supporting-power of water. It is known as the “centre of buoyancy.” This term is applied to the centre of gravity of the water displaced by a ship. It may promote a thorough understanding of the buoyancy question if I deal with the law of flotation by means of several suppositions. Let us suppose that when a vessel is floating in still water we could freeze the water all around and under her, and that it was then possible to lift her completely out of her bed of ice; the cavity from which she had been lifted would be the space from which she had expelled or” displaced “the water; the cubic contents of this cavity would represent the measure of what is called her “displacement.” To put it in another way: Let us suppose the cavity to be gradually filled with water, measured into it ton by ton, then the number of tons which were required to completely fill it would be spoken of as the number of “tons displacement” which the ship possessed at the draught of water at which she was floating. This amount would correspond in weight to the weight of the ship and her contents.

Let us next suppose that we could freeze the water which had been introduced into the cavity, and that we could then lift out the mass and handle it without its melting; it is evident that it would represent in bulk, in form, and in weight the water displaced by the ship. It would then be possible, if we could balance this mass in different positions, to ascertain the location of its centre of gravity. This point would be the one which I have alluded to as the centre of buoyancy.

Let us perform in another way the equivalent of the supposed operation. I have here a model of the under-water portion of H.M.S. “Captain,” representing just such a mass of ice as that supposed above. It is a homogeneous piece of pine, and has a small eye inserted in one side, opposite to its centre of gravity; and you will observe, when it is suspended, that its longitudinal centre-line lies horizontally, while its flat surface, representing the water-level, hangs vertically. It follows, as before shown, that the centre of gravity must be at the intersection of the longitudinal centre-line with a perpendicular drawn from the point of suspension.

Of course, in actual practice the foregoing freezing experiments are impossible, and the knowledge desired is therefore obtained by calculation from the vessel's lines and sections. The model before you, however, agrees exactly with the calculations made for the “Captain,” and therefore shows that the freezing supposition was safe as an illustration.

Having now explained the nature of the centre of buoyancy, we may proceed further with our subject. We shall find that it will simplify the consideration of this question, and materially assist us as we go forward, if we always clearly separate the question of stability, in our minds, into two parts—namely, that of the ship pressing downwards in the first place, and that of the water pressing or buoying upwards in the second place.

With this proviso, I will ask you to consider what changes are effected by careening a vessel from the upright position. Let us look first at that of the ship pressing downwards. It will be necessary to assume that no considerable part of her fittings or lading shall break away and fall to leeward when she is careened. It is then obvious that the fact of her being careened can have made no alteration in the position of her centre of gravity. Indeed, if everything held in its place she might be turned completely over without any alteration taking place in its position. We therefore see that, so far as the action of the ship is concerned, there is no difference caused by careening. She will continue to press downwards with the same energy as before, and through the same point—namely, her centre of gravity.

We may now pass to the second part—namely, that of the

water buoying up the ship. It will be necessary here also to make an assumption—namely, that no hole exists in the part brought under water by the act of careening. It will simplify our work at this stage if we deal with one cross-section of a ship—say, the midship one—and assume for the moment that the vessel from end to end is of that form. Fig.1, Plate L., will serve for this purpose. Please observe that there are two lines drawn across the section—the horizontal one representing the water-line when the vessel is inclined a few degrees, and the other when she is upright. Let us look closely at the changes which have been effected by thus careening the vessel. It at once appears that the wetted surface has been increased on one side and reduced on the other. That implies that the portion of the vessel acted upon in the inclined position by the water-pressure is not identical with that acted upon when she is upright. Does this change make any difference in the stability? Yes, in all cases, with the single exception, which I will deal with by-and-by, of a vessel whose section throughout her length, like fig. 4, Plate LI., is circular. In considering the nature of these changes please bear in mind two facts already stated—namely, that the act of careening has not added to nor reduced the total weight of the ship, and that the displaced water is, under all circumstances, exactly equal to that weight. It follows that the bulk of the vessel under water remains the same, and, as we are dealing with a vessel supposed to have the same form of cross section throughout her length, the area of that section must remain the same. As this is so, then it follows that the amount of area gained on one side in the diagram is equal to that lost upon the other. You will see that the pieces added and deducted are triangles. We may therefore define the position by saying that the triangle of immersion in the given example is equal in area to the triangle of emersion. But while this addition and deduction have not altered the total area of the section, it will be seen that they have materially altered its shape, and that, as a consequence, the centre of buoyancy must have been removed from its original position towards the enlarged or lee side of the section. This important change, then, has been effected by transfers of buoyancy, at the level of the water-line, from one side of the vessel to the other. It was this fact, of the only alteration taking place at the water-level, which caused the remark early in the paper that “if there is any part of a ship which may be considered at all analogous to a base it is the water-level section.”

We shall find the present stage a convenient one to draw another distinction—namely, between the two phases of the question of stability. I allude to the fact that every vessel which has any stability at all has an “initial stability” and a

“range of stability.” You may remember a sentence which occurred early in the paper, as follows: “The form of the bottom, it is true, has its influence on stability, but flatness of bottom in a sea-going vessel tends to reduce it.” It is “initial stability” which is thus affected. The “range of stability” is determined only by the form of the vessel in the neighbourhood of the water-level section.

As the finding of the metacentre is necessary before we can determine either of these phases of stability, I will now explain what that point is. In order to avoid this technical name as long as possible, I have alluded to it as the “culminating point of the upper pressure of the water.” It is a point which is always in a vertical line above the centre of buoyancy, but its distance from the latter usually varies at different angles of heel. A reference to fig. 1, Plate L., will serve to indicate the metacentre. First consider the section in its upright position with the centre of buoyancy at B. Then incline it, and assume that the centre of buoyancy in the new position is at b. Remember that the buoyancy acts vertically upwards through this point. Now, if a line is drawn upwards in this direction from b it is clear that it will intersect the centre-line. The point M, at which it intersects, is called the metacentre; and its height above the centre of buoyancy can be readily calculated, for an infinitely small angle of heel, by means of a well-known formula. If it was so calculated for a number of vessels, of which the centres of gravity have been ascertained under similar conditions of loading, it would afford us the data for a very fair comparison of their merits as far as the one test of initial stability is concerned.

The last paragraph brings before you for the first time, in conjunction with each other, the two points which must be determined before the measure of any vessel's stability can be ascertained. These points are the centre of gravity of the vessel and her metacentre. The distance between the two in a vertical direction is known as the metacentric height. When the metacentre is found to be above the centre of gravity the vessel is known to be stable; when their positions are reversed she is unstable; and when they coincide with each other she is indifferent, and will yield, without resistance, to any inclining force. When we know the metacentric height of a vessel we can form a good idea of the amount of resistance which she will, at the outset, offer to an inclining force. It is not of itself the measure of this first act of resistance. known as initial stability; but its value—as will be proved directly—is comparative, because it always bears, in different vessels, at a minute angle of heel, a certain proportion to another measure in each, known as the “righting-lever.” The convenience of its use consists in the fact that the calculation

for it stops short at an early stage of the more complicated one required to ascertain the range of stability.

We may now pass from initial stability to consider what the range of stability is. It is not only of importance that we should know that a vessel can present a fair amount of initial resistance to an inclining force, but that she can increase and maintain it up to large angles. It will be here necessary to explain what the righting-lever is. It has been shown that when a vessel is at rest her weight is pressing down through its centre and the buoyancy up through its centre in the same vertical line. Hence a condition of equilibrium exists. Two equal forces are acting upon a given point in opposite directions. But let some power be applied to careen her—say the usual one of the wind blowing sideways on her sails. This will destroy the first condition of equilibrium, and a struggle will take place for a time between the wind and the vessel's stability. She will yield easily at first, but, at some particular angle, will have acquired such an access of stability that the wind can press her no further. Thus another condition of equilibrium is produced. The wind and the stability have both met with their match. Can we ascertain the force which each is exerting? Yes; by first ascertaining the length of the righting-lever which she possesses at the given angle of heel.

We must proceed by calculating the centre of buoyancy in the inclined position, and then draw a perpendicular line upwards from it. Then we must find, by the experiment to be explained presently, the position of the centre of gravity of the ship, and draw a line perpendicularly downwards from it. The horizontal distance between these two lines, representing the direction of forces, may be considered as a lever or couple. This is known as the righting-lever. Now, the weight and buoyancy are known to be equal. Therefore, if we multiply either of them—say the buoyancy—in tons by the length of the lever in decimals of a foot we shall get an expression of foot-tons as the actual measure of stability. The force of the wind has been shown to be exactly equivalent to this resisting-power, or stability of the vessel, seeing that it succeeded in forcing her to, and keeping her at, a certain angle of inclination.

It will be seen now that, while the metacentric height is not the actual multiplier for obtaining the measure of stability, yet, if its relation to the length of righting-lever is constant in all vessels at equal angles of heel, it must be very valuable as a comparative measure of stability as between them. Their relationship may be further explained, and the promised proof given, thus: If at a given angle the centre of buoyancy appears further to leeward than at some lesser angle it is evident that

the perpendicular drawn upwards from it will intersect the centre-line of the upright position at a higher point, and thus make the metacentric height greater. At the same time, it will be seen that this perpendicular is further to leeward of the line falling from the ship's centre of gravity, and consequently the righting-lever is longer. Now, if I can show that there is in all cases a proportionate increase of these two measurements I have proved the value of the metacentric height as a comparative measure of stability. The proof is as follows: If we careen several vessels, whose relative stability we wish to know, to any given angle, ascertain their centres of gravity, and calculate their metacentric heights, and then construct a triangle on the section of each ship from its own ascertained measurements, we shall find that the three angles of each triangle are similar in all cases. The upper angle is that of the inclination; that between the righting-lever and the perpendicular to the metacentre is a right-angle; while the third is equal to a right-angle minus the angle of inclination. We have therefore a series of triangles, all of whose angles are similar. In such cases it follows, also, that their sides must be in the same proportion throughout. This being so, the metacentric height and righting-lever, being two of them, are, as above stated, always in the same proportion to each other.

Let us now return, from this further explanation of its important relationship, to the consideration of the righting-lever. It will be evident that, as we can calculate this measure for one angle, we can do it for as many as may seem desirable, and thus obtain the range of stability. The largeness or smallness of this range depends entirely upon the relative form of the vessel's sides immediately above and below the water-level section.

Before branching off just now into the division of the question of stability into two phases, I had shown, in the case supposed, that the act of careening had so altered the underwater form of the vessel that the centre of buoyancy had been removed from its original position towards the enlarged or lee side of the section. It has since been shown that this results in the lengthening of the righting-lever, and consequently in a gain of stability. Now, let us assume that the length of this lever has been ascertained for a vessel at 10°, 20°, 30°, 40°, 50°, &c., of inclination. Having obtained these lengths, set them up as ordinates from a base-line previously divided into the respective angles of heel. Through the points so obtained run a line, which will be that referred to by Mr. Barnaby in 1871 as a curve of stability, then for the first time calculated for an actual ship. Having traced this curve, we can read off upon it the length of

righting-lever at any angles intermediate to those actually calculated, and, by multiplying each by the displacement, get an expression of stability in foot-tons at each angle. If this process were applied to several vessels of different types we could, by a comparison of their respective curves, judge of the variation in, and relative values of, their stability. Some of them might possess a small, some a large, and others a medium range of stability. Some might show that they rapidly attained to a considerable amount of stability, and then went on increasing very gradually. Others, by a steady progression, might increase up to a very large angle. Others, again, might reach their maximum at 30° or 40° of heel, and then steadily diminish. Please observe the line on the diagram (PI. L.) which represents the curve of stability of H.M.S. “Captain.” This vessel steadily gained up to 21°—a very small angle. From this point her stability fell steadily, until at 54° it vanished altogether. A reference to her midship section readily explains the reason of this. You will see that, owing to the low free-board, the gunwale reaches the water at only 14° of heel. The triangle of immersion then begins to lose its area at its broadest end very rapidly, and the width of the water-line decreases with each angle of heel. The result is that the centre of buoyancy, after moving satisfactorily to leeward up to 17°, does so more slowly up to 21°, and then actually retraces its steps, until at 54° it has come back to its starting-point, when the vessel was upright, and is found perpendicularly below the centre of gravity of the vessel. The slightest additional puff of wind will then, owing to meeting with no resistance, cause her to capsize. The width of the respective water-lines referred to is as follows: When upright, 53ft.; at 14°, 54ft.; at 21°, 48ft.; and at 54°, 35ft. The low freeboard, resulting in a great reduction of her range of stability, while at the same time she was fully rigged, was the cause of the loss of this valuable ship and of many lives.

A great difference of opinion formerly existed as to the relative advantage of a good beam or of a high freeboard in affording a large range of stability. In 1871 Mr. Barnaby read a paper which finally settled the controversy in favour of the high freeboard. I can give you ocular demonstration of several facts in stability, but will at the moment only show by experiment the case of the “Captain.” This model is accurately made from the vessel's lines. It is weighted so as to draw the same water as the ship did when starting on her fatal cruise. Moreover, the centre of gravity of the model corresponds in position with that of the actual ship. When I hook this cord into the eyebolt in her side, and steadily cause her to list, you will see how soon her gunwale becomes immersed. It takes a fair amount of force to careen her at

first, and up to 21°, but after that she gradually lessens her resistance, and at last the least pull turns her over. A very simple analogy will illustrate this question of “range of stability.” If, while I am standing up, a pressure is applied sideways to my right shoulder I shall be in danger of falling to the left. But as long as it is possible for me to move my left foot outwards in a direction opposite to the pressure, and to continue doing this as the pressure is increased, I shall be able to make a prolonged resistance. But if anything obstructs the outward movement of my foot at any point it makes me unable any longer to resist the pressure, and I must therefore fall. In lieu of the outward movement of the foot, a vessel has to depend upon the increasing support afforded by the leeward movement of her centre of buoyancy. This can only be maintained as long as her form above water is such as to continually increase with each addition to the inclination the moment of the area of that side of her section. The low freeboard of the “Captain,” as we have seen, first checked the due increase of that moment, and then began to seriously undermine it.

All that has so far been said upon stability refers only to the measure of the energy with which a ship endeavours to regain the vertical position. This is known as “statical stability.” I have shown, when a ship is careened to and held at a given angle by the force of the wind, that a condition of equilibrium between the two forces of wind and stability has been attained. Such a condition might also be produced at the same angle by suspending a large weight from, say, the mainyard-arm: It would have to be adjusted as follows: Suspend a plumb-line from the yard-arm and measure the horizontal distance from it to the centre of gravity of the ship; then divide the stability measure expressed in foot-tons by this distance. The result will be the number of tons which must be suspended from the yard-arm to produce the given inclination. It is a simple question of balancing, and may be compared to the before-mentioned case of an ordinary steelyard, where a large weight is balanced by a small one having greater leverage. The moment of each acting at the fulcrum balances the other, and is equal to its weight multiplied by its distance from the fulcrum. In the case of the ship the moment is spoken of as being equal to so many foot-tons; in the case of the steelyard it might be termed inch-pounds. While this measure indicates the steady resisting-power of a vessel, yet it does not express the whole problem, seeing that it takes no account of the work performed in bringing about the careening. It generally happens that the act of careening raises the centre of gravity of the vessel, or, in other words, that it lifts her whole weight to a higher level. Such an effect cannot be produced without an expenditure of power. This

expenditure may be measured by calculating the height through which the vessel has been lifted and multiplying it by her weight. The operation is rendered simple by the knowledge of the fact that a ship's weight corresponds to that of the water which she displaces. In listing to a given angle, we have seen, under our assumption that a mere section represents the solid, that the area of the section is increased on the lee side and reduced to windward by the area of the respective triangles of immersion and emersion. We have further seen that, while these triangles are equal in area, they are, in all but circular sections, dissimilar in form, and have therefore different horizontal moments. In all cases, therefore, where the moment of immersion is greater than that of emersion, the centre of buoyancy is moved to leeward. The additional fact to which I now wish to ask your attention is that these triangles have different vertical moments, and that they consequently raise the centre of buoyancy vertically. Having ascertained by measurement of the triangles what this vertical rise amounts to, we have simply to multiply it by the area of one of them to obtain a comparative measure of the work done in the act of careening. It may also be found by multiplying the rise of the centre of buoyancy by the total area of the inclined midship section. This measure, when solid is substituted for area, is known as the dynamical stability at the given angle of heel.

The different nature of these two measures may be illustrated by a reference to fig. 3, Plate LI., which represents a cylindrical model when rolled up an inclined plane. The statical energy of the body in either of the two right-hand positions is measured by its weight multiplied into the length of the respective righting-levers, or the distance in each case from its point of contact to the perpendicular from the centre of gravity. The dynamical work done in raising it to these positions is measured by its weight multiplied into the respective vertical distances through which its centre of gravity has been raised. This latter measure is different from the condition of balancing It consists of an amount of work done upon, and stored up in, the body which will be given out again during its return to the upright position. In the case of a ship we can imagine her lying at a wharf, and that the inclination was produced by hooking a crane-chain to her rail and heaving away at the handles. When she had been careened, if the handles were let go, they would be made to fly round by her return to the upright position. A clock-weight, after being wound up, does just the same thing, and in running down makes the clock go by giving out again the work stored up in it.

It will scarcely be necessary to remind you that stability is a measure which varies with every change in the stowage

of a ship's cargo, even though her draught of water remains the same. This is because the height of her centre of gravity will thereby be altered. It is also evident that the buoyancy varies with any increase or decrease in the mean draught of water, or from an alteration in trim—i.e., in the draughts of water forward and aft respectively. A variation in the position of the centre of buoyancy results from these latter changes. It therefore follows that, as a vessel on a long voyage consumes water, stores, or coal, she alters both elements which determine her stability. Her centre of gravity is altered in position by the change in her lading, and her centre of buoyancy by the reduction in her mean draught of water, while it is more than likely that she has risen more at one end than at the other. A responsibility, therefore, rests not only with her designer to consider these possible changes and provide for sufficient stability under the worst of ordinary conditions, but with the captain also, who should obtain some scientific knowledge of her peculiarities, so that he may stow the cargo in such a way as to prevent the occurrence of any extraordinary conditions.

The main explanations of the principles of stability have now been made; but I wish to refer to and explain three assumptions which it seemed desirable to make with the object of simplifying for the moment certain portions. The first one made was in dealing with the centre of gravity, and was as follows: “It will be necessary to assume that no considerable part of her fittings or lading shall break away and fall to leeward when she is careened.” This reservation was necessary to the explanation as it was given, and to the statement that the centre of gravity did not alter its position by reason of a vessel being careened. The fact of cargoes being shifted by stress of weather, however, is not by any means uncommon. Again, the presence of a large quantity of water in the bilges may seriously affect stability, and the same result will follow if a water-ballast tank is only partially filled. It is not beyond our power to calculate the effect of any such change of condition as may be supposed to take place. The caisson for closing the entrance of a graving-dock is made to sink into its place by the admission of water into certain compartments. It would not be safe, however, to admit water into such a structure except into limited watertight compartments. In the absence of divisions, the water by its movements would cease to act as ballast, and would become a source of great danger to the stability of the caisson, and probably cause it to do damage to its own structure and to that of the dock.

The second assumption was in reference to the buoyancy of a vessel remaining intact after she was careened, and read

as follows: “It will be necessary here also to make an assumption—viz., that no hole exists in the part brought under water by the act of careening the ship.” In making this reservation I had in my mind the case of the sinking of the s.s. “Austral” in Sydney Harbour. For a long time after that vessel was raised and sent to sea again a great deal of prejudice existed as to her supposed want of stability. This idea was entirely groundless; and I believe that few safer or better ships ever floated. The fact was that the covers had been removed from the coaling-ports which pierced her sides amidships; coal was being introduced into her bunkers through these ports, and the operation was continued until the vessel bad sunk low enough for the water to enter them. The result was inevitable. The introduction of a comparatively small quantity of water would not only cause her to sink lower, and so increase the inflow every moment, but would cause her to become slightly unstable, and therefore probably to list enough to cover the whole area of the ports very quickly. The great inrush so caused would very soon sink her. Again, in the case of a war-ship the piercing of the top-sides would, if it led to an influx of water, very quickly alter the former conditions of stability. Carelessness in leaving the cabin ports of a passenger-steamer open in rough weather might soon produce the same results.

The third assumption was in reference to the form of the vessel which I took for the purpose of careening. It reads as follows: “It will simplify our work at this stage if we deal with one cross-section of a ship—say, the midship one—and assume for the moment that the vessel from end to end is of that form.” Of course we never see a vessel so shaped, but the device enabled me to show the results of the change of form effected by careening more simply by assuming them to be concentrated in one representative section. You will readily see that the portions immersed to leeward and emerged to windward are not mere areas, as for the moment assumed, but solid wedges extending the whole length of the ship, and that, by reason of the fining of the lines and the alteration in form of the vertical sections towards the bow and stern, these are of irregular shape. On the strength of this third assumption I made the following statement: “The triangle of immersion in the given example is equal in area to the triangle of emersion.” To understand the intention of this, you must substitute” solid “for” triangle,” and understand the sentence to read as follows: “The solid of immersion is equal in bulk to the solid of emersion.”

To save myself from a possible misunderstanding, it maybe as well, by way of endeavouring to state the fact exactly, to make another slight reservation upon the last statement. It

should be remembered that I have only dealt with stability in still water, because it will readily appear that several of the statements made are not applicable to a vessel's movements in a seaway and in stress of weather, nor would they apply to the case of a vessel anchored, or moored bow and stern between buoys in a tideway. But even in still water the pressure of a wind which careens a ship may not act in a direction precisely parallel to the water-surface. In such a case, the effect may be either to slightly lift or slightly depress the ship, and thus cause an equivalent change of displacement. If this ever happens, as it may do, then the solids of immersion and emersion are to that extent not exactly equal to each other. For practical purposes, however, this need not be considered.

There is a peculiarity about these solids, however, which is well worth notice. Each of them has a centre of gravity of its own, and it will very often happen that these are not located at the same point, in a fore-and-aft direction, as that of the main displacement when the ship is upright. When such is the case it is evident that the centre of buoyancy when the ship is careened will not be in the same position as it was when she was upright. The balance of the ship is thus disturbed in the fore-and-aft direction, and the visible effect will be that she will either rise at the bow and sink at the stern, or else do exactly the reverse. It is evident, therefore, that a vessel defectively designed in this particular (for it is a defect) will, with every careening movement, combine a certain amount of pitching and scending. If this happens in still water it is likely to increase the liveliness of the vessel amongst waves at sea. I should, speaking from my own feelings at least, consider this quite an unnecessary aggravation.

Another reservation was necessarily made once or twice regarding the exceptional actions of a body with a circular section. You see when I place such a model in water that it has no stability, and it may therefore be as well to explain the reason of this Owing to its being a homogeneous body, its centre of gravity lies in its central axis. Again, owing to its circular section, the act of careening does not alter the form of the under-water portion. As a consequence, the solids of immersion and emersion are exactly alike, not merely in bulk (which is always the case), but in form also, and therefore in moment. The result is that their addition and deduction does not affect the position of the main centre of buoyancy, or make it move out to leeward as usual. It therefore remains vertically below the centre of gravity of the model, so that no righting-lever is formed, and therefore no resistance is offered to an inclining force, and no effort made to return to the former position.

We can, however, give stability to a model of this section by lowering its centre of gravity. If a small weight is attached to the lower part of the model it will do this. If it is then careened the centre of gravity will move out from the upright centre-line, up which the centre of buoyancy still acts, and will thus form a righting-lever. This lever would continue to increase in length up to an angle of 90°, and the stability would increase at the same rate. The model, under both conditions, acts in the same way if placed on a plane surface. The reason is that the point of support in both cases acts in the vertical line falling from the centre of rotation. Fig. 4 shows the direction of the forces for the weighted model both in and out of water.

Another way of giving stability to a model of circular section without removing its centre of gravity from the central axis is as follows: I will take off the weight used in the last experiment, and attach a bolster or fender to each side opposite to the centre-line, as shown in fig. 5, Plate LI. It is obvious that the bolsters do not change the position of the centre of gravity, but as soon as either of them touches the water it affords stability. The reason, following the lines of former explanations, is that the solid of immersion, while still of the same volume as that of emersion, is, owing to one bolster being immersed, of a different form, and therefore possessed of a greater moment. It therefore draws the centre of buoyancy to leeward forms a righting-lever, and endows the model with a measure of statical stability. A little further observation will show that the centre of buoyancy has risen vertically at the same time. This shows that the model has also acquired dynamical stability.

A device analogous to this addition of bolsters will occur to some present as being used sometimes to give stability to a sailing-vessel when it may be necessary to shift her after discharging cargo. A square log of timber, such as a spare spar which she may carry for the purpose of making a topmast or lower yard from, is secured by two ropes and lowered over each side into the water. After this, if the vessel takes a list she lifts the windward balk out of the water, and leaves the other floating free. The weight of the balk thus lifted influences the ship's centre of gravity slightly downwards and to windward, and therefore tends to right her

The effectiveness of this plan can be increased if necessary by passing a rope tightly under the ship's bottom and securing it to both balks. If she then takes a list she hauls one balk down under water at the same time that she lifts the other out. One effect of this modification is to draw the centre of gravity rather more down, but not at all out to windward. The other, and the principal effect, is to increase

the moment of the solid of Immersion and to reduce that of emersion. This draws the centre of buoyancy to windward, and so increases the length of the righting-lever.

The first method merely acts upon the ship's centre of gravity, whereas the second acts upon her centre of buoyancy as well.

The same principle might be adopted to add to the stability of a sponsoned ferry-boat. Such a balk might be secured to each side of the boat above the stays which support the sponsons. With a light load of passengers this would be above water, but the ends should nevertheless be eased off to reduce the resistance when it is immersed by heavier loads. In any case where this might be deemed insufficient the range of stability could be very much more increased by planking over the outside of the stays from the hull right up to the sponsons and making this watertight. The weight thus added would possibly not lower the centre of gravity of the steamer, but it would very greatly increase the moment of the immersed solid when she was careened to the edge of the sponsons, and thus draw the centre of buoyancy to windward, and greatly lengthen the righting-lever.

It is hardly safe to give any arbitrary rules for stability, but it may safely be affirmed, where a vessel's initial stability is satisfactory, that if the width of her water-line goes on increasing as the angle of heel gets larger she must have a good range of stability. A ferry-boat's lading is peculiarly dangerous, because it is not only generally carried high above her centre of gravity, but is a live weight, which in case of panic is almost sure to rush to the lee side. Hence a large range of stability, in the interest of public safety, is imperative. As such boats usually ply in smooth water, there is not the same objection to a great fall-out above the water-line which would attach to a sea-going vessel. In the latter the great leverage which it would afford to the waves would result in heavy rolling, and the receipt of very ugly blows from the seas.

A rather telling illustration of the great stability afforded by a large fall outwards above the water-line is afforded by the preference which a square log shows when floating. If a number of these are rafted together they can be made to float on their flat sides, but if one is floating by itself it will always lie cornerwise. Here is a section of one, and I will place it in water. You will see that it cannot be got to float in any other way than with one corner down. We may first see why it will not float on its flat by referring to fig. 6, Plate LI. As it is a square figure, and is homogeneous, its centre of gravity will be at the intersection of lines drawn cornerwise. Similarly, the under-water portion being rectangular, the centre of buoyancy will be at the half-height and half-width of this portion.

Now look at the change brought about by careening. The centre of buoyancy moves to leeward to the position b, but the centre of gravity moves still further to leeward. The downward pressure of the weight and the upward pressure of the buoyancy are, it will be seen, both acting in the same direction to overturn the log, because the metacentre falls below the centre of gravity. Instead of a righting-lever it possesses an upsetting-lever. These are the conditions which make it impossible for it to float on its side. It consequently assumes the other position—viz., with onecorner down.

Let us now see by reference to fig. 7, Plate LI., why it prefers this way. The centre of gravity is of course just where it was, but the centre of buoyancy is at the point B. Now look at it when inclined, and you will see that the centre of buoyancy moves to leeward to b, and the perpendicular passes to leeward of the centre of gravity, places the metacentre above it, and thus forms a satisfactory righting-lever, and resists the inclining force.

This model will further serve to illustrate the case of the “Captain.” A very little more inclination than that shown would bring its angle under water, and its range of stability would fall off as a consequence, and its breadth at water-line would continue to decrease until it would fall over.

A very different variety of midship section from that of the “Captain,” but still a very objectionable one, is represented in an exaggerated form in fig. 2, Plate L. The greatest breadth is considerably below the water-line, and the tumble-home starts from this point, and is large. Such a vessel may have a fair amount of initial stability, although her metacentre must be low; but it is impossible that she can have a long “range” of stability. About the year 1864 a batch of large sailing-ships was built in the north of England for Liverpool shipowners. They were all deep in proportion to beam; their greatest breadth was at one-third up, and they were heavily rigged. They all required ballasting as soon as the builders had run up their topmasts. One of them while loading coal for her first voyage listed against the dock side until her yard-arms touched the quay after she had taken in 800 tons, fully half her lading. This one was lost off the Hebrides on her first voyage. Most, if not all, of the crew reached land in one of the boats. The captain reported that, while sailing along quite satisfactorily to all appearance, she took a further list as the breeze freshened, and steadily settled down on her broadside, just as the “Captain” did. The remaining ships which were not completed were altered as far as possible. Several feet were taken off their lower masts, and in one or two cases the space under the hold-ceiling between the floors was filled in with bricks and cement (with the exception of a

small watercourse), all with a view of lowering the centre of gravity. In spite of this these vessels could never possess the most important quality—viz., a good range of stability. It is still abundantly evident that there is much need for a greater diffusion of sound information upon this subject, and for an equally extensive use of it by shipbuilders.

The Transactions of the Institution of Naval Architects for several years past abound with papers upon this subject. Instead of the old jealousy and desire for secrecy, competitors in business have vied with each other in giving full explanations of many new methods which they have adopted for arriving at the desired results more quickly and certainly. The naval architects at the Admiralty have also done equally well, and have greatly advanced the interest which has been taken in the science.

It may be well to say a few words about bilge-keels or rolling-chocks, as it is often stated that these add to a ship's stability. This is quite an erroneous opinion. They are always under water, and therefore cannot affect the position of the centre of buoyancy at any degree of inclination. Their functions are quite different from those of the “bolsters” which were affixed to our circular model, for the simple reason that the latter, being at or above the water-level, increased by inclination the moment of the solid of immersion, and so formed a righting-lever. The work which bilge-keels do is to reduce the range and violence of rolling by presenting a drag to the water. When rolling has ceased they simply do nothing. They increase the steadiness, but do not affect the stability.

I have purposely left a description of one of the most interesting operations to the last. I refer to the method adopted for finding the height of the centre of gravity of a ship. The plan is a most ingenious one, and could not fail to interest any one having a taste for figures, statics, or mechanics. It will at once occur to every one that you cannot handle such an object as a ship or suspend her from various points as we can these models. Neither would it be possible to find it by experimenting with ever such a carefully-prepared model, because no ship is homogeneous in structure, but every ship is so complicated that no model could represent her as to the weight of all her parts. While we are unable to lift and suspend the ship, however, we know the laws which govern the support which the water affords to her. We must therefore cause her to assume different positions in this element, and then work backwards in order to get what we want. It is necessary to measure the exact amount of power applied to produce these changes of position. When we have found out all the facts surrounding, so to speak, the one which we want

to get at we are able to deduce from them the required information—viz., that the centre of gravity must be at a given spot; otherwise the result of the application of the known power could not have been precisely what it was.

The device made use of is to put on board and move a known weight through a measured distance across the vessel, and to note its effect as shown by the change produced in the vessel's inclination. The shipmust be in smooth water, and there must be no wind. She must be moored at each end only; the ropes must be attached at the centre-line, and must not be hauled too taut. Everything must be in its sea-going position, and only enough men to shift the weights must remain on board; those who stay must, when any measurement is being taken, range themselves in the same position on each occasion. These precautions are for the purpose of preventing any force operating to careen the vessel except that of the weights to be moved.

Square cast-iron weights with hand-hole and bar are very handy as the power to be used for careening. They should be stacked up in rectangular form as near to the bulwarks amid-ship as possible. A board must be fixed up and down in the hatchway, and a plummet or pendulum attached to it for recording the angle of heel. When all is ready, and the men are at their station, the observer notes the exact position. The weights are then carried across the deck and stacked up as far from their former position as possible. The exact distance between the centres of the two positions is taken. This, when multiplied by the weight moved, will give the moment of the power applied. The men return to their station, and the observer notes the change of inclination. This ends the experiment; the draught of water at each end of the ship is carefully taken and drawn across the sections on the drawings. The draughtsman now calculates the buoyancy, centre of buoyancy, and metacentre at the given draught when upright, and carefully ascertains the moments of the solids of immersion and emersion for the inclination produced by the power applied. From these facts he deduces the metacentric height necessary to account for the change of inclination, and, setting it down, from the metacentre obtains the position of the centre of gravity of ship and weights combined. The weights used for careening are finally allowed for, and then he knows the position of the centre of gravity of the ship alone. The operation all through is certainly a great triumph of ingenuity, skill, and accuracy.

This method could be applied to a loaded ship if desired, or, after making the above experiment, a prediction of the condition of such a ship if loaded with any homogeneous cargo could be made by calculating her contents of holds and their