Tonnage of a Stip.

It will also be worth while to add the following exact rule of Mr Parkins, who was many years foreman of the shipwrights in Chatham dockyard.

1. For Men of War.

Take the length of the gun-deck from the rabbet of the stem to the rabbet of the stern post. of this is to be assumed as the length for tonnage, = L. Take the extreme breadth from outside to outside of the plauk; add this to the length, and take of the sum; call this the depth for tonnage, = D.

Set up this height from the limber strake, and at that height take a breadth also from outside to outside of plank in the timber when the extreme breadth is found, and another breadth in the middle between that and the limber strake; add together the extreme breadth and these two breadths, and take of the sum for the breadth for tonnage, D.

Multiply L, D, and B together, and divide by 49. The quotient is the burthen in tons.

The following proof may be given of the accuracy of this rule. Column 1. is the tonnage or burthen by the king's measurement; col. 2. is the tonnage by this rule; and, col. 3. is the weight actually received on board these ships at Blackstakes:

also the additional weight necessary to bring her down to the load water line.

In order to construct this scale for a given ship, it is necessary to calculate the quantity of water displaced by the keel, and by that part of the bottom below each water line in the draught. Since the areas of the several water lines are already computed for the eighty-gun ship laid down in Plates CCCCXC. and CCCCXCI. the contents of these parts may hence be easily found for that ship, and are as follow.

3d w. line

'}

4

I

23574-63 778 1795

London

90

1845 1575

1677

1614

1369 1141

965

Dist. 31 and 7

870

886

2d. w. line S

Daphne

∞ ∞

7

51476.21700 1231

79288.32619 766

8

Scale of Solidity.

Add the length of the lower deck to the extreme breadth from outside to outside of plank; and take of the sum for the depth for tonnage, = D.

Set up that depth from the limber strake, and at this height take a breadth from outside to outside. Take another at of this height, and another at of the height. Add the extreme breadth and these three breadths, and take the 4th of the sum for the breadth for tonnage, B.

Multiply L, D, and B, and divide by 36. The quotient is the burthen in tons.

This rule rests on the authority of many such trials, as the following:

Construct any convenient scale of equal parts to represent tons, as scale N° 1. and another to represent feet, as N° 2.

Plate

60

Draw the line AB (fig. 36.) limited at A, but pro- ccccxen. duced indefinitely towards B. Make AC equal to the depth of the keel, 2 feet 3 inches from scale N° 2. and Constructhrough C draw a line parallel to AB, which will re- t'on of the scale of sopresent the upper edge of the keel; upon which set off lidity for Cc equal to 21 tons 1855 lbs. taken from scale N° 1. the ship of Again, make AD equal to the distance between the eighty lower edge of the keel and the fifth water line, namely, guns. 6 feet 4 inches, and a line drawn through D parallel to AB will be the representation of the lower water line; and make Db equal to 305 tons 848 lbs. the corresponding tonnage. In like manner draw the other water lines, and lay off the corresponding tonnages accordingly then through the points A, c, b, c, f, g, h, draw the curve Ac befgh. Through h draw h B perpendicular to AB, and it will be the greatest limit of the quantity of water expressed in tons displaced by the bottom of the ship, or that when she is brought down to the load water line. And since the ship displaces 1788 tons at her light water-mark, take therefore that quantity from the scale N° 1. which being laid upon AB from A to K, and KL drawn perpendicular to AB, will be the representation of the light

:

water

Vessel.

Tfits of AB (fig. 50.), which being acted upon by the forces 2- Water A a, Cc, Dd, Bb, may be maintained in equilibrio, to bend a provided it has a sufficient degree of stiffness: but as soon as it begins to give way, it is evident it must bend in a convex manner, since its middle would obey the forces Cc and Dd, while its extremities would be actually drawn downwards by the forces A a and B b.

Plate

The vessel is generally found in such a situation; and since similar efforts continually act whilst the vessel is immersed in the water, it happens but too often that the keel experiences the bad effect of a strain. It is therefore very important to inquire into the true cause of this accident.

For this purpose, let us conceive the vessel to be divided into two parts by a transverse section through the vertical axis of the vessel, in which both the centre of gravity G (fig. 51.) of the whole vessel and that of ccccxcv. the immersed part are situated: so that one of them 5. will represent the head part, and the other that of the stern, each of which will be considered separately. Let g be the centre of gravity of the entire weight of the first, and that of the immersed part corresponding. In like manner, let y be the centre of gravity of the whole after part, and w that of its immediate portion. Now it is plain, that the head will be acted upon by the two forces g m and o n, of which the first will press it down, and the latter push it up. In the same manner, the stern will be pressed down by the force y, and pushed by the force wy. But these four forces will maintain themselves in equilibrium, as well as the total forces reunited in the points G and O, which are equivalent to them; but whilst neither the forces before 64 The cause nor those behind fall in the same direction, the vessel of a ship's will evidently sustain efforts tending to bend the keel bogging, upwards, if the two points are nearer the middle than the two other forces gm and yμ. A contrary effect would happen if the points and were more distant from the middle than the points g and y.

65 and sag

ging.

Practical

But the first of these two causes usually takes place almost in all vessels, since they have a greater breadth towards the middle, and become more and more narrow towards the extremities; whilst the weight of the vessel is in proportion much more considerable towards the extremities than at the middle. From whence we see, that the greater this difference becomes, the more also will the vessel be subject to the forces which tend to bend its keel upwards. It is therefore from thence that we must judge how much strength it is necessary to give to this part of the vessel, in order to avoid such a consequence.

If other circumstances would permit either to load the vessel more in the middle, or to give to the part immer sed a greater capacity towards the head and stern, such an effect would no longer be apprehended. But the destination of most vessels is entirely opposite to such an arrangement: by which means we are obliged to strengthen the keel as much as may be necessary, in

order to avoid such a disaster.

We shall conclude this chapter with the following practical observations on the hogging and sagging of ships by Mr Hutchinson of Liverpool:

"When ships with long floors happen to be laid aSeaman. dry upon mud or sand, which makes a solid resistance ship, p. 13. against the long straight floors aniidships, in comparison with the two sharp ends, the entrance and run meet with

Vessel.

little support, but are pressed down lower than the flat Efforts of of the floor, and in proportion hogs the ship amid- the Water ships; which is too well known from experience to oc- to bend a casion many total losses, or do so much damage by hogging them, as to require a vast deal of trouble and expence to save and repair them, so as to get the hog taken out and brought to their proper sheer again: and to do this the more effectually, the owners have often been induced to go to the expence of lengthening them; and by the common method, in proportion as they adds to the burden of these ships, by lengthening their too long straight floors in their main bodies amidships, so much do they add to their general weakness to hearhardships either on the ground or afloat; for the scantling of their old timber and plank is not proportionable to bear the additional burden that is added to them.

"But defects of this kind are best proved from real and incontestable facts in common practice. At the very time I was writing upon this subject, I was called upon for my advice by the commander of one of those strong, long, straight floored ships, who was in much trouble and distraction of mind for the damage his ship had taken by the pilot laying her on a hard, gentle slop ing sand, at the outside of our docks at Liverpool, where it is common for ships that will take the ground to lie for a tide, when it proves too late to get into our wetdocks. After recommending a proper ship carpenter, I went to the ship, which lay with only a small keel, yet was greatly hogged, and the butts of her upper works strained greatly on the lee side; and the seams of her bottom, at the lower futtock heads, vastly opened on the weather side all which strained parts were agreed upon not to be caulked, but filled with tallow, putty, or clay, &c. with raw bullocks hides, or canvas, nailed with battons on her bottom, which prevented her sinking with the flow of the tide, without hindering the pressure of water from righting and closing the seams again as she floated, so as to enable them to keep her free with pumping. This vessel, like many other instances of ships of this construction that I have known, was saved and repaired at a very great expence in our dry repairing docks. And that their bottoms not only hog upwards, but sag (or curve) down.wards, to dangerous and fatal degrees, according to the strain or pressure that prevails upon them, will be proved from the following facts:

:

"It has been long known from experience, that when ships load deep with very heavy cargoes or materials · that are stowed too low, it makes them so very laboursome at sea, when the waves run high, as to roll away their masts; and after that misfortune causes them to labour and roll the more, so as to endanger their working and straining themselves to pieces: to prevent which, it has been long a common practice to leave a great part of their fore and after holds empty, and to stow them as high as possible in the main body at midships, which causes the bottoms of these long straightfloored ships to sag downwards, in proportion as the weight of the cargo stowed there exceeds the pressure of the water upwards, so much as to make them dangerously and fatally leaky.

"I have known many instances of those strong ships. of 500 or 600 tons burdens built with long straight floors, on the east coast of England, for the coal and timber trade, come loaded with timber from the Baltic

Vessel.

said to be possessed of stability; or it will continue in Stability t its inclined state; or, lastly, the inclination will increase Ships. until the vessel is overturned. With regard to the first case, it is evident that a sufficient degree of stability is necessary in order to sustain the efforts of the wind; but neither of the other two cases must be permitted to have place in vessels.

Efforts of to Liverpool, where they commonly load deep with the Water rock salt, which is too heavy to fill their holds, so that to bend a for the above reasons they stowed it high amidships, and left large empty spaces in their fore and after holds, which caused their long straight floors to sag downwards, so much as to make their hold stanchions amidships, at the main hatchway, settle from the beams three or four inches, and their mainmasts settle so much as to oblige them to set up the main rigging when rolling hard at sea, to prevent the masts being rolled away; and they were rendered so leaky as to be obliged to return to Liverpool to get their leaks stopped at great expence. And in order to save the time and expence in discharging them, endeavours were made to find out and stop their leaks by laying them ashore dry on a level sand; but without effect: for though their bottoms were thus sagged down by their cargoes when afloat, yet when they came a-dry upon the sand, some of their bottoms hogged upwards so much as to raise their mainmasts and pumps so high as to tear their coats from their decks; so that they have been obliged to discharge their cargoes, and give them a repair in the repairing dock, and in some to double their bottoms, to enable them to carry their cargoes with safety, stowed in this manner. From this cause I have known one of these strong ships to founder.

"Among the many instances of ships that have been distressed by carrying cargoes of lead, one saited from hence bound to Marseilles, which was soon obliged to put back again in great distress, having had four feet water in the hold, by the commander's account, owing to the ship's bottom sagging down to such a degree as made the hold stanchions settle six inches from the lower deck beams amidships; yet it is common with these long straight floored ships, when these heavy cargoes are discharged that make their bottoms sag down, then to hog upwards: so that when they are put into a dry repairing dock, with empty holds, upon straight blocks, they commonly either split the blocks close fore and aft, or damage their keels there, by the whole weight of the ship lying upon them, when none lies upon the blocks under the flat of their floors amidships, that being hogged upwards; which was the case of this ship's bottom; though sagged downwards six inches by her cargo, it was now found hogged so much that her keel did not touch the blocks amidships, which occasioned so much damage to the after part of the keel, as to oblige them to repair it; which is commonly the case with these ships, and therefore deserving particular

notice."

In order to prevent these defects in ships, "they should all be built with the floors or bottoms lengthwise, to form an arch with the projecting part downwards, which will naturally not only contribute greatly to prevent their taking damage by their bottoms hogging and straining upwards, either aground or afloat, as has been mentioned, but will, among other advantages, be a help to their sailing, steering, staying, and waring."

CHAP. III. Of the Stability of Ships.

WHEN a vessel receives an impulse or pressure in a horizontal direction, so as to be inclined in a small degree, the vessel will then either regain its former position as the pressure is taken off and is in this case

Let CED (fig. 52.) be the section of a ship passing Fig. 52. through its centre of gravity, and perpendicular to the sheer and floor plans; which let be in equilibrium in a fluid; AB being the water line, G the centre of gravity of the whole body, and g that of the immersed part AEB. Let the body receive now a very small inclination, so that a Eb becomes the immersed part, and its centre of gravity. From y draw y M perpendicular to a b, and meeting g G, produced, if necessary, in M. If, then, the point M thus found is higher than G the centre of gravity of the whole body, the body will, in this case, return to its former position, the pressure being taken off. If the point M coincides with G, the vessel will remain in its inclined state; but if M be below G, the inclination of the vessel will continually increase until it is entirely over

set.

The point of intersection M is called the metacenter, and is the limit of the altitude of the centre of gravity of the whole vessel. Whence it is evident, from what has already been said, that the stability of the vessel increases with the altitude of the metacenter above the centre of gravity: But when the metacenter coincides with the centre of gravity, the vessel has no tendency whatever to move out of the situation into which it may be put. Thus, if the vessel be inclined either to the right or left side, it will remain in that position until a new force is impressed upon it: in this case, therefore, the vessel would not be able to carry sail, and is hence unfit for the purposes of navigation. If the metacenter is below the common centre of gravity, the vessel will instantly overset.

As the determination of the metacenter is of the utmost importance in the construction of ships, it is therefore thought necessary to illustrate this subject more particularly.

Let AEB (fig. 52.) be a section of a ship perpendicular to the keel, and also to the plane of elevation, and passing through the centre of gravity of the ship, and also through the centre of gravity of the immersed part, which let be g.

Now let the ship be supposed to receive a very small inclination, so that the line of floatation is a, b, and y the centre of gravity of the immersed part a Eb. From y draw M perpendicular to a b, and intersecting GM in M, the metacenter, as before. Hence the pressure of the water will be in the direction M.

In order to determine the point M, the metacenter, the position of with respect to the lines AB and g G, must be previously ascertained. For this purpose, let the ship be supposed to be divided into a great number of sections by planes perpendicular to the keel, and parallel to each other, and to that formerly drawn, these planes being supposed equidistant. Let AEB (fig. 53-) Fig. 53 be one of these sections, g the centre of gravity of the immersed part before inclination, and y the centre of gravity of the immersed part when the ship is in its inclined state; the distance gy between the two centres