13 



SHIP. 



when afloat heel (the plane of its masts to incline) through equal 

 angles by means of weights applied successively to a mast, and made 

 to act horizontally at different distances above the deck ; these weights 

 being reduced to directions perpendicular to the inclining mast (by 

 multiplying them into the cosine of the inclination), and then multi- 

 plied into their respective distances from the unknown centre of 

 gravity of the ship, will give two products which are equal to one 

 another ; each of them being equal to the momentum of the resistance 

 by which the water tends to prevent heeling ; hence by algebra the 

 distance of the centre of gravity from either of the points at which 

 the weights are applied may be found. 



In the expression for the momentum arising from the pressure of 

 the wind against the sails, it is usual to consider the whole force of the 

 wind as acting at the centre of gravity of the sails ; and this point may 

 be found by multiplying separately the area of each sail into the 

 distance of its centre of gravity above a horizontal axis passing through 

 the centre of gravity of the ship. The quotient arising from the sum 

 of these momenta divided by the sum of the areas of all the sails will 

 give the distance of the required centre of gravity above that axis ; 

 and similarly the position of the centre of gravity of the sails with 

 respect to any vertical line as an axis may be obtained. 



To find the centre of gravity of the displacement, or of the immersed 

 part of the ship supposed to be homogeneous, when the plane of a 

 ship's masts is made to incline by the lateral action of the wind, the 

 axis of rotation being supposed to be a horizontal line passing through 

 the centre of gravity of the whole ship, there must be first obtained by 

 trial the position of a horizontal line in which the plane of the surface 

 of the water will cut the body of the ship when in the upright and 

 inclined positions respectively, so that the volume of the part raised 

 above the water in consequence of the inclination may be equal to that 

 of the part depressed. Let a line passing through D, fig. 1, perpendicu- 

 larly to the paper, be that horizontal line ; then the sum of the 

 momenta of the elevated and depressed volumes may be found by com- 

 puting the areas of the trilineal figures A' D if, B' D N, in all the vertical 

 sections taken at equal distances from one another in the direction of 

 the ship's length, multiplying them separately by the distances of their 

 centres of gravity from a vertical plane passing through the same 

 horizontal line, and then adding all the products together by one of 

 the formula; above given. In the ' Quarterly Journal of Science,' April, 



1830, the area of either triangle, a* A' DM, is expressed by 



sin i 9, where 7= DM, y" = DA.', y=a line drawn from D to A'M, 

 bisecting the angle A'D y, or 8 (the angle of heeling). Also the momentum 

 of the same triangle with respect to the point D is expressed approxi- 

 matively, and supposing the angle of heeling to be 7 (the greatest at 

 which a ship of war can use her windward guns), by .Q2Q3>ry"('r +"/') 



In order to find an expression for the stability of a ship, let o be its 

 centre of gravity, and when the ship floats upright let g be the centre 

 of gravity of the immersed part supposed to be homogeneous. Now 

 when the plane of the masts is inclined, </ will be situated at r, and in 

 that cage let B be the place of the centre of gravity last mentioned ; 

 then by mechanics, r will be equal to the quotient arising from the 

 division of the sum of the momenta of the elevated and depressed 

 volumes by the volume of the immersed part of the ship. But if 9 be 

 the angle of inclination, we shall have F./ = OF sin 9; therefore J/H or 

 o K may be found. This being multiplied by the weight of the ship 

 and its burden ( = the force of the reaction of the water in the 

 direction H s), gives the expression for the stability. 



The plane of a ship's masts is made to decline from a vertical posi- 

 tion not only by the action of the wind against the sails when the 

 direction of the wind does not coincide with that plane, but also by a 

 wave striking the ship in a direction oblique to the horizon and to the 

 plane of the masts ; and in both cases the variations in the force by 

 which the inclination is produced and the re-action by which the water 

 tends to bring back the plane of the masts to a vertical position cause 

 the ship to roll about some longitudinal axis, which is supposed to pass 

 horizontally through the centre of gravity of the whole ship. Now, if 

 a horizontal plane coincident with the plane of floatation pass through 

 A B when the ship floats upright, and o, the centre of gravity of the 

 ship, be below that plane, as in fig. 1 ; in order to preserve the 

 equality of the immersed volume when the ship is inclined, the plane 

 which passed through AH must take xuch a position as A'B'. This 

 will cause o to ascend ; that is, the ship will rise on the water. On 

 the other band, if o had been above A B when the ship was upright, 

 the latter would descend on the water when it is made to take an 

 inclined position. Such rising or descending is a cause of the ship 

 being shook or strained in rolling ; and this evil can be avoided only 

 by baring the' centre of gravity, o, coincident with the plane of floata- 

 tion. It is necessary to observe, on the other hand, that by keeping 

 that centre higher, or bringing it nearer to the meta-centre s, the 

 stability of the ship, which varies directly with the distance o s or o K, 

 is proportionally diminished. The pitching of a ship, that is, the 

 alternate elevation or depression of either extremity of the ship a* tin; 

 latter passes oer a wave, is attended by a corresponding rising or 

 descending of the wholn ship ; and the strain thus produced will evi- 

 dently be so much the less a* the centre of gravity is nearer the level 

 of the plane of floatation and the middle of the ship's length. It 



ABTS AMD SCI. DIV. VOL. VII. 



SHIP. 6U 



should be stated here that, since a ship in tacking is supposed to turn 

 horizontally about a vertical axis passing through its centre of gravity, 

 the resistance then experienced, which is proportional to the square of 

 the distances of its extremities from that axis, will be a minimum 

 when the centre of gravity is in the middle of the ship's length ; but, 

 on the other hand, the power of the rudder depending on its distance 

 from the same axis of rotation, that power would be increased by 

 having the centre of gravity at some distance before the middle 

 point. 



When a vessel which is partly immersed in a fluid moves through 

 that fluid, it always experiences a resistance in a direction contrary to 

 that of its motion, in consequence of the inertia of the water ; but it 

 experiences also a resistance on account of the particles of water which 

 are immediately struck by the vessel, and those immediately beyond 

 them to a certain distance, being for a time compressed on all sides by 

 the vessel and the surrounding fluid, and thus compelled to rise above 

 the general level. The elevated fluid will be highest before the middle 

 point at the bows of the vessel ; and the hydrostatical pressure arising 

 from the elevation, combined with the reaction of the neighbouring fluid, 

 will cause the particles to flow off laterally in the direction of some 

 curve-line whose convexity is towards the vessel, after which they will 

 mix with the fluid on each side. Now let A D B, fy. 3, be a horizontal 



rig. 3. 



section through the ship at the general level of the water, and let c E D 

 be the space occupied by the confined water in front of the ship ; then 

 if an artificial prow of that acute form were given to the ship, the 

 particles of water contiguous to the sides of such prow would create 

 very little resistance in addition to that which arises from the inertia 

 of the water, while the latter resistance' will evidently be so much the 

 greater as the bows are more obtuse. Beyond D and E the particles 

 flowing along the side exert forces arising from friction, adhesion, and 

 the lateral pressure of the neighbouring water ; and at certain points, 

 as F and o, they pass off in the directions of tangents at those points. 

 The force of friction and adhesion is very considerable, particularly if 

 the surface is rough and unequal ; and if the vessel is moving with or 

 against a current, the pressure against its sides is equal to that which 

 would be experienced if the water were at rest, diminished or increased 

 on any given area by the weight of a column of the fluid whose base is 

 that area, and whose height is that which is due to the velocity of the 

 water. It has been found moreover by experiment, that if both vessel 

 and fluid are in motion, with equal velocities in the same direction, 

 the buoyancy of the vessel is the same as if both were at rest ; but 

 when the velocity of the vessel is less or greater than that of the fluid 

 in the same direction, the vessel either sinks or rises in the fluid by a 

 quantity equal to the height due to the difference of the velocities, 

 and this circumstance must in some measure modify the resistance of 

 the water against the vessel. 



Besides the resistance arising from the friction of the water along 

 the sides of the vessel, there must be noticed the diminution of pres- 

 sure against the after part, in consequence of the water displaced by 

 the motion not falling in behind with sufficient velocity to bring the 

 surface there to the same level as in front. The particles of water 

 diverging from the sides of the vessel in oblique directions, as F u, are 

 by the lateral resistance of the neighbouring fluid deflected so as to 

 describe curve-lines which finally unite behind the stern in some point, 

 as L. But the force exerted to deflect the particles from the direction 

 F H causes a diminution of the pressure which the water would have 

 otherwise exerted against the after part of the vessel ; and consequently 

 it is to be considered as an additional power opposing the forward 

 movement of the vessel. The force of deflection, and consequently 

 the retardation, will evidently be less in proportion as the tangent F H 

 is nearer to the side of the vessel, or as the point F is more distant 

 from the stern ; and this circumstance indicates the advantage which 

 ships of considerable length have over others. It is easy to understand 

 however from the breaking and foaming of the water at the head and 

 stern of a vessel when moving with considerable velocity, that the 

 effects of the resistances will be greatly modified by the collisions of 

 the particles of water with each other, and with the surface of the 

 vessel, in consequence of the shocks produced by its motion, and by 

 the effort of the water to return to a state of equilibrium. 



In order to obtain an expression for the resistance of the water 

 against a ship, the part of the immersed surface which is before the 

 greatest transverse vertical section is supposed to be divided by a 

 number of such transverse sections at equal distances from one another, 

 measured perpendicularly between them, and by a number of sections 

 parallel to the plane of floatation at equal distances from one another 

 vertically. Thus the surface of the immersed part in front of the 

 greatest transverse section is divided into trapezoidal figures ; and a 

 like division of the immersed part of the ship's surface abaft of the 



I, L 



