priated to passenger accommodation from the nett register "tonnage, and multiply the remainder by the factor 1." This rule is based on experience, about 67 cubic feet being the average space required for each ton-weight of cargo carried, when allowance is made for the provisions and stores needed on a voyage of average length.

A few words will suffice as to freight tonnage. Merchants and shipowners make considerable use of this measurement, although it has no legal authority; it is also used. in the Admiralty service in connection with store-ships and yard-craft. A freight-ton, or " unit of measurement cargo, simply means 40 cubic feet of space available for cargo, and is therefore two-fifths of a register ton. Mr. Moorsom says that for an average length of voyage the nett register tonnage less the tonnage of the passenger space, when multiplied by the factor 1, will give a fair approximation to the freight-tons for cargo stowage. This rule has the same basis as that for dead-weight cargo given above. The freight-ton is, of course, a purely arbitrary measure, but has a definite meaning, and is of service in the stowage of ships.

CHAPTER III.

THE STATICAL STABILITY OF SHIPS.

A SHIP floating freely and at rest in still water must fulfil two conditions: first, she must displace a weight of water equal to her own weight; second, 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." In the opening chapter the truth of the first condition was established, and it was shown that the circumstances of the surrounding water were unchanged, whether the cavity of the displacement was filled by the ship or by a volume of water having the same weight as the ship. When the ship occupies the cavity, the whole of her weight may be supposed to be concentrated at her centre of gravity, and to act vertically downwards. When the cavity is filled with water, its weight may be supposed to be concentrated at the centre of gravity of the volume occupied (i. e. at the centre of buoyancy), and to act vertically downwards; the downward pressure must necessarily be balanced by the equal upward pressures, or "buoyancy," of the surrounding water; therefore these upward pressures must have a resultant also passing through the centre of buoyancy. In Fig. 28, a ship is represented (in profile and transverse section) floating freely and at rest in still water. Her total weight may be supposed to act vertically downward through the centre of gravity G; the buoyancy acting vertically upwards through the centre of buoyancy B. If (as in the diagram) the line joining the centres G and B is vertical, it obviously repre

sents the common line of action of the weight and buoyancy, which are equal and opposite vertical forces; in that case the ship is subject to no disturbing forces, and remains at rest, the horizontal fluid pressures which act upon her being balanced amongst themselves. But if (as represented in Fig. 29) the centres G and B are not in the same vertical line, the equal and opposite forces of the weight and buoy

ancy do not balance each other, but form a "mechanical couple," tending to disturb the ship, either by heeling her or by producing change of trim. If D = total weight of the ship (in tons), and GZ = perpendicular distance between the parallel lines of action of the weight and buoyancy (in feet), Moment of couple = D × GZ (foot-tons).

If the vessel is left free to move from this position, not being subjected to the action of external forces other than the fluid pressures, she will either heel or change trim, until the consequent alteration in the form of the displacement brings the centre of buoyancy into the same vertical with the centre of gravity G. It is important to note that, for any specified distribution of weights in a ship, supposing no change of place in those weights to accompany her transverse or

longitudinal inclinations, the centre of gravity is a fixed point in the ship, the position of which may be correctly ascertained by calculation. On the contrary, the centre of buoyancy varies in position as the ship is inclined, because the form of the displacement changes. Hence, in treating of the stability of ships, it is usual to assume that the position of the centre of gravity is known, and to determine the place of the centre of buoyancy for the volume of displacement corresponding to any assigned position of the ship. The value of the "arm" (GZ) of the mechanical couple formed by the weight and buoyancy can then be determined. If it is zero, the vessel floats freely and at rest, in other words, occupies a "position of equilibrium;" if the arm (GZ) has a certain value, the moment of the couple (D × GZ) measures the effort of the ship to change her position in order to reach a position of equilibrium. In this latter case the vessel can only be retained in the supposed position (see Fig. 29) by means of the action of external forces; and if her volume of displacement is to remain the same as when she floats freely, these external forces may be supposed to act along horizontal lines. For example, a ship may be sailing at a steady angle of heel, and the resultant pressure of the wind on the sails may be represented by the pressure P in Fig. 29 (section) acting along a horizontal line. When the vessel has attained a uniform rate of drift to leeward, the resistance of the water will contribute a horizontal pressure, P, equal and opposite to the wind-pressure; and if d be the vertical distance between the lines of action of these pressures, we have

Moment of couple formed by

horizontal forces.

}

=Px d (foot-tons);

which moment will be balanced by that of the couple formed by the weight and buoyancy. Hence

Dx GZ = P x d,

is an equation enabling one to ascertain the angle of steady

heel for a particular ship, with a given spread of sail, and a certain force of wind.

Supposing a ship, when floating upright and at rest, to be in a position of equilibrium, which is the common case: let her be inclined through a very small angle from the initial position by the action of horizontal forces. If, when the inclining forces are removed, she returns toward the initial position, she is said to have been in stable equilibrium when upright; if, on the contrary, she moves further away from the initial position, she is said to have been in unstable equilibrium when upright; if, as may happen, she simply rests in the slightly inclined position, neither tending to return to the upright nor to move from it, she is said to be in neutral or indifferent equilibrium. This last-named condition has, however, little practical interest in connection with ships, for which stability and instability are alone important. A well-designed ship floats in stable equilibrium when upright; but many ships, when floating light, without cargo or ballast, are in unstable equilibrium when upright, and consequently "loll over" to one side or the other when acted upon by very small disturbing forces.

The statical stability of a ship may be defined as the effort which she makes when inclined by external forces acting horizontally, and held steadily at that inclination, to return towards her natural position of equilibrium-the upright-in which she rests when floating freely. This effort, as explained above, is measured by the moment of the couple formed by the weight and buoyancy. Hence we may write, for any angle of inclination,

Moment of statical stability = D × GZ.

But in doing so, it must be noted that in all ships, when large angles of inclination are attained, the line of action of the buoyancy, instead of falling to the right of G (as in section, Fig. 29), and so tending to restore the ship to the upright, will fall to the left and tend to upset her or make