Before discussing dead-weight tonnage, which is applied to the weight of cargo and fuel which vessels can carry, it will be best to explain displacement tonnage.
The displacement ton is a unit applied to vessels and not to cargo, but in order to ascertain the dead-weight tonnage a vessel can carry it is first necessary to determine the vessel's displacement tonnage.
The displacement tonnage of a vessel is its weight in tons of 2,240 pounds avoirdupois, and is equal to the weight of water displaced by the vessel when afloat. Unless the term is qualified, the displacement tonnage of a vessel is the weight of the ship with its crew and supplies on board, but without fuel, passengers, or cargo.
This is a vessel's displacement "light." The weight of water displaced by a vessel when loaded to its "deep-load line" is its displacement " loaded." The difference between the displacement tonnage of a vessel when "light" and when loaded to its "deep-load line" is its dead-weight tonnage, which is the maximum weight of fuel, cargo, and passengers that a vessel can carry.
Calculating the Displacement Tonnage
A cubic foot of sea water weighs 64 pounds, or one-thirty fifth of an English long ton of 2,240 pounds avoirdupois. Thus the contents in cubic feet of that part of the vessel's hull that is below the water line divided by 35 equal the vessel's displacement tonnage.
If a ship were box-shaped—that is, if it were a parallelepiped—the product of its three dimensions in feet, its length, breadth, and its depth below the water line, divided by 35 would be the displacement tonnage; but, as vessel hulls are not parallelepiped, the cubical contents of the hull of a ship have to be calculated by means of special, mathematical rules, such as Simpson's rules or the trapezoidal rules.
The ratio of the actual contents of the submerged portion of a ship's hull to the contents of a parallelepiped having length, breadth, and depth corresponding to the length, breadth, and draft of the ship is the vessel's "block coefficient" or its "coefficient of fineness."
A full-shaped, slow freight steamer has a " block coefficient " of about 0.8—i. e., the submerged portion of the hull has a volume equal to 0.8 of the volume of a parallelepiped with equal dimensions.
The "block coefficient" or "coefficient of fineness" of the average freight steamer varies from 0.7 to 0.75, while the coefficient of a combination freight and passenger steamer is about 0.65; that of a fast passenger steamer is about 0.6, while racing yachts may have a coefficient as low as 0.4.
When the "coefficient of fineness" of a vessel is known, its displacement tonnage is determined by multiplying its length, breadth, and draft by its "coefficient of fineness" and dividing the product by 35.
In commercial practice it is desirable to know a vessel's displacement tonnage at any given draft between its "light" and "loaded" lines, for the reason that the difference between the displacement of a vessel "light" and the tonnage of its actual displacement indicates the weight of what the ship contains other than a crew and supplies.
Displacement Tonnage or Weight of a Ship
The displacement tonnage or weight of any particular ship at any given draft is shown by the vessel's "displacement curve" and scale. Figure 27 reproduces a typical displacement curve.
Figure 27: Displacement Curve and Scale. Click to view larger image.
Figure 27 presents the displacement scale for a small vessel which draws but 7 feet of water when light, its displacement "light" being 550 tons. The vessel may load to a maximum draft of 14 feet, at which draft its displacement is 1,400 tons.
The dead-weight capacity of the ship is thus 850 tons. It may be noted in passing that the ship is permitted to be loaded, so that it has but 2 feet of freeboard, the freeboard being the distance between the level of the upper deck and the "deep-load line." Vessels engaged in the oversea trade would not be permitted to have such a small freeboard.
Drawing the Ship's Displacement Curve
The figure also gives the ship's displacement curve. The curve is drawn as follows:
At the left the draft of the vessel and its freeboard are given in a perpendicular scale, which may be assumed to have been drawn to a scale of 1 inch to 1 foot. From the top of this vertical scale, a horizontal scale is so constructed that 1 inch equals 100 tons of displacement.
By drawing horizontal lines through the points indicating the draft of the vessel at different drafts from zero to 14 feet and by drawing vertical lines through the points in the horizontal scale corresponding to the number of tons of displacement at various drafts from zero to 14 feet, and by drawing a curve through the points of the intersection of the horizontal and vertical lines, the curve of the ship's displacement is located.
With this displacement curve known, the displacement of the vessel at any given point in its draft can be read off from the displacement scale.
 Mathematical' rules for the calculation of the contents of the halls of ships are explained, among other places, In Chapter X of the book Know Your Own Ship, by Thomas Walton, London, 1909.
Johnson, Emory Richard, Measurement of Vessels for the Panama Canal, Volume 2, Government Printing Office, Washington, DC 1913, Pages 36-37