Among the methods that have been proposed for the determination of the tonnage of ships, that of Chap man, in the eleventh chapter of his Traite de la Con struction des raisscaux, is founded on the true elements of the calculation; it has, however, this serious disad vantage—that different divisors are taken at the will of the person who makes the calculation, according to his judgment of the relative fulness of the body be tween the load and light draughts of water.
That there would be considerable trouble in obtain ing the correct tonnage of all the ships of the mer chant navy, must be admitted; of the ships of the Roy al Navy the trouble would be much less, as it could be calculated from the drawings by which they were built, which are always preserved in the Navy Office. But the correct tonnage, even of all merchant ships, might be obtained in a few years; and when the ton nage of the ships now afloat should be known, the great difficulty would have been surmounted, as the tonnage of every new ship could be calculated with comparatively little trouble. A scale of tonnage should be calculated for every ship, previously to its being launched, either from the drawing (if built from one,) or from the ship itself. The light water line might he determined when the ship is fully equipped, with every thing on board except the lading, and trans ferred to the scale of tonnage previously made; the tonnage betwen this and the load water line would be the true tonnage, or weight of lading of the ship. The lading on board, when the ship swam at any in termediate line between the light and load water lines, would be immediately known by reference to the com puted scale.
If it be objected, that many persons who are now capable of measuring the tonnage of ships would he unable to make these additional calculations, it may be answered, that as the number required to perform this service would be but small, sufficient persons might be found from those at present employed in this work, fully competent to undertake it; and indeed, that the calculations arc so simple, that all mint soon be perfectly acquainted with them.
Atwood gives in his paper on the stability of ships, in the Philosophical Transactions of the Royal Society of London, for 1798, p. 301, the tonnage of the Caff nells, an East Indiaman, between the load water sec tion and six successive horizo2jal sections below it, at two feet apart. The total drrplacement of this ship he determines to be 3410 tons.
The water-section, No. 12, is the load-water-section.
Fr&ii/othese calculations a scale of tonnage may be formed, by which the weight of lading which would bring down this ship any distance between the load and light draughts of water may be immediately found.
The following method of calculating the tonnage of ships, although by no means superseding the propriety of scales of tonnage, may be considered superior to the rule at present in use, being founded on the true elements of the tonnage, the length and breadth of the ship, and the depth between the load and light draughts of water, and approximating very nearly to the true tonnage.
Let a b, Fig. 7, Plate CCCCXCII. represent the load-water-line, and c d the light water-line; take the arithmetical mean of a c and b d, which call e; let the length of the load water line, a b, be taken from the fore part of the rabbet of the stem to the after part of the rabbet of the stern-post, which calif; and let the greatest breadth at the load water line be repre sented by g. Multiply these three quantities together; then —. ef g will be the tonnage, in cubic feet, of sea-water, —x representing the fraction expressing the proportional part of the whole solid.
By obtaining the correct tonnage of different ships, by rules for calculating the contents of solids, it is found that may be substituted for subject to 4 certain corrections, determined by reference to the ships whose tonnage is required. This correction may be most easily applied when reduced to a per tentage, according to the different degrees of fulness of the part of the body contained between the load and light-water-lines, which may be determined by the following method:— Draw e f parallel to a b, and at a distance below it equal to half the mean of a c and b d, and let g t h, Fig. 8, represent the horizontal view of this section; divide the whole length g h into eight equal parts, and at the points of division draw i q, k r, 1 s, nb t, n u, o v, and p w, perpendicular to the middle line g Ti. Take the sum of the lengths of these seven ordinates, and add to the part of the tonnage already found per cent. for every one per cent. that this sum exceeds six times the length of the longest of these ordinates. This will give an approximate value of the tonnage to a great degree of accuracy.
Rule.
Take the length of the ship from the fore part of the rabbet of the stem to the after part of the rabbet of the stern-post at the height of the load water line, the greatest breadth of the ship at this height, and the mean depth between the light andload water lines; multiply these three dimensions together, and take the product, and divide by 35.
Then divide the length of the ship at half the mean depth between the light and load water-lines into eight equal parts, take the sum of the lengths of the seven half-breadths to the outside of the ship, and add to the above quantity II per cent. for every one per cent. this sum exceeds six times the length of the greatest of these half-breadths.
The result is the tonnage, or the weight in tons, that will be required to bring the ship down in the water from the light to the load-water line.