I shall say something concerning it:
The Shipwrights have a Custom of measuring at London thus; They multiply the length of the Keel into the breadth of the Ship at the broadest place, taken from outside to outside, and the Product of that by the half Breadth; this 2d Product of the Multiplication they divide by 94, or sometimes 100, and according to that Division, the Quotient thereof is so many Tuns; as suppose the Length 60 Foot, and being multiplied by 20, the Breadth, produce 1200; and 1200 again multiplied by 10, the half Breadth 12000; if you divide by 100, you need do no more than cut off the last Figures towards the Right hand, which shall be the Answer, which rendereth the Ship to be 120 Tuns; but if you divide the Sum 12000 by 94, you will have 127 2/3 of a Tun very near: But this cannot be the true Ability of the Ship to carry, because two Ships by this Rule, of equal Breadth and Length, shall be of equal Burthen, notwithstanding the fulnes of sharpness of those Vessels, which may differ them very much, or the one Ship may have more Timber than the other in her Building, and so carry less: but the true way of Measure, must be by measuring of the Body and Bulk of the Ship under Water, for if one Ship be longer in the Floor than another of the same Breadth and Length, she shall be more in Burthen than the other; as a Flemish Ship shall carry more than a French or Italian Vessel of the same Length or Breadth; therefore, I say, the Measure of a Ship is known by measuring her, as a piece of Timber may be measured of the Form, to the draught of the Water, assign'd her, the weight of the same Body of the same Water that the Ship swimmeth in, shall be the exact Weight of the Ship, and all things therein, Loading, Rigging, Victuals included therein: then if the Ship be measured to her light Mark, as she will swim at being launched, the Weight of so much Water being taken or subtracted from the Weight of the Water when she is laden, the Residue shall be the Weight that must load Ability of carrying, called her Burthen. By this means you may know the Weight of the Ship light, and what she will carry to every Foot of Water assigned to her, which can be done by no general Rules in Arithmetick, because of their great Irregularity, according to the differing Forms of Ship; you may, if you please, first measure the Content of the Keel, Post, Stem and Rudder, all of it that is without the Plank, and under the Water-line, and note it by it self; then measure the Body of the Ship in the Mid-ships, by multiplying of the depth of the Water-line, and the breadth; then you may find the Content of the Want by the circular part of the Ship under Water, being narrowed downward, and subtract this from the whole Content of the Body found, by the depth of the Water-line and breadth of the Ship, and this shall be the solid Content of that part of the Ship, I mean, of solid Foot Measure, of 1728 Inches to the Foot; then proceed to the fore part or after part of a Ship, and to 3 or 4 Timbers more, find the mean Breadth at the narrowing aloft at the Waterline, and allow at the Floor and the mean Depth, and measure that piece of the Ship, as I told you of the middle part of the Ship, and so measure the whole Ship by pieces, and add them together; and so many Feet as it maketh, so many Feet of Water shall be the Weight of the said Ship, and the Reason may be considered thus: There is a Ponderosity in the Water, but there is a greater in the Air; and there is a Ponderosity in the Water it self, but not so much as in other things more solid, as in Iron: Suppose a Gun or an Anchor of Iron it sinketh in the Water, but yet is not so heavy in the Water as in the Air, by the weight of so much Water as shall make a Body equal to the Body of a Gun, or an Anchor in Magnitude; which Weight substracted [sic] from the Weight of the Iron Body weighed in the Air, and so much must be the Weight of it in the Water.
Again, if a Body be lighter in weight than Water of the same bigness, it hath an Ability of lifting the Water, and can lift or carry so much as is that difference: as a piece of Cork or Wood of Fir-Trees. being lighter than Water, it swimmeth off the face of the water, and refuseth to be depressed without more weight added to it.
Thus a Ship being a Concave Body, is made capable of lifting, according to the greatness or littleness of this Concavity, respect being had to the greatness of the Timber put into it, or the Nature of it, all which maketh a Ship swim deeper or lighter in the Water.
I have proved by the Thames Water, that fresh Water is lighter than salt Water; so then salt Water being heavier than fresh, causeth that a Ship swimmeth deeper in fresh Water than in salt.
I shall not need to say any thing more concerning measuring of Ships, for it will be understood by those that have Judgement in the measuring of solid Bodies, the Matter it self being but a Nicety, rather than useful. I only touched it, to shew those that are curious minded, which way they may accomplish their Desires. I shall forbear to give Examples, because it will much increase this Treatise, and augment the Price, which might prove more prejudical to young Men, than advantagious.
The Sea-Man's Vade Mecum, London, 1707. pp 127-131.
Transcribed by Lars Bruzelius
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