William Bourne

A Treasure for Travellers

Text transcribed and modernised from the 1578 edition by R.A.Barker.

(Manuscript 1572; second edition 1641, as A Mate for Mariners and a Treasure for Travellers).

The principle of displacement of ships and how to measure it is clearly established her. The concepts of load marks and deadweight measurement appear, but are not new. At much the same time, Mathew Baker was measuring the areas of hull sections. It is not clear that the ship-carpenters' link-engine was previously used for more than copying shapes. A hundred years later, Deane is credited (by Pepys) with being the first to be able to do the calculations to predict draught on launching, but little more evidence is extant for that than calculations in the style of Baker's work. Even Deane's work did not lead to routine measurements of these kinds: the benefits were not commensurate with the effort required, when so few individuals could carry out the work. John Dee is referred to here, but there is nothing known in his work that relates to shipbuilding, other than aspirations to use mathematics in all the mechanical disciplines, new and old. Works by Archimedes were however circulating in Europe in the sixteenth century, and efforts to gauge barrels are still older.

Fourth Book

…and not before this time mentioned by any other, but only by that famous and learned man Master John Dee, who has made mention thereof in his Mathematical Preface, wherein I have had my principal instructions, as touching that art or science……

Chapter II

The second chapter shows how to measure the proportion of the mould of any ship, whereby is known the weight of any ship with all her lading and furniture

To know how to measure the proportion of the mould of a ship, whereby may be known her weight, with all her lading, it is somewhat tedious, and asks for long work, and must be precisely handled, because it keeps no form long together, therefore it must be measured in many parts.

And to measure the mould of any ship, the ship must be brought aground. And then begin at the broadest place of the ship in this manner.

And now this being done exactly (as it may be done with precise diligence), you knowing the true contents of how many feet the soaled [sic: solid] body of the mould of the ship contains as much as buried into the water, you may know justly the whole weight of that ship that you have so measured, with all her lading, ordnance, tackle, anchor, and cables, with all other implements in her, as thus: Take of that water that the ship swims in, and make a cube of metal or wood of just 12 inches square, and deep: for that 12 inches square every way, makes a foot, and then weigh the water justly how many pounds and parts of a pound the water contains in weight, and that shall show you justly how many pounds and parts of a pound every foot square of the mould of the ship weighs justly. And then if you multiply the contents of the number of feet, that the mould is, and the weight that one foot of the water weighs in pounds and parts, then according unto that number, the ship with all her lading, weighs justly without any fail [fayle ?: or tally], so that you have measured the mould of the ship truly, and also weighed justly the contents of one foot of the water. And then by that number you may say justly that it contains so many tons [tunnes] in weight, as thus: by dividing the number of the weight of the ship by 2240, because a ton contains 20 hundred weight, and every hundred weight contains 112 pounds.

And furthermore, you may measure the mould of a ship in this manner, with such a thing as the ship carpenters do take the mould of a ship, and that they do call a mould, or link engine [lynck ginne], and that is made of many pieces, a foot long, or thereabouts, and it is clenched together with roves and clench nails, that the jointing will be put to and fro at your pleasure, and will stand stiff as you do leave it.

And now with this instrument, you may work more easily than is rehearsed above, for to know the contents or quantity of the mould of any ship in this manner, take at every place the half of the true breadth of the ship, and then in like manner the true deepness that the ship goes into the water, at every place that you do measure the ship at, for that all ships do draw more water at the stern, than they do at the head. And then you may put three pins of wood into the ground, the one pin to be at the middle of the ship, the other to be for the outside of the ship, and the third to be for the middle of the keel of the ship, and to set them truly in distance, according unto the half breadth of the ship, and the other unto the true deepness that the ship goes into the water, and so shall that pin for the middle of the ship, make a square angle unto the pin for the side and keel of the ship. And then with the instrument lay that unto the side of the ship and put it in and out as the ship rounds from the place of the upper edge of the water unto the keel, and then lay that mould of the ship unto the two pins, that is to say, to that pin for the side, and the pin for the keel of the ship. And then measuring that in closer, as you do a flat form, the truth of the contents shall appear, and then doubling that number, it will show you the contents of the whole breadth of the ship. And then to multiply so much in length as keeps one proportion. And thus doing as often as the proportion of the mould alters, and then adding all your numbers together, and casting the contents in all points, as is rehearsed above, the truth of the solid body of the mould of the ship shall appear, and so taking the true weight of one foot of that water, as before is expressed in all points. And thus I do make an end of the measuring of the mould of ships, for that nothing is wanting or lacking, but to show how to measure flat forms, and for these matters there are divers books extant sufficient enough for that purpose, as Master Leonard Digges in his book called Tectonicon, and Master Thomas Digges his book called Pantometria, with other.

Chapter III

The third chapter shows you an easier way than rehearsed above, by the Art Statical, to know the true weight of any ship, with all her lading, and all the rest of her furniture

And furthermore, because it somewhat tedious and asks for long work, besides divers other encumbrances that must be used to measure the true proportion of the mould of a ship, I will show unto you a more pleasant and easy way (by the Art Statical), both very true and exact, to know the true weight of any ship, with all her lading, masts, sails, anchors, cables and ordnance, with all other implements in her.

And any noble man or gentleman may do it at home in his chamber, that has any knowledge in the mathematical sciences, as thus;

First cause the carpenter that does build the ship, or otherwise, if you desire to know it for any other ship that is already built, if that ship have any occasion to come aground. Then get some cunning carpenter to take the true mould of that ship, as though he should build another of that mould and proportion in all points, as much as is buried into the water, when the ship is loaded unto her load mark. That being exactly done, then cause him to make the true mould and proportion. Then cause the carpenter to cut out of a peece of timber the true proportion of the mould of the ship in all points, as thus:

For every foot in length, make the mould [model] in timber an inch in length; and for the breadth in like manner, make every foot make the other an inch, and also for every foot in deepness, that the ship swims into the water, make the mould in timber one inch. And so consequently every part and place both of the run and [fore-]way, and floor, with the quarters of the ship, to cut the mould for every foot, and part of a foot, an inch, with those parts, even as the work [? woorke] or mould of the ship does run, in all points. And that being exactly done, then let there be made in some kind of metal, as lead or tin, the true proportion of the mould, hollow, and tight, that it may hold water, as the mould in wood will show or lead them how to do it very truly. And then that being done, then cause another square vessel to be made of metal in cubic wise, such a one as you may measure its hollow as easily as you may measure a square piece of timber, and if there were lines or pricks at every inch in deepness, it were all the better.

And then this being done, fill that vessel that is made for the mould of the ship, with that water that the ship swims in, and that being exactly filled, then put that water into the other vessel, and look that there be none of the water shed [spilled], then you may know justly how many inches square that the water is, by measuring the water with an inch rule; and that being known, then you do know how many feet that the solid body of the mould of the ship contains. And then weighing justly one foot square every way of that water, and then knowing how many pounds and parts of a pound, that one foot square of water weighs, then multiply the number of feet of the ship, with that you have found before by pouring the water into the square vessel. And then for every inch, the ship is a foot, and so by that number multiplied by the number of the weight of the pounds, and parts of pounds, the true weight of the ship shall appear. And if you do commit any error, the fault shall be in not weighing, and measuring of it truly.