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.
To the reader….
…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……
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.
First, measure the breadth of the ship from outside to outside, at that very place of the upper edge that the ship swims in deepness into the water. Then that being known, measure the true deepness that the ship swims into the water at that place of the broadest part of the ship. Then that being known, take the true contents of half the breadth of the ship, and then with a rod or pole lay the end of the rod or pole that is just the length of half the breadth of the ship, unto just the half keel in breadth at that place before spoken of, and then with another rod or pole of the just length that the ship swims in deepness into the water, lay the end of that rod or pole at that place that the upper edge of the water touches: and then let both the other ends of the two rods or poles touch just together, and so they will make a square angle. And then measuring or trying between the ship and the two rods or poles as you do in the measuring of superficial flat forms, so shall you know the contents of that part that is within the inside of the ship, by subtracting or taking away of that measure between the two rods or poles with the outside of the ship, since you must consider that it is a square enclosed from the middle of the inside of the ship, unto the deepness that the ship swims in the water, and unto the two rods or poles, and has four square or right angles or corners. And then if you multiply it according unto the breadth of the ship and the deepness that the ship goes into the water as you would do if it were a flat form, then pulling away the contents of that same being doubled that the measure is between the ship's side, and the two rods or poles, then that which remains shall be the true contents of that part which is within the inside of the ship as though it were a flat form. And then look how many feet long it runs in that form and proportion in breadth and roundness of the side, then according unto the length multiply the one by the other, that is to say, the contents of the measure before taken of the inside of the ship, and the length that the mould keeps in one proportion, and then cast the contents thereof. And that being done, do as is rehearsed above, according unto the breadth of the ship in another place: then according to the deepness that the ship swims in the water, and then doing with the two rods or poles as is rehearsed above, and so trying between the ship's side, and the two rods or poles, and casting the contents in all points as is rehearsed above: and thus you must do in as many places and as often as the proportion of the mould alters. And then adding them all together you may see how many feet that the ship contains, if it were all one whole piece of timber, and not hollow within.
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.
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.
And for your better understanding hereof, you shall have an example of that matter rehearsed above, by a ship of 100 tons, and the length of the mould of the ship, to be 50 feet long, and the broadest place of the mould to be 20 feet broad, and the deepness that the ship goes into the water, to be 12 feet. And I first caused the carpenter to take the true mould of the ship, and also to cut the mould in wood, according unto the length, breadth and deepness, that is to say for the 50 feet long, to be 50 inches, and for the 20 feet broad, to be 20 inches, and for the 12 feet deep to be 12 inches, with all the other proportion of the mould of the ship, to be one inch for a foot. And that done, there was caused to be made a mould in lead, agreeable in all points to the mould of the ship, as lead will mark easily enough. And then there was made the other vessel in lead of 12 inches square, and 48 inches deep. And then the mould for the ship was filled with water, and that being justly and equally filled, the water was put into the square vessel, and then the deepness of the water was exactly measured, and was found to be 42 inches in deepness, and therefore since the vessel was 12 inches square, 12 times 12 is 144, and so many inches there is at one inch deep. And then as it is 42 inches in deepness, multiply 144 by 42 and that makes 6048, so that you may conclude that the mould of the ship, as much as is under the water, if it were not hollow within, would contain 6048 feet of timber. And now suppose that the water was of our water, here at Gravesend, and that is not of the lightest sort, neither of the heaviest sort, and a foot square of that water weighs 55 pounds [sic: a curious error, not simply a typographical one], and that makes 332640, so then you may conclude that the ship weighs 332640 pounds. And then as is declared in the chapter above, to know how many tons the ship weighs, divide that by 2240, and then there will stand in the quantity line 148, and there will remain over 11209 [sic: 1120], so that you may conclude that the whole ship with all her lading, and all other furniture and implements in her, weighs 148 tons and a half of a ton. And by this order you may know the true weight of any ship, howsoever great or small it may be, or boat, or any other thing that swims.
And furthermore you may know by this Art Statical, the true weight of any ship, without putting water into the square vessel, although you do not know the contents, how many feet square, that there is in the ship, thus: the mould of the ship being taken, as declared above, and the proportion of the mould, made in metal, hollow, as is rehearsed above.
And furthermore you may make the mould lesser than rehearsed above, that is to say, you may make the proportion of the mould, for every foot that the ship is in length, breadth and deepness, you may make it but half an inch, or but a quarter of an inch, at your discretion. And then filling that with water, and then weighing the water truly, look how many times the length of that mould that is filled with water, is in the length of the ship, multiply the weight of the water with that number cubickly, and that shall show you the true weight of the ship, with all her lading. As for example by that ship, rehearsed above, that was 50 feet long and 20 feet broad and 12 feet in deepness.
And now I caused the mould to be made for every foot, but a quarter of an inch, so that for the 50 feet long the mould was made 12 inches and a half, and for the 20 feet broad, but 5 inches, and for the 12 inches deep, but 3 inches. And that being filled with water, the water being weighed, did contain in weight 3 pounds and 2 of 73 parts [sic: probably derived from the ratio of Troy to Avoirdupois pounds as 60:73. 1/30 Troy pound, 2/5 of a Troy ounce, is 0.438 ounces Avoirdupois. Bourne presumably experimented with a set of Troy weights] of a pound, and that is scant half an ounce, and the true contents of the weight of the water. And then from that you see that the proportion of the length of the mould, is but 12 inches, and one of 2 parts; that is, but the 48[th] part of the length of the ship. Therefore multiply it in this manner 48 times 48 and that makes 2304 and then multiply it by 48 again, and then it makes 110592. Wherefore now multiply 110592 by the weight of the water, that is to say 110592 times 3 and 2 of 73 parts. And that makes 334620, so that you may conclude that the ship weighs 334640 pounds [actually 334806].
And now to know how many tons the ship weighs, by dividing by 2240 as declared above, and so further as rehearsed above. And furthermore, you may cause in the proportion of the mould of lead or tin, to be certain parallel lines, to be made but a quarter of an inch asunder, as many as you like, and then you may know by those lines what weight the ship is of, when she is not laden. And also, if you wish, you may know how many tons more in weight, will load the ship, as often as you do know how many feet or inches the ship lacks from her load mark.
And yet furthermore you may know, how to know the weight of any ship with all her loading, although you have not made the hollow mould of the ship, as thus: by that mould that the ship carpenter has made, the wood being not so heavy as the water, then make certain holes in the metal mould, then at those holes put in lead, until such time as the mould is heavier than the water, and then stop the holes again, that no water may go into them, and cut off that part that there is more than the mould of the ship. And that done, then in some small thing or vessel put in water unto some certain mark, and then put into that water the mould for that ship which you desire to know the weight of, and be sure that the water covers all the mould. And then take out all that water very precisely, that is fed by that means of the mould of the ship, until such time as the water be just in that height that it was before the mould was put in. And then weighing that water truly, doing as rehearsed above, to multiply the length of the mould of the ship according as is declared above, cubickly, and then the weight of that water that is raised more than it was before the mould was put into the water, and the weight of that water being perfectly known [it is] to be multiplyed by that cubic number, shall show justly the true weight of the ship, as is declared above in all points.
And by these rules or order, you may know the just weight of any thing that swims in the water, saving that you must have consideration, that any mould made of wood, when it is dry, receives or drinks up water, and when it is wet, it swells the bigger with the water.