Whole-moulding: a preliminary study of early English and other sources

© Richard Barker

February 2001

Introduction

Fournier's Hydrographie of 1643 has long been noted as containing a geometrical midship section (Fig.1) which he termed the ancient method¹, unfortunately without specifying how ancient, or where it was practised. It has an archaic appearance about it: a simple quadrant arc is raised on a flat floor, with a longer radius arc extending the side upwards above that. The majority of known frame shapes from the period around 1570 onwards, when they come to be recorded widely, are much more angular in the bilges and at the maximum breadth, resulting from the use, typically, of three arcs in place of the single quadrant.

If as seems likely, this method was part of a wider shipbuilding tradition employed (but not necessarily originating) on the Atlantic coast of northern Europe, we might especially note the possible link to the somewhat mysterious "whole-moulding" that first appears only in texts of the eighteenth century, and in several of which the midship section is based on that same simple quadrant linking a flat floor and a vertical side, albeit only representing small open boats at that stage.

It is a moot point whether "whole-moulding" takes its name from forming the whole hull from a single mould (which is never actually achieved in full), or from the more restricted fact that the whole midship section is created from a single mould. The rest of the hull is formed with rising and narrowing scales (sometimes marked on staffs) for that mould, without any rotation and consequently with a generally constant angle of the side; and that same mould is inverted to form the hollowing curve between bilge and keel. The degree of rising and narrowing is relatively empirical, either from a drawing, or by copying previous examples with the same markings (the surmarks) for the consecutive, adjusted positions of the mould(s) and rising square.

Though Fournier gives no supporting text, it seems quite possible that what he is describing is actually a form of "whole-moulding". This is in fact as close to the "Mediterranean" method as it is to the method of all English treatises from 1570 to 1711, when Sutherland first mentions whole-moulding as one method of design; and for ships, not just for the small boats which are the case from Murray (1765) onwards. That is, the key difference between whole-moulding and the fully developed Mediterranean method is that the legno in ramo or trébuchement is nil: the mould is not rotated about the bilge. By contrast, the English treatisers' method from the end of the sixteenth century does not use a single mould for the side, and is based on adjusting a series of tangent arcs within a grid that itself has narrowings and risings applied to it. This gives great flexibility in forming the hull shape, since the side is not formed by a single rigid mould, while still using only a small set of moulds for an entire ship. (Indeed it is not unknown for the term whole-moulding to be applied loosely or anachronistically for the treatisers' method, on that basis²).

This paper will consider the implications of these observations, taken together with a wider range of evidence for occurrences in documents and archaeology of similar characteristics, to explore the possible origins of what is known as whole-moulding, and thence perhaps of European moulding more generally. To that end it also considers some of the lesser known English sources. It arises from a combination of circumstances, including the Workshop on History of shipbuilding and ship design at Max Planck Institut, Berlin in November 2001, and compilation of the report of the work by Barker and Loewen on the Mary Rose. The evidence, both documentary and archaeological, available for this subject is rapidly expanding, and inevitably requires continuous review of earlier theories. Lest some of the remarks below appear unduly critical of other researchers, it is perfectly apparent that some of this writer's earlier texts contain errors and misunderstandings too, not to mention omissions. Indeed sources only scanned for other purposes in the past have yielded significant surprises. This paper is merely a contribution to a long-term debate. It will be apparent from this text that there is a fatal dearth of evidence to resolve the many hypotheses.

History of whole-moulding in the North

We are not currently able to say where this eighteenth century English whole-moulding method came from, or whether it was earlier than the more sophisticated methods fully formed in England by 1509 at the latest. This writer first discussed the issue long ago³, and Rieth has elaborated that discussion in a recent article in Neptunia⁴. We should preface this section with Rieth's sub-title: "a memory of the Mediterranean shipyards of the Middle Ages", which seems to be undeniable; bar only any evidence of continuity, if we read memory for mémoire, rather than simply a reminiscence.

The history of the English methods is obscure. Until around 1460 there is no record of frame-first shipbuilding at all, and it is not known what the earliest influences were. Genoese and Venetian traders conspicuously visited English ports from the fourteenth century, and of course English ships with their carpenters went to the Crusades from the twelfth century. Many large foreign ships, especially Genoese, were purchased or captured and used in English fleets over a long period. Bayonne had close links, and built very large English ships around 1419, albeit ostensibly shell-built clinker hulls at that stage. Bayonne may indeed be the continuing geographic link that explains the similarity of the moulding systems of the Mary Rose of 1509 and the Basque Red Bay whaler of 1565, though we have no knowledge of which way the system travelled. Northern French shipbuilders adopted frame-first building at about the same time as the earliest English records (excepting only that the Clos des Galées at Rouen was building French vessels - galleys essentially - in the Mediterranean style much earlier, apparently in isolation).

The earliest "carvels" known in the north were built by Portuguese shipwrights for the Duke of Burgundy about 1439; but we should note that that followed his marriage to Isabella of Portugal, who had spent many weeks in England at the end of 1429 with her close Royal relatives, on the way to Flanders, with a large Portuguese armada⁵. (Not for nothing is it called the Old Alliance, though while there is evidence for a flourishing trade⁶, and indeed for mutual support in naval operations⁷, none seems to have survived for shipbuilding in this period). Whatever the first occurrences may have been, the first large English warship so built was reputedly the Regent of 1489⁸.

It is well known that by the time of Henry VIII, Venetian shipbuilders in particular were employed in the English dockyards, but not what their specific role was - it may have been confined to galley construction. The first instance of which this writer is aware is 1541⁹, and then 1570, and both these can be inferred as for galleys.

The first recorded midship sections from English methods are only from the 1570's (though they include a late record of four ships of 1546), and they do not use the Mediterranean method at all, but a system of tangent arcs - though the evidence for these examples is for the midship section only, not its variation. Just such a system has been found by Barker and Loewen in the framing of the Mary Rose, built in 1509. There is no trace of the eighteenth century whole-moulding by name in any of these documents, until William Sutherland's The Shipbuilders Assistant, of 1711¹⁰, at least to this writer's knowledge. This is followed in 1765 by Mungo Murray's A treatise on shipbuilding and navigation, and Marmaduke Stalkartt's Naval Architecture, or the rudiments and rules of shipbuilding, of 1781. These are both for small open boats, and unlike treatises for the design of large ships, they hardly differ. They do refer to the use of a similar system for relatively large ships until recent times; the method appears regularly in encyclopaedias for many more decades - it is in the third edition of Steel's Elements and practice of Naval Architecture in 1822, for example¹¹. It still exists in use in small boats, as in Trinity Bay, Newfoundland¹².

It is worth noting that at an early stage of frame-first construction in the north, the French and Scots (and others too) were in possession of large ships, such as the Great Michael of 1511, built by a French shipwright. Unfortunately there seems to be negligible information about methods of either ally for long afterwards. However, soon after the accession of James I (VI of Scotland) in England in 1603, Scottish shipbuilders were working in Denmark producing plans that are remarkably like Baker's in style and content (Baker was by then in his 70's and not active [see Postscript]). The search has to be wider than England and France, the Mediterranean and Iberia.

William Sutherland

William Sutherland's Shipbuilders Assistant of 1711 presents a number of problems of interpretation. It is a brief, perplexing and inconsistent work. As noted, it does refer to whole-moulding by name, once. The main figure has three scales for surmarks included on it, the rising staff, the half breadth staff and because it is for a large ship not a boat, a half breadth of top-timber staff. The first two correspond to staffs still found in current methods. However, Sutherland also compares whole-moulding with a "more exact way, and yet as easy"; and generally he has risings and narrowings for both the floor and breadth - which is not whole-moulding. He also uses some quadrant arcs. That is, although his reference to whole-moulding is almost in passing, in this context the work does require some consideration. What it describes is in part certainly a case of whole-moulding large ships (p80):

In some instances Sutherland unquestionably uses simple quadrant arcs in midship moulds, and uses moulds for the hollowing curves. He traces a history of attempts to produce mathematically perfect hulls, solids of least resistance, from Pett, Wallis, Newton. Some phrases are worth noting:

Let us now describe what is actually drawn for his first examples. Sutherland's Fig.B (Plate fp4) (Fig.2) shows views of a ship (at very small scale) with sections along most of the length, which appear to have identical shapes with a narrow flat floor. The main mould is a quadrant (the text has "perfectly circular"), there is no hollowing mould. This is superposed on a drawing showing four different narrowing and rising lines that run the full length of keel and posts in just the form used by for example Mathew Baker. This figure then purports to mimick the solid of least resistance with a quadrant arc, but is not whole-moulding. It also has a top-timber narrowing line.

Immediately below this a similar "blunter bowed" figure, D (Fig.2), has hollowing moulds added, which appear to be the same arc as the main mould; in the woodcut at least it has lost the line for the narrowing of the floor, and has two lower rising lines, unexplained. The mould appears to be a similar quadrant, except for the last two sections aft, which are also unexplained.

Fig.C (p6) (Fig.3) has a quadrant at the midship in a sketchy body-plan to accompany Figs B and D, with four sections drawn fore and aft that might use the same mould, but with no hollowing mould.

However this cannot all be true as a pure quadrant mould would require equal risings and equal narrowings at the floor and breadth. The sections appear to end on the upper rising line, but we then notice that the intersections must be offset longitudinally by the half breadth - it is a false line, and the centres of some of the quadrants apparently lie above it; or it may in fact be a line of wale ? As far as one can tell from the woodcut, the sections follow the upper breadth line, and the lower narrowing line is false. It could thus be a case of whole-moulding, undeclared, and confused in the woodcut. The text then moves to other issues. A subsequent work by Sutherland may throw light on this (see below).

When moulding resumes, Fig.A (Plate fp58) (Fig.4) shows the two longitudinal sections, with distinct narrowings and risings for the floor, the breadth, and the top-timbers, formed as ellipses. The text mentions only four of these lines clearly: the narrowing of the breadth and the rising of the floor are mentioned more elliptically, but can be read into the text. In the figure, all four main lines now run the full length between posts. It seems impossible to be sure what was intended here too. The next step describes with a small figure (Fig.B, Plate fp58) (Fig.5) a stretched midship section: starting with a quadrant, the result is again an ellipse. Above that a second "height of breadth" is marked, giving a short length of vertical side, which "causes it to carry sail, and renders the top-timbers beautiful and more gibous" (p59). The elliptical section thereafter seems to disappear from the text, though the vertical side remains (and is indeed as seen in ships such as the Victory).

Moulding is described (pp77-84) as the process of using a pattern to mark and measure. Sutherland describes the mould-loft floor, spacious, well-lit, very even, black-sized for the chalk to show; the dry seasoned split-deal that is planed for the moulds themselves; and the sweeps, instruments to mark out the curves. This latter might include laths, especially for the longitudinal curves, but it certainly sounds as though they originated with circular arcs. The process of marking up the floor is called "crossing the moulds" (pp82-3), and care has to be taken to mark the surmark between the main side mould and the hollowing curve. This indeed is marked on the plate (fp82) (Fig.6) accompanying the description, but we have another puzzle here: while the midship section reverts to a simple quadrant up to the lower height of breadth, most or all of the sections fore and aft use a sharper arc: they apparently do not match the mould of the midship section as would be expected, yet this is not referred to in the text ¹³. The hollowing mould to the keel however does seem to use a constant arc, equal to the midship mould, and with a flat attached. Similar patterns appear in the arcs used above the breadth, termed working the hollow out (aft) and in (forward on). He proceeds to take bevels at the surmarks from the mould loft.

Interestingly, "it would also be very proper to try the line of ribbons, whether they are truly circular…" (p83), that is, he prefers to fair out his diagonal rather than make the water-lines fair. This would of course destroy the drawn ellipses: perhaps he is checking that those lines have been correctly generated in the mould loft from what are only three intermediate points fore and aft in the drawings. The objective of using the diagonal is explicit: to have a fair surface for the line of both plank and water flow. In his work of 1717 the benefit has become swift-sailing (see below).

In short, Sutherland is certainly describing aspects of whole-moulding as in use for ships, but it is not his primary method. The origin of his longitudinal rising and narrowing is in drawing, in which he follows the treatisers, yet he has none of their geometric sophistication in the section. Indeed he has a phrase "… strike the circle which will describe a midship bend more agreeable, and less perplexing, than if you was to chalk out one hundred segments of circles. 'Tis said indeed that the catanera (sic: catenary ?) line will describe a shape of the greatest gravity [for the section ostensibly, but in fact for longitudinal curves ?]; but I shall leave such nice demonstrations for the present, and proceed to shew an intelligible method to suit and forward young beginners" (p79). That is his only reference to the more elaborate geometric and arithmetic methods described by the earlier treatisers, except for the use of longitudinal curves which are in fact (though not so named) ellipses. (It is virtually certain that the final intervals at stem and stern were smoothed out with laths, and did not end perpendicular to the axis as an ellipse does).

One curious aspect of all this is that it is as though Sutherland was arguing for a new introduction in many of his phrases: was he advocating a system of moulding to suit the fine theories, or pointing out tartly that the older methods had been best all along ? We are left unable to determine whether Sutherland's method is older than the treatisers; parallel to it; or a simplification of it, wishing to use the quadrant arc. What is striking is precisely that quadrant arc, just as used by Fournier. At the same time, the method described by Sutherland in most of the longitudinal plans is not whole-moulding, nor the same as Fournier's (see below), because Sutherland uses two distinct and independent narrowing lines (and two rising lines) in most of his figures, where Fournier appears to have identical narrowings alow and aloft.

Sutherland's other work, Britain's glory; or shipbuilding unvail'd, of 1717, has only a single page on moulding (pp1-2), and one plate (fp4) (Fig.7), which shows a quadrant section. Curiously it has a dedication to King George and table of contents all written in French. It calls the rising line of the floor timbers the "lipping"; otherwise it is more concerned with forming ships as conoids. Therein may lie the clue to what Sutherland is doing ?

This appears to mean that he actually wishes to introduce circular sections more widely. Whether he is really following the mathematicians' approach to least resistance is of no interest here; but he certainly realises that it is not achievable in a real ship.

And

Now the figure shows longitudinal narrowing and rising lines that are not simple arcs, nor from their acute ends, ellipses - there is no construction shown or described in the text. All run to the posts, not the ends of the keel, there is apparently a significant dead-flat amidships. The section shows the midship, undeniably a quadrant, and one section in each extremity fore and aft, also apparently including quadrants, but of much reduced radii. (A hollowing mould and upperworks are superposed to that quadrant). There is no text, but relying on the small figure, and the simple fact that a quadrant in this system must have the same offset between breadth and floor both as narrowing and rising, we may observe that most of the run of his ship has a quadrant of close to its radius amidships, but that it reduces rapidly, as the rising of the floor kicks in, and that the resulting radius is much as shown in the sections. For this to be the case, the two rising lines, and the two breadth lines, have to be reconciled so that the distances between them are equal at any section. They cannot all be formal geometric curves; and this may in turn be the origin of a need to fair the diagonal ?

Furthermore, this could explain why the later and most complete figure (fp82) (Fig.6) in his 1711 text has no line for narrowing of the floor drawn in: it is left to follow the quadrant defined by the two risings and the breadth line. This explanation does not appear to work for all the earlier figures in 1711.

Sutherland has another delightful phrase, after recounting that many major warships required girdling, or suffered other "dismal miscarriages". At first sight, it implicitly refers to the treatisers' method of multiple arcs:

The meaning changes when one realises that addice is adze, not a subtle instrument required in geometrical methods. It perhaps suggests, again, that Sutherland did not approve of multiple arcs, compared with his quadrants. He is not, however, describing whole-moulding as known to Murray or Stalkartt. The features in common are the quadrant arc, and the fact that the simple rising and narrowing are controlled by two lines extending the whole length of the hull, at the breadth. However, there is no single mould, except for a central portion that is, or is close to, a dead-flat - at all other sections the quadrant mould has a radius controlled by the rising line of the floor. This method appears to be Sutherland's "more exact way, yet as easy"; and he appears to recognise a pre-existing version which he calls whole-moulding. But while he has no name for the treatisers' method but a disparaging reference in each book, to a hundred segments of circles, and to reconciling moulds, discussion of the different methods becomes difficult. Perhaps we might borrow a phrase from Sutherland to describe his more exact, easy way: that of the hanging conoid.

The manifestation of whole-moulding as in Murray could have been a degenerate form that spread outwards from the main dockyards, for smaller vessels that did not need the full elaboration of the treatises to produce a satisfactory hull shape. A feasible mechanism would have been the impressment of shipwrights from around the country to work on major Royal projects during the sixteenth century, when they would have observed at least components of the full methods. Lavery on the other hand suggests that the earliest way to create the complex shape of a hull was to use the same shape for all the frames, moving it inwards and upwards, "probably the original meaning of whole-moulding, for a single mould or template could be used to cut out the whole frame"; and adds that this had been transformed by 1586 at latest (that is, by the first evidence in Baker's work of the treatisers' methods). In the light of new evidence from the Mary Rose this must have been a short-lived phase, though the older method could have continued in parallel. Sutherland's evidence is that whole-moulding pre-dated the method he describes as aiming at solids of least resistance, but cannot therefore explain the origin of whole-moulding.
 
 

It may be worth noting what is in other English material prior to Sutherland, though there seems to be nothing earlier that touches directly on whole-moulding. Bond, and Miller (The compleat modellist, first edition 1660) are concerned entirely with masts, rigging and similar issues. Deane's MS Doctrine of about 1670 is mentioned above (fn13).

Bushnell (The complete ship-wright, 1664) is far more relevant. Possibly uniquely amongst English sources it uses a midship mould (Fig.8) with two arcs that are not (necessarily) tangent. One runs up from the wronghead and the other down from the breadth, meeting on a diagonal of breadth and depth. The top-timber is a straight line tangent to the extended futtock arc. He "could have cited other ways, but I judge this way sufficient" (p9). His four main narrowing and rising lines (Fig.9) are all arcs of circles, with a dead-flat amidships, and the measures are to be calculated arithmetically. Moulding then proceeds in a mould loft, or floor. Three moulds are made, with the radii matching the floor and futtock sweeps, and with their initial surmarks. The narrowing of the floor and hauling down of the futtock and top-timber are then marked on the moulds on the mould loft floor, after aligning the surmarks with their adjusted positions at successive frames. Nowhere is the knuckle between the arcs referred to. (It is plausible that Bushnell is the target of Sutherland's jibe about the adze as reconciling mould). The method is otherwise a variation on the treatisers' method, and certainly not whole-moulding. There are extensive tables to assist the repetitive calculations of risings and narrowings. This book was re-issued many times, and as late as 1748.

It is worth a brief discussion of the problem of tangency in two-arc methods. The 1546 galleasses of Baker's Fragments have a valid solution for a pair of tangent arcs, the upper of which is part of a quadrant, constrained to have its upper surmark and its centre both at the height of the breadth. There is little flexibility in the choice of the pair of radii for any given proportion of breadth, depth and floor (and ignoring the problem that the breadth and depth are outside the apparent initial grid for the design); and in practice there is little difference between the shape resulting and a quadrant. There is a choice for the first radius, for the wronghead, however. Baker's construction may perhaps reveal the truth of avoiding a messy process of trial and error: the precise breadth (or depth) achieved is the result of specifiying the depth (or breadth) and the two radii first. This is not a system that was likely to survive.

The more usual system of this kind in Fragments is to end the second arc with its surmark on the upper corner of a predetermined grid of breadth and depth, but without other constraint. This is actually flexible and direct, allowing any choice of floor, and two radii; but the true breadth and depth exceed the grid values. The breadth is formed by the third arc - it is not a two-arc system in that sense.

In Bushnell's method, he adds a requirement that both arcs must pass through a geometrically defined point in the bilge area. The result is that while his two arc centres are on defined lines over the end of the floor and along the height of breadth, there is only a single solution to the radius of each. In general, at least, these two cannot also be tangent to each other, whence the problem. It is not a question of trial and error, because each radius is an explicit function of breadth, depth, floor, and in Bushnell's case dead rising too. Whether or not the curves are tangent is thus related to a happy choice of those four parameters, and there is certainly no quick analytical solution available to find it; Bushnell defines breadth and depth before the arcs, removing any flexibility. Some degree of knuckle is almost certain, as indeed his figure (p8) suggests.

Wallis' Cono-Cuneus: or the shipwright's circular wedge of 1684, which Sutherland refers to, is part of the search for solids of least resistance, but of no practical interest. Fagge (see Mariner's Mirror, Vol.40, 1954, p156) and Hardingham have not been seen by this writer.

Some details of the other English sources

Rieth introduces the Venetian connection to English shipbuilding, but only in terms of a development by Henry VIII. The weaknesses with that are numerous. There is no explicit evidence for when Venetians were first formally employed (1541 is noted as one occasion), or that they were doing more than work on galleys. Linked to the Mary Rose, begun in 1509, shipbuilding initiatives are in all probability the legacy of Henry VII, not Henry VIII (especially bearing in mind the time it would have taken to summon shipwrights from Venice on Henry VIII's accession, in 1509). But the Mary Rose is only the first ship for which we have much evidence, not the first large ship built in frame-first mode in England. Again, if Venetian methods had been so significant during the growth of Henry VIII's navy, it is strange that no record, either text or technical, can be found. (We must however note the still unresolved curiosity that Baker does label some of his draughts as being the Venetian method - for the midship frame at least - and some of the few explicitly identified ships, built around 1570, are amongst them). In parallel with that, we might observe that the massive, irregular timbering of the Mary Rose has absolutely nothing to do with Mediterranean styles - if Venetians had been involved with the geometry, they assuredly were not with the actual timbers - a strange split if the Venetians were there to teach the methods from scratch.

Rieth then notes a brief and cryptic remark by Mathew Baker to the effect that no Englishman knew the full details of the linaramo del sesto method¹⁴, using it to suggest that Baker is saying that at that point (perhaps 1580's in the case of that isolated note on a twice re-used page) Englishmen must have been building most vessels using the method, without trébuchement, that later came to be called whole-moulding. The general weakness of this notion is that Baker never refers to this in his own elaborate material of the 1570's, even though he includes material that he labels as Venetian; and specifically there is another interpretation of the remarks, discussed below. Neither is there any trace in other treatises of the next generation. Most telling, though, is that the Mary Rose includes not whole-moulding, nor trébuchement, but virtually the system as used by Baker three generations later. There simply is no evidence yet identified for whole-moulding as a term until 1711, though Fournier may be referring to something of the sort.

In fact Rieth's footnote (following Bellabarba) citing Fragments p16 gives only part of a very cryptic text, whose meaning and context is far from clear. The whole passage, which bears no relation to the pages on either side, nor possibly to the underlying drawing of a typical early Baker midship section (with breadth arc starting at the grid-point of breadth and depth, and whose earlier function in the manuscript had been calculation of area) is:

That is, many English builders were using drawings in their design, a feature of adjusted tangent arc systems, not of trébuchement methods; they were perhaps still building on three frames and ribbands since they do not understand the circular lines, which in context this writer believes is more likely to be a reference to the longitudinal curves of narrowing and rising that much of Baker's work illustrates.

That is, they take a measure for the maximum value of the rising and narrowing (at the quarter frames), and if those used aft of midship lead to fair curves to end on the tuck and transom, that is the desired result; though the finer points of the remark remain unclear. The Venetians would set a meia-lua at the quarter frame, and a breadth at the transom; beyond the quarter frame here, a ribband will probably be fitted by eye.

Now Rieth¹⁵ equates linaramo del sesto with trébuchement, the measure of frame rotation. (In this he is actually following Bellabarba's earlier article, to be discussed again below). In Baker's example that follows the text cited, related to labelled modifications added to his base drawing, it is quite clear from the labelling of the figure that Baker meant by ramo del sesto a scale of "hauling down" applied at the bilge, not the rotation measured at the breadth. So there is some question that Baker may just have been referring vaguely to his own method of moulding in its fullest development. (On the other hand Baker could just have confused the labelling for the method, which after all is not the system that his manuscript is concerned with in practice). There is also some ambiguity as to which words are objected to, and what his answer was to be is not known.

Could this also just mean that English builders did not use the geometric system of meia-lua for the partison ? This would correspond with the fact that Baker nowhere uses it either - a conspicuous feature of Fragments, in that sense. It does not occur in English treatises until the seventeenth century - it appears in the 1620-5 Treatise on shipbuilding¹⁶, but only for the hollowing of the upperworks. Baker was using string lines or arithmetic for the purpose (in so far as he discusses the issue in what is effectively a note-book, not a coherent treatise), but the commonest approach seems by default to be a circular arc; which is described more elaborately in subsequent treatises as late as Deane (1670) for example. How literally a pure circular arc in a drawing of a large scale, or in a ship built without full lofting, is unclear, but bows or splines are a close approximation and certainly serve the same function of ensuring a fair curve. (Use of bow or spline has not actually been determined so early as this, but a trammel is impracticable and a stretched cord not very accurate. What is certain is that Baker had a mechanical aid to create his immaculate curved lines. Even so, Baker's main concern was the problem of accuracy in scaling up measurements from a notionally precise drawing to full size).

Bellabarba mentions the Baker manuscript reference to linaramo del sesto in an earlier paper¹⁷. He makes the equation of the full partison method including legno in ramo (trébuchement) and scorer del sesto (recalement), with the English methods described by Baker and Wells. He also states that the function of the scorer del sesto in the Mediterranean system was to perfect the alignment of the arcs of the timbers at the bilge, following the rotation of the side frame: this is simply not correct, as the centre of rotation is not the centre of either arc, and what it actually does is to lower the whole side, so that the gunwale has a lesser sheer than the curve of risings of the floor¹⁸. But he extends that statement, by explicitly equating it with the English "hauling down" of the futtock. Since the English system of Baker's texts (and all other contemporary treatises) fixes the height of the side frame in the process of design completely independently of the hauling down, they are not equivalent at all, other than visually. In English whole-moulding, by contrast, there is no hauling down at all, so there is again no equivalence. (It is however true that a surmark exists for the hollowing curve to the keel, but this is not usually included in discussions of hauling down of the futtocks; in whole-moulding, the futtock mould is integral with the floor timber mould, and is not adjusted from station to station).

We might insert some further observations on the implications of the Fragments at this point. Firstly, Rieth suggests (p19) that the presence of these Italian terms is without doubt due to Baker's voyage to Chios in 1552. However, this is not necessarily so: Rieth also suggests that Venetians were heavily involved from the time of Henry VIII on in creating frame-first carvel building in England - long before 1552, as above; and Baker worked alongside one Levello at roughly the time he was compiling his notes. The Greek mould alone is perhaps most likely to have been collected in Chios; otherwise some doubt remains about where the Venetian information came from.

It is true that Baker collects material identified as Venetian, dated roughly 1550-70, but we might note that to refer to it we have to cite a string of page numbers - it is scattered and incomplete, with no evidence that Baker was using it himself. He does however label as Venetian a four-arc midship mould system which is clearly in use in named ships around 1570. Unfortunately it does not correspond with extant Italian records, based on offsets, though this writer believes that that is because those records are not design documents but a means of conveniently transmitting the results, perhaps for contract purposes. At the same time we ought not to confuse the shape of the master frame with the method of varying it along the hull.

According to G.Juan in 1771¹⁹, as Rieth tells us, whole-moulding was an alternative to building on a master frame and ribbands, for large vessels. It is not immediately clear whether it was used in Spain, as Juan associates it directly with English whole-moulding. This had been used for several centuries until recently displaced by methods based on plans. Rieth remarks that in 1771 Juan could not have been inspired by Stalkartt (1781), but in fact he could have found the method in Murray's work, published six years earlier in England (or even in Sutherland's). In fact the method itself is beginning to look so widespread that it seems unnecessary to demonstrate a link between the authors.

Fournier's method

Returning to Fournier, at the end of his work he has a table of dimensions for the lengths of the main beams of a ship²⁰, from the maximum section to the sternframe, and for the width of the floors. Ignoring for the moment the problem that he has narrowings for the floor at the same station as the transom of the sternframe, where there is no keel, let alone floor, it is conspicuous that the narrowing is identical at the floor and at the main beam. The curve is arrived at from a quasi-geometric device, calculated using sines²¹. In other words, the method is "whole-moulding", not trébuchement. That is, the French were also using whole-moulding at some point before 1643. It is not explicit, but the table may be linked directly to the ancienne méthode, as the maximum breadth of the ship is identical, at 27-1/3 pieds in both the ancienne méthode and the table, while his example of the "modern" style²² is for 44 pieds breadth. (Against that it might be argued that there is also a standard 300 ton ship of 27-1/3 pieds and the same 10-1/2 depth in a table in Book I, Chapter VII, to which the text for the modern method refers; but only if we then accept that Fournier must be describing whole-moulding in his modern method). Does that, interestingly, suggest that the ancient method was still in use, to offer the example of narrowings ? Such might be supposed from the opening remark of Chapter IX, on the modern method, which also links the change to English and Dutch builders. (Ships built on the older method were too round and rolled too much, Fournier says; though actually there is no inherent link between midship frame shape and method). Other examples in that part of the book relate to the port of Havre, and a northern French context is thus probable; though more generally Fournier compares terminology of Marseilles and Italy too.

Intuitively, while Fournier's midship section (Fig.1) employs a simple quadrant, there would indeed be little point in rotating the side timber mould in the "Mediterranean" system of trébuchement, or espalhamento. Not least, since trébuchement is outwards (creating the flare of a seaworthy hull, while allowing the fine entry and run required at a lower level), there would be a tendency for the bilge to fall below the point of the turn of the bilge, unless the rising of the floor is pronounced. Trébuchement, we might observe, is commonly applied in hulls where there is a sharp transition from a flattish floor to a steeply rising side, only faired out locally, which is the key weakness of that method.

But consider Baker's final method, that of the subsequent treatisers. Two narrowings and two risings are independent, and carried close to the ends of the ship (though actual moulding with the midships templates was only carried that far as an ideal, as it was not fully achievable, and certainly beyond the ends of the keel, with its discontinuity of boundary conditions). The basis of this method almost calls for a moulding floor (not necessarily a permanent structure, for which there is no contemporary evidence), from which templates could be made for each piece of each frame. Or rather, where the set of standard templates for the major arcs could be adjusted against each other. The surmarks could be marked at overlaps - a fixed point at one end of a template, and at the other end a new mark for each frame position along the hull.

This leads to the expression "hauling down" of the futtock, though this writer will insist that hauling down - a term widely seen in English texts, is not the title of a method, but the consequence of adjusting tangent arcs with predetermined narrowings and risings - a form of moulding the vessel whole (to avoid the term whole-moulding here). Hauling down is one practical component of the method, not the method itself. We might further note that in the shipyard it is very visible to all the ship-carpenters, and difficult for the masters to hide from those doing the manual work, in the contexts of both supposed secrecy and possible dissemination.

If each timber has its own pair of surmarks - points of overlap and alignment of the arcs, assembly is assisted; whether on the ground, or within the growing ship. Together with a separate temporary control of breadth of the frame, plumb-bob, horning of the timbers, etc, the final shape is assured to within practicable limits.

On balance, since the perimeter of a vessel is less at the ends than at the midship, there will tend to be a hauling down, but it does not follow that a particular shape of hull might not require a local "putting up" of the futtock in a corresponding position; and within the vessel as a whole both can be expected to arise.

But in this system we have something different from the Mediterranean method. The progressive adjustment of frames along the hull is no longer by a geometric device such as the meia-lua (which is more or less guaranteed to produce a fair surface, but only over the central section of the hull; and strictly it may not be fair for real planking runs or water flows). Each frame has its own variations from the midship section, which, though the results using Baker's methods or similar will remain fair over a greater length, are unpredictable. They can be calculated as chords between surmarks, direct from the narrowings and risings defined, as was done in Baker's time (though only really practicable after the development of logarithms²³). They can also be marked directly on the template on the moulding floor - which Sutherland effectively does in his text of 1711, taking great care to mark the curve of surmarks on his body plan.

This is also what eighteenth century whole-moulding does: it has no inherent system of geometry, but records a prior operation, whether a plan (originally, perhaps), or a previous vessel. It remains valid while the curves of narrowings and risings are fair curves, either calculated, lofted, or copied with or without incremental alterations.

But this has said nothing of which version was the older, or where either came from. One of the few things we do now know, from preliminary work on the Mary Rose, is that this ship was not whole-moulded in the English dockyards in 1509 (very early in the frame-first system in England), but for much of her length she has repeating tangent arcs adjusted in the treatisers' method, or something like it, with some hauling down of the futtock apparent, and upper and lower narrowings and risings differentiated.

Older traces of framed construction in the north

A further possibility for the origins of northern moulding is that there was a completely independent system in the Channel-Biscay area, even perhaps pre-Roman, from the Veneti, whose heavy ships are described by Julius Caesar. This, supposing it might have been the origin of whole-moulding, might have omitted geometry in the narrowings and risings and frame shape, and have used no rotation of the side. That in turn could have produced elaborations when larger frame-built ships were required - more arcs, if not the geometric risings and narrowings. That could have led to the stage discussed below, when the tumblehome was added.

Frame-first construction, which is considered to be inextricably linked to the ability to mould the shape of at least critical parts of a ship in advance, is known archaeologically from the third century, in a "Gallo-Roman" wreck found off Guernsey²⁴. The report clearly states that heavy floor timbers were erected at previously marked positions on keel planks, and postulates a sequence of shaping those timbers (which this writer finds implausible, without questioning that the construction was frame-first: the broader question is why the report does not even consider the question of how the floor timber shapes were determined, but resorts to a three-stage process to arrive at the lands for planking of very variable width). The survival of timbers is not sufficient to judge the form of any moulding used.

A further frame-first vessel from the area of interest is the Port Berteau II wreck²⁵, from around 600 AD. Unfortunately the critical areas for any moulding that may have been present at the bilge are lost in this case, as the hull survived upside-down (what survives is round-bilge carvel without edge-joining), but the sides show no rotation and frame-first construction implies the selection and shaping of some floor timbers at least to a pre-determined shape.

These examples are however only representative of a much larger and steadily expanding group of "Romano-Celtic" vessels from north-west Europe, including Blackfriars II, Barlands Farm and vessels on the Rhine. These all have the characteristic of frame-first construction, to a greater or lesser degree, though geometry is not their most conspicuous characteristic - many are flat-floored types too. There has been the same lack of continuity through to the written sources, however: the methods employed seemed to disappear at roughly the end of the Roman period (though they probably pre-dated the Romans, on Caesar's evidence, so the disappearance may be coincidental). Clearly Port Berteau II starts to fill the gap in those terms, but it does not solve the problem. We also note in passing that these frame-first vessels are older than almost all Mediterranean examples found to date. Numerous small boat types exist in England which could have preserved components of frame-first techniques from antiquity.

Tonnage measurement aspects of enlarged hulls

One aspect of this whole debate, which is also linked closely to early methods of tonnage measurement by formula, is worth considering in some detail. It is the step from ships of a single weather deck, to ships with two or more decks, whether they were conceived as merchantmen or warships, or just ships. Single deck for this purpose includes open boats and ignores any orlop deep in the hold in larger vessels: one key characteristic is that many such vessels will have sides that are still flared outwards at their gunwales, simply to be ship-shape and survive in rough waters.

For such a vessel, the method of trébuchement is quite appropriate, as it characteristically does create or increase that flare by rotation of the side outwards, fore and aft. It is not essential however, as the side may be angled at midships, as it is in most small Mediterranean boats, and as occurs for example in the Serçe Liman wreck from the eleventh century, with little or no outwards rotation, but a clear suggestion of the graduated risings and narrowings (as fn3 above). In the smallest vessels, with flat bottoms, the constant side angle is even determined by the characteristic growth pattern of the tree species providing the knee at the bilge²⁶. The early Punic ship is an exception - see below.

In that sense, the upright side of the eighteenth century whole-moulding of English texts is something of a mystery: possibly a sign of a degenerate method, rather than something that has evolved. The method as such, presumably even in those specific early examples of warships' boats (which may atypically have been intended for rowing, for stowage inboard, etc), was however perfectly capable of producing successful boats, and W.A.Baker (a naval architect as well as an early researcher in this field) reports so using it in small boats²⁷.

There is good circumstantial evidence, from terminology and rationale, that early methods of calculating tonnage by rule²⁸ were based on hulls of this single-deck kind. The methods specify bocha, maximum breadth (probably excluding the bulwarks in a decked hull), and when second decks occur they are initially treated as additions. Depths related to the bocha too, but this creates problems when ships acquire more decks - the block coefficients of the original hull (or of its usable spaces) and of the higher deck are not the same, but the equations employed do not distinguish. By the late sixteenth century the methods tended to be based on two or three deck ships, but were consequently not so satisfactory for smaller vessels.

For reasons of stability, if nothing else (timber supply, defensive shape come to mind²⁹), additional decks above the waterline were generally narrower than the main deck: ships were given tumblehome. To some extent that was true in earlier ships too³⁰ - probably reflecting the basic truth that stability relates to breadth at the waterline, or more immediately practical issues such as robustness of ships heeling at berths and against each other. Early Portuguese moulds clearly show tumblehome, but that results from using a single arc for the whole side frame. When ships acquired additional decks for artillery and accommodation tumblehome became pronounced, and required a short radius arc at or close above the maximum breadth, itself just above the waterline. Some of the early sections in Baker's Fragments show features that suggest that what happened was literally an extension of the old single deck form. At a point corresponding to the top of the old flared side, another arc was added, tangential to it, and correspondingly that included the real maximum breadth of the new hull. (We might observe that that is effectively what Fournier's method does). Construction of the old hull was defined around the maximum beam, the bocha, at the top of the old side; and the extended hull also, for a while, retained a "breadth" measured at that point. Baker's grid lines in a few early cases make that possibility very clear. In Baker's case that system did not last long: the majority of designs in Fragments have a grid that corresponds to the true maximum breadth. Correspondingly, in the interim, there would be a problem of recording tonnage dimensions. The shipwright, if asked, might furnish his design breadth, probably a nice round number of feet, at the old bocha. If the ship was physically measured, a larger, and fractional number would result. The same ship might have more than one calculated tonnage; the old divisor would not suit the new system. (In the case of the Mary Rose, it seems that the true moulded breadth was not a round number of English feet, but neither did this problem arise, as perversely it appears to use the "later" system). The Red Bay ship, much later, is said to have a true moulded breadth as a round number of codos.

But what of the implications for the Mediterranean system ? There is nothing to prevent the midship section associated with trébuchement incorporating an additional arc, and tumblehome³¹. If however, we add the tumblehome to the side and apply trébuchement, we may be creating a very unsatisfactory shape in the upperworks, as the rotation at the bilge cancels out the very tumblehome introduced at the midship, and in proportion to the height above the bilge. With no other corrections, the system requires an excessive tumblehome at the midship, to retain sufficient tumblehome nearer the ends. We might notice Sutherland's additional whole-moulding control for a ship: the "half breadth of top-timber staff".

At an intuitive level, then (and the evidence is and will be so sparse and contradictory that little more is achievable in this whole debate) the trébuchement method originated with small vessels, but was not as satisfactory in larger vessels. (Notwithstanding that, it was evident more widely in France at the end of the seventeenth century³²). It presumably developed as an enhancement of the still earlier system in which there was narrowing and rising of the bilge, but no rotation of the side. (It is still extant, if not necessarily with geometric risings and narrowings). Possibly the English whole-moulding reflects something similar. It is only known for small craft, it has no rotation of the side. Perhaps the quadrant bilge reflects a different timber supply, and different conditions of sea, use and capacity.

Discussion of the origins of whole-moulding

The complete absence of any clear early documentary evidence for whole-moulding remains a mystery. We have seen that it only appears by name in the eighteenth century, but that Fournier may imply its use in England and Holland as well as France, long before 1643, and possibly for almost two centuries before that, if it were linked to the advent of frame-first construction. Sutherland appears to be describing a form of whole-moulding for ships in 1711, and without a real context. The method was also known to a Spanish writer, and while his source is not known, one possible inference is that the method was practised in Spain in the late eighteenth century.

Archaeological evidence may place a comparable system in the Mediterranean no later than the eleventh century, in the Serçe Liman wreck of around 1025 (which has no trébuchement); similarities can be found even in some modern small craft. There were too systems of heavy hull construction indigenous to northern Europe - western France, Channel, southern North Sea - from a period before Roman occupation, even if our knowledge of them is still slender. Yet Bellabarba³³ actually provides a near-perfect archaeological example in the Marsala Punic ship, excavated by Honor Frost and published in Italy as long ago as 1981. The reconstruction given by Bellabarba even has a frame shape that is so close to a quadrant as to leave little real doubt that that is what was intended in the vessel itself. It is adjusted along the hull by rising and narrowing³⁴, and has no rotation. Even if the vessel is shell-built, that implies some close control of form with moulds, and at least three of them. (More than that would beg a question about shell-building³⁵). Bellabarba does not use the term, or comment on the similarity, but that is whole-moulding in all but name. It is also much closer to the system of moulding the entasis in classical columns of that very period, for which we have the very direct evidence of Didyma, around 334BC³⁶. Again, archaeology is slowly filling the gaps, with a range of evidence emerging for the sixth and seventh centuries to suggest frame-first building in the Mediterranean.

A further early example is the Venetian Roccafortis of 1268, where dimensions are recorded in documents, but no drawing. Jal knew of the evidence, but Carr Laughton reinterpreted it as essentially Fournier's old method³⁷.

Bellabarba collects evidence of mostly Italian documents that clearly use the terminology of the partison methods no later than 1275. Legno in ramo appears in the Fabrica di galere, which he describes as a copy of a document of 1410, but is now believed to be copied from a manuscript by Michael of Rhodes, and begun as a collection in 1434³⁸. That is, the full Mediterranean partison method, with trébuchement, was developed long before there is any question that the method came north for early frame-first ships in the second half of the fifteenth century.

There is other Mediterranean evidence, in contemporary small boats. Damianidis describes³⁹ a wide variety of systems termed monochnaro (literally, single mould⁴⁰), one of which is hardly different from Stalkartt - differing essentially in the flare given to the side. There is every reason to suppose that the method is old in its Greek context; Greek builders have also retained forms of partison that differ from other common systems such as the meia-lua.

What we do not have for any of these isolated records is the slightest evidence for continuity or transmission. As noted above, a further possibility suggested long ago by this writer is that whole-moulding actually represents a degraded version (sufficient for small ships and boats), of a sophisticated geometrical system that was imported, adapted, or developed locally in the north, at the end of the fifteenth century with the advent of large frame-built ships, and spread on the England-France-Biscay axis in ways unknown. In the light of the Punic ship, and indeed some of the more recent Eastern Mediterranean sources, that may be less tenable, but continuity cannot be demonstrated.

Granted the relatively short interval between the introduction of frame-first methods in England and the fully developed form of adjusted tangent arcs as seen in the Mary Rose, the absence of records for whole-moulding, if it had a separate existence amongst technically-literate shipbuilders at that time, is not too surprising. The indigenous vessels were either clinker-built, or small boats, so long established that they needed no record, or even elaborate moulding at all. Larger frame-built vessels when they appeared in England could have been variously purchased abroad, built by foreigners, simply copied piecemeal (using methods hinted at by William Bourne), or a genuine new development. The very style of building was changing in other ways too, at the same time: the first square-stern ships are known from the 1470's, and spread rapidly, ostensibly from Spanish Atlantic origins. That is perhaps significant in the sense that many sources seem to relate moulding methods to the use of a template for the sternframe that might also be used for the hollowing curve to the keel. The Mary Rose appears to have this feature by 1509.

The issue of timber supply in the Basque area may be relevant, given the two or three generations it takes to grow trained frame timbers, but is not likely to be conclusive here, partly because shell-built vessels of comparable size also require heavy frame timbers of much the same shapes, and partly because we have no knowledge of methods in Biscay at the critical period, except that Bayonne was still building its biggest ships by shell techniques around 1419⁴¹.

Conclusion

Can we find any pattern amongst the many disparate records, short of actual origins or continuity ? It is clear that forms of whole-moulding existed in the Mediterranean in antiquity, but we cannot say categorically that they used formal geometry (rather than say a catenary, or slowly evolved empirical measures) for the rising and narrowing of the floor - only that there was suitable geometry in place in classical architecture; and that the first examples occur without any apparent rotation of the side frame. The earliest (the Punic ship) happens to use a quadrant, but the other (Serçe Liman) does not - there is no pattern in that; either could be argued as the more sophisticated, depending on whether geometry or potential performance at sea is the criterion.

It seems that between say 1100 and 1400, the use of rotation and then sliding of the side began to appear. That corresponds to the period of powerful city states, and Byzantine rather than high Renaissance. This is the origin of the developed form of "Mediterranean" moulding, still widely in use, but increasingly replaced for large vessels after say 1800 by the use of plans. How the Mediterranean handled the transition to multi-deck vessels is rather uncertain, but tonnage measurement methods may be an indicator of how and when it became a significant issue. We still have the example of Greek small boats using precisely "whole-moulding", with geometrical methods, but without the quadrant side (and Bellabarba reports other examples). What we do observe is that the records of "offsets" to define frame shape in Venetian documents are an unsatisfactory explanation of method, and probably mask an origin in systems of arcs⁴². There is another enigma for the Mediterranean: what happened to the no-rotation system of moulding, applied to larger vessels, after the advent of rotation, which was in place before the north adopted carvels ? Only if it remained generally in use for large vessels could it have later travelled north to yield whole-moulding.

What of the north ? We apparently have structural methods using frame-first construction, earlier than in the Mediterranean (Blackfriars II, Guernsey, Port Berteau II and many others), but so far there is nothing to indicate how the frames were shaped and the hull form controlled. None shows any clear sign of quadrant or of geometry. However, if such methods survived until the fifteenth century, while the dominant methods were shell-based, they did so in small vessels, with no need of further development. There is certainly no actual evidence of transmission from the Mediterranean, least of all for the geometric aspects; but then Gothic masonry construction arose in the north apparently unaided (and indeed was so named by Italians who did not like this independent development). Nonetheless, Phoenicians and others travelled the western sea-lanes, however rarely, and have left their cultural marks in other respects - but before the development of the frame-rotation method.

Very soon after the re-introduction of frame-first building in the north in the fifteenth century, which we have generally supposed was entirely based on importing the system from Portugal, or using designers directly from Mediterranean areas, builders were called on to create large vessels in this system, and furthermore to support heavy artillery. The puzzle is that it now seems that a new departure took place, abandoning rotation of the side frame (if indeed it was ever used by northern builders), though one element in a new guise (sliding of the moulds, the "hauling down") reappears in the treatises (or survives, since it is already implicit in the Mary Rose). The floor seems to have continued to be built as it was in Mediterranean methods, with a controlled narrowing and rising (though large shell vessels would have used some system to control shape in that critical area too); except that timbering in the Mary Rose has nothing of the Mediterranean about it. Multiple tangent arcs were used, capable of handling any desired hull shape; and all this was in place, categorically, before 1509 (Mary Rose), and probably over a wider area of the Atlantic coasts of northern Europe. (Red Bay indicates well established systems before 1565; and Mary Rose the re-use of side moulds for the sternframe soon after its introduction). The method uses the same idea of partison as both Mediterranean systems, but there is no direct link, or commonality of methods to achieve it. Neither is there any evidence for rotation of the side in any English document. Whatever the origin of the new method in England, we do know that Henry VIII chose to employ Venetians (possibly only for galleys), and that Baker took some interest in Mediterranean methods, and it is not least from his records that suspicions arise about the secondary nature of the Venetian offsets. Alternatively, perhaps the use of multiple arcs arose in Venice or another city state precisely to handle multiple decks, which led to a recognition that the side could be divided at the breadth, even if the old rotation methods were retained below the breadth ?

However, in parallel with these sophisticated methods of tangent arcs⁴³, we have in Fournier (1643), and in other texts of the eighteenth century (Juan and Stalkartt), statements that something actually termed whole-moulding (first by Sutherland in 1711, as a pre-existing method) was a widely used method until "recently", and had been for several centuries. Yet there is no actual evidence in the English case (which has the most early relevant records) for anything of the sort before 1711, and by 1765 its use is actually confined to small boats employing quadrants (and again the method survives, if not with pure quadrants). It is this enigma that we seem to be no nearer solving.

To explain the northern texts, we almost have to find an early survival of whole-moulding that owes no traceable origin to the Mediterranean (or, indeed, a hanging conoid); and to explain some of the southern wrecks, a method of forming the frames by frame-first methods in the shell-building era. If northern whole-moulding was indeed adopted from the Mediterranean, we still need to explain how and why, when frame-first construction came north around 1460-1500, the version of moulding that came north was of the older Mediterranean form, when the Mediterranean itself had already developed the trébuchement refinement long before. Though Rieth notes that the full method with trébuchement could still be written of as a mystery at the end of the seventeenth century, Bellabarba states (1996, p284) that it existed in the Mediterranean by the early fifteenth century, though it was certainly not widespread in extant texts from before 1489. Yet it was presumably developed for significant ships, not boats, and it was precisely for those ships that it supposedly came north.

As a parting shot, let us introduce two stray pieces of evidence. Firstly, that John Dee (magus, mathematician, courtier), had in his library about 1583 a Naupegia Itali, cujusdam, cum figuris, papyro, 4^o, that is, a manuscript on Italian shipbuilding, not otherwise identified. We may wonder whether that was in fact the manuscript now known in the British Library, currently identified as by Giorgio Trombetta. That too is paper, 4^o, and the first 60 leaves of the present manuscript are mostly in Italian from one source, and the whole collection of 293 leaves was bound and listed around 1600, according to Anderson⁴⁴. It does seem quite likely.

Secondly, from around 1270, Roger Bacon's Communia Mathematica⁴⁵ has sections on practical and theoretical geometry, which includes, for practical geometry, an intriguing phrase: "Et pars quarta est in fabricacione canalium et conductuum aquarum, et pontium ingeniosorum, et navium, et instrumentorum natandi, et permanendi sub aquis". It has uses in the building of ships. What uses, we may wonder. At that period English shipbuilding was clinker-shell construction, usually deemed (erroneously in this writer's view) to have nothing to do with geometry. Is this, then, for creating moulds, for setting out keel and posts and achieving symmetry, for tonnage measures ? Euclid, a wide range of geometric methods, even the extraction of the cube root, were all available at that time, and much of it in daily use in construction. Why do we know so little about its early application to ships ?

While addressing mathematical sources, we might also correct a false impression given in earlier papers about the origin of the term naval architecture. While Dee and Harriot both used the root naupeg-, and Dee included architecture more generally in his scheme of mathematics in 1570, they do not seem to have gone further. However, it emerges that Thomas Digges in his military manual Stratioticos of 1579, promises a future "brief treatise of architecture nautical", which does not in fact seem to have been written. It is also the case that Robert Dudley, author of Dell'Arcano del Mare, habitually used the term naval architecture, certainly from not much later than his arrival in Italy about 1605; and he was of course a former pupil of Mathew Baker. It is thus no longer possible to regard Lavanha's Livro primeiro da architectura naval of about 1614 as even the first printed use of the term naval architecture. The term had been circulating for more than a generation before that amongst the English mathematical practitioners.
 
 
 
 

Figures

Fig.1 Fournier 1643. Book 1, Chapter III. Midship mould - ancienne méthode.

Fig.2 Sutherland 1711. Facing page 4, figs B and D. Longitudinal.

Fig.3 Sutherland 1711. Page 6, fig C. Sections.

Fig.4 Sutherland 1711. Facing page 58, fig A. Longitudinal.

Fig.5 Sutherland 1711. Facing page 58, fig B. Section.

Fig.6 Sutherland 1711. Facing page 82. Body plan.

Fig.7 Sutherland 1717. Facing page 4. Lines plans.

Fig.8 Bushnell 1664. Page 8. Midship mould. (From 4th ed.1678)

Fig.9 Bushnell 1664. Facing page 6. Longitudinal. (From 4th ed.1678)
 
 
 
 
 
 

Postscript, July 2003

It was suggested above that Baker was inactive at the time James I came to the throne. This was partly due to changes in patronage, but he is also on record as declining Dudley's 1607 invitation to work in Italy, on the grounds of age (then 77). He did offer to send "models" (modelli et strumenti), but it is not known whether that happened, apart from the old problem of knowing whether the first term meant mould, drawing, or model as now used. The source for that period is J.Temple Leader's Life of Sir Robert Dudley, Florence 1895.

More recently, further work while formally translating shipbuilding sections of Hydrographie has revealed that Fournier's other modern method⁴⁶ for the midship mould is interesting in its own right, and not all that it appears.

Some very similar observations can be made about the early midship moulds in Fragments of Ancient English Shipwrightry, in particular the six that use four arcs from floor to breadth (including that identified as the method used by the Venetians twenty years previously). Current work on these is in preparation for the intended Navy Records Society/ Pepys Library publication of the manuscript.

This paper first appeared on the Max Planck Institut website in 2002 when it was entitled "The Ancienne Méthod as a special case of whole-moulding ?".
 
 

Footnotes

1 G.Fournier, Hydrographie, Paris 1643, Book I, Chapter VIII, p23

2 In this context we might note that Bellabarba is partly at fault here, using the term whole-moulding for a general "Atlantic" method (S.Bellabarba, "The origins of the ancient methods of designing hulls", in Mariner's Mirror, Vol.82, 1996, pp 259-268, note 12 especially). "…whole-moulding… deriving the shape of all the frames from the mainframe, varying the curves at some points" also gives a false impression. He does then make a point that whole-moulding could have been identical to the partial "Mediterranean" method when that was first adopted in the North - without trébuchement, but does not distinguish between that and the treatisers' methods, never called whole-moulding by contemporary writers; recognise the absence of evidence for the term; or note that there were many methods developed on the Atlantic coasts, just as there had been a development in the Mediterranean method that renders it different from "whole-moulding" in most recorded examples. See also further comments below.

Chapelle's omission of a source for his whole-moulding of English warships up to the 1730's (Rieth, 2000, p12/n7) may reflect the same point: he actually meant the treatisers' method ?

3 R.A.Barker, "'Many may peruse us': ribbands, moulds and models in the dockyards", in Revista da Universidade de Coimbra, Vol.XXXIV, 1988, pp539-559, esp pp557-9, notes the possible interest of Fournier, and the Serçe Liman wreck, for whole-moulding, for example, and the distinct possibility that continuity of geometrical method might eventually be traced back to antiquity.

4 É.Rieth, "La méthode moderne de conception des carènes du whole-moulding", in Neptunia No.220, Paris 2000, pp10-21.

5 T.W.E.Roche, Philippa…., Chichester 1971, pp92-3; Chronique d'Antonio Morosini, Vol.III, Paris 1901, p242.

6 V.M.Shillington & A.B.Wallis Chapman, The commercial relations of England and Portugal, New York 1907, esp p19.

7 Almost a forgotten chapter: research is in hand.

8 This rests on the supply of carvel nails for the construction of the Regent; the Sovereign of 1488 (believed to be the "Woolwich ship") was definitely built clench, and rebuilt carvel in 1509.

9 M.Oppenheim, History of the administration of the Royal Navy, 1509-1660, London 1896, p59. Abell (cited by Rieth) gives no source for a remark that Edward Howard brought shipwrights from abroad, chiefly Italy, but he only received his instructions as Admiral in 1512, and was killed just one year later.

10 There is a facsimile edition, Rothersfield 1989. We should perhaps note a comment by the late Frank Howard (Sailing ships of war, 1400-1860, 1979, p256) to the effect that later editions of Sutherland contain information (specifically for fitting out) that was increasingly out of date, some of it going back to around 1650.

11 D.Steel, 1822, Plate XXIX, "Longboat for an 80-gun ship showing the nature of construction by whole-moulding". (First edition 1805).

12 D.A.Taylor, A survey of traditional systems of boat design used in the vicinity of Trinity Bay…., PhD thesis, Memorial University of Newfoundland, 1989, pp100-2 and notes. Taylor uses the term whole-moulding rather loosely in his historical discussion (even using it to include Portuguese and Italian methods), following other authors.

13 Lavery discusses similar developments in Deane's work (only one of several areas where his Doctrine does not really reveal as much about his methods as Pepys supposed): B.Lavery, Deane's Doctrine of Naval Architecture, 1670, London 1981, esp.pp25-6. While ostensibly following the earlier treatisers' methods using constant arcs in his text, in fact he varies the radii of those arcs along the hull. This causes a step-change in the effort of making moulds, and is certainly no longer whole-moulding.

14 Rieth 2000, pp19-20, note 43

15 Rieth 2000, p19.

16 Ed. W.Salisbury and R.C.Anderson, SNR Occ.Pub. No.6, London 1958, p38.

17 S.Bellabarba, "The ancient method of designing hulls", in Mariner's Mirror, Vol.79, 1993, pp274-292, especially p288. (This is the first part of the article of note 2 above).

18 It is true that the side could be rotated outwards by sliding the futtock timber over the floor, using their common centre and arc, but if that were the intention there would be no need for separate measures for the sliding and for the outwards movement at the top of the frame.

19 G.Juan, Examen maritime théorique et pratique…, French translation, Nantes 1783.

20 1643, Book XVIII, Chapter XVII, pp782-3

21 We might also note that the calculation is carried to for example 2-198/300 feet, as well as its use of sines: while it is English shipbuilding that is noted for its use of sometimes advanced arithmetic methods up to this period, shipbuilding design is clearly not an activity for the numerically illiterate. The same is true of fifteenth century Italian methods, which need to calculate proportional dimensions, and indeed manuscripts then compiled for merchants and seamen concern themselves with the calculation of the cube root.

22 1643, Book I, Chapter IX, p24

23 Recalling that John Wells, Baker's protégé at Deptford (though not himself a shipbuilder) was actually involved in helping to create the first set of log tables in 1617, after Napier's work of 1614. Pages to prove that exist in the Fragments of Ancient English Shipwrightry, with the comments that logarithmic calculation was much easier than traditional methods for some of Baker's calculations. (Bushnell's printed tables represent an alternative approach).

24 M.Rule & J.Monaghan, A Gallo-Roman trading vessel from Guernsey (3rd C), Guernsey Museum Monograph 5, 1993.

25 É.Rieth et al, L'épave de Port Berteau II (Charente-Maritime), Documents d'archéologie française 86, Paris 2001.

26 H.Poilroux, "La nacelle des étangs du Languedoc", in Le petit perroquet, No.16, nd - 1975?, pp15-26. The side angle of the nacelle is said to be constant at about 120 degrees (p16), "determined by those which occur naturally between the trunk and branches of pines used for the ribs". Perhaps not very constant, as he proceeds to relate that the developed form, the bette, has angles of about 110-115 degrees.

27 eg W.A.Baker, The Mayflower and other colonial vessels, London 1983, p17.

28 Distinct from methods of hoop-gauging, reported from documents of about 1500 onwards by Leonor Freire Costa in Naus e galeões na Ribeira de Lisboa…., Patrimonia, Cascais 1997, pp59ff.

29 R.A.Barker, "Why tumblehome ?", in Mariner's Mirror, Vol.84, 1998, pp95-7.

30 Perhaps we could cite the remarkable bronze ex-voto from Beth-Maré, dated to around 121AD, Plate XI in H.Seyrig, "Antiquités Syriennes", in Syria, Vol.XXVIII, Paris 1951, pp101-113+plates.

31 In that sense, the midship section alone cannot necessarily distinguish between the two processes for adjusting it along the ship's length. In practice, the evidence of for example the Portuguese manuscript drawings where espalhamento was to be used, is that the side was most often a single arc, carried to the level of the floor in design, and faired in with a very short radius arc (Oliveira, conspicuously, did not even draw in the fairing arc, leaving an apparent hard chine). In Italian systems the side is now commonly said to be close to a parabola - perhaps originally a compound arc, as elsewhere - but the same feature occurs - a relatively sharp transition in the midship frame at the bilge. What evidence we have suggests that the northern methods used a much more rounded form, with more distinct arcs. The Mary Rose is one example, the four galleasses of 1546, built by James Baker for Henry VIII and recorded by Mathew, are another.

32 Rieth, 2000, op.cit.,p18.

33 Op.cit., 1996, Figs.4-6.

34 Bellabarba says (op.cit., 1996, p264) that he has not identified the pattern of risings and narrowings. Based (perilously, perhaps) on an enlargement of the published drawing, Fig.5, it seems probable that both narrowing and rising follow a meia-lua or equivalent at least from the central station 16 to station 10. Stations 12 to 10 have a constant ratio of narrowing and rising, with apparent rogue data for the risings at stations 14 and 13. The rising certainly cannot go much further on that pattern, but the narrowing is a remarkably good fit as far as station 4. Of eleven intermediate values, one is not given, but there are just two rogues at stations 13 and 6. It is not possible to distinguish between most of the known geometric systems at this level, as they all approximate to square laws.

35 Bellabarba suggests (1996, p264) that most of the floor timbers may have been cut with moulds ("prefabricated") in this and in the atypical Nemi ship, and that does indeed seem very likely. In the Marsala Punic ship, with its rising floor and hollowing curve to the keel, that sits very uneasily with shell-building; suggesting some very "active" moulds, in fact.

36 L.Haselberger, "The construction plans for the Temple of Apollo at Didyma" in Scientific American, Dec.1985, pp114-122.

37 L.G.Carr Laughton, "The Roccafortis of Venice, 1268", in Mariner's Mirror, Vol.42, 1956, pp267-278. (Subsequent work by Dotson, and Pryor, adds nothing for our purposes).

38 Sotheby's Sale Catalogue, Western MSS, London, 5 December 2000, pp60-72, which is a text by Andreas Mayor, originally for a sale in 1966.

39 K.Damianidis, ?? T????????? ???? ???????? ????????? ?????, Athens 1986, with extensive illustrations; or a summary version in English in "The diachronic 'Road of dialogue' of Mediterranean shipbuilding", in Cultural and commercial exchanges between the Orient and the Greek world, Athens 1991, pp97-108. The first item is the source of Rieth's figures 10, 11, inadvertently omitted from his note 23.

40 It is perhaps worth noting that Damianidis states on various occasions (eg op.cit., 1991, p102 or TIP, XIII, 1998, p219) that the term covers all forms of working with one mould, including those with and without trébuchement. Rieth, page 16 appears to imply that the term covers only the simplest form, equivalent to English whole-moulding, but that is actually a minority example of the term in Damianidis' examples. Otherwise it does not affect Rieth's argument.

41 G.E.Manwaring, "A ship of 1419", in Mariner's Mirror, Vol.8, 1922, p376 (and L.G.Carr Laughton, "The great ship of 1419", in Vol.9, 1923, pp83-7). Brad Loewen has written on the occurrence of terms (hameron = hammerhead, as in Baker's Fragments) that suggest some moulding of this large clinker hull, in "Bayonne 1419. Lapstraking and moulded frames in the same hull ?", in Mariner's Mirror, Vol.83, pp328-331. The link to hameron=amura, tack, had been noted by R.C.Anderson in "The Mary Gonson", in Mariner's Mirror, Vol.46, 1960, pp199-204. The Mary Gonson, despite its early date (variously ca 1512-20) is little help here, as the text records only dimensions, not shape, which is subject to some interpretation. What it does reveal is tumblehome, however, with a significantly greater breadth between its two decks than at the actual beams - a feature that also occurs in Portuguese methods, for example.

42 Touched on in R.A.Barker, "English shipbuilding….", in É.Rieth, ed, Concevoir et Construire les Navires, Technologies, Idéologies, Pratiques, Vol.XIII, 1998, pp109-126, esp. p119; and in a forthcoming paper.

43 Noting however that "whole-moulding" is also a system of tangent arcs, but perhaps using only one arc, reversed for the hollowing curve.

44 J.O.Halliwell, ed, The private diary of Dr John Dee and the catalogue of his library of manuscripts, Camden Society 1842, p72. R.C.Anderson, "Italian naval architecture about 1445", in Mariner's Mirror, Vol.11, 1925, pp135-163. The manuscript is British Library (not British Museum, as recently printed) Cotton MSS, Titus A XXVI, (not, note, 26 as given by Anderson), item 3, ff27b-60.

45 British Library Sloane MS 2156 and Bodleian Library MS Digby 76, edited by R.Steele, Communia Mathematica Fratris Rogeri, Opera hactenus inedita Rogeri Baconi, Fasc XVI, Oxford 1940, p43.

46 Op.cit., 1643, Book 1, Chapter IX: "fait à la moderne".