By the late 1680s or 1690s this problem seems to have been overcome. For example, in the Cochois frigate draft, the diagonals forward are extended all the way to the stem (Figure 18). Unlike in *La Belle*'s design, the Toulon flute draft, and the *Profond* draft, the Cochois floor diagonal no longer ends at a design frame position forward. Duhamel du Monceau describes a clever method of adjusting the last increment of the equilateral triangle proportionately to the distance from the forwardmost design frame to the stem at the height of each diagonal (Duhamel 1758:244–245). Since the termination point of *La Belle*'s floor diagonal was used to establish frame position *XIIA* and the forward frame spacing, I do not think any such proportional adjustments were applied to *La Belle*'s forward offset sequences.

Three additional diagonals were reconstructed to delineate the probable runs of the curves of *La Belle*'s upperworks for the forward part of the hull. The two almost parallel topside diagonals in Figure 44b were reconstructed by first drawing the main sheer line from its height at amidships to the top of the stem. The resulting flat sheer is similar to that of the Cochois frigate in Figure 18. The recurve diagonal was set down from the sheer diagonal on the stem the same amount as at the midship frame. A supplementary breadth diagonal for use in design was reconstructed with a height at the center of 7 ft 6 inches versus the 13 ft 6 inches listed in the *devis*. Using these diagonals, several design scenarios were reconstructed for subdividing the forward diagonals and then drawing the forward design frame shapes. The reconstructed frame shapes from one of these scenarios are depicted in light gray in Figure 44b. These reconstructed frame shapes correspond well with the archaeological evidence; however, due to their speculative nature and the need for additional research, the methods by which they were generated will not be presented in detail in this essay. Nonetheless, several definitive observations can be made with regard to the design of the forward part of the hull.

The offset sequences were adjusted individually for each of the diagonals. I achieved this by altering the angles of the diagonals on an equilateral triangle constructed on the basis of the forward floor diagonal's offset sequence. Since the angles for the upper diagonals on the triangle were extreme, it is possible that separate convexity of arcs drawings or some other method was employed to generate the offset sequences for each diagonal individually.

Before amidships there is proportionally more curvature change in a shorter horizontal and vertical distance than abaft amidships. Therefore, the sides of the hull above the bilge have to be splayed out in order to have a relatively sharp entrance low in the hull and yet maintain deck space higher up. To achieve this result, I suspect that arcs with a standard radius of 7 ft 6 inches were used for the bottom sections of the curves above the upper bilge diagonal. NEXT

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