and bevelling cdges respectively; where h, h; is equal to ah and laik;
t k.
Olin fig. IO4 let AB, A'B' be the traces of the plane of the moulding
edge of the frame in the sheer and half-breadth plans respectively.
b When, as in the figure, neither trace is perpendicular to
D°';§ the base line, the frame is said to be a double canted
f°::mee frame, or a double cant. Let IL, 2L, 3L be the projections
of level lines in the three plans, B, Q, R in the
sheer plan being their point of intersection with AB. The

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must be laid off so that the normal distance between it and the moulding edge can be used for marking the bevelling in the same way as the normal distance between consecutive frames' of the square body is used. To obtain the traces of the plane of the bevelling edge, in fig. Io4a let AB, AB' be the traces of the moulding edge plane; nm drawn perpendicular to AB and mm' perpendicular to the axis are the traces of a plane perpendicular to the plane of the moulding edge and to the vertical or sheer plane. If mM be drawn perpendicular to nm and equal to mm', nM is the intersection of the planes BAB' and nmm' rabatted on to the sheer plane, and mH perpendicular to nM is the rabatted position of a line perpendicular to the plane of the moulding edge. Make HK equal to the chosen distance of the bevelling edge plane from the moulding edge plane; draw Kk parallel to Mn cutting nm in k; through k draw DkE parallel to AB and through D, where DE meets the base ine, draw DE' parallel to AB'; then DE, DE' are the traces of the plane of the bevelling edge arranged at the required perpendicular distance from the plane of the moulding edge. In laying off the bevelling edge it is first projected on to the plane of the moulding edge, and the latter then rabatted into the body plane. To effect this operation the horizontal trace Am'i, of a plane perpendicular to the double cant plane and intersecting it in the vertical V I. BASE L.//vs - trace AB must be drawn, which is done by the construction shown in fig. Io4a, where nm is, as before, perpendicular to AB through any point 71 in it other than A, and n'm'1, drawn through n', the horizontal projection of n, is perpendicular to AB'. The projections of the traces with the " B E R V r V 3|-Q U g I, iw lj l I Pl | '|tI 'L I I P I D2 z AJ AN I

' ji

j l' I ll li 2' -=' I: . B E' I I ill gg .' . | |ll 'B E I I / Il |l|:| // ll ll, I ( / 1 ~ several level planes of the plane of the bevelling edge, such / m' BM E' as U'°w' and the rejections of the bevelling edge ltwv in the sheer plan and f?t"w'v' in the half-breadth are obtained in exactly the same way as in the case of the moulding edge. The pro ections such as Q'~w', , of the traces with

- | k r the several level planes of the plane whose traces are AB

|, | 40 '5L and Am', , in fig. Io4a are also drawn parallel to Am'|, A67 W through the horizontal projections of P, Q, R, &c. The n | ' " / ZL vertical ro'ection w of the point w' in which Qu/1 //» P# 1- I g . || meets Uw produced, is found and AQUQ set up on the A -, - " r ggi) ' ' ' 'f middle line of the body equal to the #perpendicular distance |m A' q U' ' AUDDLE HNE of wi from AC. A level line 211 in the body plan is | W; drawn at a distance from the base line equal to the perpen| dicular distance of w from AC and a point w2 found in it | F IG. IO4. such that the radius Ugwz is equal to 'w'1'w' in the half breadth. wg is then the rabatted position of the projection | on the plane of the moulding edge of the point in the I bevellingdedge whose térojectioni are ru arid ug. lgojrits | l, t an v correspond ing to the rejections an t m: dnd i', v and v' are found in a siinilar manner and' a FIG xo A curve drawn through litgwgvg is the bevelling edge laid 4 ' ~ off in the body plan in the correct relation to the laid horizontal the figure horizontal horizontal projections of these points are found as indicated in where Q' on the middle line of the half breadth is the projection of Q. The line Q'q' parallel to A'B' is the projection of the line of intersection of the double cant plane with the level plane 2L, and q, obtained by the construction shown, is the vertical projection of the point where this line of intersection cuts the surface of the ship, q' being the horizontal projection of the same point. The projections of other points in the intersection of the double cant plane with the surface of the ship are found in a similar manner by the help of other level lines; and the projections s' and s of the ending where the line of half siding of the fiat keel cuts the double cant plane are found by the construction indicated. The projections of the moulding edge of the double cant frame spqr in the sheer plan and s'p'q'r' in the half-breadth are thus determined. The true form of the moulding edge is laid off in the body plan by a double process of rabatment of the double cant plane, first about the trace AB to bring it perpendicular to the sheer plan, and then about a normal to the sheer plan through A to bring it parallel to the body plan, in the following manner. Set off PQ, Qi, R2 on the middle line of the body so that their distances from Af are equal to AP, AQ, AR measured along the trace AB in the sheer plan. Draw AC in the sheer plan perpendicular to AB and measure the heights parallel to AB of the points p, q and r above AC. Draw level lines Il-'. 2L'. 3L' in the body plan at distances above the base line equal to these heights, and from the centres P¢, QQ, R1 describe circles cutting 1L', 2L', 3L' in pg, qi, rg, &c., so that the radius Qzqg is equal to Q'q', &c. The curve pzqm is the true form of the moulding edge of the double cant laid off in the body plan. The plane of the bevelling edge is parallel to that of the moulding edge and at a perpendicular distance from it suitable for use as the base of a bevelling triangle similar to that which is described for the ordinary frames. The width of the bevelling board is made equal to this perpendicular distance, corresponding to the frame space in the case of the ordinary frames, and the bevel ing edge ol? position of the moulding edge for the bevellings to be taken. Additional points in the rabatted shape of the double canted frame may be obtained by the use of diagonals when B I l .... - . - .... ' Q . rg 1 W, P M . L ~ lc, I | I I I I ¢ I | I i i I I

Lg l I I A "r 1 r, nazi

- } I I

o 2 I 9 I; uc i ' j - I I rx, 1 .- L V j I 9 E, Q = T' ' pi" ci I FIG. -105. desired. In fig. 105 AB, A'B' are the traces of the double canted plane; cd, cida are the projections of a diagonal line in the body and

f