In Fig. 414 is shown the method of obtaining the miter against the planceer of a deck cornice formed by the molding covering a hip, which occurs between the main roof and that part which forms the transition from a square at the base to an octagon shape at the top. The roof is of the character sometimes employed upon towers which arc square in a portion of their hight and octagon in another portion, the transition from square to octagon occurring in the roof. The hip molding in question covers what may be called a transition hip, being a diagonal line starting from one of the corners of the square part and ending at one of the corners of the octagon above. A carefully drawn plan, together with a section through one of the sides of the roof, giving the pitch, will be the first requisites to solving the problem, both of which are shown in the engraving. The first operation will be the construction of a section upon the line of the hip, which may be done as follows: Assume any point, as A, in the section of the roof from which to measure hight and projection. If a horizontal line from A and a vertical line from the top of the roof surface B be intersected in C, then B C will represent the hight and A C the projection of the part of the roof assumed. Set off the projection C A at right angles to the top line of the plan C E, as shown by C A1, and carry a line through A1 parallel to C1 E till it cuts the plan of hip E Q at D; then D E will form the base and B C the hight of the required section, which may be obtained for convenience by lines projected from D E at right angles, all as shown. The line B1 D2 then represents the real angle at which the hip mold meets the planceer or level line at the top.

The next operation will consist in obtaining a correct section of the hip mold from the data given and in placing it in correct position in the diagonal section. Take any point, G, in the plan at a convenient distance from the angle W D A1. Set off G1 at the same distance from the angle on the opposite side. From the points G and G1 carry lines at right angles to and cutting D2 C2 in the points H2 and O2, and from these points carry them parallel with the line D2 B1 indefinitely. At right angles to D2 B1 draw a line, as shown by Z H1, intersecting with the lines last drawn in the points H1 and O. From H1, along the line H1 H2, set off a distance equal to H G of the plan, and from O, in the line Z H1, set off a distance equal to O1 G1 of the plan, as shown by O G2 Connect the intersection of Z H1 and D2 B2 with the points G3 and G2, which will give the correct section through the angle of the roof. Having thus determined the angle of the hip molding finish, a representation of it is indicated in the drawing by adding the flanges and the roll. Since the miter required is the junction between the hip molding, the profile of which has just been drawn, and a horizontal planceer, the remaining step in the development of the pattern consists simply in dividing the profile into any convenient number of parts, and carrying points against the line of the planceer, as shown near B1, and thence carrying them across to the stretchout, as indicated. It is evident, however, upon inspection of the elevation, that the apron or fascia strips in connection with the planceer which miter with the flanges of the hip molding will form a different joint upon the side cur-responding to the transition piece of the roof than upon the side corresponding to the normal pitch of the roof, owing, to the difference in pitch of these two sides. To obtain the lines for this miter an additional section must be constructed, corresponding to a center line through the transition piece, as shown by W L in plan. Prolong C2 D2, as indicated, in the direction of W1, and lay off W1 L1, equal to W L of the plan. From L1 erect a perpendicular, as shown by L1 B2, equal to C B of the original section. Connect W and B2, against the face of which draw a section of the apron or fascia strip belonging to the planceer, as shown, and from the points in it carry lines parallel to B2 B1 until they intersect lines drawn from the flange of the hip molding lying against that side of the roof, all as indicated by U X. From these points carry lines, cutting corresponding lines in the stretchout. The lines of the fascia belonging to the other side are the same as if projected from the normal section at B, or as they appear in the elevation. Having obtained these points proceed as follows: At right angles to the lines of the molding in the diagonal section lay off the stretchout of the hip molding S T, and through the points draw the usual measuring lines, as shown. Place the T-square at right angles to the lines of the molding, or, what is the same, parallel to the stretchout line, and, bringing it successively against the points formed by the intersection of the lines drawn from the hip molding and the planceer line B1, cut the corresponding measuring lines, as shown. In like manner bring the T-square against the points U and X, above described, and Y and V, points corresponding with the opposite side of the hip molding, and cut corresponding lines. Then a line traced through these several points of intersection, as shown by U1 X1 Y1 V1, will be the pattern sought.

Fig. 414.   The Pattern for a Hip Molding Mitering Against the Planeeer of a Deck Cornice on a Mansard Roof Which is Square at the

Fig. 414. - The Pattern for a Hip Molding Mitering Against the Planeeer of a Deck Cornice on a Mansard Roof Which is Square at the

Eaves and Octagon at the Top.