When bending the points on theline HK, it is necessary to have a stay or profile so that we may know at what angle the bend should be made. To obtain this stay, erect from the corner B in Fig. 325 a line intersecting the base-line J H at c, from which point, at right angles to J K, draw c d. Using c as center, and c d as radius, strike an arc intersecting J H at e. From e drop a vertical line meeting A G in plan at d'. Set off i B1 equal to i B, and draw a line from B to d' to B1, which is the true profile after which the pattern in Fig. 326 is to be bent. If the stay in Fig. 325 has been correctly developed, then d' or d' B must equal c a in FIg. 326 on both sides.

In Fig. 327 is shown a finished elevation of a hipped roof, on the four corners of which a hip ridge A A butts against the upper base B and cuts off on a vertical line at the bottom, as C and C. To obtain the true profile of this hip ridge, together with the top and lower cuts and the patterns for the lower heads, proceed as shown in Fig. 328, where the front elevation has been omitted, this not being necessary, as only the part plan and diagonal elevation are required. First draw the part plan as shown by A B C D E F A, placing the hip or diagonal line F C in a horizontal position; and make the distances between the lines F A and C B and between F E and C D equal, because the roof in this case has equal pitch all around. (The same principles, however, would be used if the roofs had unequal pitches.) Above the plan, draw the line G H. From the points F and C in plan, erect the lines F G and C I, extending C I to C1 so that I C1 will be the required height of the roof above G I at the point C in plan. Draw a line from G to C1, and from C1 draw a horizontal and vertical line indefinitely, as shown. Then will I G C1 be a true section on the line of the roof on F C in plan.

Fig. 325.

Fig. 326.

The next step is to obtain a true section of the angle of the roof at right angles to the hip line G C1 in elevation. This is done by drawing at right angles to F C in plan, any line, as a b, intersecting the lines F A and F E as shown. Extend a b until it cuts the base-line G I in elevation at c. From c, at right angles to G C1, draw a line, as c d, intersecting G C1 at d. Take the distance c d, and place it in plan on the line F C, measuring from i to d'. Draw a line from a to d' to b, which is the true angle desired. On this angle, construct the desired shape of the hip ridge as shown by J, each half of which divide into equal spaces, as shown by the figures 1 to 6 to 1. As the line G C1 represents the line of the roof, and as the point d' in plan in the true angle also represents that line, then take a tracing of the profile J with the various points of intersection on same, together with the true angle a d' b, and place it in the elevation as shown by J1 and a' d" b', being careful to place the point d" on the line G C1, making a' b' parallel to G C1. From the various points of intersection in the profile J, draw lines parallel to F C, intersecting B C and A F at points from 1 to 6, as shown. As both sides of the profile J are symmetrical, it is necessary only to draw lines through one-half.

Fig. 327.

In similar manner, in elevation, parallel to G C1, draw lines through the various intersections in J1, which intersect by lines drawn at right angles to F C in plan from similarly numbered points on A F and BC. Trace a line through the points thus obtained. Then will K L be the miter -line at the bottom, andM N the miter-line at the top.

Fig. 328.

For the pattern, draw any line, as O P, at right angles to G C1, upon which place the stretchout of J in plan or J1 in elevation, as shown by the figures 1 to 6 to 1 on O P; and through these numbered points, at right angles to O P, draw lines, which intersect by lines drawn at right angles to G C1 from similar intersections in the lower miter-line K L and upper miter-line N M. Trace a line through the points thus obtained. Then will R S T U be the desired pattern.

In practice it is necessary only to obtain one miter-cut - either the top or the bottom - and use the reverse for the opposite side. In other words, U T is that part falling out of R S, the same as R S is that part which cuts away from U T. The upper miter-cut butts against B in Fig. 327; while the lower cut requires a flat head, as shown at C. To obtain this flat head, extend the line I G in Fig. 328, as I W, upon which place twice the amount of spaces contained on the line A F in plan, as 6, 3 - 5, 4, 1, 2, as shown by similar figures on either side of 6 on the line V W. From these divisions erect vertical lines, which intersect by lines drawn parallel to V W from similarly numbered intersections in the miter-line KLG. A line traced through the points thus obtained, as shown by X Y Z, will be the pattern for the heads.

Where a hip ridge is required to miter with the apron of a deck moulding, as shown in Fig. 329, in which B represents the apron of the deck cornice, A and A the hip ridges inhering at a and a, a slightly different process from that described in the preceding problem is used. In this case the part elevation of the mansard roof must first be drawn as shown in Fig. 330. Let ABC K represent the part elevation of the mansard, the section of the deck moulding and apron being shown by D B E. Draw E X parallel to B C. E X then represents the line of the roof. In its proper position, at right angles to B C, draw a half-section of the hip mould, as shown by F G, which is an exact reproduction of B E of the deck mould. Through the corners of the hip mould at Y and G, draw lines parallel to B C, which intersect by lines drawn parallel to B A from V, W, and E in the deck cornice. Draw the miter-line H I, which completes the part elevation of the mansard.