Under this heading come the practical shop problems. The problems which will follow should be drawn to any desired scale by the student, developed, and bent from stiff cardboard to prove the accuracy of the pattern. If the student cannot use the small brake in the shop and test his patterns cut from metal, he can use the dull blade of a table knife, over which the bends can be made, when using cardboard patterns. This at once proves interesting and instructive. Should there be any problem which is not clear, he should write at once for further information; or, should any problem arise on which he desires information, the School will inform him which problem in his textbooks contains similar principles, or will prepare such a problem for him.

The first problem will be to obtain the development of a square return miter, such as would occur when a moulding had to return around the corner of a building, as shown in Fig. 276. In Fig. 277, are shown two methods of obtaining the pattern. The first method which will be described is the "long" method, in which are set forth all the principles applicable to obtaining patterns for mouldings, no matter what angle the plan may have. The second method is the "short" rule generally employed in the shop, which, however, can be used only when the angle H G F in plan is 90°, or a right angle.

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Fig. 276.

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Fig. 277.

To obtain the pattern by the first method, proceed as follows: First, draw the elevation of the mould as shown by 1, B, A, 11, drawing the coves by the rule previously given. Divide the curves into equal spaces; and number these, including the corners of the fillets as shown by the small figures 1 to 11. In its proper position below the elevation, draw the soffit plan as shown by C D E F G H. Bisect the angle H G F by the line G D, which is drawn at an angle of 45°. From the various intersections in the elevation, drop lines intersecting the miter-line as shown. At right angles to H G, draw the stretchout line 1' 11', upon which place the stretchout of the mould 1 11 in elevation, as shown by similar figures on the line 1' 11'. At right angles to 1' 11', and from the numbered points thereon, draw lines, which intersect by lines drawn at right angles to H G from similarly numbered intersections on the miter-line G D. Trace a line through the intersections thus obtained, as shown by J G. Then will 1' G J 11' be the desired pattern. This gives the pattern by using the miter-line in plan.

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Fig. 278.

In developing the pattern by the short method, on the other hand, the plan is not required. At right angles to 1 B in elevation, draw the stretchout line 1" 11", upon which place the stretchout of the profile 1 11 in elevation, as shown by similar figures on 1" 11", at right angles to which draw lines through the numbered points as shown, which intersect by lines drawn at right angles to 1 B from similarly numbered intersections in the profile in elevation. Trace a line through points thus obtained, as shown by G K. Then will G 1" 11" K be similar to J G 1' 11' obtained from the plan.

In Fig. 278 is shown a horizontal moulding butting against a plane surface oblique in elevation. A miter cut of this kind would be required when the return moulding of a dormer window would butt against a mansard or other pitched roof. In this case we assume A to be the return butting against the pitched roof B. The method of obtaining a pattern of this kind is shown in Fig. 279. Let A B C D represent the elevation of the return, A D representing the pitch of the roof. In its proper position as shown, draw the section 1 11, which divide into equal spaces as shown, and from which, parallel to A B, draw line intersecting the slant line A D from1 to 11, as shown. At right angles to A B erect the stretchout line 1' 11', upon which place the stretchout of the section as shown by similar figures on 1' 11'.

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Fig. 279.

At right angles to 1' 11', and through the numbered points thereon, draw lines, which intersect by lines drawn at right angles to A B from similarly numbered intersections on the slant line A D. Through the various intersections thus obtained, draw E F. Then will E F 11' Y be the desired pattern.

It is sometimes the case that the roof against which the moulding butts, has a curved surface either concave or convex, as shown by B C in Fig. 280, which surface is convex. Complete the elevation of the moulding, as D E; and in its proper position draw the section 1 9, which divide into equal spaces as shown by the small figures, from which draw horizontal lines until they intersect the curved line B C, which is struck from the center point A. At right angles to the line of the moulding erect the line 1' 9', upon which place the stretchout of the section, as shown by the figures on the stretchout line. Through the numbered points, at right angles to 1' 9', draw lines, which intersect by lines drawn at right angles to 2 D from similarly numbered intersections on the curve B C, thus resulting in the intersections 1" to 9" in the pattern, as shown. The arcs 2" 3" and 7" 8" are simply reproductions of the arcs 2 3 and 7 9 on B C. These arcs can be traced by any convenient method; or, if the radius A C is not too long to make it inconvenient to use, the arcs in the pattern may be obtained as follows: Using A C as radius, and 7" and 8" as centers, describe arcs intersecting each other at A'; in similar manner, using 2" and 3" as centers, and with the same radius, describe arcs intersecting each other at A2. With the same radius, and with A1 and A2 as centers, draw the arcs 8" 7" and 3" 2" respectively. Trace a line through the other various intersections as shown. Then will 1' 1" 9" 9' be the desired pattern. In Fig. 281 is shown an elevation of an oblong or rectangular panel for which a miter-cut is desired on the line a b - known as a "panel" or "face" miter The rule to apply in obtaining this pattern is shown in Fig. 282.