At right angles to U V, and from the figures, draw lines, which intersect with those of similar numbers drawn at right angles to YZ.

Through these points, trace a line.

Then will U XYZ be the half-pattern for the shape of the opening to be cut into the main roof.

For the pattern for the ventilating shafts or louvers, should they be required in the dormer, proceed as shown in Fig. 334. In this figure, A B C is a reproduction of the inside opening shown in Fig. 333.

Let 1, 2, 3, 4, 5 in Fig. 334 represent the sections of the louvers which will be placed in this opening. As the methods of obtaining the patterns for all louvers are alike, the pattern for louver No. 4 will illustrate the principles employed. Number the various bends of louver No. 4 as shown by points 6, 7, 8, and 9. At right angles to A B, and from these points, draw lines intersecting the curve A C as 61, 71, 41, 81, and 91. On B A extended as E D, place the stretchout of louver No. 4 as shown by the figures on ED. Since the miter-line AC is a curve, it will be necessary to introduce intermediate points between 7 and 8 of the profile, in order to obtain this curve in the pattern. In this instance the point marked 4 has been added.

Fig. 334.

Now, at right angles to DE, and through the figures, draw lines, which intersect with those of similar numbers, drawn parallel to AB from intersections 61 to 91 on the curve AC. A line traced through the points thus obtained, as FKJH, will be the half-pattern for louver No. 4. The pattern for the face of the dormer is pricked onto the metal direct from the front view in Fig. 333, in which A 8 B C is the half-pattern. In laying out the patterns for bay window work, it often happens that each side of the window has an unequal projection, as is shown in Fig. 335, in which DEF shows an elevation of an octagonal base of a bay window having unequal projections. All that part of the bay above the line AB is obtained by the method shown in Fig. 290, while the finish of the bay shown by ABC in Fig. 335 will be treated here. In some cases the lower ball C is a half-spun ball. A1 B1 F1 is a true section through A B. It will be noticed that the lines Ca, Cc, and Cd, drawn respectively at right angles to ab, bc, and cd, are each of different lengths, thereby making it necessary to obtain a true profile on each of these lines, before the patterns can be obtained. This is clearly explained in connection with Fig. 336, in which only a half-elevation and plan are required as both sides are symmetrical. First draw the center line AB, on which draw the half-elevation of the base of the bay, as shown by CDE. At right angles to AB draw the wall line in plan, as FK; and in its proper position in relation to the line CD in elevation, draw the desired half-plan, as shown by GHIJ. From the corners H and I draw the miter-line HF and IF, as shown. As DE represents the given profile through FG in plan, then divide the profile DE into an equal number of spaces as shown by the figures 1 to 13.

Fig. 335.

Fig. 336.

From these points drop vertical lines intersecting the miter-line FH in plan, as shown. From these intersections, parallel to HI, draw lines intersecting the miter-line IF, from which points, parallel to IJ, draw lines intersecting the center line FB. Through the various points of intersection in DE, draw horizontal lines indefinitely right and left as shown.

If for any reason it is desired to show the elevation of the miter-line FI in plan (it not being necessary in the development of the pattern), then erect vertical lines from the various intersections on FI, intersecting similar lines in elevation. To avoid a confusion in the drawing, these lines have not been shown. Trace a line through points thus obtained, as shown by D1 13, which is the desired miter-line in elevation.

The next step is to obtain the true profile at right angles to HI and IJ in plan. To obtain the true profile through No. 3 in plan, take a tracing of J F, with the various intersections thereon, and place it on a line drawn parallel to CD in elevation, as J1 F1, with the intersections 1 to 13, as shown. From these intersections, at right angles to J1 F1, erect lines intersecting similar lines drawn through the profile DE in elevation. Trace a line through the points thus obtained, as shown by 1' to 13', which represents the true profile for part 3 in plan. At right angles to IH in plan, draw any line, as ML, and extend the various lines drawn parallel to IH until they intersect LM at points 1 to 13, as shown.

Take a tracing of LM, with the various points of intersection, and place it on any horizontal line, as L1 M1, as shown by the figures 1 to 13, from which, at right angles to L1 M1, erect vertical lines intersecting similarly numbered horizontal lines drawn through the profile DE. Trace a line through the points thus obtained. Then will 1" - 13" be the true profile through No. 2 in plan at right angles to HI.

For the pattern for No. 1 in plan, extend the line FK, as NO, upon which place the stretchout of the profile DE as shown by the figures 1 to 13 on NO. At right angles to NO, and from the figures, draw lines, which intersect with lines (partly shown) drawn parallel to FG from similar intersections on the miter-line FH. Trace a line through the points thus obtained; then will 1 P 13 be the pattern for part 1 in plan.

At right angles to H I, draw any line, as T U, upon which place the stretchout of profile No. 2, being careful to measure each space separately, as they are all unequal, as shown by the small figures 1" to 13" on TU. Through these figures, at right angles to TU, draw lines as shown, which intersect by lines (not shown in the drawing) drawn at right angles to I H from similar points on the miter-lines HF and FI.

Trace a line through the points thus obtained. Then will V W X be the pattern for part 2 in plan.

For the half-pattern for part 3 in plan, extend the center line A B in plan as B R, upon which place the stretchout of the true profile for 3, being careful to measure each space separately, as shown by the figures 1' to 13' on BR. At right angle to B R draw lines through the figures, which intersect by lines drawn at right angles to J I from similar points of intersection on the miter-line F 1. A line traced through points thus obtained, as 1' S 13', will be the half-pattern for part 3.