This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
The principles applied to cylinder developments as explained in the Tinsmithing and Sheet Metal Work courses, under the heading of "Parallel-Line Developments," are also applicable for obtaining the patterns for any moulding where all members run parallel; for it makes no difference what profile is employed, so long as the lines run parallel to one another, the parallel-line method is used. While this method is chiefly employed in cornice work, other problems will arise, in which the "Radial-Law" and "Triangulation" methods (explained in previous Papers) will be of service.
The term generally used in the shop for pattern cutting on cornice work is miiter cutting. To illustrate, suppose two pieces of mouldings are to be joined together at angle of 90o, as shown in Fig. 255. The first step necessary would be to bisect the given angle and obtain the miterline and cut each piece so that they would miter together. If a carpenter had to make a joint of this kind, he would place his moulding in the miter-box, and cut one piece right and one piece left at an angle pf 45o, and he would be careful to hold the moulding in its proper position before sawing; or else he may, instead of having a return miter as shown, have a face miter as in a picture frame, shown in Fig. 267. The sheet-metal cornicemaker cannot, after his moulding is formed, place it in the miterbox to cut the miter, but must lay it out - or, in other words, develop it - on a flat surface or sheet of metal. He must also be careful to place the profile in its proper position with the miterline; or else, instead of having a return miter as shown in Fig. 266, he will have a face miter as shown in Fig. 267. If he lays out his work correctly, he can then cut two pieces, form one right and the other left, when a miter will result between the two pieces of moulding and will look as shown in Fig. 266. If, however, a face miter is desired, as shown in Fig. 267, which is used when miters are desired for panels and other purposes, the method of laying them out will be explained as we proceed. The same principles required for developing Figs. 266 and 267 are used, whether the mouldings are mitered at angles of 90o or otherwise. The method of raking the mouldings - or, in other words, changing their profile to admit the mitering of some other moulding at various angles - will also be thoroughly explained as we proceed.