To any one wishing to pursue pattern cutting as a profession it is essential not only that he know how to solve a large number of intricate problems, but that he understand thoroughly the principles which underlie such operations. It is, therefore, appropriate, before introducing pattern problems, that some attention should be given to the explanation of such principles in order that the reasons for the steps taken in the demonstrations following may be readily understood. Underlying the entire range of problems peculiar to sheet metal work are certain fundamental principles, which, when thoroughly understood, make plain and simple that which otherwise would appear arbitrary, if not actually mysterious. So true is this that nothing is risked in asserting that any (me who thoroughly comprehends all the steps in connection with cutting a simple square miter is able to cut any miter whatsoever. Since almost any one ean cut a square miter, the question at once arises, in view of this statement, why is it that he cannot cut a raking miter, or a pinnacle miter, or any other equally difficult form? The answer is, because he does not understand how he cuts the square miter. He may perform the operation just as he has been taught, and produce results entirely satisfactory from a mechanicalstandpoint, without being intelligent as to all that he has done. He does not comprehend the why and wherefore of the steps taken. Hence it is that when he undertakes some other miter he finds himself deficient.

There is a wide difference between the skill that produces a pattern by rote - by a mere effort of the memory - and that which reasons out the successive steps. One is worth but very little, while the other renders its possessor independent. It is with a desire to put the student in possession of this latter kind of skill, to render him intelligent as to every operation to be performed, that the present chapter is written.

The forms with which the pattern cutter has to deal may be divided, for convenience of description, into three general classes:

I. The first of these embraces moldings, pipes and regular continuous forms, and may be called forms of parallel lines, or as a shorter and more convenient name to use, parallel forms.

II. The second, which will be called regular tapering forms, comprehends all shapes derived from cones or pyramids, or from solids having any of the regular geometric figures as a base and which terminate in an apex.

III. The third class will be called irregular forms, and will include everything not classified under either of the two previous heads. Many of these might be properly called transition pieces - that is, pieces which have figures of various outlines placed at various angles as their bases, and have figures with differing outlines variously placed, as their upper terminations, thus forming transitions, or connecting pieces between the form which lies next them at one end and the adjacent form on the other end.

While pieces of metal of any shape necessary to form the covering of a solid of any shape may properly be called patterns, the shapes of pieces necessary to form the joints between moldings meeting at an angle are known distinctively as miters. This name applies equally well in sheet metal work if the two arms of the moldiag are not of the same profile, or to a single arm coming against any plain or irregular surface. These forms comprise the first class referred to above and, so far as principle is concerned, come under the same general rules, which will be subsequently given.

Conical forms, with very little taper, coming against other forms are also said to miter with them. In fact, the word miter has come into such general use that it is often applied to any joint between pieces of metal; but the term can scarcely be considered as correct when the forms have very much taper. The principle involved in the development of such patterns, however, is the same as that applied to the development of the surfaces of all other regular tapering forms, referred to above as the second class, whose characteristics will be considered in their proper chapter.

The method employed for developing the patterns for forms of the third class has been termed triangula-tion, and is adopted on account of its simplicity, as it does away with the reduction or subdivision of an irregular form into a number of smaller regular forms, each one of which would have to be treated separately and perhaps by a different method. In fact, there are some shapes which have arisen from force of circumstances which it would be impossible to separate into regular parts, and even if they could be so separated such a course would result in tedious and complicated operations.

After principles have been thoroughly explained the problems in this work will follow in three sections or departments of the final chapter, arranged according to the above classification.

Fig. 233.   Profile of a Molding.

Fig. 233. - Profile of a Molding.

Fig. 234.   A Stay.

Fig. 234. - A Stay.

Fig. 235.   A Reverse Stay.

Fig. 235. - A Reverse Stay.

Two conditions exist in regard to the work of developing patterns of all forms, no matter to which of the three classes above defined they may belong:

First - In very many cases a simple elevation or plan of the intersecting parts, together with their profiles, is all that is necessary to begin the work of developing the pattern - that is, the plan or elevation, as the case may be, shows the line (either straight or curved) which represents the surface against which another part is to be fitted; in other words, the much sought for "miter line."

Second - In numerous other instances, however, no view can be drawn either in elevation, oblique or otherwise, or in plan, in which the miter or junction of the parts will appear as a simple straight or curved line against which the points can be dropped. In such cases it becomes necessary to do some preliminary work in order to prepare the way to the actual work of laying out the pattern. A view of the joint must be developed by means of intersections of lines which will show it as it appears in connection with the elevation or plan to be used in developing the pattern.

This is one of the instances in which the pattern cutter is required to be something of an architectural draftsman, and to this end a chapter on Linear Drawing (Chap. III) has been introduced, in which attention is given to this phase of the work, and to which the student is referred.

The arrangement of the problems in each of the sections of the succeeding chapter will be made with reference to these two conditions, the simpler ones being placed before those in which preliminary drawing is required.