To clear up these doubts in the mind of the stu-dent an illustration of the short method of cutting a square miter is here introduced, and afterward the long method, or the plan which is in strict accordance with the rule above given, will be presented, combined with the short method, thus showing the relationship and correspondence between the two.

Fig. 240 shows the usual method of developing a square return miter, being that in which no plan line is employed. The profile A B is divided into any convenient number of spaces, as indicated by the small figures in the engraving. The stretch-out E F is laid off at right angles to the lines of the moldings, and, through the points in it, measuring lines are drawn parallel to the lines of moldings. From the points established in the profile lines are dropped cutting corresponding measuring lines. Then the pattern or miter cut G H is obtained by tracing a line through these points of intersection. In this operation it will be noticed that the stipulations of the first part of the rule have been fully complied with - that is, the stretch-out line has been drawn at right angles to the lines of the molding, and measuring lines have been drawn parallel to those lines, but it would seem that the second and third parts of the rule as given are not applicable. Apparently no miter line has been employed, but the points have been dropped directly from the profile into the measuring lines.

In order to make this clear Fig. 241 is here introduced in which the proper relation of parts is shown and in which the pattern is developed according to rule, and in which is also shown the short method and how it is derived from the long method.

As the angle of a return miter can only be shown by a plan, the plan becomes the first necessity according to the rule and is shown in the cut by H F K M G L, F G showing the line upon which the two anus of the molding meet - that is, the miter line. The profile A B appears duly in line with one arm of the plan H F G L. This arm, then, is the part of which the pattern is about to be developed; accordingly the stretch-out line is then drawn at right angles to this arm, as shown at C' D', and the measuring lines drawn parallel to the arm.

The second part of the rule is now carried out; that is, lines are dropped from the points in the profile A B to the miter line F G and from thence at right angles to F H into the measuring lines, thus obtaining the pattern C'E',

In the upper part of this figure another stretch-out, C D, is introduced into which lines have been dropped directly from the points in the profile, thus producing the pattern at C E, making this part of the figure a reduplication of the method employed in the previous figure.

By comparison it will be seen that the two patterns C E and C E' are identical. Since the two arms of the miter are identical and at right angles to each other, the miter line must bisect the angle H F K and be at an angle of 45 degrees to either of the two faces H F and F K. From this it appears at once that the projection of any and all points upon F G from the plan line G L toward II is exactly the same as from the plan line G M toward K and that the relationship between C E and the miter line, and C E' and the miter line, is, therefore, the same. Dropping points from a profile against a line inclined 45 degrees, as F G, and thence on to a stretch-out, gives the same result as dropping them on the stretch-out in the first place. Hence it is that the portion of the operation shown in the lower part of the engraving may be dispensed with. This relationship could never occur were the angle of the miter anything else than a right angle.

Another and perhaps simpler explanation of this is given in connection with Problem 3, in Section 1 of Chapter VI (Pattern Problems).

A very common mistake made by beginners in attempting to apply the general rule for cutting miters as given, is that of getting the miter line in a wrong position with reference to the profile. For example, instead of drawing a complete plan, as shown by L H F K M in Fig. 241, by which the miter line is located to a certainty, and in connection with which it is a simple matter to correctly place the profile, it is not uncommon to attempt the operation by drawing the miter line only, placing it either above, below or at one side of the profile. The mistake is made by having the line at the side of the profile when it should be either above or below it, and vice versa. Fig. 242 illustrates a case in point. The engraving was made from the drawing of a person who attempted to cut a square return miter by the rule, using a miter line only. By placing the miter line E F at the side instead of below the profile, a square face miter - such as would be used in the molding running around a panel or a picture frame - was produced in place of what was desired.

Fig. 242 - A Square Face Miter Produced Where a Square Return Miter was Intended.

In order to avoid such errors the reader is recommended to a careful perusal of the chapter on Linear Drawing (Chapter III (Linear Drawing)), where the relation existing between plans, elevations and sections or profiles is thorough' explained. It is better to draw a complete plan, as shown in Fig. 241, thus demonstrating to a cerPrinciples of Pattern Cutting. 79 tainty the correct relationship of the parts, than to save a little labor and run the risk of error.

As remarked in the earlier part of this chapter, some labor is often necessary before the requirements mentioned above in connection with the rule can be fulfilled. Sometimes a miter line must first be developed, and sometimes the profile of a molding must undergo a change of profile known as raking. It is believed that the principles underlying these operations are made sufficiently clear in connection with the problems in which they arc involved not to need especial explanation in this connection. Suffice it to say that, in many instances, half the work is done in the getting ready.