In the elevation B C E D, and plan FGHKLI, of Fig. 390 is presented a set of conditions which necessitate a change of profile in either the horizontal or raking molding, in order to accomplish a miter joint at I H in the plan. In other words, the conditions are such that with a given profile, as shown by A1, in the raking molding, the profile of the horizontal molding forming the return will require to be modified, as shown by the profile A3, in order to form a miter upon the line I H in the plan.

The reason for this is easily found. If a vertical line be erected from point 9 in profile A2 it will be seen that each line emanating from a point in the normal profile A1 becomes depressed after passing this vertical line, more or less, according as its distance away from this line increases, all in proportion to the amount of rake or incline of the face molding, as shown by the dotted lines. If, on the contrary, the profile A2 be considered as the normal profile, the profile A1 will have to be changed or "raked," in this case increased in hight, in proportion to the inclination. (These conditions are treated in the succeeding problem.) The vertical hight of the profile of the return may be measured in the side elevation and compared with that of the inclined molding by measuring across the latter at right angle's to the line B C.

In this problem it is assumed that the profile as well as the pitch, or rake, of the cornice B C are established and that the profile of the horizontal return is to be modified, or "raked," to suit it. To obtain this profile, first draw the normal profile in the raking cornice, as shown by A', placing it to correspond to the lines of the cornice, as shown. Draw another profile corresponding to it in all parts, directly above or below the foot of the raking cornice, in line with the face of the new profile to be constructed, placing this profile A so that its vertical lines shall correspond with the vertical lines of the horizontal cornice. Divide the profiles A and A' into the same number of parts, and through the points thus obtained draw lines, those from A1 being parallel to the lines of the raking corniee, and those from A intersecting them vertically. Through these points of intersection of like numbers trace a line, which gives the modified profile, as shown by A2. Then A2 is the profile of the horizontal return, indi-cated by G H L F in the plan. It is also the elevation of the miter line I H of the plan. Therefore at any convenient point at right angles to the lines of the raking cornice lay off the stretchout M N of the profile A1, through the points in which draw measuring lines in the usual manner. Place the T-square at right angles to the lines of the raking cornice, and. bringing it successively against the points in the profile A2, cut the corresponding measuring lines just described. Through the points of intersection trace a line, as shown by O P R. Then O P R will be the shape of the lower end of the raking cornice inhering against the return. For the pattern of the return proceed as follows: Construct a side elevation of the return, as shown by S V U T, making the profile V U the same as the profile A' of the elevation. Let the length of the return correspond to the return, as shown in the plan by F I. In the profile V U set off points corresponding to the points in the profile A3 as shown from B to D. At right angles to the elevation of the return lay off a stretchout of V U. or. what is the same, of the profile A5, as shown by W X, through the points in which draw measuring lines in the usual manner. Placing the T-square parallel to this stretchout line, and bringing it successively against the points in V U, cut the corresponding measuring lines. Then a line traced through these points of intersection, as usual, from Y to Z, will be the pattern of the horizontal return.

Fig. 390. - To Obeatin the Prefile of a Horizontal Feturn at the Foot of a Gable, Necessary to Miter at Right Angles in. Plan with an Inclined Molding of Normal Profile, and the Patterns of Both.