Now, what has been done in Fig. 237 illustrates what is called "miter cutting," which in other words consists in describing upon a flat surface the shape of a given form or envelope, so that when the envelope is cut out of the flat surface and formed up to the stay from which its stretchout was derived, the finished molding will fit against a given surface at a given angle previously specified.
The pattern shown in the lower part of Fig. 237, which has been obtained by means of a clay model, and measurements for which were obtained from the lines drawn on the surface of the clay model - may be obtained just as well from a drawing. The question then is, how can the same results be obtained by lines drawn upon a flat surface as were obtained by measurements on lines drawn along the surface of a molding?
In moving the stay along the clay molding, certain lines were made by means of the points affixed. If the reader will carefully examine Fig. 237 he will notice that the lines upon the molding made by this means corresponded in number and position with the points in the profile when it is laid flat on its side, in a position exactly opposite the end of the model, as shown.
Hence, if the profile be drawn upon paper and in line with it, the elevation terminated by the oblique line, which represents the surface against which it is required to miter, the same results can be accomplished, care only being necessary that the relative positions of the parts be correctly maintained.
This is illustrated in Fig. 238, which is to be compared with Fig. 237, and shows: First, that the profile A is drawn in correct position. Next, that from it the elevation F CDG of the molding is proof the Same.
Projected, as follows: Use the T-square in the general position shown by B in the engraving, bringing it against the several points in A in order to draw the lines. Draw a line for each of the angles in the profile A, and also one corresponding to each of the intermediate points in the curved parts of the stay. Draw the line F G, representing the oblique cut, and the line C D, representing the straight end. Then it will be seen that F C D G of Fig. 988, so far as lines are concerned, is exactly the same as the molding made of clay, shown in Fig. 237. The line F G, by the definition of a miter., is the "miter line" of this molding. It represents the surface against which the end of the molding is supposed to lit. Next lay off a stretchout of the profile A, in the same manner as described in connection which Fig. 237. all as shown by H K in Fig. 238 through the points in which draw measuring lines at right angles to it, or, what is the same, parallel to the lines of the moldings. Now, make each of these lines equal in length to the line of corresponding number drawn across the elevation from C D to F G.
Fig. 237. - The Use of Lines in Obtaining the Envelope of a Molding from a Model
Fig. 238. - Obtaining the Envelope of a Molding from a Drawing of the Same by the
Use of the T-Square.
If, as suggested in the previous illustration - that is, by using a pair of dividers to measure the length of the molding from C D to F G on the several lines - these lengths be set off on corresponding lines drawn from the stretchout line H K, a pattern will be obtained in all respects corresponding to the pattern shown in Fig. 237, already referred to. By inspection of the result thus obtained, however, it will be seen that each point in L M is directly under the point of corresponding number in line F G, and that the same thing may be accomplished by using the T-square placed in the position shown by the dotted lines in Fig. 238. Therefore, instead of using the dividers proceed as follows: Place the T-square as shown at E, and, bringing it successively against the points in F G, cut measuring lines of corresponding number by means of a dot or short dash placed across the line. Then aline traced as before through the points of intersection thus obtained, as shown from L to M, will be the shape of the pattern necessary to make it fit against a surface placed at the angle represented by the miter line F G. By this illustration it is shown that the T-square may be used with great advantage in transferring measurements under almost all circumstances. Since now the T-square is to be used instead of the dividers to locate the points in the patterns, the stretchout line is not needed as a starting point from which to measure lengths and may, therefore, be located at will. For convenience, it should be placed as near to the miter line as possible. Hence, in practical work, supposing that the molding represented by F C D G is not a very short piece, the stretchout line, instead of being opposite the end C D, would be placed somewhere near the line of the blade of the T-square when in its position at E. Should the arm required be short, a line drawn opposite the square end will serve the double purpose of a stretch-out line and of the outline of the square end of the pattern.
By further inspection of Fig. 238, it will be seen that, instead of drawing the lines from the points in the profile A the entire length of the molding, as there shown, all that is necessary to the operation is a short line corresponding to each of the points of the profile. extending only across the miter line F G. The use of these lines, it is evident, is only to locate intersections upon the miter line. In other words, all that is needed is the points in the profile A transferred to the miter line F G. The operation of transferring these points by short lines, as above described, is termed "dropping the points " from the profile to the miter line.