Fig. 11. Testing 45° Angle (45° Triangle).

Triangles are used in drawing lines at right angles to the T-square, Fig. 12, and at an angle with the horizontal, Fig. 13. If it is desired to draw a line through the point P, Fig. 14, parallel to a given line E F, two triangles should be used. First, place triangle A with one edge coinciding with the given line. Now take triangle B and place one of its edges in contact with the bottom edge of triangle A. Holding triangle B firmly with the left hand, slide triangle A to the right or to the left until its edge reaches the point P. The line M N may then be drawn passing through the point P. In place of the triangle B any straight-edge such as a T-square may be used.

Fig. 12. Drawing Vertical Parallel Lines.

Fig. 13. Drawing Parallel Lines at an Angle with the Horizontal.

A line may be drawn through a point, perpendicular to a given line by means of triangles as follows: Let E F, Fig. 15, be the given line, and let the point be D. Place the longest side of triangle A so that it coincides with the line E F. Place the other triangle (or any straight-edge) in the position of the triangle B; then holding B with the left hand, place the triangle A in the position C, so that the longest side passes through the point D. A line may then be drawn through the point D perpendicular to E F,

In previous figures it has been shown how lines may be drawn making angles of 30, 45, 60, and 90 degrees with the horizontal.

Fig. 14. Drawing a Line Parallel to a Given Line.

Fig. 15. Drawing a Line Perpendicular to a Given Line.

It is possible to draw lines forming angles of 15 and 75 degrees by placing the triangles as shown in Fig. 16.

Fig. 16. Drawing Angle of 15° and 75°.

By the use of the triangles and T-square almost any line may be drawn. Suppose it is desired to draw a rectangle having one side horizontal. First draw by means or the T-square the sides A B and D C horizontal and parallel, Fig. 17. Now place one of the triangles on the T-square and in positions E and F draw the vertical lines D A and B C.

Fig. 17. Drawing a Rectangle with T-Square and Triangle.

If the rectangle is to be drawn in some other position on the board, as shown in Fig.

18, place the 45-degree triangle

F so that the longest edge is in the required direction of the side

D C. Now, hold the triangle F in position and place another triangle in position H. By holding H in position and sliding triangle F, the sides A B and D C may be drawn. To draw the sides A D and B C change triangle

A to position E and repeat the process.

Compasses. Compasses are used for drawing circles and arcs of circles. The cheaper class of instruments are made of brass, but they are unsatisfactory on account of the odor and the tendency to tarnish. The best material is Grerman silver, as it does not soil the hands, has no odor, and is easy to keep clean. Aluminum instruments possess the advantage of lightness, but on account of the softness of the metal they do not wear well.

The compasses are made in the form shown in Fig. 19 and are provided with pencil and pen points. Fig. 20 shows the compass in position for drawing circles. One leg has a socket into which the shank of the pencil or pen mounting may be inserted. The other leg is fitted with a needle point which is placed at the center of the circle. In most instruments the needle point projects through a piece of round steel wire with a square shoulder at one or both ends. In some instruments the joints are held in position by lock nuts, made of thin disks of steel, with notches for using a wrench or forked key. Fig. 21 shows the detail of the joint of a high grade instrument.

Fig. 18. Rectangle Drawn with Triangles.

Fig. 19. Compasses and Attachments.

Both legs are alike at the joint, and two pivoted screws are inserted in the yoke. This permits ample movement of the legs, yet gives the proper stiffness. The flat surface of one leg is faced with steel, the other with German silver, so that the rubbing parts may be of different metals. Small set screws are used to prevent the pivoted screws from turning in the yoke. The contact surfaces of this joint are made circular to exclude dirt and to prevent rusting of the steel face.

The details of the socket are shown in Fig. 22, Fig. 23, and Fig. 21; in some instruments the shank and socket are pentagonal. Fig. 22, the shank entering the socket loosely, and being held in place by means of the screw. Unless used very carefully this arrangement is not durable because the sharp corners soon wear, and the pressure on the set screw is not sufficient to hold the shank firmly in place.

In Fig. 23 is shown a round shank, the shank having a flat top, with a set screw to hold the shank in position. A still better form of socket is shown in Fig;. 24 the hole being circular and tapered. The shank fits accurately into the split socket and is clamped by a screw on the side; it is held in perfect alignment by a small steel key. Both legs of the compass are jointed in order that the lower part of the legs may be perpendicular to the paper while drawing circles. In this way the needle point makes but a small hole in the paper, and both nibs of the pen will press equally on the paper. In penciling circles it is not as necessary that the pencil should be kept vertical, it is a good plan, however, to learn to use them in this way both in penciling and inking. The compasses should be held loosely between the thumb and forefinger. If the needle point is sharp, as it should be, only a slight pressure will be required to keep it in place. While drawing the circle, incline the compasses slightly in the direction of revolution and press lightly on the pencil or pen.