Focal Points

The focal point of a circle is its center, and is called the focus. But an ellipse has two focal points, called foci, represented by F, F in Fig. 148, and by B, B in Fig. 149.

A produced line is one which extends out beyond the marking point. Thus in Fig. 148 that part of the line K between F and G represents the produced portion of line K.

Spirals

There is no more difficult figure to make with a bow or a circle pen than a spiral. In Fig. 150 a horizontal and a vertical line (A, B), respectively, are drawn, and at their intersection a small circle (C) is formed. This now provides for four centering points for the circle pen, on the two lines (A, B). Intermediate these points indicate a second set of marks halfway between the marks on the lines. If you will now set the point of the compass at, say, the mark 3, and the pencil point of the compass at D, and make a curved mark one-eighth of the way around, say, to the radial line (E), then put the point of the compass to 4, and extend the pencil point of the compass so it coincides with the curved line just drawn, and then again make another curve, one-eighth of a complete circle, and so on around the entire circle of marking points, successively, you will produce a spiral, which, although not absolutely accurate, is the nearest approach with a circle pen. To make this neatly requires care and patience.

Perpendicular And Vertical

A few words now as to terms. The boy is often confused in determining the difference between perpendicular and vertical. There is a pronounced difference. Vertical means up and down. It is on a line in the direction a ball takes when it falls straight toward the center of the earth. The word perpendicular, as usually employed in astronomy, means the same thing, but in geometry, or in drafting, or in its use in the arts it means that a perpendicular line is at right angles to some other line. Suppose you put a square upon a roof so that one leg of the square extends up and down on the roof, and the other leg projects outwardly from the roof. In this case the projecting leg is perpendicular to the roof. Never use the word vertical in this connection.

Signs To Indicate Measurements

The small circle (°) is always used to designate degree. Thus 10° means ten degrees.

Feet are indicated by the single mark '; and two closely allied marks " are for inches. Thus five feet ten inches should be written 5' 10". A large cross (×) indicates the word "by," and in expressing the term six feet by three feet two inches, it should be written 6' × 3'2".

The foregoing figures give some of the fundamentals necessary to be acquired, and it may be said that if the boy will learn the principles involved in the drawings he will have no difficulty in producing intelligible work; but as this is not a treatise on drawing we cannot go into the more refined phases of the subject.