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 ( deg.) is always used to
designate _degree_. Thus 10 deg. 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 (x) indicates the word "by," and in expressing the term six
feet by three feet two inches, it should be written 6' x 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.

DEFINITIONS.--The following figures show the various geometrical forms
and their definitions:

[Illustration: _Fig. 151.-Fig. 165._]

151. _Abscissa._--The point in a curve, A, which is referred to by
certain lines, such as B, which extend out from an axis, X, or the
ordinate line Z.

152. _Angle._--The inclosed space near the point where two lines meet.

153. _Apothegm._--The perpendicular line A from the center to one side
of a regular polygon. It represents the radial line of a polygon the
same as the radius represents half the diameter of a circle.

154. _Apsides_ or _Apsis_.--One of two points, A, A, of an orbit, oval
or ellipse farthest from the axis, or the two small dots.

155. _Chord._--A right line, as A, uniting the extremities of the arc of
a circle or a curve.

156. _Convolute_ (see also _Involute_).--Usually employed to designate a
wave or folds in opposite directions. A double involute.

157. _Conic Section._--Having the form of or resembling a cone. Formed