0.5

1 cm

28

ENGINEER AND MACHINIST’S DRAWING-BOOK.

pose, the triangle of 60° is preferable to that of 45°, as it

is longer and lighter.

When the parallels and perpendiculars do not coincide

in direction with the edges of the board, the square may

be adjusted with its bevel stock to the obliquity required,

and the lines may be drawn as before. This is probably

the best plan when the oblique lines are numerous or

extensive. In most cases, however, oblique lines are only

occasional, and when their position is given they may be

drawn with a straight-edge. When the oblique parallels

and perpendiculars are short, as in oblique framing, short

rods, or bars, bolt-heads, and the like, the combined use of

the straight-edge and triangle is expedient. Thus, to draw

a perpendicular to the oblique line A B (Fig. 118), at the

point C, set the straight-

edge and set-square in

conjunction, to bring

the long edge of the

square to coincide with

the given line at a b;

then shift the square

into the position show-

ing in dotting, while the straight-edge is held fast,

and draw the perpendicular. When a number of short

parallels are to be drawn to an oblique line A B (Fig. 119),

through given points C, D, E, set the triangle and

straight-edge as before, with the side a b coincident with

the given line; then slide the triangle into the positions

shown in dotting, to set the edge upon the given points,

and draw the parallels as required. The straight-edge, in

these cases, is oblique to the given line, and may in some

cases be inconveniently placed, requiring re-adjustment,

when a number of lines are to be drawn. It is thus some-

times convenient to employ a supplementary triangle ; in

the second case, for example, the triangle might be set to

the given line, slid down to the position E, and fixed

there ; and a second triangle placed on its edge E, which

would form a sliding surface parallel to the given line,

from which perpendiculars might be drawn. Or, the tri-

angle a b c (Fig. 120) may be placed with its edge a c to

coincide with the given line, and the straight-edge applied

to the side b c; sliding the triangle into the position a' b' c,

the edge a'd now forms a base-line parallel to the given

line from which perpendiculars may be drawn with a

second triangle d.

Parallel rulers are also frequently used for drawing

oblique lines. We have no great opinion of them, except

for sketching jobs, as they are at best inconvenient for

working, and liable to derangement at the joints.

It remains to consider the utility of the sector in draw-

ing oblique parallel lines. This instrument should be stiff

enough at the joint not to yield too readily; and by set-

ting it to the obliquity required, it may be slid along the

square-blade, and may thus command the entire range of

the board. By sliding the triangle upon the sector, oblique

perpendiculars may also be drawn, as in (Fig. 118).

Frequently, short oblique lines, perpendicular to each

other, require to be drawn at the same place; this may

occasionally be done in one setting of the sector or straight-

edge, by placing the slant side of the triangle next it, and

exposing the right angle.

Thus, in drawing a

square nut n (Fig. 121), it

is plain from the figure,

that by presenting the

two edges of the tri-

angle successively, all

the sides of the nut may be drawn.

Square figures may be quickly described with the use

of the board. If they are to be described on a given

centre, C (Fig. 122), describe a circle with the radius C D

equal to half the side of the square, draw parallels A B,

E F, with the square, touching the top and bottom of the

circle, which may be very correctly drawn as tangents by

the eye, and with the set-square draw the upright tan-

gents, in the manner shown in dotting, to complete the

figure.

(.Fig. 122.) (Fig. 123.)

If the square is to be drawn upon a given line A B

(Fig. 123), draw the diagonal lines A F, BE, from the ends

of the line, by means of the set-square of 45°, as exempli-

fied in the figure, and draw perpendiculars from the same

points, cutting the diagonals at E, F ; join E F to com-

plete the figure.

To draw an octagon, apply the set-square of 45° to the

corners, after completing a square figure, and draw tan-

gents to the inscribed circle, as, for example, the line h k,

(Fig. 114).

To draw an equilateral triangle upon a given line A B

(Fig. 124), it is only necessary to apply the slant edge of the

set-square of 60°, to each end of the base, with the short

ENGINEER AND MACHINIST’S DRAWING-BOOK.

pose, the triangle of 60° is preferable to that of 45°, as it

is longer and lighter.

When the parallels and perpendiculars do not coincide

in direction with the edges of the board, the square may

be adjusted with its bevel stock to the obliquity required,

and the lines may be drawn as before. This is probably

the best plan when the oblique lines are numerous or

extensive. In most cases, however, oblique lines are only

occasional, and when their position is given they may be

drawn with a straight-edge. When the oblique parallels

and perpendiculars are short, as in oblique framing, short

rods, or bars, bolt-heads, and the like, the combined use of

the straight-edge and triangle is expedient. Thus, to draw

a perpendicular to the oblique line A B (Fig. 118), at the

point C, set the straight-

edge and set-square in

conjunction, to bring

the long edge of the

square to coincide with

the given line at a b;

then shift the square

into the position show-

ing in dotting, while the straight-edge is held fast,

and draw the perpendicular. When a number of short

parallels are to be drawn to an oblique line A B (Fig. 119),

through given points C, D, E, set the triangle and

straight-edge as before, with the side a b coincident with

the given line; then slide the triangle into the positions

shown in dotting, to set the edge upon the given points,

and draw the parallels as required. The straight-edge, in

these cases, is oblique to the given line, and may in some

cases be inconveniently placed, requiring re-adjustment,

when a number of lines are to be drawn. It is thus some-

times convenient to employ a supplementary triangle ; in

the second case, for example, the triangle might be set to

the given line, slid down to the position E, and fixed

there ; and a second triangle placed on its edge E, which

would form a sliding surface parallel to the given line,

from which perpendiculars might be drawn. Or, the tri-

angle a b c (Fig. 120) may be placed with its edge a c to

coincide with the given line, and the straight-edge applied

to the side b c; sliding the triangle into the position a' b' c,

the edge a'd now forms a base-line parallel to the given

line from which perpendiculars may be drawn with a

second triangle d.

Parallel rulers are also frequently used for drawing

oblique lines. We have no great opinion of them, except

for sketching jobs, as they are at best inconvenient for

working, and liable to derangement at the joints.

It remains to consider the utility of the sector in draw-

ing oblique parallel lines. This instrument should be stiff

enough at the joint not to yield too readily; and by set-

ting it to the obliquity required, it may be slid along the

square-blade, and may thus command the entire range of

the board. By sliding the triangle upon the sector, oblique

perpendiculars may also be drawn, as in (Fig. 118).

Frequently, short oblique lines, perpendicular to each

other, require to be drawn at the same place; this may

occasionally be done in one setting of the sector or straight-

edge, by placing the slant side of the triangle next it, and

exposing the right angle.

Thus, in drawing a

square nut n (Fig. 121), it

is plain from the figure,

that by presenting the

two edges of the tri-

angle successively, all

the sides of the nut may be drawn.

Square figures may be quickly described with the use

of the board. If they are to be described on a given

centre, C (Fig. 122), describe a circle with the radius C D

equal to half the side of the square, draw parallels A B,

E F, with the square, touching the top and bottom of the

circle, which may be very correctly drawn as tangents by

the eye, and with the set-square draw the upright tan-

gents, in the manner shown in dotting, to complete the

figure.

(.Fig. 122.) (Fig. 123.)

If the square is to be drawn upon a given line A B

(Fig. 123), draw the diagonal lines A F, BE, from the ends

of the line, by means of the set-square of 45°, as exempli-

fied in the figure, and draw perpendiculars from the same

points, cutting the diagonals at E, F ; join E F to com-

plete the figure.

To draw an octagon, apply the set-square of 45° to the

corners, after completing a square figure, and draw tan-

gents to the inscribed circle, as, for example, the line h k,

(Fig. 114).

To draw an equilateral triangle upon a given line A B

(Fig. 124), it is only necessary to apply the slant edge of the

set-square of 60°, to each end of the base, with the short