0.5

1 cm

PERSPECTIVE.

Ill

point lines parallel to the sides of the object to intersect the

picture-line. The points of intersection, or vanishing

points, for the sides and edg’es of the plate are, like the sta-

tion-point, beyond the limits of the paper. We have chosen

in this case such a point of view for the picture, and such

a, distance as would throw the station and vanishing

points beyond the limits of the paper advisedly, as these

are conditions of constant occurrence in practice, and it

is right that the learner should at the outset be made

acquainted with the difficulties of the art and the means

of overcoming them. These means in this case may be

two. The first and most ready is to fix slips of lath to the

drawing-board, on which the horizon-line may be extended

to the requisite distance. The other is to draw the con-

verging lines by the centrolinead invented by Mr. Nicol-

son. This instrument, however, is not so applicable to

the drawing of machinery as of architecture, as it requires

frequent alteration to adjust it to the various vanishing

points. We prefer, therefore, the simple plan of fixing

laths to the board, and inserting at each vanishing point

a needle, against which the straight-edge may work as a

centre. We shall now proceed to describe the process in

detail.

Fig. 1 A is a plan of the wall, the iron plate, and the

nuts at the top of the plate. We have already described

the manner of drawing the extreme visual rays, picture-

line, and central plane; these being drawn, we proceed to

draw the visual rays from the various points of the plan.

We then prepare for the perspective representation, as

in Fig. 1 B, by drawing the ground-line of the picture

4 4, the horizon-line 5 5, the latter at such a height as the

eye of the spectator is supposed to be; and the vertical pro-

jection of the central plane 0 0. Now let us trace the

drawing of any point in the plan, as A, to its perspective

representation. From A draw the visual line A a, cutting

the picture-line in a, and produce the line B A to the

picture-line in A'. Transfer the point A' to the ground-

line of the perspective at A', and draw A' A2 indefinitely

at right angles to the ground-line. This line then being

in the plane of the picture, on it is to be set up the origi-

nal height of the objects in the plane B A, measured from

the geometrical drawing. In the same way transfer the

point A to a in the perspective, and draw through it an

indefinite perpendicular to the ground-line. This line is

the indefinite perspective representation of the corner of

the Plate A. The ground-line in the perspective drawing

is assumed at the level of the bottom of the plate, there-

fore from A draw to the left hand vanishing point a line

to represent the perspective of the bottom of the plate, and

its intersection with a A is the perspective of the bottom of

the hither corner. To find the perspective of the top edge

of the plate, from A' on the ground-line set up from the

geometrical drawing the height of the plate in c, and

through c draw to the vanishing point the line c d, which

is the indefinite perspective of the top edge of the plate,

and its hither angle is defined by the perpendicular from a.

To find the further vertical edge of the plate, it is only

necessary from the point B on the plan to draw the visual

ray B b, and to transfer its distance from the central plane

o O b to the ground-line in the perspective at b, and from

this to draw the perpendicular to B, produced to intersect

the perspectives of the top and bottom edges. The heights

of the perspectives of the horizontal parts of the rim of

the plate are also set up on the line A' A2, and the vertical

parts are obtained by drawing visual rays. The perspec-

tive of the return or thickness of the hither edge of the

plate is obtained by drawing from the upper and lower

corners, lines to the right hand vanishing point, and de-

fining their extent by drawing the visual ray E e, and

transferring the distance O e to the perspective ground-

line in e.

The perspective of all the other objects in the ground-

plane, such as the nuts, it will be seen, are obtained first

by drawing visual rays from the points of the objects;

transferring the points in which these intersect the picture-

line to the perspective ground-line; from these, drawing

indefinite perpendiculars, and then obtaining their heights

by producing the plane of the object, such as that of the

face of the nuts F /, to the picture-line, and transferring

the point of intersection / to the ground-line, and drawing

a perpendicular on which the heights are to be set up.

The perspective of the curve in the plate is found thus:—

The absolute depth of the curve is shown in the ground-

plan at A g. The small drawing 1 c shows the vertical

elevation, and from this the height of the points of inter-

section of the curve with the wall is obtained at h h, and

set up on the plane of the wall produced to meet the pic-

ture, while the height of the point g of the curve is set

up on the plane of g g, produced to intersect the picture.

The remainder of the drawing will elucidate itself.

Plate 68, fig. 2 A (Perspective Lesson, Part Second).

To the ground plan we now add the circles representing

the horizontal bevel-wheel, and the profiles of the vertical

bevel-wheels. To find the perspectives of circles, as we

already know, we have to draw the perspectives of their

circumscribing squares. Each circle is accordingly found

in this drawing, by first drawing the square within which

it is inscribed, an operation which must be familiar to the

student who has attended to the elementary part of the

treatise, and need not therefore be described. The bevel-

gear being frustrums of cones, the perspectives of the lines

of their teeth will, like the same lines in the geometrical

drawing, converge to a point where the apices of the cones

meet. This point is found in the perspective, by drawing-

through the centre of the horizontal wheel (the point

where the diagonals of the square intersect each other) a

vertical line intersecting at ft a line drawn through the

centres of the vertical wheels to the left hand vanishing

point. The ellipses, which are the perspectives of the

circles, should be drawn by the simple mode shown and

described, ante pp. 105, 106.

Plate 69, figs. 3 A and 3 B (Perspective Lesson, Part

Third). We now add the teeth of the wheels. Their

divisions may be found in two ways, and both are here

exemplified. It is quite a matter of indifference which

we use, and the draughtsman suits his own conveni-

Ill

point lines parallel to the sides of the object to intersect the

picture-line. The points of intersection, or vanishing

points, for the sides and edg’es of the plate are, like the sta-

tion-point, beyond the limits of the paper. We have chosen

in this case such a point of view for the picture, and such

a, distance as would throw the station and vanishing

points beyond the limits of the paper advisedly, as these

are conditions of constant occurrence in practice, and it

is right that the learner should at the outset be made

acquainted with the difficulties of the art and the means

of overcoming them. These means in this case may be

two. The first and most ready is to fix slips of lath to the

drawing-board, on which the horizon-line may be extended

to the requisite distance. The other is to draw the con-

verging lines by the centrolinead invented by Mr. Nicol-

son. This instrument, however, is not so applicable to

the drawing of machinery as of architecture, as it requires

frequent alteration to adjust it to the various vanishing

points. We prefer, therefore, the simple plan of fixing

laths to the board, and inserting at each vanishing point

a needle, against which the straight-edge may work as a

centre. We shall now proceed to describe the process in

detail.

Fig. 1 A is a plan of the wall, the iron plate, and the

nuts at the top of the plate. We have already described

the manner of drawing the extreme visual rays, picture-

line, and central plane; these being drawn, we proceed to

draw the visual rays from the various points of the plan.

We then prepare for the perspective representation, as

in Fig. 1 B, by drawing the ground-line of the picture

4 4, the horizon-line 5 5, the latter at such a height as the

eye of the spectator is supposed to be; and the vertical pro-

jection of the central plane 0 0. Now let us trace the

drawing of any point in the plan, as A, to its perspective

representation. From A draw the visual line A a, cutting

the picture-line in a, and produce the line B A to the

picture-line in A'. Transfer the point A' to the ground-

line of the perspective at A', and draw A' A2 indefinitely

at right angles to the ground-line. This line then being

in the plane of the picture, on it is to be set up the origi-

nal height of the objects in the plane B A, measured from

the geometrical drawing. In the same way transfer the

point A to a in the perspective, and draw through it an

indefinite perpendicular to the ground-line. This line is

the indefinite perspective representation of the corner of

the Plate A. The ground-line in the perspective drawing

is assumed at the level of the bottom of the plate, there-

fore from A draw to the left hand vanishing point a line

to represent the perspective of the bottom of the plate, and

its intersection with a A is the perspective of the bottom of

the hither corner. To find the perspective of the top edge

of the plate, from A' on the ground-line set up from the

geometrical drawing the height of the plate in c, and

through c draw to the vanishing point the line c d, which

is the indefinite perspective of the top edge of the plate,

and its hither angle is defined by the perpendicular from a.

To find the further vertical edge of the plate, it is only

necessary from the point B on the plan to draw the visual

ray B b, and to transfer its distance from the central plane

o O b to the ground-line in the perspective at b, and from

this to draw the perpendicular to B, produced to intersect

the perspectives of the top and bottom edges. The heights

of the perspectives of the horizontal parts of the rim of

the plate are also set up on the line A' A2, and the vertical

parts are obtained by drawing visual rays. The perspec-

tive of the return or thickness of the hither edge of the

plate is obtained by drawing from the upper and lower

corners, lines to the right hand vanishing point, and de-

fining their extent by drawing the visual ray E e, and

transferring the distance O e to the perspective ground-

line in e.

The perspective of all the other objects in the ground-

plane, such as the nuts, it will be seen, are obtained first

by drawing visual rays from the points of the objects;

transferring the points in which these intersect the picture-

line to the perspective ground-line; from these, drawing

indefinite perpendiculars, and then obtaining their heights

by producing the plane of the object, such as that of the

face of the nuts F /, to the picture-line, and transferring

the point of intersection / to the ground-line, and drawing

a perpendicular on which the heights are to be set up.

The perspective of the curve in the plate is found thus:—

The absolute depth of the curve is shown in the ground-

plan at A g. The small drawing 1 c shows the vertical

elevation, and from this the height of the points of inter-

section of the curve with the wall is obtained at h h, and

set up on the plane of the wall produced to meet the pic-

ture, while the height of the point g of the curve is set

up on the plane of g g, produced to intersect the picture.

The remainder of the drawing will elucidate itself.

Plate 68, fig. 2 A (Perspective Lesson, Part Second).

To the ground plan we now add the circles representing

the horizontal bevel-wheel, and the profiles of the vertical

bevel-wheels. To find the perspectives of circles, as we

already know, we have to draw the perspectives of their

circumscribing squares. Each circle is accordingly found

in this drawing, by first drawing the square within which

it is inscribed, an operation which must be familiar to the

student who has attended to the elementary part of the

treatise, and need not therefore be described. The bevel-

gear being frustrums of cones, the perspectives of the lines

of their teeth will, like the same lines in the geometrical

drawing, converge to a point where the apices of the cones

meet. This point is found in the perspective, by drawing-

through the centre of the horizontal wheel (the point

where the diagonals of the square intersect each other) a

vertical line intersecting at ft a line drawn through the

centres of the vertical wheels to the left hand vanishing

point. The ellipses, which are the perspectives of the

circles, should be drawn by the simple mode shown and

described, ante pp. 105, 106.

Plate 69, figs. 3 A and 3 B (Perspective Lesson, Part

Third). We now add the teeth of the wheels. Their

divisions may be found in two ways, and both are here

exemplified. It is quite a matter of indifference which

we use, and the draughtsman suits his own conveni-