The human eye may be briefly described as a chamber of a spherical or
globular form, with a circular opening in front. This circular opening
is called the pupil, and through it the visual rays pass to the interior
of the eye. The visual rays, passing from space in all directions
through the small pupil, are received upon what may be called the
interior wall of the globular chamber forming the eye (see fig. 305).
This interior wall is called the retina, and upon it the impressions of
external objects are received, just as they are received upon a screen
in a dark chamber. These impressions are conveyed by the optic nerve
from the retina to the brain.
In front of the pupil is a segment of a small sphere, composed of the
cornea and the aqueous humor, both of which are transparent, and from
their shape and density have a convergent effect upon the rays passing
through them.
Behind the pupil is the transparent crystalline lens, which, from its
shape and its elasticity, is a powerful agent in aiding the convergence
of the rays, and in bringing objects at various distances to a clear
focus upon the retina.
[Illustration: Fig. 305.]
The pupil has the power of contraction and dilation, which is influenced
by the quantity of light entering the eye, but when it is dilated to the
utmost its size is very small in comparison with the great chamber
forming the body of the eye.
In fig. 305 we have a rough sectional diagram of the eye and an object
in front of it. This object, an arrow, is seen by means of the visual
rays proceeding from it, the principal two of which are shown. The
visual ray from _A_ passes through the pupil and is received upon the
retina at _a_. In the same way the visual ray from _B_ passes through
the pupil and is received upon the retina at _b_. It will thus be seen
that the impressions or images received upon the retina are inverted;
but, by long reason and experience, the mind has acquired the habit of
determining the real positions of objects, and does not, though the
image is so received, imagine them to be upside down.
It will also be observed, in the same way, that that portion of an
object which is upon the right will be pictured upon the retina upon the
left, and _vice versa_, but the mind, for the reasons before stated,
never imagines the object to be reversed. This fact is another proof
that, as mentioned at the commencement of our study, to see accurately
is a matter of education and practice.
And first of Optics; it was asserted, page 252, that we see by the
agency of light which passes from objects to our eyes in straight lines
which are called Visual Rays.
We see by the agency of light, as all objects, except such as may be
styled self-luminous, when placed in a dark chamber are not perceivable
by us, except by touch, smell or hearing; we cannot _see_ them; they are
invisible. But when, by removing a shutter or igniting a flame, we
introduce something to the chamber which was not present when the
chamber was dark, we become at once conscious of the appearance of the
object, we perceive it by the sense of sight.
This something which must always be present to enable us to see, is
called Light; all objects are made visible to the sense of seeing by its
agency.
Without light, natural or artificial, it would be impossible to
distinguish one object from another.
[Illustration: Fig. 306.]
That the Visual Rays pass from objects in straight lines to the eye may
be proved by the following experiment (see fig. 306):--Pierce two
screens with a large pin, and place them so that the holes are in a
straight line with a flame, as the light of a candle or lamp. On fixing
the eye to one of these holes we are able to see the flame; but if we
slightly move the flame, one of the screens, or the eye, the flame is no
longer visible. To be visible, the flame, the holes in the screens, and
the eye must all be in the same straight line. See fig. 306.
In fig. 299 the picture plane is represented by the rectangle _W X Y Z_.
Although the picture plane is here shown as a rectangle, it may be of
any shape or of any size.
The observer is at _S_, looking through the picture plane at the cross
_R C O H_. The observer is standing upon a horizontal surface, which is
called the ground plane. If we are in a room, the window may be called a
picture plane and the floor a ground plane.
The picture plane rests, as it were, upon the ground plane, in a line
which passes from _Y_ to _Z_. The two planes meet or intersect in this
line, which is called the ground line. The ground line is sometimes
called the picture line, or the measuring line.
The visual rays, by means of which the observer sees the cross, will, in
their course from it to the eye, pass through the picture plane. These
visual rays will intersect the picture plane in a number of points, and
if we mark the true positions of these points the result will be a
perspective image of the cross.
The rays are shown passing from the cross to the eye of the observer,
and meeting the picture plane in points _r_, _c_, _o_, _h_; _r_ being
joined to _o_, and _c_ to _h_, we have the perspective image of the
cross as it would appear to the observer at _S_. Of course an infinite
number of rays proceed from the cross to the eye of the observer; but it
is quite evident that we need only consider those proceeding from the
extremities of the object.
Scale or Approximate Perspective.
Real, or true perspective, represents the object exactly as it is seen
in nature, where the parts that are far away from the eye of the
observer appear smaller than those nearby. Occasions arise, however,
in practical life, with its numerous phases of industrial
requirements, where the convenience of showing the complete form of
the object in a single view might preferably be coupled with the
convenience of scale dimensions.
This has led to a modified perspective, that sacrifices some of the
accuracy in the appearance of the object to gain the advantage of scale
dimensions; this form of perspective may be distinguished by the
name--_approximate or scale perspective_--which does not represent the
object exactly as seen in nature, but where those parts that are afar
off are shown of the same size as those that are near by, and where the
lines that run out into space are parallel to each other and do not
converge into a vanishing point.
To represent an object in perspective, the horizon and the point of
vision will have to appear in the drawing as the fundamental starting
points.
Three dimensions are distinguished for the fixing of an object in space
from a certain reference point. They are height, breadth and thickness,
and are in their direction square to each other. The height is the
fundamental direction, being derived from the direction of gravity, that
invariably extends to the center of the earth.
All directions in the perspective determination of an object are
parallel to these.
Vertical lines and planes point toward the center of the earth, while
horizontal planes, including the directions of breadth and thickness,
are square to the vertical direction. In this, the principal visual ray
extends in the direction of thickness.
For a clear understanding of perspective, it must be firmly fixed in
mind, that for each prominent point of the object behind the picture
plane, a corresponding point lies in the picture plane, in that position
where a straight line or ray of sight that is going from the eye to the
point of the object, cuts through the picture plane.
Suppose we could replace these rays of sight by thin, visible threads of
wire that would go through little holes in the picture plane, we could
then walk around this bundle of rays, and by looking at it from three
different directions, we would get three different views of it. We may
look upon it from the top, from the side or from the end, where the
bundle of rays all concentrate in the eye of the observer.
[Illustration: Fig. 307.]
Figs. 307 and 308 show, in two cases, how these three views would
appear. The end views are those where the perspective picture appears on
the plane, while the top and side views only show where the rays
intersect the picture plane. The top view shows how far, for example,
point _A_ is distant from a vertical line _O Z_, while the side view
shows how far point _A_ is below horizontal line _O X_, which is at the
same height above the ground as the eye of the observer, _O_. Thus, all
points of the cube can be located on the picture plane, and the outlines
of the cube reproduced in perspective.
[Illustration: Fig. 308.]
Modified arrangements are shown in figs. 309 and 310 for parallel and
angular perspective.
[Illustration: Fig. 309.]
The views are so arranged in relation to each other that the picture
plane in the top view is parallel to the horizon and the ground-line,
which latter is the intersection of the picture plane with the level
ground of the end or perspective view. At the same time the eye of the
observer is in one and the same vertical line for both views, two
vanishing points may be found in the horizon outside of the principal
visual ray. To find the position of these two vanishing points in the
picture plane, the modified top view, fig. 310, is used.
[Illustration: Fig. 310.]
As all lines that end in a vanishing point must be parallel in reality,
this parallelism may be seen in the top view and lines through the eye
of the observer, parallel to the directions of the main lines of the
object, will cut the picture plane at the vanishing points.
Through these two vanishing points the directions of two sets of lines
are found, the starting points of which are determined from the plane of
measurement. The third set of lines, being vertical, also appears
vertical and parallel in the picture.
The position of each vertical line is found in the top view, where the
light rays from the observing eye to the ends of the vertical lines
intersect with the picture plane. Projecting these points down upon the
rays to the vanishing points produces the vertical lines in the picture.
For example, in fig. 311, the purpose of perspective is entirely
defeated by placing the eye of the observer directly in front of the
object and arriving at the view taken in mechanical drawing which needs
supplementary views for complete comprehension of the form of the
object.
[Illustration: Fig. 311.]
In fig. 312 the eye of the observer is first placed directly opposite
the object, then it sees the object to the left but a short distance
away, while in the third figure the observer is farther away from the
object. In each case the picture plane and plane of measurement is at
the front face of the cube.
[Illustration: Fig. 312.]
[Illustration: Fig. 312 (second part).]
For such simple objects, it is not necessary to draw the top view at
all. The only reminder of the top view is the eye or point of vision,
the picture plane that falls together for the sake of convenience with
the horizon of the end view and the ray that determines the measurement
point _M_, which is, in this suppressed reproduction, absolutely
necessary, in order to find the apparent position of the real corners
behind the picture plane.
So far, only square or sharp-cornered objects have been represented in
perspective.
It is evident, however, that round objects can also be shown in linear
perspective, placing reference lines on the object and representing
these as if they were real lines. A cylinder is thus shown in fig. 313
of which the end planes will appear very distinctly in sharp outlines.
[Illustration: Fig. 313.]
Vertically, only the outlines of the cylinder, as contrasted against
space, will appear as distinct outlines, while the reference lines will
not appear and are therefore shown only as dotted lines.
Fig. 314 shows the approximate or scale perspective with all the axes
drawn and the corresponding angles and scales marked. The outlines of
the object running in these directions appear all parallel to the axes.
The approximate or scale perspective completely avoids all the
difficulties of choosing a point of sight, of having several views,
vanishing points and measurement points, and thus offers a
representative view, with a great saving of time and labor. Particularly
for mechanical purposes, where an artistic impression is not called for,
it presents a distinct advantage over the true or real perspective.
[Illustration: Fig. 314.]
[Illustration: TABLES