TO FIND THE VANISHING-POINT OF LINES PERPENDICULAR TO THE SURFACE OF A
GIVEN INCLINED PLANE.
[Illustration: Fig. 50.]
As the inclined plane is given, one of its steepest lines must be given,
or may be ascertained.
Let _AB_, Fig. 50., be a portion of a steepest line in the given plane,
and _V_ the vanishing-point of its relative horizontal.
Through _V_ draw the vertical _GF_ upwards and downwards.
From _A_ set off any portion of the relative horizontal _AC_, and on
_AC_ describe a semicircle in a vertical plane, _ADC_, cutting _AB_ in
_E_.
Join _EC_, and produce it to cut _GF_ in _F_.
Then _F_ is the vanishing-point required.
For, because _AEC_ is an angle in a semicircle, it is a right angle;
and therefore the line _EF_ is at right angles to the line _AB_; and
similarly all lines drawn to _F_, and therefore parallel to _EF_, are
at right angles with any line which cuts them, drawn to the
vanishing-point of _AB_.
And because the semicircle _ADC_ is in a vertical plane, and its
diameter _AC_ is at right angles to the horizontal lines traversing
the surface of the inclined plane, the line _EC_, being in this
semicircle, is also at right angles to such traversing lines. And
therefore the line _EC_, being at right angles to the steepest lines
in the plane, and to the horizontal lines in it, is perpendicular to
its surface.
* * * * *
The preceding series of constructions, with the examples in the first
Article of the Appendix, put it in the power of the student to draw
any form, however complicated,[30] which does not involve intersection
of curved surfaces. I shall not proceed to the analysis of any of
these more complex problems, as they are entirely useless in the
ordinary practice of artists. For a few words only I must ask the
reader’s further patience, respecting the general placing and scale of
the picture.
As the horizontal sight-line is drawn through the sight-point, and the
sight-point is opposite the eye, the sight-line is always on a level
with the eye. Above and below the sight-line, the eye comprehends, as
it is raised or depressed while the head is held upright, about an
equal space; and, on each side of the sight-point, about the same
space is easily seen without turning the head; so that if a picture
represented the true field of easy vision, it ought to be circular,
and have the sight-point in its center. But because some parts of any
given view are usually more interesting than others, either the
uninteresting parts are left out, or somewhat more than would
generally be seen of the interesting parts is included, by moving the
field of the picture a little upwards or downwards, so as to throw the
sight-point low or high. The operation will be understood in a moment
by cutting an aperture in a piece of pasteboard, and moving it up and
down in front of the eye, without moving the eye. It will be seen to
embrace sometimes the low, sometimes the high objects, without
altering their perspective, only the eye will be opposite the lower
part of the aperture when it sees the higher objects, and _vice
versâ_.
There is no reason, in the laws of perspective, why the picture should
not be moved to the right or left of the sight-point, as well as up or
down. But there is this practical reason. The moment the spectator
sees the horizon in a picture high, he tries to hold his head high,
that is, in its right place. When he sees the horizon in a picture
low, he similarly tries to put his head low. But, if the sight-point
is thrown to the left hand or right hand, he does not understand that
he is to step a little to the right or left; and if he places himself,
as usual, in the middle, all the perspective is distorted. Hence it is
generally unadvisable to remove the sight-point laterally, from the
center of the picture. The Dutch painters, however, fearlessly take
the license of placing it to the right or left; and often with good
effect.
The rectilinear limitation of the sides, top, and base of the picture
is of course quite arbitrary, as the space of a landscape would be
which was seen through a window; less or more being seen at the
spectator’s pleasure, as he retires or advances.
The distance of the station-point is not so arbitrary. In ordinary
cases it should not be less than the intended greatest dimension
(height or breadth) of the picture. In most works by the great masters
it is more; they not only calculate on their pictures being seen at
considerable distances, but they like breadth of mass in buildings,
and dislike the sharp angles which always result from station-points
at short distances.[31]
Whenever perspective, done by true rule, looks wrong, it is always
because the station-point is too near. Determine, in the outset, at
what distance the spectator is likely to examine the work, and never
use a station-point within a less distance.
There is yet another and a very important reason, not only for care in
placing the station-point, but for that accurate calculation of
distance and observance of measurement which have been insisted on
throughout this work. All drawings of objects on a reduced scale are,
if rightly executed, drawings of the appearance of the object at the
distance which in true perspective reduces it to that scale. They are
not _small_ drawings of the object seen near, but drawings the _real
size_ of the object seen far off. Thus if you draw a mountain in a
landscape, three inches high, you do not reduce all the features of
the near mountain so as to come into three inches of paper. You could
not do that. All that you can do is to give the appearance of the
mountain, when it is so far off that three inches of paper would
really hide it from you. It is precisely the same in drawing any other
object. A face can no more be reduced in scale than a mountain can. It
is infinitely delicate already; it can only be quite rightly rendered
on its own scale, or at least on the slightly diminished scale which
would be fixed by placing the plate of glass, supposed to represent
the field of the picture, close to the figures. Correggio and Raphael
were both fond of this slightly subdued magnitude of figure. Colossal
painting, in which Correggio excelled all others, is usually the
enlargement of a small picture (as a colossal sculpture is of a small
statue), in order to permit the subject of it to be discerned at a
distance. The treatment of colossal (as distinguished from ordinary)
paintings will depend therefore, in general, on the principles of
optics more than on those of perspective, though, occasionally,
portions may be represented as if they were the projection of near
objects on a plane behind them. In all points the subject is one of
great difficulty and subtlety; and its examination does not fall
within the compass of this essay.
Lastly, it will follow from these considerations, and the conclusion
is one of great practical importance, that, though pictures may be
enlarged, they cannot be reduced, in copying them. All attempts to
engrave pictures completely on a reduced scale are, for this reason,
nugatory. The best that can be done is to give the aspect of the
picture at the distance which reduces it in perspective to the size
required; or, in other words, to make a drawing of the distant effect
of the picture. Good painting, like nature’s own work, is infinite,
and unreduceable.
I wish this book had less tendency towards the infinite and
unreduceable. It has so far exceeded the limits I hoped to give it,
that I doubt not the reader will pardon an abruptness of conclusion,
and be thankful, as I am myself, to get to an end on any terms.
[30] As in algebraic science, much depends, in complicated
perspective, on the student’s ready invention of expedients,
and on his quick sight of the shortest way in which the
solution may be accomplished, when there are several ways.
[31] The greatest masters are also fond of parallel perspective,
that is to say, of having one side of their buildings fronting
them full, and therefore parallel to the picture plane, while
the other side vanishes to the sight-point. This is almost
always done in figure backgrounds, securing simple and balanced
lines.