e appearance approach the horizontal line so long as it is
viewed from the same position. On the contrary, if the spectator
retreats from the picture plane _K_ (which we suppose to be
transparent), the point remaining at the same place, the perspective
appearance of this point will approach the ground-line in proportion to
the distance of the spectator.

[Illustrations:
Fig. 35.
Fig. 36.
The spectator at two different distances from the picture.]

Therefore the position of a given point in perspective above the
ground-line or below the horizon is in proportion to the distance of the
spectator from the picture, or the picture from the point.

[Illustration: Fig. 37.]

[Illustrations:
The picture at two different distances from the point.
Fig. 38.
Fig. 39.]

Figures 38 and 39 are two views of the same gallery from different
distances. In Fig. 38, where the distance is too short, there is a want
of proportion between the near and far objects, which is corrected in
Fig. 39 by taking a much longer distance.

RULE 10

Horizontals in the same plane which are drawn to the same point on the
horizon are parallel to each other.

[Illustration: Fig. 40.]

This is a very important rule, for all our perspective drawing depends
upon it. When we say that parallels are drawn to the same point on the
horizon it does not imply that they meet at that point, which would be a
contradiction; perspective parallels never reach that point, although
they appear to do so. Fig. 40 will explain this.

Suppose _S_ to be the spectator, _AB_ a transparent vertical plane which
represents the picture seen edgeways, and _HS_ and _DC_ two parallel
lines, mark off spaces between these parallels equal to _SC_, the height
of the eye of the spectator, and raise verticals 2, 3, 4, 5, &c.,
forming so many squares. Vertical line 2 viewed from _S_ will appear on
_AB_ but half its length, vertical 3 will be only a third, vertical 4 a
fourth, and so on, and if we multiplied these spaces _ad infinitum_ we
must keep on dividing the line _AB_ by the same number. So if we suppose
_AB_ to be a yard high and the distance from one vertical to another to
be also a yard, then if one of these were a thousand yards away its
representation at _AB_ would be the thousandth part of a yard, or ten
thousand yards away, its representation at _AB_ would be the
ten-thousandth part, and whatever the distance it must always be
something; and therefo