the visual ray passing
from the eye of the spectator to the foot of his image, and is the
diagonal of a rectangle, therefore it cuts _AB_ in the centre _o_, and
_AO_ represents _a'b'_ to the spectator. This is an experiment that any
one may try for himself. Perhaps the above fact may have something to do
with the remarks I made about Titian at the beginning of this chapter.

[Illustration: Fig. 295.]

[Illustration: Fig. 296.]

CLXVIII

THE MIRROR AT AN ANGLE

If an object or line _AB_ is inclined at an angle of 45 deg to the mirror
_RR_, then the angle _BAC_ will be a right angle, and this angle is
exactly divided in two by the reflecting plane _RR_. And whatever the
angle of the object or line makes with its reflection that angle will
also be exactly divided.

[Illustration: Fig. 297.]

[Illustration: Fig. 298.]

Now suppose our mirror to be standing on a horizontal plane and on a
pivot, so that it can be inclined either way. Whatever angle the mirror
is to the plane the reflection of that plane in the mirror will be at
the same angle on the other side of it, so that if the mirror _OA_ (Fig.
298) is at 45 deg to the plane _RR_ then the reflection of that plane in
the mirror will be 45 deg on the other side of it, or at right angles,
and the reflected plane will appear perpendicular, as shown in Fig. 299,
where we have a front view of a mirror leaning forward at an angle of
45 deg and reflecting the square _aob_ with a cube standing upon it, only
in the reflection the cube appears to be projecting from an upright
plane or wall.

[Illustration: Fig. 299.]

If we increase the angle from 45 deg to 60 deg, then the reflection of the
plane and cube will lean backwards as shown in Fig. 300. If we place it
on a level with the original plane, the cube will be standing upright
twice the distance away. If the mirror is still farther tilted till it
makes an angle of 135 deg as at _E_ (Fig. 298), or 45 deg on the other
side of the vertical _Oc_, then the plane and cube would disappear, and
objects exactly over that plane, such as the ceiling, would come into
view.

In Fig. 300 the mirror is at 60 deg to the plane _mn_, and the plane
itself at about 15 deg to the plane _an_ (so that here we are using
angular perspective, _V_ being the accessible vanishing point). The
reflection of the plane and cube is seen leaning back at an angle of
60 deg. Note the way the reflection of this cube is found by the