igure they
pass underneath it; but the same principle holds good, that is, we draw
lines from the guiding points in the arch, 1, 2, 3, &c., at the same
angle of 45 deg to meet the traces of those rays on the plane of shade,
and so get the shadow of the archway, as here shown.

[Illustration: Fig. 269.]

CLI

THE SUN BEHIND THE PICTURE

We have seen that when the sun's altitude is at an angle of 45 deg the
shadows on the horizontal plane are the same length as the height of the
objects that cast them. Here (Fig. 270), the sun still being at 45 deg
altitude, although behind the picture, and consequently throwing the
shadow of _B_ forwards, that shadow must be the same length as the
height of cube _B_, which will be seen is the case, for the shadow _C_
is a square in perspective.

[Illustration: Fig. 270.]

To find the angle of altitude and the angle of the sun to the picture,
we must first find the distance of the spectator from the foot of the
luminary.

[Illustration: Fig. 271.]

From point of sight _S_ (Fig. 270) drop perpendicular to _T_, the
station-point. From _T_ draw _TF_ at 45 deg to meet horizon at _F_. With
radius _FT_ make _FO_ equal to it. Then _O_ is the position of the
spectator. From _F_ raise vertical _FL_, and from _O_ draw a line at
45 deg to meet _FL_ at _L_, which is the luminary at an altitude of
45 deg, and at an angle of 45 deg to the picture.

Fig. 272 is similar to the foregoing, only the angles of altitude and of
the sun to the picture are altered.

_Note._--The sun being at 50 deg to the picture instead of 45 deg, is
nearer the point of sight; at 90 deg it would be exactly opposite the
spectator, and so on. Again, the elevation being less (40 deg instead of
45 deg) the shadow is longer. Owing to the changed position of the sun
two sides of the cube throw a shadow. Note also that the outlines of the
shadow, 1 2, 2 3, are drawn to the same vanishing points as the cube
itself.

It will not be necessary to mark the angles each time we make a drawing,
as it must be seen we can place the luminary in any position that suits
our convenience.

[Illustration: Fig. 272.]

CLII

SUN BEHIND THE PICTURE, SHADOWS THROWN ON A WALL

As here we change the conditions we must also change our procedure. An
upright wall now becomes the plane of shade, therefore as the principle
of shadows must always remain the same we have to change the relative
positions of the luminar