When the shadow of an object such as _A_, Fig. 268, which would fall upon the plane, is interrupted by another object _B_, then the outline of the shadow is still drawn on the plane, but being interrupted by the surface _B_ at _C_, the shadow runs up that plane till it meets the rays 1, 2, which define the shadow on plane _B_. This is an important point, but is quite explained by the figure.
Although we have said that the rays pass over the top of the object casting the shadow, in the case of an archway or similar figure 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° to meet the traces of those rays on the plane of shade, and so get the shadow of the archway, as here shown.
We have seen that when the sun's altitude is at an angle of 45° 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° 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.
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.
From point of sight _S_ (Fig. 270) drop perpendicular to _T_, the station-point. From _T_ draw _TF_ at 45° 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° to meet _FL_ at _L_, which is the luminary at an altitude of 45°, and at an angle of 45° 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° to the picture instead of 45°, is nearer the point of sight; at 90° it would be exactly opposite the spectator, and so on. Again, the elevation being less (40° instead of 45°) 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.