The Compound Derivative Shadow and Its Boundaries
A pyramid diagram showing how derivative shadow lightens with distance from the shadow-casting body
Continuing the Fifth Part of the Treatise on Painting, this page explains that compound lights and compound shadows always border together, the outer edge of the compound shadow being simple shadow. Chapter [560] argues that the boundary of the simple shadow is less distinct than that of the compound when the shadowy body lies nearer the light, because the angle then grows more obtuse. Chapter [561] treats the compound derivative shadow, which loses darkness the farther it lies from the simple derivative shadow. A lettered pen diagram of two nested light-and-shadow pyramids (labels a, b, o, k, f, g and c) demonstrates that at g the surface receives only three quarters of the light a b.
On this page
Boundaries of simple and compound shadow
Compound lights and compound shadows always border together, but the outer boundary of the compound shadow is the simple shadow, and that of the compound light the simple illuminated part. The edge of the simple shadow is less distinct than that of the compound when the shadowy body is nearer the light, because the angle of the compound shadow and light is more obtuse.
Pyramid diagram of the derivative shadow
Let a b be the luminous body and b o the shadowy body, a b f the luminous pyramid and b o k the pyramid of the simple derivative. At g the surface is illuminated by only c f, three quarters of the light, so it receives a quarter less light than at f, which sees the whole of a b.
Compound derivative shadow lightens with distance
The compound derivative shadow loses the more of its darkness the more remote it becomes from the simple derivative shadow. This follows because a shadow is of less darkness where it is seen by a greater quantity of the luminous body.