The notions of the penumbra and umbra are important in considering eclipses (q.v.).
In the neighbourhood surrounding the penumbra the granules appear to be packed more closely, forming brilliant patches called faculae.
The first, taken alone, might seem to bear out Wilson's theory, but the others show that the penumbra is really very unsymmetrical and much broader on the side towards the limb, apart from anything which perspective may have to say.
There will be a gradual increase of brightness in the penumbra from total darkness at the edge next the geometrical shadow to full illumination at the outer edge.
The amount of want of illumination in each portion of the penumbra is roughly indicated by the shading.