Light and shadow, the balance, and sunbeams through clouds
Ray diagrams of a window's penumbra with notes on equilibrium and solar rays; a reclining figure above
A large irregular sheet combining optical and mechanical studies. A prominent ray diagram fanning from a light source through an opening treats the lights, shadows and penumbra cast at a window, its lines labelled with letters, while adjoining notes describe solar rays penetrating the gaps between clouds and illuminating the air, and the varied shapes of clouds shaped by the winds. In finer script are two studies of the balance, on the mathematical centre of rotation and the impossibility of equal weights moving one another, together with a note on the resistance of a support near its fixed point, and a small column of arithmetical figures. A reclining draped figure is drawn across the top of the sheet, and additional untranscribed notes appear elsewhere on the leaf.
On this page
Sunbeams through gaps in the clouds
The solar rays penetrate the gaps set between the rounded masses of the clouds and illuminate with their straightness the whole passage between earth and gap, tingeing every place where they intersect. Their course runs straight and widening down to the earth, lighting all the air they pass through.
Light, shade and penumbra at a window
The labelled lines record how much of a luminous body each sightline sees: the line e d sees the whole luminous body, b K sees half of it, and p q sees both the shaded portion c p and the luminous portion a c. From this the space q g grows less dark the nearer it lies to the line d g, while g f is correspondingly less bright.
The balance and its mathematical centre
The balance never has equal arms unless it stands at the position of equality. Were the arcs described by the arm-ends exactly equal, the centre of rotation would be mathematical, which is impossible, since its oscillation would be annulled and a bodiless mathematical centre could not sustain the balance. It is therefore impossible for equal weights to move one another on equal arms.
Resistance of a support near its fixed point
A small balance sketch is captioned on the strength of a support. The part of the support that lies nearer its fixed point resists more, and conversely the part more remote from that fixing resists less.
Reclining draped figure
A reclining figure, its head to the left and body draped, is drawn across the top of the sheet in a lighter hand. It is not covered by the transcription and is described here only from the drawing itself.
Column of figures
A short column of numerals is set down at one side, running through partial products to a total of 120000. It reads as a worked multiplication or reckoning jotted beside the studies.