Gear Teeth, Clock Timing, Joints, and the Sun at the Horizon
Which teeth should be wider, why clocks run uneven, jointed links and chained arches, and the enlarged rising sun
A wide-ranging leaf that begins with gear teeth ('crowded here for scarcity of paper'): whichever member drives the other should carry the wider teeth, and if the two drive each other reciprocally the tooth-spacing must be equal. Because a tip meeting a tooth-root acts on a shorter lever, clocks built of many wheels strike unevenly, hurrying or dragging, so fewer wheels give steadier time. The upper diagram then turns to the sky: Leonardo states that the sun shows a much larger figure at the horizon, some crediting the thick, variable medium that bends the rays outward, a reason he rejects, since otherwise the sun would throw its rays westward before it rose. A jointed link and a note on 'ways of joints that bend or unbend' sit at the middle, and drawings of arches at the foot carry a 'rule for chaining arches.'
On this page
Which teeth should be wider: pinion, wheel, or equal spacing
If the pinion is to drive the wheel, its teeth should be somewhat wider than the wheel's; if the wheel drives the pinion, the wheel's teeth should be wider. But where pinion and wheel drive each other reciprocally, as in many instruments, the tooth-spacing of both must be equal.
Why clocks of many wheels strike unevenly, from fast to slow
A tip meeting a tooth-root works on a shorter lever nearer the wheel's centre, so the mover tires more. Hence clocks of many wheels vary their striking, hurrying when tips sit in the roots of the next wheels and dragging in the contrary case; the fewer the wheels, the less the timekeeping breaks up.
Why the sun shows a larger figure at the horizon than overhead
When the sun appears at the horizon, or leaves it, it is of much greater figure than when it stands above us, and more distant by half the diameter of the earth, as shown in a b.
Leonardo rejects atmospheric refraction as the cause of the enlarged sun
Some say the cause is the medium of many thicknesses, which twists and curves the rays outward, away from the central line running from the eye to the centre of the sun. But to Leonardo this reason does not hold, for then the sun would cast its rays outside itself in the west before it rose at the horizon.
Joints of pieces that can bend or unbend
A drawn link of several coupled pieces is labelled as 'various ways of joints of pieces that can bend or unjoint,' a study of flexible mechanical connections.
Rule for chaining (tying) arches
The arch and vault sketches at the foot of the page carry the caption 'rule for chaining arches,' concerning how arches are tied or bound together.