Reducing Friction on a Pole, and the Thrust of Arches
A roller-mounted pivot, closed water conduits, and where an arch or dome presses most
The leaf gathers several mechanical problems. A large drawing at upper right shows a device that relieves the friction of an upright pole by unloading it from pole m onto two supporting wheels (n, f), the motion being easier the larger the wheels; Leonardo notes the pole touches the wheels at a single point, at a right angle to the line to their centers. Below, two arch and dome cross-sections labelled 'arches of the Grazie' illustrate that a 'disunited' weight presses hardest near its center of gravity, so an arch bears harder inside (b, c) than outside (a, d), and that a perpendicular member (g p) resists more than a curved one (f g). A short note at top adds that water carried through closed channels cannot rise as high as it descended.
On this page
Roller-mounted pivot to relieve friction (m, n, f)
A way of relieving the friction of a pole set upright on its support: its load is taken off the pole m and carried onto the two poles n f, which run on wheels. The larger the circuit of the supporting wheels, the easier the motion is for the mover.
Point contact and right angle of the pivot
The area of contact that pole m has with the wheels at x z touches only at a point. The motion makes a right angle with the line that runs from the contact to the center of the wheels.
Where an arch or dome presses most (b, c versus a, d)
That part of a disunited weight presses more which lies nearer to the center of its gravity. Hence the inner part of an arch or dome presses more, at the places b c, than the outer part at a d.
Perpendicular resists more than curve (g p vs f g)
The perpendicular member g p resists more than the curved f g, by the fifth proposition of the ninth book. The point is set beside the lower arch study.
Water in closed conduits cannot rise to its source
No quantity of water can raise itself as much as it descends — meaning water conducted through closed channels, where no air is admitted.