Beam deflection, water weighed in a pump, and stable supports
How length and load bend a rod; measuring water's push in a galley-pump; when a base stays firm
The upper note works out how a rod's stiffness changes with length: the arm n o, being half as long as m o, is half again as strong, so the same weight that would sink one span produces only half the deflection (saetta) when moved to the quarter-point of the rod. A second experiment weighs a galley-pump (tronba da galea) full of water — about 100 pounds — first free and then resting on a balance cord, the loss of weight revealing how much the water presses against the vessel's sides, with the middle of the base bearing most. A closing rule states that a support has little permanence whenever the centre of the load loading it does not fall perpendicularly above the centre of the support.
On this page
Length, load, and the deflection of a rod
Because n o is half the length of m o it is half again as strong; the arm n o, which by nature would resist a load of 8 as it sinks toward x, drops only half-way, so the same weight of m suffices. Placing 4 pounds at the quarter-point of a rod gives exactly half the deflection they would give at its middle.
Weighing the water inside a galley-pump
Weigh all the water that fills the galley-pump — say 100 pounds — then set the pump on a balance cord and weigh it again; the weight lost shows how strongly the water pushes against the sides. Leonardo judges the water over the middle of the base presses hardest, growing lighter toward the top.
Galley-pump mounted on a balance stand
The cylindrical galley-pump is drawn upright on a footed stand, its base hung from a balance cord so that the water it holds can be weighed in place while the pump stays supported.
When a loaded support stays stable
A support has little permanence when the centre of the weight loading it does not stand perpendicularly above the centre of the support — the rule illustrated by the leaning posts and the squat T-shaped support at the foot of the page.
