De Ponderibus: Experiments on Weights and Supports
Test rigs for weights pressing into earth and loaded iron wires; a support of double diameter
Headed 'De ponderibus' (On Weights), this sheet sets out two designed experiments and a demonstration about the strength of supports. One rig stands two equal staffs, loaded with one and two pounds, upright in soft potter's earth to measure how far each sinks in the same time; another loads bundles of one, two, and eight square iron wires to find when they begin to bend. A final diagram argues that a support of double diameter but equal height bears eight times as much (100 against 800). Leonardo insists that each trial be repeated two or three times before any general rule is drawn.
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Experiment: weights pressing supports into potter's earth
Saw a staff in half, equalize the two pieces with wax on a balance, and stand them upright in worked, flattened potter's earth, passing them through equal holes in a thin board. Load one with a pound and the other with two, let them stand an hour, then measure the holes made. Before making a rule, try it two or three times to see whether the trials agree.
Experiment: load-bearing of one, two, and eight iron wires
Take iron wires drawn by a square wire-drawing machine, fix one at the end and load it until it just begins to bend, verifying with a counterweighted wire and noting the load. Then double the wires, bind them with thin silk, and observe that experience confirms the reasoning. Prove it likewise for four doubles and onward by degrees.
A support of double diameter bears eight times the load (100 to 800)
A support with a diameter twice that of another, at equal height, bears eight times as much. The doubled support contains four of the smaller within itself, so at proportionate height it would bear four times as much; but being only four diameters tall it loses half its due height and grows stronger by as much again. Doubling that fourfold strength gives eight hundred pounds.