The lever law: weight against distance from the fulcrum
A ladder of balances doubling the arm from 1 to 128 spaces, summing to 255.
This page states the principle of the balance: the part of a beam farther from its fulcrum moves more easily, and the resistance at the fulcrum must be proportionally the heavier. A descending ladder of small balance diagrams then illustrates the rule for arms of 1, 2, 4, 8, 16, 32, 64 and 128 spaces against a single space, each requiring a weight equal to that number set against one. A larger figure at the right sums the eight balances into a single beam bearing 255 against 8.
On this page
Distance from the fulcrum eases motion
The part of the arm situated farther from its fulcrum is the easier to move. By as much as that motion is made easier, by so much, proportionally, must the resistance within the fulcrum be the heavier. This is the reciprocal law of the lever stated in words.
Doubling the arm, doubling the counterweight
A series of balance beams pairs a growing arm-space against a single space: one against one needs one weight; four spaces against one need a weight of four; sixteen spaces need sixteen; thirty-two need thirty-two, and so up to 128 hung in one space against 128. Each rung doubles the previous, keeping the beam in equilibrium.
The eight balances summed to 255
The figure at right stands 255 against 8, being the weights of the eight balances alongside summed together (1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255). It gathers the whole doubling series into one demonstration.