The balance with unequal arms: counterweights and their proportions
Two columns on the law of the steelyard, a weighted balance figure, and red-chalk machine studies
Two dense columns work through the statics of a balance whose arms are of unequal length, arguing that the counterweights each arm supplies to the other stand in the same proportion as the distances from the fulcrum (the 'pole') to the centers of gravity of the arms. The left column also defines terms: a uniform rod suspended at a pivot is called a balance or steelyard, and its projecting parts the arms. A small figure marks a balance loaded 6-6, and the lower half of the sheet carries two machine studies in red chalk, one captioned with a rule about keeping a saw's weight centered on its stone. Further mechanical drawings on the sheet are catalogued by the Ambrosiana under defensive rotating-blade devices and crossbows.
On this page
Counterweights of unequal arms follow the ratio of the arms
The counterweights that the two unequal arms give one another stand in the same proportion as the opposite spaces measured between the fulcrum and each arm's center of gravity. When the arms are unequal, the opposite counterweights act one against the other with that same unequal proportion. The share of itself that one arm gives as counterweight to the other matches the ratio of those enclosed spaces.
Definition of the balance, the steelyard, and its arms
Let a rod of uniform weight and thickness be suspended at a pivot, either at its middle or at some point along its length. Such a suspended rod is to be called a balance or a steelyard, and the parts that project beyond its pivot are called the arms of the balance. The spaces between the pivot and the centers of gravity of the arms carry the same proportion as the opposite counterweights of each arm.
Rule for a saw kept centered on the stone
One of the two red-chalk machine studies at the foot of the sheet carries a working rule: make sure that the center of the saw's weight never leaves the stone. The note governs the balance of a sawing mechanism so its load stays over the material being cut.
Machine studies catalogued as defensive devices
The lower half of the leaf is occupied by two machine assemblies drawn in red chalk, one built around a disc or wheel. In the Ambrosiana's Codex Atlanticus subject index these mechanisms are classified under a rotating-blade device for the defense of walls and under crossbows. Only the saw caption is written out here; the remaining machinery is untranscribed.