Center of Gravity of Balance Arms
Reckoning arm-weights and counterweights on a suspended double beam
Leonardo studies where the true center of gravity of a balance arm lies, arguing that for an arm of uniform thickness it sits at the middle of its length. Using a suspended beam whose pole is n and whose arm-centers are c and a, he works a numerical example: placing 2 at a and 4 at c, he shows how one side lightens the other and how much counterweight restores equilibrium. The upper drawing shows a hanging rectangular frame carrying a lettered horizontal balance beam.
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The true center of gravity lies at mid-length of a uniform arm
For a balance arm of uniform thickness, the whole weight of that arm may be treated as concentrated at the middle of its length. Leonardo names n the pole of the balance m b, with the centers of its two arms at c and a.
Balancing arm-weights 2 and 4 with a counterweight
Placing 2 at a for the weight of its two arms and 4 at c for the weight of its four arms, the 2 lightens c by one pound, leaving 3. To equalize, he sets 3 at b against the 3 at c so the equal arms stay level, then treats 2 at a against 3 at b as a balance carrying 5 of weight, to which 4 of counterweight is given.
Suspended double-beam balance apparatus
The top of the sheet is drawn with a hanging rectangular frame from which a horizontal balance beam is suspended, its points lettered along the bar. Short strokes mark the divisions and the pole from which the arms extend.