A rod hung by two cords: how its weight is shared
Numbered rod diagrams with two propositions on how a rod's weight divides between the cords that hold it
The leaf continues the balance studies of the facing pages with rods drawn in pen and red chalk, tick-marked and annotated with numbers and fractions. Two prose propositions state the underlying rule: when two cords support a rod at its ends its weight divides equally between them, but when one cord is slid from the end toward the middle, the lightening of the load stands in a fixed proportion to how far the rod projects beyond the cords. The numeric columns (fractions such as 35/6 and 42/6) carry out the corresponding calculations.
On this page
Two cords at the ends share the load equally
If two cords support a rod at its ends, the rod's weight is distributed equally between those cords. The rule is illustrated by a rod marked 4-4 at the right of the sheet.
Sliding a cord toward the middle lightens the load in proportion
When one of the two cords is pulled from the end of the rod toward the middle, the lightening of the weight relieved bears the same proportion to the cord remaining at the opposite end as the projecting part of the rod bears to the part enclosed between the two cords.
Fractional reductions of the rod loads
The rod schemes are worked out numerically in columns of fractions, such as 2 2/3, 6, 2 1/3, 35/6 and 42/6. These reduce the shares of the load to a common denominator to check the balance of the beam.