Balances of Proportional Weights and Divided Beams
Many weighed balance-arms with numbers and fractions demonstrating the law of the lever
The sheet is crowded with balance-beam diagrams whose arms carry numbers and fractions, working out how a load distributes itself along a lever in inverse proportion to the distances from the fulcrum. Two lettered examples make the reasoning explicit: on the arm m o n a, because a n is one-third of n m the weight resolves into 4 at m and 8 at n; and on c r b a, because a b is half of b c the six units split into 3 at c and 9 at b. A note at the right treats how weight passes between cords when one moves toward another, extending the analysis to pulley ropes.
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Proportional weights on the arm m o n a
Because a n is one-third of n m, it draws from n m a number one-third of itself, namely one; whence n remains with 8 weights, of which m has 4. And because n o is half of o m, the weight 4 at m is half of the 8 at n.
Dividing six units along the beam c r b a
a b is half of b c, so from c b it draws a number half of b c, leaving 6 distributed as 3 in c and 9 in b. And because 3 is one-third of 9, so b r is one-third of r c, matching the split of load to the lever's segments.
Tables of balance weights
Numerous balance-arms are entered with values and fractions, from whole numbers like 60, 40, 24 and 12 down to fractions such as 7 1/5, 24/5 and 4 4/5, tabulating the weights that keep each beam in equilibrium.
Weight transferred between cords
A note at the right considers cords: if one cord moves toward another, weight is drawn from the other and joins with it; if one cord is fixed and the other moves toward it, weight is moved from the fixed cord and joins to the moving one, in proportion to each of the first weights.