Conclusions on the Balance and the Descent of Weights
Statics of the arm-balance: equal weights, oblique arms, and the loss of effective weight
A page of numbered conclusions on the science of weights, set out around a drawn arm-balance whose beam carries pans and hanging weights over a pivot marked with concentric circles. Leonardo argues that weights hung at equal distances stay in equilibrium and return to it if disturbed, that a weight becomes lighter the further it departs from the position of equality, and that on unequal arms the longer arm causes the motion. A marginal note observes that the heavy body always seeks to get under the lighter, and that circular motion has nothing 'natural' in it except its starting point. Two side diagrams add that shorter arms make weights lighter on the same pivot, and that every heavy body overcomes a friction resistance equal to a quarter of its weight.
On this page
Equilibrium and the loss of weight away from the position of equality
Equal weights hung at equal distances stay at rest and, if displaced by accident, settle back into the first position; unequal suspension-cords make no difference. Any weight that departs from equality becomes lighter, and the more it departs the lighter it grows. On unequal arms, the longer arm is the cause of the motion, and the weight nearer the centre of the balance becomes the lighter.
Shorter arms make weights lighter on one pivot
A marginal balance schema labelled n - b states the rule that the shorter arms make the weights lighter upon one and the same pole (pivot). It condenses into an instrument-sketch the argument of the main column about arm length and effective weight.
Friction resistance a quarter of the weight
A left-hand balance schema labelled f d b a c e - n carries the note that every heavy body is overcome by a resistance of friction equal to the fourth part of its heaviness, with the addition 'greater proportion.' A further small figure marks a b as the line of direction and e d as the line of equality.
Drawn arm-balance with pans and weights
The sheet is built around a balance beam pivoting on a hub of concentric circles, with cords and pear-shaped weights hanging from the arms. The apparatus illustrates the written conclusions on equilibrium, oblique arms and the descent of weights.