Friction, Balance and Centres of Gravity
Diagrams of friction at the balance pole and centres of gravity, with a note on Hercules for the Medici garden.
The sheet is filled with diagrams and notes on the science of the balance: the friction (confregazione) at the pole, the position of the centre of gravity relative to the pole, and the definition of the central line running from the suspended weight to the centre of the world. Two small sketches show a wheel turning about a fixed pivot and a wheel turning together with its pivot on a support. Columns of figures work out ratios such as 36 being a quarter of 144. In the upper left a personal memorandum records 'The Labours of Hercules, for Piero Ginori' and 'the garden of the Medici'.
On this page
Friction at the pole of the balance
The centre of gravity a b lies below the centre of the balance's pole, and it must be reckoned by the weights ab and by the arm of their friction, not by the weights alone. With the pole loaded at 12, giving 3 of friction, one must add 2 to part a (or 4 from b) to overcome the friction. Neither weight overcomes the other unless the excess equals the friction of the pole.
Central line and centre of gravity defined
The centre of gravity of a balance and its weights falls at the end of the central line running to the centre of the world, and on a perpendicular above the contact of the pole with its support when the arms are in equality. A straight line is the shortest extension from one point to another; the central line extends from the accidental centre of the suspended weight to the centre of the world; all central lines are straight.
Wheel turning on a fixed pivot
One small figure shows a wheel that turns about an immobile pole. An analogous figure shows a wheel that turns together with its pole, while the pole in turn revolves upon its support. Both illustrate how friction arises at the axle.
Ratios of friction: 36 is a quarter of 144
A marginal calculation gives 36/11 of friction and 144 as the body subjected to friction, noting that 36 is one quarter of 144, and 12/11. The friction diagrams repeatedly test quarter-ratios, such as 7/2 against 28/2 where 7 is a quarter of 28.
Hercules for Piero Ginori; the Medici garden
A brief memorandum in the upper left corner reads 'The Labours of Hercules, for Piero Ginori' and 'the garden of the Medici'. It stands apart from the mechanical studies that fill the rest of the sheet.