Simple equality of balances and the arithmetic of friction

Friction (confregazione) in the balance of equal arms

With a roller (subbio) of 2 pounds and a weight of 2, the 4 pounds yield 1 pound of friction marked at b; balancing 3 against 3 on equal arms is upset because a quarter of the 3 (that is 3/4) goes into friction, so a further pound must be added at e until frictions and weight equalise. The whole scheme treats friction as a real resisting power at the pole.

Computing the counterweight in fractions

Dividing 3/8 by 7 gives 3/56, the fourth of the friction; clothing it yields 12/56 for the increased weight, and adding its fourth (3/56) to the 21/56 above gives 24/56 of friction against 12/56 of weight. The counterweight is reached entirely through fraction arithmetic.

Rule: divide the friction by the arm-number

Because on an equal arm the 3/4 was divided into 3 parts, on a double arm the friction is divided into 7, on a triple into 11, on a quadruple into 15 and on a quintuple into 19; and one always clothes a fraction with its body by multiplying it by 4, since a sub-quadruple part of the body goes into friction.

The roller (subbio) used as a weight

The calculations take a roller or beam (subbio) weighing 2 pounds as one of the loads hung on the balance. A cylindrical roller mounted on a trestle is drawn at the lower left of 41v, alongside the balance diagrams.

0041 v

Nel margine destro in alto tre figure con lettere e numeri.

Al centro figura con lettere e numeri:

A lato della figura:

Nel margine destro, al centro del foglio, figura con numeri.

A lato della figura:

In basso a destra quattro figure con numeri.

0040 r

Figura con lettere e numeri:

A lato della figura:

Figura con numeri:

A lato della figura:

Figura con numeri.

A lato della figura:

Sotto la figura:

In the right margin above, three figures with letters and numbers.

At the centre, a figure with letters and numbers:

Beside the figure:

In the right margin, at the centre of the sheet, a figure with numbers.

Beside the figure:

At the bottom right, four figures with numbers.

Figure with letters and numbers:

Beside the figure:

Figure with numbers:

Beside the figure:

Figure with numbers.

Beside the figure:

Below the figure:

Simple equality of balances and the arithmetic of friction

On this page

Friction (confregazione) in the balance of equal arms

Computing the counterweight in fractions

Rule: divide the friction by the arm-number

The roller (subbio) used as a weight