The Friction of a Counterweight on a Balance

Friction of the counterweight from the friction of 4

The friction of 4 is 1; divided by 3 it yields 1/3, and this 1/3 is the very 'one' set apart earlier, being the friction of the counterweight sought.

General rule for a counterweight's friction

Multiply the arm of the counterweight by four as many times as it contains the friction arm, subtract one from the sum, divide the friction by the remainder, then multiply the result by four to obtain the counterweight itself.

Worked computation giving three quarters

Multiplying the friction arm by four and subtracting one leaves 3, which divides the 4 to give 3/4; clothing that 3/4 with its weight by multiplying by four yields 12 quarters, and the 'one' set apart is named as a 3/4.

Graduated two-armed balance

An L-shaped balance with graduated arms is drawn at the left, labelled c b a with the values 4 and 8, the mechanical device on which the friction rule is exercised.

In basso, da destra a sinistra. Schema per la confregazione:

Analogo schema senza numeri:

Analogo schema, con:

A sinistra sopra gli scritti precedenti. Schema di bilancia, con:

Altro schema, con:

Numeri d'altra mano - foglio girato sul lato destro:

Diagonalmente:

Below, from right to left. Scheme for the friction:

Analogous scheme without numbers:

Analogous scheme, with:

To the left, over the preceding writing. Balance scheme, with:

Another scheme, with:

Numbers in another hand — sheet turned on its right side:

Diagonally:

The Friction of a Counterweight on a Balance

On this page

Friction of the counterweight from the friction of 4

General rule for a counterweight's friction

Worked computation giving three quarters

Graduated two-armed balance