True Weight from False Balance

Theorem

Unequal Arms

Let $B$ be a body whose weight is $W$.

Let $B$ be weighed in a false balance with unequal arms.

Let the readings of the weight of $B$ be $a$ and $b$ when placed in opposite pans.

Then:

$W = \sqrt {a b}$

Imbalanced Pans

Let $B$ be a body whose weight is $W$.

Let $B$ be weighed in a false balance with imbalanced pans.

Let the readings of the weight of $B$ be $a$ and $b$ when placed in opposite pans.

Then:

$W = \dfrac {a + b} 2$