An introduction to mathematics, by A. N. Whitehead.

METHODS OF APPLICATION 39
in air, and w lb. be the weight of the water
which it displaces when completely immersed,
W- w would be the extra upward force
necessary to sustain the crown as it hung in
water.
Now, this upward force can easily be ascertained by weighing the body as it hangs in
water, as shown in the annexed figure. If.-.Weigbts
The.... _ --- _crown
Fig. 3.
the weights in the right-hand scale come to
F lb., then the apparent weight of the crown
in water is F lb.; and we thus have
F= W-w
and thus w = W - F
W W
and = W F (A)
w W-F
where W and F are determined by the easy,
and fairly precise, operation of weighting.