Page:IntroductionToMathematicsWhitehead.pdf/43

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in air, and lb. be the weight of the water which it displaces when completely immersed, 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

the weights in the right-hand scale come to lb., then the apparent weight of the crown in water is lb.; and we thus have

and thus

,

and


where and are determined by the easy, and fairly precise, operation of weighting.

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