to the work done in suddenly compressing the gas) from volume to volume .
Here we have
An Exercise.
Prove the ordinary mensuration formula, that the area of a circle whose radius is , is equal to .
Consider an elementary zone or annulus of the surface (Fig 59), of breadth , situated at a distance
from the centre. We may consider the entire surface as consisting of such narrow zones, and the whole area will simply be the integral of all