Page:Great Neapolitan Earthquake of 1857.djvu/178

130 5th. In the case of a hollow cylinder overturned (Fig. 97).



Let the altitude of the right circular cylinder be $$\alpha$$, the exterior and interior diameters of its base $$\beta, \beta'$$ so that the thickness of the wall $$= \frac{\beta - \beta^2}{2}$$ then

which is the case of the solid cylinder when $$\beta' = 0$$, and when the thickness of the wall is so small in relation to the other dimensions that it may be neglected

In either case, the distance of the centre of gravity from the axis or point of rotation at the base is

Hence, in the first case,

and in the second case,

and