The attraction of the whole shell evidently acts in CO.
Let OP revolve about 0 through a small angle de in the plane MOP; then rde is the space described by P. Again, let OPM revolve about OC through a small angle do, then r sin 0 do is the space described by P. And the thickness of the shell is dr. Hence the volume of the elementary portion of the shell thus formed at P equals rdo.r sin Odp. dr ultimately, since its sides are ultimately at right angles to each other.
Then, if the unit of attraction be so chosen, that it equals the attraction of the unit of mass at the unit of distance, the attraction of the elementary mass at P on C in the direction CP
.. attraction of P on C in CO pr2 sin 0 drdėdo c
We shall eliminate O from this equation by means of
To obtain the attraction of all the particles of the shell we integrate this with respect to o and y, the limits of O and 2π, those of y being c-r and c+r;