Fig. 3 shows how to derive W directly (as Z was derived) from the geometrical relations of pendulum and sectors. Let r, r', s, p, and t, be as before, but now let
width of the band (i.e., the arc BA') = W;
that is, the band, instead of extending as before from where P begins to hide the green sector to where P ceases to hide the same, is now to extend from the point at which P ceases to hide any part of the red sector to the point where it just commences again to hide the same.
Then
| t = | W + p , |
| r |
and
| t = | W + s , |
| r' |
therefore