If, in Fig. 2, we have a disc (composed of a green and a red sector) and a pendulum, moving to the right, and if _P_ represents the pendulum at the instant when the green sector _AOB_ is beginning to pass behind it, it follows that some other position farther to the right, as _P'_, will represent the pendulum just as the last part of the sector is passing out from behind it. Some part at least of the sector has been hidden during the entire interval in which the pendulum was passing from _P_ to _P'_. Clearly the arc _BA'_ measures the band _BOA'_, in which the green stimulation from the sector _AOB_ is thus at least partially suppressed, that is, on which a relatively red band is being produced. If the illusion really depends on the successive eclipse of the sectors by the pendulum, as has been described, it will be possible to express BA', that is, the width of a band, in terms of the widths and rates of movement of the two sectors and of the pendulum. This expression will be an equation, and from this it will be possible to derive the phenomena which the bands of the illusion actually present as the speeds of disc and rod, and the widths of sectors and rod, are varied. [Illustration: Fig 2.] Now in Fig. 2 let the width of the band (_i.e._, the arc BA') = Z speed of pendulum = r degrees per second; speed of disc = r' degrees per second; width of sector AOB (_i.e._, the arc AB) = s degrees of arc; width of pendulum (_i.e._, the arc BC) = p degrees of arc; time in which the pendulum moves from P to P' = t seconds. Now arc CA' t = -------; r but, since in the same time the green sector AOB moves from _B_ to B', we know also that arc BB' t = -------; r' then arc CA' arc BB' ------- = -------, r r' or, omitting the word "arc" and clearing of fractions, r'(CA') = r(BB'). But now CA' = BA' - BC, while BA' = Z and BC = p; therefore CA' = Z-p. Similarly BB' = BA' + A'B' = Z + s. Substituting for _CA'_ and _BB'_ their values, we get r'(Z-p) = r(Z+s), or Z(r' - r) = rs + pr', or Z = rs + pr' / r' - r. It is to be remembered that _s_ is the width of the sector which undergoes eclipse, and that it is the color of that same sector which is subtracted from the band _Z_ in question. Therefore, whether _Z_ represents a green or a red band, _s_ of the formula must refer to the _oppositely colored_ sector, _i.e._, the one which is at that time being hidden.