The movement of the system arises when the rate of the rod is slightly less or more than one fifth that of the disc.  If slightly less, the bands formed at each rotation of the rod do not lie precisely over those of the previous rotation, but a little to the rear of them.  The new set still lies mostly superposed on the previous sets, and so fuses into a regular appearance of bands, but, since each new increment lags a bit behind, the entire system appears to rotate backward.  The apparatus is actually a cinematograph, but one which gives so many pictures in the second that they entirely fuse and the strobic movement has no trace of discontinuity.

If the rod moves a trifle more than one fifth as fast as the disc, it is clear that the system of bands will rotate forward, since each new set of bands will lie slightly ahead of the old ones with which it fuses.  The farther the ratio between the rates of rod and disc departs from exactly 1:5, whether less or greater, the more rapid will the strobic movement, backward or forward, be; until finally the divergence is too great, the newly forming bands lie too far ahead or behind those already formed to fuse with them and so be apperceived as one system, and so the bands are lost in confusion.  Thus the cycle of movement as observed on the disc is explained.  As the rate of the rod comes up to and passes one fifth that of the disc, the system of four bands of each color forms in rapid backward rotation.  Its movement grows slower and slower, it comes to rest, then begins to whirl forward, faster and faster, till it breaks up again.

The same thing happens as the rate of the rod reaches and exceeds just one fourth that of the disc.  The system contains three bands of each color.  The system of two bands of each color corresponds to the ratio 1:3 between the rates, while one band of each color (the two lying opposite) corresponds to the ratio 1:2.

If the rod and the disc rotate in opposite directions, the phenomena are changed only in so far as the changed geometrical relations require.  For the ratio 1:3 between the two rates, the strobic system has four bands of each color; for 1:2, three bands of each color; while when the two rates are equal, there are two bands of each color, forming a diameter.  As would be expected from the geometrical conditions, a system of one band of each color cannot be generated when rod and disc have opposite motions.  For of course the rod cannot now hide two or more times in succession a sector at any given point, without hiding the same sector just as often at the opposite point, 180 deg. away.  Here, too, the cycle of strobic movements is different.  It is reversed.  Let the disc be said to rotate forward, then if the rate of the rod is slightly less than one fourth, etc., that of the disc, the system will rotate forward; if greater, it will rotate backward.  So that as the rate of the rod increases, any system on its appearance will move forward, then stand still, and lastly rotate backward.  The reason for this will be seen from an instant’s consideration of where the rod will hide a given sector.