The rod should be black and not more than a quarter of an inch broad. It may be passed before the rotating disc by hand. For the sake of more careful study, however, the rod should be moved at a constant rate by some mechanical device, such as the pendulum and works of a Maelzel metronome removed from their case. The pendulum is fixed just in front of the color-disc. A further commendable simplification of the conditions consists in arranging the pendulum and disc to move concentrically, and attaching to the pendulum an isosceles-triangular shield, so cut that it forms a true radial sector of the disc behind it. All the colored bands of the illusion then appear as radial sectors. The radial shields should be made in several sizes (from 3 to 50 degrees of arc) in black, but the smallest size should also be prepared in colors matching the several discs. Such a disposition, then, presents a disc of fused color, rotating at a uniform rate, and in front of this a radial sector oscillating from side to side concentrically with the disc, and likewise at a uniform rate. Several variations of this apparatus will be described as the need and purpose of them become clear. II. PREVIOUS DISCUSSION OF THE ILLUSION. Although Jastrow and Moorehouse (_op. cit._) have published a somewhat detailed study of these illusion-bands, and cleared up certain points, they have not explained them. Indeed, no explanation of the bands has as yet been given. The authors mentioned (_ibid._, p. 204) write of producing the illusion by another method. "This consists in sliding two half discs of the same color over one another leaving an open sector of any desired size up to 180 degrees and rotating this against a background of a markedly different color, in other words we substitute for the disc composed of a large amount of one color, which for brevity we may call the 'majority color,' and a small amount of another, the 'minority color,' one in which the second color is in the background and is viewed through an opening in the first. With such an arrangement we find that we get the series of bands both when the wire is passed in front of the disc and when passed in back between disc and background; and further experimentation shows that the time relations of the two are the same. (There is, of course, no essential difference between the two methods when the wire is passed in front of the disc.)" That is true, but it is to be borne in mind that there is a difference when the wire is passed behind the disc, as these authors themselves state (_loc. cit._, note):--"The time-relations in the two cases are the same, but the _color-phenomena_ considerably _different_." However, "these facts enable us to formulate our first generalization, viz., that for all purposes here relevant [_i.e._, to a study of the _time-relations_] the seeing of a wire now against one background and then immediately against another is the same as its now