5. We next come to an observation (p. 174, No. 5) concerning the number of bands seen at any one time. The 'geometrical deduction of the bands,' it is remembered, was concerned solely with the amount of color which was to be deducted from the fused color of the disc. _W_ and _w_ represented the widths of the areas whereon such deduction was to be made. In observation 5 we come on new considerations, _i.e._, as to the color from which the deduction is to be made, and the fate of the momentarily hidden area which suffers deduction, _after_ the pendulum has passed on. We shall best consider these matters in terms of a concept of which Marbe[3] has made admirable use: the 'characteristic effect.' The Talbot-Plateau law states that when two or more periodically alternating stimulations are given to the retina, there is a certain minimal rate of alternation required to produce a just constant sensation. This minimal speed of succession is called the critical period. Now, Marbe calls the effect on the retina of a light-stimulation which lasts for the unit of time, the 'photo-chemical unit-effect.' And he says (_op. cit._, S. 387): "If we call the unit of time 1[sigma], the sensation for each point on the retina in each unit of time is a function of the simultaneous and the few immediately preceding unit-effects; this is the characteristic effect." [3] 'Marbe, K.: 'Die stroboskopischen Erscheinungen,' _Phil. Studien._, 1898, XIV., S. 376. We may now think of the illusion-bands as being so and so many different 'characteristic effects' given simultaneously in so and so many contiguous positions on the retina. But so also may we think of the geometrical interception-bands, and for these we can deduce a number of further properties. So far the observed illusion-bands and the interception-bands have been found identical, that is, in so far as their widths under various conditions are concerned. We have now to see if they present further points of identity. As to the characteristic effects incident to the interception-bands; in Fig. 7 (Plate V.), let _A'C'_ represent at a given moment _M_, the total circumference of a color-disc, _A'B'_ represent a green sector of 90°, and _B'C'_ a red complementary sector of 270°. If the disc is supposed to rotate from left to right, it is clear that a moment previous to _M_ the two sectors and their intersection _B_ will have occupied a position slightly to the left. If distance perpendicularly above _A'C'_ is conceived to represent time previous to _M_, the corresponding previous positions of the sectors will be represented by the oblique bands of the figure. The narrow bands (_GG_, _GG_) are the loci of the successive positions of the green sector; the broader bands (_RR_, _RR_), of the red sector. In the figure, 0.25 mm. vertically = the unit of time = 1[sigma]. The successive stimulations given to the retina by the disc _A'C'_, say at a point _A'_, during the interval preceding the moment _M_ will be