We are now prepared to continue our identification of these geometrical interception-bands with the bands observed in the illusion.  It is to be noted in passing that this graphic representation of the interception-bands as characteristic effects (Fig. 7) is in every way consistent with the previous equational treatment of the same bands.  A little consideration of the figure will show that variations of the widths and rates of sectors and pendulum will modify the widths of the bands exactly as has been shown in the equations.

The observation next at hand (p. 174, No. 5) is that “The total number of bands seen at any one time is approximately constant, howsoever the widths of the sectors and the width and rate of the rod may vary.  But the number of bands is inversely proportional (Jastrow and Moorehouse) to the time of rotation of the disc; that is, the faster the disc, the more bands.”

[Illustration:  PSYCHOLOGICAL REVIEW.  MONOGRAPH SUPPLEMENT, 17.  PLATE V.
               Fig. 7.  Fig. 8.  Fig. 9.]

This is true, point for point, of the interception-bands of Fig. 7.  It is clear that the number of bands depends on the number of intersections of PP’ with the several locus-bands RR, GG, RR, etc.  Since the two sectors are complementary, having a constant sum of 360 deg., their relative widths will not affect the number of such intersections.  Nor yet will the width of the rod P affect it.  As to the speed of P, if the locus-bands are parallel to the line A’C’, that is, of the disc moved infinitely rapidly, there would be the same number of intersections, no matter what the rate of P, that is, whatever the obliqueness of PP’.  But although the disc does not rotate with infinite speed, it is still true that for a considerable range of values for the speed of the pendulum the number of intersections is constant.  The observations of Jastrow and Moorehouse were probably made within such a range of values of r.  For while their disc varied in speed from 12 to 33 revolutions per second, that is, 4,320 to 11,880 degrees per second, the rod was merely passed to and fro by hand through an excursion of six inches (J. and M., op. cit., pp. 203-5), a method which could have given no speed of the rod comparable to that of the disc.  Indeed, their fastest speed for the rod, to calculate from certain of their data, was less than 19 inches per second.

The present writer used about the same rates, except that for the disc no rate below 24 revolutions per second was employed.  This is about the rate which v.  Helmholtz[4] gives as the slowest which will yield fusion from a bi-sectored disc in good illumination.  It is hard to imagine how, amid the confusing flicker of a disc revolving but 12 times in the second, Jastrow succeeded in taking any reliable observations at all of the bands.  Now if, in Fig. 8 (Plate V.), 0.25