mm. on the base-line equals one degree, and in the vertical direction equals 1[sigma], the locus-bands of the sectors (here equal to each other in width), make such an angle with A’C’ as represents the disc to be rotating exactly 36 times in a second.  It will be seen that the speed of the rod may vary from that shown by the locus P’P to that shown by P’A; and the speeds represented are respectively 68.96 and 1,482.64 degrees per second; and throughout this range of speeds the locus-band of P intercepts the loci of the sectors always the same number of times.  Thus, if the disc revolves 36 times a second, the pendulum may move anywhere from 69 to 1,483 degrees per second without changing the number of bands seen at a time.

   [4] v.  Helmholtz, H.:  ‘Handbuch d. physiolog.  Optik,’ Hamburg
   u.  Leipzig, 1896, S. 489.

And from the figure it will be seen that this is true whether the pendulum moves in the same direction as the disc, or in the opposite direction.  This range of speed is far greater than the concentrically swinging metronome of the present writer would give.  The rate of Jastrow’s rod, of 19 inches per second, cannot of course be exactly translated into degrees, but it probably did not exceed the limit of 1,483.  Therefore, although beyond certain wide limits the rate of the pendulum will change the total number of deduction-bands seen, yet the observations were, in all probability (and those of the present writer, surely), taken within the aforesaid limits.  So that as the observations have it, “The total number of bands seen at any one time is approximately constant, howsoever ... the rate of the rod may vary.”  On this score, also, the illusion-bands and the deduction-bands present no differences.

But outside of this range it can indeed be observed that the number of bands does vary with the rate of the rod.  If this rate (r) is increased beyond the limits of the previous observations, it will approach the rate of the disc (r’).  Let us increase r until r = r’.  To observe the resulting bands, we have but to attach the rod or pendulum to the front of the disc and let both rotate together.  No bands are seen, i.e., the number of bands has become zero.  And this, of course, is just what should have been expected from a consideration of the deduction-bands in Fig. 8.

One other point in regard to the total number of bands seen:  it was observed (page 174, No. 5) that, “The faster the disc, the more bands.”  This too would hold of the deduction-bands, for the faster the disc and sectors move, the narrower and more nearly parallel to A’C’ (Fig. 7) will be their locus-bands, and the more of these bands will be contained within the vertical distance A’A (or C’C), which, it is remembered, represents the age of the oldest after-image which still contributes to the characteristic effect. PP’ will therefore intercept more loci of sectors, and more deduction-bands will be generated.