Sixteen Experimental Investigations from the Harvard Psychological Laboratory by Hugo Münsterberg (100 books to read .txt) 📕

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

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.

6. “The colors of the bands (page 175, No. 6) approximate those of the

two sectors; the transition-bands present the adjacent ‘pure colors’

merging into each other. But all the bands are modified in favor of

the moving rod. If, now, the rod is itself the same in color as one of

the sectors, the bands which should have been of the other color are

not to be distinguished from the fused color of the disc when no rod

moves before it.”

These items are equally true of the deduction-bands, since a deduction

of a part of one of the components from a fused color must leave an

approximation to the other component. And clearly, too, by as much as

either color is deducted, by so much must the color of the pendulum

itself be added. So that, if the pendulum is like one of the sectors

in color, whenever that sector is hidden the deduction for concealment

will exactly equal the added allowance for the color of the pendulum,

and there will be no bands of the other color distinguishable from the

fused color of the disc.

It is clear from Fig. 7 why a transition-band shades gradually from

one pure-color band over into the other. Let us consider the

transition-band 2-3 (Fig. 7). Next it on the right is a green band, on

the left a red. Now at the right-hand edge of the transition-band it

is seen that the deduction is mostly red and very little green, a

ratio which changes toward the left to one of mostly green and very

little red. Thus, next to the red band the transition-band will be

mostly red, and it will shade continuously over into green on the side

adjacent to the green band.

7. The next observation given (page 175, No. 7) was that, “The bands

are more strikingly visible when the two sectors differ considerably

in luminosity.” This is to be expected, since the greater the

contrast, whether in regard to color, saturation, or intensity,

between the sectors, the greater will be such contrast between the two

deductions, and hence the greater will it be between the resulting

bands. And, therefore, the bands will be more strikingly

distinguishable from each other, that is, ‘visible.’

8. “A broad but slowly-moving rod shows the bands lying over itself.

Other bands can also be seen behind it on the disc.”

In Fig. 9 (Plate V.) are shown the characteristic effects produced by

a broad and slowly-moving rod. Suppose it to be black. It can be so

broad and move so slowly that for a space the characteristic effect is

largely black (Fig. 9 on both sides of x). Specially will this be

true between x and y, for here, while the pendulum contributes no

more photo-chemical unit-effects, it will contribute the newer one,

and howsoever many unit-effects go to make up the characteristic

effect, the newer units are undoubtedly the more potent elements in

determining this effect. The old units have partly faded. One may say

that the newest units are ‘weighted.’

Black will predominate, then, on both sides of x, but specially

between x and y. For a space, then, the characteristic effect will

contain enough black to yield a ‘perception of the rod.’ The width of

this region depends on the width and speed of the rod, but in Fig. 9

it will be roughly coincident with xy, though somewhat behind (to

the left of) it. The characteristic will be either wholly black, as

just at x, or else largely black with the yet contributory

after-images (shown in the triangle aby). Some bands will thus be

seen overlying the rod (1-8), and others lying back of it (9-16).

We have now reviewed all the phenomena so far enumerated of the

illusion-bands, and for every case we have identified these bands with

the bands which must be generated on the retina by the mere

concealment of the rotating sectors by the moving rod. It has been

more feasible thus far to treat these deduction-bands as if possibly

they were other than the bands of the illusion; for although the

former must certainly appear on the retina, yet it was not clear that

the illusion-bands did not involve additional and complicated retinal

or central processes. The showing that the two sets of bands have in

every case identical properties, shows that they are themselves

identical. The illusion-bands are thus explained to be due merely to

the successive concealment of the sectors of the disc as each passes

in turn behind the moving pendulum. The only physiological phenomena

involved in this explanation have been the persistence as after-images

of retinal stimulations, and the summation of these persisting images

into characteristic effects—both familiar phenomena.

From this point on it is permissible to simplify the point of view by

accounting the deduction-bands and the bands of the illusion fully

identified, and by referring to them under either name indifferently.

Figs. 1 to 9, then, are diagrams of the bands which we actually

observe on the rotating disc. We have next briefly to consider a few

special complications produced by a greater breadth or slower movement

of the rod, or by both together. These conditions are called

‘complicating’ not arbitrarily, but because in fact they yield the

bands in confusing form. If the rod is broad, the bands appear to

overlap; and if the rod moves back and forth, at first rapidly but

with decreasing speed, periods of mere confusion occur which defy

description; but the bands of the minor color may be broader or _may

be narrower_ than those of the other color.

VII. FURTHER COMPLICATIONS OF THE ILLUSION.

9. If the rod is broad and moves slowly, the narrower bands are like

colored, not with the broader, as before, but with the narrower

sector.

The conditions are shown in Fig. 9. From 1 to 2 the deduction is

increasingly green, and yet the remainder of the characteristic effect

is also mostly green at 1, decreasingly so to the right, and at 2 is

preponderantly red; and so on to 8; while a like consideration

necessitates bands from x to 16. All the bands are in a sense

transition-bands, but 1-2 will be mostly green, 2-3 mostly red, and so

forth. Clearly the widths of the bands will be here proportional to

the widths of the like-colored sectors, and not as before to the

oppositely colored.

It may reasonably be objected that there should be here no bands at

all, since the same considerations would give an increasingly red band

from B’ to A’, whereas by hypothesis the disc rotates so fast as

to give an entirely uniform color. It is true that when the

characteristic effect is A’ A entire, the fusion-color is so well

established as to assimilate a fresh stimulus of either of the

component colors, without itself being modified. But on the area from

1 to 16 the case is different, for here the fusion-color is less well

established, a part of the essential colored units having been

replaced by black, the color of the rod; and black is no stimulation.

So that the same increment of component color, before ineffective, is

now able to modify the enfeebled fusion-color.

Observation confirms this interpretation, in that band y-1 is not

red, but merely the fusion-color slightly darkened by an increment of

black. Furthermore, if the rod is broad and slow in motion, but white

instead of black, no bands can be seen overlying the rod. For here the

small successive increments which would otherwise produce the bands

1-2, 2-3, etc., have no effect on the remainder of the fusion-color

plus the relatively intense increment of white.

It may be said here that