 |
Again (op. cit., p. 205), these authors say: "It has been already observed that the distance between the bands diminishes as the rotation rate and the rate of movement of the rod increases." But what had been said before is (ibid., p. 203) that 'the bands are separated by smaller and smaller spaces as the rate of movement of the rod becomes slower and slower'; and this is equivalent to saying that the distance between the bands diminishes as the rate of movement of the rod decreases. The statements are contradictory. But there is no doubt as to which is the wrong one—it is the first. What these authors have called 'distance between the bands' has here been shown to be itself a band. Now, no point about this illusion can be more readily observed than that the widths of both kinds of band vary directly with the speed of the rod, inversely, however (as Jastrow and Moorehouse have noted), with the speed of the disc.
Perhaps least satisfactory of all is their statement (ibid., p. 206) that "A brief acquaintance with the illusion sufficed to convince us that its appearance was due to contrast of some form, though the precise nature of this contrast is the most difficult point of all." The present discussion undertakes to explain with considerable minuteness every factor of the illusion, yet the writer does not see how in any essential sense contrast could be said to be involved.
With the other observations of these authors, as that the general effect of an increase in the width of the interrupting rod was to render the illusion less distinct and the bands wider, etc., the observations of the present writer fully coincide. These will systematically be given later, and we may now drop the discussion of this paper.
The only other mention to be found of these resolution-bands is one by Sanford,[2] who says, apparently merely reiterating the results of Jastrow and Moorehouse, that the illusion is probably produced by the sudden appearance, by contrast, of the rod as the lighter sector passes behind it, and by its relative disappearance as the dark sector comes behind. He thus compares the appearance of several rods to the appearance of several dots in intermittent illumination of the strobic wheel. If this were the correct explanation, the bands could not be seen when both sectors were equal in luminosity; for if both were dark, the rod could never appear, and if both were light, it could never disappear. The bands can, however, be seen, as was stated above, when both the sectors are light or both are dark. Furthermore, this explanation would make the bands to be of the same color as the rod. But they are of other colors. Therefore Sanford's explanation cannot be admitted.
[2] Sanford, E.C.: 'A Course in Experimental Psychology,' Boston, 1898, Part I., p. 167.
And finally, the suggestions toward explanation, whether of Sanford, or of Jastrow and Moorehouse, are once for all disproved by the observation that if the moving rod is fairly broad (say three quarters of an inch) and moves slowly, the bands are seen nowhere so well as on the rod itself. One sees the rod vaguely through the bands, as could scarcely happen if the bands were images of the rod, or contrast-effects of the rod against the sectors.
The case when the rod is broad and moves slowly is to be accounted a special case. The following observations, up to No. 8, were made with a narrow rod about five degrees in width (narrower will do), moved by a metronome at less than sixty beats per minute.
III. OUTLINE OF THE FACTS OBSERVED.
A careful study of the illusion yields the following points:
1. If the two sectors of the disc are unequal in arc, the bands are unequal in width, and the narrower bands correspond in color to the larger sector. Equal sectors give equally broad bands.
2. The faster the rod moves, the broader become the bands, but not in like proportions; broad bands widen relatively more than narrow ones; equal bands widen equally. As the bands widen out it necessarily follows that the alternate bands come to be farther apart.
3. The width of the bands increases if the speed of the revolving disc decreases, but varies directly, as was before noted, with the speed of the pendulating rod.
4. Adjacent bands are not sharply separated from each other, the transition from one color to the other being gradual. The sharpest definition is obtained when the rod is very narrow. It is appropriate to name the regions where one band shades over into the next 'transition-bands.' These transition-bands, then, partake of the colors of both the sectors on the disc. It is extremely difficult to distinguish in observation between vagueness of the illusion due to feebleness in the after-image depending on faint illumination, dark-colored discs or lack of the desirable difference in luminosity between the sectors (cf. p. 171) and the indefiniteness which is due to broad transition-bands existing between the (relatively) pure-color bands. Thus much, however, seems certain (Jastrow and Moorehouse have reported the same, op. cit., p. 203): the wider the rod, the wider the transition-bands. It is to be noticed, moreover, that, for rather swift movements of the rod, the bands are more sharply defined if this movement is contrary to that of the disc than if it is in like direction with that of the disc. That is, the transition-bands are broader when rod and disc move in the same, than when in opposite directions.
5. The total number of bands seen (the two colors being alternately arranged and with transition-bands between) 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, as Jastrow and Moorehouse have shown (see above, p. 169), to the time of rotation of the disc; that is, the faster the disc, the more bands. Wherefore, if the bands are broad (No. 2), they extend over a large part of the disc; but if narrow, they cover only a small strip lying immediately behind the rod.
6. The colors of the bands 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 color 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.
7. The bands are more strikingly visible when the two sectors differ considerably in luminosity. But Jastrow's observation, that a difference in luminosity is necessary, could not be confirmed. Rather, on the contrary, sectors of the closest obtainable luminosity still yielded the illusion, although faintly.
8. A broad but slowly moving rod shows the bands overlying itself. Other bands can be seen left behind it on the disc.
9. But a case of a rod which is broad, or slowly-moving, or both, is a special complication which involves several other and seemingly quite contradictory phenomena to those already noted. Since these suffice to show the principles by which the illusion is to be explained, enumeration of the special variations is deferred.
IV. THE GEOMETRICAL RELATIONS BETWEEN THE ROD AND THE SECTORS OF THE DISC.
It should seem that any attempt to explain the illusion-bands ought to begin with a consideration of the purely geometrical relations holding between the slowly-moving rod and the swiftly-revolving disc. First of all, then, it is evident that the rod lies in front of each sector successively.
Let Fig. 1 represent the upper portion of a color-wheel, with center at O, and with equal sectors A and B, in front of which a rod P oscillates to right and left on the same axis as that of the wheel. Let the disc rotate clockwise, and let P be observed in its rightward oscillation. Since the disc moves faster than the rod, the front of the sector A will at some point come up to and pass behind the rod P, say at p^{A}. P now hides a part of A and both are moving in the same direction. Since the disc still moves the faster, the front of A will presently emerge from behind P, then more and more of A will emerge, until finally no part of it is hidden by P. If, now, P were merely a line (having no width) and were not moving, the last of A would emerge just where its front edge had gone behind P, namely at p^{A}. But P has a certain width and a certain rate of motion, so that A will wholly emerge from behind P at some point to the right, say p^{B}. How far to the right this will be depends on the speed and width of A, and on the speed and width of P.
Now, similarly, at p^{B} the sector B has come around and begins to pass behind P. It in turn will emerge at some point to the right, say p^{C}. And so the process will continue. From p^{A} to p^{B} the pendulum covers some part of the sector A; from p^{B} to p^{C} some part of sector B; from p^{C} to P^{D} some part of A again, and so on.
If, now, the eye which watches this process is kept from moving, these relations will be reproduced on the retina. For the retinal area corresponding to the triangle p^{A}Op^{B}, there will be less stimulation from the sector A than there would have been if the pendulum had not partly hidden it. That is, the triangle in question will not be seen of the fused color of A and B, but will lose a part of its A-component. In the same way the triangle p^{B}OpC will lose a part of its B-component; and so on alternately. And by as much as either component is lost, by so much will the color of the intercepting pendulum (in this case, black) be present to make up the deficiency.
We see, then, that the purely geometrical relations of disc and pendulum necessarily involve for vision a certain banded appearance of the area which is swept by the pendulum, if the eye is held at rest. We have now to ask, Are these the bands which we set out to study? Clearly enough these geometrically inevitable bands can be exactly calculated, and their necessary changes formulated for any given change in the speed or width of A, B, or P. If it can be shown that they must always vary just as the bands we set out to study are observed to vary, it will be certain that the bands of the illusion have no other cause than the interception of retinal stimulation by the sectors of the disc, due to the purely geometrical relations between the sectors and the pendulum which hides them.
And exactly this will be found to be the case. The widths of the bands of the illusion depend on the speed and widths of the sectors and of the pendulum used; the colors and intensities of the bands depend on the colors and intensities of the sectors (and of the pendulum); while the total number of bands seen at one time depends on all these factors.
V. GEOMETRICAL DEDUCTION OF THE BANDS.
In the first place, it is to be noted that if the pendulum proceeds from left to right, for instance, before the disc, that portion of the latter which lies in front of the advancing rod will as yet not have been hidden by it, and will therefore be seen of the unmodified, fused color. Only behind the pendulum, where rotating sectors have been hidden, can the bands appear. And this accords with the first observation (p. 167), that "The rod appears to leave behind it on the disc a number of parallel bands." It is as if the rod, as it passes, painted them on the disc.
Clearly the bands are not formed simultaneously, but one after another as the pendulum passes through successive positions. And of course the newest bands are those which lie immediately behind the pendulum. It must now be asked, Why, if these bands are produced successively, are they seen simultaneously? To this, Jastrow and Moorehouse have given the answer, "We are dealing with the phenomena of after-images." The bands persist as after-images while new ones are being generated. The very oldest, however, disappear pari-passu with the generation of the new. We have already seen (p. 169) how well these authors have shown this, in proving that the number of bands seen, multiplied by the rate of rotation of the disc, is a constant bearing some relation to the duration of a retinal image of similar brightness to the bands. It is to be noted now, however, that as soon as the rod has produced a band and passed on, the after-image of that band on the retina is exposed to the same stimulation from the rotating disc as before, that is, is exposed to the fused color; and this would tend to obliterate the after-images. Thus the oldest bands would have to disappear more quickly than an unmolested after-image of the same original brightness. We ought, then, to see somewhat fewer bands than the formula of Jastrow and Moorehouse would indicate. In other words, we should find on applying the formula that the 'duration of the after-image' must be decreased by a small amount before the numerical relations would hold. Since Jastrow and Moorehouse did not determine the relation of the after-image by an independent measurement, their work neither confirms nor refutes this conjecture.
What they failed to emphasize is that the real origin of the bands is not the intermittent appearances of the rod opposite the lighter sector, as they seem to believe, but the successive eclipse by the rod of each sector in turn.
If, in Fig. 2, we have a disc (composed of a green and a red sector) and a pendulum, moving to the right, and if P represents the pendulum at the instant when the green sector AOB is beginning to pass behind it, it follows that some other position farther to the right, as P', will represent the pendulum just as the last part of the sector is passing out from behind it. Some part at least of the sector has been hidden during the entire interval in which the pendulum was passing from P to P'. Clearly the arc BA' measures the band BOA', in which the green stimulation from the sector AOB is thus at least partially suppressed, that is, on which a relatively red band is being produced. If the illusion really depends on the successive eclipse of the sectors by the pendulum, as has been described, it will be possible to express BA', that is, the width of a band, in terms of the widths and rates of movement of the two sectors and of the pendulum. This expression will be an equation, and from this it will be possible to derive the phenomena which the bands of the illusion actually present as the speeds of disc and rod, and the widths of sectors and rod, are varied.
Now in Fig. 2 let the width of the band (i.e., the arc BA') = Z speed of pendulum = r degrees per second; speed of disc = r' degrees per second; width of sector AOB (i.e., the arc AB) = s degrees of arc; width of pendulum (i.e., the arc BC) = p degrees of arc; time in which the pendulum moves from P to P' = t seconds.
Now arc CA' t = ———-; r
but, since in the same time the green sector AOB moves from B to B', we know also that arc BB' t = ———-; r' then arc CA' arc BB' ———- = ———-, r r'
or, omitting the word "arc" and clearing of fractions,
r'(CA') = r(BB'). But now CA' = BA' - BC, while BA' = Z and BC = p; therefore CA' = Z-p. Similarly BB' = BA' + A'B' = Z + s.
Substituting for CA' and BB' their values, we get
r'(Z-p) = r(Z+s), or Z(r' - r) = rs + pr', or Z = rs + pr' / r' - r.
It is to be remembered that s is the width of the sector which undergoes eclipse, and that it is the color of that same sector which is subtracted from the band Z in question. Therefore, whether Z represents a green or a red band, s of the formula must refer to the oppositely colored sector, i.e., the one which is at that time being hidden.
We have now to take cognizance of an item thus far neglected. When the green sector has reached the position A'B', that is, is just emerging wholly from behind the pendulum, the front of the red sector must already be in eclipse. The generation of a green band (red sector in eclipse) will have commenced somewhat before the generation of the red band (green sector in eclipse) has ended. For a moment the pendulum will lie over parts of both sectors, and while the red band ends at point A', the green band will have already commenced at a point somewhat to the left (and, indeed, to the left by a trifle more than the width of the pendulum). In other words, the two bands overlap.
This area of overlapping may itself be accounted a band, since here the pendulum hides partly red and partly green, and obviously the result for sensation will not be the same as for those areas where red or green alone is hidden. We may call the overlapped area a 'transition-band,' and we must then ask if it corresponds to the 'transition-bands' spoken of in the observations.
Now the formula obtained for Z includes two such transition-bands, one generated in the vicinity of OB and one near OA'. To find the formula for a band produced while the pendulum conceals solely one, the oppositely colored sector (we may call this a 'pure-color' band and let its width = W), we must find the formula for the width (w) of a transition-band, multiply it by two, and subtract the product from the value for Z already found.
The formula for an overlapping or transition-band can be readily found by considering it to be a band formed by the passage behind P of a sector whose width is zero. Thus if, in the expression for Z already found, we substitute zero for s, we shall get w; that is,
o + pr' pr' w = ———- = ——— r' - r r' - r Since W = Z - 2w, we have rs + pr' pr' W = ———— = 2 ———, r' - r r' - r or rs - pr' W = ———— (1) r' - r
Fig. 3 shows how to derive W directly (as Z was derived) from the geometrical relations of pendulum and sectors. Let r, r', s, p, and t, be as before, but now let
width of the band (i.e., the arc BA') = W;
that is, the band, instead of extending as before from where P begins to hide the green sector to where P ceases to hide the same, is now to extend from the point at which P ceases to hide any part of the red sector to the point where it just commences again to hide the same.
Then W + p t = ———- , r and W + s t = ———- , r'
therefore W + p W + s ———- = ———- , r r'
r'(W + p) = r(W + s) ,
W (r' - r) = rs - pr' , and, again, rs - pr' W = ———— . r' - r
Before asking if this pure-color band W can be identified with the bands observed in the illusion, we have to remember that the value which we have found for W is true only if disc and pendulum are moving in the same direction; whereas the illusion-bands are observed indifferently as disc and pendulum move in the same or in opposite directions. Nor is any difference in their width easily observable in the two cases, although it is to be borne in mind that there may be a difference too small to be noticed unless some measuring device is used.
From Fig. 4 we can find the width of a pure-color band (W) when pendulum and disc move in opposite directions. The letters are used as in the preceding case, and W will include no transition-band.
We have
W + p t = ——-, r and s - W t = ——-, r'
r'(W + p) = r(s - W) ,
W(r' + r) = rs - pr' ,
rs - pr' W = ———— . (2) r' + r
Now when pendulum and disc move in the same direction,
rs - pr' W = ————- , (1) r' - r
so that to include both cases we may say that
rs - pr' W = ———— . (3) r' +- r
The width (W) of the transition-bands can be found, similarly, from the geometrical relations between pendulum and disc, as shown in Figs. 5 and 6. In Fig. 5 rod and disc are moving in the same direction, and
w = BB'.
Now W - p t = ———- , r'
w t = —- , r'
r'(w-p) = rw ,
w(r'-r) = pr' ,
pr' w = ———- . (4) r'-r
In Fig. 6 rod and disc are moving in opposite directions, and
w = BB',
p - w t = ———- , r
w t = —- , r'
r'(p - w) = rw ,
w(r' + r) = pr' ,
pr' w = ———— . r' + r (5)
So that to include both cases (of movement in the same or in opposite directions), we have that
pr' w = ———— . r' +- r (6)
VI. APPLICATION OF THE FORMULAS TO THE BANDS OF THE ILLUSION.
Will these formulas, now, explain the phenomena which the bands of the illusion actually present in respect to their width?
1. The first phenomenon noticed (p. 173, No. 1) is that "If the two sectors of the disc are unequal in arc, the bands are unequal in width; and the narrower bands correspond in color to the larger sector. Equal sectors give equally broad bands."
In formula 3, W represents the width of a band, and s the width of the oppositely colored sector. Therefore, if a disc is composed, for example, of a red and a green sector, then
rs(green) - pr' W(red) = ————————— , r' +- r and rs(red) - pr' W(green) = ————————— , r' +- r
therefore, by dividing,
W(red) rs(green) - pr' ————- = —————————- . W(green) rs(red) - pr'
From this last equation it is clear that unless s(green) = s(red), W(red) cannot equal W(green). That is, if the two sectors are unequal in width, the bands are also unequal. This was the first feature of the illusion above noted.
Again, if one sector is larger, the oppositely colored bands will be larger, that is, the light-colored bands will be narrower; or, in other words, 'the narrower bands correspond in color to the larger sector.'
Finally, if the sectors are equal, the bands must also be equal.
So far, then, the bands geometrically deduced present the same variations as the bands observed in the illusion.
2. Secondly (p. 174, No. 2), "The faster the rod moves the broader become the bands, but not in like proportions; broad bands widen relatively more than narrow ones." The speed of the rod or pendulum, in degrees per second, equals _r_. Now if _W_ increases when _r_ increases, _D_{[tau]}W_ must be positive or greater than zero for all values of _r_ which lie in question.
Now rs - pr' W = ————- , r' +- r and (r' +- r)s [+-] (rs - pr') D_{[tau]}W = ————————————— , (r +- r')
or reduced, r'(s +- p) = —————- (r' +- r) squared
Since r' (the speed of the disc) is always positive, and s is always greater than p (cf. p. 173), and since the denominator is a square and therefore positive, it follows that
D_{[tau]}W > 0
or that W increases if r increases.
Furthermore, if W is a wide band, s is the wider sector. The rate of increase of W as r increases is
r'(s +- p) D_{[tau]}W = —————- (r' +- r) squared
which is larger if s is larger (s and r being always positive). That is, as r increases, 'broad bands widen relatively more than narrow ones.'
3. Thirdly (p. 174, No. 3), "The width of The bands increases if the speed of the revolving disc decreases." This speed is r'. That the observed fact is equally true of the geometrical bands is clear from inspection, since in
rs - pr' W = ————- , r' +- r
as r' decreases, the denominator of the right-hand member decreases while the numerator increases.
4. We now come to the transition-bands, where one color shades over into the other. It was observed (p. 174, No. 4) that, "These partake of the colors of both the sectors on the disc. The wider the rod the wider the transition-bands."
We have already seen (p. 180) that at intervals the pendulum conceals a portion of both the sectors, so that at those points the color of the band will be found not by deducting either color alone from the fused color, but by deducting a small amount of both colors in definite proportions. The locus of the positions where both colors are to be thus deducted we have provisionally called (in the geometrical section) 'transition-bands.' Just as for pure-color bands, this locus is a radial sector, and we have found its width to be (formula 6, p. 184) pr' W = ————- , r' +- r
Now, are these bands of bi-color deduction identical with the transition-bands observed in the illusion? Since the total concealing capacity of the pendulum for any given speed is fixed, less of either color can be deducted for a transition-band than is deducted of one color for a pure-color band. Therefore, a transition-band will never be so different from the original fusion-color as will either 'pure-color' band; that is, compared with the pure color-bands, the transition-bands will 'partake of the colors of both the sectors on the disc.' Since pr' W = ————- , r' +- r
it is clear that an increase of p will give an increase of w; i.e., 'the wider the rod, the wider the transition-bands.'
Since r is the rate of the rod and is always less than r', the more rapidly the rod moves, the wider will be the transition-bands when rod and disc move in the same direction, that is, when
pr' W = ————- , r' - r
But the contrary will be true when they move in opposite directions, for then
pr' W = ————- , r' + r
that is, the larger r is, the narrower is w.
The present writer could not be sure whether or not the width of transition-bands varied with r. He did observe, however (page 174) that 'the transition-bands are broader when rod and disc move in the same, than when in opposite directions.' This will be true likewise for the geometrical bands, for, whatever r (up to and including r = r'),
pr' pr' —— > —— r'-r r'+r
In the observation, of course, r, the rate of the rod, was never so large as r', the rate of the disc.
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 deg., and B'C' a red complementary sector of 270 deg.. 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
green 10[sigma], red 30[sigma], green 10[sigma], red 30[sigma], etc.
Now a certain number of these stimulations which immediately precede M will determine the characteristic effect, the fusion color, for the point A' at the moment M. We do not know the number of unit-stimulations which contribute to this characteristic effect, nor do we need to, but it will be a constant, and can be represented by a distance x = A'A above the line A'C'. Then A'A will represent the total stimulus which determines the characteristic effect at A'. Stimuli earlier than A are no longer represented in the after-image. AC is parallel to A'C', and the characteristic effect for any point is found by drawing the perpendicular at that point between the two lines A'C and AC.
Just as the movement of the disc, so can that of the concealing pendulum be represented. The only difference is that the pendulum is narrower, and moves more slowly. The slower rate is represented by a steeper locus-band, PP', than those of the swifter sectors.
We are now able to consider geometrically deduced bands as 'characteristic effects,' and we have a graphic representation of the color-deduction determined by the interception of the pendulum. The deduction-value of the pendulum is the distance (xy) which it intercepts on a line drawn perpendicular to A'C'.
Lines drawn perpendicular to A'C' through the points of intersection of the locus-band of the pendulum with those of the sectors will give a 'plot' on A'C' of the deduction-bands. Thus from 1 to 2 the deduction is red and the band green; from 2 to 3 the deduction is decreasingly red and increasingly green, a transition-band; from 3 to 4 the deduction is green and the band red; and so forth.
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."
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 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 the bands 1-2, 2-3, etc., are less intense than the bands x-9, 9-10, etc., because there the recent or weighted unit-effects are black, while here they are the respective colors. Also the bands grow dimmer from x-9 to 15-16, that is, as they become older, for the small increment of one color which would give band 15-16 is almost wholly overridden by the larger and fresher mass of stimulation which makes for mere fusion. This last is true of the bands always, whatever the rate or width of the rod.
10. In general, equal sectors give equal bands, but if one sector is considerably more intense than the other, the bands of the brighter color will, for a broad and swiftly-moving rod, be the broader. The brighter sector, though equal in width to the other, contributes more toward determining the fusion-color; and this fact is represented by an intrusion of the stronger color into the transition-bands, at the expense of the weaker. For in these, even the decreased amount of the stronger color, on the side next a strong-color band, is yet more potent than the increased amount of the feebler color. In order to observe this fact one must have the rod broad, so as to give a broad transition-band on which the encroachment of the stronger color may be evident. The process is the same with a narrow rod and narrow transition-bands, but, being more limited in extent, it is less easily observed. The rod must also move rapidly, for otherwise the bands overlap and become obscure, as will be seen in the next paragraph.
11. If the disc consists of a broad and narrow sector, and if the rod is broad and moves at first rapidly but more slowly with each new stroke, there are seen at first broad, faint bands of the minority-color, and narrow bands of the majority-color. The former grow continuously more intense as the rod moves more slowly, and grow narrower in width down to zero; whereupon the other bands seem to overlap, the overlapped part being doubly deep in color, while the non-overlapped part has come to be more nearly the color of the minor sector. The overlapped portion grows in width. As the rate of the rod now further decreases, a confused state ensues which cannot be described. When, finally, the rod is moving very slowly, the phenomena described above in paragraph 9 occur.
The successive changes in appearance as the rod moves more and more slowly, are due to the factors previously mentioned, and to one other which follows necessarily from the given conditions but has not yet been considered. This is the last new principle in the illusion which we shall have to take up. Just as the transition-bands are regions where two pure-color bands overlap, so, when the rod is broad and moves slowly, other overlappings occur to produce more complicated arrangements.
These can be more compactly shown by diagram than by words. Fig. 10, a, b and c (Plate VI.), show successively slower speeds of the rod, while all the other factors are the same. In practice the tendency is to perceive the transition-bands as parts of the broad faint band of the minor color, which lies between them. It can be seen, then, how the narrow major-color bands grow only slightly wider (Fig. 10, a, b) until they overlap (c); how the broad minor-color bands grow very narrow and more intense in color, there being always more of the major color deducted (in b they are reduced exactly to zero, z, z, z). In c the major-color bands overlap (o, o, o) to give a narrow but doubly intense major-color band since, although with one major, two minor locus-bands are deducted. The other bands also overlap to give complicated combinations between the o-bands. These mixed bands will be, in part at least, minor-color bands (q, q, q), since, although a minor locus-band is here deducted, yet nearly two major locus-bands are also taken, leaving the minor color to predominate. This corresponds with the observation above, that, '... the non-overlapped part has come to be more nearly the color of the minor sector.'
A slightly slower speed of the rod would give an irreducible confusion of bands, since the order in which they overlap becomes very complicated. Finally, when the rod comes to move very slowly, as in Fig. 9, the appearance suffers no further change, except for a gradual narrowing of all the bands, up to the moment when the rod comes to rest.
It is clear that this last principle adduced, of the multiple overlapping of bands when the rod is broad and moves slowly, can give for varying speeds of the rod the greatest variety of combinations of the bands. Among these is to be included that of no bands at all, as will be understood from Fig. 11 (Plate VII). And in fact, a little practice will enable the observer so to adjust the rate of the (broad) rod to that of the disc that no bands are observable. But care must be taken here that the eye is rigidly fixated and not attracted into movement by the rod, since of course if the eye moves with the rod, no bands can be seen, whatever the rate of movement may be.
Thus, all the phenomena of these illusion-bands have been explained as the result solely of the hiding by the rod of successive sectors of the disc. The only physiological principles involved are those (1) of the duration of after-images, and (2) of their summation into a characteristic effect. It may have seemed to the reader tedious and unnecessary so minutely to study the bands, especially the details last mentioned; yet it was necessary to show how all the possible observable phenomena arise from the purely geometrical fact that sectors are successively hidden. Otherwise the assertions of previous students of the illusion, that more intricate physiological processes are involved, could not have been refuted. The present writer does not assert that no processes like contrast, induction, etc., come into play to modify somewhat the saturation, etc., of the colors in the bands. It must be here as in every other case of vision. But it is now demonstrated that these remoter physiological processes contribute nothing essential to the illusion. For these could be dispensed with and the illusion would still remain.
If any reader still suspects that more is involved than the persistence of after-images, and their summation into a characteristic effect, he will find it interesting to study the illusion with a camera. The 'physiological' functions referred to belong as well to the dry-plate as to the retina, while the former exhibits, presumably, neither contrast nor induction. The illusion-bands can be easily photographed in a strong light, if white and black sectors are used in place of colored ones. It is best to arrange the other variable factors so as to make the transition-bands as narrow as possible (p. 174, No. 4). The writer has two negatives which show the bands very well, although so delicately that it is not feasible to try to reproduce them.
VIII. SOME CONVENIENT DEVICES FOR EXHIBITING THE ILLUSION.
The influence of the width of sector is prettily shown by a special disc like that shown in Fig. 12 (Plate VII.), where the colors are dark-red and light-green, the shaded being the darker sector. A narrow rod passed before such a disc by hand at a moderate rate will give over the outer ring equally wide green and red bands; but on the inner rings the red bands grow narrower, the green broader.
The fact that the bands are not 'images of the rod' can be shown by another disc (Fig. 13, Plate VII.). In all three rings the lighter (green) sector is 60 deg. wide, but disposed on the disc as shown. The bands are broken into zigzags. The parts over the outer ring lag behind those over the middle, and these behind those over the inner ring—'behind,' that is, farther behind the rod.
Another effective variation is to use rods alike in color with one or the other of the sectors. Here it is clear that when the rod hides the oppositely-colored sector, the deduction of that color is replaced (not by black, as happens if the rod is black) but by the very color which is already characteristic of that band. But when the rod hides the sector of its own color, the deduction is replaced by the very same color. Thus, bands like colored with the rod gain in depth of tone, while the other pure-color bands present simply the fusion-color.
IX. A STROBOSCOPE WHICH DEPENDS ON THE SAME PRINCIPLE.
If one produce the illusion by using for rod, not the pendulum of a metronome, but a black cardboard sector on a second color-mixer placed in front of the first and rotating concentrically with it, that is, with the color-disc, one will observe with the higher speeds of the rod which are now obtainable several further phenomena, all of which follow simply from the geometrical relations of disc and rod (now a rotating sector), as discussed above. The color-mixer in front, which bears the sector (let it still be called a 'rod'), should rotate by hand and independently of the disc behind, whose two sectors are to give the bands. The sectors of the disc should now be equal, and the rod needs to be broader than before, say 50 deg. or 60 deg., since it is to revolve very rapidly.
First, let the rod and disc rotate in the same direction, the disc at its former rate, while the rod begins slowly and moves faster and faster. At first there is a confused appearance of vague, radial shadows shuffling to and fro. This is because the rod is broad and moves slowly (cf. p. 196, paragraph II).
As the velocity of the rod increases, a moment will come when the confusing shadows will resolve themselves into four (sometimes five) radial bands of one color with four of the other color and the appropriate transition-bands between them. The bands of either color are symmetrically disposed over the disc, that is, they lie at right angles to one another (if there are five bands they lie at angles of 72 deg., etc.). But this entire system of bands, instead of lying motionless over the disc as did the systems hitherto described, itself rotates rapidly in the opposite direction from disc to rod. As the rod rotates forward yet faster, no change is seen except that the system of bands moves backward more and more slowly. Thus, if one rotate the rod with one's own hand, one has the feeling that the backward movement of the bands is an inverse function of the increase in velocity of the rod. And, indeed, as this velocity still increases, the bands gradually come to rest, although both the disc and the rod are rotating rapidly.
But the system of bands is at rest for only a particular rate of the rod. As the latter rotates yet faster, the system of bands now commences to rotate slowly forward (with the disc and rod), then more and more rapidly (the velocity of the rod still increasing), until it finally disintegrates and the bands vanish into the confused flicker of shadows with which the phenomenon commenced.
This cycle now plays itself off in the reverse order if the speed of the rod is allowed gradually to decrease. The bands appear first moving forward, then more slowly till they come to rest, then moving backward until finally they relapse into confusion.
But let the rate of the rod be not decreased but always steadily increased. The bands will reappear, this time three of each color with six transition-bands. As before, the system at first rotates backward, then lies still, and then moves forward until it is dissolved. As the rod moves still faster, another system appears, two bands of each color forming a diameter and the two diameters lying at right angles. This system goes through the same cycle of movements. When the increased velocity of the rod destroys this system, another appears having one band of each color, the two lying on opposite sides of the center. The system goes through the same phases and is likewise dissolved. Now, at this point the rod will be found to be rotating at the same speed as the disc itself.
The explanation of the phenomenon is simple. The bands are not produced by a single interruption of the vision of a sector by a rod, but each band is made up of successive superpositions on the retina of many such single-interruption bands. The overlapping of bands has been already described (cf. Fig. 10 and pp. 196-198); superposition depends of course on the same principle.
At the moment when a system of four bands of either color is seen at rest, the rod is moving just one fifth as rapidly as the disc; so that, while the rod goes once around, either sector, say the green one, will have passed behind it exactly four times, and at points which lie 90 deg. apart. Thus, four red bands are produced which lie at right angles to one another. But the disc is revolving at least 24 times in a second, the rod therefore at least 4.8 times, so that within the interval of time during which successive stimuli still contribute to the characteristic effect the rod will have revolved several times, and with each revolution four red bands at right angles to one another will have been formed. And if the rod is moving exactly one fifth as fast as the disc, each new band will be generated at exactly that position on the disc where was the corresponding band of the preceding four. The system of bands thus appear motionless on the disc.
The movement of the system arises when the rate of the rod is slightly less or more than one fifth that of the disc. If slightly less, the bands formed at each rotation of the rod do not lie precisely over those of the previous rotation, but a little to the rear of them. The new set still lies mostly superposed on the previous sets, and so fuses into a regular appearance of bands, but, since each new increment lags a bit behind, the entire system appears to rotate backward. The apparatus is actually a cinematograph, but one which gives so many pictures in the second that they entirely fuse and the strobic movement has no trace of discontinuity.
If the rod moves a trifle more than one fifth as fast as the disc, it is clear that the system of bands will rotate forward, since each new set of bands will lie slightly ahead of the old ones with which it fuses. The farther the ratio between the rates of rod and disc departs from exactly 1:5, whether less or greater, the more rapid will the strobic movement, backward or forward, be; until finally the divergence is too great, the newly forming bands lie too far ahead or behind those already formed to fuse with them and so be apperceived as one system, and so the bands are lost in confusion. Thus the cycle of movement as observed on the disc is explained. As the rate of the rod comes up to and passes one fifth that of the disc, the system of four bands of each color forms in rapid backward rotation. Its movement grows slower and slower, it comes to rest, then begins to whirl forward, faster and faster, till it breaks up again.
The same thing happens as the rate of the rod reaches and exceeds just one fourth that of the disc. The system contains three bands of each color. The system of two bands of each color corresponds to the ratio 1:3 between the rates, while one band of each color (the two lying opposite) corresponds to the ratio 1:2.
If the rod and the disc rotate in opposite directions, the phenomena are changed only in so far as the changed geometrical relations require. For the ratio 1:3 between the two rates, the strobic system has four bands of each color; for 1:2, three bands of each color; while when the two rates are equal, there are two bands of each color, forming a diameter. As would be expected from the geometrical conditions, a system of one band of each color cannot be generated when rod and disc have opposite motions. For of course the rod cannot now hide two or more times in succession a sector at any given point, without hiding the same sector just as often at the opposite point, 180 deg. away. Here, too, the cycle of strobic movements is different. It is reversed. Let the disc be said to rotate forward, then if the rate of the rod is slightly less than one fourth, etc., that of the disc, the system will rotate forward; if greater, it will rotate backward. So that as the rate of the rod increases, any system on its appearance will move forward, then stand still, and lastly rotate backward. The reason for this will be seen from an instant's consideration of where the rod will hide a given sector.
It is clear that if, instead of using as 'rod' a single radial sector, one were to rotate two or more such sectors disposed at equal angular intervals about the axis, one would have the same strobic phenomena, although they would be more complicated. Indeed, a large number of rather narrow sectors can be used or, what is the same thing, a second disc with a row of holes at equal intervals about the circumference. The disc used by the writer had a radius of 11 inches, and a concentric ring of 64 holes, each 3/8 of an inch in diameter, lying 10 inches from the center. The observer looks through these holes at the color-disc behind. The two discs need not be placed concentrically.
When produced in this way, the strobic illusion is exceedingly pretty. Instead of straight, radial bands, one sees a number of brightly colored balls lying within a curving band of the other color and whirling backward or forward, or sometimes standing still. Then these break up and another set forms, perhaps with the two colors changed about, and this then oscillates one way or the other. A rainbow disc substituted for the disc of two sectors gives an indescribably complicated and brilliant effect; but the front disc must rotate more slowly. This disc should in any case be geared for high speeds and should be turned by hand for the sake of variations in rate, and consequently in the strobic movement.
It has been seen that this stroboscope is not different in principle from the illusion of the resolution-bands which this paper has aimed to explain. The resolution-bands depend wholly on the purely geometrical relations between the rod and the disc, whereby as both move the rod hides one sector after the other. The only physiological principles involved are the familiar processes by which stimulations produce after-images, and by which the after-images of rapidly succeeding stimulations are summed, a certain number at a time, into a characteristic effect.
* * * * *
STUDIES IN MEMORY.
* * * * *
RECALL OF WORDS, OBJECTS AND MOVEMENTS.
BY HARVEY A. PETERSON.
Kirkpatrick,[1] in experimenting with 379 school children and college students, found that 3-1/3 times as many objects were recalled as visual words after an interval of three days. The experiment consisted in showing successively 10 written names of common objects in the one case and 10 objects in the other at the rate of one every two seconds. Three days later the persons were asked to recall as many of each series as possible, putting all of one series together. The averages thus obtained were 1.89 words, 6.29 objects. The children were not more dependent on the objects than the college students.
[1] Kirkpatrick, E.A.: PSYCHOLOGICAL, REVIEW, 1894, Vol. I., p. 602.
Since the experiment just described was performed without laboratory facilities, Calkins[2] repeated it with 50 college women, substituting lantern pictures for objects. She obtained in recall, after two days, the averages 4.82 words, 7.45 pictures. The figures, however, are the number of objects or words remembered out of ten, not necessarily correctly placed. Kirkpatrick's corresponding figures for college women were 3.22 words, 5.44 objects. The two experiments substantially agree, Calkins' higher averages being probably due to the shortening of the interval to two days.
[2] Calkins, M.W.: PSYCHOLOGICAL, REVIEW, 1898, Vol. V., p. 451.
Assuming, thus, that objects are better remembered than names in deferred recall, the question arises whether this holds true when the objects and names are coupled with strange and arbitrary symbols—a question which is clearly of great practical interest from the educational point of view, as it is involved in the pedagogical problem whether a person seeking to acquire the vocabulary of a foreign language ought to connect the foreign words with the familiar words or with the objects themselves. And the further question arises: what are the facts in the case of movements instead of objects, and correspondingly in that of verbs instead of nouns. Both questions are the problems of the following investigation.
As foreign symbols, either the two-figure numbers were used or nonsense-words of regularly varying length. As familiar material, nouns, objects, verbs and movements were used. The words were always concrete, not abstract, by which it is meant that their meaning was capable of demonstration to the senses. With the exception of a few later specified series they were monosyllabic words. The nouns might denote objects of any size perceptible to the eye; the objects, however, were all of such a size that they could be shown through a 14x12 cm. aperture and still leave a margin. Their size was therefore limited.
Concerning the verbs and movements it is evident that, while still being concrete, they might be simple or complicated activities consuming little or much time, and further, might be movements of parts of the body merely, or movements employing other objects as well. In this experiment complicated activities were avoided even in the verb series. Simple activities which could be easily and quickly imaged or made were better for the purpose in view.
THE A SET.
The A set contained sixteen series, A^{1}, A^{2}, A^{3}, etc., to A^{16}. They were divided as follows:
Numbers and nouns: A^{1}, A^{5}, A^{9}, A^{13}. Numbers and objects: A^{2}, A^{6}, A^{10}, A^{14}. Numbers and verbs: A^{3}, A^{7}, A^{11}, A^{15}. Numbers and movements: A^{4}, A^{8}, A^{12}, A^{16}.
The first week A^{1-4} were given, the second week A^{5-8}, etc., so that each week one series of each of the four types was given the subject.
In place of foreign symbols the numbers from 1 to 99 were used, except in A^{13-15}, in which three-figure numbers were used.
Each series contained seven couplets, except A^{13-16}, which, on account of the greater difficulty of three-figure numbers, contained five. Each couplet was composed of a number and a noun, object, verb, or movement.
Certain rules were observed in the composition of the series. Since the test was for permanence, to avoid confusion no number was used in more than one couplet. No two numbers of a given series were chosen from the same decade or contained identical final figures. No word was used in more than one couplet. Their vowels, and initial and final consonants were so varied within a single series as to eliminate phonetic aids, viz., alliteration, rhyme, and assonance. The kind of assonance avoided was identity of final sounded consonants in successive words, e.g., lane, vine.
The series were composed in the following manner: After the twenty-eight numbers for four series had been chosen, the words which entered a given series were selected one from each of a number of lists of words. These lists were words of like-sounded vowels. After one word had been chosen from each list, another was taken from the first list, etc. As a consequence of observing the rules by which alliteration, rhyme, and assonance were eliminated, the words of a series usually represented unlike categories of thought, but where two words naturally tended to suggest each other one of them was rejected and the next eligible word in the same column was chosen. The following is a typical series from the A set.
A^{1}. Numbers and Nouns.
19 42 87 74 11 63 38 desk girl pond muff lane hoop vine
The apparatus used in the A set and also in all the later sets may be described as follows: Across the length of a table ran a large, black cardboard screen in the center of which was an oblong aperture 14 cm. high and 12 cm. wide. The center of the aperture was on a level with the eyes of the subject, who sat at the table. The aperture was opened and closed by a pneumatic shutter fastened to the back of the screen. This shutter consisted of two doors of black cardboard sliding to either side. By means of a large bulb the length of exposure could be regulated by the operator, who stood behind the table.
The series—consisting of cards 4x21/2 cm., each containing a printed couplet—was carried on a car which moved on a track behind and slightly below the aperture. The car was a horizontal board 150 cm. long and 15 cm. wide, fixed on two four-wheeled trucks. It was divided by vertical partitions of black cardboard into ten compartments, each slightly wider than the aperture to correspond with the visual angle. A curtain fastened to the back of the car afforded a black background to the compartments. The couplets were supported by being inserted into a groove running the length of the car, 3 cm. from the front. A shutter 2 cm. high also running the length of the car in front of the groove, fastened by hinges whose free arms were extensible, concealed either the upper or the lower halves of the cards at the will of the operator; i.e., either the foreign symbols or the words, respectively. A screen 15 cm. high and the same length as the car, sliding in vertical grooves just behind the cards and in front of the vertical partitions, shut off the objects when desired, leaving only the cards in view. Thus the apparatus could be used for all four types of series.
The method of presentation and the time conditions of the A set were as follows:—A metronome beating seconds was used. It was kept in a sound-proof box and its loudness was therefore under control. It was just clearly audible to both operator and subject. In learning, each couplet was exposed 3 secs., during about 2 secs. of which the shutter was fully open and motionless. During this time the subject read the couplet inaudibly as often as he wished, but usually in time with the metronome. His object was to associate the terms of the couplet. There was an interval of 2 secs. after the exposure of each couplet, and this was required to be filled with repetition of only the immediately preceding couplet. After the series had been presented once there was an interval of 2 secs. additional, then a second presentation of it commenced and after that a third. At the completion of the third presentation there was an interval of 6 secs. additional instead of the 2, at the expiration of which the test commenced.
A^{13-16} had five presentations instead of three. The test consisted in showing the subject either the numbers or the words in altered order and requiring him to write as many of the absent terms as he could. In the object and movement series the objects were also shown and the movements repeated by the subject if words were the given terms. The time conditions in the test were,
Exposure of a term 3 secs. Post-term interval in A^{1-12} 4 secs. Post-term interval in A^{13-16} 6 secs.
This allowed the subject 7 secs. for recalling and writing each term in A^{1-12} and 9 sec. in A^{13-16}. If a word was recalled after that time it was inserted, but no further insertions were made after the test of a series had been completed. An interval of 3 min. elapsed between the end of the test of one series and the beginning of the next series, during which the subject recorded the English word of any couplet in which an indirect association had occurred, and also his success in obtaining visual images if the series was a noun or a verb series.
As already indicated, four series—a noun, an object, a verb, and a movement series—given within a half hour, constituted a day's work throughout the year. Thus variations due to changes in the physiological condition of the subject had to affect all four types of series.
Two days later these series were tested for permanence, and in the same way as the tests for immediate recall, with this exception:
Post-term interval in A^{13-16} 8 secs.
Thus 11 secs. were allowed for the deferred recall of each term in A^{13-16}.
In the movement series of this set, to avoid hesitation and confusion, the operator demonstrated to the subject immediately before the series began, once for each word, how the movements were to be made.
The A set was given to three subjects. The results of each subject are arranged separately in the following table. In the tests the words were required in A^{1-4}, in A^{5-16} the numbers. The figures show the number of terms correctly recalled out of seven couplets in A^{1-12} and out of five couplets in A^{13-16}, exclusive of indirect association couplets. The figures in brackets indicate the number of correctly recalled couplets per series in which indirect associations occurred. The total number correctly recalled in any series is their sum. The figures in the per cent. row give the percentage of correctly recalled couplets left after discarding both from the number recalled and from the total number of couplets given those in which indirect associations occurred. This simply diminished the subject's number of chances. A discussion of the propriety of this elimination will be found later. In A^{1-12} the absent terms had to be recalled exactly in order, to be correct, but in A^{13-16}, on account of the greater difficulty of the three-place numbers, any were considered correct when two of the three figures were recalled, or when all three figures were correct but two were reversed in position, e.g., 532 instead of 523. N means noun series, O object, V verb, and M movement series. Series A^{1}, A^{5}, A^{9}, A^{13} are to be found in the first and third columns, A^{2}, A^{6}, A^{10}, A^{14} in the second and fourth, A^{3}, A^{7}, A^{11}, A^{15}, in the fifth and seventh, and A^{4}, A^{8}, A^{12}, A^{16} in the sixth and eighth columns.
TABLE I.
SHOWING IMMEDIATE RECALL AND RECALL AFTER TWO DAYS.
M. Series. Im. Rec. Two Days. Im. Rec. Two Days. N. O. N. O. V. M. V. M. A^{1-4} 6 7 3 1 6 7 2 1 A^{5-8} 5(1) 6 3(1) 6 6(1) 7 5(1) 6 A^{9-12} 7 7 4 6 7 6(1) 7 6(1) A^{13-16} 4 5 2 2 5 3 2 2 Total. 22(1) 25 12(1) 15 24(1) 23(1) 16(1) 15(1) Per cent. 88 96 48 58 96 92 64 66
S. Series. Im. Rec. Two Days. Im. Rec. Two Days. N. O. N. O. V. M. V. M. A^{1-4} 6(1) 6 0 0 7 7 0 0 A^{5-8} 6 7 1 3 6 7 0 3 A^{9-12} 7 6 2 2 5 7 0 0 A^{13-16} 5 5 0 0 5 5 3 0 Total. 24(1) 24 3 5 23 26 3 3 Per cent. 96 92 12 19 88 100 12 12
Hu. Series. Im. Rec. Two Days. Im. Rec. Two Days. N. O. N. O. V. M. V. M. A^{1-4} 6 7 0 1 5 6(1) 0 2 A^{5-8} 5(2) 7 1(2) 1 7 7 1 0 A^{9-12} 6(1) 7 2 2 6 7 0 5 A^{13-16} 4(1) 4(1) 0 2 5 5 0 1 Total. 21(4) 25(1) 3(2) 6 23 25(1) 1 8 Per cent. 95 100 14 24 88 100 4 32
These results will be included in the discussion of the results of the B set.
THE B SET.
A new material was needed for foreign symbols. After considerable experimentation nonsense words were found to be the best adapted for our purpose. The reasons for this are their regularly varying length and their comparative freedom from indirect associations. An objection to using nonsense syllables in any work dealing with the permanence of memory is their sameness. On this account they are not remembered long. To secure a longer retention of the material, nonsense words were devised in substantially the same manner as that in which Mueller and Schumann made nonsense syllables, except that these varied regularly in length from four to six letters. Thus the number of letters, not the number of syllables was the criterion of variation, though of course irregular variation in the number of syllables was a necessary consequence.
When the nonsense words were used it was found that far fewer indirect associations occurred than with nonsense syllables. By indirect association I mean the association of a foreign symbol and its word by means of a third term suggested to the subject by either of the others and connected at least in his experience with both. Usually this third term is a word phonetically similar to the foreign symbol and ideationally suggestive of the word to be associated. It is a very common form of mnemonic in language material. The following are examples:
cax, stone (Caxton); teg, bib (get bib); laj, girl (large girl); xug, pond (noise heard from a pond); gan, mud (gander mud).
For both of these reasons nonsense words were the material used as foreign symbols in the B set.
The nonsense words were composed in the following manner. From a box containing four of each of the vowels and two of each of the consonants the letters were chosen by chance for a four-letter, a five-letter, and a six-letter word in turn. The letters were then returned to the box, mixed, and three more words were composed. At the completion of a set of twelve any which were not readily pronounceable or were words or noticeably suggested words were rejected and others composed in their places.
The series of the B set were four couplets long. Each series contained one three-letter, one four-letter, one five-letter, and one six-letter nonsense word. The position in the series occupied by each kind was constantly varied. In all other respects the same principles were followed in constructing the B set as were observed in the A set with the following substitutions:
No two foreign symbols of a series and no two terms of a couplet contained the same sounded vowel in accented syllables.
The rule for the avoidance of alliteration, rhyme, and assonance was extended to the foreign symbols, and to the two terms of a couplet.
The English pronounciation was used in the nonsense words. The subjects were not informed what the nonsense words were. They were called foreign words.
Free body movements were used in the movement series as in the A set. Rarely an object was involved, e.g., the table on which the subject wrote. The movements were demonstrated to the subject in advance of learning, as in the A set.
The following are typical B series:
B2. Nonsense words and objects.
quaro rudv xem lihkez lid cent starch thorn
B3. Nonsense words and verbs.
dalbva fomso bloi kyvi poke limp hug eat
B4. Nonsense words and movements.
ohv wecolu uxpa haymj gnash cross frown twist
The time conditions for presenting a series remained practically the same. In learning, the series was shown three times as before. The interval between learning and testing was shortened to 4 seconds, and in the test the post-term interval of A^{13-16} retained (6 secs.). This allowed the subject 9 secs. for recalling and writing each term. The only important change was an extension of the number of tests from two to four. The third test was one week after the second, and the fourth one week after the third. In these tests the familiar word was always the term required, as in A^{1-4}, on account of the difficulty of dealing statistically with the nonsense words. The intervals for testing permanence in the B set may be most easily understood by giving the time record of one subject.
TIME RECORD OF Hu.
Series. Im. Rec. Two Days. Nine Days. Sixteen Days. B^{1-4} Feb. 12 Feb. 14 Feb. 21 Feb. 28 B^{5-8} Feb. 19 Feb. 21 Feb. 28 Mch. 7 B^{9-12} Feb. 26 Feb. 28 Mch. 7 Mch. 14 B^{13-16} Mch. 5 Mch. 7 Mch. 14 Mch. 21
The two half-hours in a week during which all the work of one subject was done fell on approximately the same part of the day. When a number of groups of 4 series each were to be tested on a given day they were taken in the order of their recency of learning. Thus on March 7 the order for Hu was B^{13-16}, B^{9-12}, B^{5-8}.
Henceforth there was also rotation within a given four series. As there were always sixteen series in a set, the effects of practice and fatigue within a given half-hour were thus eliminated.
In the following table the results of the B set are given. Its arrangement is the same as in Table 1., except that the figures indicate the number of absent terms correctly recalled out of four couplets instead of seven or five. Where blanks occur, the series was discontinued on account of lack of recall. As in Table 1., the tables in the first, third and fifth columns show successive stages of the same series. Immediate recall is omitted because with rare exceptions it was perfect, the test being given merely as an aid in learning.
TABLE II.
SHOWING RECALL AFTER TWO, NINE, AND SIXTEEN DAYS.
Days. Two. Nine. Sixteen. Two. Nine. Sixteen. N. O. N. O. N. O. V. M. V. M. V. M. Series. M. B^{1-4} 2(1) 4 1(1) 2 1(1) 2 4 4 4 2 4 2 B^{5-8} 3 1 2 1 1 1 2 2 2 1 1 1 B^{9-12} 2 3 0 3 0 2 3 2 2 0 2 2 B^{13-16} 2(1) 3 2(1) 0 2(1) 0 1 2 1 0 1 0 Total 9(2) 11 5(2) 6 4(2) 5 10 10 9 3 8 5 Per cent. 64 69 36 38 29 31 63 63 56 19 50 31
S. B^{1-4} 0 2 0 0 0 1 0 1 B^{5-8} 0 0 0 0 B^{9-12} 0 1 0 0 0 1 0 0 B^{13-16} squared 0(2) 1 0(2) 1 0(2) 1 0 0(1) 0 0(1) 0 0(1) Total 0(2) 4 0(2) 1 0(2) 1 0 2(1) 0 1(1) 0 0(1) Per cent. 0 25 0 6 0 6 0 13 0 7 0 0
Hu. B^{1-4} 1(1) 4 0(1) 1 0(1) 2 1 3 0 2 0 0 B^{5-8} 0 1(1) 0 0(1) 0 0(1) 0 1 0 1 0 1 B^{9-12} 0 1 0 0 0 1 0 0 0 1 0 0 B^{13-16} 0(1) 0 0(1) 0 0(1) 0 0 4 0 0 0 0 Total 1(2) 6(1) 0(2) 1(1) 0(2) 3(1) 1 8 0 4 0 1 Per cent. 7 40 0 7 0 20 6 50 0 25 0 6
B. B^{1-4} 1 1(1) 0 0 0 0(1) 0 0 B^{6-8} 1 2 1 2 1 1 1 0 1 0 1 0 B^{9-12} 0 2(1) 0 0(1) 0 0(1) 0(1) 2 0 2 0 1 B^{13-16} 1 3 1 1 1 1 1 2 0 1 0 1 Total 3 8(2) 2 3(1) 2 2(1) 2(1) 4(1) 1 3 1 2 Per cent. 19 57 13 21 13 13 13 27 7 20 7 13
Ho. B^{1-4} 3 2(1) 2 2(1) 1 0(1) 1(2) 1(2) 1(2) 0(2) 0(2) 0(2) B^{6-8} 1 1(1) 1 0(1) 1 0 0 1(1) 1 1 0 1 B^{9-12} 0(1) 1 0(1) 1 0(1) 0 1 1 1 1 0 0 B^{13-16} cubed 0 0 0 0 0 0 0(1) 4 0(1) 2 0(1) 0 Total 4(1) 4(2) 3(1) 3(2) 2(1) 0(1) 2(3) 7(3) 3(3) 4(2) 0(3) 1(2) Percent. 33 30 25 23 17 0 17 58 25 33 0 8
Mo. B^{1-4} 3 3 3 1 4 1 0 2 0 2 0 2 B^{5-8} 1 4 1 1 1 2 1 2(2) 1 1(2) 1 1(2) B^{9-12} 2 4 2 4 1 4 0(1) 3(1) 1(1) 3(1) 1(1) 2 B^{13-16} 2(2) 4 2(2) 4 2(2) 2 1 4 1 4 1 4 Total 8(2) 15 8(2) 10 8(2) 9 2(1) 11(3) 3(1) 10(3) 3(1) 9(2) Percent. 57 94 57 63 57 56 13 85 20 79 20 69
Four presentations in learning. squaredFive presentations in learning. cubedFive days' interval instead of two.
In the following summary the recall after two days is combined from Tables I. and II. for the three subjects M, S and Hu, there being no important difference in the conditions of experimentation. For the three other subjects this summary is merely a resume of Table II. The recall after nine and sixteen days in Table II. is omitted, and will be taken up later. The figures are in all cases based on the remainders left after those couplets in which indirect associations occurred were eliminated both from the total number of couplets learned and from the total number correctly recalled. E.g., in the case of nouns, M learned, in all, 42 couplets in the A and B sets, but since in 3 of them indirect associations occurred, only 39 couplets are left, of which 21 were correctly recalled. This gives 54 per cent.
SUMMARY OF RECALL AFTER TWO DAYS.—FROM TABLES I. AND II.
N. O. V. M. M. 54 per cent. 62 per cent. 63 per cent. 61 per cent. S. 8 " 21 " 7 " 12 " Hu. 11 " 30 " 5 " 59 " B. 19 " 57 " 13 " 27 " Ho. 33 " 30 " 17 " 58 " Mo. 57 " 94 " 13 " 85 " Av. 30 per cent. 49 per cent. 20 per cent. 50 per cent.
Av. gain in object couplets, 19 per cent. " " " movement couplets, 30 per cent.
The first question which occurs in examining the foregoing tables is concerning the method of treating the indirect associations, i.e., obtaining the per cents. The number of couplets correctly recalled may be divided into two classes: those in which indirect associations did not occur, and those in which they did occur. Those in which they did not occur furnish us exactly what we want, for they are results which are entirely free from indirect associations. In them, therefore, a comparison can be made between series using objects and activities and others using images. On the other hand, those correctly recalled couplets in which indirect associations did occur are not for our purposes pure material, for they contain not only the object-image factor but the indirect association factor also. The solution is to eliminate these latter couplets, i.e., subtract them both from the number correctly recalled and from the total number of couplets in the set for a given subject. By so doing and by dividing the first remainder by the second the per cents, in the tables were obtained. There is one exception to this treatment. The few couplets in which indirect associations occurred but which were nevertheless incorrectly recalled are subtracted only from the total number of couplets in the set.
The method by which the occurrence of indirect associations was recorded has been already described. It is considered entirely trustworthy. There is usually little doubt in the mind of a subject who comprehends what is meant by an indirect association whether or not such were present in the particular series which has just been learned. If none occurred in it the subjects always recorded the fact. That an indirect association should occasionally be present on one day and absent on a subsequent one is not strange. That a second term should effect a union between a first and third and thereafter disappear from consciousness is not an uncommon phenomenon of association. There were thirteen such cases out of sixty-eight indirect associations in the A, B and C sets. In the tables they are given as present because their effects are present. When the reverse was the case, namely, when an indirect association occurred on the second, ninth or sixteenth day for the first time, it aided in later recall and was counted thereafter. There were eight such cases among the sixty-eight indirect associations.
Is it possible that the occurrence of indirect associations in, e.g., two of the four couplets of a series renders the retention of the other two easier? This could only be so when the intervals between two couplets in learning were used for review, but such was never the case. The subjects were required to fill such intervals with repetitions of the preceding couplet only.
The elimination of the indirect association couplets and the acceptance of the remainders as fair portrayals of the influence of objects and movements on recall is therefore a much nearer approach to truth than would be the retention of the indirectly associated couplets.
The following conclusions deal with recall after two days only. The recall after longer intervals will be discussed after Table III.
The summary from Tables I. and II. shows that when objects and nouns are coupled each with a foreign symbol, four of the six subjects recall real objects better than images of objects, while two, M and Ho, show little or no preference. The summary also shows that when body movements and verbs are coupled each with a foreign symbol, five of the six subjects recall actual movements better than images of movements, while one subject, M, shows no preference. The same subject also showed no preference for objects. With the subjects S and B the preference for actual movements is not marked, and has importance only in the light of later experiments to be reported.
The great difference in the retentive power of different subjects is, as we should expect, very evident. Roughly, they may be divided into two groups. M and Mo recall much more than the other four. The small percentage of recall in the case of these four suggested the next change in the conditions of experimentation, namely, to shorten with them the intervals between the tests for permanence. This was accordingly done in the C set. But before giving an account of the next set we may supplement these results by results obtained from other subjects.
It was impossible to repeat this set with the same subjects, and inconvenient, on account of the scarcity of suitable words, to devise another set just like it. Accordingly, the B set was repeated with six new subjects. We may interpolate the results here, and then resume our experiments with the other subjects. The conditions remained the same as for the other subjects in all respects except the following. The tests after nine and sixteen days were omitted, and the remaining test for deferred recall was given after one day instead of after two. In learning the series, each series was shown four times instead of three. The results are summarized in the following table. The figures in the left half show the number of words out of sixteen which were correctly recalled. The figures in parentheses separate, as before, the correctly recalled indirect-association couplets. In the right half of the table the same results, omitting indirect-association couplets, are given in per cents, to facilitate comparison with the summary from Tables I. and II.
TABLE III.
SHOWING RECALL AFTER ONE DAY.
N. O. V. M. N. O. V. M. Bur. 6 10(1) 7(1) 5(4) 38 67 44 31 W. 5(3) 12(1) 6 9 31 75 38 56 Du. 1 11(1) 8 9 6 69 50 56 H. 9(1) 14 8 12 56 88 50 75 Da. 1(3) 7(4) 3(1) 9(3) 7 44 20 56 R. 7(2) 3(3) 5 5(1) 44 19 31 31 Total, 29(9) 57(10) 37(2) 49(8) Av., 30 60 39 51
Av. gain in object couplets, 30 per cent. " " " movement couplets, 12 per cent.
The table shows that five subjects recall objects better than images of objects, while one subject recalls images of objects better. Similarly, three subjects recall actual movements of the body better than images of the same, while with three neither type has any advantage.
THE C SET.
In the C set certain conditions were different from the conditions of the A and B sets. These changes will be described under three heads: changes in the material; changes in the time conditions; and changes in the method of presentation.
For lack of monosyllabic English words the verbs and movements were dissyllabic words. The nouns and objects were monosyllabic, as before. All were still concrete, and the movements, whether made or imaged, were still simple. But the movements employed objects, instead of being merely movements of the body.
For two of the subjects, M and Mo, the time intervals between the tests remained as in the A and the B sets, namely, two days, nine days, and sixteen days. With the four other subjects, S, Hu, B, and Ho, the number of tests was reduced to three and the intervals were as follows:
The I. test, which as before was a part of the learning process, was not counted. The II. test followed from 41/2 to 61/2 hours, or an average of 5-3/8 hours, after the I. test. The III. test was approximately 16 hours after the II. test for all four subjects.
The series were learned between 10 a.m. and 1:30 p.m., the II. test was the same day between 4:30 and 5:10 p.m., and the III. test was the following morning between 8:30 and 9:10 a.m. Each subject of course came at the same hour each week.
Each series was shown three times, as in the B set.
A change had to be made in the length of exposure of each couplet in the movement series. For, as a rule, movements employing objects required a longer time to execute than mere movements of the body. Five seconds was found to be a suitable length of exposure. To keep the three other types of series comparable with the movement series, if possible, their exposure was also increased from 3 to 5 secs. The interval of 2 secs, at the end of a presentation was omitted, and the interval between learning and testing reduced from 4 secs, in the B set to 2 secs.
In the movement series of the A and B sets, movements of parts of the body were chosen. But the number of such movements which a person can conveniently make while reading words shown through an aperture is limited, and as stated above no single word was ever used in two couplets. These were now exhausted. In the C set, therefore, movements employing objects were substituted. The objects lay on the table in a row in front of the subject, occupying a space about 50 cm. from left to right, and were covered by a black cambric cloth. They were thus all exposed at the same moment by the subject who, at a signal, laid back the cloth immediately before the series began, and in the same manner covered them at the end of the third presentation. Thus the objects were or might be all in view at once, and as a result the subject usually formed a single mental image of the four objects. |
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