The prevalent, although ill-founded, impression that mice have an exceedingly keen sense of smell might lead a critic of these experiments to claim that discrimination in all probability was olfactory rather than visual. As precautions against this possibility the cardboards were renewed frequently, so that no odor from the body of the mouse itself should serve as a guiding condition, different kinds of cardboard were used from time to time, and, as a final test, the cardboards were coated with sh.e.l.lac so that whatever characteristic odor they may have had for the dancer was disguised if not totally destroyed. Despite all these precautions the discrimination of the boxes continued. A still more conclusive proof that we have to do with brightness discrimination, and that alone, in these experiments is furnished by the results of white- black tests made with an apparatus which was so arranged that light was transmitted into the two electric-boxes through a ground gla.s.s plate in the end of each box. No cardboards were used. The illumination of each box was controlled by changes in the position of the sources of light. Under these conditions, so far as could be ascertained by critical examination of the results, in addition to careful observation of the behavior of the animals as they made their choices, there was no other guiding factor than brightness difference. Nevertheless the mice discriminated the white from the black perfectly. This renders unnecessary any discussion of the possibility of discrimination by the texture or form of the cardboards.

Since a variety of precautionary tests failed to reveal the presence, in these experiments, of any condition other than brightness difference by which the mice were enabled to choose correctly, and since evidence of ability to discriminate brightness differences was obtained by the use of both reflected light (cardboards) and transmitted light (lamps behind ground gla.s.s), it is necessary to conclude that the dancer possesses brightness vision.

CHAPTER VIII

THE SENSE OF SIGHT: BRIGHTNESS VISION (Continued)

Since the ability of the dancer to perceive brightness has been demonstrated by the experiments of the previous chapter, the next step in this investigation of the nature of vision is a study of the delicacy of brightness discrimination, and of the relation of the just perceivable difference to brightness value. Expressed in another way, the problems of this portion of the investigation are to determine how slight a difference in brightness enables the dancer to discriminate one light from another, and what is the relation between the absolute brightnesses of two lights and that amount of difference which is just sufficient to render the lights distinguishable. It has been discovered in the case of the human being that a stimulus must be increased by a certain definite fraction of its own value if it is to seem different. For brightness, within certain intensity limits, this increase must be about one one-hundredth; a brightness of 100 units, for example, is just perceivably different from one of 101 units. The formulation of this relation between the amount of a stimulus and the amount of change which is necessary that a difference be noted is known as Weber's law. Does this law, in any form, hold for the brightness vision of the dancing mouse?

Two methods were used in the study of these problems. For the first problem, that of the delicacy of brightness discrimination, I first used light which was reflected from gray papers, according to the method of Chapter VII. For the second, the Weber's law test, transmitted light was used, in an apparatus which will be described later. Either of these methods might have been used for the solution of both problems. Which of them is the more satisfactory is definitely decided by the results which make up the material of this chapter, Under natural conditions the dancer probably sees objects which reflect light more frequently than it does those which transmit it; it would seem fairer, therefore, to require it to discriminate surfaces which differ in brightness. This the use of gray papers does. But, on the other hand, gray papers are open to the objections that they may not be entirely colorless (neutral), and that their brightness values cannot be changed readily by the experimenter. As will be made clear in the subsequent description of the experiments with transmitted light, neither of these objections can be raised in connection with the second method of experimentation.

To determine the delicacy of discrimination with reflected light it is necessary to have a series of neutral grays (colorless) whose adjacent members differ from one another in brightness by less than the threshold of discrimination of the animal to be tested. A series which promised to fulfill these conditions was that of Richard Nendel of Berlin. It consists of fifty papers, beginning with pure white, numbered 1, and pa.s.sing by almost imperceptible steps of decrease in brightness through the grays to black, which is numbered 50. For the present we may a.s.sume that these papers are so nearly neutral that whatever discrimination occurs is due to brightness. The differences between successive papers of the series are perceptible to man. The question is, can they, under favorable conditions of illumination, be perceived by the dancer?

On the basis of the fact that the dancer can discriminate between white and black, two grays which differed from one another in brightness by a considerable amount were chosen from the Nendel series; these were numbers 10 and 20. It seemed certain, from the results of previous experiments, that the discrimination of these papers by brightness difference would be possible, and that therefore the use of papers between these two extremes would suffice to demonstrate the delicacy of discrimination. In Figure 16 we have a fairly accurate representation of the relative brightness of the Nendel papers Nos. 10, 15, and 20.

[Ill.u.s.tration: FIGURE 16. Three of Nendel's gray papers: Nos. 10, 15, and 20. To exhibit differences in brightness.]

Pieces of the gray papers were pasted upon cardboard carriers so that they might be placed in the discrimination box as were the white and black cardboards in the tests of brightness vision previously described. Mice which had been trained to choose the white box by series of white-black tests were now tested with light gray (No. 10) and dark gray (No. 20), my a.s.sumption being that they would immediately choose the brighter of the two if they were able to detect the difference. As a matter of fact this did not always occur; some individuals had to be trained to discriminate gray No. 10 from gray No. 20. As soon as an individual had been so trained that the ability to choose the lighter of these grays was perfect, it was tested with No. 10 in combination with No. 15. If these in turn proved to be discriminable, No. 10 could be used with No. 14, with No. 13, and so on until either the limit of discrimination or that of the series had been reached.

That it was not necessary to use other combinations than 10 with 20, and 10 with 15 is demonstrated by the results of Table 13. Mouse No. 420, whose behavior was not essentially different from that of three other individuals which were tested for gray discrimination, learned with difficulty to choose gray No. 10 even when it was used with No. 20. Two series of ten tests each were given to this mouse daily, and not until the twentieth of these series (200 tests) did he succeed in making ten correct choices in succession. Immediately after this series of correct choices, tests with grays No. 10 and No. 15 were begun. In the case of this amount of brightness difference twenty series failed to reveal discrimination.

The average number of right choices in the series is slightly in excess of the mistakes, 5.8 as compared with 4.2.

From the experiments with gray papers we may conclude that under the conditions of the tests the amount by which Nendel's gray No. 10 differs in brightness from No. 20 is near the threshold of discrimination, or, in other words, that the difference in the brightness of the adjacent grays of Figure 16 is scarcely sufficient to enable the dancer to distinguish them.

TABLE 13

GRAY DISCRIMINATION

The Delicacy of Brightness Discrimination

No. 420

GRAYS NOS. 10 GRAYS NOS. 20 AND 20 AND 15 SERIES DATE DATE NO. 10 NO. 2 NO. 10 NO. 15 (RIGHT) (WRONG) (RIGHT) (WRONG)

1 Jan. 26 5 5 Feb. 6 8 2 2 27 8 2 6 5 5 3 28 6 4 7 9 1 4 28 2 8 7 7 3 5 29 1 9 8 5 5 6 29 6 4 8 6 4 7 30 9 1 9 5 5 8 30 7 3 9 6 4 9 31 6 4 10 8 2 10 31 4 6 10 3 7 11 Feb. 1 7 3 11 4 6 12 1 8 2 11 4 6 13 2 7 3 12 7 3 14 2 8 2 12 7 3 15 3 9 1 13 6 4 16 3 9 1 13 4 6 17 4 6 4 14 4 6 18 4 9 1 14 5 5 19 5 6 4 15 5 5 20 5 10 0 15 8 2

Averages 6.6 3.4 5.8 4.2

This result of the tests with gray papers surprised me very much at the time of the experiments, for all my previous observation of the dancer had led me to believe that it is very sensitive to light. It was only after a long series of tests with transmitted light, in what is now to be described as the Weber's law apparatus, that I was able to account for the meager power of discrimination which the mice exhibited in the gray tests.

As it happened, the Weber's law experiment contributed quite as importantly to the solution of our first problem as to that of the second, for which it was especially planned.

For the Weber's law experiment a box similar to that used in the previous brightness discrimination experiments (Figure 14) was so arranged that its two electric-boxes could be illuminated independently by the light from incandescent lamps directly above them. The arrangements of the light-box and the lamps, as well as their relations to the other important parts of the apparatus, are shown in Figure 17. The light-box consisted of two compartments, of which one may be considered as the upward extension of the left electric-box and the other of the right electric-box. The light- box was pivoted at A and could be turned through an angle of 180 by the experimenter. Thus, by the turning of the light-box, the lamp which in the case of one test illuminated the left electric-box could be brought into such a position that in the case of the next test it illuminated the right electric-box. The practical convenience of this will be appreciated when the number of times that the brightnesses of the two boxes had to be reversed is considered. The light-box was left open at the top for ventilation and the prevention of any considerable increase in the temperature of the experiment box. In one side of each of the compartments of the light-box a slit (B, B of the figure) was cut out for an incandescent lamp holder. A strip of leatherette, fitted closely into inch grooves at the edges of the slit, prevented light from escaping through these openings in the sides of the light-box. By moving the strips of leatherette, one of which appears in the figure, C, the lamps could be changed in position with reference to the bottom of the electric-box. A scale, S, at the edge of each slit enabled the experimenter to determine the distance of the lamp from the floor of the electric-box. The front of the light-box was closed, instead of being open as it appears in the figure.

[Ill.u.s.tration: Figure l7.--Weber's law apparatus for testing brightness discrimination. Lower part, discrimination box similar to that of Figure 14. Upper part, rotatory light-box, pivoted at A, and divided into two compartments by a part.i.tion P in the middle. L, L, incandescent lamps movable in slits, B, B, in which a narrow strip of leatherette, C, serves to prevent the escape of light. S, scale.]

This apparatus has the following advantages. First, the electric-boxes, between which the mouse is expected to discriminate by means of their difference in brightness, are illuminated from above and the light therefore does not shine directly from the lamps into the eyes of the animal, as it approaches the entrances to the boxes. Choice is required, therefore, between illuminated s.p.a.ces instead of between two directly illuminated surfaces. Second, the amount of illumination of each electric- box can be accurately measured by the use of a photometer. Third, since the same kind of lamp is used in each box, and further, since the lamps may be interchanged at any time, discrimination by qualitative instead of quant.i.tative difference in illumination is excluded. And finally, fourth, the tests can be made expeditiously, conveniently, and under such simple conditions that there should be no considerable error of measurement or of observation within the range of brightness which must be used.

It was my purpose in the experiment with this apparatus to ascertain how great the difference in the illumination of the two electric-boxes must be in order that the mouse should be able to choose the brighter of them.

This I attempted to do by fixing an incandescent lamp of a certain known illuminating power at such a position in one compartment of the light-box that the electric-box below it was illuminated by what I call a standard value, and by moving the incandescent lamp in the other compartment of the light-box until the illumination of the electric-box below it was just sufficiently less than that of the standard to enable the dancer to distinguish them, and thereby to choose the brighter one. The light which was changed from series to series I shall call the _variable_, in contrast with the _standard_, which was unchanged.

The tests, which were made in a dark-room under uniform conditions, were given in series of fifty each; usually only one such series was given per day, but sometimes one was given in the morning and another in the afternoon of the same day. To prevent choice by position the lights were reversed in position irregularly, first one, then the other, illuminating the right electric-box. For the fifty tests of each initial series the order of the changes in position was as follows: standard (brighter light) on the _l_ (left), _l, r_ (right), _r, l, l, r, r, l, r, l, r, l, l, r, r, l, l, r, r, l, l, l, r, r, r, l, r, l, r, r, r, l, l, l, r, r, r, l, l, r, l, r, l, r, l, r, l, r, l_. Twenty-five times in fifty the standard light illuminated the right electric-box, and the same number of times it illuminated the left electric-box. When a second series was given under the same conditions of illumination, a different order of change was followed.

In order to discover whether Weber's law holds in the case of the brightness vision of the dancer it was necessary for me to determine the just perceivable difference between the standard and the variable lights for two or more standard values. I chose to work with three values, 5, 20, and 80 hefners, and I was able to discover with a fair degree of accuracy how much less than 5, 20, or 80 hefners, as the case might be, the variable light had to be in order that it should be discriminable from the other. For the work with the 5 hefner standard I used 2-candle-power lamps,[1] for the 20, 4-candle-power, and for the 80, 16-candle-power.

[Footnote 1: I give merely the commercial markings of the lamps. They had been photometered carefully by two observers by means of a Lummer-Brodhun photometer and a Hefner amyl acetate lamp previous to their use in the experiment. For the photometric measurements in connection with the Weber's law tests I made use of the Hefner lamp with the hope of attaining greater accuracy than had been possible with a standard paraffine candle, in the case of measurements which I had made in connection with the experiments on color vision that are reported in Chapters IX and X. The Hefner unit is the amount of light produced by an amyl acetate lamp at a flame height of 40 mm. (See Stine's "Photometrical Measurements.") A paraffine candle at a flame height of 50 mm. is equal to 1.2 Hefner units.]

For reasons which will soon appear, Weber's law tests were made with only one dancer. This individual, No. 51, had been thoroughly trained in white- black discrimination previous to the experiments in the apparatus which is represented in Figure 17. Having given No. 51 more than two hundred preliminary tests in the Weber's law apparatus with the electric-boxes sufficiently different in brightness to enable her to discriminate readily, I began my experiments by trying to ascertain how much less the value of the illumination of one electric-box must be in order that it should be discriminable from a value of 20 hefners in the other electric- box. In recording the several series of tests and their results hereafter, I shall state in Hefner units the value of the fixed or standard light and the value of the variable light, the difference between the two in terms of the former, and the average number of wrong choices in per cent.

With the lamps so placed that the difference in the illumination of the two electric-boxes was .53 of the value of the standard, that is about one half, No. 51 made twenty wrong choices in one hundred, or 20 per cent.

When the difference was reduced to .36 (one third) the number of errors increased to 36 per cent, and with an intermediate difference of .48 there were 26 per cent of errors (see Table 14).

Are these results indicative of discrimination, or are the errors in choice too numerous to justify the statement that the dancer was able to distinguish the boxes by their difference in brightness? Evidently this question cannot be answered satisfactorily until we have decided what the percentage of correct choices should be in order that it be accepted as evidence of ability to discriminate, or, to put it in terms of errors, what percentage of wrong choices is indicative of the point of just perceivable difference in brightness. Theoretically, there should be as many mistakes as right choices, 50 per cent of each, when the two electric-boxes are equally illuminated (indiscriminable), but in practice this does not prove to be the case because the dancer tends to return to that electric-box through which in the previous test it pa.s.sed safely, whereas it does not tend in similar fashion to reenter the box in which it has just received an electric shock. The result is that the percentage of right choices, especially in the case of series which have the right box in the same position two, three, or four times in succession, rises as high as 60 or 70, even when the visual conditions are indiscriminable.

Abundant evidence in support of this statement is presented in Chapters VII and IX, but at this point I may further call attention to the results of an experiment in the Weber's law apparatus which was made especially to test the matter. The results appear under the date of May 27 in Table 14.

In this experiment, despite the fact that both boxes were illuminated by 80 hefners, the mouse chose the standard (the illumination in which it was not shocked) 59 times in 100. In other words the percentage of error was 41 instead of 50. It is evident, therefore, that as low a percentage of errors as 40 is not necessarily indicative of discrimination. Anything below 40 per cent is likely, however, to be the result of ability to distinguish the brighter from the darker box. To be on the safe side we may agree to consider 25 wrong choices per 100 as indicative of a just perceivable difference in illumination. Fewer mistakes we shall consider indicative of a difference in illumination which is readily perceivable, and more as indicative of a difference which the mouse cannot detect. The reader will bear in mind as he examines Table 14 that 25 per cent of wrong choices indicates the point of just perceivable difference in brightness.

TABLE 14

RESULTS OF WEBER'S LAW EXPERIMENTS Brightness vision

DATE NUMBER STANDARD VARIABLE DIFFERENCE % OF ERRORS OF TESTS LIGHT LIGHT

May 13 100 20 9.4 .53 20 15 100 20 12.8 .36 36 16 100 20 10.8 .46 26 20 50 80 37.6 .53 6 21 50 80 51.3 .36 10 22 100 80 71.1 .11 35 24 100 80 60.0 .25 21 25 100 80 65.0 .19 25 27 100 80 80 0 41 28 50 5 2.5 .50 18 29 50 5 4.0 .20 14 29 100 5 4.5 .10 25 31 50 5 4.25 .15 20 June 1 50 5 4.85 .03 48 2 50 20 15.0 .25 16 3 50 20 17.4 .13 22 3 100 20 18.0 .10 22 4 100 80 72.0 .10 18 5 100 5 4.5 .10 12 7 100 5 4.67 .067 46 8 50 80 74.67 .067 56 9 50 20 18.67 .067 44

If we apply this rule to the results of the first tests, reported above, it appears that a standard of 20 hefners was distinguished from a variable of 9.4 hefners (.53 difference), for the percentage of errors was only 20.

But in the case of a difference of .36 in the illuminations lack of discrimination is indicated by 36 per cent of errors. A difference of .46 gave a frequency of error so close to the required 25 (26 per cent) that I accepted the result as a satisfactory determination of the just perceivable difference for the 20 hefner standard and proceeded to experiment with another standard value.

The results which were obtained in the case of this second standard, the value of which was 80 hefners, are strikingly different from those for the 20 hefner standard. Naturally I began the tests with this new standard by making the differences the same as those for which determinations had been made in the case of the 20 standard. Much to my surprise only 6 per cent of errors resulted when the difference in illumination was .53. I finally discovered that about .19 difference (about one fifth) could be discriminated with that degree of accuracy which is indicated by 25 per cent of mistakes.

So far as I could judge from the results of determinations for the 20 and the 80 hefner standards, Weber's law does not hold for the dancer. With the former a difference of almost one half was necessary for discrimination; with the latter a difference of about one fifth could be perceived. But before presenting additional results I should explain the construction of Table 14, and comment upon the number of experiments which const.i.tutes a set.

The table contains the condensed results of several weeks of difficult experimentation. From left to right the columns give the date of the initial series of a given set of experiments, the number of experiments in the set, the value of the standard light in hefners, the value of the variable light, the difference between the lights in terms of the standard (the variable was always less than the standard), and the percentage of errors or wrong choices. Very early in the investigation I discovered that one hundred tests with any given values of the lights sufficed to reveal whatever discriminating ability the mouse possessed at the time. In some instances either the presence or the lack of discrimination was so clear, as the result of 50 tests (first series), that the second series of 50 was not given. Consequently in the table the number of tests for the various values of the lights is sometimes 100, sometimes 50.

After finishing the experiments with the 80 standard on May 27 (see table) I decided, in spite of the evidence against Weber's law, to make tests with 5 as the standard, for it seemed not impossible that the lights were too bright for the dancer to discriminate readily. I even suspected that I might have been working outside of the brightness limits in which Weber's law holds, if it holds at all. The tests soon showed that a difference of one tenth made discrimination possible in the case of this standard. If the reader will examine the data of the table, he will note that a difference of .20 gave 14 per cent of mistakes; a difference of .03, 48 per cent. Evidently the former difference is above the threshold, the latter below it. But what of the interpretation of the results in terms of Weber's law? The difference instead of being one half or one fifth, as it was in the cases of the 20 and 80 standards respectively, has now become one tenth. Another surprise and another contradiction!

Had these three differences either increased or decreased regularly with the value of the standard I should have suspected that they indicated a principle or relationship which is different from but no less interesting than that which Weber's law expresses. But instead of reading 5 standard, difference one tenth; 20 standard, difference one fifth; 80 standard, difference one half: or 5 standard, difference one half; 20 standard, difference one fifth; 80 standard, difference one tenth: they read 5 standard, difference one tenth; 20 standard, difference one half; 80 standard, difference one fifth. What does this mean? I could think of no other explanation than that of the influence of training. It seemed not impossible, although not probable, that the mouse had been improving in ability to discriminate day by day. It is true that this in itself would be quite as interesting a fact as any which the experiment might reveal.

To test the value of my supposition, I made additional experiments with the 20 standard, the results of which appear under the dates June 2 and 3 of the table. These results indicate quite definitely that the animal had been, and still was, improving in her ability to discriminate. For instead of requiring a difference of about one half in order that she might distinguish the 20 standard from the variable light she was now able to discriminate with only 22 per cent of errors when the difference was one tenth.