to it. When I tried to do the latter, the results were not always satisfactory, because the head and eyes of the person would frequently, in the process of adjustment, move beyond the goal and thus lead me into error. An attempt was made to make each judgment as independent as possible of the preceding one. But usually, after a few tests, an unintentional association became established between certain attitudes and the different places in the series of papers. Often all that was necessary was to observe the experimenter in order to know which of the places he had in mind, it was not necessary to look at the papers at all. Every change in the position of the person would, of course, make the association thus established, useless.
Later, the subjects and I changed rôles, I took the part of the experimenter and they the part of the "horse". The number of tests in each case was 200 as before. Here, too, errors were, with but one exception, never more than of one place to either side. Whether the error was one place to the right or one place to the left appeared to depend upon the position of the person making the judgment, i. e., it depended on whether he stood at my right or at my left. The following results were obtained:
| Subject ("horse"): | v. A. | B. | C. | Mrs. v. H. | K. | Miss v. L. |
| Correct inferences: | 76% | 79% | 75% | 81% | 77% | 74% |
A certain agreement can be seen in these results. The average of correct inferences is somewhat lower than that which was obtained by me ([page 135]), 77% as over against 82%. This is probably due to the fact that the subjects had had so little practice compared with me.
With one of these subjects, Mr. Koffka, a student of philosophy, I carried these tests somewhat further, varying them partly by increasing the number of sheets of paper, partly by decreasing the distance between them. The increase in the number of sheets made only a slight difference in the results. With 200 tests in each case I obtained the following results:
| No. of sheets | : | 5 | 6 | 7 | 8 | 9 | 10 |
| Correct inferences | : | 77% | 72% | 72% | 69% | 73% | 68% |
With but few exceptions, the errors were, as a rule, of one place. The series with an odd number of sheets (5, 7, 9) gave better results than those with an even number (6, 8, 10). In the tests with the odd number of sheets the experimenter (K.) stood in front of the middle sheet, so that it was at the apex of a right angle made by the series of papers and the median plane of the subject's body; whereas in the case of the even number of papers the subject stood opposite the space between the two middle sheets, thus making the position of the sheets less favorable.
In the preceding tests the distance between the centers of the neighboring sheets was always 50 centimeters, so that the angle through which the median plane of the experimenter's body would have to turn in order to pass from one sheet to the next, was about 3¾ degrees. In the following tests these distances were gradually decreased. The sheets, always five in number, were replaced by ever narrower white strips of paper mounted on dark cardboard and illumined by a Nernst lamp. The following table shows the decrease in correct inferences running parallel with the decrease of the angle through which the subject would have to turn in order to be in line with the several pieces of a series successively. The percentage in each case is based upon at least 100 tests.
| Angle: | 3¾° | 3° | 2½° | 2° | 1½° | 1° |
| Distance between the centres of two neighboring papers: | 50cm. | 39cm. | 33cm. | 26cm. | 20cm. | 13cm. |
| No. of correct inferences: | 77% | 73% | 71% | 68% | 66% | 61% |
A curious and unexpected change was here noted in the subject, Mr. Koffka, who, while concentrating his attention to the uttermost, began unawares to develop a new system of expressive movements of the head. When the distance between the sheets was relatively great, he had been in the habit of turning his head and eyes in the direction of the sheet intended, and as the distances became less he had reacted only by a turning of the eyes. But now, as the distances were still further decreased, he began again to react by means of head movements, and these were of exaggerated magnitude, for which he would compensate, as it were, by an eye-movement in the opposite direction. Although the head movements decreased in scope as the distances between the sheets were steadily decreased, they still were always decidedly greater than the eye movements, which I was now normally led to expect and which could be judged without much difficulty. This form of reaction was much more satisfactory as a cue, and therefore it came to pass that, whereas in the preceding series I had made only 60% correct inferences when the angle was 1 degree, I now found that—the angle remaining the same—80% of my inferences were correct. (My final judgment I continued to base, as before, upon the position, and not upon the movement, of head and eye). The number of correct inferences continued relatively high, even after the distance between the papers was decreased tenfold,—as will be seen from the following table: