TABLE I.
| Left. | Right. | |||
|---|---|---|---|---|
| Div. | M.V. | Div. | M.V. | |
| A | 54 | 2.6 | 50 | 3.4 |
| B | 46 | 4.5 | 49 | 5.7 |
| C | 75 | 1.8 | 71 | 1.6 |
| D | 62 | 4.4 | 56 | 4.1 |
| E¹ | 57 | 10.7 | 60 | 8.7 |
| F | 69 | 2.6 | 69 | 1.6 |
| G | 65 | 3.7 | 64 | 2.7 |
| H | 72 | 3.8 | 67 | 2.1 |
| J | 46 | 1.9 | 48 | 1.3 |
| — | — | — | — | |
| Total | 60 | 3.9 | 59 | 3.5 |
| Golden Section = 61.1. | ||||
¹These are E's general averages on 36 judgments. Fig. 1, however, represents two averages on each side the center, for which the figures are, on the left, 43 with M.V. 3.6; and 66 with M.V. 5.3. On the right, 49, M.V. 3.1; and 67, M.V. 2.7. For the full sixty judgments, his total average was 63 on the left, and 65 on the right, with mean variations of 9.8 and 7.1 respectively. The four that E² in Fig. 1 shows graphically were, for the left, 43 with M.V. 3.6; and 68, M.V. 5.1. On the right, 49, M.V. 3.1; and 69, M.V. 3.4.
Fig. 1.
Results such as are given in Fig. 1, appear to warrant the criticism of former experimentation. Starting with the golden section, we find the two lines representing the total averages running surprisingly close to it. This line, however, out of a possible eighteen chances, only twice (subjects D and G) falls wholly within the mode representing the maximum number of judgments of any single subject. In six cases (C twice, F, H, J twice) it falls wholly without any mode whatever; and in seven (A, B twice, E, F, G, H) within modes very near the minimum. Glancing for a moment at the individual averages, we see that none coincides with the total (although D is very near), and that out of eighteen, only four (D twice, G twice) come within five millimeters of the general average, while eight (B, C, J twice each, F, H) lie between ten and fifteen millimeters away. The two total averages (although near the golden section), are thus chiefly conspicuous in showing those regions of the line that were avoided as not beautiful. Within a range of ninety millimeters, divided into eighteen sections of five millimeters each, there are ten such sections (50 mm.) each of which represents the maximum of some one subject. The range of maximum judgments is thus about one third the whole line. From such wide limits it is, I think, a methodological error to pick out some single point, and maintain that any explanation whatever of the divisions there made interprets adequately our pleasure in unequal division. Can, above all, the golden section, which in only two cases (D, G) falls within the maximum mode; in five (A, C, F, J twice) entirely outside all modes, and in no single instance within the maximum on both sides the center—can this seriously play the role of æsthetic norm?
I may state here, briefly, the results of several sets of judgments on lines of the same length as the first but wider, and on other lines of the same width but shorter. There were not enough judgments in either case to make an exact comparison of averages valuable, but in three successively shorter lines, only one subject out of eight varied in a constant direction, making his divisions, as the line grew shorter, absolutely nearer the ends. He himself felt, in fact, that he kept about the same absolute position on the line, regardless of the successive shortenings, made by covering up the ends. This I found to be practically true, and it accounts for the increasing variation toward the ends. Further, with all the subjects but one, two out of three pairs of averages (one pair for each length of line) bore the same relative positions to the center as in the normal line. That is, if the average was nearer the center on the left than on the right, then the same held true for the smaller lines. Not only this. With one exception, the positions of the averages of the various subjects, when considered relatively to one another, stood the same in the shorter lines, in two cases out of three. In short, not only did the pair of averages of each subject on each of the shorter lines retain the same relative positions as in the normal line, but the zone of preference of any subject bore the same relation to that of any other. Such approximations are near enough, perhaps, to warrant the statement that the absolute length of line makes no appreciable difference in the æsthetic judgment. In the wider lines the agreement of the judgments with those of the normal line was, as might be expected, still closer. In these tests only six subjects were used. As in the former case, however, E was here the exception, his averages being appreciably nearer the center than in the original line. But his judgments of this line, taken during the same period, were so much on the central tack that a comparison of them with those of the wider lines shows very close similarity. The following table will show how E's judgments varied constantly towards the center:
| AVERAGE. | ||
|---|---|---|
| L. | R. | |
| 1. Twenty-one judgments (11 on L. and 10 on R.) during experimentation on I¹, I², etc., but not on same days. | 64 | 65 |
| 2. Twenty at different times, but immediately before judging on I¹, I², etc. | 69 | 71 |
| 3. Eighteen similar judgments, but immediately after judging on I¹, I², etc. | 72 | 71 |
| 4. Twelve taken after all experimentation with I¹, I², etc., had ceased. | 71 | 69 |
The measurements are always from the ends of the line. It looks as if the judgments in (3) were pushed further to the center by being immediately preceded by those on the shorter and the wider lines, but those in (1) and (2) differ markedly, and yet were under no such influences.
From the work on the simple line, with its variations in width and length, these conclusions seem to me of interest. (1) The records offer no one division that can be validly taken to represent 'the most pleasing proportion' and from which interpretation may issue. (2) With one exception (E) the subjects, while differing widely from one another in elasticity of judgment, confined themselves severally to pretty constant regions of choice, which hold, relatively, for different lengths and widths of line. (3) Towards the extremities judgments seldom stray beyond a point that would divide the line into fourths, but they approach the center very closely. Most of the subjects, however, found a slight remove from the center disagreeable. (4) Introspectively the subjects were ordinarily aware of a range within which judgments might give equal pleasure, although a slight disturbance of any particular judgment would usually be recognized as a departure from the point of maximum pleasingness. This feeling of potential elasticity of judgment, combined with that of certainty in regard to any particular instance, demands—when the other results are also kept in mind—an interpretative theory to take account of every judgment, and forbids it to seize on an average as the basis of explanation for judgments that persist in maintaining their æsthetic autonomy.