Chapter 3

The present paper reports the beginnings of an investigation designed to throw light on the psychological basis of our æsthetic pleasure in unequal division. It is confined to horizontal division. Owing to the prestige of the golden section, that is, of that division of the simple line which gives a short part bearing the same ratio to the long part that the latter bears to the whole line, experimentation of this sort has been fettered. Investigators have confined their efforts to statistical records of approximations to, or deviations from, the golden section. This exalts it into a possible æsthetic norm. But such a gratuitous supposition, by limiting the inquiry to the verification of this norm, distorts the results, tempting one to forget the provisional nature of the assumption, and to consider divergence from the golden section as an error, instead of another example, merely, of unequal division. We have, as a matter of fact, on one hand, investigations that do not verify the golden section, and, on the other hand, a series of attempts to account for our pleasure in it, as if it were, beyond dispute, the norm. In this way the statistical inquiries have been narrowed in scope, and interpretation retarded and misdirected. Statistically our aim should be to ascertain within how wide limits æsthetically pleasing unequal divisions fall; and an interpretative principle must be flexible enough to include persistent variations from any hypothetical norm, unless they can be otherwise accounted for. If it is not forced on us, we have, in either case, nothing to do with the golden section.

Since Fechner, the chief investigation in the æsthetics of simple forms is that of Witmer, in 1893.[1] Only a small part of his work relates to horizontal division, but enough to show what seems to me a radical defect in statistical method, namely, that of accepting a general average of the average judgments of the several subjects, as 'the most pleasing relation' or 'the most pleasing proportion.'[2] Such a total average may fall wholly without the range of judgments of every subject concerned, and tells us nothing certain about the specific judgments of any one. Even in the case of the individual subject, if he shows in the course of long experimentation that he has two distinct sets of judgments, it is not valid to say that his real norm lies between the two; much less when several subjects are concerned. If averages are data to be psychophysically explained, they must fall well within actual individual ranges of judgment, else they correspond to no empirically determinable psychophysical processes. Each individual is a locus of possible æsthetic satisfactions. Since such a locus is our ultimate basis for interpretation, it is inept to choose, as 'the most pleasing proportion,' one that may have no correspondent empirical reference. The normal or ideal individual, which such a norm implies, is not a psychophysical entity which may serve as a basis of explanation, but a mathematical construction.

[1] Witmer, Lightner: 'Zur experimentellen Aesthetik einfacher räumlicher Formverhältnisse,' _Phil. Studien_, 1893, IX., S. 96-144, 209-263.

This criticism would apply to judgments of unequal division on either side the center of a horizontal line. It would apply all the more to any general average of judgments including both sides, for, as we shall soon see, the judgments of individuals differ materially on the two sides, and this difference itself may demand its explanation. And if we should include within this average, judgments above and below the center of a vertical line, we should have under one heading four distinct sets of averages, each of which, in the individual cases, might show important variations from the others, and therefore require some variation of explanation. And yet that great leveller, the general average, has obliterated these vital differences, and is recorded as indicating the 'most pleasing proportion.'[3] That such an average falls near the golden section is immaterial. Witmer himself, as we shall see,[4] does not set much store by this coincidence as a starting point for explanation, since he is averse to any mathematical interpretation, but he does consider the average in question representative of the most pleasing division.

[2] _op. cit._, 212-215.

[3] Witmer: _op. cit._, S. 212-215.

[4] _op. cit._, S. 262.

I shall now, before proceeding to the details of the experiment to be recorded, review, very briefly, former interpretative tendencies. Zeising found that the golden section satisfied his demand for unity and infinity in the same beautiful object.[5] In the golden section, says Wundt,[6] there is a unity involving the whole; it is therefore more beautiful than symmetry, according to the æsthetic principle that that unification of spatial forms which occurs without marked effort, which, however, embraces the greater manifold, is the more pleasing. But to me this manifold, to be æsthetic, must be a sensible manifold, and it is still a question whether the golden section set of relations has an actual correlate in sensations. Witmer,[7] however, wrote, at the conclusion of his careful researches, that scientific æsthetics allows no more exact statement, in interpretation of the golden section, than that it forms 'die rechte Mitte' between a too great and a too small variety. Nine years later, in 1902, he says[8] that the preference for proportion over symmetry is not a demand for an equality of ratios, but merely for greater variety, and that 'the amount of unlikeness or variety that is pleasing will depend upon the general character of the object, and upon the individual's grade of intelligence and æsthetic taste.' Külpe[9] sees in the golden section 'a special case of the constancy of the relative sensible discrimination, or of Weber's law.' The division of a line at the golden section produces 'apparently equal differences' between minor and major, and major and whole. It is 'the pleasingness of apparently equal differences.'

[5] Zelsing, A.: 'Aesthetische Forschungen,' 1855, S. 172; 'Neue Lehre von den Proportionen des menschlichen Körpera,' 1854, S. 133-174.

[6] Wundt, W.: 'Physiologische Psychologie,' 4te Aufl., Leipzig, 1893, Bd. II., S. 240 ff.

[7] _op. cit._, S. 262.

[8] Witmer, L.: 'Analytical Psychology,' Boston, 1902, p. 74.

[9] Külpe, O.: 'Outlines of Psychology,' Eng. Trans., London, 1895, pp. 253-255.

These citations show, in brief form, the history of the interpretation of our pleasure in unequal division. Zeising and Wundt were alike in error in taking the golden section as the norm. Zeising used it to support a philosophical theory of the beautiful. Wundt and others too hastily conclude that the mathematical ratios, intellectually discriminated, are also sensibly discriminated, and form thus the basis of our æsthetic pleasure. An extension of this principle would make our pleasure in any arrangement of forms depend on the mathematical relations of their parts. We should, of course, have no special reason for choosing one set of relationships rather than another, nor for halting at any intricacy of formulæ. But we cannot make experimental æsthetics a branch of applied mathematics. A theory, if we are to have psychological explanation at all, must be pertinent to actual psychic experience. Witmer, while avoiding and condemning mathematical explanation, does not attempt to push interpretation beyond the honored category of unity in variety, which is applicable to anything, and, in principle, is akin to Zeising's unity and infinity. We wish to know what actual psychophysical functionings correspond to this unity in variety. Külpe's interpretation is such an attempt, but it seems clear that Weber's law cannot be applied to the division at the golden section. It would require of us to estimate the difference between the long side and the short side to be equal to that of the long side and the whole. A glance at the division shows that such complex estimation would compare incomparable facts, since the short and the long parts are separated, while the long part is inclosed in the whole. Besides, such an interpretation could not apply to divisions widely variant from the golden section.

This paper, as I said, reports but the beginnings of an investigation into unequal division, confined as it is to results obtained from the division of a simple horizontal line, and to variations introduced as hints towards interpretation. The tests were made in a partially darkened room. The apparatus rested on a table of ordinary height, the part exposed to the subject consisting of an upright screen, 45 cm. high by 61 cm. broad, covered with black cardboard, approximately in the center of which was a horizontal opening of considerable size, backed by opal glass. Between the glass and the cardboard, flush with the edges of the opening so that no stray light could get through, a cardboard slide was inserted from behind, into which was cut the exposed figure. A covered electric light illuminated the figure with a yellowish-white light, so that all the subject saw, besides a dim outline of the apparatus and the walls of the room, was the illuminated figure. An upright strip of steel, 1½ mm. wide, movable in either direction horizontally by means of strings, and controlled by the subject, who sat about four feet in front of the table, divided the horizontal line at any point. On the line, of course, this appeared as a movable dot. The line itself was arbitrarily made 160 mm. long, and 1½ mm. wide. The subject was asked to divide the line unequally at the most pleasing place, moving the divider from one end slowly to the other, far enough to pass outside any pleasing range, or, perhaps, quite off the line; then, having seen the divider at all points of the line, he moved it back to that position which appealed to him as most pleasing. Record having been made of this, by means of a millimeter scale, the subject, without again going off the line, moved to the pleasing position on the other side of the center. He then moved the divider wholly off the line, and made two more judgments, beginning his movement from the other end of the line. These four judgments usually sufficed for the simple line for one experiment. In the course of the experimentation each of nine subjects gave thirty-six such judgments on either side the center, or seventy-two in all.

In Fig. 1, I have represented graphically the results of these judgments. The letters at the left, with the exception of _X_, mark the subjects. Beginning with the most extreme judgments on either side the center, I have erected modes to represent the number of judgments made within each ensuing five millimeters, the number in each case being denoted by the figure at the top of the mode. The two vertical dot-and-dash lines represent the means of the several averages of all the subjects, or the total averages. The short lines, dropped from each of the horizontals, mark the individual averages of the divisions either side the center, and at _X_ these have been concentrated into one line. Subject _E_ obviously shows two pretty distinct fields of choice, so that it would have been inaccurate to condense them all into one average. I have therefore given two on each side the center, in each case subsuming the judgments represented by the four end modes under one average. In all, sixty judgments were made by _E_ on each half the line. Letter _E¹_ represents the first thirty-six; _E²_ the full number. A comparison of the two shows how easily averages shift; how suddenly judgments may concentrate in one region after having been for months fairly uniformly distributed. The introduction of one more subject might have varied the total averages by several points. Table I. shows the various averages and mean variations in tabular form.

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.

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.

I shall now proceed to the interpretative part of the paper. Bilateral symmetry has long been recognized as a primary principle in æsthetic composition. We inveterately seek to arrange the elements of a figure so as to secure, horizontally, on either side of a central point of reference, an objective equivalence of lines and masses. At one extreme this may be the rigid mathematical symmetry of geometrically similar halves; at the other, an intricate system of compensations in which size on one side is balanced by distance on the other, elaboration of design by mass, and so on. Physiologically speaking, there is here a corresponding equality of muscular innervations, a setting free of bilaterally equal organic energies. Introspection will localize the basis of these in seemingly equal eye movements, in a strain of the head from side to side, as one half the field is regarded, or the other, and in the tendency of one half the body towards a massed horizontal movement, which is nevertheless held in check by a similar impulse, on the part of the other half, in the opposite direction, so that equilibrium results. The psychic accompaniment is a feeling of balance; the mind is æsthetically satisfied, at rest. And through whatever bewildering variety of elements in the figure, it is this simple bilateral equivalence that brings us to æsthetic rest. If, however, the symmetry is not good, if we find a gap in design where we expected a filling, the accustomed equilibrium of the organism does not result; psychically there is lack of balance, and the object is æsthetically painful. We seem to have, then, in symmetry, three aspects. First, the objective quantitative equality of sides; second, a corresponding equivalence of bilaterally disposed organic energies, brought into equilibrium because acting in opposite directions; third, a feeling of balance, which is, in symmetry, our æsthetic satisfaction.

It would be possible, as I have intimated, to arrange a series of symmetrical figures in which the first would show simple geometrical reduplication of one side by the other, obvious at a glance; and the last, such a qualitative variety of compensating elements that only painstaking experimentation could make apparent what elements balanced others. The second, through its more subtle exemplification of the rule of quantitative equivalence, might be called a higher order of symmetry. Suppose now that we find given, objects which, æsthetically pleasing, nevertheless present, on one side of a point of reference, or center of division, elements that actually have none corresponding to them on the other; where there is not, in short, _objective_ bilateral equivalence, however subtly manifested, but, rather, a complete lack of compensation, a striking asymmetry. The simplest, most convincing case of this is the horizontal straight line, unequally divided. Must we, because of the lack of objective equality of sides, also say that the bilaterally equivalent muscular innervations are likewise lacking, and that our pleasure consequently does not arise from the feeling of balance? A new aspect of psychophysical æsthetics thus presents itself. Must we invoke a new principle for horizontal unequal division, or is it but a subtly disguised variation of the more familiar symmetry? And in vertical unequal division, what principle governs? A further paper will deal with vertical division. The present paper, as I have said, offers a theory for the horizontal.

To this end, there were introduced, along with the simple line figures already described, more varied ones, designed to suggest interpretation. One whole class of figures was tried and discarded because the variations, being introduced at the ends of the simple line, suggested at once the up-and-down balance of the lever about the division point as a fulcrum, and became, therefore, instances of simple symmetry. The parallel between such figures and the simple line failed, also, in the lack of homogeneity on either side the division point in the former, so that the figure did not appear to center at, or issue from the point of division, but rather to terminate or concentrate in the end variations. A class of figures that obviated both these difficulties was finally adopted and adhered to throughout the work. As exposed, the figures were as long as the simple line, but of varying widths. On one side, by means of horizontal parallels, the horizontality of the original line was emphasized, while on the other there were introduced various patterns (fillings). Each figure was movable to the right or the left, behind a stationary opening 160 mm. in length, so that one side might be shortened to any desired degree and the other at the same time lengthened, the total length remaining constant. In this way the division point (the junction of the two sides) could be made to occupy any position on the figure. The figures were also reversible, in order to present the variety-filling on the right or the left.

If it were found that such a filling in one figure varied from one in another so that it obviously presented more than the other of some clearly distinguishable element, and yielded divisions in which it occupied constantly a shorter space than the other, then we could, theoretically, shorten the divisions at will by adding to the filling in the one respect. If this were true it would be evident that what we demand is an equivalence of fillings--a shorter length being made equivalent to the longer horizontal parallels by the addition of more of the element in which the two short fillings essentially differ. It would then be a fair inference that the different lengths allotted by the various subjects to the short division of the simple line result from varying degrees of substitution of the element, reduced to its simplest terms, in which our filling varied. Unequal division would thus be an instance of bilateral symmetry.

The thought is plausible. For, in regarding the short part of the line with the long still in vision, one would be likely, from the æsthetic tendency to introduce symmetry into the arrangement of objects, to be irritated by the discrepant inequality of the two lengths, and, in order to obtain the equality, would attribute an added significance to the short length. If the assumption of bilateral equivalence underlying this is correct, then the repetition, in quantitative terms, on one side, of what we have on the other, constitutes the unity in the horizontal disposition of æsthetic elements; a unity receptive to an almost infinite variety of actual visual forms--quantitative identity in qualitative diversity. If presented material resists objective symmetrical arrangement (which gives, with the minimum expenditure of energy, the corresponding bilateral equivalence of organic energies) we obtain our organic equivalence in supplementing the weaker part by a contribution of energies for which it presents no obvious visual, or objective, basis. From this there results, by reaction, an objective equivalence, for the psychic correlate of the additional energies freed is an attribution to the weaker part, in order to secure this feeling of balance, of some added qualities, which at first it did not appear to have. In the case of the simple line the lack of objective symmetry that everywhere meets us is represented by an unequal division. The enhanced significance acquired by the shorter part, and its psychophysical basis, will engage us further in the introspection of the subjects, and in the final paragraph of the paper. In general, however, the phenomenon that we found in the division of the line--the variety of divisions given by any one object, and the variations among the several subjects--is easily accounted for by the suggested theory, for the different subjects merely exemplify more fixedly the shifting psychophysical states of any one subject.

In all, five sets of the corrected figures were used. Only the second, however, and the fifth (chronologically speaking) appeared indubitably to isolate one element above others, and gave uniform results. But time lacked to develop the fifth sufficiently to warrant positive statement. Certain uniformities appeared, nevertheless, in all the sets, and find due mention in the ensuing discussion. The two figures of the second set are shown in Fig. 2. Variation No. III. shows a design similar to that of No. II., but with its parts set more closely together and offering, therefore, a greater complexity. In Table II. are given the average divisions of the nine subjects. The total length of the figure was, as usual, 160 mm. Varying numbers of judgments were made on the different subjects.

TABLE II.

No. I. No. II. No. I. (reversed). No. II. (reversed). L. R. L. R. R. L. R. L.

A 55 0 48 0 59 0 50 0 B 59 0 44 0 63 0 52 0 C 58 0 56 0 52 0 50 0 D 60 0 56 0 60 0 55 0 E 74 59 73 65 74 60 75 67 F 61 67 60 66 65 64 62 65 G 64 64 62 68 63 64 53 67 H 76 68 75 64 66 73 67 71 J 49 0 41 0 50 0 42 0 -- -- -- -- -- -- -- -- Total. 61 64 57 65 61 65 54 67

With the complex fillings at the left, it will be seen, firstly, that in every case the left judgment on No. III. is less than that on No. II. With the figures reversed, the right judgments on No. III. are less than on No. II., with the exception of subjects _E_ and _H_. Secondly, four of the subjects only (_E_, _F_, _G_ and _H_) had judgments also on the side which gave the complex filling the larger space; to _E_, _F_ and _G_, these were secondary preferences; to _H_ they were always primary. Thirdly, the judgments on No. III. are less, in spite of the fact that the larger component parts of No. II., might be taken as additional weight to that side of the line, and given, therefore, the shorter space, according to the principle of the lever.

The subjects, then, that appear not to substantiate our suggested theory are _E_ and _H_, who in the reversed figures give the shorter space to the less complex filling, and _F_ and _G_, who, together with _E_ and _H_, have always secondary judgments that allot to either complex filling a larger space than to the simple horizontal. Consider, first, subjects _E_ and _H_. For each, the difference in division of II. and III. is in any case very slight. Further, subject _E_, in judgments where the complex filling _exceeds_ the horizontal parallels in length, still gives the more complex of the two fillings markedly the shorter space, showing, apparently, that its additional complexity works there in accord with the theory. There was, according to his introspection, another principle at work. As a figure, he emphatically preferred II. to III. The filling of II. made up, he found, by its greater interest, for lack of length. He here secured a balance, in which the interest of the complex material compensated for the greater _extent_ of the simpler horizontals. This accounts for its small variation from III., and even for its occupying the smaller space. But in judgments giving the two complex fillings the larger space, the more interesting material _exceeded_ in extent the less interesting. In such divisions the balance was no longer uppermost in mind, but the desire to get as much as possible of the interesting filling. To this end the horizontal parallels were shortened as far as they could be without becoming insignificant. But unless some element of balance were there (although not present to introspection) each complex filling, when up for judgment, would have been pushed to the same limit. It, therefore, does seem, in cases where the complex fillings occupied a larger space than the horizontals, that the subject, not trying consciously to secure a balance of _interests_, was influenced more purely by the factor of complexity, and that his judgments lend support to our theory.

Subject H was the only subject who consistently _preferred_ to have all complex fillings occupy the larger space. Introspection invariably revealed the same principle of procedure--he strove to get as much of the interesting material as he could. He thought, therefore, that in every case he moved the complex filling to that limit of the pleasing range that he found on the simple line, which would yield him most of the filling. Balance did not appear prominent in his introspection. A glance, however, at the results shows that his introspection is contradicted. For he maintains approximately the same division on the right in all the figures, whether reversed or not, and similarly on the left. The average on the right for all four is 67; on the left it is 74. Comparing these with the averages on the simple line, we see that the right averages coincide exactly, while the left but slightly differ. I suspect, indeed, that the fillings did not mean much to _H_, except that they were 'interesting' or 'uninteresting'; that aside from this he was really abstracting from the filling and making the same judgments that he would make on the simple line. Since he was continually aware that they fell within the 'pleasing range' on the simple line, this conclusion is the more plausible.

Perhaps these remarks account for the respective uniformities of the judgments of _E_ and _H_, and their departure from the tendency of the other subjects to give the more complex filling constantly the shorter space. But subjects _F_ and _G_ also had judgments (secondary with both of them) giving to the complex filling a larger extent than to the parallels. With them one of two principles, I think, applies: The judgments are either instances of abstraction from the filling, as with _H_, or one of simpler gravity or vertical balance, as distinguished from the horizontal equivalence which I conceive to be at the basis of the other divisions. With _F_ it is likely to be the latter, since the divisions of the figures under discussion do not approach very closely those of the simple line, and because introspectively he found that the divisions giving the complex the larger space were 'balance' divisions, while the others were determined with 'reference to the character of the fillings.' From _G_ I had no introspection, and the approximation of his judgments to those he gave for the simple line make it probable that with him the changes in the character of the filling had little significance. The average of his judgments in which the complex filling held the greater space is 66, while the averages on the simple line were 65 on the left, and 64 on the right. And, in general, abstraction from filling was easy, and to be guarded against. Subject _C_, in the course of the work, confessed to it, quite unsolicited, and corrected himself by giving thenceforth _all_ complex fillings much smaller space than before. Two others noticed that it was particularly hard not to abstract. Further, none of the four subjects mentioned (with that possible exception of _E_) showed a sensitiveness similar to that of the other five.

With the exception of _H_, and in accord with the constant practice of the other five, these subjects, too, occasionally found no pleasing division in which the complex filling preponderated in length over the horizontals. It was uniformly true, furthermore, in every variation introduced in the course of the investigation, involving a complex and a simple filling, that all the nine subjects but _H_ _preferred_ the complex in the shorter space; that five refused any divisions offering it in the larger space; that these five showed more sensitiveness to differences in the character of fillings; and that with one exception (_C_) the divisions of the simple line which these subjects gave were nearer the ends than those of the others. It surely seems plausible that those most endowed with æsthetic sensitiveness would find a division near the center more unequal than one nearer the end; for one side only slightly shorter than the other would at once seem to mean the same thing to them, and yet, because of the obvious difference in length, be something markedly different, and they would therefore demand a part short enough to give them sharp qualitative difference, with, however, in some way, quantitative equivalence. When the short part is too long, it is overcharged with significance, it strives to be two things at once and yet neither in its fulness.

We thus return to the simple line. I have considered a series of judgments on it, and a series on two different figures, varying in the degree of complexity presented, in one of their fillings. It remains very briefly to see if the introspection on the simple line furnishes further warrant for carrying the complexities over into the simple line and so giving additional validity to the outlined theory of substitution. The following phrases are from introspective notes.

_A_. Sweep wanted over long part. More attention to short. Significance of whole in short. Certainly a concentration of interest in the short. Short is efficacious. Long means rest; short is the center of things. Long, an effortless activity; short, a more strenuous activity. When complex fillings are introduced, subject is helped out; does not have to put so much into the short division. In simple line, subject _introduces_ the concentration. In complex figures the concentration is objectified. In _equal_ division subject has little to do with it; the _unequal_ depends on the subject--it calls for appreciation. Center of references is the division point, and the eye movements to right and left begin here, and here return. The line centers there. The balance is a horizontal affair.

_B_. Center a more reposing division. Chief attention to division point, with side excursions to right and left, when refreshment of perception is needed. The balance is horizontal and not vertical.

_C_. A balance with variety, or without symmetry. Centers at division point and wants sweep over long part. More concentration on short part. Subjective activity there--an introduction of energy. A contraction of the muscles used in active attention. Long side easier, takes care of itself, self-poised. Line centers at division point. Active with short division. Introduces activity, which is equivalent to the filling that the complex figures have; in these the introduced activity is objectified--made graphic.

_D_. Focal point at division point: wants the interesting things in a picture to occupy the left (when short division is also on left). Short division the more interesting and means greater complication. When the pleasing division is made, eyes move first over long and then over short. Division point the center of real reference from which movements are made.

_E_. No reference to center in making judgments; hurries over center. All portions of simple line of equal interest; but in unequal division the short gets a non-apparent importance, for the line is then a scheme for the representation of materials of different interest values. When the division is too short, the imagination refuses to give it the proportionally greater importance that it would demand. When too long it is too near equality. In enjoying line, the division point is fixed, with shifts of attention from side to side. An underlying intellectual assignment of more value to short side, and then the sense-pleasure comes; the two sides have then an equality.

_F_. Middle vulgar, common, prosaic; unequal lively. Prefers the lively. Eyes rest on division point, moving to the end of long and then of short. Ease, simplicity and restfulness are proper to the long part of complex figures. Short part of simple line looks wider, brighter and more important than long.

_G_. Unequal better than equal. Eye likes movement over long and then over short. Subject interested only in division point. Short part gives the æsthetic quality to the line.

_H_. Center not wanted. Division point the center of interest. (No further noteworthy introspection from _H_, but concerning complex figures he said that he wanted simple or the compact on the short, and the interesting on the long.)

These introspective notes were given at different times, and any repetitions serve only to show constancy. The subjects were usually very certain of their introspection. In general it appears to me to warrant these three statements: (1) That the center of interest is the division point, whence eye-movements, or innervations involving, perhaps, the whole motor system, are made to either side. (2) That there is some sort of balance or equivalence obtained (a bilateral symmetry), which is not, however, a vertical balance--that is, one of weights pulling downwards, according to the principle of the lever. All the subjects repudiated the suggestion of vertical balance. (3) That the long side means ease and simplicity, and represents graphically exactly what it means; that the short side means greater intensity, concentration, or complexity, and that this is substituted by the subject; the short division, unlike the long, means something that it does not graphically represent.

So much for the relation between what is objectively given and the significance subjectively attributed to it. There remains still the translation into psychophysical terms. The results on the complex figures (showing that a division may be shortened by making the innervations on that side increasingly more involved) lend plausibility to the interpretation that the additional significance is, in visual terms, a greater intricacy or difficulty of eye-movement, actual or reproduced; or, in more general terms, a greater tension of the entire motor system. In such figures the psychophysical conditions for our pleasure in the unequal division of the simple horizontal line are merely graphically symbolized, not necessarily duplicated. On page 553 I roughly suggested what occurs in regarding the unequally divided line. More exactly, this: the long section of the line gives a free sweep of the eyes from the division point, the center, to the end; or again, a free innervation of the motor system. The sweep the subject makes sure of. Then, with that as standard, the æsthetic impulse is to secure an equal and similar movement, from the center, in the opposite direction. It is checked, however, by the end point of the short side. The result is the innervation of antagonistic muscles, by which the impression is intensified. For any given subject, then, the pleasing unequal division is at that point which causes quantitatively equal physiological discharges, consisting of the simple movement, on one hand, and, on the other, the same kind of movement, compounded with the additional innervation of the antagonists resulting from the resistance of the end point. Since, when the characteristic movements are being made for one side, the other is always in simultaneous vision, the sweep receives, by contrast, further accentuation, and the innervation of antagonists doubtless begins as soon as movement on the short side is begun. The whole of the short movement is, therefore, really a resultant of the tendency to sweep and this necessary innervation of antagonists. The correlate of the equivalent innervations is equal sensations of energy of movement coming from the two sides. Hence the feeling of balance. Hence (from the lack of unimpeded movement on the short side) the feeling there of 'intensity,' or 'concentration,' or 'greater significance.' Hence, too, the 'ease,' the 'simplicity,' the 'placidity' of the long side.

As in traditional symmetry, the element of unity or identity, in unequal division, is a repetition, in quantitative terms, on one side, of what is given on the other. In the simple line the _equal_ division gives us obviously exact objective repetition, so that the psychophysical correlates are more easily inferred, while the _unequal_ offers apparently no compensation. But the psychophysical contribution of energies is not gratuitous. The function of the increment of length on one side, which in the centrally divided line makes the divisions equal, is assumed in unequal division by the end point of the short side; the uniform motor innervations in the former become, in the latter, the additional innervation of antagonists, which gives the equality. The two are separated only in degree. The latter may truly be called, however, a symmetry of a higher order, because objectively the disposition of its elements is not graphically obvious, and psychophysically, the quantitative unity is attained through a greater variety of processes. Thus, in complex works of art, what at first appears to be an unsymmetrical composition, is, if beautiful, only a subtle symmetry. There is present, of course, an arithmetically unequal division of horizontal extent, aside from the filling. But our pleasure in this, _without_ filling, has been seen to be also a pleasure in symmetry. We have, then, the symmetry of equally divided extents and of unequally divided extents. They have in common bilateral equivalence of psychophysical processes; the nature of these differs. In both the principle of unity is the same. The variety through which it works is different.

* * * * *

STUDIES IN ANIMAL PSYCHOLOGY.

* * * * *

HABIT FORMATION IN THE CRAWFISH CAMBARUS AFFINIS.[1]

BY ROBERT M. YERKES AND GURRY E. HUGGINS.

[1] See also Yerkes, Robert: 'Habit-Formation in the Green Crab, _Carcinus Granulalus_,' _Biological Bulletin_, Vol. III., 1902, pp. 241-244.

This paper is an account of some experiments made for the purpose of testing the ability of the crawfish to profit by experience. It is well known that most vertebrates are able to learn, but of the invertebrates there are several classes which have not as yet been tested.

The only experimental study of habit formation in a crustacean which we have found is that of Albrecht Bethe[2] on the crab, _Carcinus maenas_. In his excellent paper on the structure of the nervous system of _Carcinus_ Bethe calls attention to a few experiments which he made to determine, as he puts it, whether the crab possesses psychic processes. The following are the observations made by him. Experiment I. A crab was placed in a basin which contained in its darkest corner an _Eledone_ (a Cephalopod). The crab at once moved into the dark region because of its instinct to hide, and was seized by the _Eledone_ and drawn under its mantle. The experimenter then quickly freed the crab from its enemy and returned it to the other end of the basin. But again the crab returned to the dark and was seized. This was repeated with one animal five times and with another six times without the least evidence that the crabs profited by their experiences with the _Eledone_. Experiment 2. Crabs in an aquarium were baited with meat. The experimenter held his hand above the food and each time the hungry crab seized it he caught the animal and maltreated it, thus trying to teach the crabs that meat meant danger. But as in the previous experiment several repetitions of the experience failed to teach the crabs that the hand should be avoided. From these observations Bethe concludes that _Carcinus_ has no 'psychic qualities' (_i.e._, is unable to profit by experience), but is a reflex machine.

[2] Bethe, Albrecht: 'Das Centralnervensystem von _Carcinus maenas_,' II. Theil., _Arch. f. mikr. Anat._, Bd. 51, 1898, S. 447.

Bethe's first test is unsatisfactory because the crabs have a strong tendency to hide from the experimenter in the darkest corner. Hence, if an association was formed, there would necessarily be a conflict of impulses, and the region in which the animal would remain would depend upon the relative strengths of its fear of the experimenter and of the _Eledone_. This objection is not so weighty, however, as is that which must obviously be made to the number of observations upon which the conclusions are based. Five or even twenty-five repetitions of such an experiment would be an inadequate basis for the statements made by Bethe. At least a hundred trials should have been made. The same objection holds in case of the second experiment. In all probability Bethe's statements were made in the light of long and close observation of the life habits of _Carcinus_; we do not wish, therefore, to deny the value of his observations, but before accepting his conclusions it is our purpose to make a more thorough test of the ability of crustaceans to learn.

For determining whether the crawfish is able to learn a simple form of the labyrinth method was employed. A wooden box (Fig. 1) 35 cm. long, 24 cm. wide and 15 cm. deep, with one end open, and at the other end a triangular compartment which communicated with the main portion of the box by an opening 5 cm. wide, served as an experiment box. At the open end of this box a partition (_P_) 6 cm. long divided the opening into two passages of equal width. Either of these passages could be closed with a glass plate (_G_), and the subject thus forced to escape from the box by the choice of a certain passage. This box, during the experiments, was placed in the aquarium in which the animals lived. In order to facilitate the movement of the crawfish toward the water, the open end was placed on a level with the water in the aquarium, and the other end was raised so that the box made an angle of 6° with the horizontal.

Experiments were made under uniform conditions, as follows. A subject was taken from the aquarium and placed in a dry jar for about five minutes, in order to increase the desire to return to the water; it was then put into the triangular space of the experiment box and allowed to find its way to the aquarium. Only one choice of direction was necessary in this, namely, at the opening where one of the passages was closed. That the animal should not be disturbed during the experiment the observer stood motionless immediately behind the box.

Before the glass plate was introduced a preliminary series of tests was made to see whether the animals had any tendency to go to one side on account of inequality of illumination, of the action of gravity, or any other stimulus which might not be apparent to the experimenter. Three subjects were used, with the results tabulated.

Exit by Exit by Right Passage Left Passage. No. 1 6 4 No. 2 7 3 No. 3 3 7 16 14

Since there were more cases of exit by the right-hand passage, it was closed with the glass plate, and a series of experiments made to determine whether the crawfish would learn to avoid the blocked passage and escape to the aquarium by the most direct path. Between March 13 and April 14 each of the three animals was given sixty trials, an average of two a day. In Table I. the results of these trials are arranged in groups of ten, according to the choice of passages at the exit. Whenever an animal moved beyond the level of the partition (_P_) on the side of the closed passage the trial was counted in favor of the closed passage, even though the animal turned back before touching the glass plate and escaped by the open passage.

TABLE I.

HABIT FORMATION IN THE CRAWFISH.¹

Experiments. No. 1 No. 2 No. 3 Totals Per cent Open Closed Open Closed Open Closed Open Closed Open 1-10 8 2 5 5 2 8 15 15 50.0 11-20 4 6 8 2 6 4 18 12 60.0 21-30 6 3² 8 2 8 2 22 7 75.8 31-40 9 1 8 2 8 2 25 5 83.3 41-50 8 2 8 2 7 3 23 7 76.6 51-60 10 0 8 2 9 1 27 3 90.0

TEST OF PERMANENCY OF HABIT AFTER 14 DAYS' REST.

61-70 6 4 8 2 8 2 22 8 73.3 (1-10) 71-80 6 4 8 2 7 3 21 9 70.0 (11-20)

¹The experiments of this table were made by F.D. Bosworth.

²One trial in which the subject failed to return to the water within thirty minutes.

In these experiments there is a gradual increase in the number of correct choices (_i.e._, choice of the 'open' passage) from 50 per cent. for the first ten trials to 90 per cent. for the last ten (trials 51-60). The test of permanency, made after two weeks, shows that the habit persisted.

Although the observations just recorded indicate the ability of the crawfish to learn a simple habit, it seems desirable to test the matter more carefully under somewhat different conditions. For in the experiments described the animals were allowed to go through the box day after day without any change in the floor over which they passed, and as it was noted that they frequently applied their antennae to the bottom of the box as they moved along, it is possible that they were merely following a path marked by an odor or by moistness due to the previous trips. To discover whether this was really the case experiments were made in which the box was thoroughly washed out after each trip.

The nature of the test in the experiments now to be recorded is the same as the preceding, but a new box was used. Fig. 2 is the floor plan and side view of this apparatus. It was 44.5 cm. long, 23.5 cm. wide and 20 cm. deep. The partition at the exit was 8.5 cm. in length. Instead of placing this apparatus in the aquarium, as was done in the previous experiments, a tray containing sand and water was used to receive the animals as they escaped from the box. The angle of inclination was also changed to 7°. For the triangular space in which the animals were started in the preceding tests a rectangular box was substituted, and from this an opening 8 cm. wide by 5 cm. deep gave access to the main compartment of the box.

A large healthy crawfish was selected and subjected to tests in this apparatus in series of ten experiments given in quick succession. One series a day was given. After each test the floor was washed; as a result the experiments were separated from one another by a three-minute interval, and each series occupied from thirty minutes to an hour. Table II. gives in groups of five these series of ten observations each. The groups, indicated by Roman numerals, run from I. to IX., there being, therefore, 450 experiments in all. Groups I. and II., or the first 100 experiments, were made without having either of the exit passages closed, in order to see whether the animal would develop a habit of going out by one side or the other. It did very quickly, as a matter of fact, get into the habit of using the left passage (L.). The last sixty experiments (Groups I. and II.) show not a single case of escape by the right passage. The left passage was now closed. Group III. gives the result. The time column (_i.e._, the third column of the table) gives for each series of observations the average time in seconds occupied by the animal in escaping from the box. It is to be noted that the closing of the Left passage caused an increase in the time from 30.9 seconds for the last series of the second group to 90 seconds for the first series of the third group. In this there is unmistakable evidence of the influence of the change in conditions. The animal after a very few experiences under the new conditions began going to the Right in most cases; and after 250 experiences it had ceased to make mistakes. Group VII. indicates only one mistake in fifty choices.

TABLE II.

HABIT FORMATION AND THE MODIFICATION OF HABITS IN THE CRAWFISH.

Results in Series of Ten. Avs. in Groups of 50. Series L. R. Time. L. R. L. R. Time. Group I. 1 9 1 45 Per Cent. 2 3 7 69 3 9 1 20 4 4 6 72 5 10 31 -- -- 35 15 70 30 47.4

II. 1 10 29 2 10 30 3 10 30 4 10 28.8 5 10 30.9 -- ---- 50 100 30 .... .... III. 1 4 6 90 2 2 2 8 89.2 1 3 1 9 36.7 1 4 2 8 51 2 5 1 9 43 2 -- -- -- 10 40 7 20 80 62 .... .... IV. 1 3 7 124 1 2 2 8 44 5 3 2 8 37 4 4 10 34 5 2 8 1 -- -- -- 9 41 11 18 82 60 .... .... V. 1 10 44 2 2 10 35 4 3 3 7 76 3 4 2 8 50 7 5 1 9 50 4 -- -- -- 6 44 20 12 88 51 .... .... VI. 1 2 8 45 2 2 10 41 5 3 1 9 41.8 7 4 10 32.7 7 5 10 8 -- -- -- 3 47 29 6 94 40 .... .... VII. 1 1 9 39 4 2 10 38 7 3 10 30.7 3 4 10 42 6 5 10 48 4 -- -- -- 1 49 24 2 98 39.5

R. L. .... .... VIII. 1 8 2 147 1 2 9 1 26 3 8 2 49 2 4 9 1 38 2 5 9 1 41 -- -- -- 43 7 5 86 14 60.2 .... .... IX. 1 1 9 41 2 2 8 39 1 3 10 29 4 1 9 47 5 1 9 32 1 10 90 38 -- -- -- 5 45 2

The dotted lines at the beginning of groups indicate the closed passage.

At the beginning of Group VIII. the Right instead of the Left passage was closed in order to test the ability of the animal to change its newly formed habit. As a result of this change in the conditions the animal almost immediately began going to the Left. What is most significant, however, is the fact that in the first trial after the change it was completely confused and spent over fifteen minutes wandering about, and trying to escape by the old way (Fig. 4 represents the path taken). At the end of the preceding group the time of a trip was about 48 seconds, while for the first ten trips of Group VIII. the time increased to 147 seconds. This remarkable increase is due almost entirely to the great length of time of the first trip, in which the animal thoroughly explored the whole of the box and made persistent efforts to get out by the Right passage as it had been accustomed to do. It is at the same time noteworthy that the average time for the second series of Group VIII. is only 26 seconds.

For Group IX. the conditions were again reversed, this time the Left passage being closed. Here the first trial was one of long and careful exploration, but thereafter no more mistakes were made in the first series, and in the group of fifty tests there were only five wrong choices.

The fifth column, R. L. and L. R., of Table II. contains cases in which the subject started toward one side and then changed its course before reaching the partition. In Group III., for instance, when the Left passage was closed, the subject started toward the Left seven times, but in each case changed to the Right before reaching the partition. This is the best evidence of the importance of vision that these experiments furnish.

The first experiments on habit formation proved conclusively that the crawfish is able to learn. The observations which have just been described prove that the labyrinth habit is not merely the following of a path by the senses of smell, taste or touch, but that other sensory data, in the absence of those mentioned, direct the animals. So far as these experiments go there appear to be at least four sensory factors of importance in the formation of a simple labyrinth habit: the chemical sense, touch, vision and the muscle sense. That the chemical sense and touch are valuable guiding senses is evident from even superficial observation, and of the importance of vision and the muscle sense we are certain from the experimental evidence at hand.

Of the significance of the sensations due to the 'direction of turning' in these habits the best evidence that is furnished by this work is that of the following observations. In case of the tests of Table II. the subject was, after 100 preliminary tests, trained by 250 experiences to escape by the Right-hand passage. Now, in Groups III. to VII., the subject's usual manner of getting out of the closed passage, when by a wrong choice it happened to get into it, was to draw back on the curled abdomen, after the antennae and chelæ had touched the glass plate, and then move the chelæ slowly along the Right wall of the partition until it came to the upper end; it would then walk around the partition and out by the open passage. Fig. 3 represents such a course. In Group VIII. the Right passage was closed, instead of the Left as previously. The first time the animal tried to get out of the box after this change in the conditions it walked directly into the Right passage. Finding this closed it at once turned to the Right, _as it had been accustomed to do when it came in contact with the glass plate_, and moved along the side of the box just as it did in trying to get around the end of the partition. The path taken by the crawfish in this experiment is represented in Fig. 4. It is very complex, for the animal wandered about more than fifteen minutes before escaping.

The experiment just described to show the importance of the tendency to turn in a certain direction was the first one of the first series after the change in conditions. When given its second chance in this series the subject escaped directly by the Left passage in 33 seconds, and for the three following trips the time was respectively 25, 25 and 30 seconds.

Upon the experimental evidence presented we base the conclusion that crawfish are able to profit by experience in much the same way that insects do, but far more slowly.

It was thought that a study of the way in which crawfish right themselves when placed upon their backs on a smooth surface might furnish further evidence concerning the ability of the animals to profit by experience.

Dearborn[3] from some observations of his concludes that there is no one method by which an individual usually rights itself, and, furthermore, that the animals cannot be trained to any one method. His experiments, like Bethe's, are too few to warrant any conclusions as to the possibility of habit formation.

[3] Dearborn, G.V.N.: 'Notes on the Individual Psychophysiology of the Crayfish,' _Amer. Jour. Physiol._, Vol. 3, 1900, pp. 404-433.

For the following experiments the subject was placed on its back on a smooth surface in the air and permitted to turn over in any way it could. Our purpose was to determine (1) whether there was any marked tendency to turn in a certain way, (2) whether if such was not the case a tendency could be developed by changing the conditions, and (3) how alteration in the conditions of the test would affect the turning.

A great many records were taken, but we shall give in detail only a representative series. In Table III., 557 tests made upon four subjects have been arranged in four groups for convenience of comparison of the conditions at different periods of the training process. Each of these groups, if perfect, would contain 40 tests for each of the four subjects, but as a result of accidents II., III., and IV. are incomplete.

TABLE III.

RE-TURNING OF CRAWFISH.

Group. Number of L. R. Time in Tests. Animal. Per cent. Seconds. I. 2 22.5 77.5 14.6 40 3 42.5 57.5 2.6 40 4 52.8 47.2 4.3 38 16 44.5 55.5 22.5 45 -- ---- ---- ---- --- 40.6 59.4 10.8 163

Group. Number of L. R. Time in Tests. Animal. Per cent. Seconds. II 2 28 72 50 43 3 32 68 6.2 50 4 -- 100 6.8 40 16 31.3 68.7 39.3 42 -- ---- ---- ---- --- 22.8 77.2 25.6 175

Group. Number of L. R. Time in Tests. Animal. Per cent. Seconds. III 2 2.5 97.5 46.5 40 -- -- -- -- -- 4 20 80 5.5 40 16 41 59 15 49 -- ---- ---- ---- --- 21.2 78.8 22 129

Group. Number of L. R. Time in Tests. Animal. Per cent. Seconds. IV. 2 2 98 41 50 -- -- -- -- -- 4 32.5 67.5 7.3 40 -- ---- ---- ---- --- 17 83 24 90

Group I., representing 163 tests, shows 59 per cent. to the right, with a time interval of 10.8 seconds (_i.e._, the time occupied in turning). Group II. shows 77 per cent. to the right; and so throughout the table there is an increase in the number of returnings to the right. These figures at first sight seem to indicate the formation of a habit, but in such case we would expect, also, a shortening of the time of turning. It may be, however, that the animals were gradually developing a tendency to turn in the easiest manner, and that at the same time they were becoming more accustomed to the unusual position and were no longer so strongly stimulated, when placed on their backs, to attempt to right themselves.

All the subjects were measured and weighed in order to discover whether there were inequalities of the two sides of the body which would make it easier to turn to the one side than to the other. The chelæ were measured from the inner angle of the joint of the protopodite to the angle of articulation with the dactylopodite. The carapace was measured on each side, from the anterior margin of the cephalic groove to the posterior extremity of the lateral edge. The median length of the carapace was taken, from the tip of the rostrum to the posterior edge, and the length of the abdomen was taken from this point to the edge of the telson. These measurements, together with the weights of three of the subjects, are given in the accompanying table.

TABLE IV.

MEASUREMENTS OF CRAWFISH.

Chelæ. Carapace. Abdomen. Weight. Left. Right. Left. Right. Median.

No. 2, 9.8 10.0 38.2 38.7 47.3 48.1 29.7 No. 4, 7.7 7.7 33.6 33.8 39.4 42.3 17.7 No. 16, 12.5 12.4 37.6 37.6 46.4 53.2 36.2

Since these measurements indicate slightly greater size on the right it is very probable that we have in this fact an explanation of the tendency to turn to that side.

To test the effect of a change in the conditions, No. 16 was tried on a surface slanted at an angle of 1° 12'. Upon this surface the subject was each time so placed that the slant would favor turning to the right. Under these conditions No. 16 gave the following results in two series of tests. In the first series, consisting of 46 turns, 82.6 per cent. were to the right, and the average time for turning was 17.4 seconds; in the second series, of 41 tests, there were 97.5 per cent, to the right, with an average time of 2.5 seconds. We have here an immediate change in the animal's method of re-turning caused by a slight change in the conditions. The subject was now tested again on a level surface, with the result that in 49 tests only 59 per cent. were toward the right, and the time was 15 seconds.

SUMMARY.

1. Experiments with crawfish prove that they are able to learn simple labyrinth habits. They profit by experience rather slowly, from fifty to one hundred experiences being necessary to cause a perfect association.

2. In the crawfish the chief factors in the formation of such habits are the chemical sense (probably both smell and taste), touch, sight and the muscular sensations resulting from the direction of turning. The animals are able to learn a path when the possibility of following a scent is excluded.

3. The ease with which a simple labyrinth habit may be modified depends upon the number of experiences the animal has had; the more familiar the animal is with the situation, the more quickly it changes its habits. If the habit is one involving the choice of one of two passages, reversal of the conditions confuses the subject much more the first time than in subsequent cases.

4. Crawfish right themselves, when placed on their backs, by the easiest method; and this is found to depend usually upon the relative weight of the two sides of the body. When placed upon a surface which is not level they take advantage, after a few experiences, of the inclination by turning toward the lower side.

* * * * *

THE INSTINCTS, HABITS, AND REACTIONS OF THE FROG.

BY ROBERT MEARNS YERKES.