་

and of the simple mathematical proportions as found in the relations of the vibrations of the components of musical harmonies, he constructed a series of figures of the simplest designcrosses, ellipses, parallelograms-and gave to each mathematical proportion a representative within each class of figure. From each such series the most pleasing figure was chosen by a large number of persons; the figure receiving the greatest number of choices was regarded as having the most pleasing proportions. The results of the chosen proportions in different series of figures show considerable disagreement, which was probably due to imperfections in Fechner's method.

A better method affords a choice, not limited to a set of arbitrarily chosen proportions, but open to a series of figures whose mathematical proportions vary in a constant ratio between the proportion of 1: 1 and 1: x (x being any desired large number). In other words a series (of crosses for example) should be employed, wherein as far as necessary or practicable for purposes of experiment, every possible mathematical proportion is represented by a figure, whose place in the series is determined by the relative size of the mathematical proportions of its parts. This method permits of the easy observation of the relative increase or decrease in the aesthetic feeling attaching to the regularly increasing proportions. For each group of figures and for each observer will be found a curve of" æsthetic pleasure,' which rises and falls with the mathematical proportions of the figures.

A research carried out by this method with many series of figures, all however, of the simplest design, gave the following results:-For all groups of figures and for all positions of the figure, there are but two pleasing proportions: the ratio 1: 1, or "perfect Symmetry" and a ratio which lies between 2: 3 and 1: 2, the most pleasing proportion. The former proportion 1: 1 stands æsthetically so apart from all other proportions, that a comparison between it and any one other proportion on the same terms as between the other proportions among themselves is impossible. Excepting the proportion 1: 1, the relative pleasing quality of all mathematical proportions can be expressed by a curve which ises from 1: x (x=5 or any large number) first rapidly, then more slowly to a maximum between 1: 2 and 2:3, whence the curve falls more rapidly than it 10se to a proportion but a little distance from 1:1. The maximum of this curve lies in nearly all series between 1: 2, and 2: 3, and the average

of all results places it so near the "golden section," that this formula might well be employed to express in mathematical terms "the most pleasing proportion." The use of this formula is, however, in so far objectionable, as it carries with it the implication that the aesthetic value of the "most pleasing proportion," is dependent upon the mathematical properties of the 'golden section." My experiments go to prove that its æsthetic value does not lie, as Zeising believed, in the pleasing and complex equality of the relations of the parts of a figure, but in a pleasing difference of parts. In other words, the most pleasing aesthetic proportion subsumes itself under æsthetic contrast. For this reason, the proportion is not clearly discoverable in complex designs and objects, as the demand for the best contrast of parts may easily give way to other considerations.

In the discussion that followed, Professor BALDWIN asked:

(1) Whether Dr. Lightner-Witmer's "Curve of Esthetic Pleasure included negative as well as positive hedonic values, i.e., whether the observers found that the contemplation of certain proportions was attended with distinctly disagreeable feelings; (2) whether Dr. Witmer had taken care to exclude any possible effect on æsthetic judgment caused by the outline of the platform on which the figures were placed.

Dr. LIGHTNER-WITMER answered:

(1) That his curve did include negative values, representing actual displeasure experienced by the observers: and (2) that he had uniformly taken the greatest care to exclude any possible influence of the border of the paper on which the figures were drawn; this paper being always placed against a background of the same colour.

Professor SULLY asked:

Whether, in referring preferences to the operation of contrast, Dr. Lightner-Witmer meant that the particular range of ratios preferred answered to a maximum effect of contrast, as was the case with the approximately complementary combinations which are said by Brücke to be preferred in the case of colour-contrasts. In other words, could the particular selections made by his subjects be deduced from an æsthetic or psychological law of contrast?

Dr. LIGHTNER-WITMER said:

That he did not mean to explain his results in this way, as necessary deductions from a principle of contrast.

Mr. EDWARD T. DIXON asked:

Whether the most æsthetic proportion had been determined from a series of straight lines cut at various points, or only from a series of crosses of various forms approximately the same. For in the first case it seemed possible to realize, in the neighbourhood of the " 'golden section," that the ratio of the lesser part to the greater was equal to the ratio of the greater part to the whole; whereas in the second case it did not seem easy to effect mentally the necessary summation of the parts.

Dr. LIGHTNER-WITMER answered:

That he had always experimented with crosses and similar simple figures but that as the design of the figures was as simple as possible and the general form of course similar in each series, he found that the observer's attention was always directed to the varying element in each set of comparisons—the proportions of the parts.

The following paper was then read:

Natural Selection and Music,

By Dr. RICHARD WALLASCHEK.

Among arts, music in especial seems to have such scanty relations with the necessary conditions of life, that the question naturally suggests itself how this art could attain that climax of importance which it undoubtedly occupies to-day. To be sure one hears not unfrequently that all art, and music especially, is a "luxury," that we do not derive from it any profit or, advantage, and that its development therefore cannot be explained by the same natural laws which elsewhere govern the struggle for existence. But I fear that one is prone to consider music too much from the abstract point of view of our time. and not to consider sufficiently the position which it still occupies with primitive man.

Above all, one must keep in mind that primitive music has no necessary connection with a higher training and evolution. of the sense of hearing and that the whole development of music, beginning from primaval times to the present period, has not changed the human ear in any respect. All attempts to establish a connection between music and the exercise of the organs of hearing, must therefore be strictly excluded from our investigation. The oldest music we know of is no effect of

the sense of hearing, but of the conception of time; it is primarily a rhythmic movement, divisible into equal bars, and consists only in later stages of melody and harmony. We must consider music in the form, in which it occurs with primitive man, viz., in connection with dance and mimic representation. In regard to the origin of art Mr. Herbert Spencer's theory of the "surplus of vigour" is evidently the correct one, as far as it goes. The expression "surplus," however, implies too much an unecessary overflow of energy, on the basis of which it is easy to consider all that is effected by it as a "luxury," an unintentional effect. I cannot make up my mind to accept this view. It seems to me that even the higher animals have no surplus of energy for the struggle for existence, but with them a fight is a rarer occurrence, than with the lower animals, because they are able to annihilate the enemy, where the lower animals just manage to escape; therefore I should rather speak of the inapplicability of energy.

Primitive man is, in this respect, placed in exactly the same position as the higher animals. The war is transmuted into a war-dance after the battle is over, one and the same sound is war-cry and primitive song, the swinging of the spear is their mode of fighting and also of beating time, the same ponderous step is attack and joyous dance. Therefore these dances are necessary to prepare for the hunt or war, and afterwards to preserve and develop the power of those taking part in them. All examples of savage life go to show that the war-dance is a war-play, a preparation for, and preservation of common action. The same is the case with pantomimic representations, the oldest form of which is the animal-pantomime. These pantomimes manifest an extraordinary power of observation and a great familiarity with the character of animals, they keep those representing in them in constant practice, awaken interest in hunting in all the spectators, and give to them, one may say, an instructive example which may prove of use to them in case of need.

Some time ago the London papers contained the report that it was customary among the street arabs of the East-end to play constable, magistrate and criminal. No small indignation was expressed at this style of amusement, because (as was claimed) the children are in this way familiarized too much with the ingenuity of the police, the proceedings in court, the tricks of criminals, and all the particulars of an exciting life, in which revolt against the most necessary social restrictions plays a very important part. In the same way in which these games are a

school for crime, the games of the savages are a school for savage life-war and hunting, i.e., the struggle for existence.

So far this primitive pantomime; but what has music got to do with all this? If these representations were the work of single actors, as now-a-days, music might be missing, or it would only be of accessory importance. But in those representations the whole tribe takes a part and this action en masse is only possible, if it manifests itself in the well-arranged form of march and dance. The war-play as well as the animal-pantomime are choral dances of the whole tribe and the precision with which they are executed is only possible if a high degree of natural rhythmic sense exists (this time-sense is the psychological origin of music). Primitive music, in its actual aspects, with the rhythmical element strongly pronounced, is an organizing power which holds together the participants in the dance and makes a common action possible. This custom of the whole tribe to act in common as one body, and the skill evinced in doing this, cannot be without influence in the struggle for existence. It is only because primitive music was so perfectly united with the wants of daily life, because it had such practical aims, that it has with such difficulty severed itself from these wants and has so late developed into an independent art. In former times, it was inseparably connected with the war and hunting play. It is to the warriors that we owe the first rhythmical beating of time, to them we owe the first fixed melodies (signals), to them the first choral song and the first orchestra; all this is only too plainly shown in the life of the African savages. This primitive music has in all respects the same function, that the drummers, trumpeters and fife-players still have in the army and in public processions. Their music is in no wise an effect of the sense of hearing regarded in its musical aspect, and in no way a luxury which might just as well be wanting. Attempt to arrange a march, a dance, or a public procession without the organizing force of time (in the musical sense) and you will at once recognise how great and important this force is, and how it may be brought to serve practical ends.

A tribe which does not practice common action, which does not prepare and preserve its energy by war games, will have less pro-pect of success in real battle. These games (choral dances) however, are possible only in combination with primitive music, and this circumstance brings all musical ability within the scope of the law of natural selection.