unity, in order to accommodate the result to the requirements of human conception. It was shown also that the occasion for these efforts arises from the variety everywhere characterising the natural forms of which the artist is obliged to construct his products. Everything that has been unfolded since this was said, has had to do with methods of arrangement through which factors of a form, while exhibiting variety, can, nevertheless, be made to exhibit unity. But in none of these methods has there been necessitated such an absolute blending of the appearances of the two as in progress. In this the variety which in most of the arrangements is accepted as a necessary and accidental evil becomes essential. There can be no progress except of something that is clearly recognised to be a unity. But it is equally true that there can be none except as that which is a unity is perceived to be characterised by variety also. In progress, therefore, all the methods of art-composition that we have been considering seem to culminate. Before leaving this subject it would be well for the reader to recall what was said on page 33 with reference to the relation between art-composition as explained in Chapters XIV. and XV. and the requirements of beauty as discussed in Chapter II. An examination of the Appendix, too, page 387, will reveal that all these methods of composition fulfil exactly the underlying condition of assimilation which the great majority of physiological psychologists deem requisite tc the effects of beauty.

CHAPTER XVI.

RHYTHM AND PROPORTION.

Rhythm not Originated by Art-It Exists in Nature-In Nerve ActionRequired by the Natural Action of the Mind-Elements of Rhythm Existing in Speech-How Developed in Metre and Verse-In Music -Poetic Measures-General Comment-Meaning of Proportion-Result of a Natural Tendency to Make Like Measurements--Manifested Everywhere-Proportion in Nature-An Important Art-Principle— Result of Comparing Measurements not Actually Made, but Possible to Make-Not Actually Alike, but Apparently so-Proportion Puts Like Measurements with Like--Fulfilling Principles in Chapters XIV and XV.-Why Proportional Ratios must be Represented by Small Numbers-How Larger Numbers may be Used--Rectilinear Proportions-Of Allied Rectangles-Of Irregular Complex Figures-Must be Accompanied by Outlines of Simple and Regular Figures-Proportions of Human Form and Clothing—Countenance-Greek Type of Face not the only Beautiful One-Why Other Types may Seem Beautiful-Proportions of Human Body Indicated by Circles and Ellipses-Binocular Vision-Its Relation to Ellipses-Why the Curve Is the Line of Beauty-Shapes of Vases-Relation of Like Curves to Proportion Illustrated in Curves of the Human Form-Conclusion.

ACCORDING to the chart on page 277, the methods of

art-composition indicated in it result, as applied to duration, in rhythm; as applied to extension, in proportion; and, as applied to quality and pitch, whether of note or colour, in harmony. Of these, let us consider, first, rhythm. Art did not originate this, nor the satisfaction derivable from it. Long before the times of the first artists, men had had practical experience of its pleasures. Long

before the age of poetry, or music, or dancing, or even of fences or schoolboys, the primitive man had sat upon a log and kicked with his heels, producing a rhythm as perfect, in its way, as that of his representatives of the present who in Africa take delight in stamping their feet and clapping their hands, and in America in playing upon drums and tambourines, in order to keep time to the movements of dancers and the tunes of singers.

When we come to ask why rhythm should be produced thus, either by itself or in connection with poetry or music-in short, why it should be, as seems to be the case, a natural mode of expression, we cannot avoid having it suggested, at once, that it corresponds to a method characterising all natural movement whatever, whether appealing to the eye or ear, or whether produced by a human being or perceived in external nature. There is rhythm in the beating of our pulses, in the alternate lifting and falling of our chests while breathing, in our accenting and leaving unaccented the syllables of our speech, in our pausing for breath between consecutive phrases, and in our balancing from side to side and pushing forward one leg or one arm and then another, while walking. There is rhythm in the manifestations of all the life about us, in the flapping of the wings of the bird, in the changing phases of its song, even in the minutest trills that make up its melody, and in the throbbings of its throat to utter them; in the rising and falling of the sounds of the wind, and of the swaying to and fro of the trees, as well as in the flow and ebb of the surf on the seashore, and in the jarring of the thunder and the zigzag course of the lightning. In fact, rhythm seems to be almost as intimately associated with everything that a man can see or hear, as is the beating of his own heart with his own life. Even

the stars, like the rockets that we send toward them, speed onward in paths that return upon themselves, and the phrase "music of the spheres" is a logical as well as a poetical result of an endeavour to classify the grandest of all movements in accordance with a method which is conceived to be universal. No wonder, then, that men should feel the use of rhythm to be appropriate in artproducts modelled upon natural products. No wonder that, connected as it is with natural movement and life and the enjoyment inseparably associated with life, it should seem to the civilised to be-what certainly it seems to the uncivilised-an artistic end in itself.

Nor is this view of it suggested as a result merely of superficial observation. It is substantiated by the more searching experiments of the scientists. There have been discovered, for instance, in addition to the regular beat of the heart, and independent of it, rhythmical contractions and expansions of the walls of the arteries, increasing and decreasing at regular intervals the supply of blood. Such processes, which, according to Foster in his "Physiology," page 307, may be observed in the arteries of a frog's foot or a rabbit's ear, may be checked by cutting the nerves connecting it and the vaso-motor system; and this fact is taken to indicate that there is a rhythmic form of activity in the nerve-centres themselves. Regular periodic contractions have been observed, too, in the hearts of certain animals after being removed from the body; and this fact has been attributed to the presence in them of nerve-ganglia, acting according to some characteristic method. Movements of the same kind are mentioned, also, by Isaac Ott in his "Observations upon the Physiology of the Spinal Cord," in "Studies from the Biological Laboratory of Johns Hopkins Uni

versity," No. II., as taking place in certain parts of the bodies of dogs, cats, and rabbits after the severing of the spinal cord.

Such facts with reference to the rhythmic character of nerve-action seem to indicate a possibility of the same in mental action. Acting upon this suggestion, Dr. Thaddeus L. Bolton, Demonstrator and Fellow in Clark University, conducted, a few years ago, a series of interesting experiments, which are described by him in a thesis on "Rhythm," published in the American Journal of Psychol ogy, vol. vi., No. 2. "The first and most important object" of these experiments is said to have been to determine "what the mind did with a series of simple auditory impressions, in which there was absolutely no change of intensity, pitch, quality, or time-interval." As a result it was found that, out of fifty who were asked to listen to clicks produced by an instrument prepared for the purpose, two alone failed to divide these clicks into groups, the number in each group being determined, mainly, by the relative rapidity with which the clicks were produced. The groups were usually of twos or threes, though, with greater rapidity, they passed into groups of fours, sixes, and eights, always, however, when the members were many, with a tendency to divide into twos, threes, and fours. It was found, moreover, that, whenever a second, third, or fourth click was made louder than the others, the inclination to divide the clicks into corresponding groups of twos, threes, or fours was increased.

With such facts in mind, let us recall that speech, from which we have found both music and poetry to be developed, is composed of syllables, each uttered with an individual stress which separates it from other syllables.