A curve which fulfils more perfectly the demands of our dictum is that of an elastic thread, to which we have already alluded. If the two ends of a straight steel hair be brought towards each other by simple pressure, the intervening spring may be put into a series of various forms,simple undulations, and those more complicated, a figure 8, loops turning alternately opposite ways, loops turning all one way, and finally a circle. Now the whole of this variety is the result of subjecting each part of the curve to a law more simple than that of the cycloid. The elastic curve is a curve which bends or curves exactly in proportion to its distance from a given straight line. According to the canon, therefore, this curve should be beautiful; and it is acknowledged to be so in the examples given by the bending osier and the waving grain,also by the few who have seen full drawings of all the forms. And the mathematician finds in it a new beauty, from its marvellous correspondence with the motions of a pendulum,the algebraic expression of the two being identical.
The forms of organic life afford, however, the best examples of the dominion of our fundamental canon. The infinite variety of vegetable forms, all beautiful, and each one different in its beauty, is all the result of simple laws. It is true that these simple laws are not as yet all discovered; but the one great discovery of Phyllotaxis, which shows that all plants follow one law in the arrangement of their leaves upon the stem, thereby intimates in unmistakable language the simplicity and unity of all organic vegetable laws; and a similar assurance is given by the morphological reduction of all parts to a metamorphosed leaf.
The law of phyllotaxis, like that of the elastic curve, is carried out in time as well as in space. As the formula for the elastic curve is the same as that for the pendulum, so the law by which the spaces of the leaves are divided in scattering them round the stem, to give each its opportunity for light and air, is the same as that by which the times of the planets are proportioned to keep them scattered about the sun, and prevent them from gathering on one side of their central orb.
The forms of plants and trees are dependent upon the arrangement of the branches, and the arrangement of the branches depends upon that of the buds or leaves. The leaves are arranged by this numerical law,that the angular distance about the stem between two successive leaves shall be in such ratio to the whole circumference as may be expressed by a continued fraction composed wholly of the figure 1. It is, then, true, that all the beauty of the vegetable world which depends on the arrangement of partsthe graceful symmetry or more graceful apparent disregard of symmetry in the general form of plants, all the charm of the varying forms of forest trees, which adds such loveliness to the winter landscape, and such a refined source of pleasure to the exhilaration of the winter morning walkis the result of the simplest variations in a simple numerical law; and is thus clearly brought under our fundamental canon. It is the perception of this unity in diversity, of this similarity of plan, for instance, in all tree-like forms, however diverse,the sprig of mignonette, the rose-bush, the fir, the cedar, the fan-shaped elm, the oval rock-maple, the columnar hickory, the dense and slender shaft of the poplar,which charms the eye of those who have never heard in what algebraic or arithmetical terms this unity may be defined, in what geometrical or architectural figures this diversity may be expressed.
When we look at the animal kingdom, we recognize there also the presence of simple, all-pervading laws. The four great types of animal structures are readily discerned by the dullest eye: no man fails to see the likeness among all vertebrates, or the likeness among all articulates, the likeness among alt mollusks, or the likeness among all radiates. These four types show, moreover, a certain unity, even to the untaught eye: we call them all by one name, animals, and feel that there is a likeness between them deeper than the widest differences in their structure; there are analogies where there are not homologies.
The difference between the four types of animals is marked at a very early period in the embryo,the embryo taking one of four different forms, according to the department to which it belongs; and Peirce has shown that these four forms are all embodiments of one single law of position. If, then, one single algebraic law of form includes the four diverse forms of the four great branches of the animal kingdom, is it extravagant to suppose that the diversities in each branch are also capable of being included in simple generalizations of form? Is it unreasonable to believe that the exceeding beauty of animated forms, and of the highest, the human form, arises from the fact that these forms are the result of some simple intellectual law, a simple conception of the Divine Geometer, assuming varied developments in the great series of animated beings? It is the unity of the form, arising from the simplicity of its law, and the multiplicity of its manifestations or details, arising from the generality of its law, that, intuitively perceived by the eye, although the intellect may not apprehend them, give the charm to the figures of the animate creation.
The subject, even in the narrow limits which we have imposed upon ourselves, would admit of a much longer discussion. The various animals might, for instance, be compared with each other, and the beauty of the most beautiful could be clearly shown to be owing to the greater variety in the outline, or the greater variety of position, which they included in equal unity of general effect. And should we step outside the bounds which we have prescribed to ourselves, we should find that in other things than questions of mere form the general canon holds true, that laws produce beauty in proportion to their own simplicity and to the variety of their effects. As a single example, take the most beautiful of the fine arts, the art which is free from the laws of space, and subject only to those of time, and in which, therefore, we find a beauty removed as far as possible from that of curvilinear outlines. How exceedingly simple are the fundamental laws of music, of simple rhythm and simple harmony yet how infinitely varied, and how inexpressibly touching are its effects! In studying music as a mere matter of intellectual science, all is simple; it is only an easy chapter in acoustics. But in studying it on the side of the emotions, in studying the laws of counterpoint and of musical form, which are governed by the effect upon the ear and the heart, we find intricacy and difficulties, increased beyond our power of understanding.
So in the harmony of the spheres, in the varied beauty which clothes the earth and pervades the heavens, in the beauty which addresses itself to eye and ear, and in the beauty which addresses only the inward sense,the harmonious arrangements of the social world, and the adjustment of domestic, civil, and political relations,there is an infinite diversity of result, infinitely varied in its effect upon the observer. But could we behold the Kosmos as it is beheld by its Creator, we should perchance find the whole encyclopedia of our science resting upon a few great, but simple laws; we should see that the whole universe, in all its infinite complication, is the fulfilment of perhaps a single simple thought of the Divine Mind, and that it is this unity pervading the diversity which makes it the Kosmos, Beauty.
FOUND AND LOST
And he sold his birth-right unto Jacob. Then Jacob gave Esau bread and pottage of lentiles.
GEN. xxv. 33, 34.
So! I let fall the curtain; he was dead. For at least half an hour I had stood there with the manuscript in my hand, watching that face settling in its last stillness, watching the finger of the Composer smoothing out the deeply furrowed lines on cheek and forehead,the faint recollection of the light that had perhaps burned behind his childish eyes struggling up through the swarthy cheek, as if to clear the last world's-dust from the atmosphere surrounding the man who had just refound his youth. His head rested on his hand,and so satisfied and content was his quiet attitude, that he looked as if resting from a long, wearisome piece of work he was glad to have finished. I don't know how it was, but I thought, oddly enough, in connection with him, of a little school-fellow of mine years ago, who one day, in his eagerness to prove that he could jump farther than some of his companions, upset an ink-stand over his prize essay, and, overcome with mortification, disappointment, and vexation, burst into tears, hastily scratched his name from the list of competitors, and then rushed out of doors to tear his ruined essay into fragments; and we found him that afternoon lying on the grass, with his head on his hand, just as he lay now, having sobbed himself to sleep.
FOUND AND LOST
And he sold his birth-right unto Jacob. Then Jacob gave Esau bread and pottage of lentiles.
GEN. xxv. 33, 34.
So! I let fall the curtain; he was dead. For at least half an hour I had stood there with the manuscript in my hand, watching that face settling in its last stillness, watching the finger of the Composer smoothing out the deeply furrowed lines on cheek and forehead,the faint recollection of the light that had perhaps burned behind his childish eyes struggling up through the swarthy cheek, as if to clear the last world's-dust from the atmosphere surrounding the man who had just refound his youth. His head rested on his hand,and so satisfied and content was his quiet attitude, that he looked as if resting from a long, wearisome piece of work he was glad to have finished. I don't know how it was, but I thought, oddly enough, in connection with him, of a little school-fellow of mine years ago, who one day, in his eagerness to prove that he could jump farther than some of his companions, upset an ink-stand over his prize essay, and, overcome with mortification, disappointment, and vexation, burst into tears, hastily scratched his name from the list of competitors, and then rushed out of doors to tear his ruined essay into fragments; and we found him that afternoon lying on the grass, with his head on his hand, just as he lay now, having sobbed himself to sleep.
I dropped the curtains of the bed, drew those of the window more closely, to exclude the shrill winter wind that was blowing the slant sleet against the clattering window-panes, broke up the lump of cannel coal in the grate into a bright blaze that subsided into a warm, steady glow of heat and light, drew an arm-chair and a little table up to the cheerful fire, and sat down to read the manuscript which the quiet man behind the curtains had given me. Why shouldn't I (I was his physician) make myself as comfortable as was possible at two o'clock of a stormy winter night, in a house that contained but two persons beside my German patient,a half-stupid serving-man, doubtless already asleep down-stairs, and myself? This is what I read that night, with the comfortable fire on one side, and Death, holding strange colloquy with the fitful, screaming, moaning wind, on the other.
As I wish simply to relate what has happened to me, (thus the manuscript began,) what I attempted, in what I sinned, and how I failed, I deem no introduction or genealogies necessary to the first part of my life. I was an only child of parents who were passionately fond of me,the more, perhaps, because an accident that had happened to me in my childhood rendered me for some years a partial invalid. One day, (I was about five years old then,) a gentleman paid a visit to my father, riding a splendid Arabian horse. Upon dismounting, he tied the horse near the steps of the piazza instead of the horseblock, so that I found I was just upon the level with the stirrup, standing at a certain elevation. Half as an experiment, to try whether I could touch the horse without his starting, I managed to get my foot into the stirrup, and so mounted upon his back. The horse, feeling the light burden, did start, broke from his fastening, and sped away with me on his back at the top of his speed. He ran several miles without stopping, and finished by pitching me off his back upon the ground, in leaping a fence. This fall produced some disease of the spine, which clung to me till I was twelve years old, when it was almost miraculously cured by an itinerant Arab physician. He was generally pronounced to be a quack, but he certainly effected many wonderful cures, mine among others.
I had always been an imaginative child; and my long-continued sedentary life compelling me (a welcome compulsion) to reading as my chief occupation and amusement, I acquired much knowledge beyond my years.
My reading generally had one peculiar tone: a certain kind of mystery was an essential ingredient in the fascination that books which I considered interesting had for me. My earliest fairy tales were not those unexciting stories in which the good genius appears at the beginning of the book, endowing the hero with such an invincible talisman that suspense is banished from the reader's mind, too well enabled to foresee the triumph at the end; but stories of long, painful quests after hidden treasure,mysterious enchantments thrown around certain persons by witch or wizard, drawing the subject in charmed circles nearer and nearer to his royal or ruinous destiny,strange spells cast upon bewitched houses or places, that could be removed only by the one hand appointed by Fate. So I pored over the misty legends of the San Grail, and the sweet story of "The Sleeping Beauty," as my first literature; and as the rough years of practical boyhood trooped up to elbow my dreaming childhood out of existence, I fed the same hunger for the hidden and mysterious with Detective-Police stories, Captain Kidd's voyages, and wild tales of wrecks on the Spanish Main, of those vessels of fabulous wealth that strewed the deep sea's lap with gems (so the stories ran) of lustre almost rare enough to light the paths to their secret hiding-places.
But in the last year of my captivity as an invalid a new pleasure fell into my hands. I discovered my first book of travels in my father's library, and as with a magical key unlocked the gate of an enchanted realm of wondrous and ceaseless beauty. It was Sir John Mandeville who introduced me to this field of exhaustless delight; not a very trustworthy guide, it must be confessed,but my knowledge at that time was too limited to check the boundless faith I reposed in his narrative. It was such an astonishment to discover that men, black-coated and black-trousered men, such as I saw in crowds every day in the street from my sofa-corner, (we had moved to the city shortly after my accident,) had actually broken away from that steady stream of people, and had traversed countries as wild and unknown as the lands in the Nibelungen Lied, that my respect for the race rose amazingly. I scanned eagerly the sleek, complacent faces of the portly burghers, or those of the threadbare schoolmasters, thinned like carving-knives by perpetual sharpening on the steel of Latin syntax, in search of men who could have dared the ghastly terrors of the North with Ross or Parry, or the scorching jungles of the Equator with Burckhardt and Park. Cut off for so long a time from actual contact with the outside world, I could better imagine the brooding stillness of the Great Desert, I could more easily picture the weird ice-palaces of the Pole, waiting, waiting forever in awful state, like the deserted halls of the Walhalla for their slain gods to return, than many of the common street-scenes in my own city, which I had only vaguely heard mentioned.
I followed the footsteps of the Great Seekers over the wastes, the untrodden paths of the world; I tracked Columbus across the pathless Atlantic,heard, with Balboa, the "wave of the loud-roaring ocean break upon the long shore, and the vast sea of the Pacific forever crash on the beach,"gazed with Cortés on the temples of the Sun in the startling Mexican empire,or wandered with Pizarro through the silver-lined palaces of Peru. But a secret affection drew me to the mysterious regions of the East and South,towards Arabia, the wild Ishmael bequeathing sworded Korans and subtile Aristotles as legacies to the sons of the freed-woman,to solemn Egypt, riddle of nations, the vast, silent, impenetrable mystery of the world. By continual pondering over the footsteps of the Seekers, the Sought-for seemed to grow to vast proportions, and the Found to shrink to inappreciable littleness. For me, over the dreary ice-plains of the Poles, over the profound bosom of Africa, the far-stretching steppes of Asia, and the rocky wilds of America, a great silence brooded, and in the unexplored void faint footfalls could be heard here and there, threading their way in the darkness. But while the longing to plunge, myself, into these dim regions of expectation grew more intense each day, the prison-chains that had always bound me still kept their habitual hold upon me, even after my recovery. I dreamt not of making even the vaguest plans for undertaking explorations myself. So I read and dreamt, filling my room with wild African or monotonous Egyptian scenery, until I was almost weaned from ordinary Occidental life.