CORNELL UNIVERSITY LIBRARY "^EKli^HS;)^ ^daapJatten Cornell University Library BD581 .C77 Curves of life: being an account of spir ■'"a '*»;,.. Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924028937179 THE CURVES OF LIFE La Nature c'est le modele variable el infini qui conlienl loits les styles. Elle ^lous enlouve mats nous ne la voyons pas.- Rodin. THE CURVES OF LIFE BEING AN ACCOUNT OF SPIRAL FORMATIONS AND THEIR APPLICATION TO GROWTH IN NATURE, TO SCIENCE AND TO ART; WITH SPECIAL REFERENCE TO THE MANUSCRIPTS OF LEONARDO DA VINCI BY THEODORE ANDREA COOK M.A. F.S.A. Author of^^ Old Toii}-nint\" '''' Koiioi," etc., etc. WITH ELEJ'EN PLATES AND 415 ILLUSTRATIONS LONDON CONSTABLE AND COMPANY LTD 10 ORANGE STREET LEICESTER SQUARE WC 1914 I) / ^ -X. v V -V ^ ^ -^ ^^ ^. ^ Cv ;\^'Y PREFACE Considerate la vostra semenza; Fatti non foste a viver come bruti. Ma per seguir virtute e conoscenza. — Dante. When my attention was first turned to the subject of spiral formations, more ttian twenty years ago, it was in connection witli an artistic problem, rather than with a biological question, that I investigated them. As was inevitable, I found myself obliged to examine the forms of natural life ; and I learnt that this extraordinary and beautiful formation is to be seen throughout organic nature, from the microicopical foraminifera and from life forms even smaller still. In shells, in plants, in the bodily structures of men and animals, the spiral formation is cer- tainly a common factor in a multitude of phenomena apparently widely different. As my investigations broadened I had to secure the assistance of expert authorities in separate divisions of research, to whom I cannot be sufficiently grateful, and I mention this in order to answer the obvious criticism that no one man would in these days be considered competent to deal with the separate branches of knowledge which my inquiry has gradually necessitated. This is one reason why anyone who is interested in the rough programme sketched in my first chapter may choose his own path to the last one, which sums up the whole. He may read of shells in Chapters III. and IV. and X. ; of plants and flowers in Chapters V. to IX. and in XI. ; of horns in Chapter XII. ; of anatomy and lefthandedness in the two next ; of the growth of patterns in the fifteenth ; of architecture in XVI. and XVII. ; of the attribution of a building to Leonardo da Vinci in XVIII. ; or of Albert Diirer's mathematics in the nineteenth. The mere recitation of so varied a list of necessary subjects leads me here to lay immediate stress upon the value of human curiosity about the world around us, upon that thirst for a rational explanation of phenomena which Comte so loftily despised, which Aristotle and Spinoza so clearly acknowledged. Such writers as Mach and Kirchhoff seem to me to have gone back to Comte's most vulnerable position when they limit the use of science to description. For we do not want mere catalogues. If every generation of great thinkers had not thirsted for explanations also, we should never have evolved the complexity and beauty of modern science at all. Only by some such discovery of relation- ships can we ever try to deal rationally with that " perpetual flux " which (as is more and more clearly recognised) the viii PREFACE phenomena of life and nature present. There is a deep-seated instinct which attracts our minds towards those " desperate feats of thinking " which have achieved the greater victories of humanity ; and it is by them that we must surely stand the ultimate test of our survival. Modern research is gradually becoming free both from accidental prejudices and from meretricious standards. There is a new spirit at work upon constructive philosophy which has never been so urgent, so creative, or so strong; and knowledge has become much more accessible at the very time when its transmission over the whole world has been enormously facilitated by new methods of communication. This means that thought is becoming clearer and more critical, and that a breadth of outlook and a freedom of imagination have resulted which must impel alike the laziest to look about him, and the busiest to linger and inquire. Some ripple of that widespread impulse has produced this book ; but the very process just described has created its own difficulty ; for specialisation is in these days so sternly necessitated by the obvious benefits of the division of labour, that it becomes an increasingly complicated task to put the various results of separate investigations in their true relation with each other. Analysis, therefore, has been my first aim. Not till my last two chapters have I ventured to elaborate the synthesis which completes and justifies my catalogue of details ; and for this I have ventured to propose a convenient instrument which may be usefully employed in dealing with the varied multiplicity of natural phenomena. It may be said that with very few exceptions the spiral forma- tion is intimately connected with the phenomena of life and growth. When it is found in inorganic phenomena the logarithmic spiral is again connected with those forms of energy which are most closely comparable with the energy we describe as life and growth, such, for instance, as the mathematical definition of electrical phenomena, or the spiral nebulse of the astronomer. Newton arrived at his theory of the movements of the celestial bodies in our own solar system by postulating perfect movement and by calculating from that the apparently erratic orbits of the planets. In just the same way may it not be possible to postulate perfect growth and from that to calculate and define the apparently erratic growths and forms of living things ? In each case the Higher Mathematics will very properly be the instrument of philosophic inquiry, for the science of mathematics, useless as an end in itself, is, in the right hands, the most supple and perfect instrument for defining the relations of things, and classifying phenomena in the manner so eagerly desired by every intelligent PREFACE IX ■^ mind. It was Sir John Leslie who first drew attention to the " organic aspect " of the logarithmic spiral (see p. 58). Canon Moseley then applied it to the examination of certain turbine shells. Professor Goodsir sought in it the basis of some physiological law which should rule the form and growth of organism as gravitation prevails in the physical world. Mr. A. H. Church, of Oxford, ha founded on it, in quite recent years, the whole theory of modern phyllotaxis ; and if the symbol illustrated on the cover of this book is correctly interpreted in its Appendix, it would appear that Chinese philosophy had adopted the logarithmic spiral as a symbol of growth as long ago as the twelfth century. But the exact form of logarithmic spiral most suitable to the fundamental conceptions involved had never yet been satisfactorily discovered. JThe jFormula for Growth now suggested in this book is here called the[(j) spiral, or Spiral of Pheidias, a new mathematical conception wdfkecT out from an ancient principle by Mr. Mark Barr and Mr. William Schooling ; and Mr. Schooling's exposition of some of its possibilities will be found in my twentieth chapter and the pages which immediately follow it. There is a very significant characteristic of the application of the spiral to organic forms ; that application invariably results in the discovery that nothing which is alive is ever simplv mathematical. In other words, there is in every organic object a factor which baffles mathematics, as we have hitherto developed them — a factor which we can only describe as Life. The nautilus is perhaps the natural object which most closely approximates to a logarithmic spiral ; but it is onl}/ an approximation ; the nautilus is alive and, therefore, it cannot be exactly expressed by any simple mathematical conception ; we may in the future be able to define a given nautilus in the terms of its differences from a given logarithmic spiral ; and it is these differences which are one characteristic of life. It will be observed that from another point of view Darwin had long ago stated almost the same proposition when he showed that the origin of species and the survival of the fittest were largely due to those differences from type, those minute adaptations to environment, which enabled one living creature to pass on its bodily improvements to an improved descendant. One link between these theories of life and growth and a similar theory of beauty — or, if you wish, of art — is contained in this same observation of minute variations and subtle differen- tiations. Nothing that is simply mathematically correct can ever exhibit either the characteristics of hfe or the attractiveness of beauty. It is by the subtle variations, which express his own characteristic personahty, that the artist gives his individual X PREFACE charm to e\-erythmg which he creates ; and the creations oi art are just as rebelhous against the simple formuL-E of mathematics as are the phenomena of organic hfe. It is for this reason that I have used the spiral formation (and especially the (j) spiral, or Ratio of Pheidias) as a kind of key, not merely to natural phenomena, but to artistic and architectural phenomena as well, and I ha^•e therefore thought it right to add examples of art and architecture to the hundreds of specimens of natural growth v\hich are published in these pages. It may appear that the attempts of scientific analysts to formulate the laws of beauty follow too much the line of objective qualities. Some artists may see a champion of their view in Kant when he says that beauty has no quality in things in themselves, but that it exists only in the mind which contemplates them ; or in Mr. Arthur Balfour, when he analyses the qualities we call " sublime," " beautiful," " pathetic," " humorous," " melodious," and denies them any kind of existence apart from feeling. " Are they to be measured," he asks, " except by the emotions they produce ? Are they indeed anything but these very emotions illegitimately ' objectified ' ? . . . We cannot describe the higher beauties of beautiful objects except in terms of sesthetic feeling, and ex vi termini such descriptions are subjective." But it is no escape from the inevitability of Nature and her ways (which are called objective) to talk about mental operations. What happens in the mind (though the word subjective may be dragged in, as it too often is) has just as much of Nature's inexorable qualitv as the formation of a mountain or the rusting of iron. Both may be subject to laws — namely, to sequences of events — though we may not easily find or ever find the laws. Stated in terms as subjective as possible, beauty is a question of " Fit to us." If the overpowering evidence of continuitv is good for anything (and for some men it has given more majesty to life than any religious tenet), it gives us the hint of a transcen- dental " fitting " among ah things. If I am pleased by a vase from King-te-Chen, qualities of me and qualities of the vase make up some fragment of a transcendental equation. This is true, too, if I dislike the vase. A man of science, seeing a phenomenon— the attraction of gravity, the bloom of a rose, the melting of metal, or even the rise of an emotion — wishes to express it. That is not spoiling it. He would have more, not less of it. Mr. Mark Barr, to whose luminous suggestions this book has owed so much, imagines that the first man of science was he who found that Echo was no sprite. He asked for more of Echo, not less. And when he learned how much more there was than another creature's voice, he found more enthrahing mystery (if that is PREFACE XI what is wanted), not less. It is not the hope of science to dispel real mystery. Mystery is widened every day. Struck by the evidence of continuity and ordered causation, the man of Science may sometimes become obsessed by the idea of formulation. Reaction against that prejudice is natural enough ; but an opposite extreme is reached when men of artistic temperament resist too bitterly what they are pleased to call the " mechanistic theory." The aesthetically moved man looks with too much intolerance upon the claims of science, and his intoler- ance is quite intelligible, because artistic creation, no matter how arduous it be, tends to encourage lazy habits of mind. Since analyses of things as they are play a less necessary part in his work, the artist is impatient of analysis. But there is another important fact. Appreciation of art depends largely on free gifts which we all possess in some measure. Artistic creations, there- fore, make an immediate appeal to the many. Music soothes even the untutored savage ; and hence the artistic worker lives in a ready-made world of admiration, and very naturally resents any disturbance of the creative atmosphere or the receptive attitude. With the young Edgar Allan Poe, he cries out to Science ; — "Hast thou not dragged Diana from her car, And driven the Hamadryad from the wood To seek a shelter in some happier star ? " No, would Mr. Barr reply, that has never been either the aim or the result of scientific analysis. Yet for many years, it is but too true, the formulation of beauty has been the centre of a hot-headed wrangle, due, chiefly, to the diverse use of words. And even if antagonists may agree as to the meaning of certain words, impatience and prejudice too often cloud the issue. In this book I am bold enough to take it for granted that there is a desire to agree. If so, the man of science will drive general principles less violently, while the man of aesthetic temperament will take the argument of science slowly in steps, over which intuitive people wish to bound impatiently. For my modest purposes, standpoint is everything ; and I feel sure we can reach some guiding principles. The attempt to do so has been far from limited to the scientific analyst. Dante, Durer, Goethe are fore-runners on the enchanted track. This same combination of the scientific study of Nature with the principles of art is the keynote of the manuscripts from which we can still strive to estimate the many-sided intellect of Leonardo da Vinci. I have reproduced a very large number of drawings from this source, because they illustrate my main theme and provide innumerable suggestions for the theory set forth in my xii PREFACE twentieth chapter, a theory which is not, I dare to beheve, without its interest for both the professional artist and the general public. It sugge:^ts the application of the (f> spiral (essentially a formula for natural growth) to the proportions of a great picture, or, if you prefer it, to the principles which underHe the instinctive " good taste " of a great artist. In " Criticism and Beauty " (1910) Mr. Arthur Balfour, speaking of the two great divisions of the emotions, said : " Of highest value m the contemplative division is the feeling of beauty ; of highest value in the active division is the feehng of love. . . . Love is governed by no abstract prin- ciples ; it obeys no universal rules. It knows no objective standard. It is obstinately recalcitrant to logic. Why should we be impatient because we can give no account of the charac- teristics common to all that is beautiful, when we can give no account of the characteristics common to all that is lovable ? . . . For us, here and now, it must suffice that, however clearly we may recognise the failure of critical theory to establish the ' objective ' reality of beauty, the failure finds a parallel in other regions of speculation, and that nevertheless, with or without theoretical support, admiration and love are the best and greatest possessions which we have it in our power to enjoy." The words " here and now " in the above passage refer to the Romanes Lecture delivered at Oxford in 1909. But, even for " the home of lost causes," it must be too depressing to seek con- solation for failure in one direction by recognising failure in another. A mercilessly logical analysis of the foundations of art criticism had produced the conviction in Mr. Balfour's mind that it was " absolutely hopeless to find a scale [in matters Eesthetic] which shall represent, even in the roughest approxi- mation, the experiences of mankind." Now I shall not, of course, attempt the arrogance of announcing that so difficult a problem has here been solved. I suggest only that it has been mitigated, and mitigated by a formula which does " represent the experi- ences," not of " mankind " only, but of all life as we know it, by that new conception, called the ^ Progression, which explains not only the phenomena of vital growth, but also the principles which underlie both the artist's expression of the beautiful and our own appreciation of it. This Ratio of Pheidias does not, of course, provide a recipe by which any modern mathematician can produce a rival to the masterpieces of Hellenic sculpture or to the paintings of a Turner or a Botticelh. For <|) is no royal road to Beauty ; nor does it in any way diminish the charm and wonder of the artist's achievement ; but it does imply that, if we realise the variations and divergences observ- able both in Beauty and in Life, we may discover that each PREFACE xiii is visibly expressed to us in terms of the same fundamental principle. Art interprets that Nature of which she is herself a part ; and it is therefore only logical that the syllables of her interpretation should be recognisably an echo of the language by which they were inspired. Those who care to pursue my subject a little further will find it possible to apply the processes I have ventured to suggest to the philosophy of human knowledge, as well as to the theories of growth and art, which are the main subject of this book ; for what we describe as a " rule " in science or a " law " in Nature, is in reality the mere expression, in shorthand, of our knowledge at the moment concerning certain phenomena which we have been able to observe. To carp at a Law because it does not explain everything, would be a grave error in outlook and understanding ; for Laws do not explain ; they describe what happens, and their description should be both helpful and suggestive. But they are the instruments of Science, not its aim. The really important thing is not the " rule " or " law " itself which merely records the investigations of the past. It is the exception ; for this brings the sudden appreciation of facts hitherto unknown, and of their relation to ourselves, which leads us to the discovery of the future, to higher worlds of life and thought than we had ever realised before. It was, no doubt, the observation of discrepancies in Laplace's famous theory and its developments, which led Henri Poincare to say that it could only be a special case of a more general hypo- thesis ; and though all astronomical arguments must at present be conditioned by the fact that the stars whose movements we have observed are only a fraction of the total even of those our telescopes and cameras reveal, yet we have discovered certain differences in their movements and related these differences to the varying ages of various stars. The new " theory of origins " suggested by Professor H. H. Turner {Bedrock, January, 1914) has not only explained such new and apparently disconnected facts, but has also stated the nebular hypothesis in a novel form which gives every promise of more exact progress in the future ; and it was the observation of apparent "exceptions" which enabled him to do so. Nature has no watertight compartments. Every phenomenon affects and is affected by every other phenomenon. Any phenomenon which we choose to examine is to us conditioned by what we see and know. We exclude deliberately all other con- ditions. But Nature does not exclude them. A Nautilus growing in the Pacific is affected by every one of the miUion stars we see — or do not see — in the universe. But we examine it only by the xiv PREFACE light of what we know. Leibnitz and Newton enabled us to know a great deal more than was ever imagined possible before their time. But they could not exhaust the universe. In this book I have been often obliged to use a short phrase to indicate a process that is really long and complex. One of these phrases, in the light of the considerations just developed, I must at once explain and justify. I put the case shortly by saying, " Nature abhors mathematics." \Miat I really mean is that simple mathematics, as we have hitherto developed them, can never express the whole complex truth of natural phenomena. In other words, we must use such instruments as we have, such formulae as are convenient, such mathematical conventions as suit our human minds, suchhypotheses as Newton's, Darwin's, or another's. But Nature, eUe nc s'y vide pas, as the Frenchman said. She knows. We try to know. We cannot find her formula however hard we try. But we shall play the game out with her to the end, and go on trying all the time ; only so shall we get nearer and nearer every day ; for only in that stern chase is any life worth living : "to follow after valour and understanding." Spirality (if the word may be allowed) is a generalisation of far- reaching importance. The logarithmic spiral is an expression of growth. Such complex things as life and beauty cannot be expected to conform with any one simple law, and it is largely by noting approximations to spirality, to the <^ Progression, as I suggest, or any other suitable principle, and then investi- gating the deviations, that " knowledge grows from more to more." Discrepancies lead to Discovery. Just as the human organism is more complex than that of the lower organisms, just as English life in the twentieth centuiy is more complex than that of a primitive tribe, just as organisms are more complex than inorganic objects, so the highest thought and the greatest art are more complex than primitive knowledge or early ornamentation. The more highly developed phenomena are the result of more complex forces, and are therefore the more difficult to explain. Considerations of this kind at least afford reasons for the exist- ence of greater and more numerous deviations from one simple law in the higher phenomena than in the lower ; they support my contention that Nature exhibits Diversity rather than Unity, and that living things and the highest forms of art cannot be expected to show conformity with any one or a few simple laws of Nature to which it is at present poss ble to give mathematical definition. They justify also the opinions I have expressed that deviations are one cause of beauty and one manifestation of life ; and this is why the study of exceptions is the road to progress. PREFACE XV I have to thank the proprietors of the Field for permission to make use o' the articles which originally appeared in the pages of that newspaper. For the complete form of this volume, not only in the matter of correcting proofs, but also in the arrange- ment of the Index and Appendix, I have to thank m^^ friend, Mr. William Schooling, who undertook this laborious task at a time when illness prevented ms from attempting the difficult but inevitable work involved. A great deal has been done to improve and develope the first statement of the case. I have included a selection from the very large number of letters and illustrations forwarded to the Field by numerous correspondents while my original series of articles was appearing in that paper. These letters have been arranged at the end of the various chapters to which they refer, and will be found to contribute a number of very interesting iUustrations and comments from all parts of the world. T. A. C. Chelsea, March 28th, 1914 LIST OF ILLUSTRATIONS (CLASSIFIED) I.— AXATOMY (HUMAN) Umbilical C(.)rd, Left-hand Spiral of Human Humerus, Spiral Formation of . Ear, Laminas of Coclilea of Internal . Tfiighbone, Internal Structure of Human Femur, Bone Lamelte in . Ear, Cochlea of Human . Umbilical Cord, Spiral Arteries in Gall Bladder, Spiral Valve in Duct of Sweat Gland, Spiral Arrangement of Duct of Skin Papilte, Spiral Pattern of Heart, Dissection of the Apex of Heart, Diagram of the Foetal . Clavicle, Human. Pelvic Bone, Left Rib, Seventh on the Right Side Anatomical Study by Leonardo da Vinci FIG. NO. PAGE lO 9 II 9 39 29 252 222 2,53 222 254 223 255 224 256 225 257 225 258 226 260 228 262 229 264 230 266 231 282 259 II.— ANATOMY (ANIMAL) Heart, Left Ventricle of Sheep's Spirillum Rubrum, The Bacillus Polyzoan, Spiral Form of . . . Devonian Lampshell, Dorsal Valve and Arms Glass-Sponge, The ..... Caddis-fljr, Case made by Larva of . Narwhal's Tusk, Part of . Elephant's Tusk ..... Elephant's Tusk . . ■ . Bower-bird, Nest of .... Frog, Capillary or Arteriole in Web of Beaver, Heel of a . Elephant, Bones of the Left Fore Leg Feathers and Wings, Spiral Twist of . Stanley's Chevrotain, Colic Hehcene of Musk Ox, Colic Helicene of Dogfish, Colon of . Shark's Egg, Capsule of Spirochete gigantciini Bacillus from Putrefying Flesh-infusion Ciliate Protozoa ... Shark, Jaw of the Port Jackson Shark, Dental Plates of the Cochliodus Cochliodus, Section of Dental Plate of Ray Rhinobatiis, Upper Dentition of the C.L. 3 4 6 6 7 6 8 7 9 8 12 10 186 156 187 156 188 157 210 169 259 227 263 229 265 231 267 232 268 233 269 233 270 234 271 234 272 235 273 236 274 237 403 452 404 453 405 453 406 454 XVlll LIST OF ILLUSTRATIONS III.— ARCHITECTURE Parthenon. Painted Frieze from C>ld Volute from Temple of Diana at Ephesus X'olutes from the Erechtheum . lMyceua?an Lamp, Marble Shaft of a . " Prentice's Pillar " at Rosslyn Chartres Cathedral, Spiral Colonnettes in Perro-concrete, Spiral Staircase of Autun Cathedral, Spiral Staircase in . Primitive Spiral Staircase Colchester Castle, Staircase in . Westminster, Staircase in Painted Chamber Lincoln Cathedral, Spiral Stair in St. Wolfgang's, Rothenburg, Oak Staircase in Fyvie Castle, The Great Staircase of Elaborate Spiral Staircase Tamworth Church Tower, Double Staircase Palazzo Contarini, Venice, Spiral Staircase Palazzo Contarini, Venice, Scala del Bovolo Pisa, The Leaning Tower of Chartres, Queen Bertha's Staircase Blois, Staircase in the Castle of Blois, Spiral Staircase in Chateau of . Blois, Balustrades of Open Staircase at Parthenon, The .... Design for Church, by Leonardo da Vinci Design for Church, by Leonardo da Vinci St. Paul's, Spiral Staircase from Crypt of St. Paul's, Wren's " Geometrical Staircase Blois, Inside of the Open Staircase at Blois, Exterior of the Open Staircase at Blois, The Open Staircase at Blois, The Open Staircase at French Renaissance Chateau, Staircase from Sketch for Staircases, by Leonardo da Vinci Sketch for Staircases, by Leonardo da Vinci Design for Spiral Staircase, by Leonardo da Vinci Clos Luce, Door of the Chateau of Amboise, drawn by Leonardo da Vinci Sketch for a Castle, by Leonardo da Vinci Chambord, Plan of . St. Peter's at Rome, Plan of Diirer's Design for an Ionic Volute . FIG. NO. FAGE 2gi 276 293 278 294 279 313 296 314 297 315 298 316 300 317 301 318 304 319 305 320 306 321 307 322 309 323 310 3^4 311 325 313 326 317 329 320 330 320 332 322 333 323 334 325 336 326 338 334 339 344 340 345 341 347 342 348 343 350 344 352 345 355 346 356 347 357 357 367 358 368 359 369 360 370 361 371 362 372 363 374 364 375 373 389 IV.—ART Rouen, Carving from Palais de Justice at Lincoln Cathedral, Misericorde in AUegoria. La Maldicenza, by Bellini " Leda," I-eonardo da Vinci's Study for Scipio Africanus, Bust by Leonardo of Japanese Design of Chrysanthemums Minoan Temple in Crete, Marine Subjects from 24 20 25 20 26 21 104 64 105 64 131 78 197 161 LIST OF ILLUSTRATIONS XIX Minoan Clay Seal, Triton Shells from Leonardo da Vinci, Portrait of . Leonardo da Vinci, Sketch by . Arab Horse, Sketch by Leonardo da Vinci Leonardo da Vinci, Drawing by Horse's Head, Carved by Aurignacian Men Reindeer's Antler, Carved Fragment of New Grange, Spirals carved on a Stone at New Grange, Neohthic Boundary Stone at Island of Gavr'inis, Carved Stone in the Minoan Vase of Faience from Cnossos Bronze Celt of the Danish Palstave Type Etruscan Vase, Two large Spirals on Vase, Spiral Pattern on Greek . Armlet of Bronze Violin, Head of Eighteenth Century Gold Disc of Gaulish Workmanship Bronze Double Spiral Brooch . Bronze Brooch showing Four Spirals Maori War Canoe, Wooden Figurehead on Door Lintel from New Zealand Neck Ornament from New Zealand . House Board from Borneo Brooch worn by West Tibetan Women Hinge from Notre Dame . Spirals in Stonework Violin, Head of, by Mathius Albani . Violin, Front View, by Mathius Albani Torque, Five-coiled Gold . Torque, Gaulish Bronze . Torque, Bronze .... " Cavallo," Study for, by Leonardo da Vinci Francesco Sforza, Study for Statue of " The Knight, Death, and the Devil," by Durer Diirer's Invention for Perspective Drawing v.— BOTANY Polvgoniim baldsclnianicum. Left-hand Ahtrcemeria, Spiral Leaves in . Apios tiiberosa, Right-hand Lilium auratuni, Young Plant from above Fern, Frond of growing , Chestnut Tree, Twisted Trunk of Melon, Spiral Vessels of . Tecoma, Right-hand Spiral of . Honeysuckle, Left-hand Spiral of Fern, Unrolling its Spiral Tradescantia virginica, Portions of Leaf of Cyclamen europcBum, Fruit Stalks of . Cyclamen. The Upright Spiral Cyclamen, showing Flat Spiral (from above) Cyclamen, showing Flat Spiral (from beneath) Lilium auratuni. Spiral Formation of Leaves FIG. NO. PAGE 198 162 275 240 276 241 280 247 281 257 • 283 268 . 284 269 . 285 272 . 286 272 . 287 273 . 288 273 289 274' 290 275 292 277 • 295 280 296 282 ■ 297 283 . 298 284 • 299 284 300 285 • 301 286 302 286 • 303 287 • 304 287 ■ 305 288 306 289 ■ 307 290 • 308 291 • 309 292 • 310 293 • 311 293 . 365 381 , 366 382 • 367 383 ■ 368 384 13 10 I-l 12 15 13 19 15 37 29 43 31 . 58 37 59 37 60 37 61 39 ■ 92 54 • 124 75 121 73 122 74 ■ 123 74 128, 129 77 h 2 XX LIST OF ILLUSTRATIONS Chrysanthemum, showing Spiral folding Araiicaria, Leafy Shoot Spiral System Stangeria, Male Cone of . Cci'eiis, Spiral Spines in . Houseleek. Spiral Rosette Scuipfn'iviiin. Spiral Rosette . Echinocactus. Spiral Tufts or Spines Gasteria, show-ing Maximum Superposition Gasteria nigricans .... Gasteria, Young Plants of, showing Torsion Ptnits aitstriaca (Dry Cone) Heliantlnis anmius . Araucaria excelsa, Diagram of . Echeveria aracknoideiun Amaranthus (" Love Lies Bleeding Rochea falcata Echeveria agavoides . Anthuriuin sclierzerianmn Liliiim anralum. Young Plant . Finns ponderosa Pinus excelsa .... Pinus excelsa .... Pinus maritima. Two Views of Cone Pinus maritima, Abnormal Growth of Cone Pinus radiata, showing LTnsymmetrical Forjn Pinus niuricata, Two Views of the Cone Nymphcpa gladstoni (Water Lilj-) Liliiim longiflorum .... Liliiim pyrenaicuni .... Pinus pinea ..... Pinus pinea ..... Wax Palm and Date Palm Fuchsia ...... Pandanus millore from the Nicobar Island: Pandanus utilis .... Cyperus alternifolius Helicteres ixora, Seed-pod of Neottia spiralis (" Lady's Tresses ") . Ranunculus, Spirally-folded Petals of Giant Vine in Madagascar Cape Silver Tree, " Parachute " Fruit of Pinus austriaca. Seeds from Cone of . Bignonia, " Aeroplane " Seed of Helicodiceros, I^adder-leaves of . Begonia, Spiral Leaves of Hybrid Beech, Twisted Stem of (Right-hand) Chestnuts, showing Right- and Left-hand Twist Lapageria rosea, Left-hand Lardizabala biternata. Right-hand Muehlenbeckia cliilensis. Left-hand Wistaria involuta, Right-hand . Bryonia dioica Hops, Left-hand Spiral in FIG. NO. PAGE 130 77 13- 82 133 83 134 84 135 8.5 136 86 137 87 138 88 139 89 140 90 141 91 144 98 146 lOI 147 102 I4S 103 140 104 150 105 151 106 15^ 107 153 108 154 108 155 108 I5O 109 157 no 1.58 III 159 112 160 "3 161 113 162 114 164 119 165 120 166 121 167 122 168 123 169 124 170 125 171 125 172 126 173 129 174 130 175 136 176 137 177 139 178 147 179 149 180 152 181 153 211 171 212 171 213 172 214 172 215 173 216 174 LIST OF ILLUSTRATIONS XXI Schubertia physianthiis, Kight-hand Convolvulus arvensis, Right-hand Gourd, Spiral Tendrils of Smilax . Passion Flower Virginia Creeper Vine Ampelopsis Black Bryony. Climbing Plant, Diagram of Movements Marsh Marigold and Wood Anemone Growth of Flowers, Study of the Job's Tears ..... A Leaf from Leonardo's Note Books Suniiower, Head of Giant Begonia (Colman) .... VI.— HORN Marco Polo's Argali (Ovis aniinon poll) Senegambian Eland (Taurotragiis derbianus Greater Kudu ..... Alaskan Bighorn .... Diagram to show Angle of Axis in Horns Suleman Markhor (Capra falconeri jerdoni) Gilgit INIarkhor (Capra falconeri) Pallas's Tur (Capra cylindricornis) Wild Sheep of the Gobi Desert Merino Ram ..... Tibetan Argali (Ovis amnion hodgsoni) Nyala (Tragelaphus angasi) Lesser Kudu ..... Situtunga (Tragelaphus spekei) . Ordinary Mouflon .... Senegambian Eland (Taurotragus derbianus Tibetan Shawl Goat (tame) Ancient Egyptian Drawings Arui or Barbary Sheep (Ammoiragus lervia Cyprian Red Sheep (Ovis orienialis) . Bharal [Pscitdois nahura) Ibex or Sind Wild Goat . Asiatic Ibex (Capra sibirica dauvergnei) Indian Jamnapuri Goat (tame) Common Domesticated Goat Cabul ^Markhor (Capra falconeri megaceros) Circassian Domesticated Goat . Wallachian Sheep (Ovis aries strepsiceros) Ram from Wei-Hai-Wei, Four-horned Albanian Sheep (showing both Curve and Twist) Albanian Sheep (Perversion in Twist) Ram's Horns, Study of Spirals by Leonardo Flat Spiral, Right-hand Flat Spiral, Left-hand VI I , -^MATHEMATICS IG. NO. PAGE 217 176 218 176 219 177 220 178 221 179 222 181 223 182 224 183 225 184 226 185 277 242 348 360 379 395 380 397 386 416 395 436 20 16 21 17 22 18 48 34 227 190 228 191 229 192 230 193 231 193 232 194 233 194 234 196 235 197 236 200 237 201 238 202 239 203 240 206 241 209 242 210 243 210 244 211 245 211 246 212 247 213 248 214 249 215 250 216 251 217 A 219 B 219 352 363 29 25 30 25 xxu LIST OF ILLUSTRATIONS Logarithmic Spiral . Conical Helix .... Conical Helix, How to construct a Cylindrical Helix, Construction of Cylindrical Helix, Construction of Cylindrical Helix, Construction of Cylindrical Heli.x, Construction of Logarithmic or Equiangular Spiral Logarithmic Spiral, Theoretical Diagram of Theoretical Construction of a (3 + 5) System Conical Helix from Flat Spiral, Diirer Spiral Crozier and " Line of the Leaf," Diirer Diirer's " Line of the Shell " . Diirer's Plan for a Cyhndrical Helix . Diirer's Logarithmic Spiral Logarithmic Spiral with Radii . Diagram for a Regular Curve System of 5 -f 8 Diagram for Eccentric Curve System of 5 + 8 Pheidias Spiral ..... Swastika in Phi Proportions VHL— SHELLS AND FORAMINIFERA Orbicidina admea Eocene Tertiary Foraminifer Polystomella crispa . Siliquaria striata Phiirotomaria conoidea Pleufotoma elegans . Ammonite from Lyme Regis Ammonite, Section of Solarium perspectivimi Lamprostoma maculata Solarium maximum Turbinella pvrum Harpa conoidalis Turbo marmoratus, Operculum of Choristes elegans (showing Operculum Tntbo cormitus, Operculum of Pleurotoma nionterosatoi . Awl-shell (Terebra) Truncatulina tenera Rotalia calcar . Peneroplis aricetinus, Section of Globigerina linnceana Globigerina cretacea (Fossil) Globigerina aqitilateralis . Bulimina contraria . Pteroceras oceani Malaptera ponti Oyster Shell, Growth of Telescopium telescopium . Ainberleya goniata . Fulgurofusus quercollis, Protoconch of FIG. NO. PAGE 31 26 49 34 50 35 54 36 55 36 56 36 57 36 97 58 145 100 163 117 369 385 370 386 371 387 37^ 388 374 390 385 414 387 418 388 419 389 421 391 423 2 4 4 5 5 5 16 13 17 14 18 14 32 27 33 28 34 28 35 28 ■ 36 29 41 30 42 30 45 32 46 33 47 33 53 36 62 41 • 63 42 . 64 42 ■ 65 43 66 43 • 67 43 68 44 . 6g 44 70 44 71 44 72 45 73 46 74 46 75 46 LIST OF ILLUSTRATIONS XXlll Clavellojusus spiratns, Protoconch of Cirrus nodosus Valuta vespertilio, Dexiotropic Fasciolaria filamentaria Terebra maculata Mitra papalis Mitra papalis . Valuta bicorona Valuta scalans Scalaria scalaris Turritella lentiginasa Auricula auris-midcs Ceritheum giganleum Turritella duplicata . Valuta vespertilio, Section of Valuta miisica. Turbinella pvruin Valuta pacifica Turbinella fusus Nautilus pompilius, Section of Ammonite from Lyme Regis (Fossil) Burtoa nilotica Vasum turbinellus Haliotis splendens Arganauta arga Spirula peranii Haplophragniium scitulum. Section o Carnuspira foliacea . Cyclammina cancellata Cristellaria tricarinella Cristellaria siddalliana Mela ethiapicus (showing Uprigfit Spira]) Mela ethiapicus (showing Flat Spiral) Trophan geversianus Acanthina imbricata Canus tesselatus Pyrula ficoides Eburna spiraia Dolium maculatum . Dolium perdix Harpa ventricasa Valuta vespertilia Mtirex saxatilis Sycotypus canaliculatus Caralliaphila deburghi(s Planispirina contraria, Section of Whelk, Common Living . Whelk, Fusus antiquus (Red Crag) Fossil Achatina hamillei Lanistes ovum Valuta vespertilia, Section of Valuta vespertilio, Leiotropic Neptunea antiqua FIG. NO. PAGE 76 46 77 48 78 48 79 49 80 49 81 50 82 50 83 51 84 51 85 51 86 51 87 51 88 52 89 5^ 90 53 91 53 93 54 94 55 95 55 96 57 98 58 99 59 100 60 lOI 61 102 52 103 63 106 65 107 65 108 65 109 67 no 67 III 68 112 68 113 69 114 69 ii.'i 70 116 70 117 71 118 71 119 72 120 73 125 76 126 76 127 75 142 92 143 92 182 154 183 154 184 155 185 155 i8g 158 190 158 191 159 XXIV LIST OF ILLUSTRATIONS Neptuiiea coniraria . Helix lapicida (from beneath) Helix lapicida {from above) Tiirbiiiella rapa Voluta solandri Sliells worn bv Magdalenians Nonionina stelligei-a Polystomella maceUa Discorbina opercularis Ci'istellai'ia ctiHrata . Cristellaria calcay Discorbina globiilaris Neritopsis coiupressa Neriiopsis coiupressa NantUus orbictiliis . Land Snail {Acavus phcenix) from Ceylon Terebra dimidiata Terebra consobrina . Ammonite, Study of Flat Spiral by Leonardo Cymbiitm diadeiiia .... Doliuni galea ..... Rembrandt's Etching of the Shell Conus siriatus .... Gradual Increase of Spaces in a Shell Trochiis maximiis Trochiis, Under-side of Dolium perdix Facelaria Haliotis corritgata Fusus in Eocene Rock, Fossilised Section of Nautilus poiupilius, Section of . Isocardia vulgaris, Front View of Congeria subglobosa. Front View of Diceras arietintiin, Front View of Purpura planispira, Terminal Aspect of Nautilus poiupilius, Shell and Animal of FIG. NO. PAGE 192 159 193 160 194 I Co 195 160 196 160 399 i<33 201 164 202 164 203 165 204 165 205 165 2o5 165 207 166 208 166 261 228 312 294 327 318 328 318 353 364 375 391 376 392 377 393 378 394 390 422 393 434 394 435 396 437 397 438 398 440 399 448 400 449 407 455 408 455 409 455 410 455 411 457 MISCELLANEOUS Spiral Nebula in Canes Venatici The " Unit of Direction " Illusion Flat Spiral of ^^'atch Spring Clock-face .... Sulphur, Crv.stals of Prochlorite, Spiral Crystals of . Ionic Volute from Shell . Coinmon Screw Screw with large Thread . Postage Stamp from Tra^-ancore Swastika, The Lucky Leonardo da Vinci, Signature of Leonardo da Vmci, A Page of his Handwriting Wood-turning, Examples of I 2 23 19 27 25 28 25 38 29 40 29 44 32 51 3G 52 3G 200 if>3 209 157 278 243 279 245 331 321 LIST OF ILLUSTRATIONS XXV Spirals formed in Water, Study of Spiral Eddies, Study of . Spirals formed by Smoke and Dust, Study of Screw, Drawing of a Left-hand Screws, Drawings of Left-hand Twist, Drawing of a Left-hand Nebula in Andromeda Spiral Nebula in Ursa Major Spiral Nebula in Cygnus . Spirals in Clouds and Water, Study of Korean National Badge . Prehistoric Altar from Central America ^endnlum-dra^vings with Spiral Formations Pendulum-drawings -with Spiral Formations Pendulum-drawings with Spiral Formations Pendulum-drawings vdth. Spiral Formations G. NO. PAGE 349 361 35° 361 351 362 354 365 355 365 356 365 382 410 383 411 384 412 392 429 401 451 402 451 412 459 413 460 414 460 415 460 PLATES I. Right and Left Spirals in Plants II. Right and Left Spirals in Plants III. Homonymous and Heteronymous Horns IV. Diagrams of Twists and Curves in Horns . V. Diagram of the Inverted Cone VI. Symbols derived from the Nautilus Shell. VII. The Laughing Cavalier, by Franz Hals VIII. Venus, by Sandro Botticelli . IX. An Artist's Model. X. Ulysses Deriding Polyphemus, by J. M. W. Turner XL A Scale of Phi Proportions . ■ • ■ 134 144 199 204 208 450 465 466 467 468 469 TABLE OF CONTENTS CHAPTER I INTRODUCTORY — THE SPIRAL Growth and Beauty and Spiral Formations — Letters from Sir E. Ray Lankester and Dr. A. R. Wallace— Measurement of Bones — Nature not mathematically exact — Gravity and Perfect Motion : Spirals and Perfect Growth— Spirals in Shells, Whirlwinds, Human Organs, Nebula;, etc. — Classifica- tion, Utility, and Antiquity of Spirals— Need of Theory pp. I — 22 CHAPTER II MATHEMATICAL DEFINITIONS Spiral Appearances subjective — Flat Spirals — Left Hand and Right Hand — Conical and Cylindrical — Ionic Volute drawn by means of a Shell — Ways of making Spirals — Curious Nomenclature used by Botanists . . . . pp. 2,^ — 40 CHAPTER III UPRIGHT SPIRALS IN SHELLS Formation of Spirals in Shells — Tube coiled round Axis — Life History of a Series in One Shell — Acceleration and Retarda- tion — Natural Selection — Adjustment to Environment — Survival and Spiral Variation — Right-hand and Left-hand Shells — Ammonite and Nautilus — External and Internal Spirals — Supporting the Central Column — Comparison with Insects and Plants — Multiple Spirals . . . pp. 41 — 56 CHAPTER IV FLAT SPIRALS IN SHELLS Nautilus and Logarithmic Spiral — Equiangular Spiral a Manifesta- tion of Energy — Deviation from Curve of Perfect Growth — Leonardo da Vinci as Student of Shells — Work of Professor Goodsir — Varying Inversely as the Cube and the Square — Significance of the Position of the Siphuncle — Vertical and Horizontal Views of Shells and Plants . . . pp. 57 — 80 CHAPTER V BOTANY — THE MEANING OF SPIRAL LEAF ARRANGEMENTS Provision for Air and Sunlight — Overlapping of Old Leaves by Young — Advantages of Overlapping in Intense Glare — Spiral Plan for Minimum Overlap — The Ideal Angle — Fibonacci Series — Mr. A. H. Church on Logarithmic Spirals in Phyllotaxis pp. 81 — 93 ( I ( ( I xxviii TABLE OF CONTENTS CHAPTER VI SPECIAL PHKXOMEXA IX CONNECTIOX WITH SPIRAL PHYLLOTAXIS The Spiral Theoiy of Schimper — Growing Systems in place of Adult Construction— A Logarithmic Spiral on a Plane Surface— The Fibonacci Series again— Radial Growth and Spiral Patterns— A Standard for Comparison— Examples of Difterent Systems PP- 94— ii4 CHAPTER Vn RIGHT-HAXD AND LEFT-HAND SPIRAL GROWTH EFFECTS IN PLANTS Twist Effects : (i.) Spiral Leaf Arrangements ; (ii.) Overlapping Effects ; (iii.) Unequal Growth in Main Axis ; (iv.) Spiral Mo^'ement of Growing Ends ; (v.) Spiral Growth of Twining Plants ; (vi.) Spiral Effects after Death — Nomenclature of Spirals — Numerical Proportions of Right and Left Hand pp. 115— 131 CHAPTER Vni RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH EFFECTS IN PLANTS {continued) DEAD TISSUES AND SPINNING SEEDS Spiral Twisting of Dead Tissues — Coiling when Drying : Straighten- ing when ^^'et — Predominance of Right-hand Fibres — Seed Spinning in Flight — The Mechanism of Winged Fruits pp. 132— 141 CHAPTER LX RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH EFFECTS IN PLANTS {conti^med) SOJIE SPECIAL CASES Anomalous Variation producing Spirals — " Spiral Staircase " Con- struction — Peculiarities of Spiral Spermatozoids — Male Cells of Cycads and Chinese Maidenhair Tree — Spirals and Loco- motion — Prevalence of Right-hand and Left-hand Spirals pp. 142—150 CHAPTER X RIGHT-HAND AND LEFT-HAND SPIRALS IN SHELLS Contrast of Trees with Shells — Spiral Fossils in Nebraska — Deter- mination of Hand in Shells — Different Hand in Fossils and Survivors of same Species — Left-hand Spirals of Tusks — Sinistral Shell, but Dextral Animal — Shells among Primitive Peoples — Following the Sun — The Swastika — Spiral Forma- tion and the Principle of Life .... pp. 151 — 169 CHAPTER XI CLIMBING PLANTS The Purpose of Climbing— \A'ith and ^^■ithout Tendrils— Hand and Species— Mr. G. A. B. Dewar on Chmbers — " Feeling " for Supports — Inheritance and Memoiy — Circumnutating — " Sense Organs " for Gra\'ity and Light— The Statohth Theory —Influence of Light and Moisture— Effects of Climate- Reversal of Spirals pp, 170—189 TABLE OF CONTENTS xxix CHAPTER XII THE SPIRALS OF HORNS Pairs of Horns— Odd-toed and Even-toed Hoofed Animals— The Angle of the Axis in Horns— Suggested Geometrical Classifica- tion—Distinctions between Horns of Wild Animals and Tame —Homonymous Horns—" Perversion " and Heteronymous Horns— Comparison with other Spiral Growths, as of Plants and Shells— Exceptions to Dr.Wherry'sRule— Tame Animals showing Twists of their Wild Ancestors — Development or Degeneration ? — The Problem stated . . .pp. 190—219 CHAPTER XIII SPIRAL FORMATIONS IN THE HUMAN BODY Natural Objects do not consciously produce Spirals — Deviation ^rom^Mechanical Accuracy — SpiralFormations of Upper End of Thigh Bone — Growth and Change — Corresponding Struc- tures in Birds and Mammals — Conical Spiral of Cochlea — Spiral Formations : Umbilical Cord, Skin, Muscular Fibres of Heart, Tendo Achillis, The Humerus (Torsion), Ribs, Joints, Wings and Feathers, Eggs, Animalculse . . pp. 220 — 238 CHAPTER XIV RIGHT AND LEFT-HANDED MEN Right and Lef t-hancledness — Legs and Arms of Babies — Leonardo da Vinci — Preference of Orientals for Left-hand Spirals — I^rehistoric Man generally Right-handed — Skill of Left-handed MeiH Example¥~from the Bible— The Hand of Torques — The Rule of the Road — Left-handed Sportsmen : Anglers, Archers, etc. — Left-handed Artists — More about Leonardo — Letter from Mr. A. E. Crawley .... pp. 239 — 265 CHAPTER XV ARTIFICIAL AND CONVENTIONAL SPIRALS Spiral Decoration in Prehistoric Times — The Successive Races of Man — Artistic Skill of Aurignacians — Magdalenian Ci\'ilisa- tion — The Spiral as a Link between Aurignacians and Greeks — The Mycenfean and Jlinoan Age — Late Neolithic Ornamen- tation — Distribution of Spirals in United Kingdom — Scandi- navi-a and Ireland — Egyptian Spiral in Danish Celts — Neo- lithic Stones and Etruscan Vases — The Sacred Lotus — The " Unlucky " Swastika — Spirals in Greek Art — Origin of the Volute — Theory and Experiment — The Iron Age — Un- civilised Communities of the Present Day — I\Iedi£eval Gothic — Violin Heads — Cylindrical Spirals : Torques, Armlets, " Collars " . . ' pp. 266—295 CHAPTER XVI THE DEVELOPMENT OF THE SPIRAL STAIRCASE Spiral Columns— Rarity of Left-hand Spirals— Right-handed • Architects and Workmen — Accidental Cause of a Twisted XXX TABLE OF CONTENTS Spire— Efficiency and Beautj- — Practical Origin of Spiral Staircases — Gradual Evolution — Central Support — The Hand Rail— Defence against Attack— Double Spiral Staircases pp. 296—314 CHAPTER XVn SPIRALS IN NATURE AND ART Shells and Spiral Staircases — Practical Problems and Beauty of Design — Efficiency and Beauty — Leaning Campaniles Inten- tionally Designed — Charm of Irregularity — The Parthenon — Architecture and Life — Quality of Variation in Greek Archi- tecture — Expression of Emotions — Artistic Selection from Nature pp. 315—340 CHAPTER XVIII THE OPEN STAIRCASE OF BLOIS The staircase designed by Leonardo da Vinci — Voluta Vesper- tilio — The King's Architect — A Left-handed Man — Work of Italians in France — Leonardo's Manuscripts — His Theories of Art pp. 341—379 CHAPTER XIX SOME PRINCIPLES OF GROWTH AND BEAUTY Diirer and the " Cavallo " — Diirer's Mathematical Studies — Dante, Leonardo, Goethe — The Experimental Method — Beauty is "Fitness Expressed" — The Value of Delicate Variations — "Good Taste" — Processes of Scientific Thought ........ pp. 380 — 406 CHAPTER XX FINAL RESULTS The Logarithmic Spiral as an Abstract Conception of Perfect Growth — Spiral Nebulfe — Dr. Johnstone Stoney's Spiral of the Elements — Infinite Series and the Rhythmic Beat — Phyllotaxis — The Ratio of Pheidias — The 4> Spiral — Space Proportion — Art and Anatomy — The Theory of Exceptions — Value of a " Law " — Complexities of the Higher Organism — " A FlaiTie to Curiosity " — The Methods of Science . pp. 407 — 432 APPENDIX I. Nature and Mathematics {illustrated) . . . p. 433 II. The (^ Progression. By Wilham Schoohng . . p. 441 III. Infinite Series and the Theory of Grouping . . p, aaj IV. Origins of a Symbol {illustrated) ■ . . . p. 448 V. The Spiral in Pavement-toothed Sharks and Rays {illustrated). By R. Lydekker . . . p. 452 VI. The Spiral in Bivalve Shells (iZ/Msiffl/gf^). By R. Lydekker P- 454 VII. The Sliell of Travancore ..... p^ 4^5 VIII. The Growth of Sliells {illustrated) ■ . . p. 457 IX. The 4, Progression in Art and Anatomy {illustrated) p. 461 CHAPTER I Introductory — The Spiral "Painting embraces within itself all the forms of Nature . . . you cannot be a good master unless you have a universal power of representing by your art all the varieties of the forms in Nature. . . . Do you not see how many and how varied are the actions performed by men alone — how many kinds of animals there are, of trees and plants and flowers — how many kinds of springs, rivers, buildings and cities, of instruments fitted for man's use, of costumes, ornaments, and arts ? All these things should be rendered with equal facility and grace by anyone deserving the name of a good painter." — Leonardo da Vinci (Bib!. Nat. MSS.). GROWTH AND BEAUTY AND SPIRAL FORMATIONS — LETTERS FROM SIR E. RAY LANKESTER AND DR. A. R. WALLACE — MEASURE- MENT OF BONES NATURE NOT MATHEMATICALLY EXACT GRAVITY AND PERFECT .MOTION : SPIRALS AND PERFECT GROWTH — SPIRALS IN SHELLS, WHIRLWINDS, HUMAN ORGANS, NEBULiE, ETC. CLASSIFICATION, UTILITY, AND ANTIQUITY OF SPIRALS — NEED OF THEORY. The reason for connecting my search for certain principles of growth and beauty with an inquiry into various examples of spiral formation which may be found in art or Nature, can only become clear to my readers at a later stage. That connection arose in my own mind chiefly owing to the lucky accident of meeting a biologist whose vivid imagination recalled the columella of a shell when he was shown the central column of a staircase. His enthusiasm inspired me to study various natural objects with a delight that has been increasing for the last twenty years ; and for the existence of these chapters upon spiral formations no other apology is needed than the interest and beauty of an investigation which has hitherto only been suggested in a few scattered pamphlets and disconnected references. But an excuse should certainly be forthcoming for the fact that the pages dealing with natural history (which are the majority of those appearing in this book) have been prepared for pubhcation by one whose knowledge of botany and biology was originally as slight as his C.L. B THE CURVES OF LIFE skill in mathematics or his erudition in the development of art. A thorough grasp of at least four or more divisions of science seemed indispensable ; vet, since a profound acquaintance with only two of them would'be of no avail, I have ventured, perhaps too boldly, to believe that to have specialised in none, and to have the keenest sympathy with each, is as good a qualification as may be attained for the moment. I have the further consolation that every specialist will delightedly correct those errors which occur in ground famihar to him, while he may perhaps be tempted —by their mere proximity— to consider questions which hitherto he has too often set aside as being beyond his special province. This, therefore, is one reason why, in later pages, I shall venture on the hope that the artist or the archi- tect will consider the biologist in a kindlier light, and that the mathematician and the botanist may lie down together. When Captain Scott was in winter quar- ters near the South Pole, he overheard a biologist of his party offering their geolo- gist a pair of socks for a little sound in- struction in geology. So fruitful an atti- tude of mind need not be limited to the Antarctic region. Though I must mention two of the most distinguished helpers who have permitted me to publish their general opinions, I do not give the names of many who have offered me the kindest and most generous assistance in detail during the twenty years or so in which these matters have occupied a large part of my leisure. All of them are conscious of my gratitude. None of them might wish to be held even remotely responsible for suggestions that are unfettered by too keen an appreciation of the technical difficulties involved. When he was aware of my efforts, Sir E. Ray Lankester wrote as follows : — " / have often thought that if the public knew more of the real beauties of nature our museums would be far more thronged with visitors than is Fig. I. -Spiral Nebula, ilESSiER 51, Canes Venatici. INTRODUCTORY— THE SPIRAL 3 the case at present. Every effort is made in many of them to display the various specimens to their best advantage, and to explain clearly what they are. But something more is often needed, and the man who knows most about these matters is not always the man who has time to write about them. Moreover, the writings of the specialist are too often necessarily expressed in language that is fully intelligible only to a few. Yet if the energetic worker in other fields will pause a while to consider what he can learn from biology or botany, he will, I think, be rewarded far beyond his expectations. . . . " . . . I know many of the steps you have taken to arrive at your conclusions, and I think your analysis of the growth of horns (for instance) and your investigation of the growth of plaits upon the columella of a shell might be distinctly useful to the biologist, apart from any connection in which they may be found in your pages. " The hope that mathematicians may in time produce a system of definitions that will be of use, both to the biological and to the artistic morphologist, is by no means new. But every fresh instance that tends to make it more probable must contribute to the advantage alike of science and of art." After this, I was still more encouraged to proceed with this publication by receiving, in January, 1912, the following letter from the late Alfred Russell Wallace, which was pubhshed during that year with his permission : — " I was very much interested in your work on ' Spirals ' in Nature, as it is one of the finest illustrations of that extreme ' diversity ' in every part of the material universe from suns and planets to every detail of our earth's surface, and every detail of structure in plants and animals, culminating in an equal diversity in the mental character, as well as the physical structure of man. This final result, as I have suggested in my latest book, The World of Life,' is the whole purpose of tJte material universe, inasmuch as it leads to the development of an infinite diversity of ever- living and progressing spirittial beings. Tliis diversity has been brought about through wliat we term tite ' laws of Nature ' — really the ' forces ' of Nature — acting on matter, which itself seems to be an aggregation of more refined forces, acting and reacting for the most part in wliat appear to be fixed and determinate ways. We are now learning that these forces them- selves are never identical, and never act in an identical manner. TJie atoms, once thouglit to be absolutely identical, absolutely incompressible, etc. are now perceived to be each a vast complex of forces, probably no two identical. So, the chemical atoms, long thouglit to be fixed, of definite atomic weights, and combining in definite proportions , are now found to be in all probability diverse, and their atomic iveigJtts not commensurable with each otlter. " Tills atomic and sub-atomic diversity is, I believe, tIte cause, or rather the basic condition of the exquisite forms in Nature, never producing straight lines but an endless variety of curves, and spirals. Absolute uniformity of atoms and of forces would probably have led to the production of straight lines, true circles, or other closed curves. Inequality starts B 2 4 THE CURVES OF LIFE curves, and when growth is diverted from the direct path it almost neces- sarily leads to the production of that most beautiful of curves — the spiral. " Yours truly, " Alfred R. Wallace." I was irresistibly reminded, by this letter, of the last sentence in " The Origin of Species." " There is grandeur," wrote Mr. Wallace's great contemporary, " in this view of life, with its several powers, having been originally breathed by the Creator into a few forms or into one ; and that, while this planet has gone cychng on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been and are being evolved." It is as a line to a guide our researches among these " endless forms most beautiful " that I have here chosen the spiral because Fig. 2. — Orbiculina admea (ungulatus stage) x 30. (Brady's Foraminifera. Challengev Reports.) Fig. 3. — Left Ventricle of Sheep's Heart. (Pettigrew.) it is prominently connected with so many of them. I do not ask you to believe that the occurrence of similar curvilinear formations in various organic and inorganic phenomena is a proof of " conscious design." I only suggest that it indicates a community of process imposed by the operation of universal laws. I am, in fact, not so much concerned with origins or reasons as with relations or resemblances. It is still more important not to see in any given natural object that spiral formation which may merely be a useful convention of the mind. The science of mathematics has been defined as " the great instrument of exact statement and mental manipulation," and when it is combined with the extraordinary power of visual imagination possessed by such men as Kelvin, Clark Maxwell, Rayleigh, or J. J. Thomson, we see to what astounding results it may lead the human intellect. But we must not imagine that " Nature " is ever " mathematical " or that any natural object " knows what a spiral means." Yet the neglect of mathematics by the average INTRODUCTORY— THE SPIRAL 5 biologist is sometimes embarrassing. When I tried to compare the bones of Persimmon with those of his direct ancestor, Echpse, I found that the world of science had not decided how bones should be measured. They have not decided yet. It was only in 1898 that the first scientific description of the curves of horns was attempted by Dr. Wherry. In several departments of the present inquiry my chief justification for its existence hes in the fact that no answer yet exists to many of the questions obviously involved. At the end of the fifteenth century, Leonardo da Vinci summed up the knowledge possible to his day in a sentence which has caused a great deal of controversy ever since it was discovered among his long-lost manuscripts. " In this," he wrote, " the eye surpasses Nature, inasmuch as the works of Nature are finite, while the things which can be accomplished by the handiwork. Fig. 4. — Section of an Eocene Tertiary Foraminifer. Nummtilina nummularis. (Nicholson.) Fig. 5. POLYSTOMELLA CRISPA. One of the microscopic Forami- nifera figured in Nicholson's PalcBontology. at the command of the eye, are infinite." In modern language we might express this by saying that the fact that the logarithmic spiral (for instance) can never be reached in Nature is due to the truth that Nature is finite while the logarithmic spiral is infinite and goes on for ever, as no living organism does. But it is possible to bring the two together mathematically, and so closely, that small variations in the daily growth of an organism would be enough to account for any further discrepancies. For instance, in order to approximate to a finite organism, any infinite curves of growth must be slowed down, and we may thus obtain a retardation spiral by a method something like that applied to Newton's Second Law of Motion. Hyatt and Cope have dis- covered the law of acceleration in the development of such shells as Fusus, and Cope has announced the complementary law of retardation. Canon Moseley, making a geometrical examination of certain turbine shells, found that the curve wound round their central axis was logarithmic, and from it he framed a series of 6 THE CURVES OF LIFE formula by which other conditions could be predicted as they were found to exist. In the same way our retardation spiral can be adapted to suit different rates of slowing down as the organism grows older, and slower, till it dies. Conversely, acceleration might be noticeable when the organism was young. But never would the organism exhibit mathematical uniformity, and its growth would not be necessarily centric, indeed, nearly invariably eccentric. Just as Newton began by postulating Perfect Motion, and thence explained the working of the solar system, so it may be possible to postulate Perfect Growth (by means of a logarithmic spiral) and thence arrive at some law ruling the forms of Fig. 6. — Spirillum rubrum, Fig. 7. — Spiral Form of Polyzoan. Magnified 1,000 Diameters. Flustra cribriformis. (From Kolle and Wassermann, Handbuch (Torres Straits.) der Pathogenen Jlikroorganismen, Atlas.) organic objects as gravitation is held to prevail in the physical world. Is the logarithmic spiral the manifestation of the law which is at work in the increase of organic bodies ? If so, it may be significant that Newton showed in his Principia, that if attraction had generally varied as the inverse cube instead of as the inverse square of the distance, the heavenly bodies would not have revolved in ellipses but would have rushed off into space in logarithmic spirals. Professor Goodsir therefore asked, if the law of the square is the law of attraction, is the law of the cube (that is, of the cell) the law of production ? Can we connect this with Goethe's idea that while the straight line was masculine, the spiral was feminine in its essence ? As Dr. Wherry has pointed out, many of the problems of spiral growth are deep and difficult. They touch upon the funda- INTRODUCTORY— THE SPIRAL mental laws which regulate the world, and instinctively direct the art of man. As an introduction to our search I have selected a few typical instances of the many spiral formations to be found in Nature, from the microscopic foraminifer (Figs. 2, 4, 5), and the even smaller bacilli (Fig. 6) to the enormous nebulae (Fig. i) in the firmaments of space. The usual rotation of air currents in our northern hemisphere is from left to right hand, while that in the southern is from right to left. This fact has been offered as an explanation of many phenomena which have not been sufficiently examined ; but it may well be that hurricanes, tornadoes, and whirlwinds are produced by the sudden meeting of strong air currents originally moving in opposite directions. The effect of wind on sand is often to produce the whirling spirals usually seen in sandstorms, which are occasionally reproduced on a small scale even on a dusty road in this country. The waterspout is a more complex instance of the same force, and has been explained as the meeting of a rotating and inverted cone of cloud with a similar but upright cone of water, the two cones having originally started under the same influence of the wind blowing at different levels, and eventually exerting a mutual attrac- tion upon each other. They thus meet at the apex of each cone to form a rapidly rotating column composed of water from beneath, mixed with vapour from above. Some of the smaller kinds of spirals observable in crystals will be given in due course. But it is important, even at this early stage of our inquiry, to remember that the spiral (whether flat or upright) is not necessarily connected with vitality, yet it may be per- fectly true that when a spiral formation is observable in organic subjects, it may express in them the same results of stress or energy which are observable in such lifeless or inorganic forms as the starry nebulae, the waterspout, or certain forms of crystals. It may also be noted in this connection that the relation of the direction of the magnetic force, due to an electric current, to the direction of that current itself is the relation involved in a right-hand spiral. It is, however, mainly with the organic forms of life in animals and plants that I am dealing here ; and when we once begin, in these great divisions of the universe, to look for spirals, it will I think, be astonishing to find the enormous number and Fig. 8. — Dorsal Valve AND "Arms" of Devonian Lamp-shell Uncites gryphus. (Davidson.) 8 THE CURVES OF LIFE variety of such formations which can be discovered. In plants, spirals are observable from seeds and seed cases and cells, to stems and flowers, and fruit. In animals, and in man, the spiral may be said to follow the whole course of vital development from the spermatozoon to the muscular structure of the heart ; from the umbilical cord or the cochlea of the ear to the form and frame- work of the great bones of the body (Figs. lo and ii). It may be noted that the spiral of the cochlea hidden in the ear is one of the proofs that the bone containing it belongs to a mammal. Hermann von Meyer once acciden- tally dropped a skull which had previously been con- sidered to be that of a lizard. The breakage re- vealed the cochlea, prov- ing that the bones were those of a mammal, which was christened Zeuglodon\ Three examples of: ex- traordinarily minute ani- mal life exhibiting a spiral have been drawn in Figs. 4, 5, 6. In the magnificent illustrations of Dr. F. Ritter v. Stein's " Der Organismus derlnfusions- thiere " (Leipzig, 1867), a large number of others may be examined, such as Spirostomum ambiguum, Stentor coenilens, Euglena spirogyra, and many more. The ciUa on the top of Vorticdla are set in a spiral to create a vortex of water that will suck in food. The gills of Sahella unispira no doubt produce the same result, and have been beautifully drawn in the atlas to " Le Regne Animal," by G. uvier. The egg capsules of certain sharks {e.g., Cestracion philippi) show a xtry beautiful external spiral ; and the case Fig. g. — The Glass-Sponge (Euplectella aspergillum), or Venus's Flower Basket. C INTRODUCTORY— THE SPIRAL 9 made by the larvae of the caddis fly {Phryganeida) is formed by a ribbon exquisitely twisted up into a right-hand spiral (Fig. 12). The whole phenomena of animal locomotion are largely based (as the late Professor Pettigrew so learnedly showed) upon spiral movements, and the same lamented investigator (in the post- humous volumes called "Design in Nature,") has left a series of drawings and observations demonstrating that a bird's wing is twisted on itself structurally and is a screw functionally. He showed that the propeller of a steamship exhibits the same func- tions as the fin of a fish, the wing of a bird, or the limbs of a quadruped ; and that in the whole range of animal locomotion these functions are most exquisitely displayed in flight. To Fig. 10. — Left-hand Spiral of Human Umbilical Cord. (Pettigrew.) Fig. II. — Spiral For- mation OF THE Humerus. (Pettigrew.) suggestions in this author's works I owe several of the examples of spirals which have been specially drawn for these pages. In the interesting book called " The Growth of a Planet," by Mr. Edwin Sharpe Grew, a very convincing explanation of spiral nebulas is given, which is intelligible to the ordinary lay- man apart from the technical astronomer. Mr. Grew writes as follows : — " The discovery of spiral nebulas was originally made by Lord Rosse. . . . The shape of some nebulae seems to demand the hypothesis that there was a partial collision between two stars. The heat arising from the impact, or from what in mechanics is called ' arrested momentum,' taken together with the mutual attraction of the two stars, would impart a rotary movement of the highest order to the two systems. In some instances the consequences might be the fusion of the two stars into one giant nebula. Or if there were a partial arrest of the forward motion of one or other, then certain parts of 10 THE CURVES OF LIFE either star might escape from the main spiral. Such a catastrophe is possibly visible in the nebula in Canes Venatici," It is this nebula which is reproduced in this chapter (Fig. i) as an example of the formations described. (Compare Chapter XX.) . There is another theory which is worth transcribing here from the same instructive volume : — " Sir Robert Ball's variant of the spiral hypothesis sets out by laying down the proposition that a sphere of moving particles has a tendency to spread itself out as a disc. He deduces this from the fact that in any system of moving forces the sum total of the results of the Fig. 12. — Case MADE BY Larva OF Caddis-fly. (Enlarged.) Fig. 13. — Left-hand Polygonum baldschua- NicuM. (Bokhara.) interactions of the forces (or what is called the ' moment of momentum') will always remain the same ; but that the ' energy ' of the system diminishes with each collision of its particles. The particles after collision would drift towards the centre, and the system tends to that form which combines a minimum of energy with the preservation of its original momentum (or shall we say ' life force ' ?). This form can be shown to be a flat disc widely stretched out." [This of course would only hold good if the particles were not small enough to be influenced by light pressure to a greater extent than by gravity. — T. A. C] " The drift of particles towards the disc's central portion would cause this part to rotate more rapidly than the outer part. Spiral structure would be the result of these differentiated movements. By some process, of which we cannot trace the details, knots or nuclei appeared on the whorls of the spirals, and these formed the embryos of the planets." INTRODUCTORY— THE SPIRAL ii In 1904 Professor J. M. Schaeberle announced his discovery of a double spiral structure in the great cluster in Hercules, the more pronounced spiral, formed by outgoing matter, being clockwise (or, as I should say, left hand) the other being counter- clockwise and containing returning matter. There is little doubt that spirality is becoming more and more widely recognised as one of the great cosmic laws, and as being distantly hinted at even by the antipodal disturbances of the sun. This has implied the further recognition that in astronomy, as in every other branch of science, one set of facts dovetails into the next ; none can be properly considered apart from the rest. Though the old imposing facade of exact theory remains erect, as Miss Agnes Gierke happily put it, the building behind is rapidly disintegrating as more and more possibilities come to light in the advancement of our knowledge. In nearly all the apparently fantastic irregularities of the visible nebulae we observe that spiral conformation which intimates the action of known or discoverable laws in the stupendous enigma of sidereal relationships. 'TEe whole history of the heavens, the more clearly it becomes understood, involves more certainly the laws of spirality, from single and comparatively small examples to such vast masses of nebulosity as that which encompasses the Pleiades. The first eight of the figures illustrating this chapter are all examples of plane or conical spirals. The remainder are more or less cylindrical in form, and I would now direct attention more especially to the leaves in Fig. 14, which are so exactly like a screw-propeller, or the feather of a bird's wing in flight, and then to the climbing plants, from Bokhara and North America, shown in Figs. 13 and 15. I do so because these latter give me another opportunity of showing how much recent inventions have con- tributed to our knowledge of these things. If the high capacities of modern telescopes have revealed the spiral nebulae, it is not too much to say that the kinematoscope (with or without the assistance of the microscope) has very notably advanced our appreciation both of the smaller hving organisms and of the growth of flowers and plants. Mrs. Dukinfield H. Scott suggested the use of a kinematograph for showing, at an accelerated speed, those movements (of climbing plants, for instance) which are, in nature, too slow to 'be clearly appreciated by the most constantly watchful human gye. This is a very interesting development of a mechanism |which usually enables us to see those movements (of a gallop- ing horse, for example) which are, in Nature, too quick to be seen by the human eye. The mechanism analyses these 12 THE CURVES OF LIFE speedy movements in a way which enables us, when we wish, to examine separately one single photograph (out of a long series) which reveals to us a position we may never have realised as actually occurring or even possible ; and a very educational use of such photographs (in rowing or boxing, for instance) might be developed. But Mrs. Dukinfield Scott's suggestion that the process might be reversed has only just, I understand, beei, practically demonstrated since she first wrote about it in 1904 and you may now see a plant visibly moving, by concentrating, into a few minutes a series of photographs which have taker/i many hours to record from the natural growth. Mrs. Dukinfielcji Scott in 1904 pro- duced a simple and,', cheap machine whicli registered 350 photo- graphs round a disc; 12 inches in diameter], which enabled her iiji the case of very slowly - moving plants to make a separate exposure every fifteen minutes. She also surmounted the mechanical diffi- culties of uniform ex- posure and absolute steadiness, and event- ually continued her photographs at night by artificial light. Recent develop- ments have solved a good many of the inevitable mechanical problems ; and it has even become possible for the scientific inquirer to carry out his own researches by the new method of photography and tn, reproduce the results on a screen in his own study. The kine J matograph for ordinary field work takes sixteen pictures a second / A high-speed micro-kinematograph camera in France register \ 300 pictures a second taken by electric sparks. The reverse process implies a proportionate reduction in speed. Takin-" sixteen a second, or 960 pictures a minute, as the normal, if wi desire to watch the rapid development of a natural growth which in reality, takes three days, we must spread our 960 picture equally over the 4,320 minutes of those three days ; in othe! words, we must take an instantaneous photograph every foui Fig. 14.- - Radiating Whorl of Spiral Leaves IN Alstrcemeria. (Pettigrew.) INTRODUCTORY— THE SPIRAL 13 and a half minutes for seventy-two hours successively. By running the film containing these 960 pictures, so taken, through the machine, at the rate of sixteen in every second, we can see the growth of three days as a visible movement of a minute's duration. The whole process should be as valuable to the investigation of spiral growth in botany as is the visible examina- tion of microscopic bacteria upon a screen in other branches of science. In Figs. 16, 17, 18, will be found three examples of the shells which are among at once the most beautiful and the most easily Fig. 15. — Right-hand Apios tuberosa. (N. America.) Fig. 16. — Siliquaria striata. (Bronn and Simroth.) examined instances of spirality in organic life. We shall hear more of the wonders of their internal structure later on. Until about 1908 the conchologist who desired to inspect the structure of the columella had to make a section by either sawing through or rubbing down what might be a valuable and beautiful specimen ; and sometimes the shell itself was too delicate to admit of such an operation being satisfactory at all. But in that year Mr. George H. Rodman published a number of pictures of moUuscal jshells in which the use of the X-rays made it possible to show the (internal structure without hurting the specimen at all ; and ithese pictures have proved of great interest and value, though 14 THE CURVES OF LIFE the uninstructed student would need warning that, in the cases mentioned, the pictures printed showed the shells reversed. I must leave to more scientific pens than mine the task — which I foresee as necessary — of classifying spirals. The broad division into those of inorganic and those of organic origin will at once be obvious ; but it is with the sub-division of the latter that the difficulty really arises. The late James Hinton thought that " growth under resistance is the chief cause of the spiral form assumed by living things." But this generalisation does not cover many of the most remarkable instances. A spiral may exist merely to save space, or to place an organ which has to be long into a situation necessarily restricted. The long intestine of the frog, for instance, is twisted up like a tight watchspring in the tadpole. In most mammals a very considerable length of Fig. 17. — Pleurotomaria Fig. 18. — Pleurotoma (An- conoidea. cytrosyrinx) elegans. (Bronn and Simroth.) (Bronn and Simroth.) intestinal tube is folded in spiral coils within the body. In some fishes, like sharks and rays, the tube is provided with an internal spiral, apparently so that every possible nourishment may be extracted from the food while it remains within the animal. Certain sharks also exhibit another use of the spiral in their curiously constructed egg-cases, which would revolve as they floated in the water and therefore travel farther, and the form in, Cestracion philippi is almost exactly like that of a kind of a.nchoir used for burrowing its way into soft mud or sand and there, holding fast. It is shown in Fig. 271 on p. 234. \ One of the most extraordinary instances of what I may calTi the " locomotory " spiral is to be found in the plant called Storksbill [Erodiiim) , which is so named from the long " beak ' ' formed in each flower as the seeds ripen. This is describee i. in greater detail later on, but I may say here that this bealaj INTRODUCTORY— THE SPIRAL 15 is composed of the long tails (or " awns ") sticking out of the top of the seeds, which are also furnished with refiexed bristles. When the seeds ripen they are freed as the awns split off the beak, and each awn begins to show hygroscopic properties of a very marked character. Laid upon water, the awn straightens out into a thin tentacle very slightly curved. When dry, it constricts into a close spiral which is like a cork- screw close to the seed and has a kind of curved arm (the free end of the awn) at the other extremity which must exert a considerable leverage in twisting. As the spiral coils and uncoils according to the presence or absence of moisture in the atmosphere, the seed moves along the ground until its sharp point pene- trates a soft bit of earth and bores downwards, the refiexed bristles pre- venting its retreat. A very similar process is observable in the Russian Feather-grass, which has a much longer awn with an extended feathery tail. This seed penetrates the ground in much the same way already described, and wiU even get through a sheep's skin, and some- times cause sufficient irritation to kill the animal, as its remorse- less spiral gradually bur- rows inwards. Other seeds show even more delicately beautiful forms of the spiral. The spherical antherozoid of Cycas revohita, for instance, carries a spiral band of minute vibratile hairs (cilia) by which it is propelled. The seeds of certain pines and other trees are pro- vided with wings constructed almost exactly like the leaves drawn in Fig. 13 or the feathers of a bird's wing, and working like a screw-propeller to distribute the life principle of the plant as far as possible through the surrounding air before it falls. The propelling force given by a screw or spiral is utilised by Nature in a hundred ways. The heart of a man and most other mammals has the formation shown in Fig. 3 for this reason. The Fig. 19. — Young Plant of Lilium auratum Photographed vertically from above to show .spiral growth of the plant and spiral twist in the leaves. i6 THE CURVES OF LIFE muscular arrangement of the stomach and bladder is very similar ; and their contents are extruded just as the blood is driven from the heart at each alternate beat. There is the combination of protection with economy of space in the cochlea of the internal ear. There is the idea of protection from the results of a fall by the springy resistance of the coiled horns of certain mountain sheep. Some illustrations of horns are given here, but this subject is dealt with more fully in a later chapter. Then there are the spirals produced when some soft, elastic substance, driven forward by its own vital energy, is unable to proceed in a direct line, either because of some slight initial obstacle at the point of emission, or because of the action of such forces as gravity after emission. Recent research also goes to show that the traces of stress on the structure of steel may be found along paths which exhibit spiral formation. In the botanical chapters. Fig. 20. — Marco Polo's Argali (Ovis ammon poli). later on, a number of beautiful examples of spirals will be given ; and in Fig. 19 I have shown that by photographing a growing plant (Lilimn auratimi) vertically, you can appreciate the spiral construction of its leaves, and their relations to each other, much better than would be the case in the position in which it is ordi- narily observed and drawn. It is, in fact, almost possible to catalogue the forms of the spiral utilised by man, in rifles, in staircases, in tunnels, in corkscrews, or a hundred other ways, and to parallel nearly every one in natural formations. In some cases there have been zealous inquirers so overwhelmed with the significance and ubiquity of this formation that their contri- butions to knowledge have been seriously weakened by their mystical or spiritual extravagances. As a warning for all who may be thus tempted, I have inserted here (Fig. 23) a picture which gives all the impression of representing a series of spiral;s originating at a common point, but which in reality is nothinjg but a cluster of concentric circles, composed of parti-coloure 'd INTRODUCTORY— THE SPIRAL 17 stripes upon a variegated background. This was first drawn by Dr. James Fraser, but it is used in these pages only to emphasise the fact that this is one of the subjects very apt to carry away the amateur investigator and lead him to assert more than he can prove. There is no need for that. The facts are wonderful enough without addition. But I must admit that I have nc^'er been deterred from comparing two natural objects which may be, in essence, entirely different, merely because the only point of similarity was the spiral formation. In my view the mere fact that such a bond may be discovered in objects otherwise so different may have the greatest significance. Few things, at first sight, would seem more different than the action of a magnet upon steel and the passage of a beam of light through the air. Yet in comparing the two, Clark Maxwell showed that the phenomena of light were due to the rhythmic movement of the same stresses in the aether observable in cases of magnetic attraction. " Omnes artes quae ad humanitatem pertinent" said Cicero, " habent quoddam com- mune vinculum." With a similar idea of searching for resemblances I have never shrunk from examining any of the artistic or historical tradi- tions of the spiral just as closely as the mechanical aspects of the screw or its artificial uses by mankind. It is certainly curious that spiral shells were used for the adornment of primitive man in the Magdalenian epoch at least 20,000 years ago ; that they are found among the relics of the earliest Medi- terranean ci^'ilisation at Knossos ; that in such carvings as those I have reproduced here from Rouen (Fig. 24) or from Lincoln Cathedral (Fig. 25) and in such allegorical pictures as that of Bellini (Fig. 26) the significance of the spiral shell seems certainly recognised. In the chapters on artificial spirals we shall find this strange formation has almost as long a history ; and in fact we shall have traced it, when we reach my closing pages, from the earliest ages of organic life upon the earth to the latest construc- tions of the modern engineer or architect. Completed in the Ionic capital, arrested at the bending-point of the acanthus-leaf in the Corinthian, it became a primal element of architectural ornament, eloquent with many meanings, representing the power Fig. 21. — The Hon. Walter Rothschild's Senegambian Eland (Taurotragus der- BIANUS). Length (straight) 36J- inches, from tip to tip 27J inches. (Photo by Rowland Ward, copyright.) C.L. i8 THE CUR\'ES OF LIFE of \va\os and winds in Greek building, typifying tiie old serpent of unending sin in Gothic workmanship. My next chapter will lay down certain necessary definitions, and give the few essential mathematical conventions that are necessary. Fig. 22. — Greater Kudu. Shot by G. Blaine. (British Central Africa, 1903. I shall then examine the upright and the flat spirals to be found in shells. Several sections will be devoted to botanical phenomena, including climbing plants, and including also the curious problem of why some spirals are left hand (or clockwise, following the sun) and others right hand. It will then be possible to investigate the growth of horns, and various other anatomica.l INTRODUCTORY— THE SPIRAL 19 examples. And not until all these have been as far as may be considered can we approach that portion of our subject which may be considered artistic, philosophical— what you will— at any rate some such conclusion of the whole matter as is inevitable at the close of a search so widespread and so full of interest. What that conclusion may be, I will not now elaborate ; but I may at least suggest that, however far our study may be pro- longed, we shall have to confess that in all efforts to define a natural object in mathematical terms, we come to a point at which Fig. 23. — The " Unit of Direction " Illusion, discovered by Dr. James Fraser, and first described by him in the British Journal of Psychology for January, 1908. In this diagram a series of perfect concentric circles composed of black and white cord have been placed one within the other ; but, owing to the chequered background, they appear in the form of a spiral. I reproduce this curious diagram by courtesy of the Strand Magazine. accurate knowledge of the involved factors ceases. All that can be said is that a logarithmic spiral (for instance) is as near as we can get in mathematics to an accurate definition of the living thing. Nor does the mathematician fare any better when he tries to express beauty in terms of measurement. In other words, the baffling factor in a natural object is its life ; just as the baffling factor in a masterpiece of creative art is its beauty. May it not then be true that beauty, like life and growth, depends not on exact measurement or merely mathematical reproduction, but on those subtle variations to which the scheme of creation, c 2 20 THE CURVES OF LIFE as we know it, owes those great laws of the Origin of Species and the Sur\'ival oi the Fittest ? --•-■"ll-T^,-— - .1/- ...11 J 'V -lilt ^ Fig. 24. ^- Fifteenth-century Carving FROM Palais de Justice at Rouen. It has been several times stated of late, by Sir George Darwin and others, that however useful the mere accumulation of facts Fig. 25. — MisERicoRDE in Lincoln Cathedral (1375). (From a Drawing by Miss Emma Phipson.) may be, it rarely letids to one of the great generalisations of science, unless there has been some definite aim in view, unless INTRODUCTORY— THE SPIRAL 21 some theory worth mvestigation is kept in mind, unless some bond of connection holds the mass together. In other words, we can recognise that the laborious collection of details may be powerless if it goes no farther ; and that the exercise of imagina tion, unrestricted, can neither convince nor gratify. But, in Fig. 26. — Allegoria. La Maldicenza. (By G. Bellini.) combination, these two can do what, for want of a better word, we call " create." This must have been Leonardo's meaning when he said that " the works of Nature are finite." They move along those orderly, those vast processes of time and space which can be reahsed by that human intelligence which is a part of them, if only it will work hard enough to collect the details. This, then, is to " know." But to " create " is greater, for creation takes that further step which must ever be based on knowledge, yet is 22 THE CURVES OF LIFE beyond knowledge ; for the things which eye and hand and mind can create " are infinite." Nature must be interrogated in such a manner that the answer is imphcit in the question. The observer can fruitfully observe only when his search is guided by the thread of a hypothesis. It is the thread of spiral formations that will guide this essay. It was the manuscripts of Leonardo da Vinci which inspired it. NOTES. Fig. 3. — Certain brachiopods contain very beautiful calcareous spiral arm-supports, formed by a ribbon of lime, and attached to the dorsal valve. In Zygospira modesta (Hudson River Group), these spiral cones are directed inwards ; in Spirifer niucronatiis (Devonian) they are directed outward and backward, and formed of many whorls ; in Koninckina leonhardi (Trias) tlie double arm-supports are flat spirals, instead of cones set on their edge, and are each composed of two lamellffi. Spiral Nebula. — These are more fully described in the last chapter. CHAPTER II Mathematical- Definitions " No investigation can strictly be called scientific unless it admits of mathe- matical demonstration." — Leonardo da Vinci {Inst, de France). m SPIRAL APPEARANCES SUBJECTIVE — FLAT SPIRALS — LEFT HAND AND RIGHT HAND — CONICAL AND CYLINDRICAL — IONIC VOLUTE DRAWN BY MEANS OF A SHELL — WAYS OF MAKING SPIRALS — CURIOUS NOMENCLATURE USED BY BOTANISTS. There are no doubt many principles of growth, as there are of beauty ; but for the present I desire to confine myself to those which are intimately connected with the various forms of a spiral, forms which are common to a very large part of the animal and vegetable kingdom. And at the very beginning, I should wish to emphasise a caution which will apply to every section of my inquiry. It is this : Because we can describe a circle by turning a radius round one of its extremities, it does not follow that circles are produced by this method in Nature. Because we can draw a spiral line through a series of developing members, it does not follow that a plant or a shell is attempting to make a spiral, or that a spiral series would be of any advantage to it. All spiral appearances should properly be considered as subjective ; and confirmation of this view that a spiral need not be directly essential to the welfare of a plant is shown by the curious fact that the effect of a spiral becomes secondarily corrected as soon as it becomes a distinct disadvantage to the plant. The same facts are observable in shells and other organic bodies, such as horns. Geometrical constructions do not, in fact, give any clue to the causes which produce them, but only express what is seen, and the subjective connection of the leaves of a plant by a spiral curve does not at all imply any inherent tendency in the plant to such a construction. This Mr. A. H. Church fully realises ; and therefore in his treatises on phyllotaxis he specifically bases all his deductions on "a single hypothesis, the mathematical proposition lor uniform growth, as that of a mechanical system in which equal distribution of energy follows definite paths which may be studied by means of geometrical constructions." It is in exactly the 24 THE CURVES OF LIFE same way that I desire my readers both to study the natural phenomena presented in these pages, and to consider the spiral formations here connected with them. Mathematics is an abstract science ; the spiral is an abstract idea in our minds which we can put on paper for the sake of greater clearness ; and we evoke that idea in order to help us to understand a concrete natural object, and even to examine that object's life and growth by means of conclusions (originally drawn from mathematics. It is only by some such means that the human mind, which hungers for finality and definite conceptions, can ever intelligibly deal with the constantly changing and bewil- deringly varied phenomena of organic life. Definition and description are always difficult. The various forms of spiral offer an admirable means of describing certain natural objects. But for the underlying causes producing the effects observed, we have to go to the biologist, the morphologist, or the botanist ; and I have only entered on this inquiry at all because it suggests so many questions to which the specialist has as yet provided no reply. In speaking of spiral formations I am faced with the initial difficulty that I must make myself clearly understood by readers who may not at first be interested at all in spirals, and who may never care to consider mere mathematical abstractions. I shall not be more mathematical than I can possibly help. But I am compelled to lay down a few preliminary definitions unless we are to speak of unintelligible and hazy uncertainties, incapable either of examination or of illustration. My object is merely to give my readers a few simple and easily understood formulae which will enable them to look at growing things and natural objects from a different point of view, and perhaps with a greater interest. There are many kinds of spirals distinguished by the mathe- matician. We have need here of only a few of them ; but we must get these few clearly into our minds. I will describe the flat spiral, the conical helix, and the cylindrical helix ; and we may begin with the simplest of all. In the ordinary flat spiral (such as a watch spring) we have a plane curve coiling round a fixed point or centre and continually receding from it, so that, though all points in the curve are in the same plane, no two of these points are at the same distance from the centre. The ratio in which the plane curve recedes from the centre sometimes defines the nature of the spiral. We can examine this for our- selves very simply. Place the most ordmary form of a flat spiral, a watch spring (Fig. 27), on the table, and next to it a watch, and it would be MATHEMATICAL DEFINITIONS 25 convenient if the hands were at twenty minutes to four for the purposes of this argument (Fig. 28). Draw upon a flat piece of paper two spirals like Fig. 29 (a right-hand spiral), and Fig. 30 (a left-hand spiral). In looking at these figures you have drawn, you will observe that the opening of the left-hand spiral is about at the minute-hand when the Fig. 27. — Flat Spiral of Watch Spring. Fig. 28. — Clock-face. clock registers twenty minutes to four, and that it is on the left- hand side of the figure. This will be an easy way to remember whether a flat spiral can be called mathematically left-hand or mathematically right-hand. For the opening of Fig. 29, the right-hand spiral, will be where the hour hand is on the clock- face close to the hour of four o'clock, and therefore on the right- hand side. A left-hand (or sinistral) spiral follows the sun, or Fig. 29. Right-hand Flat Spiral. Fig. 30. Left-hand Flat Spiral. the hands of a clock ; a right-hand (or dextral) spiral goes against the sun and contrary to the hands of a clock, in both cases when traced from the outer portions towards the inner, from M to A. An interesting point about the left-hand spiral, whether it be a flat spiral, or a conical helix, or a cylindrical helix, is this — ■ and it may be verified by the figures of flat spirals in front of you. If an insect walking in at the opening M on Fig. 30 pro- poses to reach the point A, that insect will have to keep on 26 THE CURVES OF LIFE turning to the right until it reaches A. It is always obliged to do this in left-hand spirals. On the other hand, if it starts from the opening M in Fig. 29, and tries to reach the point A, it must continually be turning to the left, and this is always neces- sary in right-hand spirals. This is why, in such upright spiral \ \ -^ ^- ■— / '^X. ^ r» /■ 1 \ 6 p. It N v. / ^ ^ ^ I / ^ \ \ \ Q^ X \ p \ \, \ X s. / \ \ V \ ^0 15 10 S \^ tJO s ( 10 5 »« / / / Fig. 31. — Logarithmic Spiral from the " Field " for April 22ND, igii. formations as are common in shells, a right hand shell which has its opening on the right side and which exhibits right-hand spiral formation is called leiotropic (turning to the left), whereas a shell exhibiting left hand characteristics is called dexiotropic (turning to the right), by the conchologist. Returning to our fiat spirals, I may quote, as a good mathe- matical example, the logarithmic spiral (Fig. 31, published in the MATHEMATICAL DEFINITIONS 27 Field for April 22nd, 1911) which afforded its yachting readers the solution to a pretty problem in navigation ; and this spiral is, to my mind, an admirable expression (see the curve AC in Fig. 50), in visible form, of the expansion of energy and growth. But I must not go too fast, and it is now my more immediate business to make it clear that the phrases " right-hand fiat spiral " or " left-hand flat spiral " are used merely as mathematical defini- tions ; they are not used as the names of actual objects. As a matter of fact, it is not always possible to say of a natural object that its flat spiral is either definitely right hand or definitely left hand, because in one aspect of that natural object you see a Fig. 32. — Ammonite from Lyme Regis. left-hand flat spiral and in another aspect of the same object you see a right-hand flat spiral. This difficulty occurs when the object is such a flat symmetrical shell as an ammonite {e.g., Figs. 32 and 33), which is exactly the same on both sides ; and, concerning- this ammonite, all you can say in this respect is that in a given position towards the spectator it exhibits a right-hand or a left- hand flat spiral, as the case may be. The same effect may be observed in Solarium and Lamprostoma in Figs. 34, 35 and 36. Other good examples of the flat spiral are, in plants, the frond of a fern (Fig. 37) and, in inanimate matter, the crystal of sulphur (Fig. 38). There is, of course, no such difficulty as I have just hinted about either cylindrical or conical helices, for t:hey are always 28 THE CURVES OF LIFE either right-hand or left-hand, and they retain that characteristic whether the}- are turned upside down or not ; but one thing can ^.' X' Fig. 33. — Section of Ammonitp:. "^m-r'm^ Fig. 34. Fig. 35, Solarium perspectivum. Lamprostoma maculata. (Shells .seen from above and from beneath.) be said concerning a fiat spiral, and this is that if it is a left-hand fiat spiral, and if you may imagine the point A pulled vertically MATHEMATICAL DEFINITIONS 29 Fig. 36. — Solarium JIaximum. upwards while the point M is fixed to the ground, you would produce a left-hand conical helix from Eig. 30. The cochlea of the human ear in Fig. 39 looks exactly as if it had been produced ^ Fig. 38. — Crystals of Sulphur. (Pettigrew.) Fig. 37. — Frond of Growing Fern. (See Fig. 6i.) in this way. See also the crystal in Fig. 40. In exactly the same way, if you pulled up the point A in Eig. 29 and held the point M upon the ground, you would produce a right-hand conical Fig. 39. — Lamina of Cochlea of Internal Ear, Fig. 40. — Spiral Crys- talline, Formation of Prochlorite. (From D. T. Dana' "Mineralogy.") (Riidinger.) helix. In this connection it should be noticed that in the case of certain shells which exhibit both flat and upright spirals, as, for instance, those in Figs, 41 and 42, when their upright spiral is right hand their flat spiral is also right hand and their 30 THE CURVES OF LIFE " entrance " on the right, and vice versa. It is also true that when the plaits on the columella show a right-hand helix, the external formation of the shell containing them will exhibit a right-hand spiral. This happens, so far as I am aware, in every instance of shells which exhibit both kinds of spiral formation. It is also interesting that in a left-hand spiral, whether it be flat, or conical, or cylindrical, the movement of a person or insect Fig. 41. Fig. 42. TURBINELLA PYRUM. HaRPA CONOIDALIS. (Shells seen from the .side and from above.) supposed to be walking round it, or ascending it, would, as I have already said, always be in the direction of the hands of a clock, and this direction seems to have influenced various customs, either sacred or secular, for we always pass the port in this same direction round the table, or, as it has sometimes been put, " through the button hole " ; and it is considered very unlucky to walk round a church from the western door in any other direc- tion. It is also, of course, the direction of the apparent movement MATHEMATICAL DEFINITIONS 31 of the sun in our northern hemisphere. Some writers {e.g., the Belgian geologist Van den Broeclc) say that the twisted trunks of trees are produced by the earth's rotation, and therefore when they exhibit a spiral they should show a right-hand spiral in the northern hemisphere and a left-hand in the southern ; like the turn of the cyclonic storms or the twist in water vortices ; but this is still open to more exact observation. It has also been suggested that, as the winds due to the earth's motion blow fairly steadily just when the trees are growing fast, the young tree may take a permanent twist, from this cause, which it never loses. Fig. 43. — Trunk of Chestnut Tree Twisted IN Right-hand Spiral. (From Onslow, Shrewsbury.) The tree reproduced in Fig. 43 was photographed for me in Onslow Park, Shrewsbury, by Mr. Ralph Wingfield. The late Professor Pettigrew has also described the strongly right-hand spiral he observed on the twisted stem of a huge Spanish chestnut (Castanea vesca) on Inchmahome, in the Lake of Menteith. Eighteen inches above ground this tree (which had been felled) was 15 feet in girth, and the spot where it lay has been beautifully described by Dr. John Brown in " Queen Mary's Child Garden." There are, of course, many examples of such spirals in tree trunks (Figs. 180, 181). I await some instances from Australia. Since I have already shown that a conical helix can be formed 32 THE CURVES OF LIFE from a flat spiral, it \\'ill not be surprising thai: the process can be reversed, and that a flat spiral can be fcnnied from a conical helix. I shall describe this, because I believe veiy strongly that if a I'iG. 44. — Right-hand Spiral of ^'oLUTE on Right Side of Ionic Capital Described with the help of the Left-hand Fossil Whelk Fusus (Cl-IKYSODOIIUS) ANTIQUUS. man can make a thing and see what he has made, he will understand it much better than if he read a score of books about it or studied a hundred diagrams and formulee. And I have pursued this method here, in defiance of all modern Fig. 45. — Inner Surface of Operculum of Turbo marmoratus. (Lile Size.) mathematical technicalities, because my main object is not mathematics, but the growth of natural objects and the beauty (either in Nature or in art) which is inherent in vitality. It is obvious that the spiral enters into certain very important architectural decorations, such, for instance, as the volute of an MATHEMATICAL DEFINITIONS 33 Ionic capital. In an ancient Greek building this volute is no more mathematically correct than the lines of the Parthenon are mathematically straight, but the Greek volute is beautiful because it exhibits just those differences from mathematical exactness which the shell, or any other natural growth, exhibit also. I can show this, I think, in a somewhat curious manner. The ordinary method of drawing a " correct " volute with the help of an inverted cone is, of course, well known, and results in a mathematically exact and Eesthetically vapid figure. But Mr. Banister F. Fletcher has shown that a shell can be used for the same purpose. Following his instructions (see Fig. 44), I took a sinistral wheUc, and wound a piece of tape, 12 inches long, round its spirals from its apex (A) to the top of the opening, Fig. 46. — Choristes elegans, showing Operculum. Fig. 47. — Operculum of Turbo cornutus (From the Pacific.) leaving a Httle of the tape over to hold the rest in position. A pencil was attached to the end of the tape touching the apex. Reversing the shell so that it stood perpendicularly upon its apex at the centre of the volute, and keeping it fixed on that point, I drew the pencil round and round the shell in the gradually increasing curves permitted me by the gradual unwinding of the string. The volute reproduced in Fig. 44 is the result. The shell used was exactly contained in a rectangular space 4xV inches long by 2I inches wide. It produced a spiral measuring lof inches across from the centre to M. Though both shell and volute^ are reduced to suit the size of these pages, the relative proportions remain the same. It will be noticed that the Fusus (Chryso- domus) antiquus employed is a specimen of a sinistral or left- hand shell, but that it has produced the right-hand spiral of the volute on the right side of the capital. The volute on the left C.L. D 34 THE CURVES OF LIFE side of the capital can be similarly drawn with the left-hand spiral produced by a common right-hand whelk. This may be one underlying reason for the fact that every right-hand plane spiral of an operculum belongs to a left-hand shell, and vice versd [See Figs. 45, 46, 47). The arrangement of the volutes on an Fig. 48. — AL,^sK.illN Bighorn. (Ovis canadensis dalli.) Ionic capital (\'iz., a right-hand spiral on its right side, and a left-hand spiral on its left side), is the same as that of the horns of the Merino ram and the Alaskan bighorn (Fig. 48), and would be described by Dr. Wherry as " homonymous." The method just described, though mechanically performed, actually reproduces those proportions of an Ionic volute which owe none of their charm to mathematics ; and whether the ancient (ireeks used a shell or not in making their designs, it is very significant that the beauty of their workmanship should exhibit so curious a harmony with the lines of an organic growth that are nearly, but not quite, the curves of a mathematical spiral. It is in this subtle difference that, I believe, their charm consists. But I must again return to our definitions. A conical spiral (more properly called a conical ^'°' He7ix°''''"^ ^'*'^'''^ """y ^'" formed, as I have said, by lifting up the centre of a watch spring and fastening its longer outside circle to the table. It may be described as the gradual winding of a spiral line round a cone from its apex (the centre of the flat spiral) to its base (the outside curve of the flat spiral). A cone is formed by the revolution of a right-angled triangle upon Its base as an axis ; and it will be found that no two points MATHEMATICAL DEFINITIONS 35 on the spiral line surrounding the cone are at the same distance from that axis (see Fig. 49). A conical helix can be visibly developed in the manner de- scribed in Fig. 50, which was drawn for me by Mr. Mark Barr. Describe a circle with centre at A, and radius AR 13! inches in length. Draw another radius AQ, and cut away the sector of the circle contained between it and AR. It will then be possible For a logarithmic spiral when r is the distance from centre, 6 is the angle turned through, a is a constant magnitude controlling dimensions of the spiral, r = Ji. Cut out the Sector contained by AQ and AR. Twist the paper into a cone with A as centre and AR = 13I inches. to fold the original paper circle up into a cone with its apex at A, and the two logarithmic spirals AB and AC (originally drawn on the flat piece of paper containing the circle) will be seen developed each into a conical helix. By twisting your cone up sharper and sharper, you will see each helix making more and more turns round the cone. The paper used should be the trans- parent linen preferred by architects. The most usual form of a conical helix is the common screw D 2 36 THE CURVES OF LIEE used by carpenters and drawn in Fig. 51. In Fig. 52 a screw is shown with a larger thread than usual, and arranged more like a true cylindrical helix, after the fashion of a staircase built Fig. 51. — CoMMOK Screw. Fig. 52. — Screw WITH Large Thread. Fig. 53. — Pleurotoma monterosatoi. (Bronn and Simroth.) with an inclined plane revolving round a central column, instead of steps fitted into that column one above the other. A cylindrical spiral is more properly called a cylindrical helix, ard is d( fined as the curve assumed by a right line drawn on Fig. 55. M Fig. 57. a plane when that plane is wrapped round a right cylinder. We can make one for ourselves as follows : — In Fig. 54 AM is a solid cylinder, with two points marked upon that part of it in front of the spectator. The rectangular figure MEAF is a piece of paper (Fig. 55). Join MA and join EF. X win be the meeting point of these two lines in the centre MATHEMATICAL DEFINITIONS 37 of the piece of paper. Fold the paper round the cyHnder in such a way that the points EM are in front of the spectator and so that the point A can be folded round to meet the point E at the top, and M will coincide with F at the bottom. The cylinder is now wrapped round by the paper (Fig 56) and shows the portions MC and DA (in Fig. 55) visible of the spiral Ime now formed by what was once the straight line MXA. This line MXA was drawn from the left lower corner to the right upper corner of the paper, so that a right-hand spiral has been formed ; the line from F to E would produce a left-hand spiral. The distance from M to A on the cylinder in Fig. 56 gives the " pitch " of the screw, or spiral, formed by the line MCXDA ; Fig. 58. — Spiral Vessels of Melon. (Pettigrew.) Fig. 59. — Right-hand Spiral of Tecoma (bignonia). Fig. 60. — Left-hand Spiral of Honey- suckle. but a cylindrical spiral may, of course, exhibit considerably more turns than this ; lor instance, the " pitch " of the cylin- drical spiral shown in Fig. 57 is the distance from K to L, from L to B, or from B to N. It is interesting to compare the shell of Fig. 53. As examples of natural spirals which may roughly be defined as cylindrical, I may take the spiral vessels of a melon (Fig. 58). In climbing plants, some grow in one direction and some in the other. Fig. 59 shows a right-hand Tecoma and Fig. 60 a left-hand honeysuckle. The human umbilical cord is a beautiful example (Fig. 10) of a left-hand spiral ; and the power of many bones in our body is owing to this shape (p. 9). No doubt all these examples suggest that there is something intimately concerned with strength and growth in the 38 THE CURVES OF LIFE spiral formation ; and it is this question which I propose to examine by considering various other instances to be seen m natural objects. It will be found useful if the preliminary pages here printed are used for reference by those readers who follow me further in our search for natural spirals. I must add here to our general considerations of spirals that it is possible to make a kind of spiral with a flat piece of paper which it would be difficult to class under any of the heads just mentioned. It is made in the following manner : — Take a flat piece of paper | inch broad and 12 inches long. Fasten one end of it upon the edge of the table with a nail in such a way that the whole length of the paper sticks out beyond the edge of the table. Place your left hand upon the nail to hold the paper steady, and with your right hand twist the other end of the flat strip of paper outwards and away from you. The method used would roughly be that employed in twisting a rope by hand. When you have twisted the paper as far as it will conveniently go, you will find that it exhibits a series of left-hand, ascending lines in a double spiral. This is the way in which the torques were made by ancient workmen out of flat ribbons of soft gold, and this is why nearly all such ancient torques exhibit a left-hand spiral, because they were made by right-handed men. Most ropes made by machinery are made as a right-handed man would twist them, and therefore exhibit a left-hand spiral. If you repeat the experiment with the strip of paper just described, only putting your right hand on the nail and twisting the paper away from you with your left hand, you will find that you have twisted it up into a right-hand spiral ; and this is why the ancient torques are so rarely found to exhibit a right-hand spiral. In the twisted piece of paper you have just used there are two edges, and therefore it is a double spiral which goes up to right and left respectively ; but the ancient workmen produced the very beauti- ful eft'ect of a fourfold spiral in precisely the same manner, only in this case they used not a flat ribbon of gold, but a ribbon so arranged that its section was exactly in the form of a cross. This gave four edges, and by the use of exactly the same process just described they produced either a right-hand or a left-hand spiral which was fourfold instead of being double (pp. 292-3.) This leads me to a question of nomenclature which is appro- priate to the opening pages of any discussion like the present. What has just been said concerning the manufacture of torques will fittingly introduce it ; for an ordinary rope in English ships exhibits that left-hand twist shown in the honeysuckle in Fig. 60, and explained in the description of the ordinary torque. The rope's twist is of this kind because it was twisted by a right- MATHEMATICAL DEFINITIONS 39 handed man. The rope-bridle carved on a prehistoric represen- tation of a horse some 20,000 years old shows a right-hand twist ; and this may be either because the drawing was made by a right- handed man or because the artist was copying a rope twisted by a left-handed man. I incline to the latter theory, because I have seen ropes made by Arabs in North Africa which showed the right-hand twist of the Tecoma in Fig. 59, and were no doubt made by a left-handed man. Now it is obvious that these two kinds of twists may each be differently described. The left-hand or sinistral may be called clockwise, as exhibiting the movements of a clock's hour-hand (for instance) from six o'clock to noon ; or it may be described as a movement from the south through Fig. 61. — The Young Fern Gradually Unrolling its Spiral. (Compare Fig. 37.) west and north to the east, if we take the cardinal points on a compass ; or it may be defined as " with the sun." In the same way, the right-hand or dextral spiral may be defined as " against the sun " or " contrary to the hands of a clock." But against one form of nomenclature, chiefl}. favoured, I understand, by botanists, I must raise a strong and immediate protest. This method proposes to call the left-hand twist on a rope " right- hand," because it results from the twist given by a right-handed man. What reason would be given for calling the honeysuckle in Fig. 60 " right-hand " ? Conchologists have certainly agreed to call left-hand shells dexiotropic, and right-hand shells leiotropic ; but they knew better than to alter the accepted nomenclature of an abstract -10 THE CURVES OF LIFE mathematical convention wlaicli has no concern either with processes of manufacture or naval customs. Numberless other considerations will occur to invalidate any connection between the origin of a spiral and its name. It is common knowledge, for instance, among ai't-critics, that in a genuine Leonardo drawing the strokes of the shading slant from left to right. It will be found on trial that such strokes are most easily made from right to left by a right-handed man. Leonardo was left- handed ; and in the spiral shells he drew for the bust of " Scipio " and the sketch for " Leda " both are the right-hand flat spirals he would naturally make (p. 64). Or, again, the famous parry of Kirchhoffer, Merignac, and other left-handed fencers is the contrc-quartL, in which the point of the sword describes the right- hand flat spiral shown in Fig. 29, whereas the easiest parry for a right-handed fencer is the left-hand spiral of contre-sixtc (away from the body, or clockwise) shown in Fig. 30. You will find by experiment that the easiest way to draw the volutes of an Ionic column (in the relative position shown in Figs. 29 and 30) is to take a pencil in each hand, with the left hand on the point M in Fig. 29 and the right hand on the point M in Fig. 30 ; each spiral can then be naturally drawn and both can be done simul- taneously. The left hand has drawn the right-hand spiral of Fig. 29, the right hand has drawn the left-hand spiral of Fig. 30. For much the same reasons most skaters find it easier to do the outside edge (a left-hand spiral) on the right foot, and when they skate on the left foot they prefer the right-hand spiral naturally made by the outside edge. In fact, to introduce a method of nomenclature based on manufacture is to make confusion thrice confounded. The way a spiral is made is, for these purposes, immaterial. The description of the mathematical figure is vital, and cannot nowadays be altered from the long-accepted conven- tions of the mathematician. I should prefer " following the sun " and " against the sun " ; but in these pages for the sake of brevity and clearness I always use the phrase " left hand " and " right hand " respectively, instead of " clockwise " and " anti- clockwise." NOTE TO CHAPTER II. Yachting Problem. — P. 26. A rudderless steamer is moving in an unknown direction straight ahead at ten miles an hour on a calm sea without tides. If a cruiser, moving twenty miles an hour cannot sight her when she has steamed from P to Q, she must inevitably find the lost steamer somewhere on the curve of the logarithmic spiral traced from Q through R to S in Fig. 3r. CHAPTER III Upright Spirals in Shells " The shells of oysters and other similar creatures whicli are born in the mud of the sea testify to us of the changes in the earth . . . for mighty rivers always flow turbid because of the earth stirred up in them through the friction of their waters upon their bed and against the banks ; and this process of destruction uncovers the tops of the ridges formed by the laj'ers of these shells which are embedded in the mud of that sea wherein they were born when the salt waters covered them . . . the shells remained walled up and dead beneath this mud, which then was raised to such a height that the bed of the sea emerged into the air, and so became hills or even loftv mountains ; and later on the rivers have worn away the sides of these mountains and laid bare the strata of the shells." — Leonardo da Vinci {Insl. de France). FORMATION OF SPIRALS IN SHELLS — TUBE COILED ROUND AXIS — LIFE HISTORY OF A SERIES IN ONE SHELL — ACCELERATION AND RETARDATION — NATURAL SELECTION — ADJUSTMENT TO ENVIRONMENT — SURVIVAL AND SPIRAL VARIATION — RIGHT- HAND AND LEFT-HAND SHELLS — AMMONITE AND NAUTILUS — EXTERNAL AND INTERNAL SPIRALS — SUPPORTING THE CENTRAL COLUMN — COMPARISON WITH INSECTS AND PLANTS — MULTIPLE SPIRALS. , I SHOULD exhaust both my reader's patience and the space available if I gave anything like a complete list of spirals in the animal kingdom alone. It will be necessary, therefore, to confine myself to a few typical examples and to those instances Fig. 62. — Awl-Shell (Tereera) Photographed by X Rays TO SHOW Internal Spiral through the Outer Wall. which may be easily found and intelligently examined by ordinary people in their everyday life. A " screwstone " is the name sometimes given to one of the joints of the " stem " of an encrinite or " stone lily," a palaeozoic crinoid plentifully found in marble, and belonging to a class of animals which are " stalked," or fixed like a plant for a part or all of their life. A " Portland screw " is a similar name bestowed on the fossil cast of the interior of Cerithimn poi'tlandicum. The 42 THE CURVES OF LIFE name of anger-shell has, for the same reasons, been given to a long-spired gastropod (Fig. 62) called Tcrehra {Bullia) scmi- plicaia, and more especially to T. maculata. It is in shells that may be found the most easily examined examples of beautiful spirality in all Nature, and the formation of spirals by shellfish seems still to be in need of a complete scientific explanation. But we may conceive the process as something of the following kind. When an elastic " bendable " substance is growing above an object and dropping at its free end, it would probably take the form of a plane spiral, under certain conditions. But if, during the growth of the mollusc it lops over at all to one side, it seems usual that it should lop over to the left. What the force is which determines this original direction in the growing shell I cannot say ; but, however slight and subtle this force may be, it is invariably " good evidence " in the case of \ 3- "'// Fig 63. — Truncatulixa TEXERA. ■' 75- Fig. 64. — KoTALiA calcar. x 50. (Brady's F'oraminifera. Challenger Reports.) such " artificial " spirals as the shavings at a carpenter's bench. As Dr. Wherry has pointed out, if these shavings are right-hand screws they are produced by a right-handed carpenter, because a right-handed man invariably drives his plane a little to the left. But I must not yet touch upon the extremely intricate problem of why a spiral is (or should be) either right hand or left hand. That must come later. I only mention the instance of the shavings in order to explain why the elastic substance growing above the young shellfish usually produces a right-hand spiral by lopping over to the left ; and it will be remembered that we have already noted that shells exhibiting a right-hand spiral are called " leiotropic " and those (far rarer) exhibiting a left-hand spiral are called " dexiotropic." We must now return to our theory of the origin of spiral growth in shells. As an organism of the kind described continues to grow, if the new piece were of accurately rectangular formation, thus : the result would conceivably be growth in a continued straight UPRIGHT SPIRALS IN SHELLS 43 line. But it never is ; for the dorsal surface of a shellfish is thm and ductile, while the ventral surface is harder and contains muscles which continually exercise a certain pull upon the tissues. So the new growth is usually of this form : ( / Since, therefore, the dorsal surface expands more easily than the ventral, while the creature goes on developing, the result is a continuation of the spiral form thus : t?^??flfe. Fig. 161. — LiLiuM longiflorum. front of the horizontally projected trumpet and probe the nectary at the base of the tube, this nectary being indicated as greenish grooves secreting honey at the base of each perianth-segment. The graceful recurvature is thus sufficient to present a white conspicuous star effect. C.L. 114 THE CURVES OF LIFE as seen in front view, and at tlie same time just uncover the essential organs. In more specialised lily flowers, such as Lilium pyrenaicum (Fig. 162), especially those visited by diurnal lepidoptera, the flowers hang vertically downwards, and the petals arch boldly, almost to a perfect circle (cf. Lilium tigrinum), thus bending up out of the way of the protruded stamens and style. In such reflexed petals the nectary grooves are much exaggerated, and are continued about half way up Lilium pyrenaicum. the segment. The reflexed surface is now conspicuous from a lateral position, while the nectary aperture is exposed just on the outer turn of the curve. The insect visitor, in probing these apertures, beats its wings against the protruded stamens and stigmatic surface, and so effects pollination. Note that the exaggeration of the curvature is correlated with increased specialisation of the mechanism, but the original phyllotaxis plan of the flower remains unchanged." CHAPTER VII Right-hand and Left-hand Spiral Growth-Effects in Plants " Leaves in their earliest growth turn themselves round towards the branch in such a way that the first leaf above grows over the sixth leaf below ; and the manner of their turning is that one turns towards its fellow on the right, the other to the left." — Leonardo da Vinci (Inst, de France). TWIST EFFECTS : (i.) SPIRAL LEAF ARRANGEMENTS ; (ii.) OVER- LAPPING EFFECTS ; (iii.) unequal GROWTH IN MAIN AXIS ; (iv.) SPIRAL MOVEMENT OF GROWING ENDS ; (v.) SPIRAL GROWTH OF TWINING PLANTS ; (vi.) SPIRAL EFFECTS AFTER DEATH — NOMENCLATURE OF SPIRALS — NUMERICAL PROPOR- TIONS OF RIGHT AND LEFT HAND. The effects of asymmetrical construction in plant shoots commonly end in the production of spiral effects, just as in the case of spiral shells and spiral horns. The effect maj^ be that of a twist, and either right hand or left hand in direction ; there are, indeed, only these two possibilities, but the cause is not necessarily the same in all cases. In fact, any asymmetrical growth-factor will induce a spiral appearance, if continued long enough, and the appearance of " twists " in a plant is always a subjective one ; the cause is always unequal growth of some sort ; but it is so usual to obtain a similar effect by twisting that we have no other word for a structure which grows in this manner. The familiar example of " Pharaoh's serpents " has much in common with the growth of a plant stem, the burning- point being representative of the apex of the shoot. The spiral effects commonly observed in plants may be distinguished under several headings, and it is well to separate them. Among the more usual may be reckoned the following phenomena, omitting many beautiful spiral manifestations in the growth of lower plants. I. The spiral leaf-arrangement at a plant apex has been already included as spiral phyllotaxis, and regarded as the expression of an inequality in the parastichy ratio of the construction system. Given such inequality, all the serial Hues traced subjectively through adjacent members are spirals. (We need not include the case of perfectly regular alternating whorls of members in which the diagonal lines of the pattern give spiral series equal in I 2 ii6 THE CURVES OF LIFE both directions, like the curves seen on an engine-turned watcli- case, since these diagonal lines are obviously complementary to a system of circles and vertical rows.) Examples of these spiral effects have been given in preceding chapters. II. Overlapping effects in the corolla of flower-buds (cf. Fuclisia) give frequently an effect distinguished as the contor- tion or convolution of the corolla, and the petals apparently expand with a twist, either right hand or left hand. III. Unequal growth in tlie main axis gives torsion or twisted effects, examples of which have been seen in Gasteria leaf-system. Such twists are common in climbing stems, also in flower stalks, and even in ovaries and fruits. IV. The spiral movement of the growing end of a shoot, or the circumnutation spiral, is seen most obviously in climbers ; this straightens out in the adult stem and is no longer seen, but is intimately associated with V. Tlie spiral growth of a twining plant ; this, as also that of a tendril, becomes fixed in the adult stage, and is then obviously right or left hand. VI. Spiral efjects may be produced after death, owing to peculiar histological construction of special cells. Such appearances are presented after desiccation in the case of hygrometric awns and portions of fruits (cf. stork's-bill and pea-pods), and the tissues when wetted again return to their original position. Such spiral phenomena are characteristic of the higher plants ; among lower types the entire organism may present spiral growth- form, as in the case of spiral bacteria, the spiral antherozoids of ferns (and the beautifully spiral ciliated coils of the antherozoids of Cycads), as also Algse in \'\-hich the thallus appears as a spiral ribbon (cf. Vidalia) and the similar spiral wing of the liverwort Riella. In Plankton there may be spiral chains of diatoms, while in Spirogyra the chloroplasts are spiral. In all cases the spiral appears as an asymmetrical growth-expression representing a stage intermediate between a straight line and a circle. In all these cases the direction of the spiral seen may be given in terms of right or left hand, according to some established convention. It does not matter much what the convention is, since there are only two possibilities, and so far clockwise, or winding with the clock sunwise or following the sun left hand, affords a good working generalisation, which is common to all the various departments of this inquiry, though I am aware that botanical writers in their technical descriptions reverse this nomenclature, and call sunwise or clockwise a " right hand " twist. To this, in these pages at any rate, I cannot agree, and I propose to go on as I began, the " clockimse " direction being RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 117 called left hand. With such a working generaUsation it may be interesting to see to what extent such right and left effects may be constant or variable ; and if the latter, do they follow in equal proportions, or does one direction predominate ? On general principles they should be : (i) constant ; or, since it might be purely a matter of chance which occurred, (2) half Fig. 103. Theoretical construction of a (3 + 5) system by uniform rate of growtli. Tlie asymmetrical addition of one new member at a time produces a subjective appear- ance of spirals. In this figure the addition of the second member (number 2, above) is shown on the right side of the first. A similar construction could be worked out if it had appeared on the left. (A. H. Church.) and half, or 50 per cent, of each ; otherwise, if there is a tendency for one form rather than the other, there would be (3) a bias. These conditions may be borne in mind in examining the spirals of plant shoots ; usually it is assumed that the chances are equal in either direction, but several interesting cases arise. For example, we may take a normal Fibonacci construction, in which new members follow in sequence at an angle of approxi- mately 137F from each other. The figure (163) iUustrates a ii8 THE CURVES OF LIFE scheme in which a new member is added in every successive stage, the whole system continuing to grow at an equal rate throughout. The direction in which the new members are added is shown by the arrow in Nos. 2 and 3, and this is ccunter-clcckwi-e or right hand. In No. 7 the series thus becomes a spiral sequence, and a single curve, the " genetic spiral," is drawn through all the members. This is, however, quite a subjective appearance ; it is not noticed in No. 8, and, as a matter of fact, other sets of spirals strike the eye even more clearly in No. 9. Still, if we take one spiral only as the test, the genetic spiral of No. 7 is certainly the one to consider ; in this case it is right hand. But if in No. 2 the second primordium had fallen on the opposite side, the whole system would have had the converse left-hand for- mation, \\c may thus talk about right and left-hand constructions according as the members, when thus seen in a ground plan, are arranged in order of development, clockwise or counter- clockwise. This is useful in dealing with flowers, a vast pro- portion of which retain a Fibonacci construction in their qitin- cuncial calyx. It is generally assumed that on a given plant the numbers of the two constructions will be equal, if sufficient specimens are at hand to allow for equal chances. But it is interesting to note how the rule may be modified under special conditions of symmetry in the inflorescence system. Thus in a symmetrical Dichasium, an inflorescence in which two lateral flowers are borne immediately below a terminal one, the two lateral flowers are always expected to be twin images, i.e., one right and one left hand, if they retain their quincuncial calyx ; while rules are fairly constant in different families for the one which remains the same as the end flower and the one which changes. The inflorescence of the spring-flowering Hellcborus iatidits is an admirable type for checking these relations. On the other hand, in the case of a Scorpioid cyme, a peculiar two- lanked inflorescence of two rows of flowers zigzagging down the apparent main axis, all the flowers on one side are right hand, and all those on the other left hand, symmetry being arranged for along an imaginary hue between the two rows. The inflo- rescence of a stork's-bill (Erodium), or that of Geraiuinn phceiim, affords a simple illustration. Although it may be assumed that equality in these respects would be found to obtain if sufficient numbers were taken, rather curious results have been obtained in deahng with com- paratively small numbers of specimens. Thus Bonnet long ago counted seventy-three chicory plants, and found forty-three right, or 58-c,o per cent., and thirty left. But numbers below RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 119 100 may be useless. Further observations on this subject, which is here considered from the standpoint of the direction of the primary spiral of the main axis of the plant, may be readily carried out by anyone interested in the matter ; it is only neces- sary to raise a batch of seedlings, and place them in two sets as soon as the direction of the first leaves becomes apparent, taking, preferably, some common plant in which Fibonacci phyllotaxis obtains, and the seedhng tends to distribute its first leaves in a flat rosette. Fig. 164. — PiNus pinea (System 5 + 8). Tran.s verse section of the apex of young seedling, 6 inches high. (A. H. Church.)" Genetic spiral, counter-clockwise = R. On the other hand, the so-called genetic spiral may be a myth ; it is only traced with difficulty in such a diagram as Fig. 145, Chap. VI., and on the adult shoot it owes its appearance to the fact that secondary elongation of the shoots has so far pulled the system apart that the series is at last only expressed as a single curve. In the case of close construction in which no secondary extension takes place, and the members retain the close-set pattern in which they were formed (cf. pine-cones, Fig. 141, Chap, v., and Fig. 156, Chap. VI.), other curved series (para- stichies) are much more readily observed (see Fig. 164), and 120 THE CURVES OF LIFE these constitute oblique series of members, often conspicuous even when a certain amount of extension obtains. The i-elation of these right and left cur^'es to tire genetic spiral is not the same in all patterns, but they may be readily checked by reference to geometrical constructions of the same numerical value, and for practical purposes these curves may be quite as readily utilised for comparing the numbers of the twin constructions. Thus, on taking cones of Pinus austriaca (Fig. 141), the curves on the circular base are eight and thirteen, of which the set of the " thirteen " curves is strikingly conspicuous ; a set of 100 cones from the same tree (counted at Oxford, 1900) gave fifty-nine of one type and forty-one of the other. A similar set of 100 cones from a tree of Pinus pumilio gave fifty-three of one and forty-seven of the other. Another set from one tree of Pinus laricio gave sixty-eight of one and thirty-two of the other. In these cases, therefore, either there was always a bias in favour of one pattern, or 100 cones is too small a num- ber to deal with. To test Fig. 165.— Pi.xus tinea. fhis 1,000 cones of the same tree of Pinus austriaca were counted during the next season. Successive batches of loo each gave : — 54:46 56 : 44 51 :49 49:51 54 : 46 57 :43 54:46 56 : 44 51 :49 54 : 46 Average 53-6 : 46 4. The same tree was examined again during the third year, with a clo.sely identical result ; while the same tree of Pinus laricio RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 121 was equally constant at a ratio of about 71 : 29. It would appear possible to say that it was in these cases a matter of mere chance ; yet the reason for the bias remains a puzzle. It is, however, quite possible that the dominant pattern was that set by the apex of the tree as a seedling, and the bias of pine- cones merely expresses the fact that homodromy is more usual than heterodromy. But these problems still require to be investigated. I. The fact that in many of these close-set spiral patterns, one set of curves is more prominent than the other (Fig. 141] P. austriaca ; Fig. 164, P. finea ; Fig. 156, etc.) is due to the progressive flattening of the leaf-member in a horizontal plane, as it becomes more leaf-Hke. In such cases the members of the lower number of curves become more conspicuous to the eye {Ayaiicaria (8 : 13), in Fig. 146) ; if, on the other hand, the members Fig. 166. — Wax Palm and Date Palm. become radially deeper, the higher number of curves is more prominent. (Sunflower (34 : 55), in Fig. 144.) In special cases, on old stems, the relics of the phyllotaxis spirals stand out as a very marked system which expresses the uniformity of the extension of the adult plant. (See the Wax Palm in Fig. 166.) II. The Fuchsia corolla (Fig. 167) affords a good example of what is technically termed contortion or convohition, each petal being rolled over an adjacent one, and under the other. In the case of the Fuchsia this is absolutely constant (except in occa- sional malformations) and is always in the same sense. Botanically, this is known as " right convolute " (Eichler, 1878), because the right-hand edge seen from the outside is external. This is not a very satisfactory reason, but is easy to remember, and some simple convention is necessary. This form of symme- trical prefloration is met with in other families ; cf. Malva (holly- hock), Vinca (periwinkle). Erica (heath), as the highest expression 12: THE CURVES OF LIFE of sj-mmetrical corolla-arrangement. It has no apparent use to the plant, since no insect ever notices or cares if the petals beautifully o^'erlap or not. Its cause is to be traced in the asymmetry of each individual petal-primordium, from its first development (a slight anisophylly) , so that the young members slip in the bud quite easily, and take up these positions, ^^'hy the Fuchsia should be right convolute rather than left convolute, or why half the flowers should not be one and half the other, remains a mystery. In the case of Malvaccce and Hypericacece some are one and some the other. In Hclianihemtim (rock rose) the two cases regularly alternate in successive flowers of Fig. 167. — Fuchsia. the same cyme ; also in the inflorescence of the cotton (Gossypium) Vinca is constant for one direction (left convolute). The oleander {Nerium) is equally constant as a generic tj^pe in the opposite sense (right convolute). III. Spiral, so-called torsion effects are particularly common in plants, and may be quite useless and accidental so far as is known, or they may subserve an important function. In any case it would appear that they must have originated as accidental growth irregularities, wii(ffl/;'o«s, in fact, and may remain as factors in the plant-mechanism, because being quite useless, natural selection has no effect on them ; or the converse has happened : having proved of use, they have been gradually perfected into a new and striking specialisation. Slight useless twisting effects RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 123 are very general, and may escape observation ; a good example is seen in the twist on the stalk of a ]'i)ica flower ; in this case also the direction appears to be constantly a left-hand twist ; and it is clearly dissociated from the prefloration twist of the petals. A singularly beautiful example of exactness in such a twist is presented in the phenomena of " resupination," seen in the case of the flowers of Lobelia and Orchis. In the former the flowerstalk, and in the latter the green inferior ovary, initiates \ Fig. 168. — Pandanus millore from the Nicobar Islands. a twist exactly restricted to 180°, so that the floral mechanism is turned upside down to face the visiting insect. In such cases, the torsion effect has been utilised and rendered very precise for an intelhgible purpose. Similar twists are again utilised as compensation effects in phyllotaxis systems ; the case of Gasteria has been already instanced as an example in which the maximum superposition of a distichous leaf-arrangement has been admirably counterbalanced by a slight growth-twist of the entire axis, just enough to uncover the leaves from their adjacent members (Fig. 140). The same type of growth is respon- sible for the wonderful three-rayed screw of Pandanus (Figs, 124 THE CURVES OF LIFE i68 and 169), the screw pine, also seen to a lesser extent in the common umbrella sedge (Cv penis altcrnifolius). In these plants the phyllotaxis is expressed by the ratio i : 2, and this would result in the adult plant in three main series of leaves, which should if they attained equal depth, and were exactly equally spaced, become three vertical rows of exactly superposed members. It is true that any deviation from these last conditions would result in the leaves forming three slightly spiral series ; but the Fig. lOg. — Paxdanus utilis. exactitude with which the entire system is built in the case of a fine specimen probably illustrates a perfectly controlled system of " twisted " growth as well. How considerable the growth- wrench may be is illustrated by a plant of Cypenis alternifolius, in which the axillary inflorescence shoots are pushing in graded lengths according to their positions behind the apex (Fig. 170). Quite as elegant examples of such secondary twisting effecting " compensation " may be observed in the case of decussate leaf-arrangements. One of the neatest is the case of the foliage shoots of the Rose of Sharon {Hypericum calycinum). 'l"he RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 125 foliage-leaves of the short shoots of this plant when growing in the open apparently He in two rows, all with their upper side to the light, and yet they are made at the apex in four vertical rows of a decussate system. The final effect is attained by an accurate twist of 90° in a different sense in each alternating Fig. 170. — Cyperus alternifolius. internode, i.e., one internode twists right and the next left, and so on. A similar phenomenon may be traced in the blue gum [Eiicalyptus), particularly in the case of lateral shoots with the blue primary leaves. Later in the life of this plant a new compen- sation has been effected by the invention of pendulous leaves of a new form ; but the apical construction may retain the ancestral decussate pattern. The case of Gasteria and Pandanns may be termed a " winding-up " effect ; that of Hypericum calycinum an " alternating " mechanism ; an increased twist may even produce what may be termed an " unwind- ing " effect. For example, if in a decussate system, a twist of 90° was put in at every internode in the same sense, the leaves would all come to lie above each other in two ranks. Hypericum might have done this, if it had not so ingeniously solved the problem with far less display of twisting power. But such effects have been noticed in plants, more particularly in the case of some freak twisted teazles [Dipsacus fuUonmn) , described by De Vries. An ordinary Fig, 171. — Seed-pod of Helicteres ixor.\. 126 THE CURVES OF LIFE teazle has its leaves in opposite pairs, but not quite decussate (reallj/ a 2 : 4 system), but if it were twisted far enough all the leaves might be brought into two crested series. This is more or less approximated in these monstrous forms. A similar good example of " unwinding " is seen in the flower spike of the common orchid, Spiraiithes auiiiinnalis or lady's-tresses ; here the flowers are arranged in the bud in ordinary close spiral series ; but as the inflorescence axis elongates, and the flowers resupine, an exten- sive twisting tends to unroll the spiral system until the genetic spiral is left almost, but not quite straight. The object of this curvature is obviously to obtain the benefit of a unilateral spike of flowers, as in the case of the foxglove. The fox- glove similarly constructed to begin with, swings each flowerstalk to the front inde- pendently ; the mechanism adopted by Spiranthcs is even more ingenious ; but it is clear that it may have originated in a perfectly accidental tendency to unequal growth in the main axis. So far it is only important to note that in all these cases, so far as is known, the direction of the twist may be either right or left so long as only one twist is concerned. Thus, in whichever direction the genetic spiral of Spiranthcs may run, a twist in either sense will tend to straighten it out, while the twist of the resupining flowers may also be in either sense in the same in- florescence. Still, quite simple observa- tions on these examples giving statistical information are requisite before it is safe to speak too dogmatically on the point. IV. and V. — With reference to the direction of the spiral of circumnutation, and the correlated direction of twining in the case of climbing plants, much interesting information is available, the general rule being that the direction may be variable in an incipient climber, but becomes very definitely constant, one way or the other, as the climbing habit becomes definitely fixed in the cecology of the plant. Out of a collection of li\'ing specimens ot twenty-three climbing plants most kindly sent to me at various times for examination from Kew and elsewhere, only six showed the left- hand formation, " following the sun " or " clockwise." They were : — Fig. 172. — Lady's Tresses. Spiramhes auiumnalis. RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 127 Polygonum haldschuanicmn (Bokhara). Kadsura chinensis (China). Humulus luptdus (Enghsh hop). Honeysuckle. Muhlenbeckia cliilensis (Chih). Lapageria rosea (Chih). In Charles Darwin's " Movements and Habits of Climbing Plants " (p. 24, ed. 1905, John Murray) a table is given of several chmbing plants, showing the direction of their growth. In all, forty-two are described. Out of these only eleven " follow the sun " and show a left-hand formation, " clockwise." They are : — • Tamus communis (Dioscoreacese). Spliarostemma marmoratum (Shizandracese). Polygonum dumetorum. Plumbago rosea. Clerodendron thomsoncB (Verbenaceffi). Adhadota cydoncefolia (Acanthaceas). Loasa atirantiaca (one plant). Scyphanthus elega^is (Loasacete). Siphomeris or Lecontea (Cinchonaceje). Manettia bicolor (Cinchonaceje). Lo)iicera hrachvpoda (Caprifoliacese). In the figures given above I have omitted two plants from Darwin's list which happened to occur in those I had previously examined. This omission does not affect the result that seven- teen out of a total of sixty-five — or about a quarter -show the left-handed formation. In the case of one plant {Hibbertia den fata), Darwin observed the movement reversed frequently from one direction to another, making a whole, or half, or quarter circle in one way and then turning in the opposite way. He decided that the more potent or persistent revolution was against the sun (or right-hand) , and observed that the plant was adapted both to ascend by twining and to ramble laterally through the thick Australian scrub. He noted a similar reversal of movement in Ipomcea jucmida, but only for a short space, and these instances of adaptation are of interest because they are rarer in twining plants than in the more highly organised tendril bearers. It is rare to find either plants of the same order or two species of the same genus twining in opposite directions ; but such a case as one species of Mikania scandens moving against the sun and another (in south Brazil) following the sun is a perfectly intelligible occurrence, for different individuals of the same species (for instance, Solanum dtdcamara) revolve and twine in two directions, and Loasa aurantiaca offers an even more curious example, Darwin raised seventeen plants of this kind, of which eight 128 THE CURVES OF LIFE revolved against the sun, five followed the sun, and four reversed their course from one direction to the other, " the petioles of the opposite leaves affording a point d'appui for the reversal of the spire. One of these four plants made seven spiral turns from right to left and five turns from left to right." Scyphanthus cicgans beha^'ed in the same strange manner, taking two or three turns in one waj' and then one or two in the other after a short intervening space of straight growth, the reversal of the curvature occurring at any point in the stem, even in the middle of an inter- node. Out of nine plants of the hybrid Loasa herbertii, which he also cultivated, six reversed their spire in ascending a support. It is noticeable that of the four plants which revolved most quickly, each taking under two hours for a single revolution, the fastest of all was Scyphanthus elegans, which made its left- hand circle in se\-enty-seven minutes ; and even this pace is beaten bj^ the tendril-bearing Passiflora gyacilis, which revolved in the same left-hand direction, following the sun, and was ob- served to make three revolutions at an average rate of sixty- four minutes each, and in hot weather of even fifty-eight minutes. But any arguments tending to suggest that movements following the sun imply greater pace will be somewhat weakened by the fact that Adhadota cydonct/oUa, which is an efficient twiner, took from twenty-six to as long as forty-eight hours to complete a circle in the case of two different shoots ; and this plant also grows left-hand, following the sun. The rate of movement, in fact, does not seem to be related to the direction of the growth. And I can only conclude, from observations made up to the present, that though a larger proportion of right-hand than of left-hand spirals has been hitherto noticeable in twining plants, it is possible that if sufficient specimens were examined there would be as many A'isible of one kind as of the other. The reason for the diversity is not yet apparent. I postpone to the next chapter the consideration of the sixth division mentioned above, namely, spiral effects produced after death. NOTES TO CHAPTER VII. Nomenclature, I^ight or Left. — On this subject Shrapnel sent me the following letter ; — " In the Times for No\-ember i8th, 1912, an interesting article appeared, which you may be able to reproduce below. I should Hke to say a word about it after having read the articles on the subject of spirals, and may I venture to express the hope that their writer will have done something towards making scientific nomenclature on this matter somewhat more clear and homogeneous than it is at present. It will be convenient to take the homely cork- screw which the writer in the Times mentions as the type for my RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 129 remavks, and I may say that both conchologists and those biologists who describe the spirals of horns would unite in calling this spiral a light-hand spiral. The writer in the Times seems to be misled with regard to conchologists. They certainly call a shell with a right-hand spiral ' leiotropic,' but this name is not given to the shell because the spiral is turned to the left. It is given to the shell because the concho- logist has considered it as a staircase up which some small insect may be supposed to be mounting from the orifice at the bottom to the tiny apex at the top, and any insect which makes this journey will invariably be turning to the left on the way up this right-hand spiral. For exactly the same reason, conchologists call a shell with a left-hand spiral (the rare form) ' dexiotropic,' and this word again does not refer to the shell, but to the fact that the insect aforesaid must always be turning to the right in going up a left-hand spiral. I need hardly remind you that it makes no difference whatever either to the formation Fig. 173. — Spirally-folded Petals OF Ranunculus. of the corkscrew or to our definition of its spiral whether the corkscrew is standing on its point or whether it is standing upside down upon its handle There may be other sources of error, but the botanists are responsible for the worst error of all. It will hardly be beheved that botanists would describe an ordinary corkscrew as a left-hand spiral, apparently for the reason that if a right-hand man is twisting the strands of a rope together with a right-hand twist he invariably pro- duces what the rest of the world would call a left-harid spiral and for this reason apparently botanists insist on calhng left hand what everybody else calls ' right hand.' This leads to an enormous amount of confusion, because the left-hand spiral m nature is really as rare, if not rarer than the left-handed man m human experience, and unless we are all to agree to call the same things by the same names we shall never get on at aU. It really does not matter what name is given to these various forms of spirals, but it seems obvious that the right-hand spiral for a corkscrew is the one which should persist m every branch of science, and I trust that there will be no further confusion such as seems suggested by the writer m the Times, whose article is as follows .- K C.L. I',0 THE CURVES OF LIFE " 'A Corkscrew Snail. " ' Anotlwr very odd little exhibit has been placed in the Insect House. The shell of the common garden snail (Helix aspersa) is spirally arranged, and ii'hen a section is cut through it the appearance presented is that of a rapidly narroicing spiral chamber twisting round a central axis. Mr. Fig. 174. — A Giant Vine in Mad,\gascar. Y. H. Mills has sent a rare monstrosity, which he obtained recently'm Pembrokeshire. The spiral chamber, instead of being compact, is pulled out into the form and shape of a corkscrew. The twist is of the same kind as that in a common corkscrew, and raises a point of nomenclature which is debated indefinitely by those who have to do with horns and shells and other spiral forms. Is such a twist to be called right handed or left handed ? RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 131 Opinions and practice differ, and it is clear that, as the line curves round the axis, the person following rmist move now to the right and now to the left, while, if it he sought to fix the designation according to whether the right or left hand is toifards the central axis, as in a spiral staircase, one must also decide whether this is to he taken in ascending or in descending. The ohvious, and probahly historically, correct distinction is that a right- handed spiral IS the tieist seen on a screw which a normal right-handed person finds it easier to use with his right hand, and a left-handed spiral that which he would naturally insert with his left hand. In this sense, the corkscrew snail at the Gardens is plainly of the right-handed type, although perhaps most conchologists would call it left handed.' " I do not think ' most conchologists ' would agree with tnis." " The spirally-twisted seed pods of Helicteres ixora have been put to strange use by certain races who assumed, by the ' doctrine of signa- tures ' that their peculiar shape (Fig. 171) would make them an admirable medicine for ' twisted bowels ' or colic. It was similarly believed that the plant called ' Jew's ear ' was a good remedy for ear- ache." Fig. 173 is a beautiful example of the spirally-folded leaves of the ranunculus. Fig. 174. — " The accompanying photograph of a giant vine m Madagascar," wrote D., " will perhaps add another to the many interesting spirals in Nature that you have published. It exhibits alternations of right and left-hand spirals in a way that, so far as I am aware, is unusual." There is little doubt that the plant is the sea bean {Entada scandens), a common giant woody climber in the tropics, sometimes known to develop spirally-twisted stems. There are examples in the museum at Kew. It has bipinnate leaves, small 3'ellow flowers, and enormous bean-like pods, a yard long and 4 inches wide, containing large, flat, dark brown seeds, 2 inches wide. These seeds are sometimes carried long distances by ocean currents ; thej' have been picked up on our coasts. K 2 CHAPTER VIII Eight-hand and Left-hand Spiral Growth Effects IN Plants [continued) Dead Tissues and Spinning Seeds. " The spirally Upward of rapture, the Downward of pain." — G. Meredith. SPIRAL TWISTING OF DEAD TISSUES — COILING WHEN DRYING : STRAIGHTENING WHEN WET PREDOMINANCE OF RIGHT- HAND FIBRES — SEEDS SPINNING IN FLIGHT — THE MECHANISM OF WINGED FRUITS. In my last chapter I mentioned that certain beautiful spiral formations may be produced after death owing to a peculiar histological construction of special cells, and I promised such instances as are observable in hygrometric awns and portions of fruits. To these, therefore, we will now return, for it will be found that they deserve separate treatment and illustration. Extremely elegant examples of spiral twisting are afforded by the wholly dead tissues of parts of certain plants which are utilised in the mechanism of fruit and seed dispersal. In such case the tendency to the assumption of spiral form is always the expression of a fundamental irregularity in the detailed histological construction of cell-walls which have been thickened and lignified. In aU thickened cell-walls the thickening layers are built up in strands which cross each other obliquely, and it thus follows that in all greatly elongated cell-derivatives these layers are spirally disposed ; hence in spiral vessels, as well as in pitted vessels and sclerenchymatous fibres, the walls of the cells present indications, often very marked, of spiral construc- tion. Thus it may be said that all elongated, thick-walled cells exhibit spiral markings, or spirally arranged pits. Such thick sclerosed fibrous cells constitute the material used in the formation of the hard parts of many fruits which present move- ments of dehiscence, and from the fundamental spiral nature of these units, spiral appearances may result when the tissues are entirely dead and dried up. The essential point of interest centres in the fact that mere accidental results, consequent on such fundamental histological details of construction, may become ultimately advantageous in the cecology of the plant, and may then be increased by the action of natural selection, until RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 133 extremely neat and even complex mechanisms may result. As examples of such phenomena may be instanced the twisting of the valves of pea-pods, the spirally twisted awns on the fruits of some grasses (oats and feather grass, Stipa) ; while the neatest example of extreme efficiency in this respect is presented by the contractile strips on the fruits of stork's-bill. (See Plate 1., Figs. 15, 19). Pea-pods, and the pods of many vetches which show still more marked spiral twisting, are lined by a sheet of woody fibres which phylogenetically are identical with the horny sheets of tissue hning the cavities of the core of an apple. The fibres are arranged obhquely across the wall of the pod, and the inner- most layers contract the most on desiccation, with the result that on complete desiccation the valves spring apart, and coil up in opposite directions, ejecting the seeds with considerable force. The more specialised the mechanism, the greater the number of coils produced ; less speciahsed pods only give half a turn or so of a spiral, while the best pods may give half a dozen coils. In this way a mechanism which may be said to have originated as a structural accident (since the oblique fibres are inherited from a long ancestry, and differentiation in contractile quality is secondary), becomes, in the course of time, a charac- teristic dijpersal-mechanism for a wide range of plants. For our present purposes it is important to note that since the more contractile walls are on the inner surfaces of the two valves of the pod, the valves coil in opposite senses, one right and the other left, with the outer wall of the fruit on the outside of the coil, so that the seeds are swept off, and the whole construction is symmetrical (ct. Plate II., Fig. 13). In other cases the direction of the spiral may be more definitely accidental, since associated with the structure of the wall of the fibrous cells themselves. Thus the single awn of Stipa, the feather grass, makes a right-hand twist (see Plate I., Fig. 16). In the case of the oat, in which two awns are characteristically present belonging to the two fruits of a single spikelet which is the por- tion shed from the plant, the direction of twisting is similarly constant and right hand in both flowers (Plate I., Fig. 13). Possibly the most remarkable spiral construction is that of the fruit of the stork's-bill {Erodium, also Pelargonium), since the awn-like strip which coils, has no morphological identity, but is merely a strip of tissue cut out from the characteristic " beak " which gives to these plants the old names of crane's-bills (Geranium), heron's-bills {Erodium), and stork's-bills {Pelar- gonium). The ancestral fruits of these plants were apparently covered with short, stiff bristles, which, as they all pointed the Plate I. — Right and Left Spirals in Plants. RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 135 DESCRIPTION OF PLATE I. 1. Cone-scale of Kauri Pine {Dammara australis), witli one median winged seed. 2. Cone-scale of Pinus (P. insignis), with two winged seeds. 3. Cone-scale of Silver Fir {Abies pedinata) with winged seeds. 4. Tailed fruit of Clematis (C. lanuginosa), \\'i\h. spiral twist. 5. Symmetrical pair of fruits of Hornbeam (Cfl:r/)!.'«Ms), with three-lobed involucre. 6. Tailed achene of Geum triflora, with slight spiral twist. 7. Winged mericarp of Ailanthus glandulosa, with right-hand twist. 8. Pair of fruits from a scale of the Hop-cone [Humulus lupulus). 9. Winged fruit of Casuarina. 10. Spiral pod of Screwbean {Prosopis sirombulifera), right-hand spiral. 11. Winged mericarps of Ma' le {Acer campestre). 12. Winged mericarps of S\ camore. 13. Fruiting spikelet of Avena sterilis, with hygro- metric awns. 14. Winged fruit of Ash {Fr ax inus), witli slight spiral twist. 15. Mericarp of Stork's bill, the largest form {Erodimn botrys). 16. Fruit of Feather-grass {Stipa pennata), with hygrometric and feathered awn. 17. Fruit of Medicago arborea. 18. Fruit of Medicago scutellata. 19. Mericarp of Erodiwu laciniata. ]S[_B — All tlie above were originally drawn to uniform scale of twice the size of nature. 136 THE CURVES OF LIFE same way, would induce a " creeping " movement, as they slipped one way, under the action of slight external mechanical agencies such as wind, and never went back. The addition of a long strip from a sterile region of the ovaiy-wall would increase the ability to creep, just as in the famihar example of the awn of the barley ; and this would appear to have been the original use of the " beak-strip," as we may call it. But owing to its construc- tion with strands of fibrous cells, the strips under desiccation would tend to coil up in the same sense as would the individual spirally constructed fibres, if these were left to themselves. At first the coihng was but shght, a mere turn or so, as persists to the present day in many geraniums, a good example being seen in the cultivated dusky geranium (G. phaum). The coiled beak-strip, twisting up under desicca- tion, and straightening out again when wetted (in about five minutes), then becomes a hygrometric driving organ which pushes the creeping fruit along with every change of condition, and a new factor has been introduced into the working capacity of the plant. Clearly the longer the strip, the stouter its hygrometric tissues, and the greater the number of coils, the more efficient the driving power behind the fruit ; and while some species of Erodiimi have strips 3 inches long or more, in others the coils when com- plete may be seventeen to eighteen in number (see Plate I., Figs. 15, 19). Two special points call for notice. All the strips coil in the same sense, since the histological differentiation is identical in ah the locuh of the same fruit ; and not only so but the tissue- units are made the same way in all erodiums, and the resultant spiral is coiL'^tanfly right hand. Further, the right-hand direction is not so simply attained as would appear at first sight, since the direction assumed on coihng is the accidental product of the fact, that in different layers of the fibres laid down in the strip itself, some are left and others right in construction, and the resultant right spiral is merely due to the fact that in this case right-hand fibres preponderate over left hand (Steinbrinck, 1805). The fruit of Erodium is thus not only a marvellous example of the fact that a succession of lucky shots (mutations), many of which may have been purely accidental and meaning- less, may, in the course of time, produce a beautifully adjusted F1G.175. — " Parachute " Fruit OF THE Cape Silver Tree (Leucadendron argenteum) (Xatiiral size.) RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 137 mechanism of spiral nature ; but in that it has been derived from a simple " beak-strip " of the Geranium phmim type, it IS equally interesting to note, how by completely ehmmating the spiral tendency, the beak strip might be made to curve to an exact circular coil. When this happened an entirely different type of dispersal mechanism became possible, and the final elaboration of the " sling " mechanism of Geraniiimixmts should be further analysed from this standpoint. From this significance of the utihsation of a spiral hygro- metric driving-mechanism, behind a creeping and boring point, we may, perhaps, pass on to include the production in dead tissues of an arrangement which will give a spiral movement to fruits and seeds as they fall through the air, or are carried laterally by the agency of the wind. So striking and apparently purposeful are these spinning movements of dry seeds and fruits that they become extremely useful, as affording examples of the wondei-ful results that may follow from a comparatively simple variation. The development of anj? seed or fruit, or appendage -Seeds from Cone of Pinus austri.\ca. (Natural size.) to such fruit as a laminar extension of the nature of a plane, will give a capacity for aerial flotation which, in that it in the long run delays the rate of faUing, must add to the efficiency of lateral distribution according to the strength of the wind. In such cases the problem of continued flotation is largely one of balancing, more particularly of placing the centre of gravity exactly in the centre of the plane (or below it). In any case of asymmetrical construction, the movement under flotation will become spiral in nature, until the case of a seed with a broad wing attached at one end gives a spinning mechanism of wonderful efficiency. It is only necessary to refer to the common examples of the seeds of pines, with membranous slip wing, of a perfectly different nature from that of the wing of the sycamore fruit, which is again quite distinct in construction and homology from that of the lime tree. The spirals of the flight of fruits and seeds, however, have a suggestive value from the standpoint of the spirals formed in the flight of birds. Thus in the case of a pine- cone two seeds are borne on the upper surface of each cone-scale, and these are each associated with a shp of tissue which is readily detached in the dry cone from the scale, and ultimately from the i^,S THE CURVES OF LIFE seed. In large eones this wing may be an inch in length [P. uisigiiis), and by itself has no special motion ; but attached to the seed it gi\-es the falling body a spin, the beauty of which is only understotid on throwing a seed into the air and watching it fall. The two seeds on one scale have an opposite asymme- trical shape, and are so far twins. It is easy to see also, on taking the two seeds from one scale of a dry cone, that they fall in opposite directions ; one spins right and the other left. It is difficult to say which ma}? be the right and which the left side of a scale, but on looking down on a scale, as drawn upright on Plate I., Figs. 2, 3, the left-hand seed will spin downwards, falling in a clockwise direction. The fact that these two seeds of Pill us spin in opposite directions is, however, the expression of the fact that the slip wing is cut off from a curved cone-scale surface, which curves as it dries ; in the more usual case of winged fruits, the wing is an outgrowth or extension of the ovary- wall, which is radially symmetrical in all cases, and the winged mericarps being of identical structure, all spin in the same sense. Thus the two mericarps (samara;) of the sycamore both spin either way, both are exactly alike, the number two does not, in this case, indicate twin construction ; the ancestral number of carpels for the sycamore being evidently five, and three-winged fruits are still quite common (see Plate I., Fig. 12). The study of such spinning fruits is so fascinating that we may extend our account to the consideration of a few cases of special interest. Wing extensions subserving dispersal by the agency of atmo- spheric currents are extremely frequent in the case of fruits and seeds of genera belonging to most diverse families of flowering plants. The mechanism thus produced may be classed as that of (i) the dart, either simple or barbed, (2) the glider, (3) the flutterer, (4) the spinner, and (5) the parachute. Parachutes and spinners fall vertically when left to them- selves, their rate of fall being merely delayed by the wing exten- sions ; in such case lateral dispersal will be effected solely by the lateral velocity of the wind. On the other hand, darts and gliders move laterally at a rate greater than that of the wind, and may be effective in almost still air, while spinners are the more useful for purposes of dispersal the greater the rate of the wind. For present purposes the parachute type is practically eliminated ; but it is clear that dart and glider types, although quite indepen- dent of spiral motion, may take on a spiral path if there is any marked tendency to asymmetrical construction. Thus the fruit of the common ash is a good example of a simple dart RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 139 (Plate I., Fig. 14). The long fruits simply shoot forwards and fall with the pointed seed-end downwards ; yet any twist on the plane-extension will tend to cause a rotation in the opposite sense, and ash fruits on some trees have been observed to present a slight left-hand twist, which will cause them to shoot in a right- hand spiral. With this may be compared the samaras of A ilanthus glanditlosa, five of which are produced from each flower, each with a seed in the middle of the lamina, and a constant right-hand twist at the apex. Such friiits thus grade from mere flutterers into spiral spinners (Plate I., Fig. 7). Glider types are extremely frequent, since the uniform exten- sion of an ovary wall, or the seed coat- — fairly equally in all direc- tions to constitute a flat lamina, more or less circular, with the seed in the centre — would represent the simplest method of Fig. 177. — " Aeroplane " Seed of Bignonia. (Natural size.) construction. The large disc-like fruits of Pierocarpus {Legu- minoscB) come under this heading, as also the samaras of the elm and the flat spiral disc of Mcdicago arborea (Plate I., Fig. 17). The finest example of a glider is probably the seed of the East Indian Oroxylum indicum, the great papery discs of which, about 3 inches by 2 inches, drift like snowflakes and describe immense spirals. True spinners depend for their spiral movement on the presence of an unilateral wing-extension, which may be morphologically of most diverse origin. Thus Finns seeds spin in virtue of a slip-membrane detached from the cone-scale ; the sycamore fruits by an extension of the ovary wafl. The hornbeam nuts possess a pecuhar leaf-like, three-lobed structure evolved from inflorescence-bracteoles ; while one large bracteole is utihsed in the case of the lime to spin a cluster of fruits, and a loose 140 THE CURVES OF LIFE subtending bract is utilised in the case of the hop (Plate I., Figs. 5, 8, ii). In Finns the spinning effect is associated with the presence of a wing with one stiff, straight edge, which is anterior in flight, and the two seeds from one scale spin in different senses with the concave side of the wing downwards. Many other conifers (Abies, Picca, Larix) agree with this type of construction. In the case of genera in which only a single seed or several are borne on the scale two lateral wings to each may occur, and these give the seed a slight glider action, and thus the seed of Sequoia giganica much resembles in appearance the fruit of BetnJa. A critical interest attaches to the seed of the New Zealand Kauri pine (Dammara) (Plate I., Fig. i), since in this case, with one seed only on each scale, a wing is developed on one side of the seed and not on the other, either right or left, on different scales ; that is to say, it would appear that an original ghder effect has been replaced by a definite spinning action. The seeds spin well, but the wing is flat, and the movement may be either right or left hand. Similar complementary cases of spinning may be observed in the peculiar fruits of the hornbeam, the two flowers of the symmetrical dichasial inflorescence being images, and the fruits spin right and left respectively, with the concave side of the main lobe downwards and the fruit up, though the -wing has no clearly defined front margin (Plate I., Fig. 5). Two fruits similarly resulting from a dichasial pair are found in the case of the common hop, and these again spin in con^'erse directions, right and left, with the concave side up or down, the wing being comparati^•ely ill-defined (Plate I., Fig. 8). More exact spinning seeds and fruits of the sycamore type are met with in most di^'erse alliances, and the samara of the sycamore may be taken as typical of the spinning wing at its best development. It closely resembles the wing of some dragon- flies, and spins either right or left, with the stiff edge in front. In many cases a distinct bias will be observed in one direcrion rather than the other, but this is merely the expression of a slight deviation from the flat plane. NOTES TO CHAPTER VIII. Fig. 175 was sent to me by " South African " with the following- remarks : — " I send you a kfe-size drawing of tne ' parachute ' fruit of the Cape ' silver tree,' which I thought you might like to add to your other interesting examples (Fig. rjs). " This common South African tree is a member of the Proteacece. Its fruits are produced in large cones, not unlike those of a large pine cone, while the pecuhar silvery foliage leaves are well known. Each RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 141 bract of the ripe cone subtends a fruit in the form of a hard nut, and the withered style and the four perianth segments of the flower persist into the fruiting stage, and are utilised to form the parachute. The perianth members close over the developing fruit as a membranous investment, and become united above it, around the slender style, while their long tips develop prominent hairy crests. When the nut is ripe it is loosened from the cone, together with these other parts The four perianth segments detach below, but, as they are united around the style, they remain connected with the fruit, only they now shp up the wiry style, until they are stopped by the stigma head. As the nut falls away, it has the appearance of a heavy bob attached by a thin wire to four membranous lobes, surmounted by four beautifully crested pieces. The whole fruit looks as if most admirably adapted to act as a parachute ; but on throwing it in the air, it will be noticed that the heavy nut falls about as rapidly without the parachute attach- ment as with it, so that the arrangement, though so striking in appear- ance, cannot be regarded as any great success from the standpoint of the flotation of the fruit in the air (nor does it produce any spiral effect). The nut would thus appear merely to retain by accident the hairy perianth lobes, which close over it and protect it externally during the maturation of the seed and the swelhng of the style head alone prevents it from slipping off the end of the slender style when detached below. To what extent the parachute effect may be a direct advantage to the plant reniains rather doubtful ; but there is no doubt as to the beauty of the fruit as we find it." Figs. 176, 177. — "M. L." wrote ; — " From your interesting table of ' Flying Seeds,' you omit two which I happen to have seen and sketched, and I therefore send them in the hope you will let me add to your collection. Fig. 176 shows the seeds from a cone of Pinus austriaca, and their likeness to a bird's wings will be at once observable. Fig. 177 shows a perfect example of the aeroplane, the seed of a bignonia, which flutters for some distance through the air before it falls lightly to earth. Both are the size of Nature." CHAPTER IX Right-hand and Left-hand Spiral Growth Effects IN Plants (continued) Some Special Cases. " Schau' alle Wirkenskraft und Samen Unci thu nicht mehr in Worten Kramen." — Goethe. anomalous variation producing spirals — " SPIRAL stair- case " construction — PECULIARITIES OF SPIRAL SPERMA- TOZOIDS — MALE CELLS OF CYCADS AND CHINESE MAIDENHAIR TREE — SPIRALS AND LOCOMOTION — PREVALENCE OF RIGHT- HAND AND LEFT-HAND SPIRALS. We may conclude the consideration of spiral effects in plants by the description of some cases of particular interest which do not come under the preceding headings, but occur as individual or specific sports, the spiral character of which is immediately recognised. On rare occasions a normally whorled phyllotaxis may vary anomalously to a special case of asymmetry which is most clearly defined as produced by the loss of one construction-curve in one sense only ; for example, a plant bearing leaves in whorls of ten (construction system, lo ; lo) may change suddenly to, say, (lo : 9) or (10 : 11). The instant effect would be the substi- tution of a ifiiiding, corkscrew-like, genetic spiral all round the axis ; and this would be retained until the system again achieves regularity and symmetrical construction. Such phenomena occurring in typically whorled plants as Hippuris and Casuarina would be regarded as freaks ; the most beautiful case occurs in Equisctuni, and a fine specimen of spiral Equisetttm telmafcei is a thing to marvel at. Somewhat similar in the production of a spiral wing effect are the remarkable plants Vidalia and Riella, which occur as somewhat isolated genera in their respective classes. Thus among the red seaweeds, a plant known as Vidalia voluhilis, growing in the Mediterranean district, shows a spiral twist like a shaving. The upright branches of the thallus attain a length of 60 mm. or more^ and with age the spiral becomes more RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 143 attenuated. In specimens figured and so far observed the direc- tion of the twist was left hand (Plate II., Fig. 2). Again, among mosses and liveworts, in which spiral construction is commonly indicated by the spiral succession of segments cut off from the apical cell, which apparently determine the arrange- ment of the leaves, a single genus alone produces a wing growth which coils in a similar spiral staircase-like frill. The best examples of this construction occiar in a rare form Riella helico- pJiylla, growing in Algiers. The plants grow submerged, and the erect shoots attain a height of 30 to 35 mm. Several plants figured in the " Exploration Scientifique de I'Algerie " (1848) agree in presenting a constant right-hand spiral (Plate II., Fig. i). The construction of these preceding cases affords so strong a suggestion of what may be termed " spiral-staircase " con- struction that it may not be amiss to point out that suggestions of a similar formation are to be found even among higher plants. Two examples call for special notice. The formation is comparatively rare, but it appears in some aroids as a normal construction, e.g., in Helicophyllum and Hdi- codiceros. In the case of Helicodiceros miiscivoriis it would seem at first sight as if two leafy shoots were springing from the base of the leaf. In reality the lamina has two sagittate basal lobes, as in many other aroids. But these branch sympodially, and the rami- fications do not spread out, but are twisted into a ladder-hke spiral, so that the leaf lobes appear as if they were arranged around a central axis ; the two systems of leaf lobes make spirals in opposite senses, and each fohage leaf thus really produces the effect of a rlouble branch system of leaf laminae (Goebel, " Organography," Vol II., p. 324). From the consideration of organisms which are more or less completely spiral in their whole organisation we may now pass on to the case of spiral spermatozoids. The sperm cells of lower algse are characteristically minute ovoid or pear-shaped bodies with a motile mechanism in the form of two long ciUa or flagellae. With increasing specialisation of the mechanism of sexual fertilisation, further speciahsation is observed in the bodies of the sperms themselves. These become much elongated, and the driving power is increased by further elongation of the ciha, or by an increased number. Owing to the development of the spermatozoid, in a fairly isodiametric mother cell, this elongation of the body can be only attained by a coihng up of the nucleus as it becomes converted into the body of the spermatozoid, and, if the elongation be continued to a distance greater than the circumference of the ceU, the sperm will take on a spiral form and continue to wind, possibly into many coils. The direction 144 THE CURVES OF LIFE I'LAiE II. — Right and Left Spirals in Plants. RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 145 DESCRIPTION OF PLATE II. 1. Riella helicophylla, whole plant, 35 mm. high. {Flore d'Algerie, 1848.) 2. Vidalia voluhiUs, whole plant, 60 mm. high, from nature. 3. Antherozoid of Chara. 4. Antherozoid of Moss, Funaria. 5. Antherozoid of Fern, Aspidium 6. Antherozoids of Cycas revoluta in pollen-tube. (Miyake, 1906.) 7. Antherozoids of Dioon edule, end view and profile. (Chamberlain, igio.) 8. Male nuclei oiFritillaria tenella, with coiled loops ; fertilisation phases. (Nawaschin, 1909.) 9. Male nuclei of Helianthns animus (Sunflower), with spirally coiled loops ; fertilisation phases. (Nawas- chin, 1900.) 10. Antherozoids of Zamia, end view. (Webber, 1901.) 11. Side view of the same 12. Spirally twisted fruits of Helicteres isora, from nature, R., L., and a case of reversed spiral twist. 13. Fruit of Spanish Broom (Spartmin), with sym- metrically coiled valves (70 mm.). 14. Fruit of Mariynia formosa, with spirally arched symmetrical horns (4 inches by 4I inches). C.L. 146 THE CURVES OF LIFE of the spiral coil, right or left, would apparently be determined by chance, according as the tip of the coiling nucleus passes one side or the other of the other extremity, and the spermatozoids of many plant forms thus present simple corkscrew coils, which may be indifferently right or left. Thus the green alga Chara possesses a spiral two-ciliated sperm, constructed as two to three coils in a discoid mother cell (Plate II., Fig. 3), and it swims with the pointed end in advance. Such spermatozoids do not wholly straighten out when set free, and the spiral construction ap- parently gives a rotating movement, which enables motion to continue in a much straighter course than in the case of simple ovoid flagellated cells. In this way a spiral form which was origin- ally induced by the necessities of the construction mechanism may become an advantage to the organism, and the spiral form is henceforward characteristic of male cells. Simple spiral sperms of this character obtain throughout the entire group of the mosses (cf. Plate II., Fig. 4). When discharged the spiral coils are obvious, but when actively swimming, and especially when penetrating the narrow neck of the archegonium, they straighten out very considerably. A more complicated form occurs among ferns (Plate II., Fig. 5). In the common type the number of coils is three to four ; the vestiges of the mother cell may be seen dragged at the posterior end, while the front coil is beset with a crown of fine cilia. The record sperm of this type is found in the rhizocarp Marsilia ; here the corkscrew-like body forms a particularly beautiful spiral of twelve to thirteen, or in extreme cases seventeen, coils ; this remarkable develop- ment being possibly associated with the fact that the spemr has to bore its way through a dense mass of mucilage to reach the archegonium. All these spermatozoids are extremely minute ; that is to say, they can only be observed satisfactorily under the highest powers of the microscope, requiring a magnification of 500 diameters to make them as clear as seen in text-book figures. The remarkable and relatively gigantic male cells of cycads and the Chinese maidenhair tree {Ginkgo), which have only been described in recent years, are of a very different character. These sperms are formed two together at the apex of the pollen tube, as large rounded nuclei, which do not change their form so much as take on a spiral band of cilia at one cud. They are £0 large that they may be just seen with the naked eye, the best cycad sperms being even one-third of a millimetre in diameter, and the effect of the spiral band is to give them a rolhng move- ment ; the distance they have to travel to meet the female cell is not great, and this rolhng motion appears to be sufficient for RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 147 the purpose and to take them as far as the narrow neck of the archegonium, through which they have to squeeze. That large motile male sperms should occur in the pollen tube of a large and quite ordinary-looking modern tree, and should be discharged to swim freely to the female cells, is one of the most remarkable facts in modern botany, as confirming the long- established views as to the origin of higher land plants from cryptogamic ancestors, whose fertilisation processes took place in open water. The discovery of such motile sperms in the case of Ginkgo by the Japanese botanist Hirase in 1896 has thus marked an epoch in the study of early seed-plants, and this was Fig. 178. — The Ladder-leaves of Helicodiceros. soon followed by descriptions of almost identical phenomena in three or four genera of modern cycads. In the case of the cycads the sperms are even larger and clearer than in Ginkgo. In Cycas they are -18 to -21 mm. in diameter. According to Miyake (1906), the spiral band makes five and a half to six turns, and constantly, or with few exceptions, so far as known, in a left-hand spiral, winding in clockwise on looking down on it (Plate II., Fig. 6). In Zaniia, an American form, according to Webber (1901), there are also five to six complete turns, and in a constant left-hand direction, the sperm being the largest yet seen, -222 to -332 mm. in diameter (Plate II., Figs. 10 — 11). Finally, in the Mexican cycad Dioon, described by Chamberlain L 2 148 THE CURVES OF LIFE (1909), the sperm, up to '300 mm. in diameter, also shows five to six turns, " almost without exception," a right-hand spire as seen from above (Plate IL, Fig. 7). What causes the direction of the spiral is still unknown ; but it is interesting to note that in these cases the sperms are always formed in a pair from sister- cells, and are differentiated in these " hack to hack." Being in this sense iwin-cells, with their nuclei derived from an initial nuclear spindle, it might have been expected that the coils would have wound in opposite sense ; but the evidence is distinctly to the contrary and the constant would appear to be a specific character, although enough work has not been done on these types to make the matter an absolute certainty. Even in higher plants indications of spiral movement and consequent spiral form have been traced in the male cells at the time of fertilisation. The two male nuclei which leave the pollen tube of flowering plants have to travel a certain distance to reach the female cell, as also the nucleus involved in endosperm formation, and it would appear that such movement must be performed on their own initiative. Beautiful figures have been given by Nawaschin for Fritillaria tenella (1909) (Plate IT, Fig. 8), in which the two sperm nuclei present a distinct coiled worm-like appearance. A still more striking case is illustrated for the fertilisation of the common sunflower {Hclianthus) (Plate IL, Fig. 9) (Nawaschin, 1900), the elongated sperms showing distinct spiral coiling, and even a kink in the middle and coiling in opposite directions at the two free ends. To what extent this assists the movement, or is merely the expression of aimless wriggling, is not clear ; but it is interesting to note the retention of spiral characters in these cells, which are not spiral by any construction processes, as in the case of the snail- like cycad sperms, which apparently put on the spiral band for purposes of locomotion, just as they slip it off again as they enter the ovum. Interesting examples of the sporadic origin of the spiral con- dition are again afforded by many remarkably constructed fruits, the torsion effect being restricted to single species among a genus, and very rarely a generic character. Very beautiful spiral patterns are commonly observed in the case of fruits derived from one or more carpels which are themselves quite straight in the flowering condition, but take on a secondary spiral growth during early stages of fruit development. Here also the spiral tM'ists may be constant in direction or a matter of chance in different cases. Rarely a group of several carpels is twisted together as in Helicteres -isora (Plate II. , Fig. 12), in which five carpels twist RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH 149 together to a close spiral of ten to fifteen coils. In this plant the spiral may be right or left. Examination of seventy-five fruits gave forty-five right and thirty left, suggesting a bias in favour of the former condition. One fruit was found which was left spiral below, and then changed to a right spiral in the upper region. The case of the fruit head of' many large forms of clematis (C. lamiginosa) affords a less perfect example of a left- hand constant spiral drift on all the tails of the achenes. Some of these feathered fruits fall in wormhke sinuous right-hand spirals, resembling those of the Stipa fruit. Very charming spiral effects are characteristic of certain genera of the Legumino^cB, in which only a single carpel is involved to constitute the pod fruit. A large number of species of Fig. 179. — Spiral Leaves of Hybrid Begonia. Medicago are constantly left hand, e.g., M. arborea (Plate I., Fig. 17), with one coil only to the flat fruit, which becomes a wind-distributed glider, or with five to six complete coils in the rolled-up ball of M. sctitdlata (Plate I., Fig. 18). Right-hand species of Medicago have been described. On the other hand, the screw beans {Prosopis) give very perfect spiral screws of as many as fifteen coils, constantly right hand ; these screws 2 to 3 inches long, so closely imitate the effect of an ordinary " right-hand screw " that it is difficult to realise that they are not artificial productions (P. puhescens, P. strombulijera). Other species of the genus may have perfectly straight pods (Plate I. Fig. 10). While the direction of coiling in the preceding examples is clearly quite immaterial to the plant itself, and can be only 150 THE CURVES OF LIFE regarded as a mere specific or generic " accident," a more elegant example of complementary twisting is seen in the two-carpelled fruits of species of Martynia ; in these large capsules two long, stiff horn-like processes curve and inarch like the horns of an antelope. This symmetrical position is said to be utihsed in the cacology of the plant, as these long, stiff processes catch in the fetlocks of animals running over the prostrate shoots (Plate IL, Fig. 14). NOTES TO CHAPTER IX. The Irish Court Yew. — In reference to the second paragraph of this chapter it may be added that the first two specimens of what is now called the Irish or Florence Court yew (Taxus baccata, var. fastigiata), in which the leaves are sub-spiraUy arranged round their axis and spreading from all sides of it, were found about 120 years ago by a farmer of Aghenteroark (co. Fermanagh) on his steading among the mountains, and he took one of them to Florence Court. The Earl of Enniskillen afterwards gave the first cuttings to Messrs. Lee and Kennedy, and they then spread all over the world. Figs. 178 and 179. — " F. R." in sending these wrote as follows : — " You speak of the ladderdike spiral noticeable in Helicodiceros miiscivoriis. I enclose a drawing of it, after Goebel (Fig. 178). " Somewhat comparable spiral staircase effects have also been noticed in certain begonias (Goebel, rgii), two ' fohage-hybrids ' of the Rex-hybrid, known as Comtesse Louise Erdody and 5. ricinifoliaf. wehleana. The former is said to be a cross between ' Alexander von Humboldt ' begonia and B. argentea ; the latter between B. heraclei- folia and B. peponifolia. The peculiar characters noticed in these cases do not obtain in the parent strains at all ; and the essential point noted is that the basal lobes of the leaf-lamina keep on growing for a considerable time, instead of passing on into adult tissue, as in the case of other begonias. The most perfect development of this spiral effect is seen when a young leaf is used for a cutting, and all adventitious buds are removed as they appear. In such case the hasal lobes continue to grow, apparently at the expense of food material in the rest of the leaf, and these growths continue from the base of the lamina as two spiral staircase laminae, winding symmetrically in converse senses. In the case of the plant figured by Goebel, the new growths show five coils, though a few weeks previously they had only two. It is not likely that these spirals will go on growing indefinitely, but they will evidently do so for some months, the limit to the pro- ceeding being set by the available food supply. The spiral effect is clearly due to the fact that the outer edge of the lobes grows more strongly than the inner edge, which resembles a thick vein. (See Fig. r79.) It is evident that here we have to do with a very remarkable and beautiful mutation, which may or may not have been produced by hybridisation ; but the utiht}' of the construction is very question- able, and the remarkable leaf would remain classed as an accidental and aimless monstrosity' ; it is curious that it should appear in two hvbrid strains." CHAPTER X Right-Hand and Left-Hand Spirals in Shells " It has been thought that the shells which are visible at the present time Within the borders of Italy, far away from the sea, and at comparatively great heights, are due to the Flood having deposited them there ; and it has been argued that the nature of these shells is to keep near the edge of the sea and that as the sea rose in height (during the Flood) the shells followed the rising waters to their highest level. But the cockle (for example) is even slower than the snail out of water, and could not possibly have travelled from the Adriatic Sea as far as Monferrati in Lombardy (about two hundred and fifty miles) in the forty days which is given as the duration of the Flood ... As a matter of fact, in the cutting of Colle Gonzoli, which has been made precipitory by the action of the Arno wearing away its base, you can see the shells in layers in the blue clay, which also contains other rehcs from the sea." — Leonardo da Vinci (Leicester MSS,). CONTRAST OF TREES WITH SHELLS— SPIRAL FOSSILS IN NEBRASKA — DETERMINATION OF HAND IN SHELLS — DIFFERENT HAND IN FOSSILS AND SURVIVORS OF SOME SPECIES — LEFT-HAND SPIRALS OF TUSKS — SINISTRAL SHELL, BUT DEXTRAL ANIMAL — SHELLS AMONG PRIMITIVE PEOPLES — FOLLOWING THE SUN THE SWASTIKA— SPIRAL FORMATION AND THE PRINCIPLE OF LIFE. In that botanical portion of our subject which has just been concluded, it will be observed that the spiral formations of plants have been examined from a different point of view from that illustrated, for instance, in our examination of the spirals of shells shown in the third section of this series. And no possible botanical authority can be given to the suggestion made in my first chapter, that a twist can be imparted to the trunks of trees either by the rotation of the earth or by the action of continuously prevailing winds. In Fig. 43, Chap. 11., I gave an example of a right-hand twist in a chestnut tree from Shrewsbury, and added that I awaited examples of the reverse formation from Australia. But the delay is now hardly necessary. In Fig. 180 will be seen a beech at Kew showing a very pronounced right-hand twist. And if this, taken with Fig. 43, and with the right-hand twist of the sweet chestnut on the left of Fig. 181, be taken as a proof that right-hand formations of this kind are more usual in the northern hemisphere, we have an ijistant contradiction in the second sweet chestnut shown in Fig. 181, which exhibits the reverse twist in spite of being the same kind of tree growing in the same locality. It is clear, therefore, that we cannot predict in botany that all specimens of the same family will show a 152 THE CURVES OF LIFE similar formation, as we can in most cases of shells ; and our uncertainty will be still further increased, I think, when we pro- ceed to investigate twining plants. But before attempting a closer examination of shells, I must give an instance of a very curious U'h.ihi by C. P. Rajnll. Fig. iSo. — Twisted Stem of Beech (Right Hand). (Sec Fig. 43.) structure concerning which scientific controversy has not yet absolutely decided whether it is of animal or vegetable origin — ■ a decision which has baffled more than one celebrated investi- gator in other cases where somewhat similar difficulties have arisen, such as the so-called Eozoon canadensc, for example. Some very extraordinary spiral fossils, found in the Bad RIGHT AND LEFT SPIRALS IN SHELLS 153 Lands of Nebraska, first attracted the attention of the scientific world some years ago ; and by the kindness of Dr. W. H. Drummond, of Montreal, a specimen will, it is hoped, soon be placed in the British Museum of Natural History. Their exact origin and nature are still the subject of discussion, but as the balance of expert opinion inclines to the belief that they are not only organic, but also plants, I have inserted what is known about them here. Professor Erwin Hinckley Barbour has published an illus- trated description of many examples of these " devil's cork- screws " or " fossil twisters," called in more scientific termino- logy DcemoncUx, which he found in large quantities at Eagle ll'kola hy C. p. Raffi/l. Fig. 181. — Two Sweet Chestnuts Showing Right and Left Hand Twist. Crag, on Pine Ridge, near Harrison, in Sioux County, Nebraska. These peculiar structures, as anomalous as they are unique, are found over an area of some 400 square miles, between the White River and the Niobrara River, and to a depth of about 200 feet. They are corkscrew-shaped columns of quartz, sometimes embedded in sandstone, sometimes " weathered out " quite clear of the original matrix. The spiral varies in length, but sometimes is as much as 20 feet long, and perfectly regular throughout. At the lower end is a large transverse attachment, not spiral but smooth, and roughly cylindrical in shape, as large round as a hogshead, and longer than the spiral growth above it. The surface of these spiral fossils is a tangle of ramifying, inter- twining tubules, about an eighth of an inch in diameter, which thicken inside into a sohd compact wall, showing (under the 154 THE CURVES OF LIFE microscope) plant tissue arranged in fibres. Every microscopic section, witliout exception, shows unmistakable plant structure. An immense lake of fresh water, in long distant periods of time, once covered the great basin east of the Rocky Mountains, of which the sand rock of the modern district, all sedimentary and of aqueous origin, is a relic. In the course of ages, this lake became fiUed up by ddriiwi poured in from the rivers, and its water plants were buried in sand. By degrees these plants decayed, and, particle by particle, were replaced by siHca, the materia] of quartz ; and in this manner the huge corkscrews of quartz, now found on Pine Ridge, have preserved the shape, Fig. 182. — Living Red Whelk, Fuses antiquus (Right Hand). (From the beach at FeUx- stowe.) Fig, 183. — Fossil Red Whelk, Fusus antiquus (Red Crag) (Left Hand). (From the cUffs along the shore at Fehxstowe.) the spiral growth, and the huge roots of the vast water weeds which flourished long ago at the bottom of the lake, and persisted in growing at various levels, one above the other, as the filling up process went on, until at last the lake became dry land, and its weeds vanished — to reappear as D^monclix. The spirals are both right hand and left hand, and their symmetrical arrange- ment round a vertical axis is alone sufficient proof that they are not the remains of any animal or of any animal's abode ; for though the skeletons of animals have, in two cases, been found in connection with them, I cannot believe that Dcsmonelix was ever a rabbit burrow. It is almost equally difficult to believe that such huge weeds could have grown in a lake and not in a RIGHT AND LEFT SPIRALS IN SHELLS 155 sea ; or that any algce had tissues strong enough to resist rotting within a few weeks of death. Other hypotheses have been put forward to explain these odd formations, one of the most likely being that two plants are involved, one of which coiled tightly round the other ; but this is not the place to enlarge upon them. It is clear that our knowledge is not yet sufficient to produce a theory that will satisfactorily explain all the facts. We are on firmer ground when Fig. 184. — AcHATiNA HAMiLLEi (Right Hand) Fig. 185. — Lanistes ovum FROM Tanganyika (always Left Hand). we turn to the examination of shells, whether the living or the fossil specimens. Some writers seem to be of the opinion that the " choice " between a right-hand or a left-hand spiral in the formation of living things is largely due to chance. If so, it must be one of those vital " chances " which seriously affect the future both of the individual organism and of the race ; for we have already observed cases where all the fossil shells of a certain species were left hand, and all the surviving specimens of the same species were right hand (see Figs. 182, 183). Are we to argue from this that ah early individual creatures of this kind which did 156 THE CURVES OF LIFE not adapt themselves to changing environment by changing theii spiral were not fit to survive ? Or should we merely say that m the age when the fossil shells flourished some continuous influence like the set of the tide gave all the young shells an " inchnation " to become left hand, whereas in more modern centuries the set of the tide has altered and the young sheUs merely show that alteration ? Near Lake Tanganyika there lives an amphibious mollusc with a rather large shell called Lanistcs (see Fig. 185) which, in that locality, always exhibits a spiral of left-hand formation. The same shell, when it is found at Lake Nyassa or the Victoria Nyanza, exhibits a dextral helix. It was suggested by Mr. J. E. S. Moore that Lake Tanganyika had had some past connection with the tides of the ocean, whereas the others are freshwater lakes. But this is now found to have no justifica- tion. I have mentioned the slight causes which maj^ give an appar- ently accidental origin to a spiral. The follicle of hair is a good example of this. In Western peoples it is generally straight, but in the negroid races the follicle is bent, and the result is the spiral shown in curly hair. The socket of a tusk or the base of a horn has much the same effect on growth. The examples of narwhal's tusk (really his front tooth), which may be seen in the Museum of the Royal College of Surgeons, show excellently the rare sinistral spiral, and the varia- tion shown by the additional curves in one of them is, no doubt, due to a slight variation in the socket. Every narwhal tusk I have ever seen (and there have been six quite lately in one naturalist's shop in London) has a left-hand spiral (Fig. 186), including a sixteenth century carved specimen, now in the Sala dei Stucchi of the Doges' Palace, and another still older tusk, preserved in St. Mark's Treasure, in Venice. But they exhibit an even more extraordinary partiality to this formation. There are seven examples known of narwhals with a double tusk. One of these Fig. 1S6. — Part OF Narwhal's Tusk (always A Left-hand Spiral). Fig. 1S7. — Ele- phant's Tusk IN Royal Col- lege OF Sur- geons, show- ing Abnormal Spiral Twist. RIGHT AND LEFT SPIRALS IN SHELLS 157 is in the British Museum of Natural History at South Kensington. Instead of following the examples of the horns I mention later and showing different spirals, this pair of tusks exhibits two spirals of the same kind, and each of them is sinistral ; and, though I only speak of what I have myself examined, the statement has been made that whenever a narwhal has two such teeth their spirals are identical, instead of exhibiting symmetrically different spirals about the middle plane of the body, as might have been expected. Dr. Wherry thinks that as an unerupted tusk exhibits a perfectly straight fibre, the direction of the spiral is formed after it leaves the bone and becomes opposed to the waves during growth, owing to the fact that the creature " plays " to one side as it ploughs through the water ; and when by a rare chance two tusks are developed, the creature preserves the habit of carrying its head on one side and so gives both tusks the sinistral twist it gives to one. This may be compared with the right-hand spiral observable on each side of the petals of Selenipedium conchiferum, which I quoted before from the same writer's observations. In the Museum of the Royal College of Surgeons there is also an elephant's tusk which exhibits a very abnormal form indeed, for, instead of being the usual segment of a circle, the tusk has grown into a sinistral ^ig. 188.— Elephant's , , ; i 1 T_ Tusk in Royal Col- spiral, so much accentuated by causes ^^^^ ^^ Surgeons, latent in the socket that the whole thing showing Abnormal has taken a complete corkscrew forma- Spiral Curve. tion (Fig. 187). Frank Buckland had certain rabbits' teeth in his collection which had grown into a spiral form owing to an injury at their base from a stray shot or some other accident (compare Fig. 188). That an alteration in the socket is quite sufficient to control the formation of a growing spiral may be proved, as I have suggested already, by placing one of the eggs called " Pharaoh's serpents" in a small tube. As soon as the spiral begins to come out of the egg it wiU exhibit a dextral hehx if the tube is dented sHghtly on the left, and a sinistral helix when the orifice of the tube has a dent upon the right. In considering the reasons why a sheh should be sinistral rather than dextral, I must distinguish between those sinistral shells which are " sports," or rare exceptions to the dextral rule common in their species, and those shells which are sinistral as a rule of their species. There is yet a third distinction, which must be made later. 158 THE CURVES OF LIFE Tiirrilites catentdatus always exhibits a conical sinistral helix. Titrrilites costatits, a fossil gastropod, commonly called the " screw shell," is found in the Portland formation as a rule. Other left-handed species are Colnmna flammea, from Prince's Island in the Gull of Guinea ; Miratesta, a freshwater shell from Celebes ; Amphidromus perversus from Java ; the pond snails Physa fontinalis in Europe ; and P. heterostropha of America. The sinistral form of Valuta vespertilio (Figs. 78 and 90) is, however, the exception to the rule of the species, which is found on the Italian coasts of the Mediterranean, and an Italian collector would be more likely to have the sinistral form of a common shell than its ordinary growth. This ordinary form is shown in Figs. 189, 190. At the present day, Mr. Fulton Fig. 189. — Section of Common Form of voluta vesper- TILIO. Fig. 190. — Common OR Leiotropic VOLUTA VESPER- TILIO. (Compare Figs 78 and 90.) informed me, specimens of the sinistral Buccinwn undatum, though not common, can be bought for a few shillings. A Billingsgate porter thinks he has a rare prize when he finds it, and is greatly disappointed when he discovers it is not worth gold. Fusus antiquns (Figs. 182 and 183), a fossil sinistral whelk, of which Mr. Morton Loder, of Woodbridge, sent me an excellent specimen, is too common to be bought by dealers at all. The genus Amphidromus is about equally divided into dextral and sinistral species. But in cases where a shell only exhibits the sinistral specimens in its fossil form, and is dextral in all living examples, I know no reason for the survival. It may be signifi- cant, however, that Tornatina, Odostomia Turhonilla, and others, though sinistral in their embryonic form, become dextral as adults, which may suggest the argument that (for some reason RIGHT AND LEFT SPIRALS IN SHELLS 159 hitherto unknown) no sinistral specimens can survive. The nght-hand iorm of Neptimca antiqua (see Fig. 191) was classed by Fischer with Fusus antiqum (Fig. 183) and in 1898 Harnier analysed both recent and fossil distributions of the shell. He found the left-hand hving variety south of the Bay of Vigo along the Portuguese coast, but further north there are more nght-hand than left-hand formations, and var. Carinata was chiefly arctic. But the most interesting point is that the fossil forms were usually right hand in the EngHsh Red Crag, and this formation, therefore, preceded the living specimens in Portugal, of which no left-hand fossils are found. The left-hand fossil form Neptimea coniraria (Fig. 192), is of the Pleiocene age (see Fig. 191. — Neptunea an- tiqua, CARINATA. (Crag, Little Oakley.) Fig. 192. — Neptunea contraria, sinistrorsa. (Pleiocene.) Simroth's " Mollusca " in Bronn's " Klassen des Tier-Reichs," P- 907)- The third distinction to be made in this matter is in such cases as Spinalis, Limacina, Meladromus, and Lanistes, in which the shell is sinistral but the animal is dextral. Here Simroth, von Ihering, and Pelseneer, explain that the shell is really ultra- dextral ; that is to say, the whorls have been, as it were, flattened, as in Planorhis, then the spire has been still further pushed down- wards, until the whole is turned inside out, becoming sinistral with its original dextral animal. The proof that this queer process has in some way occurred, is arguable from the fact that every dextral shell has a sinistral twist to the operculum, with nucleus near the columella, and vice versa (see Figs. 46 and 47), but in " ultra-dextral " shells the operculum is sinistral, in spite ]6o THE CURVES OF LIFE of occurring m what looks like a sinistral shell. There are also instances of " ultra-sinistral " shells, which appear to be dextral though their orifices are sinistral, as in the freshwater Pom- pholvx from North America, and Choanoiiiphalits from Lake Baikal, Among the organisms illustrated here are included several speci- FiG. 193. — Helix lapicida. Fig. 194.- -The Same from Above. (Photos, by J. C. Blackshaw from specimen found by J. B. Higham, Wolverliampton.) mens of right- and left-hand foraminifera from the Challenger reports. The larger shells illustrated include the Central African snails in Figs. 184, 185, in which we find Achatina with right-hand curves and Lanistes ovum with left ; Helix lapicida, an English Fig. iq6. — Right-hand voluta solandri. F'lG. 195. — Left-h.\nd Tur- BINELLA KAPA. (The sacred Chank Shell held in the hand of Vishnu.) snail, with the rare left-hand spiral (Figs. 193, 194) ; the common form of right-hand Vohita vespertilio (Fig. 189), which may be compared with her extremely rare sister shown in Fig. 90 ; and, finally, the left-hand Tiirbinclla rapa (Fig. 193). It is this last example which I would particularly emphasise, because RIGHT AND LEFT SPIRALS IN SHELLS i6i Fig 197— Marine Subjects in Faience from the Early Minoan Temple Repository (about 1600 B.C.) at Knossos in Crete. (Sir Arthur Evans.) By permission of the Committee of the British School at Athens. ;.L. 1\^ iba THE CURVES OF LIFE it is a good instance of the xery curious and general fact that when objects which usually display a dextral helix are found to show a sinistral helix, some peculiar value, and often some supernatural signification, is attached to them by the primitive races who make the first discovery. The practice is akin to the dehght of an ancient people in such marine treasures as the echinus or sea urchin which Schhemann found in the decoration of the pre- historic shields of Troy ; the half-uncoiled arms of cuttlefish on the painted cups of Knossos may be mentioned in the same connection. From "The Palace of Knossos" (1903), by Sir Arthur Evans, I am able to reproduce, by the kindness of Mr. George A. Macmillan, the striking coUection of objects in faience (Fig. 197), dating from about 1600 B.C., and showing prominently the lovely spirals of Argonauta argo at each corner. The same volume gives the Triton shells in Fig. ig8, carved on a Minoan seal ; and these, hke the shells shown in Figs. 24, 25, and 26, all show the spiral formation. Many more examples might be added ; but perhaps the most interesting is that given in Dcchelette's famous " Manual," from which Fig. 199 was redrawn for me. It shows part of a collection of 200 seashells {Nassa) arranged as a neck- lace and all tinged with red, which was found in the Grotto of Cavaillon near Mentone. In the Grotte des Enfants two skeletons showed orna- ments of Nassa neritea. Another skeleton was found on a bed of shehs, Trochus. At Laugerie Basse a skeleton showed Cvprcsa (from the Mediterranean) on forehead, arms, knees, and ankles. At Cro-Magnon Lastel found 300 perforated specimens of Littorina litiorea. At Cavaillon about 8,000 little seashells were found altogether, nearly 1,000 perforated, and almost all painted after the fashion which lasted as long as the specimens found at Knossos. A curious use of the echinus, which may be compared with that mentioned above as found in prehistoric Troy, was discovered by Mr. Worthington G. Smith, In a round barrow on Dunstable Downs he excavated some 200 fossil echinoderms which surrounded the skeletons of a mother and her child (see " Man the Primeval Savage"). The fossils were of two kinds, known by the folk-names of "heart-urchin" and " fairy loaf " or " shepherd's helmet." Another common chalk fossil, Porosphcera Fig. 198. — Two Triton Shells FROM A Minoan Clay Seal Impression Found at Knossos. (Sir Arthur Evans.) By permission of the Committee of the British School at Athens. RIGHT AND LEFT SPIRALS IN SHELLS i6,i glohularis, was a special favourite with the men of the Barrow burials, and was often strung by them into necklaces. Canon Greenwell found an ammonite beside a skeleton in a Yorkshire mound, and it appears that black ammonites are sometimes associated with the religious ceremonies of the Brahmans. In a limestone burial-cave in Belgium, M. Dupont found a collection Fig. 199. — Perforated Shells used as Necklaces by Magdalenian Children about 20,000 Years ago. Discovered in the caves at CavaiUon (Alpes Maritimes) by Rivifere, Lartet, Christy, and others. (Dechelette, p. 20S.) of shells, including Centhiwn, which must have been brought from nearly fifty miles away for the purpose. Saxon graves in Kent have revealed cowries which can only have come from the Far East ; and necklaces of " elephant's tusk " shells [Dentaliimi) have been found in British barrows. In Mr. Walter Johnson's " Byways in British Archaeology," it is also recorded that the Laplanders, who afford another in- stance of the use of sea-urchins in burials, have always treasured fossils and queerly shaped stones as fetishes. They thought snailshells were " dog-souls " {Hundsjael), and in the old days seem to have substituted them, in burials, for the more valuable hving quadrupeds. The inhabitants of Travancore believe that the sacred shell called " Sankho " is a mani- festation of the god Vishnu, some of whose attributes are indicated in the carved footprints of Buddha. In this shell the internal spiral does not turn to the right (with its " entrance " therefore also to the right), as m the case of the shell Tttrbinella pyrum (Fig. 93), and in many other examples, but turns to the left (with its " entrance " also to the left) as m Turhinella rapa (see Fig. IQ5) with the rare sinistral hehx ; and this behef survives in the drawing, conventionahsed though it be, of this sacred shell (with its opening to the left) which is t<:) be' seen upon the postage stamps now used in Travancore (Fig. 200). This " chank shell," is represented in Hindu rehgious M 2 Fig. 200. — Postage Stamp from Tra- vancore. 164 THE CURVES OF LIFE art as held in the hand ui Vishnu. It is fished for at Tuticorin, un the Gulf of Manaar, from October to May, and in 1887 a good sinistral specimen found at Jaffna was sold for Rs.700. Nearly all the common shells brought up are sent to Dacca to be sliced into bangles and anklets for Hindu women ; and this use of shells as ornaments among savage inland races, and more civilised dwellers by the sea, may be paralleled in every quarter of the globe and in the earhest periods of history. In the Indian Ocean CvprcBa iiioucta (the " money cowry ") has for ages been employed as a medium of exchange, as is CyprcBa annulus in the Pacific. In Bengal in 1854 the value of 5,120 cowries came to one rupee. In Egypt the same shell is still used as a preservative against the " evil eye." (See Appendix VII.) A pretty parallel with this may be found in a delightful legend from the folklore of Eastern Europe, related by Mr. George Fig. 201. — NoNioNiNA stel- LIGERA. X 60. (Brady's Foraminifera. Chal- lenger Reports.) Fig. 202, — Young Specimen of polystomella MACELLA. / 60. (Brady's Foramini- fera. Challenger Reports.) Calderon. It appears, that at the baptism of a Lithuanian infant,, the parents bury one of its little curls at the bottom of a hop pole, so that the child may " twine out of danger " in its lifetime, just as the left-hand spirals of the plant twine upwards to the sun. It is possible that the left-hand spiral may have had a deep signification as a symbol, in older centuries and in various climes. The four great columns set up behind the high altar in St. Mark's at Venice are all carved in left-hand spirals ; and some special value connected with that formation may be sug- gested by the tradition that they originally came from the Temple of Solomon in Jerusalem. The same spiral was also carved on the pillar of St. Bernwand at Hildesheim in 1022. Oriental races seem to prefer left-hand spirals, where choice is possible, whenever they carve a walking stick or make a screw ; and certainly the majority of the walking sticks sold by Zulus in South Africa show a left-hand spiral, though whether this is the preference of the workman, or the mere copy of some left- RIGHT AND LEFT SPIRALS IN SHELLS 165 hand spiral plant or of the left-hand twist in a rope made by a right-handed man, I cannot say. In small customs common to our daily life we are aware of a distinct choice, consecrated by tradition, between right-hand Fig. 203. — DiscoRBiNA opercu- LARIS. X 100. (Brady's Foraminifera. Challenger Reports.) Fig. 204. — Cristellaria CULTRATA. X Ij. (Brady's Foraminifera. Challenger Reports.) and left-hand forms of movement. Port decanters, for instance, must follow the sun ; and the horror of our forefathers in seeing the wine go round from left to right could only be equalled by the amazement of a modern bridge plaj^er who beheld his partner Fig. 205. — Cristellaria CALCAR. /, 25. (Brady's Foraminifera. Challenger Reports,) Fig. 206. — DiscoRBiNA globu- laris. X 75. (Brady's Foraminif 3. Challeni;er Reports ) dealing the first card to the right instead of to the left. In 1690 there was a slang word (preserved in the " Dictionary of the Canting Crew ") which is worth recalling. " Catharpin-fashion " is defined as follows : " When People in Company Drink cross and not round about from Right to the Left, or according to the sun's motion." The word " widdershins " also conveys a sug- i66 THE CURVES OF LIFE gestion of misfortune, and has been derived from the same origin as " wiederschein," to reiiect after the manner of Virgil's rain- bow : " Mille trahit varios advcrso sole colores." M'hat the origin of these customs was, it would now be almost impossible to guess ; but they suggest, at any rate, that some special signifi- cance was attached to the left-hand spiral from veiy remote times. We still waltz " with the sun," and " reverse " when we turn in the contrary direction. Many of the oldest dances of Mexico, Chili, and Spain were " sun dances," with movements arranged in the same way. The poet Hood must have alluded to the tradition when he describes how Queen Mab " waves a wand from right to left " over the head of a good child asleep. One of the most ancient and widespread of all symbols is that shown in Fig. 209, the lucky form of the Indian Swastika, the Saxon fylfot, the Greek gammadion. This form, it will be seen, is like a left-hand spiral, and the direction of the arms (or legs, perhaps— for the crest of the Isle of Man is really the same) Figs. 207 and 208. — Neritopsis compressa var. TRANSVERSA. (Bronn and Simroth.) follows the sun, while the reverse form indicates movement contraiy to the sun (with the topmost hmb pointing to the left instead of to the right), and therefore suggests misfortune. Schhemann dug up this symbol from the ruins of Mycenae and of the Troy of Priam. It is found on the archaic pottery of Cyprus, Rhodes, and Athens ; on the coins of Corinth, Sicily, and Magna Gracia ; on Samnite and Etruscan ornaments. It does not appear in Rome until the fourth century of our era ; but it spread from the Danube provinces to Great Britain through- out the Roman Empire (" The Migration of Symbols," D'Alviella, 1894). Its Indian name signifies propitiousness or prosperity, and it appears on the oldest Indian coins and on the footprints of Buddha carved at Amravati. It was found on bronzes brought from Coomassie by the last Ashanti Expedition, in prehistoric mounds in Ohio, among the ruins of Yucatan ; it is still printed on blankets made by modern Navajo Indians, in Hindu account books, on the skirts of Tibetan women. There is httle doubt that it symbohses the apparent movement of the sun through RIGHT AND LEFT SPIRALS IN SHELLS 167 (he seasons. The red eastern arm (for the earth) represents Spring and the morning ; the southern is the gold oi Summer noon ; the blue arm of the west is Autumn sunset on the sea ; Winter and white midnight are seen in the northern limb. Thus it symbohses the life-giving sun, the origin of all things, and therefore its left-hand spiral is the auspicious form. I must conclude with one more example of the connection so often observable between the spiral formation and the principle of hfe. For purposes of comparison, it is right to mention the remarkable phenomena observable in crystalhsation. A theoretical diagram has been drawn by Barlow (reprinted in Nature for December 21, 1911), to show the arrangement of the silicon and oxygen atoms in the right-hand and left-hand crystals of quartz. The white spheres of silicon are shown in a w&mm iiiip ■« mmmm ■^■i^ivx'-^v^ iiiili SHSJlSSSSIg^^^^^^ iiiiPiiiiiiii iJSHSiiiiS . iiiili iiiii W;W-:¥:¥;W:::::: iWiP "■ ] mmmm^mmmmmmmmmm :?x:Hiiiii;i:: :iii:-S?:§ iiiii iiiili ::S;S4H:¥M¥: iffffsmm mmmmmmmmm :^v^^■-^• ■••:■:•:■:■:■:•;■:■::::-:■:■;■:•■ ■■■■■:•:■:-:■;■;■:-::;: glsliiiiiiiisiPPPi Fig. 2og. — The Lucky Swastika. (Following the sun.) right-hand helix in one case, and in a left-hand helix in the other. But more important and convincing evidence of the right- and left-hand screw structure of quartz is afforded by the optical properties of the mineral, when studied with a polariscope. If a plate of right-hand quartz 375 mm. thick be placed over another of left-hand quartz and examined in the polariscope arranged for convergent light, the remarkable figures known as the " Spirals of Airy " are produced ; and all such phenomena are due to the fact that when a beam of hght is sent along the axis of a quartz crystal (see Dr. Alfred Tutton in Nature, loc. cit.) the right- or left-hand arrangement of the molecules of sihca causes the plane of vibration of the polarised light to be rotated in the same direction. In his laboratory a chemist can prepare a compound, such as tartaric acid, which will be " optically neutral," that is to say, it will exhibit a symmetric grouping of i6S THE CURVES OF LIFE right-hand and left-hand spirals. Ne\-ertheless, the one kind can be separated from the other by the introduction of an organism which feeds on one and rejects the other. Or the chemist himself, by crystallising the compound, can pick out those salt crystals with their hemi-hedral face to the right from others which exhibit a left-hand formation. But in either case the intervention of " life," in the form of the organism selecting its food, or of the chemist choosing his crystals, has been necessary before the symmetric grouping of the artificial compound could be disturbed. In fact, though recent investigations seem to indicate that Pasteur was incorrect in stating that compounds exhibiting optica] activity (and therefore molecular asymmetry) were in-\-ariably organic, yet it remains true that the only way in which a difference of property can actually be distinguished, or defined, between such right- and left-hand spirals is when they are brought in contact with the vital principle. NOTES TO CHAPTER X. The Swastika. — " In your discourse on spirals you mentioned the Swastika, that token of good luck which represents the sun on his journe^'ings, the origin of all things, the march of the seasons, the points of the compass, and many other matters. In accordance with these ideas its arms bear different colours, and I venture to send }'ou some lines upon an ancient sundial which commemorate these multi- farious properties : On a Sundial. 1. East, Spring, Morn, Red. Rosy footprints in the sky. Rosy footprints on the sod. Spring on earth and dawn on high. Give tlie opening hour to Godde. 2. South, Summer, Noon, Gold. Summer's culminating power. Noontide's radiancy of gold, Day by day and hour by hour, Godde Hys Majesty unfold. 3. West, Autumn, Sunset, Blue. Sinks the sun in Heaven's blue. Autumn dons her purple haze. Naught is changed, the law holds true. To Godde the hour to Godde the praise, 4. North, Winter, Midnight, White. Midnight robed in moonhght clear. Winter palled in silver white. To the watchful but appear Witnesses of Godde Hys might. RIGHT AND LEFT SPIRALS IN SHELLS 169 Gloria in Excelsis. Rosy Spring and Golden Noon, Purple Eve, white ^^'inters sleeping. To this song thy soul attune, " Everie houre's in Godde Hys keepinge." "F. B." For notes on the arithmetical proportions of a Swastilca, see Fig. 391 in Chapter XX. ; and for its origin, see Appendix IV. [Photo : H . Fyaiifois. Fig. 210. — Pl-wground of a Bower-bird with Snail Shells AS Decoration. Playground of .\ Bower-bird (Fig. 210).— It is interesting to note that spiral shells are chosen for decorative purposes, not only by men of prehistoric and of later times, but even by the Bower-bird of Australia and New Guinea, as this illustration shows. The collection of shells, in this species, is the first process in decorating their play- ground, after which the miniature avenue made of fine shoots of trees is'constructed. Finally, it is embellished with gleaming mother- of-pearl shells and other bright and shining objects. I was sent the photograph here reproduced by the London Electrotype Agency through the courtesy of the Illustrated London News. For Trav.'VNCORE see Appendix VII. CHAPTER XI Climbing Plants " Rally the scattered causes, and that line Which Nature twists be able to untwine." THE PURPOSE OF CLIMBING — WITH AND WITHOUT TENDRILS — HAND AND SPECIES — MR. G. A. B. DEWAR ON CLIMBERS — " FEELING " FOR SUPPORTS — INHERITANCE AND MEMORY — CIRCUMNUTATING — " SENSE ORGANS " FOR GRAVITY AND LIGHT — THE STATOLITH THEORY — INFLUENCE OF LIGHT AND MOISTURE — EFFECTS OF CLIMATE— REVERSAL OF SPIRALS. AMON(i the most interesting of all spiral developments in Nature are the phenomena of chmbing plants. Charles Darwin presumed that plants became climbers in order to reach the light, to expose their leaf surfaces to as much of the action of light and air as possible, and to do this with the least possible expenditure of organic matter. The divisions containing twining plants, leaf climbers, and tendril bearers graduate to a certain extent into one another, and nearly all have the remarkable power of spontaneously revolving. With those divisions which ascend merely by the aid of hooks, or by means of rootlets, we have little to do here, for they do not exhibit any special spiral move- ments, and their " mechanism " is by no means so perfect either as those which twine spirally round a support or as those endowed with irritable organs which clasp any object they touch. It is of these latter, therefore, that I shall chiefly speak ; and the development of tendrils or sensitive petioles may easily be imagined from the fact that plants which only twine may be more easily disturbed from their support than those which are assisted by the additional grasp of leaves or tendrils ; and it may be further noted that some twining plants need a stem of about 3 feet in length to ascend 2 feet in height, whereas, those plants which are assisted by clasping petioles or tendrils can ascend in more open spires (that is, with less expenditure in length of stem) , and often exhibit a spiral in one direction, then a portion of straight growth, and then a spiral in the other direction, all of which involves a definite saving in tissue. Dr. Wherry also thinks that the majority of climbing plants prefer to coil round upright supports and no longer climb actively if their support CLIMBING PLANTS 171 forms a smaller angle with the horizon than 45°. But the English translation of Pfeffer's " Physiology," which contains some useful records as to the thickness of supports, gives an angle for twining as low as 20°. A further distinction is that the twining plants (which are far more numerous than tendril bearers) wind round in a definite direction according to the species of the plant. The hop, for instance, invariably grows upwards in left-hand spirals (see Fig. 216) ; the majority follow the example of the convolvulus and exhibit right-hand twists (see Fig. 218). Fig. 211. Left-hand Lapageria ROSEA (Chili). Fig. 212. Right-hand Lardiza- BALA BITERNATA (ChILI) The various kinds of movements displayed by climbing plants in relation to their wants make it very difficult to accept the phrase " the power of movement " as a differentiation between plants and animals. The recent discovery of the continuity of the protoplasm through the walls of the vegetable cells by means of connecting canals or threads is another of the most startling facts in connection with plant structure, since it was held twenty years ago that a fundamental distinction between animal and vegetable structure consisted in the encasement of each vegetable cell unit in a case of cellulose, whereas animal cells, not being so imprisoned, could freely communicate with 172 THE CURVES OF LIEE one another. After this, it is less surprising that something closely corresponding to sense organs has been discovered on the roots, stems, and leaves of plants, which, like the otocysts of some animals, appear to be really " statocytes," and to exert a varying pressure according to the relations of these parts of the plant to gravity (" The Kingdom of Man," Ray Lankester). But before describing more in detail the scientific results Fig. 213. Left-hand Muehlenbeckia CHiLENSis (Chili). Fig. 214. Right-hand Wistaria iNvoLUTA (Australia). published by Francis Darwin and others concerning the phenomena of geotropism, I must direct attention to the observations of a well- known writer (ilr. G. A. B. Dewar) on some of the most curious phenomena noticeable in climbing plants. We have seen that ad\'ancing knowledge has made it more and more difficult to define satisfactorily the difference between plants and animals. The plants which feed on insects, such as the sundew, the hunts- man's horn, pitcher plant, the butterwort, the Venus' flytrap, have always been to me a standing instance of this difficulty. CLIMBING PLANTS 173 From them to the romances about man-eating orchids it seems but a shght step in imagination. But in the climbing plants an even commoner example of the kind of will power we usually associate with animals is observable. The way a wild hop strangled the roses in a garden that 1 knew in Fehxstowe presented an almost daily tragedy which could scarcely be dissociated from the relentless exercise of " conscious " power. Yet we Fig. 215. — Bryonia dioica. (H. C. Long.) know that it was not " conscious " ; we believe it to be without individuality, even without freedom ; certainly it must be more regular and enduring than any impulse guiding human conduct. Though shown in almost every leaf and root in May, this dumb passion of vitality seems specially developed in the climbing plants that strive and struggle upwards in the early summer. I shall paraphrase and shorten what Mr. Dewar says about them when I cannot quote in full, as I should like to do. He points out how the " fingers " of these plants feel towards each 174 THE CURVES OF LIFE other while they are still inches apart, with a sense of weird consciousness of a useful neighbour's presence, which can be neither hearing, sight, nor smell, as we understand those phenomena. The long, wiry-looking apparatus of the bryony points its fine tip at the neighbour it has discovered and wants to grip. Take away that neighbour and return a day or so later, and the feeler will probably be pointing somewhere else. " The blind, but in the end sure, search of the bryony trailer for support," he continues, " is one of the oddest sights I know. Sopping daj's and nights followed by hot sun will give the bryony great impetus. Yards of it will shoot up and writhe and coil about the woodland lane where a fortnight before not an inch showed above the ground. The bryony trailer when bald of leaves is one of those plants that wear an animal look. In some of the climbers one is almost oppressed by the look of half-consciousness, of a mind made up to coil and spire to the fore and top of the hedge at the cost of anything within reach ; even a look of watchfulness. Black bryony and bindweed are climbers that seem to advertise most publicly their fell purpose to grasp and smother their neighbours. " The tip of the bryony trailer has a kind of fanciful likeness to a snake. It is but a blossom in embryo, yet it might, by its appear- ance, be the most sentient part of a half-plant, half-animal. Its dark green, sometimes its bluish, lengths have a very snaky coil — they remind me of a viper reared up, wicked, ready to strike and to squirt poison. A most startling thing about the bryony trailer is when it adventures forth from a thin hedge — where, through close trimming in the autumn, there is now Httle support save grasses and small plants — feels out its path two or three feet over the lane ; and then, finding no cover within reach, turns back ! These adventures are often to be seen where bryony grows along the lanes. It is adventure with risks. Some passer-by may strike at the trailer with a careless stick or thoughtlessly give it a pluck with his hand ; or a cart wheel strike it down and cut it off ; and there is a wound that must take the bryony a week or two to cure. But if no further ill befall the trailer it will return to the hedge whence it came. " How it knows its search is vain in this direction we cannot tell. But know it must, for it will always return to shelter. Noticing this habit, is it strange we should be struck by a certain animality about this plant ? The bryony trader might be called a creature of green life. If it has no understanding of its own, what an appearance of under- standing is here ! . . ." Fig. 2i6. — Left-hand Spiral in Hops. CLIMBING PLANTS 175 Many observers will be inclined to add another instance of ' plant-intelligence " which shows that these curiously "conscious " movements are not limited to one part of the growing organism, for they have been observed in roots as well as in tendrils. There are authenticated examples of a vine's roots having got past (or round) an obstacle hke a brick wall in order to reach some special source of nourishment outside the greenhouse in which it originally grew. " The bryony," writes Mr. Dewar, " if not interfered with, returns to the hedge, I think, always in the same way ; it coils upward and round. It would seem as if it must be a great strain on the trailer to hold thus in the empty air. Every hour the weight upheld increases. But with increasing weight comes growing strength. . . . The ruthless power of these climbers and their mysterious inteUigence are worth all the study we can give tfiem. A series of exact trials with the bryonies and bindweeds might be of value. We want to know how far they can feel a neighbour plant ; and whether a plant of large bulk attracts them more than a plant of lesser bulk. It would be curious to try to cheat the bryony trailer ; on its return hedgeward, to fi.x a support in the ground just behind, so as to lure it back to the lane ; and then, if it turned back, to take away this support, and see if the chmber coiled round towards its parent hedge once more. " ' The mind of a plant ' — how our forefathers would have scouted the bare idea of such a thing ! The idea of a plant with any sensitive- ness, or feeling even, would have struck them as wholly absurd — somewhat as if one were to credit a pebble, say, with a desire for motion. Even now — with all our talk and theory about the wonderful devices of plants, their sensitiveness, the knowledge their roots often seem to have as to the best paths to take for food and sure hold — the mind of a green thing is something we can only half imagine." Let us see if we can " imagine " it a little better to-day. In his lectures on " The Physiology of Movement in Plants " (see " New Phytologist " Reprints, No. i), Francis Darwin suggests that if, in these questions, we are to reach a point of view which is physiologically valuable, we must reject the barren logic of Descartes and retain the idea of spontaneity in Dutrochet : " What we do at a particular juncture depends on the nature of our previous experiences and actions. The ' self ' which seems to be spontaneous is the balance which weighs conflicting influences. It is for this reason that even in plant physiology we want the idea of an individuahty, of a something on which the past experience of the race is written and in which the influences of the external world are weighed. I do not, of course, imply conscious weighing, nor do I mean that the plant has memory in the sense that we have memory. But a plant has memory in Bering's and S. Butler's sense of the word, according to which memory and inheritance are cUfferent aspects of the same quahty of hving things. Thus in the movements of plants . . . the individual acts by that unconscious memory we caU inheritance." 176 THE CURVES OF LIFE This is not the place in which to introduce those cumbrous forms of scientific nomenclature in which specialists usually dehght to communicate their researches to one another. But, looked at in another way, these curious words may be considered as a con^'enient form of shorthand in which a few syllables — however barbarous they sound — may express a meaning which often needs a lengthy sentence in ordinary language. It will, therefore, not be foreign to our methods if I group all cases in which a plant is stimulated by the force of gravity under the one heading of geo-pcrccpfion. There is also a useful suggestion of the same kind quoted by Francis Darwin from the new edition of Pfeffer's " Physiology." He divides all reactions into two classes : fi) Autogenic effects, usually called spontaneous, such Fig. 217. Fig. 21? schueerti.-i- physianthl's. convolvulus arvensis. Both showing right-hand spirals. as the jerking of the leaflets of Desmodiuni ; (2) ,'Etiogenic actions, performed at the suggestion of agents such as gravity, light, contact, and the like. But it is evident that, though such a classifrcation is necessary, it is not always possible to distinguish between the two classes, and, in fact, the distinctions between them may often be of less importance than the bond of associa- tion which may be found to unite them. It was, for example, the thesis of " The Power of Movement in Plants " (Charles and Francis Darwin, 1880) that the autogenic power of circum- nutation is the basis from which the varied eetiogenic curvatures have been evolved ; and obviously this assimilates Pfeffer's classes rather than differentiates them. It also reminds me to add to these " definitions" that of ciicmnniitation, intro- duced in the volume just quoted. This is the most widely prevalent movement in plants. The authors described it as CLIMBING PLANTS 177 •' essentially of the same nature as that of the stem of a chmbing plant, which bends successively to all points of the compass, so that the tip revolves. . . . Apparently every growing part of every plant IS continually circumnutating, though often on a small scale ... in this universally present movement we have the basis or groundwork Fig. 219. — Spiral Tendrils of Gourd. (Photographed at Wimbledon Park by R. N. Rose.) for the acquirement (according to the requirements of the plant) of the most diversified movements." The sentence just quoted was published in 1880, long before the discoveries in vegetable structure to which I alluded earlier in this chapter had been made. In 1906 Francis Darwin (who assisted Charles Darwin in " The Power of Movement in Plants ") pubhshed in the New C.I. N 178 THE CURVES OF LIFE Phytologist a paper describing the sense-organs for gravity and light with which it is now known that plants are provided ; and it should be pointed out that Francis Darwin is here using the phrase "sense-organs" in the same way as Haberlandt (iQOi) used " perception-organs," namely, as " ah those morpho- logical or anatomical contrivances which serve for the reception of an external stimulus, and exhibit a more or less far-reaching correspondence between structure and function in this respect." L et me now, therefore, give a slight sketch of those organs which in plants are connected with the phenomena of geoiropism, or the influence of gravity, and of hcliotropism, or the influence of light. In the case of geotropism our first question is, how the plant is able to " perceive " that it is not vertical. For instance, if a plant, growing verticafly from a pot on a table is turned through an angle of go° until its main axis becomes parallel to the level surface of the table, it is obvious that certain new strains or compressions (jf tissue will occur which might stimulate geotropism. But these are not its only means of geo ])erception, because some plants are recognisably geotropic even when supported throughout their whole length. It is neces- sary, therefore, to find some other workable hypothesis, and the famous statolith theory supplies it ; for, by this theory, the stimulus causing the move- ments of the plant being due to the difference in the specific gravity of certain parts of the cell, the heavy bodies thus implied are, in fact, the specialised form of starch grain described by Haberlandt and Nemec. These grains, or " statoliths," lie freely in the cell and gravitate towards the physically lowest region. " Thus," writes Francis Darwin {op. cit.), " in a vertical cell the pressure of the statoliths will be on the basal wall. When the cell is placed horizontally the starch will fall away from the basal wall (which is now vertical) and spread out in the lower lateial wall. In this way it is imagined that the pressure of starch grains on the different parts ot the cell walls serves as Fig. 220. — Smilax. CLIMBING PLANTS 179 signals informing the plant as to its angular position in space." As the same writer points out, it is important to notice that the method of orientation thus suggested in plants does undoubtedly occur m animals, for in the case of the crustacean Palcemon It has been proved that the power of orientation in regard to the vertical is dependent on the presence of the statohths (or otoliths) on the internal surface of the otocyst. And since our theory suggests a function of the falling starch that occurs in the endodermis, it is further of importance to notice that the ■W£». Fig. 221. — Passion Flower. starch is only found here as long as the organ is growing ; in fact, as long as it is susceptible of geotropic curvature. Again, monocotyledons, in whose leaves starch does not occur, do possess falling starch in the endodermis, and therefore enjoy geo-perception ; whereas Viscum and other plants which have lost the power of geo-perception, either entirely or in certain parts, do not possess falling starch in those parts or in the whole plant respectively. Recent research has rather strengthened than invalidated this hypothesis since 1904. Turning now to Heliotropisni, we find, from the work of Francis Darwin and others, that leaves have the power of placing them- N 2 iSo THE CURVES OF LIFE selves at right angles to incident light, and that this is effected by appropriate torsions and curvatures (see Figs. 139 and 140). Probably the act of perception in these cases would be performed by the leaf-blade, while the movement would be confined to the stalk. Haberlandt has disco^•ered the existence (in the epidermis of the leaf blade) of a primitive eye, consisting of a lens and a sensitive protoplasmic membrane, on which the light is focussed. \Mien the leaf is horizontal under a top light (in what may be called a position of equilibrium) a spot of light is thrown on the basal cell wall. When the leaf is subjected to obhque light the direction of this illumination is changed, and in each of the epidermic cells the bright spot on the basal wall will no longer be central. The stimulus thus provided tends to move the leaf until it becomes once more at right angles to the light and a con- dition of equilibrium has been restored. The various proofs of the existence of this process are too technical for insertion here, but I must at least give one of the most striking, which is that when a leaf, previously orientated by these " eyes," is submerged in water, the refraction of the lens is altered ; the plant, in fact, is " blinded," and unable to orientate itself as before. In those " velvet " leaves, in which the epidermic cells project as papillae above the general surface, this form of epidermic cell serves to prevent the leaf being " blinded " by the continuous rain of the regions where the plants in question chiefly occur. One very interesting feature may be noticed which this hypo- thesis has in common with the statolith theory just previously described. In both cases the directive element in the mechanism depends on the stimulus being apphed to certain regions of the protoplasm lining the cell walls. The organ " recognises," as it were, that it is not vertical (in one case) or that it is not at right angles to the light (in the other case) by the fact that a definite change has occurred in the position of the region receiving the stimulus. In Science Progress for January, 1912 (John Murray), Dr. J. B. Farmer, F.R.S., states his opinion that " the mecha- nisms concerned directly in producing movement aU depend upon alterations in the distribution of water " in the moving plant. This is a generahsation which has still to be proved correct for all instances, and while it may explain the mechanical process of a given movement, it does not, I think, explain the cause or stimulus which leads the plant (if I may so put it) to " think " such movement " necessary." Dr. Farmer expresses a very natural surprise that the numerous investigations in regard to the response of living protoplasm to external stimulus have added so little to exact knowledge, and, he adds, " this CLIMBING PLANTS i8i IS even true of the rhythmic movements frequently met with m growmg plants, which are not referable to any stimulating agent that can be detected readily." He mentions some move- ments due to hygroscopic change such as have been already described m previous pages, namely, those depending on the imequal expansion or contraction which occurs in the cell walls of the different parts of the motile organ, as in the instance of the valves of the gorse-fruit, which suddenly curl up and eject the seeds ; or the curious and somewhat similar action of the Fig. 222. — Virginia Creeper. cruciferous plant Anastatica, known as Rose of Jericho ; or the strangely little known phenomena concerned with the warping of timber, which is due to structural conditions involving an unequal capacity for swelling in a given direction possessed by different elements in the tissue. Perhaps his most interesting example is taken from the elaters found mixed up with the spores of most liverworts, structures which may be described as eel-like cells, pointed at each end, and possessing one or more band-like coils of spiral thickening on the inner surface of their otherwise thin membranous walls. When the moist elater gradually dies, these membranous parts of the walls sink I82 THE CURVES OF LIFE inwards until, quite suddenly, the elater twists up and immedi- ately straightens itself again with a violent spring-like movement, jerking the spores out of their capsule. Difficult as it is to explain movements due to the complex interaction of conditions in the living protoplasm, it is, as Dr. Farmer points out, no less comph- cated a problem to discover, even in more purely physical or mechanical processes, the secret of their adaptedncss to those functions which they are so well fitted to discharge. But we are gradually approaching a solution of a great many of such -,..;j Fig. 223. — Vine. problems, and every year's research is bringing greater know- ledge. If we combine these modern theories with Charles Darwin's earlier " circumnutation," and with the recent discovery of the continuity of protoplasm through the walls of vegetable cells, as is the case in animal structure, we shall arrive at a better understanding not only of those exquisite spiral formations which result from the movements of the climbing plants illustrated in these pages, but even perhaps of those questions which Swinburne asked so beautifully of the simdew ; ~ ' CLIMBING PLANTS 183 "... how it grows, If with its colour it have breath, If life taste sweet to it, if death Pain its soft petal, no one knows : Man has no sight or sense that saith." All the hedge climbers suggest to Mr. Dewar the idea of " an intelligence of the body. They suggest it," he concludes, " as much as the httle round-leaved sundew, Drosera, which we found in Blackmoor Forest with yellow asphodel. But their Fig. 224. — Ampelopsis. methods of climbing often differ widely. Black bryony is a python among plants ; it coils its cruel body round and round the victim. So does woodbine. The red bryony, as we see, steadies itself in quite another manner — a fine-pointed, twisting feeler on one side, a corresponding one on the other side. Clematis economises ; the little stalk that holds the leaf must here and there twine about a neighbour to help steady and uphold the whole plant, though how it is decreed that this stalk or petiole shall twine, and that one not twine, we do not know. Does chaos or chance decide it ? If so, it looks as if there must be some effective 1 84 THE CURVES OF LIFE ruling principles in chaos, or clematis could never be steadily reared and held in position at the hedge-top." In previous pages I have given a description of some of the twining plants specially investigated by Charles Darwin, and I specified a certain number of those which twine to the left instead of to the right, together with the speed of their respective revolutions. Every part of a revolving shoot in a climbing plant has its own separate and independent movement, described by Sachs as " revolving nutation " and by Darwin as " circum- FiG. 225. — Black Bryony near Hammam Rhira, in the Atlas Mountains of N. Africa, 2,000 feet above the Sea. This branch turned completely round upon itself in twenty-four hours. nutation," a movement which appears to be due to the more rapid growth of cells on one aspect or edge than on the other, which makes a curve in the shoot, and rotates it, as the growth alters and alternates. The result of this is that when a revolving shoot meets with a support, its motion is arrested at the point of contact, but the free projecting part goes on revolving. As this continues, higher and higher points are brought into contact with the support and there arrested, and thus the shoot winds round, just as a swinging rope which hits a stick coils roimd the stick in the direction of the swing. " Irritability " has nothing, therefore, to do with these phenomena. The shoot twines round CLIMBING PLANTS 185 Its support rather more slowly than it would revolve by itself (the difference being about i^ to i), owing to the continued disturbance of force by arrestment at various points. But when the shoot has made its first, close, firm spiral, it slips up the support in more open spirals, because it is freed from the pull of gravity. In the hop it will be noticed not only that the plant coils to the left round the support, but that the very tissue of the plant itself shows a strong left-hand twist, as though there had been continual torsion in the true axis of the growing stem. Charles Darwin showed that the axis is twisted, in all such cases, owing to the roughness of the usual natural support, which is strongly clasped by the rough, glutinous surface of the hop shoot. When some kidney beans were trained up smooth glass rods they showed scarcely any torsion at all. No doubt this twist provides an additional strengthening of the fibre, which enables Fig. 226. — Diagram to Show the Movements of a Climbing Plant. the plant to surmount inequalities. There must be some con- nection between axial twisting and the capacity for twining, and the stem gains in rigidity by the process much as a well-twisted rope is stiffer than one which is slackly twisted. The spiral twist in the horns of goats and antelopes and on the columella of certain shells may be another instance of the same strengthening process. In Chapter VII. I gave a list of seventeen climbing plants which twisted clockwise, following the sun, or (as I describe it) in left-hand spirals, out of a total of sixty-five examined ; the remainder twined to the right. Among these I illustrated the right-hand spiral of Teconia and the left-hand spiral of honey- suckle in Chapter II., while the left-hand growth of Polygonum baldschuanicum (Bokhara) was contrasted with the right-hand spiral of Afios tuberosa in Chapter I. In the present chapter, drawings are given of the left-hand curves of Lapageria rosea, with the right-hand growth of Lardizabala biternata (both i86 THE CURVES OF LIFE from Chili) ; also of the right-hand spirals of Wistaria involuta (Australia) with the left-hand twist of Mnehlenbeckia chilcnsis ; and, lastly, of the typical right-hand growth in Convolvulus arvensis or of Schiihertia physianthtis contrasted with the strongly left-hand formati<.)n both in growth and fibre of the hop. I need not multiply any further instances, for my readers will now be able to examine many more for themselves. I shall only emphasise again the curiously different rates of speed at which these various plants revolve, and add that in this climate, where twining plants die down every year, they would never have time to reach the sunlight if they climbed up large trees more than 6 inches in diameter, and so they very rarely try to do so, though one has been observed to get round a column of 9 inches in diameter at Kew. In tropical countries, of course, twining plants often ascend very large trees and flourish happily while doing so. Solanum dulcaniaia, on the other hand, can twine round a support only when this is as thin and flexible as a string or thread. It may also be noted that in some cases the lateral branches twine, and not the main stem {Taintis clephantipes) ; in others it is the leading shoot which twines, and not the branches (a variety of Asparagus). In different cases, again, some shoots re^'olve and others do not ; and, lastlv, some plants never show any inclination to twine at all till they are some distance from the groimd. A different class of climbing plant is that which possesses " irritable " or sensitive organs. Of these the leaf-climbers ascend by means of clasping petioles or by the tips of their leaves, and some few can ascend by twining spirally round a support, showing a strong tendency, in the same shoot, to revolve first in one direction and then in the opposite. But it is the tendril bearers which will be of more direct interest here. Tendrils are filamentary organs sensitive to contact, clasping any object they touch, and used exclusively for climbing. These can grow horizontally, or up and down, in distinction to those twining plants which can only coil themselves round and climb up supports that are almost upright. Whereas these latter always go round a stick in the direction of their own revolving movement of growth (which may be either to the right or the left, as we have seen), tendrils can curl indifferently to either side, according to the position of the supporting stick and the side first touched, the clasping movement of their extremity being undulatory or vermicular. The tendrils of all tendril-bearing plants contract spirally after they have caught an object— with about four exceptions, of which Smilax aspera is one ; and this contraction, says Charles Darwin, is quite independent of that power of spon- CLIMBING PLANTS 187 taneously revolving which is observable (by " nutation ") in the apex both of the shoot and the tendril ; for Ampclopsis hederacea does not revolve at all. The use of the spiral contraction of a tendril is to drag up the shoot by the shortest course towards the object clasped without any waste of growth. This same spiral contraction also makes the tendrils highly elastic, and there- fore stronger to resist the wind, so that the bryony, for example, will outride a storm like a ship with two anchors and a long range of cable that serves as a spring. In the bryony (see Fig. 215) a filiform organ grows out from the plant, as Dr. Wherry observed, and becomes " irritable " in such a fashion that, while revolving at its free end exactly as if groping for a prop, when this free end touches a twig it coils round it at once. The coiling tendril then develops a corkscrew spiral twist in one direction in one part, and in another direction in another part, with a short straight portion between. This reversal of the spirals after fixation sometimes occurs only once, sometimes as much as seven or eight times, but the number of times it appears in one direction is nearly always equal to the number of times in which it appears in another. The reason for this is to be found in the mechanical necessity for preventing excessive torsion. We have seen that a twining plant, as it binds its spiral curve round a support, develops a spiral twist also. This twining involves a twisting of the axis in the same direction which, if persisted in for too long in the same direction, would ultimately burst the tendril. But if nearly as many turns are subsequently taken by the spiral in the opposite direction, the strain involved by the twisting of the axis is removed. The best example of this double twist I have been able to find is to be seen in the tendrils of the gourd shown in Fig. 219. This curious and symmetrical structure is usually observable only when a tendril has caught and clasped a support. The firm, springy attachment created by the double spiral has only to be seen to be appreciated. I should add that the late Professor Pettigrew recorded a spiral tendril of cucumber showing " a basal coil of three turns, a reversal, a coil of three turns, a second reversal, a coil of five turns, a third reversal, a coil of four turns, a fourth reversal, and an apical coil of five turns. This tendril had clasped a cucumber leaf by its basal and central portion, its apical portion being quite free." This would indicate that, for the production of a reversed spiral, it is not always necessary, as Darwin and Sachs seemed to think, for the tendril to be fixed at each end. The Ampelofsis (Virginia creeper. Fig. 224) shows a sympodial shoot system, and has no true spontaneous circumnutation, but i88 THE CURVES OF LIFE only a movement of the internodes from light to dark. The tendril will " arrange " its branches so as to press on a given surface, and then the curved tips swell and form on their under- sides the little soft discs by which they adhere firmly, and even- tually pull forward the growth behind. An attached tendril contracts spirally, and thus becomes so highly elastic that when the main stalk is in any way disturbed the strain is equally distributed among all the discs. The vine has a similar sym- podial shoot system, in which the tendrils (as in the passion flowers) are modified flower peduncles, quite thick, and, in vigorous growths, as much as i6 inches long. They are some- times branched, and their beauty has often attracted the notice of the poet, as when Milton wrote of Eve's hair : — "... in wanton ringlets waved As the vine curls her tendrils." Taking the tendril bearers, and the most efficient of them, as an example of that " mind " in plants which I ventured to sug- gest at the beginning of this chapter, we can now realise how high in the scale of organisation such a plant may rightly be placed, and I cannot do better than conclude with Darwin's summary on the subject of the tendril bearing plant, which is as follows : — " It first places its tendrils ready for action, as a polypus places its tentacula. If the tendril be displaced, it is acted on by the force of gravity and rights itself. It is acted on by the light and bends towards or from it, or disregards it, whichever may be most advantageous. During several days the tendrils, or internodes, or both, spontaneously revolve with a steady motion. The tendril strikes some object, and quickly curls round and firmly grasps it. In the course of some hours it con- tracts into a spiral, dragging up the stem and forming an excellent spring. All movements now cease. By growth the tissues soon become wonderfully strong and durable. The tendril has done its work, and done it in an admirable manner." I could have chosen few better examples of the utility of the spiral formation in Nature. NOTES TO CHAPTER XI. Fig. 225. — When kindly sending this very interesting picture Mr. C. A. B. Dewar wrote ; — " You were good enough to quote some of my observations on the black bryony. " I now send you a photograph of a specimen {Tamus communis) CLIMBING PLANTS 189 which I observed in the Atlas Mountains, where it is very abundant, in March, 1912. This shows (Fig. 225) how the bryony made a sort of expecHtion towards an asphodel plant, changed its mind, and turned back again. The plant was within a foot of the asphodel when I first saw it, pointing straight at its head. The next day it had evidently concluded the asphodel was useless or unfriendly, for it had turned right round upon itself." CHAPTER XII The Spirals of Horns "Judge between the rams and the he-goats," — Ezekiel. PAIRS OF HORNS — ODD-TOED AND EVEN-TOED HOOFED ANIMALS — THE ANGLE OF THE AXIS IN HORNS— SUGGESTED GEOMETRICAL CLASSIFICATION — DISTINCTIONS BETWEEN HORNS OF WILD ANIMALS AND OF TAME — HOMONYMOUS HORNS — " PERVER- SION " AND HETERONYMOUS HORNS— COMPARISON WITH OTHER SPIRAL GROWTHS, AS OF PLANTS AND SHELLS- EXCEPTIONS TO DR. wherry's RULE— TAME ANIMALS SHOWING TWISTS OF THEIR WILD ANCESTORS DEVELOP MENT OR DEGENERATION ? — THE PROBLEM STATED. In most cases where natural objects occur in pairs they may be described as right hand or left hand respectively ; in fact, Fig. 227. — Diagram of the Axes of Horns. the ordinary use of the word " pair " imphes this ; for when we speak of a " pair of gloves " we do not mean two right hand or THE SPIRALS OF HORNS iqi two left hand gloves, but two gloves of which one is for the right hand and the other for the left. So the horns of animals are as properly " pairs " (except in the case of the rhinoceros) a? Fig. 22S. — Straight Twists. Sir George Roos Keppel's Suleman Markhor, Capra falconeri jerdoni (W and L'). Length (straight) 37 inches, girth 10 inches, tip to tip 32 inches. (Shot in the Kurram Valley, 1905.) This photograph is repro- duced by the courtesy of Country Life and Mr. C. E. Fagan. their legs, their ears, or their eyes, and can just as correctly be divided into right and left. That division (apart from their position on the animal's head) is usually indicated by the direc- tion of the spiral curve or spiral twist exhibited by the horn 192 THE CURVES OF LIFE under examination. I know of no instance in which this rule would not hold good. But there is the very rare case of the narwhal with two tusks (not horns), which are not twisted in a right-hand and a left-hand spiral respectively, for each shows the same left-hand spiral. They are not, in fact, a natural " pair " in the sense in which we speak of a pair of boots. Fig. 22g. — Curved Twists. The Marquess of Lansdowne's Gilgit Markhor, Capra falconeri typicus (R-' and L^). Length (curve) 57 inches, girth gf inches, tip to tip 38 inches. (Shot near the Hunza-Nagar Valley about 1891.) This photograph is reproduced by the courtesy of Country Life and Mr. C. E. Fagan. The horns of the rhinoceros, which belongs to the odd-toed series of hoofed animals, have no bony horn-core, and consist entirely of that fibrous structure of hairTike growths called " keratin," the same substance composing claws, nails, hoofs, and hair. The horns and antlers of those even-toed hoofed animals forming the " Pecora," may be classified in three divisions, and are essentially a bony outgrowth of the skull. The first division, and the most primitive, are those of the giraffe, they are present THE SPIRALS OF HORNS 193 in the unborn young in the frontal region of the skull, and remain covered with skin and hair through life. The okapi's horns, however, grow from the frontal region of the skull as conical Fig. 230,— Twisted Curves (Perversion), Pallas's Tur (Capra cylindricornis pallasi) . R'< and L'' in Fig. 227 showing the axis above the Une EF and outside the triangle BCX. This is the geometrical perversion of the curves shown in Fig. 231. (Drawn from p. 385 of Rowland Ward's " Records of Big Game." Sixth edition, 1910.) Shot in the Caucasus by Prince E. Demidoff. bones, the sharp points projecting slightly from the skin to form better fighting weapons. Secondly, the antlers of deer are bony outgrowths from the frontal region ; they usually become forked Fig. 231. — Twisted Curves. Head of Wild Sheep of the Gobi Desert (Ovis ammon mongolica), the Property of Colonel J. H. Abbot Anderson (R'' and L'). or branched ; the soft, velvety skin which covers them dies off, and every year the old antlers are shed and a new pair are grown. The reindeer is the only instance in this division in which the C.L. O 194 THE CURVES OF LIFE females have antlers like the males. The third division, with which we are chiefly concerned here, is that in which a hollow sheath of keratin (which can be removed after death) is formed to cover the bony horn-core in both males and females. This remains permanent, being added to year by year from below as growth advances, and is, therefore, never branched or forked, except in the case of the American prong buck [Antilocapi-a .'■^^'■■.,;^^•^'■ Fig. 232. — Merino Ram (R' and 'L'). americana) which sheds its horn-sheaths every year, and thus forms a remarkable link between the second and third divisions. It is with the sheath-horned group (comprising antelopes, sheep, goats and cattle) that this chapter chiefly deals, and I will begin by suggesting a simple method for classifying the spiral formations they exhibit. The diagram in Fig. 227 (p. igo) is formed in the following manner ; Draw a horizontal line EF. Bisect it with the perpendicu- FiG. 233. — Tibetan Argali (Ovis AMMON HODGSONi). lar line DX. At equal distances on each side of the point of bisec- tion take the two points B and C, so that the shaded triangle BCX shah roughly represent an animal's face, X being the tip of the nose and BC the top of the skull. From the point X draw the hues R' and L\ which pass inside the triangle, and the lines R- and L", which pass outside the triangle ; these lines will represent the axes of horns which exhibit a twist (Fig. 228) ro a curved twist (Fig. 229). From the point in the base of the triangle where the perpendicular DX bisects the horizontal THE SPIRALS OF HORNS 195 EF, draw the lines R^ and L^ which pass outside the triangle, and the lines R* and V, which pass inside the triangle : these hnes will represent the axes of horns which exhibit twisted curves, such as those drawTi in Fig. 230 (R^ and L^) or Fig. 231 (R' and L'). The order in which the horns are mentioned in this geometrical classification would, of course, only correspond with their develop- ment in Nature on a theory of gradual deteriorations. But 1 shall discuss the theory of improvements first ; and, according to this, it might plausibly be suggested by anyone who had con- sidered the origin and growth of the various spiral formations illustrated in previous chapters, that the type of horns seen in Ovis amnion hodgsoni, the Tibetan Argali which is drawn in Fig. 233, or in the merino ram shown in Fig. 232, was the ances- tral type of horns, exhibiting both the essential curves we have seen in other organic spiral growths and the twisted surfaces which usually accompany and strengthen such curves, as was noted in the case of the growing hop. We can now carry this hypothesis a little further by supposing that the wild horn- bearing animal found his horns more useful to him when the tips were elevated, and the only way in which the tip of such twisted curves as those shown in Fig. 231 could be elevated is clearly seen in the horns of Pallas's tur (Fig. 230), which exhibit what is called a " perversion " of the usual spiral. This " perversion " I shall explain more fully later on. For the moment I need only point out that it does not exhibit the change expressed by the difference between a right- and left-hand spiral, but shows that a right-hand and a left-hand spiral can each be constructed upon different plans. Continuing this hypothesis of develop- ment, I may now suggest that, just as the twisted curves of Fig. 231 (represented in the diagram by R'* and L'') have had their points hfted to R' and L^ as shown in Fig. 230, so these latter may be imagined to be still further hfted into the position of R- and L", and thus to lose their essential character of curves and to become the curved twists of the Gilgit markhor in Fig. 22g. Here I must interrupt the argument for a moment to refer to Tragelaphus angasi in Fig. 234, which shows that the Gilgit markhor is far from being alone in exhibiting horns which retain the possibility of a spiral curve in spite of being essentially a spiral twist. Take this antelope's left horn at its point of origin, C. The line from C to A might easily have developed into the flat spiral curve CAB, instead of growing into the conical spiral twist CAD. The same possibihties are observable in the Lesser Kudu (Fig. 235) and the Situtunga (Fig. 236). There is fortu- nately a most interesting corroboration of this theoretical curve (CAB) to be found in the Hume CoUection in the British Museum o J- 196 THE CURVES OF LIFE (Natural History). Number 66 in that collection shows the heteronymous twists of the male Blackbuck's horns (CAD), and number 69 shows the homonymous curves (CAB) in the horns of the female. Mr. Lydekker kindly pointed out these heads to me after my diagram (Fig. 234) had been printed. But if we follow out the theory that the points of horns have been gradually lifted from those shown in the wild sheep to those of Pallas's tur, and higher again to those of the Gilgit markhor, we eventually reach a position in which all trace of curves disappear. In the upright horns of the Suleman markhor in Fig. 228, we see the eff^ect on growth of axes placed at the angle of the lines R' and L' in the diagram printed on p. 190. These horns exhibit a Fig. 234. — Nyala (Tragelaphus angasi), showing Horns Beginning in a Flat Spiral Curve CAB, and Ending IN a Conical Spiral Twist CAD. twist of a remarkably uncompromising nature, and one that is especially adapted for fighting or for pushing through a thick growth of plants. I may add in conclusion that it seems rather more difficult to derive the curves of a merino ram from the corkscrew twists of Capra falconeri Jerdoni, whereas, the series I have suggested is at least a mechanical possibihty on the lines laid down. I will discuss the reverse order later on. If the order of development now suggested were correct, several interesting deductions could be made concerning the forms of horns shown in various animals. If, for instance, the twisted curves of Ovis ammon hodgsoni were indeed the beginning of such a series as I have described, it would be only likely that this formation would be improved by wild animals which had to fight for their living or their mates, and that it would survive THE SPIRALS OF HORNS 197 only in animals whose welfare largely depended on human mterference. It may also be significant in this connection that when the change in the elevation of the points is noticed in wild animals which exhibit these curves, that change seems Fig. 235. — Lesser Kudu (Strepsiceros imberbis). Shot by Mr. G. Blaine. (Somaliland, igog.) often to accompany a difference in breed, as in Capra cylindri- cornis compared with the merino ram, or as in the Sind wild goat (Fig. 244) as compared with the Alaskan bighorn, Ovis canadensis dalli (Fig. 48, Chap. II.). On the other hand, it 198 THE CURVES OF LIFE would be difficult to say why Ovis amnion poli (Fig. 20, Chap. I.) or Ovis ammon hodgsoni (Fig. 233) exhibit the ordinary curves of the merino ram (Fig. 232), whereas, Animotragns Icrvia (Fig. 241), Ovis oricntalis (Fig. 242}, and Psciidois naJiura (Fig. 243) all exhibit the rare perversion typified in Capra cylindricornis. But when we follow the development of the raising of the horn's tip from Capra cylindricorms (Fig. 230) to the Gilgit markhor, and even more markedly to the Suleman markhor (Fig. 228), we cannot fail to observe that the raised tips of the perversus variety are associated with wilder breeds, and are evidently more useful to animals which fight for their living than such peaceful ornaments as are worn by the domesticated merino ram. In fact, the domestic horned animals would perhaps (on this theory) have died out but for man finding them useful enough to be preserved. Another very curious fact concerning the development of both curves and twists is that when domestic animals show the twisted horns which have just been associated with wild animals, these domestic varieties exhibit (with one exception) a wholly different form of twist from that worn by wild animals. Homonymous horns (as defined by Dr. Wherry) are those which exhibit a right-hand spiral on the right side of the head and a left-hand spiral on the left side of the head, as may be seen in the Highland ram shown in I. on Plate III. on the opposite page, or the ordinary Mouflon of Fig. 237. It will be noticed at once that when horns show twisted curves of this kind (which may be compared with Figs. 20, 48, 232, 233, 237), it is physically impossible for them to exhibit any other formation than that described as homonymous. This can be easily proved if you transfer the curve AB (shown in I. on Plate III.) from the right side of the head to the left, as is done above the Mouflon's head in II. on the same Plate. It would obviously grow into the creature's back and be quite useless to it. The only difference possible in these homonymous curved horns is the " perversion " exhibited by the horns of the Red Mouflon (shown in II. on Plate III.), " twisted the wrong way for a ram's," as Billy Priske said when he met the Corsican " Mufro " in Ouiller Couch's " Sir John Constantine." As I shall explain later, these " perversion " curves are by no means the hetero- nymous curves, CD and AB, drawn just above them for the sake of contrast in II. on Plate III. They are examples of the raised tip shown in Capra cylindricornis (Fig. 230) and in the similar formations drawn in Figs. 241, 242, 243, 244. These formations are just as " homonymous " as the horns of the Highland ram, but their right and left-hand spirals respectively are of a dii^erent character. Plate III. I. Highland Ram. (Homonymous curves.) n. Mouflon. (Homonymous perversion.) III. Markhor. (Heteronymous twisted curves.) IV. Angora Goat. (Homonymous twisted curves.) 200 THE CURVES OF LIFE But in the case of twists and curved twists, Dr. Wherry's distinction is of vital importance ; for the curious fact emerges that in all existing antelopes and wild goats the twisted horns Fig. 236. — SiTUTUNGA (Tragelaphus spekei). Shot by Mr. G. Blaine. (N.E. Rhodesia, 1903.) show heteronymous formation, the right-hand spiral twist being on the left side of the head and the left-hand spiral twist on the right side of the head, as in Fig. III. of Plate III., or in Figs. 235, 236. And since the direction of a twist on a fairly THE SPIRALS OF HORNS 201 upright axis does not possess any structural importance with reference to the rest of the animal's anatomy, we might expect to find the homonymous formation as well, in which the right- hand spiral twist is on the right side of the head and the left- hand spiral twist is on the left side of the head. But this homonymous formation is (with one exception) found in domestic animals only (see Fig. IV. in Plate III.), and I know of no instance of it (in twists) in living wild animals. Though Dr. Wherry does not connect homonymous horns with domesti- city except as a distinction between wild antelopes and domestic sheep or goats, the hypothesis, just stated, that the ancestral form of spiral twists was that now shown by domestic animals, involves its natural development from such homonymous curves Fig. 237. — Sardinian Mouflon (Ovis musimon) in the British Museum. Shot by F. G. Barclay. Showing the usual homonymous curves. (Drawn from page 214 of Rowland Ward's " Records of Big Game." Sixth edition, 1910.) as those worn by the Highland Ram ; and if so, we might then conclude that, unless man had intervened, those animals which grew homonymous twists would have died out, whereas, those animals which survived were obliged to develope heteronymous twists, in order to fight better or to throw off thick herbage and undergrowth as they ran through the jungle with their chins forward and their horns flat back upon their shoulders, acting like a wedge and forcing aside the overhanging branches by the screw-like action of the grooves. These strongly marked grooves are particularly noticeable in the Senegambian Eland shown in Fig. 238, and the screw hke formation is well exhibited in Figs. 228 and 229. All three, hke the Lesser Kudu, and the Situtunga (shown in Figs. 235, 236) are examples of the heteronymous spiral twists characteristic of antelopes 202 THE CURVES OF LIFE and wild goats. The formation may be admirably studied in the biggest of the Bushbucks, the Bongo (Booccrciis euiyccros), I'lG. 23S. — SiDAN Dereian Eland (Taurotragus derbianus gigas). Shot by Mr. G. Blaine. (Bahr-el-Ghazal, 1910.) Showing the heteronymous twists cliaracteristic of wild animals, as in Figs. 235, 236, and 248. the record head of which was shot by G. St. G. Orde Browne, in the Man Forest of British East Africa. The horns measure THE SPIRALS OF HORNS 203 39i inches over the curves and 32I inches in a straight line along the axis, with a spread of i6| inches from tip to tip, and a girth of iii inches at the base. The more formid- able of the hornless animals possess not only tearing claws, but also those sharp canine teeth which are never found in horned animals unless (as in the case of the little Indian muntjac) the horns are quite small and simple. This may indicate that such weapons as the horns in Fig. 238 are an efficient substitute ; and I suggest that heteronymous twists would be more advan- tageous than any other formation. In Fig. IV. of Plate III. the homonymous twists of the domestic Angora goat are clearly depicted. You see the same homonymous twists in the Tibetan shawl-goat (Fig. 239), the common domesticated goat (Fig. 247), Fig. 239. — Tibetan Shawl Goat. Showing the homonymous twists characteristic of tame goats. and the Jamnapuri goat (Fig. 246). All these latter are domestic varieties, and I can add a pleasing example (by the kindness of Mr. Lydekker) of the accuracy of the ancient Egyptian artist, who recognised, some 4,000 years before the birth of Dr. Wherry, that the domestic, long-legged sheep of Egypt exhibited the homonymous formation in the twists of their horns (Fig. 240). The gradual improvement, therefore, suggested by our first hypothesis may be tabulated as follows : — I. Open forward curves (Fig. 231), in which the surfaces are necessarily twisted. Always homonymous. II. Open curves with points raised higher (Fig. 230) [pcrveysu^), in which the surfaces are also twisted. Always homonymous. III. Open twists, either of the form of Fig. 229, or as shown in Figs. 235 and 236, which seem the natural transition from II. to IV. As a rule, homonymous in domestic (Fig. 246) and heteronymous in wild animals. 204 THE CURVES OF LIFE IV. Close twists (Fig. 228), as a rule homonymous in domestic (Fig. 250) and heteronymous in wild animals. It should be understood that this lirst theory of development apphes rather to the form of the horns than to the animals wearing them ; and the reverse theory is possible. In Plates IV. and V. I have placed a few more diagrams to make a little clearer what has been said concerning the \'arious formations and the suggestion of classifying them. Possibly those of my readers who have been good enough to follow me through the eleven preceding chapters will be much more likely to imagine an explanation for the various forms of horns than Plate IV, — Diagrams of Twists and Curves. I. Tendril of climbing plant changing the direction of its spiral. II. The cone, in which M is the apex above, and MO tlie apex beneath, III, Left-hand spiral with apex (l\i) upwards, IV. Left-hand spiral (perversion) with apex (MO) downwards. will a student whose study of spirals has been limited to what horns alone can show him. Fig. I. on Plate IV. is a diagram of the tendril of a climbing plant such as was described in my last chapter. In its growth up to the point R and beyond it, the tendril finds that a left-hand spiral suits its needs, but from the point L onwards the curve changes to a right-hand spiral, probably because the plant found more light and air in that direction, or possibly from the effects of torsion already described. In any case, we see that the plant can move either to the right or left as it requires. In V. and VI. on the same plate are shown two horns each with the same left-hand twist that is produced in a rope made by a right-handed man. But the horn numbered V. comes from the right side of an antelope's head (compare THE SPIRALS OF HORNS 205 Fig- 234), and the horn numbered VI. comes from the left side of the head of an Angora goat. Now, if it were not for the fact stated above, that wild antelopes always show the heteronymous twists, and domestic animals usually show homonymous twists, we might just as well have expected to see the left-hand twist of Fig. V. on the left side of an antelope's head as on the right. But, obviously, the difference in the formation exhibited by the antelope is of advantage to the animal just as the change from left to right at the point R in Fig I. was advantageous to the creeper. Whether the change occurred from older homonymous animals to more recent heteronymous species, as was suggested above, I feel there is not sufficient evidence for proof. To argue that the homonymous animals only survived because they were preserved by man is, no doubt, to take too little account of the enormous periods of time necessary lor the production and the permanent duration of such a feature as the heteronymous formation. But two things can be urged in reply to this. The first is that breeding directed by human intelligence has produced such immediate and startling results (in horses and dogs, for instance) in recent decades that many men are now alive who never saw a polo-pony or one of the new terriers until within the last few years. The second considera- tion is that men who lived more than fifteen thousand years ago are known to have domesticated horses and other animals ; and since the age of man upon the planet has now been thrust back as far as 400,000 years ago, we may reasonably suggest that some animals became domesticated within a few thousand years of the beginning of that remote era. Among such animals it is only likely that such sheep and goats were included as are drawn in Figs. 239, 240, 246, and 247. The suggestion, therefore, is that these animals exhibited the homonymous formation because their horns were never so much used either for fighting their own kind or for penetrating rough brushwood ; whereas, animals less useful and less easily domesticated, such as the antelopes shown in Figs. 234, 235 or 236, and the markhors in Figs. 228 and 229, developed the heteronymous formation which throws brush- wood away from the shoulders and leaves the propelling hind- quarters free, instead of drawing the boughs inward as homony- mous horns would do. If, however, we can prove that domesti- cated animals show the same spiral formation as that of their wild ancestors, the need of a different theory from that of page 203 will be demonstrated ; and we have to recognise that among male gregarious animals a fight usually occurs, not against carnivora, but between themselves, either for leadership or the possession of the females, and by this means the qualities 2o6 THE CURVES OF LIFE of the strongest are transmitted to their young. Living, too, by preference among the mountains and plains instead of forests, they would chieify depend for safety on sight, scent, or hearing, and on swiftness of pace. Stih, it is a fact that sheep and goats (with one exception) which have been domesticated show the homonymous formation, while no heteronymous antelope has ever, to my knowledge, been domesticated. Passing (m to the other diagrams in Plate IV., I will ask you to imagine that Fig. II. is the base of a cone. If you make this base out of a wire ring and fashion your cone out of trans- parent muslin (after the fashion described in my second chapter), the ring may be placed on a flat table and the apex of the cone (M) may be pulled up so as to look like the Fig. BOK in the top right-hand diagram on Plate V. Now look at Fig. III. in Plate IV., and imagine the diagram to represent a conical helix of such organic substance as horn, the point B in the helix being Fig. 240. — Ancient Egyptian Representation of Tame Loxg-Legged Rams. (Lortet and G.aillard.) supposed to grow from the point B on the base of the cone. The helix will then gradually grow up round the cone until it reaches the apex M exactly after the fashion of the left-hand curve of the horn on the left side of the ram's head in Plate III., Fig. I. This is the ordinary form of spiral seen in homony- mous curves of Fig. 231. But another form of spiral is possible, as may be seen by holding up your wire ring (as described in the case of Plate IV., Fig. II.) and letting the transparent muslin fall through the ring until the apex of the cone (MO) is helow the ring instead of above it, very much like Fig. AOC in the top right-hand diagram on Plate V. Now look at Fig. IV. on Plate IV., and imagine the diagram to represent a conical helix of such organic substance as horn, the point BO in the helix being supposed to grow from the point B on the base of the cone. The helix will then gradually grow down round the cone until it reaches the apex MO, exactly after the fashion of the left-handed curve of the horn on the left side of the head of Pallas's tur in Fig. 230. This is the rare form THE SPIRALS OF HORNS 207 of spiral found in the homonymous curves of such animals as those drawn in Figs. 241, 242, 243 and 244. For this rare form I venture to suggest the name " perversion " ; and the addition of some such word as perverstis to the descriptions of Capra cylindricornis, Ammotragus lervia, Pseudo'is nahura, and the rest, would, I think, be a valuable indication on the labels of museums. The instances just quoted are, I believe, all animals which show this formation only and never use the common formation. But it must carefully be noted that in the mouflon we find the ordinary homonymous formation shown in Fig. 237, where the horns point forwards as in the Alaskan bighorn of Fig. 48, Chap. II. ; but we also know specimens of mouflon which exhibit the rare homonymous formation (perversus) shown in Fig. II. of Plate III., in which the horns point backwards as in Pallas's fur, and, therefore, must be so directed as to avoid piercing the animal's back. I have used the different spirals of the tendril to illustrate the differences in spiral twists. Let me now say that the possi- bility of perversus was suggested to me by the strictly analogous case of certain shells, sometimes styled perversus by conchologists. As those will remember who have read my earher chapters, the operculum always presents a spiral of a contrary direction to that exhibited by the shell itself. Most shells show a right-hand spiral formation, or leiotropic, as the conchologist would say ; and, therefore, the operculum exhibits a left-hand spiral (see Fig. 46, Chap. II.) In these cases, the shell which is usually a right-hand spiral exhibits a few rare exceptions which show a left-hand spiral ; just as shells which, in ordinary cases, may show a left-hand spiral, occasionally produce a few right-hand excep- tions. But the operculum in all these instances obeys the rule laid down above. When, therefore, we find a right-hand spiral in the shell, and also a right-hand spiral in the operculum, we at once deduce that a new condition is observable. That con- dition is indicated by calling this right-hand shell ultra-dextral instead of leiotropic ; and the process involved is exactly that by which I illustrated the difference between the ordinary homonymous curves of the Highland ram and the perverse homonymous curves of Pallas's tur. The shell, in fact, has gone through just that modification described in the cone of muslin. It began Hke an upright cone with the base on the table and the apex above. It was gradually flattened out, and the downward pressure continued until the ring or base of the cone was at the top and the apex was beneath it ; in other words, the apex M (in Fig. II. of Plate IV.) had been pushed down until it had gone right through the base and beneath it to MO. This 208 THE CURVES OF LIFE has occurred in Spirialis, Limacina, Meladromus, and Lanisles, in which a dextral animal inhabits a shell which appears to be sinistral, but is, in reahty, ultra-dextral, as explained by Simroth and Pelseneer. In the same way, Pompholyx appears to be dextral, but is in reality ultra-sinistral. No closer parallel to the different growths of horns could be imagined. That some such distinctive name as peyversus is required was first borne in upon me by the fact that I found certain eminent biologists describing the left horn of Ovis amnion hodgsoni (Fig. 233) as a left-hand spiral, and the left horn of Capra cylindricornis (Fig. 230) as a right-hand spiral ; in other words, it was imagined Plate V. — Diagrams to show the Principle of the Inverted Cone. (See text.) that Pallas's tur, the arui, the bharal, etc., exhibited the impossi- bility of heteronymous curves. There is, of course, a difference between the curves of Pallas's tur and those of the Argah sheep, but it is not a difference that can be expressed by the use of the terms right-hand or left-hand spiral. In order to show that perversus has no effect upon the right or left-handedness of the spiral, I have drawn (in Plate V.) an ordinary cylinder, ACBK, on which the black hnes of a cylindrical helix are marked, and you may note that these black hnes follow the same direction whether the cyUnder is "erect" or " upside down," whether you take AC or BK to be its base. Imagine that at the point the cylinder is so tightly constricted that two cones are the result, namely, AOC at the top and BOK THE SPIRALS OF HORNS 209 at the bottom. You will obsen-e that the black lines of the helix (now conical instead of cylindrical) have not changed their direction m the least. Now take the cone AOC and tilt it on one side so as to balance it on C, with the point O to your lett^ In the same way take the cone BOK and balance it on B with the point also to your left. The black spiral lines point m exactly the same direction in each case yet the cone BOK (at the bottom of the constricted cylinder) represents the normal form, while the cone AOC (at the top of the constricted cylinder) is pervLfsus. and is the result of pressing down the apex O until It has come through the base and out the other side, as in an ultra-dextral (or ultra-sinistral) shell, and in the horns of Pallas's Tur. To the examples of ferversits already quoted or iUustrated 1 can only at present add the Sind Wild Goat [Capra hirciis Uythi) Fig. 241. — (Perversion). Arui or Barbary Sheep (Ammotragus lervia) from N. Africa. (Drawn from p. 389 in Rowland Ward's " Records of Big Game." Sixth edition, 1910.) and the Ladak Urial {Ovis vignei typica). In all these the points of the horns go over the back of the animal's neck and away from a spectator who is looking full in the animal's face. In Ovis canadensis, Ovis amnion, the Highland ram, and the majority of homonymous curves, the points of the horns come forward towards the spectator. No doubt more examples of perversus will reward the careful investigator. Again, if we are to consider the perversus as an improvement developed by wild animals on the ordinary homonymous curves of the domesticated ram, can this process be compared with the fact that in the twisted horns of Gazella granti the points come inwards and forwards, whereas a different environment has developed points which go outwards and backwards in the other- wise identical G. granti robertsi? Various suggestions have been made as to the use of different forms of horns. Those of the Sudan Derbian Eland (Fig. 238) or the Suleman markhor (Fig. 228) C.L. p 210 THE CURVES OF LIFE are as clearly fighting weapons as those of the common (Fig. 247) or the Jamnapuri goat (Fig. 246) are peaceful ornaments. Whether the horns of the Sind ibex would be useful as scimitars or not (Fig. 244), they would certainly help to break a fall if the animal kept his head in and broke the shock upon their massive curves. Much the same use might be predicted for the firm spirals of Pallas's Tur (Fig. 230) or the Tibetan Argali sheep (Fig. 233). But I cannot agree with the theory (brought forward in the British Medical Journal for September 27th, 1902), that such an open Fig. 242. — (Perversion). Cyprian Red Sheep (Ovis orientalis). (From Biddulph, Proceedings of the Zoological Society, 1884.) Fig. 243. — (Perversion). Bharal (Pseudois nahura). (Drawn from figure on p. 387 of Rowland Ward's " Records of Big Game." Si-xth edition, 1910.) conical helix as that of a Highland ram's horn could in any way serve the purposes of a megaphone. It IS only right to quote Dr. Wherry's exact words m mentioning the theory of horn spirals which he originated. In the British Medical Journal, of September 27th, 1902, he announced " that in the antelopes the right-hand spiral is on the lejt side of the head and the left-hand spiral on the right of the head" (heteronymous), and " that in sheep the right-hand spiral is on the right of the head and the left-hand spiral on the left" (homonymous). "The wild goats agree with the antelopes m regard to the spiral direction of THE SPIRALS OF HORxNS 211 their horns, and the oxen agree with the sheep in cases where the spiral can he noted." Now it is often by apparent " exceptions " that a " rule," or theory such as this can be corrected or enlarged ; and' Mr. Fig. 244. — (Perversion). Mr. A. O. Hume's Sind Wild Goat. Shot by Col. F. Marston. (Drawn from p. 3 78 of Rowland Ward's " Records of Big Game." Sixth edition, 1910.) Lydekker has pointed out two serious exceptions to Dr. Wherry's statement which was evidently based on what he had observed. Did Dr. Wherry refer to the markhor (Figs. 228 and 229) when he used the words " wild goats " above ? If so, how is it that Fig. 245. — Dauvergne's Ibex (Capra sibirica DAUVERGNEi). (Sterndale.) all tame goats save one are homonymous, whereas the markhor is heteronymous. Is domestication a sufficient reason to assign for the change in spiral arrangement ? Surely an easier explana- tion may be drawn from the fact that the true ancestor of tame goats is not the markhor but the so-called " Persian ibex " of P 2 212 THE CURVES OF LIFE sportsmen, Capra hircits irgagnis. In Fig. 244 I have shown the " perversion "-curves of the Sind wild goat, on the head of Mr. Hume's ibex (Fig. 244). We have seen already that " per- version" is an accompaniment (though a rare one) of homonymity. But m the Field for December 13th, 1913, Mr. Lydekker pub- hshed Mr. R. A. Sterndale's drawing of an Asiatic ibex (Fig. 245), which is clearly homonymous, as may be seen by comparison with the Merino Ram (Fig. 232), or the Tibetan Argah (Fig. 233) ; and other specimens approaching it (though not so boldly curved ) may be examined in the Natural History Museum. Obviously, therefore, the homonymous spirals of the ordinary tame goat are descended from those of the wild goat, which has the same spiral as the Ibex ; and this is the explanation of the only tame goat (the Circassian) which exhibits heteronymous spirals (Fig. 249). For, as Mr. Lydekker says, a comparison of this animal with the Cabul Markhor (Fig. 248) clearly reveals a similarity which is not limited to the horn spirals. In each case the tufted chin of the ordinary tame goat is continued as a thick fringe down the throat and on into the chest. The tail, too, is of the same Indian Jamnapuri Goat (Tame). elongated type in each. There are no doubt other points of similarity. The specimen photographed in Fig. 249 was recently sent to the Natural History Museum by Captain Stanley Flower, director of the Giza Zoological Gardens, as a gift from the Egj'ptian Government. The difference in its horn spirals from those of the ordinary tame goat may be seen at once from a comparison of Fig. 249 with Figs. 239, 246, or 247, which show the domesticated breeds. The suggestion that this Circassian goat is of a different breed from other tame goats, and owes its derivation to the Markhor instead of to the Wild Goat, is strongly corroborated by the fact that the markhor extends to-day as far westward as the Ferghana province of Turkestan, which makes the possibility of such a derivation very simple. It also lends considerable probability to the suggestion of Dr. Trouessart that the markhor should be separated from other wild goats under the name of Oi-thagoceros. Certainly nothing could be much more different (in h(jrns) from the ibex. In 1909 Dr. Otto Keller reproduced from an ancient cylinder (brought by Sir Henry Layard from Constantinople) the figures of certain ruminants, which he was evidently mistaken THE SPIRALS OF HORNS 213 m describing as argali and markhor. As Mr. Lydekker pointed out, they were in charge of Syrian attendants and obviously domesticated, so they were possibly Circassian goats. It is further noteworthy that Blyth, who was quoted with respect by Darwin, reported that the wild markhor (heteronymous) bred with the domestic goats of the plains ; and it is probably in some such way that the Circassian breed of goats arose. It is also reported by Dr. Wherry that the Egyptian room in the Fitzwilliam Museum at Cambridge contams a portion of the skull with the horns of a domestic animal of about 2,000 B.C., found in the tombs at Beni Hasam. These horns show the markhor type, but are homonymous, and I venture to suggest that they were like those of Fig. 250, and belonged, not to a goat, as has been thought, but to a sheep. The Wallachian sheep (Fig. 250) has horns which are very like those of a markhor (Fig. 22S) though smaller ; but they follow Dr. Wherry's rule and are homonymous, as may be seen by Fig. 247. — Common Domesticated Goat. comparison, for the right-hand spiral of the markhor's left horn appears on the right side of the head of the WaUachian sheep, an animal to whom I must apologise for my incorrect description in a former book ; for nothing is more difficult than accuracy in these matters unless the student can test the horns by such diagrammatic models of twisted wire as have just recently been placed in the Natural History Museum. The Circassian goat, therefore, is a very definite exception to the usual rule concerning tame goats, and Mr. Lydekker has satisfactorily explained it. The only exception I have found to Dr. Wherry's rule about antelopes is almost equally signifi- cant ; for the only homonymous horn spirals in this division hitherto discovered are in Oioceros, which are known only from tertiary formations, and, if I am right in the theory expressed above, were unable to survive because they were not heterony- mous. They were first named by Charles Gaillard, in 1901, who included among them certain spiral-horned antelopes from the Lower Pliocene of Pikermi, Attica. Dr. Wherry, however, 214 THE CURVES OF LIFE has shown that the fossil horn cores of antelopes from the Upper Miocene (preserved in the Geological Museum) are heteronymous like those of their living descendants. From a study of the four-horned Asiatic sheep in the British Museum, Mr. Lydekker has concluded that the upright pair of horns in the Wei-hai-wei ram (Fig. 251) exhibit the normal homonymous spiral, whereas in the horizontal pair he sees that variety which I lf-^^>>hA< Fig, 248. — The Cabul Markhor (Capra falconeri megaceros). (From Lydekker, Proc. Zool. Soc.) have described as pcrversus, " a modification due to a secondary twist in the upper part of the horns, as a result of which the tips curve backwards over the neck, instead of bending forward by the sides of the cheeks." It would be most interesting if we could show that the perversus variation was a link in development connecting the kinds which are at present domesticated with those that are still wild. I think that the curious connection of homonymous twists with domes- THE SPIRALS OF HORNS 215 ticity in goats is satisfactorily answered by Mr. Lvdekker's explanation on p. 212, which has the added advantage of explain- ifig the apparent " exception " as well. But it "is still more cnrious that, although all open curves in the horns of sheep must necessarily be either homonymous or pcrversus. when a sheep exhibits the close twists of the ^^'allachian breed (Fig. 250) these twists are homonymous too. This important fact suggests that Fig. 249. — CiRC-\.ssi.\x Domesticated Go.\t. the order of development given on p. 203 admits, not merely of modification, but of complete re^"ersal ; and since no theory on these subjects has (as far as I am aware) yet been suggested, I feel bound to give my readers a choice ; for " the observer can only observe when his search is guided by the thread of a hypo- thesis " ; and onlv continued comparisons will determine which is the more probable. If, therefore, we now imagine that open homonymous curves and close homonymous twists (not upright) 2l6 THE CURVES OF LIFE were developed gradually from close heteronymous twists (upright), we shall start with the more scientific consideration that primeval horned animals before the advent of man, being obliged to fight for their li\-ing, had such splendid weapons as those of the Suleman Markhor (p. 191), or of the Senegambian Eland (p. 202), animals which haA^e never been domesticated ; but that, in the second stage, animals which were not yet domes- ticated, but were not such fierce fighters, found that the lower twisted curves of the Gilgit Markhor (p. 192), or the Lesser Kudu (p. 197), were sufficient for their purposes. It is then easy to imagine that this process (which is, by hypothesis, a process of slow degeneration) would soften the fibre of the horns and, by Fig. 250. — Wallachian Sheep (Ovis aries strepsiceros). (From specimens in the Natural History Museum.) compensation, would thicken them. If so, the next step would be perversus, in which the points still remain lifted upwards, as in Pallas's Tur (Fig. 230), but the horns exhibit less twist, more curve, and considerable thickening (p. 193). Lastly, we get the Merino Ram, illustrated on p. 194, which shows the lowered points of the final stage of deterioration, and therefore presented no difficulties to domestication by man, and might possibly, indeed, have died out but for the interference of man, as was the case in Oioceros. This hypothesis eliminates the difficulty of the time necessary (p. 205) for the production of a change in the spiral when that change was attributed to processes which can have existed only since man began to tame animals for his own use ; and it explains why antelopes were heteronymous in geological periods (p. 215) long before the advent of man ; but it has not THE SPIRALS OF HORNS 217 yet provided a satisfactory explanation for the substitution of tlie homonymous open curves, or homonymous twists (not upright) in tame animals, for the close heteronymous upright twists of wild animals which had to fight. To supply this gap, I can only suggest that the development may have been analogous to the process described in Fig. 234 on p. 196. There we noted Fig. 251. — Four-horned Ram from Wei-hai-wei, (From photograph by Lieutenant R. H. Lane-Poole, of H.INLS. Minotaur.) that the male blackbuck's horns exhibit heteronymous twists, but that the horns of the female of the same animal exhibit homonymous curves, possibly because she had less need to use them as weapons of attack or defence. This, therefore, may be the explanation why fighting wild animals were heteronymously equipped like the Markhor (Fig. 228), while tame animals only needed (i) homonymous curves like those of the female Blackbuck or Merino Ram (Fig. 232), the points of whose horns had dropped much lower than those of Pallas's Tur in Fig. 230 ; or (2) homony- 2iS THE CURVES OF LIFE moiis twists like these of the ^^'alIachian sheep (Fig. 250), the points of whose horns had fallen much farther apart than those of the Gilgit Markhor in Fig. 229. \\'e have seen in earlier pages that a very slight disturbance at the point of origin of a growing spiral will have a permanent effcctnapon the shape of the completed spiral. Shavings usually exhibit ^a right-hand spiral because a right-handed carpenter always dri^■es his plane a little to the left. The majority of shells exhibit a right-hand spiral because the material forming the protoconch usually " lops o\'er " slightlj^ to the left at the beginning of its growth. The hair of a negro is curly because in those races of mankind the follicle from which the hair emerges is not straight as in the case of white races. Moisture has also a curious effect on spiral growth. In the museum at Cambridge Dr. Wherry has described a sheep which was shot on damp and boggy soil, in the Falkland Islands. Each portion of its cloven hind hoof had grown to an enormous size and length, exhibiting a spiral twist of about two and a half turns, a right-hand spiral on one side and a left-hand spiral on the other, just as may be observed in the horns of a koodoo. All such details may have a bearing on our present inquiry ; yet I feel that I have made no valuable suggestions as to the reason why the spirals of horns take different shapes, or show different arrangements in various animals. But, at any rate, the problem has been stated rather more fully than has been done before, and the various analogies suggested may even be of some use in determining future classifications. NOTES TO CHAPTER XII. Essential Curves and Twisted Surfaces (p. 195). — The curve of the horn of the Abyssinian ibex [Capra walie) is the only one I have seen without a twist. But, of course, twists are quite possible without curves, as in the case of the WaUachian sheep or the Suleman markhor. Nomenclature. — The Spiral of Horns. Dr. \\'herrj' sent me the following letter ; — ■ " If in a Rock\' I\Iountain sheep the right horn were sawn off the skull and the tip inserted into the severed horn core on the skull, that liorn would, of course, still exhibit a right-handed spiral, and ' homony- mous ' is a convenient word for the arrangement on the head and the direction of the spiral in the horn. The right horn has a right spiral and left horn a left spiral — ' homonymous,' or same name. " The horn of the Indian antelope (in which, as in all antelopes, the horns go ' heteronymously ') is often made into a toasting fork ; the thick end is capped with silver, and the tip carries the fork. THE SPIRALS OF HORNS 219 Knowing that the horn is that of an antelope, 3'ou talve it up by either end, and if it has a right-hand spiral it is the left horn, or if it has a /e/if-hand spiral it is the right horn — i.e., ' heteronymous.' ' As I first used these words in this connection, I take a paternal interest in them, and venture to think that ' homonymous ' and ' heteron3mious ' will be found convenient words and useful aids for observation and memory." Curious Development of Horn-Spirals. Mr. R. Lydekker has very kindly shown me a most remarkable, and apparently unique instance (Fig. A) of the Homonymous [Perversus) spiral beginning with a curve and ending with a twist in the same horn, which is even more noteworthy than my example of the two things in the male and female of the same animal (Fig. 234). Fig. B. — Head-skin and Horns OF A Variety of the Al- banian Sheep. (From a specimen presented to the Natural History Museum by Messrs, Rowland Ward, Ltd.) Fig. a. — Head and Horns OF Albanian Sheep. (From J. G. Wood'sfigure.) Mr. Lydekker thinks this Albanian sheep is a cross between the Parnassian sheep of Macedonia and Greece, represented in the basal curves, and the Wallachian sheep, represented in the termina.l twist. Fig. B shows the horns of another Albanian sheep which point downwards instead of upwards, apparently a rare example of perversion in the twist instead of m the curve. CHAPTER XIII Spiral Formations in the Human Body ■' The earth has a spirit of growth ; its flesh is the soil ; its bones are the successive strata of the rocks ; its muscles are the tufa stone ; its blood the springs of its waters. The lake of blood that lies about the heart is like the tides' for the increase and decrease of blood in its pulses are the ebb and How of ocean." — Leonardo da Vixci (Leicester MSS.). NATURAL OBJECTS DO NOT CONSCIOUSLY PRODUCE SPIRALS DEA'IATION FROM MECHANICAL ACCURACY — SPIRAL FORMA- TIONS OF UPPER END OF THIGH BONE — GROWTH AND CHANGE — CORRESPONDING STRUCTURES IN BIRDS AND MAMMALS — CONICAL SPIRAL OF COCHLEA— SPIRAL FORMATIONS : UMBILICAL CORD, SKIN, MUSCULAR FIBRES OF HEART, TENDO ACHILLIS, THE HUMERUS (TORSION), RIBS, JOINTS, WINGS AND FEATHERS, EGGS, ANIMALCULE, My readers need not again be cautioned against the idea that any natural object consciously produces a spiral formation ; it grows after a pattern which we describe as " spiral " because that word conveys to our minds a certain conventional mathematical definition which may have no actual existence outside our minds, but permits us to label and classify the pattern shown by the natural object. We have seen, too, that mathematics will enable us to construct a theoretical figure of perfect growth and to compare it with the formations exhibited by such organic objects as plants or shells ; and thereby we may satisfy still more com- pletely the craving of the human mind for orderly explanation by stating that a particular shell differs from a particular loga- rithmic spiral in factors which may conceivably admit of isolation, if not of accurate expression But this implies the further power that by the use of mathe- matical formulae, originally conventional, we can artificially manufacture specific objects which will fulfil certain definite needs, such as a carpenter's screw, a ship's propeller, a spiral staircase, and so forth. Now we have already seen several forms of growth in Nature which can only be distinguished from artificially manufactured spirals by the fact that, since they are the result of organic development through natural processes which are more or less traceable externally, they almost invariably exhibit those subtle variations from mechanical accuracy (those SPIRAL FORMATIONS IN THE HUMAN BODY 221 inexplicable factors, " isolated," as I said above, from the simpler mathematical processes) which are essential to life, and, as I think, to beauty. It has not yet, however, come within our province in previous pages even to inquire whether the artifi- cially manufactured article (such as a spiral staircase or a screw propeller) could have been consciously copied from a natural object. But in the present chapter on spiral formations in the human frame it may at least be possible to suggest that both the object made by man (the only " manufacturer " in the world) and the growing phenomenon in Nature are conditioned by laws, fundamental for them both, which we can only describe to ourselves in terms of mathematics. A very beautiful instance of what I mean is to be found in one of the most extraordinary' structural adaptations in the human body, namely, the architecture of the upper end or neck of the thigh-bone, which has to transfer the weight of the body to the lower extremity. This has been described by Professor A. F. Dixon of Trinity College, DubKn {Journal of Anatomy and Physiology , 1910, Vol. XLIV., p. 223). Examined by X-rays, its interior is seen to be made up of a series of lamellae or needles of bone, arranged on a very definite plan. The cells which form bone (called osteoblasts) may be described as the bricklayers of the skeleton, and they lay down these lamellae within the neck of the bone on the three definite systems shown in the photograph (Fig. 252). The first of these systems, rising from the dense and compact cylinder which forms the shaft of the femur, produces a series of Gothic arches at the top of this shaft. The second springs from the underside of the neck, and passes upwards to support the weight of the body on the head of the bone. The third passes from the outer side of the cylindrical shaft into the upper part of the neck, bending in such a way as to interlace with the second or supporting series, after the manner of tie-beams, to which these tension lamellae may be compared. When examined stereoscopically by X-rays, in order to obtain a true picture, these lamellae were found by Professor Dixon to be arranged in a spiral formation (Fig. 253) ; in other words, the shaft of the bone becomes a bent cyhnder continuing into the neck by means of a left-hand and a right-hand system of spirals, quite comparable with the spiral and cylindrical pillars employed by engineers in bridge-building and other enterprises which obtain the greatest strength, with the least expenditure of material. A bridge, however, is fairly permanent, or, at any rate, does not visibly vary in size after it has once been built ; whereas the human frame exhibits gradual growth from the infant to the 222 THE CURVES OF LIFE adult, and constant change through hfe. The exact adaptation, therefore, of the anatomical architecture just described becomes even more marvellous when its control and development are clearty reahsed. For when the child learns to walk, the " brick- layers " of its little skeleton have to work out the elaborate design illustrated in Fig. 253, not once only, but many times. In fact, as the femur extends in growth the earlier systems become graclualh' useless, and are constantly replaced, which suggests that the osteoblasts (to give our " bricklayers " their Fig. 252. — X-Ray photograph of the upper part of the right human thigh-bone to sliow the internai structure. (Professor A. F. Dixon.) Fig. 253. — The spiral arrangement of the bone lamellae seen in the upper extremity of the femur when examined stereoscopically by the X-Rays. (Professor A. F. Dixon.) scientific name) are sensitive to the various stresses and strains put upon the hmbs, and build up their thighbone with a view to withstanding all those forces applied to the body of which they have any experience. This involves a form of intelligent workmanship which must remain obscure to us until we discover the conditions controUing their laborious existence ; still less can we under- stand how they are able to choose, for strengthening the human thigh-bone, just those beautiful applications of the spiral which have resulted from the mathematical researches of highly- trained engineers. Those who have followed me through earlier SPIRAL FORMATIONS IN THE HU:\IAN BODY 223 pages of this inquiry will, perhaps, be incUned to the supposition that in this sentence I have done less than justice to our osteoblasts, and have reversed the true terms of the comparison ; for may we not see in the design of the engineer a fundamental necessity for the employment of a formation which is at least as old as the origins of anatomical structure and development ? May we not find the solution of far more complicated difficulties than his engineering problems in the bodily framework he has inherited from vital processes vastly more aged than the humanity he recognises in himself ? We may be inchned to take this view even more definitely Apical turn ^^ Middle turn Basal turn ^Apical I Middle \ Basal turn Organ Corti Fig. 254. — The Cochlea of the Human Ear. (A) Viewed from the side. (B) The cochlea unrolled ( after Siebenmann). For Riidinger's drawing of the laminae, see Fig. 39, Chap. II. when we realise that the sensitiveness and aptitude for producing such spiral architectureas that of the thigh-bone must be handed on by successive series of osteoblasts, not only throughout the life of the same individual, but through the countless human genera- tions fitted with similar framework. Even more curious is the discovery of Professor Dixon that this spiral adaptation is not confined to human osteoblasts : for he has shown that the same interlacing of right-hand and left-hand spirals in the arrangement of the bony lamellae is found in the interior of the shafts of the long bones in birds and mammals. My readers will remember somewhat similar instances in substances which are not bone at all — in plants, in shells, in horns. The process, in fact, may be carried back to those dim beginnings of organic structure which 12^ THE CURVES OF LIFE can only be referred to the primeval phenomena of energy or growth. Another well-known spiral arrangement (but conical this time, instead of cylindrical) is seen in the inner ear or cochlea of man, a structure attaining its highest development in mammals and illustrated in Fig. 39, Chap. IF In Fig. 254 the artist has adapted the diagrams given by Dr. Siebenmann in Bardeleben's textbook of anatomy to show the coiling of the tube into a cone. The natural condition is given in the upper drawing (A), showing the two coils and a half in the spiral. In the lower drawing (B) the tube is un- coiled for diagrammatic purposes in order to show the nerve of hearing, its ganglion, and the organ of Corti spread out along almost its whole length. The human cochlea is derived from the short, shghtly curved tube (called lagena) found in birds and in an early Umbilical cord Umbilical vein Umbilical drieries Placenta Fig. 235. — The Termination of the Umbilical Cord on THE Placenta, showing the Left-hand Spiral made BY the Two Arteries. (After Broman.) stage of the human and mammalian embryo. It has probably de^'eloped into a spiral not merely owing to the limited space in the petrous bone containing it, but because of the retardation of growth of that side of the cochlea at which the cordhke auditory nerve enters, and the quicker growth of the other side. The nerve is, therefore, easily distributed along the organ of Corti by the convenient medium of the columeUa, or central pillar of the cochlea ; and this spiral formation does not, so far as we know, alter the form of the mechanical waves stirred by sound waves in the fluid contained by the cochlea. The spiral showm by the human umbilical cord has also been illustrated in Fig. 10, Chap. I. But m Fig. 255, the termination of this cord in the placenta is shown. The comparatively straight vein conveying oxygenated blood back from the placenta has spirally arranged but somewhat irregular folds in its linijig SPIRAL FORMATIONS IN THE HUMAN BODY 225 membrane. The two arteries carrying impure blood encircle the vein in an obvious spiral, which is usually left hand (as in Fig. 10, above). This is produced by the fact that the suspended y Hepatic duct Cystic duct \- Common bile duct Fig. 256. — Diagram to show the Spiral Valve of the Duct of the Gall Bladder. (After Charpy in Poirier's " Traite d'Anatomie.") fcetus usually turns to the right ; but why it does so, and what functional advantage there may be in the twisting of the cord (except, perhaps, that of strengthening it), we cannot tell at present. It has been suggested that the right artery may usually Ductof sweat gland. Epidermis 1|^P \ Dermis Swedtgiand. Fig. 257. — The Spiral Arrangement of the Duct of a Sweat Gland, as Represented in Henle's Anatomy. predominate ; but as a rule, they are equal in calibre, and even in the absence of the left artery the spiral of the cord persists. It is equally difficult to explain why the spiral in the cystic duct^of the gall-bladder (Fig. 256) should always be a right-hand one. It is certainly not produced, in this case, by the twisting C.L. Q 226 THE CURVES OF LIFE of the gall bladder during development, and its probable reason is to keep the duct open when it is sharply bent within the living body, very much as an internal spiral spring is used to keep a hose- pipe open and without kinks in any position. I should add that it is uncommon to see the spiral of this duct so plainly marked as it is drawn in Fig. 256. But it is always possible by dissection to reveal that the folds of its lining are spirally arranged. A number of spiral structures occur in connection with the skin, and Fig. 257 shows the duct of a sweat gland as it per- forates the epidermis. Here the advantage of the cylindrical spiral (which is right hand) must be to give such storage to the r" -s^" -^ J#- Fig. 258. — Imprints of the Index, Middle, and Ring Fingers of a Medical Student, showing Spiral Pattern of Skin Papill.^. sweat that when the skin is grasped or pressed, the sweat exudes ; and the formation may also serve to protect the gland from the invasion of infectious dust. This is another example of a spiral that has to be persistently renewed, for the cells of the epidermis are shed daily. It is weh known that on the fleshy pads of the finger tips the papillae of the skin are arranged in peculiar patterns, which have been classified by Galton, the loop form being the commonest, the flat spiral one of the rarest. The imprint shown in Fig. 258 is taken from one of the two students out of forty-five who possessed this spiral or whorl type. It has been suggested by Hepburn that these papillary patterns give security to the grasp as well as delicacy to the touch. They are found in apes SPIRAL FORMATIONS IN THE HUMAN BODY 227 and monkeys as well as man, and I am inclined to believe that the curious marks in prehistoric carvings (concentric circles, loops, and spirals) may have had their origin in the finger-tips which have provided Bertillon and Galton with subjects for comparative research and modern Scotland Yard with a test for identifying criminals. It appears that no two men exhibit the same markings. I have already mentioned that the papilla from which a negro's hair grows is bent downwards, and thus produces its distinctively " woolly " appearance. His hair- roots, which have been investigated by the late Professor Stewart and Professor Arthur Thomson, have a peculiar kink in them when compared with those of the white races ; and, ultimately, the spiral nature of the hair must be referred to a rhythmical irregularity of growth in the root. Passing on from the dermal structures, we find a number of Wallof 'drteriole Lumen of arteriole Spiral muscle fibre Fig. 259. — Diagram of a Capillary or Arteriole in the Web of the Frog, showing the Spiral Arrangement of Muscle Fibre, discovered by Lord Lister. spiral patterns occur in the circulatory system. The late Lord Lister {Trans. Roy. Soc, Edin., 1857, Vol. XXL, p. 549) described one of the most beautiful examples (which does not occur in the human system) in the finer vessels of the frog's web. The plain muscle fibres encircle these vessels in a right-hand cyhndrical spiral (Fig. 259), which produces a more perfect pressure (or occlusion) than merely circular fibres would do. The arrangement of a conical spiral may be seen in the muscular fibres of the human heart (see Fig. 260, and compare Fig. 3, Chap. I.). As seen on a superficial dissection these fibres form a right-hand spiral, and in their form alone may be compared to the beautiful Httle orhiculus, which has been illustrated in Fig. 261. The fibres begin at the base of the ventricle of the heart and end in the vortex at the apex by becoming continuous with deeper fibres. We do not know the growth mechanism which produces this complicated form, investigated by the late Professor Pettigrew and others, Q 2 228 THE CURVES OF LIFE but we can begin to understand its advantages. The emptying of the heart was a difficult problem for Nature to solve. In the lower slow-moving vertebrates she adapted a sponge-work arrangement ; but such a mechanism was too clumsy for the fast-moving higher vertebrates, birds and mammals. So a contractile, thick, and dense-walled pump had to be evolved in such a manner that the contracting muscular wall could eject its whole load of blood. This end was beautifully attained by arranging the fibres in a spiral pattern, so that one twist would close up the cavity and throw out its contents, and the next twist (reversed) would open it again ready to be fiUed, The functional meaning of the vortex at the apex of the heart has been described by Dr. Keith in Jouin. Anat. and Physiol., 1907, Fig. 260. — Dissection- of the Apex of THE Human Heart, to show the Spiral Arrangement of the Mus- cular Fibres. (Pcttigrew.) The fibres enter at a \-ortex at the apex. Fig. 261. — A Foraminifer. (From the Challenger Reports.; Greatly enlarged. Vol. XLIL, p. I. A slighter example of partial torsion may be seen in the great arterial trunks at the root of the heart. The pulmonary artery passes from the right ventricle to the lungs ; the aorta rises from the left ventricle and distributes blood to the body. In Fig. 262 (A) is illustrated the right-hand spiral formed by the pulmonary artery on the left side of the aorta. Why this artery should pass to the left and not to the right of the aorta is an unsolved question ; but it may be said that the aorta and the pulmonary artery are parts of a common trunk in the human embryo, and this condition persists in gill-breathing animals. They are separated by a septum, which always exhibits a right-hand spiral except in those rare instances of individuals in whom all the viscera are transposed as regards right and left, as shown in Fig. 262 (B). Among the many peculiar patterns shown by the muscular SPIRAL FORMATIONS IN THE HUMAN BODY 229 system a spiral arrangement is very rare ; but Mr. F. G.' Parsons (of St. Thomas's Hospital Medical School) has drawn the attention of anatomists to a beautiful example in the tcndo Achillir-, the tendon of the muscles of the calf of the leg, at its insertion into the Arch of aorta Rfght aur Aorta - Pulfn. art. left ventncle ■Apex. Right aur Apex B Fig. 262. — Diagram of the Fcetal Human Heart. Showing (A) the pulmonary artery forming a spiral on the left side of the aorta. In (B) is shown the arrangement in those uncommon cases whose viscera are transposed as regards left and right. heel. The fibres have a rope-hke twist, which is more evident in such animals as the beaver (Fig. 263), and may possibly be related to some inward movement of the sole of the foot when walking. Outer head -^ of Gastrocnemius Heel Infierhead of Gastrocnemius F/antaris Sole Fig. 263.— Twisting of the Tendons of the Muscles of the Calf at their Insertion into the Heel of a Beaver. (F. G. Parsons, Journ. Anat. and Physiol., 1894, Vol. xxviii,, p. 414-) Many cases of torsion or spiral arrangement in the bones of the human skeleton are more imaginary than real ; and in the clavicle, which is the upper bone (A) drawn in Fig. 264, the appparent twist, here very much emphasised, is due to the strong line (crossing the undersurface of the bone) made by the insertion 230 THE CURVES OF LIFE of the siibclavius muscle. The lower bone (B) in the same figure is the OS innominalnm or left pelvic bone, which is made up of at least four functional parts ; and though there is no doubt that the angles and planes in which these parts are set do undergo a certain rotation during development, yet the illustration should not be used as a means of analysing the significance of spiral formations in the body. The shaft of the humerus, however, the bone of the upper arm (Fig. ii, Chap. L), certainly shows a spiral arrangement in the markings and lines caused by muscular or nerve impressions. Torsion has occurred during the evolution Fig. 264. — A. Represents the Under Surface of the Human Clavicle, B. Represents the Inner Side of the Left Pelvic Bone. (Pettigrew.) of man, and rotation occurs in his upper and lower extremities during development ; so that the upper extremity rotates outwards and the inner surface becomes anterior, thus forming a right-hand spiral in the right arm and a left-hand spiral in the left. The lower extremity rotates in the opposite direction, so that the original inner surface becomes posterior. It is to this developmental twist that the spirals apparent on the surfaces of human bones are largely due. In the humerus the axis of the lower joint is set at right angles to the axis of the upper one, and the articular surfaces (set on different planes) are so placed as to allow the bone to move in various directions useful to the body. A functional twist, due to the same difference in the axis of the SPIRAL FORMATIONS IN THE HUMAN BODY 231 joints at its two ends, may be observed in a bone in the lower extremities. In Fig. 265 is sliown the left fore-leg of an elephant seen from the front. In the upper bone the drawing has rather exaggerated the twist and prominence of the ridge caused by the attachment of a muscle. The bones beneath it are permanently fixed in the position known as pronation, the radius turning from the outer to the inner side of the limb as it passes towards the foot. The torsion shown on this left fore- leg is seen to be a right-hand spiral, and of course the right fore-leg would show a left-hand spiral. In the case of the ribs there is a very good example of spiral twist (see Fig. 266), which possesses well - recognised functional advantages. The posterior part of the rib (the head, neck, and angle) serve as the axis round bonesoftheLeft which the rib rotates as we breathe ; and the Fore-Leg of an spiral formation of the shaft causes the rib to move outwards as it is rotated upwards, thus enlarging the capacity of the chest and causing air to enter the lungs. What has been said here by no means exhausts the spiral formations in the human body ; it merely suggests typical instances, and many more might be set forth. The joints provide several interesting examples. The condyles of the lower Fig. 265. Elephant. (Pettigrew.) //eddz Fig. 266. — Drawing of the Seventh Rib on the Right Side, to show the Spiral Twist which Facilitates Breathing Movements. end of the femur, which enter into the formation of the knee joint, are of a spiral formation, which permits the longest radius of the condyle to come into action when the knee is extended, and thus gives security in various positions of the leg. The movements called supination and pronation in the two bones of the fore-arm are of a spiral nature. The spinal column can 232 THE CURVES OF LIFE be spirally rotated in either direction. All graceful dancing and human movement is more or less spiral, as may be easily seen in fast swimming, and this makes a definite appeal of its own to Fig. 267. — Drawings to Show the Spiral Twist of a Feather, of THE Wings in a Beetle (Goliathus micans) and of a Kestrel. The upper part of each figure shows the forms at rest, and the lower part shows the spiral produced in flight. (Pettigrew.) the human aesthetic judgment. Our aesthetic approval is no doubt largely due to our appreciation of competence and efficiency combined with balance, and in the case of spirals it is due to our ancestrally-inherited and long-impressed perception of the power and " beauty " of screw-movement. SPIRAL FORMATIONS IN THE HUMAN BODY 233 When we turn to the rest of the animal kingdom many more examples of the same formation can be studied, and again I propose only to choose a few typical instances. Perhaps the most exquisite are to be found in wings and in the feathers of which those wings are composed, and I reproduce drawings of these (Fig. 267) from the posthumous edition of the late Professor Pettigrew's researches, to which reference has already been made. Instances of what I have previously described as a flat spiral occur in the intestines of many animals as well as man. In an excellent monograph dealing -with the intestinal tract of mammals {Trans. Zool. Soc, 1905, Vol. XVII., p. 437), Dr. Chalmers Mitchell has figured raany examples of the remarkable spiral arrangement of the upper part of the great bowel in ruminants. Fig. 268. — Simple Colic Fig. 269. — Upper part of Helicene of Stan- the Colic Helicene of a ley's Chevrotain. Musk Deer. (Beddard.) (Beddard.) The two illustrations given here are taken from Mr. F. E. Beddard's " Contributions to the Anatomy of Certain Ungulata " {Proc. Z. S., 1909). In Fig. 268 is shown the simple cohc hehcene of Stanley's chevrotain [Tragulus stanlcyaniis) , and in Fig. 269 are drawn the more elaborate curves of the musk-deer {Moschus moschifems). In each case the caecum is represented in black on the right, and the ingoing limb of the spiral is black, the outgoing limb is lighter ; and the spiral of each is right hand. The forms of these spirals are used by Mr. Beddard to illustrate certain technical develop- ments with which I cannot deal in these pages. But it may be said that a similar arrangement appears in the capybara. In the rabbit and hare the caecum and appendix form part of an intestinal spiral. All these formations may be considered to be the result of inequahty in the rate of growth of the various parts composing the twisted loop. One part of the cscum of ? ? 1 THE CURVES OF LIFE the rabbit {Lcpiis cuniciilm) leads to the vermiform appendix, and is wide in calibre, but diminishes somewhat towards its termination, is thin in its walls, and spiralty constructed externally in correspondence with the spiral vaWe developed internally. In the colon of the dogfish (Scvlliinii caniciila) a different and very beautiful form of upright spiral is found. The lining membrane is developed into a right-hand spiral valve, which greatly increases the absorbing surface of this part of the intestine (Fig. 270). The rotation of a bird's egg while descending the oviduct gi^'cs a spiral twist to the en\-elope as it turns in its progress, and thus the little stringy p(jrtion of " white " at each end is strengthened by the spiral formation imparted to it and Fig. 270. — Colon of Dogfish, showing Spirals of the Internal Valve. Fig. 271. — Capsule of Port Jackson Shark's Egg, show- ing External Spiral. suspends the egg within the shell. Much the same rotatory process occurs during the birth of mammals. The spiral fold within the oviduct of a shark [Cestracion fhilippi) imprints an unmistakable pattern upon the capsule of its egg (Fig. 271), which is almost precisely the shape of those " ground anchors " which sink themselves into the mud of a harbour and form securing places for mooring chains, lightships, beacons, and the like. The eggs just mentioned provide a typical instance of the generation of a spiral by two movements ; {a) rotation on the axis, [h) longitudinal movement of the rotating mass. It would be impossible to exhaust this division of the subject in the space at my command ; but I may add that the same formation can be found in the smallest forms of life, in those SPIRAL FORMATIONS IN THE HUMAN BODY 235 organic atoms which seem to partake both of animal and of vegetable characteristics, and particularly in the spirilla, spiro- chetes, and a number of the longer bacilli. A large number of the bacilh which grow into threads tend to take on a spiral form, as may be easily seen in examining unstained specimens through a microscope. One of these, Spii-iUum nibnim, has already been illustrated in Fig. 6, Chap. I. I give here two more photographs Fig. 272. — Spirochete Giganteum. Highly Magnified. (Kolle and Wassermann.) reproduced by Kolle and Wassermann. Fig. 272 shows a typical form of motile organism. Fig. 273 represents another well-known bacillus, with its vibratile cilium twisted in a corkscrew spiral. And the spermatozoa of many animals show a spiral flange formed along the cilium, which is used for boring into the egg. Both examples of bacteria given here are of course very highly magnified. Very minute, too, are the ciliate protozoa I reproduce in Fig. 274 from Haeckel's " Kiinstformen der Natur," in which the better examples are to be found on the side 236 THE CURVES OF LIFE of the plate to the left of the reader, especially in Vorticella (at the bottom corner on the left), Carchesium (which looks like a cauliflower growing on a corkscrew), next to it, and Stentor, the trumpet shape above them. The spiral cilated forms of the trumpet animalcule, and other similar shapes, have the result of producing a vortex in the water, bringing suspended particles to the apex of the spiral where the mouth is placed. NOTES TO CHAPTER XIII. For most of the facts in this chapter I am indebted to Professor Keith, but for the form of statement and for the arguments employed he is no way responsible. Fig. 273. — A Bacillus from Putrefying Flesh-Infusion, Magnified 1,500 Dia- meters. This and Fig. 272 are taken from Kolle and Wassermann's " Handbuch der Pathogenen Mikroorganismen." Atlas. Torsion. — " M. B." wrote ; — " Your article on anatomical spirals mentions the effects of torsion. Your readers may therefore be interested to know of a recent addition to the Shell Gallery in the British Museum, in the form of a working model (easily operated by the public), exhibiting the process of torsion in Gastropod MoUusca. The model is diagrammatic and generalised, and does not attempt to suggest a cause for the phenomenon." Extract from the " Lancet." — I reproduce from the Lancet the following very kindly notice, and gladly acknowledge the value of approval expressed by so high an authority on all scientific suggestions. " The most recent of the series," says this expert newspaper, " is likely to prove of particular interest to readers of the Lancet, for it deals with those organs or parts of the human body which manifest a spiral conformation. The list of such structures in the human body is more extensive than is usually beheved, several examples given by SPIRAL FORMATIONS IN THE HUMAN BODY 237 the writer in the Field being often overlooked. The first example cited is the spiral arrangement of the trabecular of long bones, the recent research of Professor A. F. Dixon on the finer structure of the human femur supplying the necessary data. The spiral arrangement ^i Fig. 274. — CiLiATE Protozoa, highly Magnified. FronxHaeckel's " Kunstformen derNatur," to show various spiral formations found in Infusoria, especially in Stentor, Vorticella, and Carchesium. of the vessels of the umbilical cord and of the canals of the cochlea are classical examples ; the ventricles of the heart provide another well- known instance with which the name of the late Professor Pettigrew is naturally associated — as indeed it must be with any inquiry into the significance of spiral formations. The spiral arrangement of the ducts of sweat glands, of the lines in certain types of finger-prints, and of 238 ' THE CURVES OF LIFE tlie muscular fibres in certain of the finer arterioles (a disco\'cr3' made by Lord Lister wliile examining the vessels of the frog's web) are less known examples. The spiral arrangement of the great arteries spring- ing from the heart (the form being reversed when the viscera are transposed), the spiral valve of the cystic duct, the spiral twist in the ribs and certain other bones are also dealt with. While in some cases the spiral arrangement gives a manifest mechanical or functional advantage, in other cases its significance is obscure or unknown. The writer in the Field has ransacked Nature's treasuries and brought together, from every kind of li\'ing things, the most striking examples where growth has developed in a spiral form. So many brilliant minds have fluttered in vain round the dazzling and fascinating problem of spirals that most inquirers, unless they are expert mathe- maticians, consign them to that lumber room of the mind where time and space and other limitless and unprofitable thoughts are buried. He however, has courage ; he does not pretend to have solved the problem of spirals in Nature. He simply sees in such formations that there is a deep problem, which if it could be solved would throw a light on many of the dark corners relating to our knowledge of the laws of growth and development. He has done biologists a service in bringing together the facts on which all endeavours to solve the biological significance of spiral formations and their relationship to growth and development must be based. We sincerely trust that these articles, which have been submitted in the first place to the readers of the Field, may be issued in book form, and be thus more accessible to biologists in particular and to that part of the general public which is interested in one of Nature's most fascinating puzzles." CHAPTER XIV Right and Left-handed Men " Ich stand am Thor ; ihr solltet schliissel sein Zwar euer Bart ist Kraus, doch hebt ihr nicht die Riegel. Geheiminssvoll am lichtcn Tag Lasst sicii Natur des Sciileiers niclit berauben." RIGHT AND LEFT HANDEDNESS — LEGS AND ARMS OF BABIES — LEONARDO DA VINCI — PREFERENCE OF ORIENTALS FOR LEFT-HAND SPIRALS — PREHISTORIC MAN GENERALLY RIGHT- HANDED — SKILL OF LEFT-HANDED MEN : EXAMPLES FROM THE BIBLE — THE HAND OF TORQUES — THE RULE OF THE ROAD — LEFT-HANDED SPORTSMEN : ANGLERS, ARCHERS, ETC. — LEFT-HANDED ARTISTS — MORE ABOUT LEONARDO —LETTER FROM MR. A. E. CRAWLEY. In the last chapter an iUustration was given (Fig. 262) of that arrangement of the heart which is found in rare cases where persons have their viscera transposed from right to left and vice versA. This transposition of the heart has been suggested as one cause for a man being left handed, just as it has been thought that the predominance of one side of the brain accounts for the majority of persons being right handed. But without discussing whether cause and effect may not also be transposed in such arguments, we can make an easy transition from the anatomical spirals discussed in the last chapter to that curious anatomical development which makes us think it odd if we see a left-handed man, and orders all our lives on the theory that the majority of us must always be right handed. That it is a development, and not an innate property, has been fairly conclusively proved ; and it will be of interest to examine the question in order to see whether there be any special quahty in right handedness or left handedness which may lead us to value one more highly than the other, or which may suggest a clue in our previous comparisons between right- and left-hand spirals ; and it is noteworthy that the sinistral spiral is pro- portionately just as rare in other divisions of Nature as left handedness is in human beings. In the average right-handed man, the right humerus and radius taken together wiU be from I inch to f inch longer than the left. This is not so at birth, for, as Dr. Wherry has pointed 240 THE CURVES OF LIFE out, though a foal is born " leggy," the legs of the human baby are actually as short as his arms until the former are pulled out by walking exercise, and our legs are the same length because we generaUy use them equally, without preference, in walking or running ; whereas the induced and educated preference for the right hand produces different lengths in our arms. Gorillas and anthropoid apes, which do not enjoy the advantage of ?/'/',j J . : -LEQNABDO- i*i ■ Fig. 275. — Portrait of the Artist. education, are naturally ambidextral, and do not develop one arm at the expense of the other. At the close of the second chapter we noted that a right-handed man makes a left-hand flat spiral more easily than he can draw a right-hand flat spiral ; and that a left-handed artist will put in his strokes of shading from left to right ; in other words, he will draw a left-hand cylindrical spiral more easily than he can draw a right-hand one. It was also pointed out that, for the RIGHT AND LEFT-HANDED MEN 241 same reasons, a left-handed fencer will probably be particularly quick with his contre-carte (a right-hand fiat spiral), while the average right-handed fencer prefers the motion of contre-sixte (a left-hand flat spiral) as being more natural to him. It is worth noticing in this connection that when Londoners had an opportunity, in March, 1902, of seeing eight of the best fencers in the world, of whom four Italians were pitted against four Frenchmen, the pair who did best of all were the two famous French left banders, Louis Merignac and Kirchhoffer. Indeed, instead of starting at a disadvantage, as is too often assumed, a left-handed artist seems often to have the advantage of his right- handed rivals, for he is usually ambidextrous by education, and probably possesses a high degree of congenital skill in the hand he prefers, as may be seen in the instance of Leonardo da Vinci, with whose draw- ings (Figs. 276, 277, 279— 282) I have illustrated this chapter, or of Hans Holbein. Dr. Wherry has pointed out that right handedness or left handedness some- times leaves definitely trace- able effects in the works of early or unskilled artists. In the archaic bust of an Apollo forty-seven curls out of sixty-one turned the way of the clock hands. In another statue, dating before the Persian war, the curls are arranged in right or left-hand spirals, accord- ing to the side of the head on which they grow, not as in Nature. I have already quoted, from the same author, the instance of shavings. The shape of shavings at a carpenter's bench might furnish another Sherlock Holmes with the proof that his murderous mechanic was left handed ; for this he most probably was if the shavings exhibit a sinistral spiral. The innocent shaving of the right-handed carpenter would be dextral because he invariably drives his plane a little to the left ; and I have C.L. R Fig. 276. — A Sketch by Leonardo ■DA Vinci. 242 THE CURVES OF LIFE also noted that Japanese and other Orientals seem to prefer a left-hand spiral, just as they write from right to left, as may be seen in many instances of their workmanship, such as the screws of watches made in India, and other matters. In this country screws are not changed from the usual right-hand spiral of the penetrating corkscrew unless some special object is in view. Two examples may be useful. The first is the coffin screw, that fortimately rare variety, which only penetrates when you turn it to the left. The other is the rifling in a Lee-Metford, which is made to turn to the left in order to counteract the pull of the P- r^'^y. 'V-rjJ- rv ' ■'s/ "t Fig. 277. — Marsh Marigold and Wood Anemone. (From a Drawing by Leonardo da Vinci.) average right-handed soldier. It is curious that all left-hand spirals look as if they were at almost double the pitch of the corresponding right-hand spirals ; perhaps because they are less familiar to the eye. The investigations of the Anthropological Society in Washington (May, 1879) go to show that, though left-handed workmen existed in the Palaeolithic Age, prehistoric man was as a rule right handed, as we shall see when we come to the interesting question of torques. The buttons of a man's dress, like the hooks and eyes of our ladies' attire, are now expressly adapted to the right han 1. So are the adze, the plane, the gimlet, the cutting end of the augur, the scythe, the fittings of a rifle, scissors, RIGHT AND LEFT-HANDED MEN 243 snuffers, shears, and other mechanical tools which must be used by one hand or the other ; or, when used by several men at once, must be used by the same hand in each man. All this, however, will not prevent one who is naturally left handed from continuing his natural practice, though it is attended by great mechanical inconvenience in all the instances mentioned. A man with only a slight bias towards his left hand will readily become ambidextrous owing to the many right-handed conventions and appliances which occur in everyday life. But the instinc- tively and strongly left handed will never change, and is usually distinguished for his skill, as Sir Daniel Wilson has pointed out in his interesting monograph on the subject. When Gideon discomfited the hosts of the Amalekites, the 700 Benjamites he selected for their superior skill in slinging were all left handed. Only the best, in fact, of the left-handed men can survive in the struggle against the vast majority of right-handed influences around them, and their skill will go on increasing, as may be seen in the case of left-handed fencers who have far more Fig. 278. — Signature of the Artist, written with his Right Hand. opportunity of practising against right-handed men than we have of getting used to them. The instances of left-handed men quoted in the Bible are worth noticing. In Judges iii. 15, we read how " the Lord raised them up a deliverer, Ehud, the son of Gera, a Benjamite, a man lefthanded." The chief value of this, in the incident which has made Ehud immortal, was that he was able to conceal his dagger beneath his raiment " upon his right thigh," where his enemy never suspected its presence, and the fatal stroke was therefore completely a surprise. The passage about the shngers, mentioned above, does not say that the 700 out of the 20,000 children of Benjamin were the only left-handed ones among them, but only emphasises the fact that these were the best slingers ; and no doubt others of them, hke Ehud, preferred to use their left hands for their daggers ; and this brings the total up to a percentage which suggests that possibly a certain group of famihes were congenitally left handed. This theory may perhaps gain consistence from the coincidence that the left-handed men, of whom " every one could shng stones at an hair breadth and not R 2 244 THE CURVES OF LIFE miss " (Judges xx. i6), " numbered seven hundred chosen men " and the inhabitants of Gibeah are also described as " seven hundred chosen men " in another verse. This is strengthened by the passage in i. Chronicles xii. 1—7, where it is recorded that among those who came to help David were " Ahiezer, then Joash, the sons of Shemaah the Gibeathite," of whom it is further said that " among the mighty men, helpers of the war, they were armed with bows, and could use both the right hand and the left in hurling stones and shooting arrows out of a bow, even of Saul's brethren of Benjamin." It is easy to see what an advantage ambidexterity would be in early warfare, and several instances of it are recorded in history ; while its benefits to prehistoric man, in hurling stones or axes, must have been yet more remarkable. Of course, in our age of " arms of precision " and of carefully- drilled regiments, it is essential that all the men in line should carry and manceuvre their rifles on the same side, and therefore, by general custom, on the right side. For the same reason, all scabbards were hung on the left side, or confusion would have resulted when a closely-packed line drew their swords. I was at first inchned to think that the persistence of the left-hand twist in prehistoric Irish torques, as may be seen from examples from Dublin, and in the British Museum, was due either to the predominance of the usual Celtic left handedness in Ireland, which is shown by the use of the light left-hand axe mentioned by Giraldus Cambrensis, or to the fact that the most skilful artificers were developed from left-handed men. But nothing is so strange about spiral formations as the results of practical experience, and I soon found that (as was described in my second chapter) the flat ribbon of soft gold from which the earliest torques are made would naturally become a left-hand spiral if twisted by a right-handed man, for he would hold down one end with his left hand, and would twist the other end outwards with his right hand, with the result that the spiral of the twisted gold would be left hand, as my readers have already proved to their own satisfaction with a long piece of narrow paper. This may account for the fact, that from the many torques I have examined, all the gold examples were left hand, the only right-hand spiral shown being a silver specimen in the Germania Museum at Nuremberg, and another silver specimen now in the Society of Antiquaries. The five-coiled armlet in the British Museum exhibits the usual left-hand twist, but has the additional charm of showing four distinct spirals, which has resulted from the use of four flat ribbons of gold united, the combined section being cruciform before the process of twisting had begun. Examples of torques are given in my next chapter. RIGHT AND LEFT-HANDED MEN 245 I have mentioned that in the case of twisting ribbons, or of fencing, the natural movement of most men's right hand (when -3^ "'■VI 'tA\Ar • I ««r-.-r./w»fc/^7' /TV v-v y rf r."~> 1 '^ r?-» 'i -t HW'i-t-r^n^ ■\ «'^i.?iif'. <^'-cy]i«1 f'^'^' JJ/»)'.W»J^ V^IAf'l -fA ^yv'-''- ^?..,-°t. Fig. 279. — A Page of Leonardo's Usual Handwriting. From his Manuscript Note Book on the FHght of Birds. This manuscript was transcribed by Giovanni Piumati and trans- lated by Charles Ravaisson Mollien. It can be most easily read when held before a mirror, as each line is written from right to left. The first two lines are as follows : "II predetto ucello sidebbe coll' aiuto del vento levare ingrande alteza e cquesta sia la sicurta perche . . " or in English, " The bird above mentioned should, with the help of the wind, raise itself to a great height, and this will be its safety because ..." it is at rest with the knuckles upwards) is to turn the wrist in the direction away from the body until the knuckles are 24'3 THE CURVES OF LIFE underneath and the flat pahn upwards. In driving, this instinctive movement of the right hand on the reins would turn a horse to the right when passing an obstacle in its way, and most nations are content that this should be so, although the coachman's seat is placed over the right wheel. The English, however, have preserved the old habits of their riding days, when all reins were held in the left hand to leave the sword arm free, and the instinctive movement of the left hand, from the position at rest with knuckles upwards, is to turn outwards until the knuckles are beneath. This movement gives a twist to the rider's reins which must turn his horse to the left, and the English still drive, as well as ride, to the left ; they like to see where their right wheel is going. This rule obtains in Portugal, Sweden, Hungary, most of the cities of Italy, certain cantons of Switzerland, and certain provinces of Austria ; and it is very singular that the practice in this matter is so varied that in some districts of a large country a notice has to be put up warning strange drivers where the change occurs. There seems little evidence to guide us in any inquiry as to why one district favours one style more than the other ; and it will be interesting to see which side will finally survive in those new rules for the traffic of the air, which will certainly have to become more fixed and universal than the old " rules of the road." The custom of keeping to the right when walking seems already in danger in London ; yet it is certainly older than any rrfle for driving past vehicles in the street ; for it must be a survival of the days when men carried weapons, and were therefore careful that their own left arm was next the left arm of a passing stranger, who might just possibly be an enemy ; and in those times the fighting arm was the right arm, which held the sword or pistol at full length. There may also be a further reason, handed down from a remoter age, for the survival of passing to your right and hfting your hat with the right hand. It gave the man you met an unobscured view of your face. I imagine that confusion in this matter may have arisen from two causes ; the first, that, when boxing became prevalent and finally ousted dueUing altogether, the left arm became the aggressor ; the second and more pacific, that when ladies took to walking about the street more than had previously been their custom, they were generally " given the wall " by their attendant swains, with the result that the side on which men walked was largely regulated by reference to their architectural surroundings. It is also noteworthy that the custom of giving a lady your right arm arose out of the peaceful promenade from the withdrawing-room to dinner. It is a custom that would hardly have been general when a man had to be ready at any RIGHT AND LEFT-HANDED MEN 247 moment to protect a woman in his charge with the strength of his sword-arm. (See Mr. A. E. Crawley's article on " The Rule of the Road " in the Field for Eebriiary 3rd, 1912.) Such changes are very natural, if only as a reaction from the irksome necessities of warfare. Peace, dehberately perhaps, selected their exact opposites, to emphasise security. m "il ' ' ' j i p 11 .'« Fig. 280. — Hind Quarters of Arab Horse. (From a Drawing by Leonardo da Vinci.) It would be a singular question to determine whether driving to the left was developed by ourselves or copied from another nation. In old days, before wheeled vehicles were common, the packhorse and the led horse always passed to the right, so that its leader might be between it and any passing traffic. Even when a waggon-team were led by the carter, the same custom prevailed, and this may have originated the right-hand driving of the United States, a country far more conservative of old 248 THE CURVES OF LIFE English habits and old Enghsh language than we are ourselves. It has been suggested that the change was only made in these islands when coaches became more common in the early seven- teenth century. But this is one of the many small details that no writer seems to have chronicled, and we can but guess at possibihties. As a matter of fact, if the rule of the road in driving was indeed changed as late as this (which I doubt, for it must be far older), it was only made law, as we know it now, in 1835, when coaches and teams were driven faster than they had ever been, and when it was essential for a coachman to have his whip hand free if he was to control the leader on the offside. The width of most country roads (then and even to-day) was not much more than enough for two teams to pass each other, and it was therefore also necessary for the coachman to have full view of that side of his vehicle which might be endangered by collision. So he was practically obliged both to sit on the right and to drive to the left. When he had to pass another vehicle from behind, that vehicle, having been first in the position in which it was overtaken, was " given the road " and stayed there, while the overtaking coachman had to steer to the other side. It may be of interest to consider a few notable examples of left-handed men who have distinguished themselves in various forms of sport. I will take angling, archery, billiards, bowls, cricket, croquet, fives, golf, lawn tennis, polo, and shooting as a fairly typical selection. Angling. Most capable anglers would be ambidextrous if they could, and George Selwyn Marryat might be quoted as the great instance of perfect mastery with either hand. In tournament work at the present day probably the most finished caster is Mr. David Campbell Muir, whose left hand is very nearly as good as his right. Archery. There have been, or are, very few left-handed archers ; only two men, as far as I know, have ever done anything, and none of the ladies have ever shot well. Both, of the men began as right- handed shots, and took to the left hand later. W. Butt on one occasion shot in one day one York Round with each hand with the following result : 100 yards. 80 yards. 60 yards. Total. Hits. Scr. Hits. Scr. Hits. Scr. Hits. Scr. 34 134 ... 2S 122 ... 21 105 ... 83 361 right handed. i5 68 ... 23 77 ... 21 95 ... 60 240 left handed. His best rounds were : — Feb. 8, 1864 48 216 ... 42 172 ... 23 113 ... 113 501 right handed. Maj' 30,1867 44 206 ... 36 154 ... 24 138 ... 104 498 left handed. RIGHT AND LEFT-HANDED MEN 249 He never shot anything hke so well at any public meeting, his best position at the Grand National having been seventh in 1870, with 152 hits, 726 score (two days). The late G. L. Aston's best score at a public meeting was at the Grand Western in 186 (., 190, 838 (two days), right handed. In 1876 he made 176, 740 (two days), left handed. His best place at the Grand National was sixth in 1893, with 153, 669, and he was seventh the next year with 162, 688. Billiards. The list of left-handed players who have distinguished them- selves at billiards is a remarkably small one. More than half a century ago Mr. Bachelor was generally acknowledged to be about the finest pyramid player of his day, whilst in the seventies, T. Morris and F. Symes were well known professional players, though neither ever attained a position even in the second class. The only really great left-handed player we have ever had was Hugh McNeil. His " touch " was superb, and there is little doubt that it lay with himself to become champion. Unhappily, however, he could never be induced to take the smallest care of himself, and he died November 27th, 1897, at the early age of thirty-two. The only left-handed amateur player of note that I can call to mind in the last forty years is Mr. W. Edgar Thomas, amateur champion of Wales. Bowls. Several of the most accomplished players at the game of bowls are left handed. The following instances are well authen- ticated ; — 1. Andrew H. Hamilton, S.S.C, of Lutton Place B.C., Edin- burgh, has represented Scotland in the International matches, has won the championship of his club six times, and was twice champion of Edinburgh and Leith. He is the secretary of the Scottish Bowling Association. 2. C. E. Dunlop, of Wellcroft B.C., Glasgow, played for Scotland in 1910, and has won the famous Moffat Tournament and the championships of the WeUcroft and Stepps Clubs. 3. Andrew Paterson, of Cathcart B.C., Glasgow — now over eighty — is one of the best players Glasgow ever had. 4. James Christie, of Queen's Park B.C. Glasgow, skipped the rink which won the Scottish Championship in 1902. 5. J. W. Clelland, of Larkhall B.C., one of the best players in Lanarkshire, played for Scotland in 1911. 6. James Fleming, of Ardmillan B.C., Edinburgh, has been champion of his club, and skipped the rink which won the Edinburgh Championship. 250 THE CURVES OF LIFE 7. Richard W, Milne, President of Lockerbie B.C., in 1910, was runner-up in the Lochmaben Open Tournament in 1910. 8. E. Lloyd, hon. secretary of the Welsh Bowling Association (of which the Earl of Plymouth is President), of the Cardiff B.C., has played for Wales in several matches (International). 9. Dr. C. Coventry, of Dinas Powis B.C., played for ^^'ales in the International match in 1912. 10. D. Wilkinson, of Dinas Powis B.C., has played for Wales in several Internationals, and was captain of the team in 1911. (Mr. Wilkinson has lost his right arm, and is an example of acquired left handedness). 11. A. Hutchins, of Penhill B.C., played for Wales in the International match of 1911. 12. W. A. Cole, of the Macintosh B.C., Cardiff, has repeatedly plavcd for ^^'ales in the Internationals. 13. T. P. Edmunds, of Cardiff B.C., is a regular skip in his club's matches. 14. John McCann, of Ormeau B.C., Belfast, has played for Ireland in the International matches. 15. Joseph A. McClune, of Ormeau B.C., Belfast, reached the semi-final in the Irish Single-handed Championship in 1909. He and Mr. John McCann (No. 14), when members of the Ormeau United B.C., which won every match it played during the two years of its existence, were respectively third man and skip of the rink that played unchanged through the nine matches. 16. Franc Brown, of Belfast B.C., has played for Ireland in the Internationals, was second in the Belfast quartette that won the Irish Rink Championship in 1909, and is a deadly player on the back hand. 17. John A. McClune, of Ulster B.C., Belfast (brother of No. 15), is a very successful skip of his club, and a winner of several single- handed championships. 18. David E. Henning, of Shaftesbury B.C., Belfast, formerly a fine cricketer, is one of the best skips of his club. 19. Dr. J. W. Taylor, of Belfast B.C., once one of the best rugby forwards in the kingdom and a capital bat, has represented Ireland, though a comparative novice at bowls, in the Inter- nationals. 20. B. D. Godlonton, of Streatham Constitutional and Dulwich Bowling Clubs, has played for England in the Internationals, and was formerly a member of the Sussex county cricket eleven. 21. H. E. Freeland, of the Mansfield B.C., London, was champion of his club in 1909, defeating D. Rice Thomas, hon. secretary of the London and Southern Counties B.A., who had RIGHT AND LEFT-HANDED MEN 251 previously beaten Henry Stubbs, now of Hernc Hill B.C., the last two well known single-handed players. 22. W. E. Warran, of the Brownswood B.C., London, president of his club in 1910, and in 1912 its hon. secretary, is an example of ambidexterity. When playing the forehand he employs his right, and when playing the backhand his left hand, using both with equal skill. He is a successful skip in his club, and in 1909 skipped the rink that made the highest score on the winning side in the annual encounter between the London and Southern Counties B.A. and the Midland Counties B.A. His method of play is unique. Cricket. In first-class cricket left-handed bowlers play a conspicuous part. A county eleven is not considered to be well equipped without one. The break-back, which is more easily acquired than the opposite break, is formidable from a left-handed bowler, because it produces catches on the offside. Hence the majority of these bowlers are of slow or medium pace, and are deadly on slow wickets. Occasionally a fast bowler possesses a strong natural break of this kind ; for instance the late Fred Morley and Hirst. Young, the Essex bowler, breaks chiefly in the opposite direction. Recently swim bowhng has been cultivated by left- as well as right-hand bowlers ; for instance. Hirst. Dean, of Lancashire, has two styles, the slow break-back and the faster swim. Batsmen are less common than bowlers. Batting is taught, and the use of the right hand has been encouraged, perhaps from the idea that left-handed batting is awkward in style, or gauche. It is difficult to repress this idea, but to a great extent it is probably illusory and subjective. A right-handed action, e.g., shaving, appears gauche when seen in a mirror. Such bats- men as Bardsley and Clement Hill seem graceful in spite of left- handedness, and the addition of Ransford makes the best Austra- han eleven remarkable for its left-handed talent. Nourse, of South Africa, is another prominent colonial instance. But left- handed bowlers have commonly a delightful freedom of action and appearance of naturalness. Owing to the reason above suggested— that batting is the product of teaching— instances of left-handed bowling combined with right-handed batting are common, especially among amateurs, as in the case of Mr. F. R. Foster. Instances of left-handed batting with right-handed bowling are not very rare. The best example is Mr. C. L. Town- send. It is so advantageous to bowl with the left hand, that it seems strange that a player who is ambidextrous enough to bat left handed and bowl right does not prefer to cultivate the left hand for both purposes. Left-handed batsmen are now much 252 THE CURVES OF LIFE sought after. It is recognised that they have different strokes from right-handers, and cause trouble to certain bowlers. They can, of course, cope better with the right-handed bowler, who relics on what to right-handed batsmen would be a leg break, and they make them bowl on the unaccustomed side of the wicket — though this change of side (fashionable as it is) is not certainly good policy. Further a left-handed batsman when associated with a right-handed causes frequent changes in the field, and so makes the game slow. This is not only valuable when time has to be killed, but also when it is desirable to stop a " rot." The victorious M.C.C. team in Australia had three left-handed batsmen and four left-handed bowlers. Ambidexterity is not unknown. A well-known club cricketer, Mr. P. Northcote, is said to have made loo runs batting right, and then another loo left in an innings. I have some remembrance that a University bowler, E. Bray {circ. 1870), bowled alternately with either hand. A schoolmaster at Ewell about 1880 habitually bowled lobs with his left, and for a change fast round right. Ambidextrous throwing in, though extremely valuable, is very seldom culti- vated. Edmund Hinkly (Kent) took all ten wickets with his left-handed bowhng in an innings against England at Ford's in 1848. Jim Lillywhite (Sussex), Peate and Peel (Yorkshire), Fred Morley and J. C. Shaw (Notts) may also be quoted as famous left-handed bowlers. Kent produced another first - rate left hander in Edgar Willsher, and George Wootton (Notts) may be cited as another instance of first-rate ability in the past. Among examples of the best left-handed batsmen of the old days may be cited Mr. Richard Newland, who captained England against Kent on the Artillery Ground at Finsbury in 1744 ; Mr. N. Felix and Mr. Richard Mills of Kent, ; James Saunders, R. Robinson, John Bowyer, and George Griffith, all of Surrey ; Richard and John Nyren, Tom Sueter, Noah Mann and " Lumpy " Stevens (who bowled left and batted right), ah from Hambledon ; Noah Mann also played for Sussex, as did the Mr. Newland mentioned above, John Hammond, Mr. E. Napper, and Mr. W. Napper ; B. Good (Notts) ; W. Searie ; T. Marsden (Sheffield) ; and James Aylward (Hants), the first man to make a hundred after the third stump had been added to the wicket. A list of modern left-handed players, for the sake of contrast, would contain many well-known names. They may perhaps be classified as follows : Left-handed bowlers may be represented by Mr. F. R. Foster, Dean, Woolley, and Rhodes, all in the English eleven for 1912, Hirst, Blythe, C. P. Mead, and Tarrant. The first and third are also good left-handed batsmen. Rhodes, Hirst, and Tarrant bat right handed. In the Australian eleven RIGHT AND LEFT-HANDED MEN 253 for the same year, Mr. W. J. Whitty and Mr. C, G. Macartney are both left-handed bowlers, but the latter is a first-rate right-handed batsman. In the South African eleven (to complete the " tri- angular " contrast), G. C. Llewellyn bowls and bats left-handed. Mr. A. D. Nourse is first rate in both bowling and batting left hand, and Mr. Carter bowls left handed. Among famous left- handed batsmen who bowl right handed, Mr. C. L. Townsend, of Gloucestershire, is the best example, and Kilhck, of Sussex' is another. Other good left-handed batsmen will occur to the memory, such as Mr. H. T. Hewett, Somerset ; Mr. F. G. J. Ford, Middlesex; Mr. J. Darling, Australia ; Scotton, Notts, and others. Croquet. In croquet there are but few first-class left-handed players, and the only ones I can think of are Mr. R. C. J. Beaton (— ij) Mr. H. Maxwell Browne ( — ji), who plays his croquet and roll strokes with a left-handed stance. He runs his hoops and shoots in the Corbally style, i.e., with his mallet between his legs, but as his left hand is nearer the head of the mallet, I consider he may be fairly classed as a left-handed player ; Mr. W. H. Fordham (o) ; Mrs. H. M. Weir (ii) ; and Mrs. W. Whitaker (ji). Other left- handed players, whose class is difficult to determine, are Miss M. Gower (4) and Mr. R. P. M. Gower (6), the sister and brother of Mrs. R. C. J. Beaton. Fives. One of the best fives players I ever saw was left-handed : H. R. Bromley Davenport, Keeper of the Fives Courts at Eton in 1888. He thus had a great advantage, as it enabled him to hit harder and much more freely than right-handed players at a ball coming over the buttress, which is on the left side of an Eton fives court. Golf. Few left-handed golfers have achieved real eminence. There has been no professional who, in the words of the old story, has " stood on the wrong side of his ba' " and won competitions nevertheless. Among amateurs Mr. Bruce Pearce, the young Tasmanian who made so favourable an impression on opponents and spectators recently, is as good as any other, with the possible exception of Mr. H. E. Reade, of Portrush. This gentleman ought to have put Mr. Travis out of the 1904 championship. On the fourteenth green from home he stood two up, but allowed his opponent to win all the remaining holes without doing anything extraordinary. Mr. Peter Jannon, another Irishman, has won countless championships on the Continent, and Mr. J. A. Healing, 254 THE CURVES OF LIFE the old Gloucestershire cricketer is distinctly a good player. \Mien Harry Vardon was engaged at Ganton, his members got rather tired of being beaten by him, though in receipt of extravagant odds. He made a futile attempt to relieve the monotony of the results by playing left-handed from a handicap of scratch. It was soon decided that he ought to owe two as a left hander. There seems here to be some connection between left handedness and Celtic blood, as we have observed before ; for the chief market for left-hand clubs is said to be in the extreme north of Scotland, where right-handed players are reported to be in the minority. Lawn Tennis. An interesting list of left-handed players in lawn tennis may be compiled ; and a few typical instances would be the following : Dwight F. Davis (America) — doubles champion of America (1899- 1901) ; his smashing overhead was remarkably severe, probably harder than any player in the world. Beals C. Wright (America) — singles champion of America, 1905 ; doubles champion of America, 1904-1906 ; represented America in Davis Cup matches in America, England, and Australia ; like Dwight Davis severe overhead ; exponent of chop stroke ; eminently sound, low volleyer. Norman E. Brookes (Australia) — singles champion of the world, 1907 ; winner of all comer's singles at Wimbledon, 1905 ; doubles champion (with Wilding), 1907 ; represented Australasia in Davis Cup matches in England and Australia ; the deadly power of his break service is well known ; relatively weak overhead ; plays his back-hand volleys with the finger tips towards the net, i.e., contrary to the usual English custom. The late Herbert Chipp (England) was well known in the eighties as a contemporary of the Renshaws. He had no orthodox back- hand stroke, but would quickly change his racket and drive nearly as hard with his right hand as with his left, as did Miss Maud Shackle, champion of Kent (1891-3) ; a sound base-liner, who could generally pass the most nimble volleyer. Kenneth Powell (England) — a recent captain of Cambridge six ; his promise of some years ago has scarcely been fulfilled ; essentially a volleyer who draws on his powers as a track athlete (he made the hurdles record [15 3-5 seconds] for Cambridge v. Oxford, 1907) to secure a winning position at the net. The late F. W. Payn (England) — champion of Scotland, 1903 ; another left hander who was essentially a volleyer. As a rule, left-handed players have developed one or two strokes more than others, and are not remarkable for their aU-round capacity. Generally speaking, as in the case of Brookes, Beals Wright and Dwight Davis, they are stronger on the volley than off the ground. RIGHT AND LEFT-HANDED MEN 255 A. E. Beamish (English International) is right handed at lawn tennis, and left handed (handicap 6) at golf. It may be added here that Mr. E. B. Noel won the rackets championship with left- hand play. Polo. The following left-handed polo players have been officially registered at Hurlingham, and may therefore be taken as good instances of the particular play for which we are looking : J. S. Bakewell, Lieut. R. C. Bayldon, R.N., H. A. Bellville, T. A. Driscoll, F. J. Grace, A. Grisar, W. P. Gwynne, L. R. S. Holway, L. Larios, G. A. Lockett, J. McConnell, Bradley Martin, jun., Baron Osy de Zegwaart, E. A. Sanderson, H. Scott Robson, Capt. A. Seymour, P. D. Sullivan, R. Wade-Palmer, W. Craig Wadsworth, Watson Webb, and iMajor F. H. Wise. Shooting. Mr. Harting tells me that he has known several left-handed shooters, some of them good shots, but only one who could shoot equally well from either shoulder. That was the late Sir Victor Brooke. Shooting one day in 1885, in his own park at Colebrook, CO. Fermanagh, he kihed 740 rabbits to his own gun. He fired exactly 1,000 cartridges, and shot from his right shoulder for one half of the day and from his left the other half. The last shot, from the left shoulder, kiUed a woodcock going back. Left-handed Artists. I have mentioned, in the first part of this chapter, the names of two left-handed artists. Sir Edwin Landseer is a well-known example of a man who could not only use either hand equally skilfully, but could also use both at once on different subjects ; and this suggests that by limiting our activities to one hand we really lose a great deal that might profitably be learnt. Whether the use of both hands would also have some kind of reflex result, beneficial to the biain, is a question outside our present inquiry. It is, however, remarkable that the greatest left-handed genius ever known was not merely one of the most skilful artists, but also one of the most extraordinarily gifted intellects the world has ever seen ; and it is for this reason that I have chosen to illustrate this chapter entirely with the drawings of Leonardo da Vinci. From the technical point of view of our immediate discussion, these drawings show that, evidently from natural preference, the lines of the shading nearly always fall from left to right (see Figs. 276, 277, etc.). The signature from the Windsor manu- scripts (Fig. 278) is so uncertainly framed because it has been done with his right hand. The natural handwriting shown in Fig. 279 256 THE CURVES OF LIFE is not only far more clear and erect, but has the further pecuharity of reading from right to left (like Hebrew) so that it has to be held before a mirror in order to be quickly deciphered. Though less than a dozen undisputed examples of Leonardo's paintings exist, it is chiefly as a painter that he is known to general fame. The bulk of his sketches and manuscripts in this country exceeds by many times the whole of those possessed by other nations, yet the value and contents of these do not seem to be so well appreciated in England as they are elsewhere. They have been investigated by Venturi, Libri, Govi, Richter, Ravaisson- Mollien, Beltrami, Miintz, Mliller-Walde, Uzielh, Sabachnikoff, Piumati, Duval, Scailles, and the editors of the facsimile edition of the Milan manuscripts, to name no more. Apart from the actual drawings and studies they contain, these manuscripts are very much like the notes that might be made by an exceptional professor for a course of very extraordinary lectures. They display a gift of literary expression and construction which lags very far behind the ardour for discovery that inspired them. For this reason their writer remained almost unheard by his contemporaries, and is scarcely yet appreciated by his posterity. His arguments are not presented in that logical form which helps a reader to understand their drift. His discussion of the connection between the scriptural Deluge and the fossil shells found upon a mountain top is one of the few cases in which the literary form of the inquiry is complete. It is therefore only natural that the isolation of his own intellectual life should have been almost reproduced in the comparative neglect of his manuscripts in later years. It was one of his favourite sayings that the strength of the painter was in solitude : " Se tu sarai solo, tu sarai hitto tuo." Another drawback is the material one of the difficulty in deciphering his writing. Whether it be true or not that it was owing to travels in the East that he took to writing from right to left, it is certain that he largely employed a cahgraphy which can best be read in a mirror (see Fig. 279), and which was also an easy accomplishment for a left-handed man. A landscape drawing in the Uffizi — the authenticity of which has never been called in question — is dated " The day of S. Mary of the Snow, the 5th day of August, 1473," when Leonardo was just twenty-one ; and Mr. M'Curdy has pointed out that this inscrip- tion shows Leonardo had already adopted the method of writing from right to left ; so that I prefer the theory that this was the natural method of the left-handed man, rather than the acquired result of any possible travels in the East. If the shading of his drawings had not revealed the peculiarity, we should have RIGHT AND LEFT-HANDED MEN 257 known that Leonardo was left handed from the statement of his friend Era Luca Pacioh, for whose book, " De Divina Proportione," he designed the figures. These are some of the reasons why the secrets of a man who .,y... j / . ' A Fig. 281, — Dr.\wing by Leonardo da Yinci. spent the last years of his life in exile at the beginning of the sixteenth century remained his own until the last years of the nineteenth. Yet his fame is only strengthened by that long oblivion. For the laws which he established or divined have been independently discovered and proved as advancing know- ledge made researches easier ; and the reputation of his c.L. s 258 THE CURVES OF LIFE successors remains untarnished, for, though their discoveries must now be antedated by three or four centuries, they made them in their turn while Leonardo's manuscripts were still unknown. A sower of ideas of which he never saw the harvest, he jealously guarded them from intrusion during his lifetime, and they never came to light till long after his death. Before me as I write are some 500 careful photographs of the originals existing in England, to which it may be hoped that a fuller justice will some day be done than I can now find to be the case. Though it was necessary to examine all of them, only a very small fraction bore upon the special subject of this work, and only a very few examples have been chosen out of these to indicate the kind of material available (see Figs. 280, etc.), and to produce the barest essentials in the progress of our argument. I have also examined the MSS. in Paris, Venice, Vienna, and Milan, where the numbering of the great " Codice Atlantico " has been corrected by the Abbe Ceriani, and the whole is being reproduced at the cost of the State. They embrace drawings of landscape and figures, which are evident!}' studies for pictures ; anatomical drawings of great beauty and skill (Fig. 282) ; botanical sketches (Fig. 277) ; architectural plans, biological notes, numerous engineering problems, many mathematical inquiries, the whole dashed down without much order in a very fervour of investigation. Though many pages that have survived cannot, under any hypothesis, be considered as prepared for pubhcation, there is some evidence in others that Leonardo not only wrote for a public, but was conscious of his literary short- comings. " Blame me not, reader," he says, for instance, in one notebook, " for the subjects are numberless, and my memory is weak, and I write at long intervals. ..." Carrying as he did, in that brain which bore so many images of beauty, not only all the science known at the beginning of the sixteenth century, but almost half of the attainments that the years since then have brought us, Leonardo lived of necessity a lonely life ; and with advancing years it is known that his thoughts turned more and more from painting to problems of natural science, and to vast collections of natural objects. His quest was that of Goethe's Faust : — " Das ich erkenne, was die Welt Im innersten zusammenhalt. Schau' alle Wirkenskraft und Samen Und thu nicht mehr in Worten Kramen." It was characteristic of his genius that the patent phenomena of Hfe did not content him. He insisted on going deeper. " Ma RIGHT AND LEFT-HANDED MEN 259 tu che vivi di sogni," he writes in the " Treatise on Flying " (Fig. 279), " ti piace piti le ragion soffistiche e barerie de f atari nelle cose grande e incerte, che delle certe, naturali, e non di tanti altura." His intellect was as sincere as it was sagacious. He penetrated the secret hiding-places of truth with a passionate industry that never shrank from toil. " Truth," he cries, " is so excellent that by her praise the very smallest things attain nobility." His method was that of Darwin, proceed- ing by an analysis which does not fear to be diffuse ; grouping isolated pieces of evidence, attaining at last a final law, or at least a hypothesis that would explain the facts. His anatomi- cal drawings, apart from their exquisite draughtsmanship, contain so many keen parallels and suggestive indications that the author of the " Origin of Species " would have perused them with delight. In the manuscripts at Windsor, for example, there are careful drawings to show that the tail in other animals existed in a modified form in man. Huxley's manuscript memoranda are, I am informed, full of dehcate drawings, and in other ways somewhat similar to those of Leonardo. It is perhaps a loss both to science and to art that the majority of Leonardo's manuscripts do not seem to have been known, as far as we are aware, either to Darwin or to Ruskin. He understood to the fuh the defini- tion of science as " the knowledge of causes " — Tore eTTtirrd/xf^a oral' ttV alriav etSa)M«'- He reahsed even more keenly the necessity that science should be largely occupied with speculations, with hypotheses, with imagina- tions, with what MiiUer in 1834 called " Phantasie." Nature must be interrogated in such a manner that the answer is imphcit in the question. The observer can only observe when his search is guided by the thread of a hypothesis. I have said that it was the thread of spiral formations which has guided these chapters. It was (let me repeat) the manuscripts of Leonardo which inspired them. s 2 ..<-(.v«,=C.o|i..,'.-.*'--3 Fig. 282. — Anatomical Study BY Leonardo da Vinci. Note the handwriting in one corner. 26o THE CURVES OF LIFE NOTES TO CHAPTER XIV. Right and Left Hand. — " In chapter five of the fourth book of his ' Enquiries into Vulgar and Common Errors ' (third edition, 1658) Sir Thomas Brown has much to say ' of the right and left hand.' He mentions the remedies of ' the left eye of an hedgehog fried in oyl to procure sleep, and the right foot of a frog in a deer's skin for the gout,* and, further, that ' good things do pass sinistrously upon us, because the left hand of man respected the right hand of the gods which handed their favours unto us.' But his most permanently valuable observa- tion is that the words ' right ' and ' left ' are purely human conventions, which may enable men and women to give intelligible directions to their comrades, but which have no reality in nature, any more than there is any certainty that the right hand of a particular man will be stronger and more skilful than his left. For some men use their left hand as most men use their right. "B. T." Survival of Left-handed Men. — See " Ambidexterity," by John Jackson (1905). Left-handed Men in the Bible. — " F. M. M." wrote : — " It is singular, and perhaps not easy to explain, that in the Hebrew of Judges iii. and xx., both Ehud and the 700 slingers are described as ' shut (bound or hindered) of the right hand ' ; but in the Greek version, the Septuagint, both the one and the other are called ' ambi- dexterous,' a meaning which it seems difficult to get from the original." Leonardo's Notebook on the " Flight of Birds " was written by Leonardo da Vinci at Florence in March and April, 1505, and left by him in 1519 to Francesco Melzi, who died in 1570. From Melzi's Villa of Vaprio it was stolen by Lelio Gavardi, and finally given by Horace Melzi to Ambrosio Mazzenta of Milan. From him it passed to Pompee Leoni, friend to Philip II. of Spain, and by his heir was sold to Galeazze Arconati, who gave it, on January 21st, 1637, to the AmbrosianLibrarj' in Milan, where its existence is recorded by Balthasar Oltrocchi between 1748 and 1797, and by Bonsignori in 1791. All thirteen MSS. of Leonardo were sent to Paris by Napoleon in 1796, the Codex Atlan- ticus to the Bibliotheque Nationale, the twelve others to the Institut de France. In 1815 the Codex Atlanticus went back to Milan, the rest remaining (by error) at the Institut, where the existence of this treatise on flight is noted by the sub-librarian in 1836. From there it was stolen by Jacques Libri, as Lalannes and Bordier noted in 1848, and was seen in Florence by Count J. Manzoni de Lugo in 1867, who bought it at Libri's death in 1868, and died himself in 1889. In 1892 it was bought by Theodore Sabachnikoff, and pubhshed in Paris in 1893. "Das ich erkenne." — " O for a glance into the earth ! To see below its dark foundations Life's embryo seeds before their birth. . . ." (Goethe's " Faustus," trans, by John Anster.) " Ma tu CHE Vivi." — " But thou who hvest in dreams art more pleased even with the sophistical reasonings and theories of philanderers RIGHT AND LEFT-HANDED MEN 261 when they deal with great and unknown matters, than with researches into tilings certain, natural, and of a lower interest." " Truth is so Excellent." — The passage begins as follows : " Ed h di tanto vilipendio la bugia, che s'ella dicessi be'gran cose di dio, ella to' di grazia a sua delta ; ed e di tanta eccellenzia la verita. . . ." Phantasie. — " Die Phantasie ist ein unentbehrliches Gut ; denn sie ist es, durch welche neue Combinationen zur Veranlassung wichtiger Entdeckungen gemacht werden. Die Kraft der Unterscheidung des isolirenden Verstandes, sowohl als die der erweiternden und zum Allgemeinen strebenden Phantasie sind dem Naturforscher in einem harmonischen Wechselwirken nothwendig. Durch Storung dieses Gleichgewichts wird der Naturforscher von der Phantasie zu Trau- mereien hingerissen, wahrend diese Gabe den talentvollen Natur- forscher von hinreichender Verstandesstarke zu den wichtigsten Entdeckungen fiihrt." — Joh, Muller, Arch, fur Anat., 1834. Right and Left. — A letter from Mr. A. E. Crawley : — " Of all the simple opposites in the world none seem so simple as right and left. There is no difficulty when the terms apply to mere position or to straight hnes. Trouble begins, both for understanding and for language, as soon as they apply to curvilinear or circular motion. This is hkely to be the experience of anyone who studies spiral forms in plant or animal structures, or the swerve of balls, or rotation of any object, or even one who has been led to meditate on rules of the road by the recent conclusion of the authorities in Paris that the Enghsh ' Keep to the left ' is better than the French ' Keep to the right.' The matter is simple enough when a bowler describes a ball as breaking from the left or off, and the batsman describes the same as from the right or off. But a projectile, whose swerve is in a plane horizontal enough to admit the terms right and left, may start its journey to the left without our knowing from the description whether the curve continues to the left or to the right. ' Curving out to the left and in to the right ' would sufficiently explain the second case. But ambiguity is often experienced, and it is necessary first to define the terminus a quo and the terminus ad quern. For both Greeks and Romans the right was the lucky quarter for the appearance of omens, but the augurs of the one people faced north, those of the other faced south, the respective lucky quarters being thus diametrically opposite. It is said that the Hebrew ' augur,' if the term may be apphed, faced east. But the result was carried farther than by the Greeks and Romans ; for the Hebrew the right-hand side and the south were identical, his front was east, his left-hand side was north, behind him was the west. Sanskrit, Old Irish (in the component of deasil, deas), and other Indo-European languages identify right and south! There would already in the days of ' seeing ' have been con- fusion of tongues and crossing of purposes, when right and left were synonymous with points of the compass. " The philology of the terms for right and left is curiously interesting, but extraneous to the present subject. Yet it is in point to observe that, as with right handedness itself, so with the terms for this pair of opposites, efficiency and convenience were first regarded long before two sidedness. Carlyle put social sohdarity in a right-handed nut- 262 THE CURVES OF LIFE shell when he invited his readers to consider what would happen if three mowers with the scythe, two being right handed and one left handed, were to try co-operation. It is curious that the name of the Hebrew tribe which supplied a corps of left-handed slingers is Ben- jamin, ' the son of the right hand.' Probably in every language, as in English, ' right ' originally signified merely ' straight,' ' straight- forward,' and thus ' normal.' ' Left ' at first was no opposite to ' right,' but meant ' weak,' 'inefficient.' We thus get the invention of the terms prior to the idea of bilaterality. ' Eyes right,' the ' right road,' ' right satin,' and so forth, are relics of the original meaning. ' Left ' gradually acquired its function of an opposite along lines corresponding rather to ' reverse,' ' abnormal,' than to bilaterality, as in the phrase ' over the left,' which in folk custom cancels or reverses the meaning of the spoken word. Putting this in another way, one has only to remember the real meaning of ' right way on,' ' right side up,' and to compare the imaginary case of a left-handed people, who, of course, would apply the word ' left ' and its series of connotations to phenomena which for us are ' right.' " The only original pair of opposites in ' English,' and the fact is instructive, is deasil and widdershins, sunwise and counter-sunwise. The industrious folklorist is too apt to explain their origin by supersti- tion. Superstition (as even etymology shows) supervenes ; reality and the expression of reality are behind it. It is surprising enough that early thought and language should have hit upon two terms which still render, better than any others, the bilateral aspects of curvilinear statics and dynamics. " The reversal of mere right and left is visualised daily in mirror images (in the literal sense). In your remarkable articles on prin- ciples of growth and beauty you note and illustrate Leonardo da Vinci's left-hand writing. Children in the pre-pubertal period rarely show a natural predominance of the right hand, and when teaching themselves to write frequently practise both hands, with results equivalent to those shown by Leonardo. A curious central moment between ' left-hand ' languages like Hebrew, written from right to left, and the modern ' right handed,' is the sporadic Greek method, known as fivi'(TTpo(f>riSdv, one line being written from right to left, and the next from left to right, saving the process of transferring the pen to the other side of the paper, but originally necessitating a change of hand, and probably of pen, for pens, hke old English nail scissors, when cut sloping, are left handed and right handed. " In ' Ahce through the Looking Glass ' Lewis Carroll denied himself the opportunity (congenial enough to the author of ' right anger,' ' acute and obtuse anger,' and other Euclidean absurdities of reduction) of developing the results of reversal. In his ' Plattner Story ' Mr. H. G. Wells connects the main idea, viz., that the right side of an object is the ' mirror image ' of the left, with atomic disintegration as the means, and the fourth dimension of space as the result. The hero on his return to this, our three-dimensional sphere, was observed to have his heart on the right side and his hver on the left, and to have become not ambidexterous, but left handed. "A simple experiment showing the simplest result of a twist in space is probably familiar to many of my readers. Take a ribbon of paper RIGHT AND LEFT-HANDED MEN 263 long enough to make, when the ends are joined, a conveniently sized circle. Make one twist in it, and then join the ends with gum. Divide it lengthwise with the help of a pair of scissors. Before division you may trace a pencil line along it, and find that the line ends on the ' side ' opposite to that whence it began. After division you will find one ring with twice the circumferential size of the original, and with a double twist. Split this as before, and two rings interlaced are the result. The experiment is usually the ' first aid ' applied to those who are commencing the study of the fourth dimension. Mr. Wells, by the way, suggests that time, duration, is the fourth dimension of objects ; but inasmuch as the first essential of an additional plane is that it should be at right angles to the other three, why not regard the reflection of an object in a mirror as its fourth dimension ? " But paradox easily becomes absurdity. An interesting detail is the useful convention by which right and left, in reference to the position of objects on a stage or in a picture, are taken as from the spectator. Here we approach the fundamental idea of right and left. In the first place, mutual understanding of their application depends on an agreement as to the terminus a quo. My right is your left when we face one another ; when we face the same way it is your right. A second point now comes in, viz., that right and left involve, not merely bilaterality, but dorsi-ventrality, fore-and-aftness. They have no meaning unless the objects concerned possess an obverse and a reverse, a front and a rear. We thus come back to the four quarters of the compass. But so far we have not got beyond the horizontal plane ; we are still dealing with objects that might be without height and depth, abstractly flat. We must therefore add a third dimension, and postulate ' length,' with its corollary of top and bottom. It will be seen that polarity is a fundamental principle of our conceptions of reality in general, no less than of our conception of this planet. Sir Thomas Browne had the notion of a dextrahty inherent in ' the heavens.' It may be suggested that the tendency to postulate the possibility or necessity of a fourth dimension really depends on the facts of verticaUty and of bilaterality. For right and left necessitate an ' upright ' standard and a point of view which is perpendicular, at right angles, to it. " The terminology of spirals, both flat and helical, if the latter term may be used to designate conical and cyhndrical and other ' developing ' spirals, is an interesting illustration of the difficulties of right and left. Here the difficulty is increased by the introduction of angular motion ; we have, as it were, to square circles. " The obvious way of describing a hehx is to call it right handed or left handed from the point of view of the spectator, who is perpendicular to its long axis. This axis in a spiral staircase is the newel, and the spectator is not in or on the staircase. His view creates two sides of the spiral, that which is obverse to his view and that which is reverse ; the former alone counts. If the obverse curves rise from his left to his right, the spiral is right hand. Quite correctly common use refuses to apply here the convention as regards pictures. It would also be well if, as you desiderate, spirals produced by a right-handed work- man were never described as right hand for that reason only. Of course, it happens that a right-hand screw is also a spiral which is 264 THE CURVES OF LIFE best suited to right-handetl action. But it is said that the Japanese prefer screws which involve the counter-rotation of the hand. "The common sense metliod of describing spiral direction is quite satisfactory, so long as the spiral has a top and bottom. In helical shells, twining plants, and staircases this proviso exists. The door, the root, and the aperture are obvious bases. " Wiesner censured the Darwms for using the common sense and popular terminology in their studies of twining plants. But modern botany in its desire for precision has only succeeded in establishing confusion. What advantage has dextrorse, for instance, over ' left handed ' in the Darwinian and popular sense ? The term itself, with its opposite, simstrovse, could hardly been worse chosen, for the older botanists, Linne and the De Candolles, used them in the very opposite senses. To Linnaeus dextrorse meant dextral, right-handed, moving from left to right (of the spectator). To the modern botanist (see Strasburger's text-book) it means sinistral, left handed, moving from right to left (of the plant itself). The absurdity of the new use is that it assigns dorsi-ventrality, a face and a back, to the hop and the honey- suckle ! This is a fine case of the pathetic fallacy of foisting the spectator's personal equation upon the object he studies. If a rope is coiled round my body from the feet upwards, so that to the spectator's view it twines from his light to his left, of course, the side seen by me, the front, twines from my left to my right. But the twining plant has no front. The matter becomes worse when English botanists ' trans- late ' dextrorse and sinistrorse by left handed and right handed respectively. Thus Mr. E. Evans, in his ' Botany for Beginners ' (1907), describes the right-hand convolvulus as twining counter-clock- wise, ' a left-handed spiral ' ; the hop, he says, makes a 'right-handed spiral.' Not only is this nomenclature incorrect and confusing, but it seems to imply that a spiral possesses hands. " It would appear that the conchologists, with their dexiotropic and leiotropic, have achieved the perfection of terminological exactitude. Starting from the base or aperture, an insect walks up the staircase. If the newel is always on its right hand the staircase is dexiotropic, and vice versa. The botanists might well borrow these terms to replace dextrorse and sinistrorse. One advantage they have is that they are in line with the tropisms of Entwicklung-niechanik. A disadvantage is that they have as their components the reverse terms to those of popular description. It might be supposed that the botanical dextrorse and sinistrorse were invested with their modern meaning for the same reasons as suggested dexiotropic and leiotropic to the conchologist. But this does not appear to be the case. " A flat, indifferent spiral, such as a watch spring, which has no top and bottom, is neither right hand nor left hand, but both, and this indifference can be illustrated by making first one side and then the other into the base, by pulling the centre first up and then down. A watch spring, when so manipulated, and viewed first from one base and then from the other, through the coils thus made conical, exhibits first one direction of coiling and then the other. If two such springs, thus coiling differently, were placed base to base round a double cone, the spiral round the whole cone would change its direction at the point of basic junction. RIGHT AND LEFT-HANDED MEN 265 "This is precisely what happens in the case of a tendril, as Darwin showed, which, after finding a hold, presents two cylindrical spirals (the number of the two sets of coils is generally exactly equal), which are joined by a ' half bend.' " Left-handed Children.— At the beginning of this chapter the reader was referred to Fig. 262 (in Chapter XIIL, p. 229), which illustrated one of those rare instances of individuals in whom all the viscera are transposed as regards right and left, and the heart is placed on the right side instead of the left. Since the locahsation of the various functions of the brain has been more accurately determined, it seems fairly certain that in the majority of cases the centres which control the movements of the right hand are on the left side of the brain, and in close juxtaposition tc the centres controlhng speech. It is, therefore, legitimate to argue the further probabihty that in the minority of cases (left-handed men and women) the centre controlhng the master hand is on the right side of the brain, and, in fact, that as regards the geography of the brain centres, a transposition has occurred somewhat similar to that exhibited in the heart illustrated in Fig. 262. If so, it would be a natural inference that the speech centre would have suffered an analogous change and would have accompanied the leading-hand centre to the right side from the left side. This would involve the possibihty of harm being inflicted upon the transposed speech centre, owing to sympathy with its neigh- bour, if any violence were done to the natural tendencies controlled by the leading-hand centre. I am unable to assert that this is actually the case. But prolonged investigations carried out by Professor Smedley, of Chicago University, a specialist in child-study, have produced the curious result that a large number of naturally left- handed children, who had been laboriously trained to use their right hands, were defective in speech and stammered. This looks as if the deliberate interference with the natural aptitudes of the child had disturbed the delicate balance of the brain centies and had resulted not only in a loss of manual skilfulness, but also in a definite injury to the powers of speech. It maj' be hoped that further study in this direction will, by degrees, contribute to a greater knowledge of both the advantages and the disabilities of what we call " lefthandedness." Professor F. Ramaley, an American naturalist (December, 1913), is confident that lefthandedness may be attributed to abnormal develop- ment of the right cerebral hemisphere. Hugh McNeil (p. 249). — No other left-hander has ever surpassed this beautiful player. But it is worth noting that in the Amateur Billiards Championship for 1914 no less than five left-handers entered, their distinguishing characteristic being a marked freedom and power of cue. CHAPTER XV Artificial and Conventional Spirals " The Beautiful is a manifestation of secret laws of Nature, which, without its presence, would never have been revealed. When Nature begins to reveal her secret to a man, he feels an irresistible longing for her worthiest interpreter, Art." — Goethe. SPIRAL DECORATION IN PREHISTORIC TIMES — THE SUCCESSIVE RACES OF MAN — ARTISTIC SKILL OF AURIGNACIANS — MAGDA- LENIAN CIVILISATION — THE SPIRAL AS A LINK BETWEEN AURIGNACIANS AND GREEKS — THE MYCEN^AN AND MINOAN AGE LATE NEOLITHIC ORNAMENTATION DISTRIBUTION OF SPIRALS IN UNITED KINGDOM — SCANDINAVIA AND IRELAND — EGYPTIAN SPIRAL IN DANISH CELTS — NEOLITHIC STONES AND ETRUSCAN VASES — THE SACRED LOTUS — THE " UNLUCKY " SWASTIKA — SPIRALS IN GREEK ART — ORIGIN OF THE VOLUTE — THEORY AND EXPERIMENT — THE IRON AGE — UNCIVILISED COMMUNITIES OF THE PRESENT DAY — MEDIEVAL GOTHIC — VIOLIN HEADS — CYLINDRICAL SPIRALS, TORQUES, ARMLETS, " COLLARS." In later pages we shall see that Leonardo da Vinci, whose wide intellect I tried to sketch in my last chapter, was especially attracted by problems in which the spiral formation was a main factor, as indeed he could hardly fail to be, when we consider that he was both a skilled artist and a patient and indefatigable student of Nature. But the multifarious occurrences and the profound significance of spirals in many natural objects must evidently have been impressed upon thoughtful minds long before his day, and in the present chapter I propose to show that they had impressed themselves upon man in the earliest epochs of which artistic history preserves any distinctive record of him ; and, after all, it is scarcely strange that prehistoric men, although unable to appreciate those functional values which alone give the spiral its unique place in Nature, in engineering, or in architecture, should have dimly perceived not only its importance, but also that element of beauty in it which must inevitably be associated with fitness and with power. I, therefore, have chosen here a few typical instances of the use of the spiral (chiefly the flat spiral) in conventional patterns which in modern centuries are evidently the successors of an ornament originally u?ed with ARTIFICIAL AND CONVENTIONAL SPIRALS 267 a mystical (or possibly magical) meaning, and they may have preserved that significance long after we can trace its presence. Curiously enough, all these patterns show the flat spiral, with very rare exceptions ; so I have been able to arrange them in the order of their historic development. The exceptions may be referred to the class of cylindrical spirals, whether they are torques, the ancient necklaces mentioned in my chapter on left-handed men, or whether they are sceptres. When this cylindrical form of spiral, used conventionally, takes on larger dimensions, in a column for instance, it will be more conveniently treated in my forthcoming division upon architecture. It will first be necessary to our inquiry to have a clear, if brief, idea of the succession of the various races of mankind ; and I have, therefore, taken the classification of the more ancient epochs from the latest pronouncements of Sir E. Ray Lankester ; and for more recent periods, such as the Bronze and Iron Ages (as they are called) , I have consulted the official publications of the British Museum. The " Quaternary " epoch is so called to distinguish it from those geological eras of vast remoteness known as tertiary, secondary, and primary. Another name for it is the " Pleisto- cene " epoch, and it is distinguished by the evidences of the life of man discovered in its river gravels, its cave deposits, and its glacier debris : rough flint implements skilfully chipped into shape but never polished. From these is derived yet a third name for this same period, which has been called " Palaeolithic " to distin- guish it from the " Neolithic " age of polished stone implements, of cromlechs, of stone circles, and of lake dwelhngs. During the early Palseohthic epoch Britain was continuous with the Continent, and so abundant are the rehcs left of the human tribes who fed on the roasted flesh of animals and usually lived in caves, that there must have been over a very considerable area a human population which developed through hrmdreds of thousands of years. During the Glacial Period or Ice Age of the Palaeohthic epoch lived the race called the Neander men, chinless, low-browed, short, bandy legged, and long armed, who disputed the possession of their caves with bears, lions, and hyenas, who hunted the mammoth on the edge of the glaciers, who have left no rehcs save their cleverly-worked flints, and a few of their own bones. It was once thought that these represented the earliest type of humanity, and that before the Ice Age man did not exist, or at any rate had left no traces. But in a prae- glacial deposit at Heidelberg a chinless jaw that must be older than that of the Neander men has been dug up ; and the recent discoveries of worked flints, striated by glacier action, in Kent , 268 THE CURVES OF LIFE seem to demonstrate that man existed in the warm pra;-glacial times in the British Islands long before the sands and clays and river gravels of the post-glacial Pleistocene received their traces of primitive humanity. It is with the post-glacial men of the Later Pleistocene that we have now to deal. When the reindeer was abundant, and the numerous herds of wild horses were used for food, the first sub-division of existing mankind were those now called " Aurig- nacians," from Aurignac in the Haute Garonne. From the very first it is their artistic skill that is the most extraordinary thing about them. The earliest generations of them of which we have any record produced the marvellously executed horse's head which is reproduced in Fig. 283 of this chapter, a complete piece of " all-round sculpture," the size of which is determined Fig. 2S3. — Horse's Head Carved by Early Aurignacian Men ABOUT 20,000 Years ago. (Piette.) by the bone from which it has been carved. Their later genera- tions produced the first conventional flat spiral, used decoratively, of which I can find any authentic record (Fig. 284) ; but before saying more about this spiral I had better complete my short description of Palaeolithic man. The Aurignacian age was followed by the Solutrian, so-called from Solutrc, near Macon ; and to this in turn succeeded that Magdalenian civilisation from which I reproduced a shell necklace in Chapter X. (Fig. 199) ; and from which came that astounding picture (incised on a cylinder) of " The Three Red Deer " which Sir E. Ray Lankester described in the Field for May 13th, igii. By this time the gradual rise in temperature had sent the reindeer further north, and in southern France the red deer was beginning largely to replace it. In the north of Spain men hunted the bison. On the walls and roofs of their caves many beautiful coloured drawings still ARTIFICIAL AND CONVENTIONAL SPIRALS 269 survive of the hunters and the hunted. Yet a fourth sub-division, the hnk between the Magdalenians and the Neohthic men, has been called the Azilian, from Mas d'Azil in the Arriege ; and though at first sight the local names by which it has been agreed to distinguish these sub-divisions may appear inadequate, yet it has been found that the distinctive characteristics of different forms of pre-historic art revealed in each of these four main excavations from the ancient French deposits are equally recognisable in contemporary deposits found in Great Britain, Belgium, Germany, and Austria ; so the main titles here given have, hitherto, been universally accepted as correctly scientific labels. It must be remembered that the skeleton of the Neander man of the Glacial period, mentioned above, differed much more from the well-grown Cromagnard type of the Magdalenian man than the Australian bush-fellow of to-day differs from the modern Fig. 284. — Fragment of Reindeer's Antler. Found in the Upper Pleistocene deposits of Les Espelunges d'Arudy, Hautes Pyrenees, carved by late Aurignacian men of the Third Palaeolithic period, about 20,000 years ago. (Piette.) Englishman ; and when we consider that it may now be taken as proved that man worked flint implements even before the Ice Age, the enormous period of time necessary for development becomes a little more realisable, and it is perhaps easier to appre- ciate that the Aurignacian who carved the horse's head of Fig. 283 or the spirals of Fig. 284, was not so " primitive " as might be imagined ; while the artist of the Magdalenian cyhnder was less " primitive " still. The late Aurignacian civilisation which prodifced the spirals of Fig. 284 was evolved by men of a " negroid " character (as is shown by skeletons found at Mentone), who were probably a branch of the race from which those bushmen of South Africa are descended whose paintings of the chase on rocks and caverns are singularly like those of their prehistoric forebears. Beneath a limestone cliff at Laussel, in the Dordogne, Aurignacian carvings in high relief have recently been discovered by Dr. Lalanne, representing a woman with strong " bushman " characteristics. 270 THE CURVES OF LIFE holding a bison's horn ; and a man apparently in the act of shooting an arrow from a bow. 1 emphasise these resemblances to the external characters of bushmen because nothing could be less like the aesthetic development of the modern savage than Aurignacian art was. In fact, this is a case where the modern representative has notably fallen off from the standard attained many thousands of years ago by men of the same race ; and it is not necessary to go so far as the modern savage to see that falling off just as clearly. For though the Neolithic period is only separated from the Aurignacian by the Azilian, the Magda- lenian and the Solutrian eras (all later Pleistocene, or Palaeolithic), yet not a trace of Aurignacian art survives in Neolithic times except the use of the conventional flat spiral. In fact, nothing to touch the horse's head in Fig. 283 is found until the Greeks of 500 B.C. The spiral is the only link that passed down consecutive generations from the Aurignacians to Attica, from Les Espelunges d'Arudy to the Acropolis of Pericles. Some diffidence is necessary in making any definite pronounce- ment on these far-off matters ; for since the publication of Dechelette's " Manuel d'Archeologie," and of Piette's " Age du Renne," discoveries have been continuous and important, and almost at any moment we may hear of some typical excavation which necessitates a rearrangement of our present classification. In calculating time, too, we are even more liable to error. One fact which is fairly certain is that the Neohthic period lasted on at least to the Swiss lake-dwellings of 7000 B.C. ; and behind them is a gap which nothing has yet bridged. Therefore we may take the latest division (the Azilian) of the later Pleistocene (or Palaeohthic) as being before that ; and if we say that the Aurignacians lived 20,000 years ago we shall be well within the mark ; and they may possibly represent a span of 50,000 years, if we consider the enormous time necessary for their development from men of the middle and early Pleistocene, and from that dawn of humanity which left its rostro-carinate flint implements beneath the Red Crag, deposited before the oldest Pleistocene of all. We have, in fact, no exact " chronometer," for even a calculation of the extension and retraction of the Alpine glaciers must be merely relative. If we cannot describe Aurignacian civilisation, in the words of the poet, as " prolem sine matre creatam," we seem compelled, as M. Salomon Reinach says, to recognise it as " Mater sine prole defuncta," so far as its chief artistic manifestations are concerned. My point now is that its conventional spiral alone seems to have passed on ; and therefore the origin of this emblem must be put much further back than many writers have hitherto thought ; for the carved reindeer's ARTIFICIAL AND CONVENTIONAL SPIRALS 271 antler shown in our Fig. 284 proves tliat the spiral was used in western Europe long before the Egyptians and the men of the ^gean used it as a fundamental motive of their decoration. The simple spiral and the double recurrent spiral of Celtic art are to be found clearly and deeply cut in Aurignacian workman- ship. It may be true that the spontaneous discovery of the flat spiral as a conventional decoration may have occurred in different places and at different times. But in the Mycenaean epoch (the Bronze Age of the jEgean) we find the spiral in the eastern Mediter- ranean, in southern Europe, and in Scandinavia ; and it is difficult to deny to such similarity both in time and style an identity of origin which is scarcely obscured by the wide area involved. It is therefore possible that the Bronze Age inherited the spiral from the Palaeolithic Aurignacians by way of the Neolithic carvings of Gavr'inis and New Grange, which I shall have to mention next. But I cannot conclude this portion of our subject without reminding you that the fondness of the Mycenaean and Minoan age for natural objects as models for their artistic work has been already emphasised in my tenth chapter. In many cases it was shells and cuttlefish which supphed a spiral motive that gradually became conventional. But convention in pattern is always a slow growth. It comes long after the naturalistic treatment of some living object ; and this is why the obviously conventional and artificial spirals of the Aurignacian artist of Les Espelunges d'Arudy (Fig. 284) are so extraordinary. They seem to prove the existence of an abstract idea in a civilisation hitherto imagined to be incapable of anything of the kind. We need not go so far as to say that here is the dawn of a mathematical conception, for a snail shell sawn in two or ground down horizon- tally would produce a flat spiral so nearly mathematical (as we saw in Chapter IV.) that the artist who copied it need have had no idea but fidelity to nature in his curves. Still, in Fig. 284, those curves are conventionahsed. The beauty of the abstract figure so produced is evidently reahsed. The spiral, in fact, has roused that aesthetic sense of which I spoke in my thirteenth chapter, the sense which appreciates the strength and power and fitness of a certain formation, and therefore takes it as a type of life and beauty. The spiral was an integral part of Mycenaean decoration, and so many examples of it are illustrated in Schliemann's " Mycenae " that it was unnecessary to reproduce them here, but I have collected a few remarks upon them in a Note to this chapter. The tumulus of New Grange, in county Meath, has been described in a careful monograph by Mr. George Coffey (1912). 272 THE CURVES OF LIFE It represents the next link in that story of the spiral in art which I am trying to relate, and it is quoted by Dechelette as an example of late Neohthic ornamentation in a form not found in Scandinavia until the Bronze Age had begun there. The united spirals, in double and even triple conjunction, are very clearly Fig. 2S5. — Spirals Carved on a Stone Found in the New Grange Tumulus (Co. Meath). (Dechelette.) carved upon the stone illustrated in Figs. 285 and 286 ; and considering that similar patterns only occur on two stones in Brittanv (of which Fig. 287 gives one example), I cannot believe that the symbol reached Ireland by way of the Morbihan. The map (made by Mr. Coffey) showing the distribution of these spiral? in what is now the United Kingdom shows a distinct line from the: F~iG. 286. — Late Neolithic Boundary Stone at New Grange, on the Banks of the Boyne. Carved by men of the Bronze Age, showing two large spirals united between two lozenges, like the pattern on Melian vases of 600 B.C. (From " New Grange," by George Coffey.) extreme north of Scotland to a pomt just west of Dublin. The furthest point south is in north Wales. This seems to indicate that the Irish spirals are more likely to have come from the Baltic than from Brittany ; and if this makes it difficult to beheve that they were the true successors of the Aurignacian symbol in Fig. 28..] we must remember that sea travel was easier than land travel among the earher civilisations, and that seafarers along the ARTIFICIAL AND CONVENTIONAL SPIRALS 273 western coasts of France were more likely to sail north by east, and keep the coasts in sight than to sail either west or north by west towards unknown latitudes. So it is quite possible that before the tin mines of Cornwall had been discovered by the southem'traders, the first commercial voyagers descended on these islands from the north-east, and worked along a slant towards the south-west. Nor is it difficult to understand, under this theory, why spirals found on stone in Ireland are first found in Fig. 2S7. — Carved Stone in the Covered Alley of the Island OF Gavr'inis (Morbihan), SHOWING Finger Prints (?) and A Spiral at the Top. (Dechelette.) Fig. 288. — MiNOAN Vase of Faience from Cnossos. (Sir Arthur Evans.) By permission of the Committee of the British School at Athens. Scandinavia on bronze only. The record of bronze-work in Ireland is extraordinarily defective, and many early examples may yet remain to be discovered ; and it seems also clear that skill in bronze-working was developed much sooner in Scandinavia than in Ireland, where the easy method of engraving curves on ■stone by a number of blows struck perpendicularly lasted far longer than has been sometimes realised. I incline to the belief that the spirals of Gavr'inis in Fig. 287 are older than those of New Grange, partly because these carv- C.L. 274 THE CURVES OF LIFE ings, almost the only ones found on a megalithic monument in France, are of ruder workmanship than the Irish examples, and partly because they recall the " fingerprint " patterns common m Palceolithic caves. It may well be that the New Grange carvings are as recent as that Prse-Mycenjean epoch in the Mgean, which lasted until about 2,000 B.C., when the Mycenaean or Bronze Age began. At this period we can trace the spiral from scarabs of the twelfth dynasty in Egypt to Crete in 3,000 B.C., from which it spread northwards along the " amber route " to Jutland and Scandinavia ; and we find the favourite double spiral of the Minoan Age upon the vase of Faience discovered by Sir Arthur Evans at Cnossos, and illustrated in Fig. 288. From this to the prominence of the spiral in Mycensan patterns is but a slight step in ordinary development. The spiral decorations on the bronze celt of the Danish palstave type, shown in Fig. 289, are of great interest in that they prove the survival in the north of the Egyptian spiral motive, together with the loop in the interstices, which is a reminiscence of the lotus ornament used in ceiling patterns. Dechelette connects the Fig. 289. — Details from Bronz : Minoan and Mycenaean spirals Celt of the Danish Palstave ^^^^^ mentioned with those of Iype, showing Survival in „ ,. . _ ^- „ 1 ,1 THE North of the Egyptian ^avr mis and New Grange by the Spiral Motive. simple argument that the latter (From " New Grange," by George were made at the end of the Neo- ° '^'^'' lithic period, and the former are the favourite pattern of the beginning of the Bronze Age. But, as has been said, I venture to support the view that though Gavr'inis maybe the older. New Grange got its spirals from the north and east, rather than from the south and west ; and Mr. George Coffey points out, in support of this, that certain peculiarities in the spiral patterns of Scandinavian bronze work are without a parallel in the Bronze Age of the rest of Europe, but are exactly the same as those found at New Grange. In fact, the same influ- ence moulded both. In one case it sur\dves in bronze alone ; in the Iri^h examples only in stone. In the Stockholm Museum is preserved a fine example of a bronze plaque, showing the con- nected spirals of Fig. 298 continued all round the circle (see M. Salomon Reinach's " Apollo "). The stone illustrated in Fig. 286 is a boundary stone found on the north of the circle of the tumulus at New Grange, and clearly shows the same use of the united spirals which survived ARTIFICIAL AND CONVENTIONAL SPIRALS 275 in such Etruscan vases as that chosen by M. Pettier from the Louvre coUection (Fig. 290), a form of pattern which certainly lasted until the sixth century B.C., and a piece of evidence which suggests that the work at New Grange is very much more recent than the megaliths at Gavr'inis. It has been considered by some authorities as an indication of the sun worship, which was probably the most widely spread cult in modern Europe. Patterns grow ; they are not made. They are evolved from pictures, and from those pictures which most often occur, and are most easily repeated. Among such pictures, those which represented the lotus would be as significant and as sacred as any known to the earhest periods of Egyptian art. The earliest pictures were not done for their own sake, as " works of art." Fig. 290. — Two Large Spirals United on an Etruscan Vase. (From Peltier's " Vases Antiques du Louvre.") They were meant to convey an idea ; they were even supposed to retain some of the powers and qualities of the original. So the lotus, as the emblem not of one god but of all, not of one sacred animal but of all, embodied an enormous amount of ancient and popular symbolism, and no doubt the widespread value attached to the spiral formation as a decorative pattern is largely due to its association with the lotus, the symbol of creative power or energy, of the strength and divinity of the sun, of the sun's birth from moisture, and of the many sacred phenomena of life. The lotus was used for the first time in the decoration of the English throne in Westminster Abbey in 1902 ; and it will be seen that modern research has largely justified a symbolism which was based rather on faith than knowledge. Professor Lethaby has pointed out that the triangular opening over the T 2 276 THE CURVES OF LIFE door of the " Treasury " at Mycenae was originally filled with slabs of dark red marble incised with spiral ornament, one of which is in the British Museum. There are also flat spirals carved between the chevrons on the column and capitals of the same building. Schliemann gives drawings of an elaborate pattern of double spirals from the Mural frescoes of the palace of Tirhyns, which are very similar to the " spectacle brooch " shown in Fig. 298. Spiral scrolls have been found on pottery in Schhemann's " First Tomb " at Mycenae ; on scarabs of an Egyptian dynasty which existed 3.900 years before Christ ; on bronze axe-heads from pre-historic Sweden. Mr. Henry Balfour possesses many examples in the Pitt Rivers Museum at Oxford. At Leyden the representative exhibit for the Malay Archipelago is unique. The ethnographic collections in Washing- ton, in Rome, and Amsterdam, are also full of similar specimens. Fig. 291. — Painted Frieze from the Old Parthenon Destroyed in 480 b.c. Throughout, the theory of spontaneous generation falls to the ground. The rule of historic development and tradition shows no exception ; and Professor W. H. Goodyear has very carefully investigated the whole subject as suggested to him first by the geometric lotuses upon the Cj'priot vases. He showed that all the Arab and Mohammedan spirals came from the Byzantine Greeks ; that they are not found at all in barbaric Africa, and that, on the other hand, they are the foundation of Malay orna- ment ; they reached Alaska, however, by means of Buddhist influence, along the Amory vaUey, through the Yakoots to the Aleutian islands. When it is realised that flve-sixths of the orna- mental patterns of ancient Egyptian art were based upon the lotus and its spiral derivatives, the number of spiral traditions which spread from the Nile valley all over the world will be better understood. The oldest forms of the spiral associated with the lotus are found in Egyptian tomb ceilings. The Greeks and Assyrians, who found the flower already conventionalised almost ARTIFICIAL AND CONVENTIONAL SPIRALS 277 out of knowledge, took the spiral accompaniments and developed them in turn to their highest pitch. The Assyrian idea of the organic connection of repeated units of design by linked curves, ending in spiral volutes, was immeasurably improved by the genius of the Greeks, which seized on elements of beauty that had hitherto remained unproductive, and gave them not merely new life, but measureless scope. The descent of the Greek palmette [anthemion) from the Egyptian lotus has never been authoritatively contradicted . The painted frieze shown in Fig .291 is a fragment from the old Parthenon on the Acropolis, which was destroyed by the Persians under Xerxes in 480 B.C., and it shows the drooping palmette alternating with the developed form of the lotus bud. Fig. 292 (a palmette from a Greek vase at Nola) shows the debased form of the design during the period Fig. 292. — Spiral Pattern on a Greek Vase of about 330 B.C. FROM Nola. of Greek decline after 330 B.C., and I have chosen it because the design includes two examples of the Swastika, or fylfot, that ancient and widespread symbol of the sun's movements which I described at the end of Chapter X. (see also note to Chapter XX.), and both of them are " unlucky "—that is to say, the arms of the cross do not follow the sun in a left-handed spiral after the manner in which we pass the port or deal the cards, but go " contrariwise," against the sun, in the way that has for many centuries been deemed unlucky. The " lucky " form is most usual, and is found ahke on bronze Scandinavian scabbards, on the stone spindle whorls of ancient Troy, on the footprints of Buddha, and on the blankets of American Indians ; but for fuller details about it I must refer the interested reader to Mr. Thomas Wilson's monograph, issued by the Smithsonian Institute of Washington D.C. And I will merely add here that the 278 THE CURVES OF LIFE " unlucky " form shown in the design in Fig. 292 has also been found in some pottery-marks from Asia Minor, on the head of an Armenian bronze pin, on a stone ball found by Dr. Schliemann beneath the site of pre-historic Troy, on an ancient iron spear- head from Brandenburg, on the base of a ruined Roman column in Algeria. Why it should also be found on a Greek vase from Nola, I am quite unable to explain. A suggestion as to its origin will be found in the Appendix. Fig. 293. — Volute of about 560 b.c. from the Capital of AN Ionic Column (British Museum) from the Archaic Temple of Diana at Ephesus. The conventional spiral reaches an even higher point at the best period of Greek art than it did in that brilliant but apparently short-lived age of Aurignacian civilisation ; and in the volutes of the Ionic capital we have it at its best. In Fig. 293 I have reproduced the photograph of a volute from the capital of an Ionic column from the ancient Temple of Diana at Ephesus, now in the British Museum. Obviously the spiral is used here not as a structural or functional necessity, but as a conventional ARTIFICIAL AND CONVENTIONAL SPIRALS 279 ornament, descended from a most ancient symbol. It has been exquisitely adapted to its new position ; and this particular use of it reminds us of the thesis propounded by Dr. W. H. R. Rivers before the meeting of the British Association (in 1912) that for the special directions taken by the process of conventionalisation one must look to factors arising out of such a blending of various cultures as is probably observable in the civilisation which pro- duced the best Hellenic art. Certainly the " conventionalisation " which produced the Ionic volute cannot be described as a mere change (from the lines of the original model in Nature) due to the usual causes of labour-saving, or of inexactitude in copying, or to the difficulties of surface or material. For nothing more Fig. 294. — Spiral Volutes of Ionic Capital in the Eastern Portico of the Erechtheum. (From Stuart and Revett's " Antiquities of Athens.") tastefully rendered than the volutes I reproduce in Figs. 293 and 294 could well be conceived in ancient architecture. In Chapter II. I reproduced a diagram (Fig. 44), first drawn by Mr. Banister Fletcher, to show the possibiHty of describing an Ionic volute by means of the fossil shell Fusus antiquus which is used as the pivot round which a gradually lengthening string is unwound from the apex of the shell (at the centre of the spiral) upwards ; and I pointed out then that the beauty of the Greek volute exhibits just those differences from mathematical exactness which are exhibited by the organic hfe of any natural object. After Mr. Fletcher made his diagram, a paper [R.I.B.A. Journal, 1903, p. 21) was pubHshed by the late Mr. Penrose, which once more attacked the old problem of the mathematical 28o THE CURVES OF LIFE definition of the Greek volute ; and the point on which the learned author seemed chiefly to congratulate himself was that his new formula was so nearly exact that its practical application to various concrete instances of the volute revealed "very few errors," and only a very small " margin of error " on the whole. It happens that the two volutes selected for Figs. 293 and 294 in this paper were among those chosen for the mathematical anti- quary's demonstration. But in that demonstration it is not the small " margin of error " which is to my mind significant. It is the fact that no mathematical formula can express the volute with any greater accuracy than it can express the growth of a shell. It seems obvious to me that the Greek architect had in his mind the same natural curves (whether taken from a living landsnail, from a fossil ammonite, or from a Mediterranean nautilus) which Fig. 295. — Armlet of Bronze Terminating in a Spiral, FOUND IN Hungary. (From the British Museum.) had appealed to the Aurignacian artist 18,000 years before him. It is certainly true that the volute was known as a " limace " or " snail shell " as late as the middle of the sixteenth century ; for Mr. Reginald Blomfield quotes a " Notice to Readers " at the end of Jean Martin's edition of Vitruvius, in wfdch Jean Goujon writes that the " spiral of the volute, otherwise cahed snail shell, is not clearly enough explained," and goes pn to say that no one has thoroughly understood the true theoijy of this volute " except Albert Durer, the painter." On this I need only say here that it seems to me far more likely that the real origin of the volute should occur to such artists as Durer or as Leonardo than that it should be mathematically solved by any antiquarian architect, whose careful measurements of such Greek master- pieces as the Parthenon have proved that the most delicate manifestations of their beauty consist rather in the divergences of their design from mathematical regularity than in the exact ARTIFICIAL AND CONVENTIONAL SPIRALS 281 accuracy of their lines and angles. I mention Diirer's work in this direction in a later chapter. Mr. Penrose's investigations irresistibly reminded me oi the researches of Mr. Gilbert Walker (a celebrated Wrangler) into the mathematical construction of the boomerangs made by Australian natives. He reached such accurate conclusions that by a given formula he could construct a boomerang which would exhibit given movements in the air when properly thrown. The native had reached similar results after generations of his ancestors had made experiments which may be compared with the various steps in the evolution of organic forms that result in the survival of the fittest. None of his lines or angles were exact, and he naturally could give no reason for them. They had " grown," as it were ; and Mr. Walker's interesting mathematics could only produce a rough definition of the real thing, though they enabled him to manu- facture other boomerangs after the formula which was latent in the native workmanship. In just the same way I have suggested that the logarithmic spiral " latent " in a nautilus can be used as the basis of an Ionic volute. In the earlier volute of 560 B.C. (Fig. 293) it will be noticed that the spiral consists of the single line of one outstanding curve winding inwards to its centre from the line immediately beneath the " egg and dart " moulding at the top of the capital. The technical carving of this spiral curve by the artist is precisely similar to that shown by the Aurignacian artist in Fig. 284. Speaking mathematically, it would be more correct, of course, to say that the spiral originates from a selected point rather to the left of the centre of the volute, and winds outwards until it reaches the straight line at the summit, and in connection with what was said above, it will be noticed that in this Asiatic example the lotus forms a definite portion of the ornamental scheme of the volute itself. In the later column from the Erechtheum, however, the volute is formed by a triple spiral, and the curves composing it start not only from the straight line immediately beneath the " egg and dart " moulding, but also from two curvilinear figures cut beneath it. This has the result not only of covering the space of stone available more completely than was the case with the volute from Ephesus, but also of giving each spiral a wider and more gracious development. The difficulty of indicating the three central points from which these three spirals originated is beautifully met by the appKcation of a sepa- rately carved disc just at that part of the volute where the tighten- ing coils of the spirals would become too small to carve and too insignificant to see from any distance, and the place and proportion of the disc itself in the whole decorative scheme is quite distinct. 282 THE CURVES OF LIFE The same central disc may be observed in the spirals of Fig. 295 and Fig. 296. The lotus, though changed in form, is still preserved in the palmettes which encircle the neck of the column, just beneath the volutes, with a band of jewelled carving. There is no doubt that as a whole this makes up the most delicate and beautiful application of the conventional spiral to architectural ornament which has ever been conceived, and I would once more point out that the chief factor in its charm consists in its neglecting Fig. 296. — Head of Eighteenth Century Violin (Early German). (Reproduced bj- courtesy of Messrs. Hill, of New Bond Street.) mathematical exactitude after the same fashion as it is neglected by the snailshell which appealed to Aurignacian artists long before Attica had developed any art at all. Professor W. R. Lethaby discusses the question in "Greek Buildings " (B. T. Batsford, 1908), p. 204, and makes some very interesting suggestions. See also his pp. 59, 61, 170 and 180. Although the mathematical attainments of the Greeks were undoubtedly very high, I do not venture to attribute to them such skill as the demonstration, given by Canon Moseley, of the logarithmic character of the spiral shown in certain shells, ARTIFICIAL AND CONVENTIONAL SPIRALS 283 especially the nautilus. But the science of the Chinese, in remote periods of historic antiquity, turns out to be more and more astonishing the more we find out about it, and the use to which their early artists put the logarithmic spiral of the nautilus, as a foundation for symbolism and patterns, is so extraordinary that I have given it special treatment in Appendix IV. So far, then, we have traced the spiral from Palaeolithic to Neolithic workmen, and through the Bronze Age of iEgean civihsation to the highest point of true Hellenic culture. Some- thing must now be said of that Iron Age, which followed the age of copper and of bronze, and may roughly be taken as succeeding the Homeric epoch in historical chronology. It is chiefly named (as we saw was the case in the Palaeolithic epoch) after the localities where typical discoveries have been made, and, therefore, its sub-divisions are called after Hallstatt in the Austrian Tyrol, Fig. 297. — Spiral Pattern on a Gold Disc of Gaulish Workmanship. and La Tene, a pile-viUage on shallows at the north end of the lake of Neufchatel. The Hallstatt period may be said to begin in 850 B.C. and end in 400 B.C., and is called " early " or " late " by reference to the year 600 B.C. Three periods are predicated of the La Tene culture, namely, the " early " from 400 B.C. ; the " middle," from 250 B.C., and the " late," which includes the first Roman occupation of Great Britain, from about 150 B.C. to the beginning of the Christian era. I shah only say so much of them as may be necessary to explain the examples of spiral decoration illustrated in this chapter. The embossed gold disc shown in Fig. 297 comes from Auvers, in the department of Seine-et-Oise ; the survival in it of the Greek palmette pattern is sufficiently evident to need no further emphasis, and the derivation thus impHed is easily intehigible at a time when classical motives were becoming common property even to the goldsmiths of early Gaul, and when Celtic transforma- 2S4 THE CURVES OF LIFE tions of Hellenic designs had become fashionable in the workman- ship of widely separated areas. In exactly the same way, some time before this gold disc was manufactured, we find almost identical elements of design on painted pottery all over France (except in Armorica and the south-east), on the Rhine, and in Fig. 298. — Bronze Double Spiral Brooch from Halstatt. Western Switzerland. It is characteristic of the La Tene art of about 450 B.C., which deliberately chose Hellenic and Etruscan motives ; and it is curious that where similar patterns occur in the pottery or wood of Brittany or England, about the first century B.C., they are always incised and not painted. Fig. 299. — Bronze Brooch Showing Four Spirals FROM Halstatt. The brooches drawn in Figs. 298 and 299 are examples of the Hallstatt civihsation. The earher brooch (Fig. 298) is called the " spectacle type " formed of two spiral coils of bronze (or sometimes iron) wire which are united exactly like those carved on the Aurignacian fragment (Fig. 284), the New Grange stone (Fig. 286), and the Minoan vase (Fig. 288). The same pattern ARTIFICIAL AND CONVENTIONAL SPIRALS 285 was found on earthenware vessels in Bosnia [Hcorner) and on a double earthenware vessel of the Hallstatt period at Langenle- bron. Reichhold gives it on a similar vessel as far afield as Central America. They are also found in the south of Italy, in the area of Magna Grfficia. The brooch of Fig. 299 is a double variation of the same pattern, and has some similarity to the Swastika, the " unlucky " variety described in this chapter. As will be seen in the Appendix, one very possible and interest- ing origin of the curved Swastika here suggested, is to be found m a similar union of two curves based on the logarithmic spirals used by early Chinese philosophers to typify infinity and to convey other profound, symbolic meanings. It very often happens (as the Pitt Rivers Museum at Oxford so beautifully illustrates) that the arts and crafts of savages or Fig. 300. — Wooden Figurehead on Prow of Maori War Canoe, the Pro- perty OF Mr. W. B. Woodgate, Carved with Tools of J.\de about the Middle of the Seventeenth Century. of comparatively rude civilisations at the present day may give us interesting parallels with the prehistoric art of vanished peoples. I have, therefore, added a few examples of what may be called the modern use of the conventional spiral from decorations made by savage or comparatively uncivilised communities. It is a well-known fact that some mediaeval monks used to say their prayers within a maze, in order to escape the pursuit of the Evil One ; and the spirals tattooed upon a Maori's face may have the same object of confusing the Devil, though it may quite as pos- sibly be a result of his inborn sense of the adaptatioa of ornament to form ; for his spirals admirably express the feature decorated, and seem to do so in a way which concentric circles never can. Spirals are found in the decorative art of such different peoples as the natives of New Guinea (especially where Melanesian influence occurs), of Borneo, of ancient Peru, of Central Africa. 286 THE CURVES OF LIFE Sometimes the form is connected with the manufacture of pottery or basketwork, and it is then definitely suggested by the structural lines of the object. Often the spiral seems the genuine expression of artistic feehng or fanciful imagination. But in no case do we r.» *»•.*•*'- Fig. 301. — Carved Door Lintel from Xtw Zealand. (British Museum.) find a savage making an abstract pattern that does not go back to Nature by a series of conventional variations. All forms of the spiral in Polynesia, for instance, can be traced to a Malay centre, and that centre took its ornaments from Hindoo or Phoenician sources. But it must carefully be remem- bered that, as Dr. W. H. R. Rivers has pointed out, the directions of conventiona- lisation cannot always be explained by purely psycho- logical or technological fac- tors. In many cases the motive must be sought in the attraction of peoples possessing different forms of artistic expression, and in factors arising out of the blend of cultures. The finest example illus- trated here is the New Zealand rostrum drawn in Fig. 300. It is really com- posed of two boards, one to affix on either side of the prow ; but the accuracy of the duplication conceals, in the photograph, the fact that a ditto board (save that it is cut and carved for port side, while the one in view is starboard) lies face to face with the one seen. The tattooing, and, in fact, all the carving, supposed to represent the jawbones of some marine animal, is reported to have Fig. 302. — New Zealand Neck Ornament Carved from a Human Skull. (British Museum.) ARTIFICIAL AND CONVENTIONAL SPIRALS 287 been executed with jade, for there was no metal known among the Maoris at the date ascribed to the manufacture of this figurehead. It was captured in the storming of a wall about i860 by the 50th Foot, and passed into the hands of Lieut. Allnutt, of the commis- ?J^^ Fig. 303. — Carved House Board from Borneo. (British Museum.) sariat department, and thence to Mr. W. B. Woodgate. The curves and carving on what might represent the nasal ridge of the marine monster are said to be tribal, and to be translatable as giving a date about temp. Charles II. of Britain (so Lieut. Allnutt Fig. 304. — Brass Brooch Worn by West Tibetan Women. (British Museum.) averred). These figureheads are said to have been cherished as tribal trophies or badges, and were religiously removed from war canoes when not on war duty afloat, and were carefully tended inland or wherever the tribe were for the moment located. Hence, apparently, the discovery of this curiosity at an inland " pah," to which the tribe had retreated for defence. 288 THE CURVES OF LIFE In the Fisheries Exhibition, 1S82, there were some figureheads of this class on exhibition ; the most conspicuous of which belonged to the then Duke of Edinburgh. But the Duke's appeared to be more modern than the one given here, for it showed Fig. 305. — Spirals in Ironwork (French Gothic). Hinge from the Porte Ste. Anne, Xotre Dame, Paris. (Thirteenth Century.) evidences of having been cut out \vith metal tools ; if so, that fact of itself would correlate it with a comparatively recent era in Maori history. The essentially spiral feature of the pattern is common in New Zealand art, and I have given two more examples : of a door-hntel in Fig. 301, and a neck ornament carved out of a human skull in Fig. 302. They seem to me to indicate that the ARTIFICIAL AND CONVENTIONAL SPIRALS 289 pattern is very old, and has persisted into modern times with very httle variation. The same motive is shown in the carved houseboard from Borneo, reproduced in Fig. 303, and m the brass brooch from Tibet in Fig. 304. Paintings with a similar pattern are reproduced by Racmet from an Australian canoe. The Gothic workmen of the thirteenth century welcomed the spiral as a decorative motive almost more warmly than their Greek predecessors had admired it before them ; and in the hinges Fig. 306. — Spirals in Stonework (French Gothic). Carving from the Cloister (Thirteenth Cen- tury) OF St. Guilhem le Desert (H^rault). of the great western door of Notre Dame I give one of the best examples possible (Fig. 305) of the ironwork thus inspired. Their exquisite adaptation of the spiral line of growth in stone carving may also be appreciated from the carving here reproduced from the old cloister of St. Guilhem le Desert in the Herault (Fig. 306). My readers may remember the beautiful little flat spiral of a fern frond gradually uncurling (Fig. 61, Chap. II.) as it grew to maturity, and from this same motive no doubt were designed such crosiers as that preserved at New College, and made in 1400 for William of Wykeham, or the still more naturalistic model of early thir- c.L. u 2qo THE CURVES OE LIFE teenth centur}' work made by Brother Hugo, and reproduced in the Architectural Review for August, 1912 (p. 72). I could not conclude this shght sketch of the artistic use of the conventional flat spiral without gi\'ing one of its loveliestinstances, the head of a violin. By the courtesy of Messrs. Hill, I reproduce (in Eigs. 307 and 308) two views of the famous workmanship of Mathius Albani in 1674. Their similarity of treatment (down to the central " eye ") to that of the Ionic volutes in Eigs. 293 Fig. 307. — Head OF Violin BY Mathius Albani, an Italian Maker who worked in the Tyrol. Period 1674. (Reproduced by courtesy of Messrs. Hill, of New Bond Street.) and 294 will be at once observable. The same " eye " motive in the centre of the spiral volute should be noted in the bronze Hungarian armlet shown in Eig. 295. Erom its very nature the cylindrical spiral does not admit of such extended use for a conventional decorative pattern as has been found in all ages for the flat spiral. But we often detect it in the decoration of what might otherwise have been a plain tube or column. The sceptre of the city of London, which is of Anglo-Saxon workmanship, has a firm spiral cut into the gold and crystal of its jewel-studded stem, and the fact that tills spiral (which might just as well have been right-hand) is ARTIFICIAL AND CONVENTIONAL SPIRALS 291 left-hand may possibly have a significance which has already been suggested and might certainly be further elaborated. But it may, on the other hand, only represent the ordinary twist given to a rope, or to a fiat ribbon of soft metal, by a right-handed workman ; and this is the twist seen on most torques, or metal necklaces, which are, after all, only a form of cylindrical spiral. Fig. 309 shows this left-hand twist very clearly in the five-coiled armlet of gold now in the British Museum. Fig. 310 is a bronze torque of Gaulish workmanship, made in a complete circle, fastened by a simple rivet. In a Gaulish burying ground at Fig. 30S. — Front View of Mathius Albani's Violin. Courtisols (Marne) a similar torque was found in a woman's grave, and, curiously enough, it had been placed not on the neck, but as a diadem on the head. The use of this spiral formation as an honourable ornament is certainly as old as the golden collar promised by Belshazzar as a reward, the Chaldee name for which was Meneka, trans- literated in the Septuagint (Dan. v. 7), as Mai'ia/|lfflpp«^' ^''li^iipj^" ,1! II .1 ii i [)----; '■-^.-^li 1 \ .V. ^- d*l 1 ll II 1 1 1 1 ! J,,;:-:fiiIB IB 1 1 HUjaBIDlM'*"''''*"" 1 iwi^ ii 1 ill I------ -pjjig IJmi II 1 1111:19 II VI "1 .. A B Fig. 318. — Primitive Spiral Staircase, with Plan of One Step. THE DEVELOPMENT OF THE SPIRAL STAIRCASE. 305 right height by an occasional staple on the way. By degrees the stone of the central column got worn into a regular groove by the constant pressure of this rope, and it soon became evident that the handrail might become not merely an integral part of the stonework of the staircase, but a very definite addition to the beauty of its decoration. When once the essential feature of the central column (or newel) Fig. 319. — Staircase'in Colchester Castle. had been reached further development became more rapid and a structure hitherto hmited to somewhat narrow shafts was seen to be capable both of improvement and of greater size. A spiral inclined plane vaulted beneath and flat upon the top was built from the central column to the wahs, and upon this the steps were placed, so that it was now possible to make them of two or three slabs each instead of only one. A well-known example of this, at Colchester Castle, has been drawn for these pages in C.L. ^ 3o6 THE CURVES OF LIFE Fig. 319. The classical instance of it is, I believe, the Vis de Saint-Gilles, which I have seen in the north corner of the ruined sanctuary of the famous church in Provence. You can realise its structure by imagining that the round arch of the doorway has been hung by the pillar on your left to the central shaft of Fic. 3.;o. — Staircase in the Painted Chamber, Westminster. the staircase, and has revolved round that shaft as it gradually rose, thus alternately supporting and covering the rising spiral of the steps. The breakage of the crown of this staircase at the top re\-eals the extraordinary delicacy of measurement necessary in cutting and laying the successive courses of twisted stone. The stairway at Colchester is of brickwork plastered over, and is an example of the left-hand spiral, as is that in the Painted THE DEVELOPMENT OF THE SPIRAL STAIRCASE. 307 Chamber at Westminster (Fig. 320), which is more hke the primitive design drawn by Viollet-le-Duc, and has no support for the centre of each stair. A good instance of Gothic vaulting used in a spiral stair is shown in Fig. 321 from Lincoln Cathedral, ^.>-: -^V- .mU^^' Fig, 321. — Spiral Stair in the S.W. Turret of Lincoln Cathedral. (From a photograph by F. H. Evans.) which I am privileged to reproduce irom one of Mr. Frederick H. Evans's beautiful photographs. The conditions of mediaeval life made spiral staircases peculiarly valuable to the feudal architect, for doors could open into them at any height in their spiral upward course ; they were at first of simple and rapid construction, which could be easily repaired. They could be held by a few men against a hundred foes ; they X 2 3o8 THE CURVES OF LIFE joined the very top of the building with the very bottom, and the slope of their ascent could be made gentle or steep at will. We have, of course, long ago rejected such useful and beautiful possibihties in London houses, which are as narrow and lofty as a feudal keep, perhaps because we could not easily get our furni- ture and other cumbrous li\-ing apparatus up and down a spiral ; yet, with these methods, it would be possible to construct two interior spirals where there is now scarce room for one narrow stairway and a set of useless landings. The danger of fire would certainly be reduced if one of these spirals were constructed of uninflammable materials, or even built outside the main walls of the building. At Hertford College, Oxford, the architect seems to have remembered a sixteenth-century model, but to have been unable to find workmen capable of carrying out a sixteenth century design. At any rate, the result is a somewhat inelegant compromise between old and new. It is strange that the modern use of this beautiful form of staircase is almost entirely restricted (in the British Islands) to lighthouse keepers ; for it is only found in towers, and dwellers in the Martello towers along the coast are rare. The Border " Peels " were built only for defence, as were probably Dacre Castle, in Cumberland, or Belsay, in Northumberland. In Ireland the form survived much later. In the old part of Blarney Castle the stone used does not contain the full circle shown at A in Fig. 318, but only half a circle, with the result that the columns in the centre of each stair are only semi-cylindrical, and exhibit one flat surface. But a very curious fact I observed there is that throughout this old part of Blarney every staircase without exception is sinistral in form, which shows that Cormack M'Carthy, the Strong, fully appreciated the ad\'antages involved in having his own right hand free to attack an ascending foe, who would only be able to use his left hand in defence. There is a spiral staircase in the stronghold of the Red Douglas, Tantallon Castle, near North Berwick, and this also is sinistral, which may be for the same military reason as that suggested at Blarney. As the country became more settled, the tower, which was first used simply for safety, was graduafly built for pleasure too, as was Nunney Castle, in Somersetshire, or Friston Tower, near Ipswich, or Middleton Tower, near Lynn, in Norfolk, which is of brick, and still (I believe) inhabited. But by far the most interesting structure of the kind, also of brick, which I have heard of in this country is Tattershall Castle, in Lincolnshire, which was designed by no less a person than William of Waynflete, Bishop of Winchester, for Ralph, Lord Cromwell, Lord Treasurer of England from 1433 to 1443, who built a stately house for him- THE DEVELOPMENT OF THE SPIRAL STAIRCASE. 309 self in his own country, just as Chenonceaux or Azay le Rideau were built by Financier-Generals of France. Apparently his family had no connection with the ancestors of Thomas, malleus monachortini, or of the still more famous Oliver, both of the same name. Many of the fireplaces in the present House of Commons were modelled after the magnificent specimens at Tattershall, Fig. 322. — Oak Staircase in St. Wolfgang's, Rothenburg. but the feature of the place which I now wish to emphasise is the grand staircase of 175 steps, which is in the south-east turret and gives communication to forty-eight separate apartments, four of which are very large. Its stone handrail, sunk into the brickwork, and beautifully moulded to afford a firm hand grasp, is original in conception and probably unique in design. This is the only staircase in a building 87 feet long, 69 feet wide, and 112 feet high, which is almost entirely constructed of small and ilO THE CURVES OF LIFE l^rilliantl)' coloured bricks from Flanders, or, as some think, from Holland. The curve of this splendid staircase is of the rare sinistral formation, and is contained within a shaft 22 feet in diameter built of enormously thick walls. The same stone handrail sunk in brickwork is to be found in the spiral staircases of Eastbury Manor House, Barking, built in 1572. In Fig. 322 I have gi\'en an example of a wooden spiral stair- case from the church of St. Wolfgang in Rothenburg. At Fig. 323. — The Great Staircase of Fyvie Castle. Shoreham, Sussex, and at Whitchurch, Hampshire, church stair- cases of wood in the same form may also be examined. But it is, of course, with stonework that we are now chiefly concerned. One of the largest stone newel staircases in the United Kingdom is that in Lord Lcith's castle of Fyvie, which is another example of the left-hand formation (Fig. 323). Billings, the author of " Baronial Antiquities of Scotland," thought it showed the same French influence observable in that built for Falkland Palace sixty 3ears before. But neither in detail nor in general character THE DEVELOPMENT OF THE SPIRAL STAIRCASE. 311 can Fyvie be described as French. Each stair is of two great slabs, and where they join the newel their straight outline is varied by two semi-circular mouldings of somewhat rough design and workmanship. They are supported upon arches moving upward at every quarter turn round the central pillar, which is adorned with a band of carving at every full turn, and never stands out, as it does in the best French examples, owing to the somewhat clumsy method of vaulting. The date " 1603," carved at the head of the stairway, probably indicates the year of its completion. A better example of ribbed vaulting, which does suggest French work, is at Linhth- gow Palace. A distinct advance was made when French architects first reahsed that spiral staircases, instead of being englobed within the thick- ness of interior masonry, might be carried in a turret clinging to a waU, or might form an indepen- dent feature (cf. Fig. 317) which would not merely be useful, but highly decorative as an addition to the main structure. One of the earliest of such stairways was that built in the Louvre (since destroyed) for Charles V. Raymond du Temple found that the Paris quarries of 1365 could not furnish big enough slabs in time, for over 6 feet in length was what he needed. So a selection of tombstones from the Churchyard of the Innocents was made ; and I can conceive no stranger material than this " derangement of epitaphs." Surely the devil on Notre Dame must have chuckled ; for of what else are made the steps which lead to hell, even if the paving stones are — on good authority — of a different substance ? It was soon found that there was a distinct gain both in freedom of access and in methods of lighting when the whole staircase was placed outside the walls, as in the famous case of the " Esca- lier a jour " at Blois. By the time that this idea was realised, the architect had made a very distinct advance, and the mason who built for him had attained a skill which seems completely lost in his profession nowadays. The dehcacy of measurement implied, for instance, in the single stone and in the completed Fig. 324. — Elaborate Spir.m. Staircase, with Plan of Improved Stonework. 312 THE CURVES OF LIEE spiral of the next stairway I reproduce from ViolIet-le-Duc (see Eig. 324), can scarcely be appreciated by anyone who has not tndea^•oured to do what is here accomplished. For it will be observed that each step is hght yet strong, and carries with it not only the central spiral, but a handrail as well, while the construction is so artfully managed that the solid central column becomes lighter and stronger as a hollow cyhnder, and, though every step is firmly balanced in its place, yet a stone dropped from the top of this staircase would fall to the bottom without touching anything. The beautiful possibihties of this method of construction were in fact soon discovered, and, as is so often the case in other matters, men went to extremes of geometrical enthusiasm which would be the despair of modern workmen. This may partly be explained by the fact that hfe in a feudal castle must have been very dull at best, and a tricky staircase like the one just mentioned may have been a godsend. Not enough of them are still in existence for me to give as many examples as I should like ; but at Cham- bord, in Touraine, there is still a tour de force in the way of spiral staircases which would be very difficult to beat. It contains two spirals, one within the other, so arranged that a man may ascend from the bottom, while the lady is tripping downwards from the top ; yet they will never meet or see each other, though their steps and voices are perfectly audible. The thing is a delight to generations and armies of tourists at the present day, and the pleasure it gave the courtiers of Francis 1. in that Gar- gantuan Abbey of Thelema, in which he combined fortress, hunting seat and pleasure palace, after the dark days of Madrid, may better be described in the pleasant tales of a Brantome or the picturesque exaggerations of a Rabelais. An earlier example of this geometrical conundrum in con- struction was solved in a simpler way in the Church of the Bernadines in Paris, which was begun by Pope Benedict XIT in 133b. According to Sauval, who published his " Antiquities of Paris " in 1724, this contained a dual spiral staircase arranged in an oval, combining a dextral with a sinistral helix, but using two newels for the purpose instead of the single central column built at Chambord. Somewhat similar double stairways are to be found at Pierrefonds, in Beverley Minster, and (among modern buildings) in the new Courts of Justice in the Strand. A simple and good example in England is the double spiral in the tower of Tamworth Church, where two left-hand curves are cleverly juxtaposed, so that one man can ascend loi steps and another can descend 106 steps without seeing each other, the same newel serving for both (Eig. 325). It is not my present purpose to go THE DEVELOPMENT OF THE SPIRAL STAIRCASE 313 more into detail concerning such jeux d' esprit, for I am in search rather of the beautiful in construction than of the merely bizarre ; but they serve to show some of the possibilities of a spiral, and of the attractions which it exerted upon a constructively imagi- native mind ; and it may be of interest to observe that all the staircases I have chosen to illustrate exhibit left-hand spiral curves. It will be appropriate to end this section of our inquiry with a quotation from that address by Professor Barr to which reference has already been made. " Some at least " (said the President 1 ' 'J ' ;' Fig. 325. — Double Spiral St.^iircase in Tamwokth Church Tower. of the Engineering Section of the British Association in 1912) " of those to whom we owe the greatest advances in the fine arts were eminent also in the arts of construction. We may claim such men as Michelangelo, Raphael, and Leonardo da Vinci as masters in the art of construction as well as in those with which their names are usually associated. ... A structure of any kind that is intended to serve a useful end should have the beauty of appropriateness for the purpose it is to serve. It should tell the truth and nothing but the truth. . . . Our works, like the highest creations in Nature, should be beautifiU and not beautified. . . . 314 THE CURVES OF LIFE From the racing yacht the designer lias been forced, by the demand for efficiency, to cast (jff every weight and the adornments that so beset the craft of earlier times, with the result that there is left only a beautifully modelled hull, plain masts, and broad sweeps of canvas, and we can hardly imagine any more beautiful or graceful product of the constructive arts. These examples will serve to illustrate the contention that the attainment of the highest efficiency brings with it the greatest artistic merit." A good modern example of this may be found in Brunei's famous railway bridge at Maidenhead, in which the quality of the bricks and the subtilty of the curve were chosen to secure the most absolute efficiency. They have resulted, as anyone may sec, in " the greatest artistic merit." It is almost exactly in accordance with these ideas that I propose, in my next chapter, to indicate how much more finely spiral staircases have been built when a great designer had the task of planning them, and to suggest a few parallels between the lines of architectural construction and the lines of Nature's handiwork. NOTES TO CHAPTER XVI. Spiral Staircases. — See " Staircases and Garden Steps," by G. C. Rotfitry (T. Werner Laurie), also "The Enghsh Staircase," by Walter H. Godfrey (Batsford), in which the most beautiful spiral formation shown is that in the hall of Sheen House, Richmond, a typical example of the best Georgian style developed by tfie Adam brotb.ers, making every part subservient to the upward gliding plane of the ascent. Illustrations are also given of the stone spirals in Castle Hedingham, Essex, and Linlithgow Palace. They are all somewhat clumsy, compared with French work. The staircase drawn in the famous ''Philosopher Meditating," by Rembrandt, is another indica- tion that neither in England nor in the rest of Europe, before the 1 8th century, had the Spiral Staircase been so beautifully developed as in France. CHAPTER XVII Spirals in Nature and Art Nosse fidem rerum diibiasque exqiiirere causas. SHELLS AND SPIRAL STAIRCASES— PRACTICAL PROBLEMS AND BEAUTY OF DESIGN — EFFICIENCY AND BEAUTY — LEANING CAMPANILES INTENTIONALLY DESIGNED — CHARM OF IRREGU- LARITY THE PARTHENON ARCHITECTURE AND LIFE ■ QUALITY OF VARIATION IN GREEK ARCHITECTURE — EXPRESSION OF EMOTIONS — ARTISTIC SELECTION FROM NATURE A CONNECTION between shells and spiral staircases, in the minds of those who were responsible for the scientific terms of conchology, as now accepted, has been already indicated. A shell exhibiting the usual right-hand spiral is called leiotropic . because an insect ascending from the mouth ■or entrance to the apex would constantly turn to the left, the columella (or central shaft) being always on its left hand and the outside wall on its right. In the same way, the rare dexiotropic shell, exhibiting a left-hand spiral, necessitates a constant turning to the right in going up its curves from the largest to the smallest. The parallel was carried further by these same scientific writers in giving such names as Solarium maximum (Fig. 36, Chap. II.) or Scalaria scalaris (Fig. 85, Chap. III.) to shells which suggested various forms of staircase, and I have set Valuta scalaris (Fig. 84) at the head of this page with an intention which will become more evident in my next chapter. It is curious that though, as I have tried to show in the last chapter, the origin and development of spiral staircases are purely practical, and though the problems they solve are always practical problems, yet as the beauty of the perfected spiral staircase grew under the hands of capable designers, so it approached more and more nearly to the forms of those natural objects which have not only grown into the lines most adaptable to their survival, but also have developed extraordinary beauty in the process. A comparison will therefore be quite possible Fig. 84. voluta scalaris. 3i6 THE CURVES OF LIFE between the two divisions, without for a moment hinting, at present, that an architect has dehberately taken any natural object as his special model for a particular staircase. And if shells have certainly suggested staircases to the scientific mind, it is equally certain that staircases have suggested shells to the popular imagination, as may be proved by the nomenclature of certain well-known architectural treasures in Italy and elsewhere, At Fiesole, for example, in the convent of San Domenico, there is a flight of eight steps (leading down to the cloister) which is so exquisitely arranged in the form of a shell that the little building is called the " Scala deUa Conchigha." At Venice a more famous example may be found in the Palazzo Contarini (Fig. 326), near the " Congregazione di Carita " (No. 4,299), which is reached through the Calle della Vida out of the Campo Manin. Its shape has earned it the name of the " Scala del Bovolo," and I have been tempted to wonder whether the architect of this dextral helix, with its exquisite rising spiral of light archways, could have seen the shell so aptly called Scalaria scalaris (Fig. 85, Chap. III.), which exhibits exactly the same formation. In this shell the mouth or entrance has gradually grown round and round with the growth of the inhabitant, leaving a little colonnette behind it as it moved, until it reached the place which is equivalent to the door in the staircase to which I compare the shell. No one, as a matter of fact, appreciates better than I do the improbability of the architect of the Palazzo Contarini having either seen Scalaria scalaris or adapted its lines in making" his design. Yet it is evident that in each case the problem involved has produced a thing of beauty, because the practical questions are answered by the architect in the best and fittest terms, and because the shell developed for Scalaria scalaris is the best and fittest formation for its survival. I think those who have followed me so far will at any rate be ready to accept this next step in our inquiry, whether they be conchologists or architects or merely intelligently interested in the work of both. And, if so, they will perhaps be gratified by a further slight coincidence which possibly suggests that the owners of the staircase were not unfamiliar with the beauty and the legends of the shell. At least BeUini may have thought so, for one of the " Allegories " which he painted for the Contarini family is now in the Gallery of Venice, and it represents the shell I reproduced in Fig. 26, Chap. I. Even when in its right place, in a staircase, the spiral in archi- tecture needs clever handling if it is to be effective, as may be seen in the clumsiness of the brickwork in the house of Tristan I'Hermite at Tours, and the ambitious failure of the clustered SPIRALS IN NATURE AND ART 317 sinistral spiral in the stone stairway of the cloisters in the same town. In each case the steps, too, are straight and inartistic. But the " Bovolo " is well done. The massive column of its newel, in which the steps are engaged, rises from base to roof, from the horizontal colonnade at the bottom to the hori- zontal colonnade at the top, with its five com- plete spiral turns between, and its carved handrail resting on a circular balus- trade which describes its even curves throughout behind the outer columns. You may see a similar effect of a continuous balustrade with colon- nettes in Terebra dimi- diata (Fig. 327), while Terebra consobrina, in its lower coils, suggests white arches curving upwards against a dark back- ground. It is the outer columns of the Scala del Bovolo, supporting light arches on their slender Fig. 326, — Spiral Staircase, Palazzo CoNTARiNi, Venice. Fig. 85. — ScALARiA SCALARIS. capitals, which are the chief beauty of the whole construction, for they rest on stepped stone bases which form an exquisitely contrasted broken line beneath and outside of the continuous balustrade ; and how infinitely finer is the formation of these ascending curves than a mere system of superimposed circles (even when the same colonnettes and arches are employed) may 3i8 THE CURVES OF LIFE be seen from a comparison of tlie whole heiglit of the " Scala del Bovolo " (Fig. 329) with the leaning tower of Pisa (Fig. 330). This astonishing Campanile is 179 feet in height and no less- than 13 feet out of the perpendicular. Its lean is more accen- tuated in the three lowest stories, and above the third story there is a deliberate effort to return towards the perpendicular by means of a delicate series f-- of changes in the pitch of the columns on the lower side, and by a slight rise in height of the galleries on the same side. The reasons for this have been somewhat too hastily and generally taken from Vasari's ex- planation in the " Lives,'' who attributes it to inex- perience of the peculiar soil of Pisa on the part of the architects Guglielmo and Bonanno. They endea- voured, he asserts, to rectify the settlement of the foun- dations (which occurred, on this theory, just when the third story had been com- pleted) by endeavouring to build back again to the per- pendicular in 1174. I cannot accept Vasari's explanation now that Pro- fessor Goodyear's researches into what may be called symmetrophobia " have been published. Vasari ^^'^^ ■^-7' Fig. 328. wrote some 400 years after Terebra dimidl.ta. Terebra coxsoerina. tj^g Campanile had been built, some time after the Itahan Renaissance had cast its scorn on what was " only Gothic," and in days when the marriage of a daughter of the Duke of Tuscany w-as celebrated by whitewashing the Gothic frescoes of the Duomo at Florence. Even if we accept Vasari's theory as to the Campanile alone, it will not explain why similar divergences occur in con- temporary buildings. The Baptistery of the Cathedral, begun in 1173, also leans 17 inches out of the perpendicular, and the SPIRALS IN NATURE AND ART 319 plinth-blocks of its foundations tilt down evenly and gradually lor exactly 9 inches in the direction of this lean. The Campanile of S. Nicol5 (built by Nicolo Pisano) leans forward in the same way, and also curves back again towards the perpendicular. The facades of the cathedral of Pisa, and of its choir, both show a similar forward lean in their original construction, curving back again to the perpendicular. These thing i Professor Goodyear has proved in the teeth of technical opposition. Its Campanile, in fact, is not the result of accident. It was originally built as it may now be seen, the most remarkable combination of Greco-Byzantine subtlety with mediaeval exalta- tion in the age which enjoyed such tours de force as the bent column of Arezzo, or the Torre del Pubblico of Ravenna or the Garisenda Tower at Bologna, which is 163 feet high and 10 feet out of the perpendicular. This furnished Dante with one of his finest similes " Qual pare a riguardar la Garisenda Sotto '1 chinato, quand un nuvol vada Sovr' essa si ched ella incontro penda : Tal parv' x^nteo a me. . . ." Goethe, whose essay on Strassburg Cathedral (about 1773) was a veritable rediscovery of mediaeval principles of beauty, explained this leaning tower of Pisa as intentionally so built as to attract the spectator's attention from the numerous ordinary straight shafts ; which may well be true, if we are to believe Benjamin o\ Tudela's statement to the effect that there were 10,000 towers in Pisa alone. It must, I think, be now taken as proved that the leaning was intentional, whatever motives may be assigned to the builders. Above the third floor there is a change in the lengths of various colonnades, which is even more noticeable in the topmost and smallest storey. This might have been taken for the rectification of an accidental lean caused by sinking foundations, and for the return to a vertical arrangement which had been originally intended. But that could only be the case if the lower part of the tower were built as a vertical structure would require. It is not. Careful measurement has proved that where the line of greater slope exists the soffit of the staircase has been dehberately increased in height, while the downward dip was so arranged that it threw the weight of the tower off the overhangmg side. This would have been quite unnecessary if the architect had meant the tower to rise up straight from its foimdations ; and above the critical point none of the precautions just described are taken : If there had been an accident, no precautions would have been 320 THE CURVES OF LIFE visible beneath, and \'ery careful adjustments would have been necessary above. The exact reverse is the case ; and it is worth observing that if the exterior colonnades had been arranged in a spiral the mathematical problems involved in the leaning con- struction would have been extremely difticult. This may, there- FlG. 329. SCALA DEL BoVOLO, FiG. 33O. ThE ToWER OF PiSA. Palazzo Contarini, Venice. fore, be one reason why the architect deliberately built tiers of circles outside, in spite of having a spiral staircase inside. He must have sacrificed the beauty of an external spiral to the oddities of his design. I cannot here commend the Campanile of Pisa for its eccentric leaning construction any more than for its superimposed circles. but I quote it as the most intelligible instance I know of the SPIRALS IN NATURE AND ART 321 deliberate avoidance of accuracy in construction for deliberate reasons. It is exaggerated, and therefore fails where the more delicate effects of the Parthenon succeed ; but its very con- spicuous quahties give a very clear example of that intentional mystification by which the old builders strove to get a look of life ; of that elemental energy which is never limited by rule ; of those principles of growth which have brought Naulilus pom- FiG. 331. — Examples of Wood-turning. The Spirals on the Right and Left are Eccentric. The Centre one is Regular. filius SO near to the logarithmic spiral without ever exactly repro- ducing the mathematical curve. In Fig. 331 I have reproduced three specimens of wood-turning by Mr. H. C. Robinson. The centre spiral, though beautifully executed, is exactly .sj'mmetrical. I beheve Mr. Robinson was the inventor of the modification in machinery which produced the far more attractive irregular spirals on the left, and the curious concave variety on the right. The smaller model on the left is peculiarly like a hving, chmbing plant, and its chief charm is that it is almost as irregular in its make as the plant is in its growth. Another example of the same dehcate irregularity is observable in the workmanship of the best medals, which nearly always show an uneven floor beneath the design, as may easily be seen C.L. Y 322 THE CURVES OF LIFE by the unequal thicknesses obser\'able along the rim. This method was well known to the classical Greek medallists and to the best of the Italians ; and in such modern work as Bertram Mackennal's medals for the Olympic Games of 1908, or in the magnificent head of the French Republic by George Dupuis, you see it still. The exigencies of modern coinage may perhaps make it difficult to use the system when money has to be capable of being stacked in regular piles of similar denominations, but this necessity does not exist in Fig. 332. — Queen Bertha's Staircase AT Chartres. Fig. Si. Mitra papalis. modern medals. Yet if we take such a recent example of the official coronation medal of Edward VII., the " floor " of the design seems so flat that the whole thing looks very like a postage stamp stuck on a thin disc, and has as little light and shade. But I am wandering from our immediate subject, and must return to it at once. SPIRALS IN NATURE AND ART 323 An even more delightful example of the close connection between a good architect's plans and the exquisite lines of Nature is to be found in the stairway called " Escalier de la Reine Berthe " at Chartres (Fig. 332). It exhibits the dehcate exterior ascending dextral helix, and even the top oiMitra papalis (Fig. Si, Chap. III.) with extraordinaiy faithful- ness, and the parallel be- comes even more complete when the position of the darkened doorway is com- pared to that of the shadowy orifice of the shell. The stall case is contained in an external turret, and the internal spiral is expressed externally by curved tim- bers and the outer side of the string-course. The sur- face is also divided by numerous vertical beams, most of which rest on the string timbers, but the three main beams go from top to Fig. 333. — Staircase in the Old Wing 1| OF THE Castle of Blois. Fig. 73. — Telescopium telescopium. bottom of the thirty-six steps which swing round the central newel. In Mitra papalis at this orifice you wiU observe the begmmngs of three internal spiral fines, which suggest that the mternal arrangements of a shell have as much to teach as its exterior forms ; and a very beautiful spiral may be seen by the aid of the X-rays continuing throughout the whole length of the long Y 2 324 THE CURVES OF LIFE pointed shells so common in the south (see Fig. 62, Chap. III. of the Tercbra photographed by X-i-a3's). The clue has been followed up, and in Chapter III. I showed that a section cut through such a shell as Tdescopium telescopimn (Fig. 73, Chap. III.) actually reveals an exquisitely firm and elegant single spiral (a dextral hehx) rising round the columella, that pillar which supports the whole ; and this at once reminds me of the spiral in a staircase (Fig. 333) built in the old part of the chateau at Blois many years before the moie famous \ving of Francois I. But I do not foi a moment suggest that there was any conscious comparison in the mind of the fifteenth century architect, and this for the very good reason that the curve of his stairway and the beautiful spiral rail (on which the left hand would rest as one ascended) are both susceptible of a simple architectural explanation ; so that all I should be inclined to say of this comparison at present is that, as the hues of the architectuie are right, and fulfil their purpose exactly, with an economy of space and strength and a sufficiency of support, they were therefore very likely to be in harmony with those lines which Nature, the best of all artificers, has de^'eloped in her shell. I should need more resemblances than this to be satisfied that one might have been taken from the other ; but, on the other hand, I shall by no means reject such a possibility, at the outset, as absurd ; for architecture is full of such copies from Nature, as everj' organically beautiful, constructive art must be, and it is full of equally suggestive lehcs of the simpler forms of shelter from which the palace slowly giew. If the Egyptian pillar is a copy of the lotus plant, so the peculiar shape of the Moorish and Saracen arch is a survival of that wind-blown tent, with conical top and bagging sides pegged closely in, which was the habitation of the Bedouin. There are far more resemblances of the kind for which we are looking in the open staircase built at Blois between 1517 and 1519 in the wing of Frangois I., the inside of which (Fig. 334) is here compared with the section of Vohita vesperiilio (Fig. 335) and the outside (Fig. 336) with the rising lines and " colonnettes " upon the exterior of the same shell (Fig. 337). Now I am dealing with this instance in greater detail in my next chapter, and it is only inserted here to complete my little quartet of typical comparisons between the unstudied loveliness of Nature and the masterpieces of the best creative art. But it happens that this open staircase (Fig. 334) was built during the last years of Leonardo's life, when he dwelt at Amboise, where the inchned plane of the spiral stairway in its tower was one of the chief features of the castle. It is only a few miles down the Loire from Blois where the single, strong curve of the staircase in Fig. 333 SPIRALS IN NATURE AND ART 325 was one of the most beautiful details in the older portion of the chateau. It also happens that the Scala del Bovolo in Venice and Scala della Conchiglia in Fiesole are of such a date that if these names had been already popu- lar, they may well have stimulated his imagination at a time when his note- books were already filled with studies of the structural forms of natural objects. And it is certainly true that no one who looks with a seeing eye at the finest of the buildings which Leonardo da Vinci might have known can fail to detect an intense percep- tion of that differ- ence in detail and Fig. 334. — Central Shaft of Spiral Staircase in THE Wing of Francois I., Chateau of Blois. (Photo by courtesy of Country Life.) Fig. 335. The Common Form of VOLUTA VESPERTILIO (Section.) harmony in mass of which Nature is the great exemplar. The " straight lines " of the Parthenon (Fig. 338) are in reaUty subtle curves, and recent investigations (by Professor Goodyear) have detected a similar delicacy of constructive measurement in ',26 THE CURVES OF LIFE the great Gothic cathedrals. The influence of the study of flowers and leaves is especially marked when the positions and proportions of the best B^'zantine arches are examined in the light of the laws w^hich govern growth. How slight and exquisite were the details on which such laws depended no one could realise better than the painter who had studied the rendering of expres- sion on a human countenance by lines so delicate that the reason for the effect produced was only visible to the few who knew. The eye is even more influenced by things which are usually " unseen " than by things which are " obvious " ; audit Fig. 336. — B.^LUsiR.\DES of the Open Staircase AT Blois. Fig. 337. The Common Form of VOLUTA VESPERTILIO. (Exterior.) is of the essence of Beauty that her origins and causes are hidden from those unworthy to appreciate her. Some of these origins and causes it may be well to state here, for though the first suggestion of their existence was made many years ago, they have never been properly appreciated by a pubhc which must, after all, be the ultimate arbiter of architectural SPIRALS IN NATURE AND ART 327 taste, and they are closely connected with those methods of Leonardo with which we are now chiefly interested. The history of architectural theory has seen a renaissance of the ideals called classical, and a revival of the school known as " Gothic," of which the former was incomparably the more valuable, because the conditions of society which made "the pointed style " possible in England, and gave birth to the " Gothic " school in the He de Erance, could never reappear, and were an essential concomitant of the architecture which expressed them. Yet an omission of equal importance was made by the revivahsts of both schools. The real "Gothic"" preserved certain delicate principles of constructive asymmetry, in the cui-ves and irregularities in the masonry of the old Greek builders ; but the " Renaissance," which pretended to go back to ancient Greek and Roman ideals, did not appreciate, even if it saw, these slight divergences from the rule of thumb which were invisible to any but the trained observer. In the same way, the Gothic revival, which attempted impossibihties by overlooking entirely the radical changes which had occurred in contemporary Hfe, was fated still more fully to destruction by its complete ignorance of the finer subtleties of mediaeval art. We have no actual proof of this lack of appreciation in each case, except the proof provided by the buildings which were themselves the products of these separate revivals. Eor apart from Vitruvius and from the invaluable Notebook of the architect Wilars de Honecourt (1250), we have very few real contemporary records of the growth of architectural principles until these theories concerning slight divergence had been wholly lost. Even the sentence in Vitruvius, which seems directly to refer to them, was never understood until the nineteenth century, and then only by the merest chance on the part of an observer whose real work was never recognised. These constructive refinements, however, died out, not meiely because no record existed of them, but for the far more vital reason that the pubhc eye was no longer delicate enough to appreciate them, though, as a matter of fact, they are the real cause of beauty in the finest of our old surviving buildings, which owe their charm not so much to the kindly hand of time, as to the deep-laid skill of their builders. When con- structions have arisen which were designed without that skill, even when they are supposed to be exact copies of the old originals, no lapse of time can ever lend them a beauty which is no concern of theirs, as may easily be seen in the " copy " of the Maison Carrie at Nimes which is called the Madeleine in Paris, and in many smoke-begrimed atrocities of modern London. In these days division of labour has lowered the capacity 328 THE CURVES OF LIFE of the indi\'idual artisan ; and machine-made redupHcations, accustoming the eye to an inartistic uniformity of ornamental details, ha^•e also destroyed its grasp of deHcate structural effects. In the old cathedrals, the mason and the architect, the artist and the artisan, were often one. By the fifteenth centurj^ a Florentine, Leon Battista x\lberti, had separated the architect from the builder. In England, it was Inigo Jones who fiist invariably insisted that his wood and stone workers should copy his designs instead of following their own fancies. Each was a great man, yet each was the unconscious origin of a great evil which has befallen the art they loved. The history of the discovery of curves in ancient Greek, even in Egyptian, architecture is romantic and interesting enough. Every one had read the passage which suggests them in Vitruvius since 1500. Stuart and Revett had measured the Parthenon in 1756. Lord Elgin's workmen noticed nothing. In 1810 Cockerell had established the fact of entasis, and in 1829 Donald- son saw the lean of the columns. But in 1812 the translation of Vitruvius, by Wilkins, only contained a note that " this great refinement . . . does not appear to have entered into the execution of the work of the ancients." Apparently it never occurred to the translator that it was worth while measuring " the work of the ancients " before making general statements about it. At last, in 1833, Mr. John Pennethome discovered the undoubted existence of convex constructive curves in the architraves of the second court of the Theban temple of Medinet Habou. Four years afterwards he stood before the Parthenon (Fig. 338) with the passage from Vitruvius in his mind, and saw those delicate irregularities which had remained invisible through- out the passage of so many uninteUigent years. About the same time two German architects, Hofer and Schaubert, saw them too, and published their discover}^ in the Wiener Bauzeitung of 1838. Save in a private pamphlet, Pennethome gave nothing to the world till 1878, although in 1851 Francis Cranmer Penrose, helped by the Dilettante Society, pubhshed the results of his measurements of the Parthenon in " Principles of Athenian Architecture."" Penrose showed that in this building no two neighbouring capitals correspond in size, diameters of columns are unequal, inter-columnar spaces are irregular, the metope spaces are of varying width, none of the apparently vertical lines are true perpendiculars, the columns all lean towards the centre of the building, as do the side walls, the antffi at the angles lean forward, the architrave and frieze lean backward, the main horizontal fines of construction are in curves which rise in vertical planes SPIRALS IN NATURE AND ART 329 to the centre ot each side, and these curves do not form parallels. Professor Goodyear, who completed the investigations of Penne- thorne at Medinet Habou, found that similar curves existed in the Maison Carree, and it is clear that while irregularities which would be easily detected or obtrusively conspicuous were avoided, there was also an unquestionable intention of avoiding exact ratios or mathematical correspondences wherever such an avoidance was calculated to produce a certain effect. That these deviations were not the result of error in the workmen, or of accidents in the lapse of centuries, is also clear from Penrose's calculation that the maximum deviation of the Parthenon in the case of lines intended to correspond (as at the two ends) is as little as the fiftieth part of an inch, while the refinement of jointing in the masonry is so great that the stones composing the great steps have actually grown together beneath the pressure of the columns they support. It is, in fact, impossible, to explain such asymmetries as these, on the theory of faulty work, of the use of varying materials from different sources, or of subsequent accidents, or of successive generations of builders being inaccu- rate ; and the principle thus found to be practised by the builders of the Parthenon have also been discovered by Professor Goodyear to exist not merely in Egyptian, Greek, and Roman buildings, but in Italo-Byzantine, Byzantine-Romanesque, and Gothic buildings, especially where Byzantine influence has been strong, in obedience to laws which fell into abeyance almost completely when the classical Renaissance fully established itself. " Much time has been spent," writes Professor Lethaby, " in trying to elucidate Greek proportions, for the .most part time wasted. ... It is quite different with modifications by curvature and other adjustments made by Greek masons ; here we have something tangible, if subtle . . . such adjustments are most natural in a highly refined school of architecture and need no explanation." It is refreshing, in 1913, to read this recognition of the. truths brought out by Professor Goodyear's researches. But I cannot agree that the " adjustments " (which I prefer to call refinements) " need no explanation " ; for they constitute to my mind, one of the chief reasons why classical Greek archi- tecture is better than any of its later copies. Again, in speaking of French Gothic, Professor Lethaby says : " Originahty was insight for the essential and the inevitable. Proportion was the result of effort and training, it was the dis- covered law of structure " (in these pages I suggest that it is the discovered law of growth) " and it may be doubted if there be any other basis for proportion than the vitahsing of necessity. 330 THE CURVES OF LIFE Nothing great or true in building seems to have been invented in the sense of wilfully designed." (What then are his " adjust- ments " made by Greek masons ?) " Beauty seems to be to art as happiness to conduct — it should come by the way, it will not yield itself to direct attacks." Surely this means no more than that the highest genius is born and not made. But when we see such a work of genius as the Parthenon, for example, is it " time wasted " to analyse those qualities in it which are absent in other work ? And if we think we can discover some of them, is it " time wasted " to suggest that new work may take account of them instead of belittling or ignoring them ? " Proportion," says Professor Lethaby, " means either the result of building according to dimensions having definite relations to one another, or it means functional fitness." Of course it means " functional fitness " if the theory I am trying here to elaborate is worth anything at all. One of the conditions of organic life is the possibility of shght deviations which will fit the fimction for its environment. One of the conditions of beauty is the use of subtle variations from exactitude. After Penrose's measure- ments, it is futile to deny that subtle variations were a large factor in the beauty of the Parthenon. After Goodyear's work on Gothic buildings, it is equally impossible to deny that the great cathedrals owed a large part of their charm to the same principle. And, in both cases, the deviations are deliberate, forecasted, planned ; not the mere result of difficulties in making a complex building join together. After stating such " obviously desirable qualities " of architec- ture as " durability, spaciousness, order, masterly construction, and a score of other qualities," Professor Lethaby says that " there is no beauty beyond these except in the expression of mind and of the temperament of the soul." I agree entirely ; but why does he sternly deprecate any analysis of that expres- sion ? Why should we not dihgently try to arrive at a few general principles, at some sort of formulation, simply enough stated, which will guide our understanding ? Why does he think that " much aesthetic intention is destructive ? " Unless the public taste is to a certain extent educated, nothing is more certain than that contemporary architecture will reflect its carelessness. Both the greatest Greek art and the greatest Gothic art were produced by a people in the deepest sympathy with every principle expressed by the buildings made for them. Every age has the architecture it deserves. Like other wonders of the world, the Parthenon makes a different appeal to almost everyone who sees it ; but nearly half of that appeal must always depend upon its setting in the marvel- SPIRALS IN NATURE AND ART 331 lous light and landscape of Attica. There is a genius of place, as there is individual influence in every personaHty ; and on the Acropolis that genius is more insistent than in any other spot I know. " You may almost hear the beating of his wings." It is not dependent on the landscape, though here, as in similar instances, the surroundings seemed made to fit their central gem ; it is not dependent upon accidents of tijne or idiosyncrasies of character, for the Parthenon, like all great works of art, makes its essential call on those primeval fibres of our common humanity through which the greatest artists of all ages have made their own appeal to all the populations of the world. But inasmuch as no other architectural composition has had quite this effect upon all beholders — has, in fact, so nobly succeeded in impressing the meaning of its builders upon every successive generation — it is worth while asking why what at first appears to be only an arrangement of straight lines of marble should have been able, in the certain mind of its creator, to express so much. If there is any answer to this, it will also be the answer to the even more insistent question : why so much architecture afterwards has been not only meaningless, but positively offensive, both to its contemporaries and to their posterity. One general consideration must be at once stated, and then left. If architecture is not a fair reflection of the age and the hfe that caUed it into being, it will fail in every other age, and will appeal to no other form of hfe. Now it is fashionable to be pessimistic about our own times and our own country. But without being that, it is possible to say that both are presented to any thinking man to-day as a far more complex environment than was the case in any country even only two centuries ago. Within that short span of history boundaries have lapsed, races and nationalities have shd into each other or changed their temperament in the melting-pot of war, distances have decreased, the material diffi- culties of time and space have almost disappeared. Pohtics present themselves under the form of compromise ; patriotisms tend to become vague generalities of colour ; nationalities are but the reflection of wide-reaching ties of blood that constant inter-marriage weakens every day. If it is difficult to appeal to a pubhc which is no longer homogenous, it is still more difficult to express that monstrous shape which shall embody its distinctive personaHty. So it is not the Enghsh architect alone who is to blame for" the absence, in this twentieth century, of any archi- tectural style that can express or reflect the age and the hfe in which he hves. That marvellous moment in the early sixteenth century when all the knowledge of his time could be garnered in a Leonardo's 332 THE CURVES OF LIFE single brain has gone ; its parallel can never more return. Knowledge has now perforce become a divided kingdom in which the specialist, in his own ring fence, explores his own few acres with very little reference to any other's work. So there is little of that unity in modern life or thought which architectural Conceptions can best reflect. In Greece, the unity and harmony of their common Hfe was the one essential characteristic which the citizens of Pericles desired to see embodied in the Parthenon. " The Hellenic temple " (writes Compton Leith) " soothes and delights the mind, persuading it of a power in man strong to achieve all things ; in every part and in the whole it is instinct with a supreme grace and continence. The columns spring like living stems ; and as, in the tree, the risen sap flows easily along the branches, so all upward effort is diffused along these entabla- tures and ebbs in a harmony of receding hues. The roof, with its broad gable, confines and embraces the whole ; its calm length, its quiet overshadowing, are symbols of a world summed, contained, pacified." The western portico of the Propylaea on the Acropolis of Athens is built with fluted Doric columns ; and three huge steps of Pentelic marble, with one dark blue Eleusinian stone, lead to the top. There is a slope of scarred soil, strewn with marble fragments and with limestone, stretching upwards for a short way beyond it. On the summit, and a little to the right, stands the Parthenon, not identical in orientation with the gateway of the Propylaea, as you notice when you stand beneath the enormous blocks of marble, over 22 feet long, which span that gateway from one pillar to another, but so placed that the play of light and shade may be varied in each building ; and the Erechtheum is set at a different angle too, its graceful outlines forming a perfect contrast to the majestic solemnity of the larger structure. This subtle quality of variation persists throughout the best Greek architecture. Besides those which I have already men- tioned, there are many more interesting instances of deliberate and delicate divergence from mathematical accuracy, and it is this divergence which gives the Parthenon its living beauty. For the essential principle of life and growth is constant variation from the rigid type. No tree grows all its branches at the same angles to the trunk, no flower springs from the earth to meet the sun in the straight lines of geometry ; and so Ictinus and CaUicrates built, between 447 and 438 B.C., a temple for the Athenians which should enshrine, in lines of imperishable marble, subtly wrought, the evanescent and essential beauty which they loved. Though bereft of well-nigh every ornament, and mutilated SPIRALS IN NATURE AND ART 333 even in the skeleton of its structural anatomy, the Parthenon retains the unfaded glamour of its first conception. Like a broken statue which suggests the marvels of the perfect master- piece, it preserves the spell which first inspired its wondrous hues, and leaves to every understanding heart the happy task of fining up the gaps at pleasure. This is the more remarkable because it is not the pathetic fragment of what was once the tenderness and grace of woman, or the resource and strength of man, or the complicated emotion of a group of human figures, or the self-sufficient majesty of serene divinities. It is a building only, erected for man's purposes after patterns man alone has made. Nor does its charm essentially depend either upon the natural surroundings which add so much to the sympathy and pleasure of the visitor who travels to that storied shrine, or upon those gifts of mellowing time which make the shadows in its fluted piUars deepen into sunset gold instead of the more frigid blues and greys that fringe the bosoming snow on mountain pastures. There is in it something of the " stuff incorporeal that baulks the grave," something of that impalpable essence which informs all living things. Who shall say, in these days when science is knocking so close upon the doors of life and death, that inorganic matter as we have understood it hitherto is in its highest forms incapable of receiving some impress of what we still must call organic energies ? At the last's last we are as incapable of defining one as we are unable to describe the other. The only thing about our own personality of the existence of which we can speak with greater certainty than of anything else connected with our being is our will, our power of choice, " the satisfaction," as it has been called, " of a passion in us of which we can give no rational explanation whatever." This is the element which assures us of a future and reheves us of that despotism of the past to which the clod of shapeless mud and the iron-bound mathematical conclusion must ahke be fettered. This is that life which is the baffling factor in all organic beings ; and in the greatest master- pieces of creative art their beauty is as baffling and intangible as Hfe. This, too, is the one hnk through which our brains can realise and our eyes can see as Pheidias, Ictinus, or Callicrates could see and reahse the Parthenon. It is, indeed, the only clue by which we may arrive at any the least success in understanding what they meant. Art, at its highest, is the expression of its maker's emotion through channels which the rest of his world may understand. And it is only that artist who gives you his own inspiration 334 THE CURVES OF LIFE r' SPIRALS IN NATURE AND ART 335 of the things and men he sees around him who will be intelligible not to his own time and his own friends alone, but to all time and to all generations of the world's posterity. For the methods by which he has expressed the emotions roused in him by his environment are precisely similar to the methods by which we shall recognise the expression of similar emotions until man shall cease to be. We recognise it because the elements that are com- mon to the artist and the spectator are inherent in humanity itself ; in the organic character which has been shared by every man since we inhabited this planet. Art, though it may be found in any human handiwork, exists in nothing else, and is discoverable only through those common channels of perception which are most efficient in the strongest and the most healthy organisms. So that art has as little to do with insanity, or decadence, or deterioration, as with morals. In a madman those channels through which his mind should direct its communications to his comrades have become clogged ; the balance between the receptive and responsive body and the creative mind has been destroyed, and so the possibility of his art's appeal is wrecked. The greatest artists have almost invariably possessed the most essential attributes of physical perfection ; they were the healthiest workers. The true artist, we may imagine, is the man whose eyes can freely see, whose ears can freely understand, as the dull senses of his fellows never will, and who transmits the emotions which his senses have conveyed to him through instruments akin to ours, but tuned to a finer melody, and harmonised to deeper chords. For him the little hills rejoice on every side, the valleys also standing thick with corn do laugh and sing. Fire and hail, snow and vapours, the heavens that are a tabernacle for the sun, " which goeth forth as a bridgeroom out of his chamber and rejoiceth as a giant to run his course " — these things appeal to him with a keener sympathy than ours, with a quicker percep- tion of that intimate, far-off progression of the race throughout the ages, with a deeper knowledge of what Nature means to man. And so, discovering the laws by which this Nature works, he frames some kindred principle on which to fashion new creations of his own. He does not merely reproduce the beauty he has seen ; he adds to the stock of beauty in the universe of his own skill and handiwork. This, then, is one reason why the greatest creations of art are not for one age, but for all time ; not for one man, or even for one class of men, but for humanity. This, too, is one reason why such buildings as the Parthenon possess something of that undying, ever-changing, elemental charm which we perceive in DJ'- THE CURVES OF LIFE hills and forests, in the rivers and the ocean, in the glow of dawning or in the splendour of the evening clouds ; something of that A'ital property of Nature which " Gives to seas and sunset skies The unspent beauty of surprise." There is no other building in the world which has achieved so certain, so age-long, and so perfect a result. In many of the best of the old buildings still surviving you may see some of the delicacies of divergence I have just described. Obhque plans are common in old churches. In Tamworth Church the chancel inclines so much to the north that a straight line drawn up the nave would hardly touch the altar. The same pccuhaiity can be seen in St. Ouen at Rouen, in Lichfield Cathedral, or the choir arch in the parish church of Wantage, where the deflection of the building has been said to represent the position of Christ's head upon the cross. Such instances, however, are of a grosser nature than the curves in constructional hne, which I wish chiefly to emphasise, and which may be seen in the walls of the nave of Westminster Abbey. These are bent inwards at about the height of the keystones of the arches, and outwards above and below this point, as Mr. Julian Moore has shown. They are not only structurally sound to this day, but have retained a greater beauty than exists in any of the numerous ruler-made copies in different modern churches of the country. In Evelyn's " Diary," there is a most interesting indication of similar divergences in Old St. Paul's. " Finding," he writes on July 27th, 1665, " the main building to recede outwards, it was the opinion of Mr. Chichly and Mr. Prat that it had been so built ah oi'igine for an effect in perspective, in regard of the height, but I was, with Dr. Wren [Sir Christopher], quite of another judgment, and so we entered it ; we plumbed the uprights in several places." This imphes that two Enghsh architects of the seventeenth century asserted a constructive existence and an optical purpose for an outward divergence from the perpendicular in the vertical lines of the nave of a Gothic cathedral, and favoured the preserva- tion of the Gothic building as far as possible. To Evelyn and Wren, however, the champions of the Renaissance, the old church was " only Gothic." Keen as they were, they had lost something which two lesser men remembered, though we shall see, later on, that Wren was not above putting a distinctively " Gothic " feature into his Renaissance plans for the new St. Paul's. Similar divergences from accurate measurement in St. Mark's at Venice have been equally overlooked by almost every visitor. The piers SPIRALS IN NATURE AND ART 337 and upper walls of the nave lean outward to an extent of 18 inches out of the perpendicular on each side, a deviation which, had it been accidental, or later than the original construction, would have disintegrated the arches supporting the dome, ruined the mosaics, and destroyed the building. Again, in the choir of Sant' Ambrogio at Milan the main piers on the right and left lean out nearly 6 inches from the perpendicular on each side ; and a similar lean may be observed in S. Maria della Pieve at Arezzo, where the queer bent column in the choir gallery is a conspicuous instance of the capricious and eccentric forms occasionally developed by the hatred of mathematical exactness. " Only Gothic ! " The phrase, in this twentieth century, strikes like a blow. What better name than " Gothic " were it possible to bestow on that indomitable wildness of aboriginal strength which so differentiates French architecture in the thirteenth century from the suave and silent calmness of the Parthenon ? For here, indeed, are the outspoken chords of " frozen music " Goethe loved so well ; here is the divine unrest of passionate endeavour. The high vaults bear down, in an imposing fierce expansion, upon the walls of the clerestory which themselves are balanced above the arches of the nave. Other arches again are built to counterbalance that resistance, with flying buttresses in tiers downweiglited by their carven pinnacles. Arch fights the expanding bow of arch, till eight together balance on one slender pier and cross like jets from some colossal fountain of stupendous energy. All seems to be pitted and opposed. Force visibly meets force as in some monstrous organism. Almost you hear the laboured breath of wrestlers, the sigh of the living creature, tense and struggling to be free, without pause and without rest ; and every stone seems surging towards ascent, until the spires above them lose their vanes among the clouds. This was the architecture " Only Gothic," an architecture of endeavouring life, full of the differences and divergences of life. The principles which guided the Greek builders seem to have lasted just as long as building was done from the freehand drawings of the artist-mastermason. No painter, even of to-day, would draw in a door in one of his pictures with a rule and com- passes ; he knows that there is a quality in the natural work of hand and eye which no artificial aids can give him, The old Egyptians and the Greeks knew that, and the tradition of it lasted on in a few cases of stone construction even when the designs were ruler-made, and when the irregularities of handiwork had become the conventions of a few skilled masons. As we have seen, two English architects in the seventeenth century C.L. Z 3^,8 THE CURVES OF LIFE jy recognised the existence of deliberate constructional inequalities. As late as the eighteenth century these principles prevailed, as may be seen in the " humped " pediment of the Mansion House in London. Even to-day the thatcher builds his cottage roof not in straight lines, but in curves, which absorb less rain water, and he achicA-es a beauty which is denied to mathematics. The old streets were full of beautiful curA'es which cannot be explained only on the theory that twisting thoroughfares were more easy to defend, or by the suggestion that the houses grew up at haphazard. Neither of these reasons can explain the beauty of the High at Oxford, or the angle at which Magdalen Tower is set to its own quad, or the superiority of Regent Street and Piccadilly to Victoria Street or the Edgware Road. The " whiff of grapeshot " has Haussmannised modern Paris into a city of straight lines, and the next step is the chessboard of the American city, in which every thoroughfare leads to nowhere in particular. When the divergences in building and in the laying out of streets were almost forgotten, the principle that underlay them still survived in that more intimate form of architecture which is furniture and domestic decoration. In the best periods of Chippendale, or Hepplewhite, or vSheraton, you find each step in a staircase gently bowed outwards, or given a waving outline ; you find, too, that the walls of the best rooms are given slight curves horizontally as well as vertically ; you find the subtle inequalities of feeling handiwork in settee, and chair, and screen. But the modern " decorator " seems so fond of Euclid that the joys of the rectangle and the parallelogram have swamped the charms of Nature. He forgets that even so common an object of his daily life as the human face has two sides which are quite different the one from the other. Fortunately, for us, Leonardo, that mighty master of the human face, hved when these principles were not so utterly forgotten as thej^ are now. He was, indeed, a painter of the Renaissance and the Renaissance influenced all his life and art. But he was a man whose personahty broke a way through the limitations of every style. He realised to the full what Whistler said long alter him, that " Nature contains the elements in colour and form of all pictures . . . but the artist is born to pick and choose, and group with science, these elements, that the result may be beautiful." He was a student of Nature who had observed that her diver- gences were even more important than her reproductions, and who did not even shrink from saying that the creative imagination of the understanding man was infinite in comparison with her. We shall see more of the designs of which he was capable in the next chapter. SPJRALS IN NATURE AND ART 339 NOTES TO CHAPTER XVII. Shells and Staircases.— The following letter is from " P. E." :— " You speak of ' a connection between shells and spiral staircases in the minds ' of both conchologists and ordinary people. Do you remember what Leoni says about them ? I quote the translated passage : " ' As for windmg stairs, which are also called Cockle-stairs, some are round, some oval, some with a newel in the middle, some open, espe- cially when room is wanting. ...'(' The Architecture of Palladio,' 1742)- The Italian for ' cockle ' is Vinca. This is odd. " Staircases (of any form) must always appeal to the imaginative mind. They always recall to me that vision of Piranesi's, in which a man is shown mounting a stair which is broken at the top. But another figure (the same man) appears beyond the chasm on a higher stair. And yet again above a third break a third figure mounts towards the sky. All good staircases give one that ' aspiring ' sensa- tion, as if to walk upwards were an easy thing." The Tower of Pisa. — The problem of this leaning tower was chscussed by Professor Goodyear in the Architectural Record, Vol. VII., No. 3, March 31st, 1898. The illustrated catalogue of the exhibition of " architectural refinements " held by Professor Goodyear in 1905 at the National Portrait GaUery in Edinburgh gives a most interesting series of examples of vertical curves, of curves in plan, of asymmetric plans, of bends in elevation, and many more matters treated of in the chapter just concluded. Organic and Inorganic Matter. — See " The Fitness of the Environment," by L. J. Henderson (MacmiUan, 1913). No Tree grows all its Branches at the same Angle. — It has, I believe, been demonstrated that variety in this angle predicates a high level of perfection in development. Greek Architecture. — "We have heard too many hot-headed statements about deviations and inflections in Greek architecture. For some people the subject is wrapped in a sacred mystery, and their attitude seems to prevent their arriving at any sort of helpful statement. Is-no statement necessary ? Are we never to understand nor to do anything in our own age ? Are we for ever to talk sentimentally about the one Renaissance, and even in our tables and chairs despair (delightedly) of our joinery and our inspirations ? Well, there are some who do not believe in synthetic a^stheticism ! There are some who wish to believe that a sacred, delicate flower will be killed by the least amount of conscious sane attention. Such people will not even try to find seeds. The beliefs have gone wrong ; not the springs of inspiration, nor the skill of eye and hand. Those who foolishly champion art against the analysis of science, and who shout to us about the exceptions, tell us very httle about the deviations or inflections. "In Greek architecture, as in every other work of man, there are three kinds of inflections. Centrally, on the average, I do believe that regular forms, based on simple rules of proportion, make the chief factor. Then there are the cleverly measured-out deviations to correct the eye, which is too far subjected by the perspective, by images of Z 2 340 THE CURVES OF LIFE irradiation and by contrasts. Tlien come the little errors in human touch, never conscious, that show skill, which so nearly made no error. Without these errors we should miss the sense of labour in the work. But there can be no forgery of such errors. If beauty is ' fitness expressed,' charming errors in workmanship are the residuum of difficulties conquered to the point where they just cease to interfere with fitness. In pure decoration the fitness is the clarity of the central law of regular form. The hand of the good workman expresses the central law of a regular form to a point where it is clear and obvious, but he does not accentuate the expression. After these inflections come the irregularities of form and colour due to age. These stir in us a different set of emotions, but the mixture of our feelings is so fine that many of us think it amorphous. Some of us, overpowered by our emotions, become hysterical, if not fanatical, worshippers. Such worshippers are seldom helpful, and they are never good workers.— M. B." CHAPTER XVlll The Open Staircase of Blois Majestati Nature Par Ingenium. THE staircase DESIGNED BY LEONARDO DA VINCI — VOLUTA VESPERTILIO THE KING'S ARCHITECT — A LEFT-HANDED MAN — WORK OF ITALIANS IN FRANCE — LEONARDO'S MANUSCRIPTS — HIS THEORIES OF ART. The Open Staircase in the courtyard of the Chateau of Blois has long been celebrated, and to my mind it is one of the most beautiful designs of its kind in the world. All direct proof as to its origin or construction has disappeared. It was built between 1516 and 1519 and all documents concerning the work at Blois during that period have been lost. This chapter collects the evidence in favour of attributing the design to Leonardo da Vinci, and the steps in the argument to be developed may be summarised as follows : - 1. When he lived in Italy Leonardo worked (Figs. 339, 340) at architecture as a pupil and collaborator of Bramante. 2. The argument that a spiral staircase is impossible, either as a design by a Renaissance architect or as a feature in Renaissance building, is met by examples of a spiral staircase by Bramante for the Vatican, and by Wren for St. Paul's (Figs. 341, 342). 3. The Open Staircase at Blois, though perhaps developed from the ordinary Vis de St. Gilles (as shown in Chapter XVI.), has many of the characteristics shown in Chapter XVII. and a few distinctive variations peculiar to itself. 4. The inside spiral shaft (Fig. 343) compared with the inside of Valuta vespertilio (Fig. 90). 5. The balustrades outside (Fig. 344) compared with the outside of Valuta vespertilio (Fig. 78). 6. Valuta vespertilio comes from the north-west coast of Italy. A section made of it. 7. The staircase exhibits a left-hand spiral. Was this taken from the rare (dexiotropic or sinistral) Valuta, or was it drawn by a left-handed man ? 8. A shell is carved upon the central shaft (Fig. 345). 9. The steps are cut in a double curve like the outline of a leaf 3p THE CURVES OF LIEE (Fig. 34b), not in a straight line as at Chateaudun (Fig. 347) and other places. 10. To recapitulate. On the hypothesis that a shell suggested the staircase, we must find an Italian who had studied shells and leaves, who was left-handed, who was Architect to the King, and who lived at or near Blois between 1516 and 1519. 11. Leonardo da Vinci studied the cur\-es of leaves and plants (Fig. 348), the spiral formations of water (Figs. 349, 350), dust (Fig. 351), horns (Fig. 352), and shells (Figs. 104, 105, 353). He came from north-western Italy. He was left-handed, and always drew left-hand spirals (Figs. 354, 355, 356). 12. He was architect to the King of France. 13. He designed square staircases (Figs. 357, 358). 14. He designed a spiral staircase in a tower (Fig. 359). 15. He lived and died, between 1516 and 1519, within a few miles of Blois, at Am^boise (Figs. 360, 361). 16. He is recorded to have done work (connected with the fountains) at Blois. 17. Other Italians are known to have worked in France. 18. The suggestion, by French writers, that Leonardo built Chambord is unfounded, but shows their readiness to accept the possibility of his architecture (Fig. 362) in France. 19. General reasons, deduced from Leonardo's manuscripts to show that, alone of architects living at that time, he could have used a shell as the suggestion for his design of the staircase. The illustrations will, of course, carry much more conviction than this bare summary of the facts. From 1519 onwards it is known that Jacques Sourdeau was Master of the Works on the wing of Francois I. at Blois, in which this Open Staircase is the most prominent feature. It is also known that the only previous record existing was preserved in the archives of the Baron du Joursan^'ault, and consists of a receipt, signed by Raymon Phelippeaux, master builder, of Blois, on July 5th, 1516, for 3,000 livres tournois to him paid over by Jacques Viart, official treasurer of the conntj', towards the expense of certain repairs being carried out by the orders of Frangois I. These two years, therefore (1516-1519), measure the interval during which it is most probable that the designs were made for a staircase of which neither the architect nor the exact date has ever been fixed, for from 1516 to 1519 no records exist. The facade on this side of the courtyard of the chateau is ver3^ simple, with its three rows of pilasters superimposed one above the other. THE OPEN STAIRCASE OF BLOIS 343 marking a distinct advance in that new movement which had already produced Chenonceaux and Langeais. It shows a restrained gravity, a fine instinct of proportion, which have produced exactly the right background for the crowning master- piece of the Open Staircase in its midst. At first that staircase seems to stand free, breaking up the ordered descent of perpen- dicular columns with its boldly projecting lines ; yet its summit is clasped by the broad cornice of the main waU, which gathers every A'arying angle into harmony with the main building. But I only draw attention to this point because it explains certain problems in the detail of the staircase itself, and renders more probable the hypothesis that, after the original architect had planned the mass of the building and the place of the stairs, the design of the detached staircase itself came from another hand, and many of its details of carved ornament were added at a still later date. Indeed, they seem to have taken so long in completion that many of the stones remain uncarved to this day, and have evidently not been touched since they were set in their places ready for the carver's chisel. Examples of this later work may be found, on the inside, in those somewhat vapid and meaningless panels of light-relief Renaissance scrollwork set between the colonnettes encircling the main central shaft. On the outside the most conspicuous additions are the canopied statues set on the columns above the first sloping balustrade. Jean Goujon was born in 1520, a year later than the interval suggested above for the design of this staircase, and the beginning of its actual building. But its completion (in such details) may weU have been postponed for five-and-twenty years ; and any one who knows the Fontaine des Innocents or the Diane Chasseresse will find it difficult to believe that these statues were not from Goujon's chisel, or, at any rate, from the hand of one who was strongly influenced by his individual style. Mr. Reginald Blomfield has shown that for the designs attri- buted to Lescot for the Louvre Jean Goujon should have the credit, and Martin (in his edition of Vitruvius already quoted) calls Goujon " architecte." He was, in fact, just that com- bination of architect and sculptor in France which the designer of the lost " Cavallo " evidently was in Italy ; and he died in Bologna about 1567, as far from his home as was the great artist who was buried at Ambaise so long before him. The geniu5 of Leonardo was of so universal a quality that I feel no real necessity for proving over again that in Italy he had 3^4 THE CURVES OF LIFE turned his attention, among many other studies, to those of archi- tn'ture. Though no building has come down to us which has yet been recognised and agreed to be by him, alone, the researches f)f J. P. Richter produce more than sufficient evidence of his skill. In 1490, at any rate, Leonardo was able to write to the Duke of Milan that ; " In time of peace I shall be of as much service to you as any one in whatever concerns the construction of buildings" ; about the same time the Vice-General of the Carmelites writes to Isabella d'Este, concerning Leonardo, that " his mathematical studies have so drawn his tastes away from painting that he will Fig. 339. Sketch for a church b\' Leonardo. scarcely hold a brvish," and Sabba da Castiglione says also that " when he should have wholly consecrated himself to painting, in which he would, no doubt, have become another Apelles, he entirely surrendered himself to the study of geometry, archi- tecture, and anatomy " ; and it is significant that between 1472 and 1499 we find many important buildings in Lombardy by unknown architects, which are so good that the tradition of collaboration between Leonardo and other architects may well be true. At Pavia Cathedral, and in the church of Santa Maria delle Grazie at Milan, this tradition was so strong that the corroboration of it lately found in Leonardo's manuscripts, preserved in Milan, was only to be expected. THE OPEN STAIRCASE OF BLOIS 345 From the manuscripts in the Institiit de France I reproduce two sketches for a church by Leonardo (Figs. 339, 340). These might certainly be attributed (apart from other evidence) to an admirer of Bramante ; and the idea of collaboration has so strongly influenced MM. Marcel-Reymond and Charles ]\Iarcel- Reymond {Gazette des Beaux Arts, June, 1913) that, as I shall show later, they use the similarity between the plan of Chambord and the plan of St. Peter's at Rome as an argument in favour of Leonardo having built Chambord. But I stand in no need of improbabilities to strengthen my position ; and for the present Fig. 340. Sketch for a church bv Leonardo. 1 am concerned chiefly with Leonardo's architectural \\-ork in Italy. Already the best minds of his day had tried to grasp the problems of a proportion in architecture which should reflect the ic laws of construction and growth exemplified throughout organi life in Nature. Leonardo took up that inc]uiry in his usual original and thorough manner, and the investigations embodied in my former chapters were in many cases suggested by materiah in his manuscripts. He has left sketches of columns with archivolts shaped like twisted cords, copied from interlacing branches. He has left drawings of flowers, such as eglantine, 34