The Curves of Life (Dover Books Explaining Science)

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, Nebulæ, etc." "Classification, Utility, and Antiquity of Spirals" Need of Theory 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 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 Retardation Natural Selection Adjustment to Environment Survival and Spiral Variation Right-hand and Life-hand Shells Ammonite and Nautilus External and Internal Spirals Supporting the Central Column Comparison with Insects and Plants Multiple Spirals CHAPTER IV FLAT SPIRALS IN SHELLS Nautilus and Logarithmic Spiral Equiangular Spiral a Manifestation of Energy Deviation from Cuve 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 Verticle and Horizontal Views of Shells and Plants 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 CHAPTER VI SPECIAL PHENOMENA IN CONNECTION WITH SPIRAL PHYLLOTAXIS The Sprial Theory 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 Different Systems CHAPTER VII RIGHT-HAND 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 Movement of Growing Ends (v.) Spiral Growth of Twining Plants (vi.) Spiral Effects after Death Nomenclature of Spirals Numerical Proportions of Right and Left Hand CHAPTER VIII RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH EFFECTS IN PLANTS (continued) DEAD TISSUES AND SPINNING SEEDS Spiral Twisting of Dead Tissues Coiling when Drying: Straightening when Wet Predominace of Right-hand Fibres Seed Spinning in Flight The Mechaanism of Winged Fruits CHAPTER IX RIGHT-HAND AND LEFT-HAND SPIRAL GROWTH EFFECTS IN PLANS (continued) SOME SPECIAL CASES Anomalous Variation producing Spirals "Spiral Staircase" Construction" Peculiarities of Spiral Spermatozoids Male Cells of Cycads and Chinese Maidenhair Tree Spirals and Locomotion Prevalance of Right-hand and Left-hand Spirals CHAPTER X RIGHT-HAND AND LEFT-HAND SPIRALS IN SHELLS Contrast of Trees with Shells Spiral Fossils in Nebraska Determination 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 Formation and the Prinicple of Life CHAPTER XI CLIMBING PLANTS 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 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 Classification 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's Rule Tame Animals showing Twists of their Wild Ancestors Development or Degeneration? The Problem stated CHAPTER XIII SPIRAL FORMATIONS IN THE HUMAN BODY Natural Objects do not consciously produce Spirals Deviation from Mechanical Accuracy Spiral Formations 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, Animalculæ" CHAPTER XIV RIGHT AND LEFT-HANDED MEN 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 CHAPTER XV ARTIFICIAL AND CONVENTIONAL SPIRALS Spiral Decoration in Prehistoric Times The Successive Races of Man Artistic Skill of Aurignacians Magdalenian Civilisation The Spiral as a Link between Aurignacians and Greeks The Mycenaean 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 Mediæval Gothic Violin Heads "Cylindrical Spirals: Torques, Armlets, "Collars" 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 Spire Efficiency and Beauty Practical Origin of Spiral Staircases Gradual Evolution Central Support The Hand Rail Defence against Attack Double Spiral Staircases CHAPTER XVII SPIRALS IN NATURE AND ART Shells and Spiral Staircases Practical Problems and Beauty of Design Efficiency and Beauty Leaning Companiles Intentionally Designed Charm of Irregularity The Parthenon Architecture and Life Quality of Variation in Greek Architecture Expression of Emotions Artistic Selection from Nature CHAPTER XVIII THE OPEN STAIRCASE OF BLOIS The Staircase designed by Leonardo da Vinci Voluta Vespertilo The King's Architect A Left-handed Man Work of Italians in France Leonardo's Manuscripts His Theories of Art CHAPTER XIX SOM "Dürer and the "Cavallo" Dürer's Mathematical Studies "Dante, Leonardo, Goethe" The Experimental Method "Beauty is "Fitness Expressed" The Value of Delicate Variations "Good Taste" Processes of Scientific Thought CHAPTER XX FINAL RESULTS The Logarithmic Spiral as an Abstract Conception of Perfect Growth Spiral Nebulæ Dr. Johnstone Stone's Spiral of the Elements Infinite Series and the Rhythmic Beat Phyllotaxis The Ratio of Pheidias The F Spiral Space Proportion Art and Anatomy The Theory of Exceptions "Value of a "Law" Complexities of the Higher Organism "A Flame to Curiosity" The Methods of Science APPENDIX I. Nature and Mathematics (illustrated) II. The F Progression. By William Schooling III. Infinite Series and the Theory of Grouping IV. Origins of a Symbol (illustrated) V. The Spiral in Pavement-toothed Sharks and Rays (illustrated). By R. Lydekker VI. The Spiral in Bivalve Shells (illustrated). By R. Lydekker VII. The Shell of Travancore VIII. The Growth of Shells (illustrated) IX. The F Progression in Art and Anatomy (illustrated)