December, 1916.
CONTENTS
| CHAP. | PAGE | |
|---|---|---|
| I. | INTRODUCTORY | [1] |
| II. | ON MAGNITUDE | [16] |
| III. | THE RATE OF GROWTH | [50] |
| IV. | ON THE INTERNAL FORM AND STRUCTURE OF THE CELL | [156] |
| V. | THE FORMS OF CELLS | [201] |
| VI. | A NOTE ON ADSORPTION | [277] |
| VII. | THE FORMS OF TISSUES, OR CELL-AGGREGATES | [293] |
| VIII. | THE SAME (continued) | [346] |
| IX. | ON CONCRETIONS, SPICULES, AND SPICULAR SKELETONS | [411] |
| X. | A PARENTHETIC NOTE ON GEODETICS | [488] |
| XI. | THE LOGARITHMIC SPIRAL | [493] |
| XII. | THE SPIRAL SHELLS OF THE FORAMINIFERA | [587] |
| XIII. | THE SHAPES OF HORNS, AND OF TEETH OR TUSKS: WITH A NOTE ON TORSION | [612] |
| XIV. | ON LEAF-ARRANGEMENT, OR PHYLLOTAXIS | [635] |
| XV. | ON THE SHAPES OF EGGS, AND OF CERTAIN OTHER HOLLOW STRUCTURES | [652] |
| XVI. | ON FORM AND MECHANICAL EFFICIENCY | [670] |
| XVII. | ON THE THEORY OF TRANSFORMATIONS, OR THE COMPARISON OF RELATED FORMS | [719] |
| EPILOGUE | [778] | |
| INDEX | [780] |
LIST OF ILLUSTRATIONS
| Fig. | Page | |
|---|---|---|
| [1]. | Nerve-cells, from larger and smaller animals (Minot, after Irving Hardesty) | 37 |
| [2]. | Relative magnitudes of some minute organisms (Zsigmondy) | 39 |
| [3]. | Curves of growth in man (Quetelet and Bowditch) | 61 |
| [4], 5. | Mean annual increments of stature and weight in man (do.) | 66, 69 |
| [6]. | The ratio, throughout life, of female weight to male (do.) | 71 |
| [7]–9. | Curves of growth of child, before and after birth (His and Rüssow) | 74–6 |
| [10]. | Curve of growth of bamboo (Ostwald, after Kraus) | 77 |
| [11]. | Coefficients of variability in human stature (Boas and Wissler) | 80 |
| [12]. | Growth in weight of mouse (Wolfgang Ostwald) | 83 |
| [13]. | Do. of silkworm (Luciani and Lo Monaco) | 84 |
| [14]. | Do. of tadpole (Ostwald, after Schaper) | 85 |
| [15]. | Larval eels, or Leptocephali, and young elver (Joh. Schmidt) | 86 |
| [16]. | Growth in length of Spirogyra (Hofmeister) | 87 |
| [17]. | Pulsations of growth in Crocus (Bose) | 88 |
| [18]. | Relative growth of brain, heart and body of man (Quetelet) | 90 |
| [19]. | Ratio of stature to span of arms (do.) | 94 |
| [20]. | Rates of growth near the tip of a bean-root (Sachs) | 96 |
| [21], 22. | The weight-length ratio of the plaice, and its annual periodic changes | 99, 100 |
| [23]. | Variability of tail-forceps in earwigs (Bateson) | 104 |
| [24]. | Variability of body-length in plaice | 105 |
| [25]. | Rate of growth in plants in relation to temperature (Sachs) | 109 |
| [26]. | Do. in maize, observed (Köppen), and calculated curves | 112 |
| [27]. | Do. in roots of peas (Miss I. Leitch) | 113 |
| [28], 29. | Rate of growth of frog in relation to temperature (Jenkinson, after O. Hertwig), and calculated curves of do. | 115, 6 |
| [30]. | Seasonal fluctuation of rate of growth in man (Daffner) | 119 |
| [31]. | Do. in the rate of growth of trees (C. E. Hall) | 120 |
| [32]. | Long-period fluctuation in the rate of growth of Arizona trees (A. E. Douglass) | 122 |
| [33], 34. | The varying form of brine-shrimps (Artemia), in relation to salinity (Abonyi) | 128, 9 |
| [35]–39. | Curves of regenerative growth in tadpoles’ tails (M. L. Durbin) | 140–145 |
| [40]. | Relation between amount of tail removed, amount restored, and time required for restoration (M. M. Ellis) | 148 |
| [41]. | Caryokinesis in trout’s egg (Prenant, after Prof. P. Bouin) | 169 |
| [42]–51. | Diagrams of mitotic cell-division (Prof. E. B. Wilson) | 171–5 |
| [52]. | Chromosomes in course of splitting and separation (Hatschek and Flemming) | 180 |
| [53]. | Annular chromosomes of mole-cricket (Wilson, after vom Rath) | 181 |
| [54]–56. | Diagrams illustrating a hypothetic field of force in caryokinesis (Prof. W. Peddie) | 182–4 |
| [57]. | An artificial figure of caryokinesis (Leduc) | 186 |
| [58]. | A segmented egg of Cerebratulus (Prenant, after Coe) | 189 |
| [59]. | Diagram of a field of force with two like poles | 189 |
| [60]. | A budding yeast-cell | 213 |
| [61]. | The roulettes of the conic sections | 218 |
| [62]. | Mode of development of an unduloid from a cylindrical tube | 220 |
| [63]–65. | Cylindrical, unduloid, nodoid and catenoid oil-globules (Plateau) | 222, 3 |
| [66]. | Diagram of the nodoid, or elastic curve | 224 |
| [67]. | Diagram of a cylinder capped by the corresponding portion of a sphere | 226 |
| [68]. | A liquid cylinder breaking up into spheres | 227 |
| [69]. | The same phenomenon in a protoplasmic cell of Trianea | 234 |
| [70]. | Some phases of a splash (A. M. Worthington) | 235 |
| [71]. | A breaking wave (do.) | 236 |
| [72]. | The calycles of some campanularian zoophytes | 237 |
| [73]. | A flagellate monad, Distigma proteus (Saville Kent) | 246 |
| [74]. | Noctiluca miliaris, diagrammatic | 246 |
| [75]. | Various species of Vorticella (Saville Kent and others) | 247 |
| [76]. | Various species of Salpingoeca (do.) | 248 |
| [77]. | Species of Tintinnus, Dinobryon and Codonella (do.) | 248 |
| [78]. | The tube or cup of Vaginicola | 248 |
| [79]. | The same of Folliculina | 249 |
| [80]. | Trachelophyllum (Wreszniowski) | 249 |
| [81]. | Trichodina pediculus | 252 |
| [82]. | Dinenymplia gracilis (Leidy) | 253 |
| [83]. | A “collar-cell” of Codosiga | 254 |
| [84]. | Various species of Lagena (Brady) | 256 |
| [85]. | Hanging drops, to illustrate the unduloid form (C. R. Darling) | 257 |
| [86]. | Diagram of a fluted cylinder | 260 |
| [87]. | Nodosaria scalaris (Brady) | 262 |
| [88]. | Fluted and pleated gonangia of certain Campanularians (Allman) | 262 |
| [89]. | Various species of Nodosaria, Sagrina and Rheophax (Brady) | 263 |
| [90]. | Trypanosoma tineae and Spirochaeta anodontae, to shew undulating membranes (Minchin and Fantham) | 266 |
| [91]. | Some species of Trichomastix and Trichomonas (Kofoid) | 267 |
| [92]. | Herpetomonas assuming the undulatory membrane of a Trypanosome (D. L. Mackinnon) | 268 |
| [93]. | Diagram of a human blood-corpuscle | 271 |
| [94]. | Sperm-cells of decapod crustacea, Inachus and Galathea (Koltzoff) | 273 |
| [95]. | The same, in saline solutions of varying density (do.) | 274 |
| [96]. | A sperm-cell of Dromia (do.) | 275 |
| [97]. | Chondriosomes in cells of kidney and pancreas (Barratt and Mathews) | 285 |
| [98]. | Adsorptive concentration of potassium salts in various plant-cells (Macallum) | 290 |
| [99]–101. | Equilibrium of surface-tension in a floating drop | 294, 5 |
| [102]. | Plateau’s “bourrelet” in plant-cells; diagrammatic (Berthold) | 298 |
| [103]. | Parenchyma of maize, shewing the same phenomenon | 298 |
| [104], 5. | Diagrams of the partition-wall between two soap-bubbles | 299, 300 |
| [106]. | Diagram of a partition in a conical cell | 300 |
| [107]. | Chains of cells in Nostoc, Anabaena and other low algae | 300 |
| [108]. | Diagram of a symmetrically divided soap-bubble | 301 |
| [109]. | Arrangement of partitions in dividing spores of Pellia (Campbell) | 302 |
| [110]. | Cells of Dictyota (Reinke) | 303 |
| [111], 2. | Terminal and other cells of Chara, and young antheridium of do. | 303 |
| [113]. | Diagram of cell-walls and partitions under various conditions of tension | 304 |
| [114], 5. | The partition-surfaces of three interconnected bubbles | 307, 8 |
| [116]. | Diagram of four interconnected cells or bubbles | 309 |
| [117]. | Various configurations of four cells in a frog’s egg (Rauber) | 311 |
| [118]. | Another diagram of two conjoined soap-bubbles | 313 |
| [119]. | A froth of bubbles, shewing its outer or “epidermal” layer | 314 |
| [120]. | A tetrahedron, or tetrahedral system, shewing its centre of symmetry | 317 |
| [121]. | A group of hexagonal cells (Bonanni) | 319 |
| [122], 3. | Artificial cellular tissues (Leduc) | 320 |
| [124]. | Epidermis of Girardia (Goebel) | 321 |
| [125]. | Soap-froth, and the same under compression (Rhumbler) | 322 |
| [126]. | Epidermal cells of Elodea canadensis (Berthold) | 322 |
| [127]. | Lithostrotion Martini (Nicholson) | 325 |
| [128]. | Cyathophyllum hexagonum (Nicholson, after Zittel) | 325 |
| [129]. | Arachnophyllum pentagonum (Nicholson) | 326 |
| [130]. | Heliolites (Woods) | 326 |
| [131]. | Confluent septa in Thamnastraea and Comoseris (Nicholson, after Zittel) | 327 |
| [132]. | Geometrical construction of a bee’s cell | 330 |
| [133]. | Stellate cells in the pith of a rush; diagrammatic | 335 |
| [134]. | Diagram of soap-films formed in a cubical wire skeleton (Plateau) | 337 |
| [135]. | Polar furrows in systems of four soap-bubbles (Robert) | 341 |
| [136]–8. | Diagrams illustrating the division of a cube by partitions of minimal area | 347–50 |
| [139]. | Cells from hairs of Sphacelaria (Berthold) | 351 |
| [140]. | The bisection of an isosceles triangle by minimal partitions | 353 |
| [141]. | The similar partitioning of spheroidal and conical cells | 353 |
| [142]. | S-shaped partitions from cells of algae and mosses (Reinke and others) | 355 |
| [143]. | Diagrammatic explanation of the S-shaped partitions | 356 |
| [144]. | Development of Erythrotrichia (Berthold) | 359 |
| [145]. | Periclinal, anticlinal and radial partitioning of a quadrant | 359 |
| [146]. | Construction for the minimal partitioning of a quadrant | 361 |
| [147]. | Another diagram of anticlinal and periclinal partitions | 362 |
| [148]. | Mode of segmentation of an artificially flattened frog’s egg (Roux) | 363 |
| [149]. | The bisection, by minimal partitions, of a prism of small angle | 364 |
| [150]. | Comparative diagram of the various modes of bisection of a prismatic sector | 365 |
| [151]. | Diagram of the further growth of the two halves of a quadrantal cell | 367 |
| [152]. | Diagram of the origin of an epidermic layer of cells | 370 |
| [153]. | A discoidal cell dividing into octants | 371 |
| [154]. | A germinating spore of Riccia (after Campbell), to shew the manner of space-partitioning in the cellular tissue | 372 |
| [155], 6. | Theoretical arrangement of successive partitions in a discoidal cell | 373 |
| [157]. | Sections of a moss-embryo (Kienitz-Gerloff) | 374 |
| [158]. | Various possible arrangements of partitions in groups of four to eight cells | 375 |
| [159]. | Three modes of partitioning in a system of six cells | 376 |
| [160], 1. | Segmenting eggs of Trochus (Robert), and of Cynthia (Conklin) | 377 |
| [162]. | Section of the apical cone of Salvinia (Pringsheim) | 377 |
| [163], 4. | Segmenting eggs of Pyrosoma (Korotneff), and of Echinus (Driesch) | 377 |
| [165]. | Segmenting egg of a cephalopod (Watase) | 378 |
| [166], 7. | Eggs segmenting under pressure: of Echinus and Nereis (Driesch), and of a frog (Roux) | 378 |
| [168]. | Various arrangements of a group of eight cells on the surface of a frog’s egg (Rauber) | 381 |
| [169]. | Diagram of the partitions and interfacial contacts in a system of eight cells | 383 |
| [170]. | Various modes of aggregation of eight oil-drops (Roux) | 384 |
| [171]. | Forms, or species, of Asterolampra (Greville) | 386 |
| [172]. | Diagrammatic section of an alcyonarian polype | 387 |
| [173], 4. | Sections of Heterophyllia (Nicholson and Martin Duncan) | 388, 9 |
| [175]. | Diagrammatic section of a ctenophore (Eucharis) | 391 |
| [176], 7. | Diagrams of the construction of a Pluteus larva | 392, 3 |
| [178], 9. | Diagrams of the development of stomata, in Sedum and in the hyacinth | 394 |
| [180]. | Various spores and pollen-grains (Berthold and others) | 396 |
| [181]. | Spore of Anthoceros (Campbell) | 397 |
| [182], 4, 9. | Diagrammatic modes of division of a cell under certain conditions of asymmetry | 400–5 |
| [183]. | Development of the embryo of Sphagnum (Campbell) | 402 |
| [185]. | The gemma of a moss (do.) | 403 |
| [186]. | The antheridium of Riccia (do.) | 404 |
| [187]. | Section of growing shoot of Selaginella, diagrammatic | 404 |
| [188]. | An embryo of Jungermannia (Kienitz-Gerloff) | 404 |
| [190]. | Development of the sporangium of Osmunda (Bower) | 406 |
| [191]. | Embryos of Phascum and of Adiantum (Kienitz-Gerloff) | 408 |
| [192]. | A section of Girardia (Goebel) | 408 |
| [193]. | An antheridium of Pteris (Strasburger) | 409 |
| [194]. | Spicules of Siphonogorgia and Anthogorgia (Studer) | 413 |
| [195]–7. | Calcospherites, deposited in white of egg (Harting) | 421, 2 |
| [198]. | Sections of the shell of Mya (Carpenter) | 422 |
| [199]. | Concretions, or spicules, artificially deposited in cartilage (Harting) | 423 |
| [200]. | Further illustrations of alcyonarian spicules: Eunicea (Studer) | 424 |
| [201]–3. | Associated, aggregated and composite calcospherites (Harting) | 425, 6 |
| [204]. | Harting’s “conostats” | 427 |
| [205]. | Liesegang’s rings (Leduc) | 428 |
| [206]. | Relay-crystals of common salt (Bowman) | 429 |
| [207]. | Wheel-like crystals in a colloid medium (do.) | 429 |
| [208]. | A concentrically striated calcospherite or spherocrystal (Harting) | 432 |
| [209]. | Otoliths of plaice, shewing “age-rings” (Wallace) | 432 |
| [210]. | Spicules, or calcospherites, of Astrosclera (Lister) | 436 |
| [211]. 2. | C- and S-shaped spicules of sponges and holothurians (Sollas and Théel) | 442 |
| [213]. | An amphidisc of Hyalonema | 442 |
| [214]–7. | Spicules of calcareous, tetractinellid and hexactinellid sponges, and of various holothurians (Haeckel, Schultze, Sollas and Théel) | 445–452 |
| [218]. | Diagram of a solid body confined by surface-energy to a liquid boundary-film | 460 |
| [219]. | Astrorhiza limicola and arenaria (Brady) | 464 |
| [220]. | A nuclear “reticulum plasmatique” (Carnoy) | 468 |
| [221]. | A spherical radiolarian, Aulonia hexagona (Haeckel) | 469 |
| [222]. | Actinomma arcadophorum (do.) | 469 |
| [223]. | Ethmosphaera conosiphonia (do.) | 470 |
| [224]. | Portions of shells of Cenosphaera favosa and vesparia (do.) | 470 |
| [225]. | Aulastrum triceros (do.) | 471 |
| [226]. | Part of the skeleton of Cannorhaphis (do.) | 472 |
| [227]. | A Nassellarian skeleton, Callimitra carolotae (do.) | 472 |
| [228], 9. | Portions of Dictyocha stapedia (do.) | 474 |
| [230]. | Diagram to illustrate the conformation of Callimitra | 476 |
| [231]. | Skeletons of various radiolarians (Haeckel) | 479 |
| [232]. | Diagrammatic structure of the skeleton of Dorataspis (do.) | 481 |
| [233], 4. | Phatnaspis cristata (Haeckel), and a diagram of the same | 483 |
| [235]. | Phractaspis prototypus (Haeckel) | 484 |
| [236]. | Annular and spiral thickenings in the walls of plant-cells | 488 |
| [237]. | A radiograph of the shell of Nautilus (Green and Gardiner) | 494 |
| [238]. | A spiral foraminifer, Globigerina (Brady) | 495 |
| [239]–42. | Diagrams to illustrate the development or growth of a logarithmic spiral | 407–501 |
| [243]. | A helicoid and a scorpioid cyme | 502 |
| [244]. | An Archimedean spiral | 503 |
| [245]–7. | More diagrams of the development of a logarithmic spiral | 505, 6 |
| [248]–57. | Various diagrams illustrating the mathematical theory of gnomons | 508–13 |
| [258]. | A shell of Haliotis, to shew how each increment of the shell constitutes a gnomon to the preexisting structure | 514 |
| [259], 60. | Spiral foraminifera, Pulvinulina and Cristellaria, to illustrate the same principle | 514, 5 |
| [261]. | Another diagram of a logarithmic spiral | 517 |
| [262]. | A diagram of the logarithmic spiral of Nautilus (Moseley) | 519 |
| [263], 4. | Opercula of Turbo and of Nerita (Moseley) | 521, 2 |
| [265]. | A section of the shell of Melo ethiopicus | 525 |
| [266]. | Shells of Harpa and Dolium, to illustrate generating curves and gene | 526 |
| [267]. | D’Orbigny’s Helicometer | 529 |
| [268]. | Section of a nautiloid shell, to shew the “protoconch” | 531 |
| [269]–73. | Diagrams of logarithmic spirals, of various angles | 532–5 |
| [274], 6, 7. | Constructions for determining the angle of a logarithmic spiral | 537, 8 |
| [275]. | An ammonite, to shew its corrugated surface pattern | 537 |
| [278]–80. | Illustrations of the “angle of retardation” | 542–4 |
| [281]. | A shell of Macroscaphites, to shew change of curvature | 550 |
| [282]. | Construction for determining the length of the coiled spire | 551 |
| [283]. | Section of the shell of Triton corrugatus (Woodward) | 554 |
| [284]. | Lamellaria perspicua and Sigaretus haliotoides (do.) | 555 |
| [285], 6. | Sections of the shells of Terebra maculata and Trochus niloticus | 559, 60 |
| [287]–9. | Diagrams illustrating the lines of growth on a lamellibranch shell | 563–5 |
| [290]. | Caprinella adversa (Woodward) | 567 |
| [291]. | Section of the shell of Productus (Woods) | 567 |
| [292]. | The “skeletal loop” of Terebratula (do.) | 568 |
| [293], 4. | The spiral arms of Spirifer and of Atrypa (do.) | 569 |
| [295]–7. | Shells of Cleodora, Hyalaea and other pteropods (Boas) | 570, 1 |
| [298], 9. | Coordinate diagrams of the shell-outline in certain pteropods | 572, 3 |
| [300]. | Development of the shell of Hyalaea tridentata (Tesch) | 573 |
| [301]. | Pteropod shells, of Cleodora and Hyalaea, viewed from the side (Boas) | 575 |
| [302], 3. | Diagrams of septa in a conical shell | 579 |
| [304]. | A section of Nautilus, shewing the logarithmic spirals of the septa to which the shell-spiral is the evolute | 581 |
| [305]. | Cast of the interior of the shell of Nautilus, to shew the contours of the septa at their junction with the shell-wall | 582 |
| [306]. | Ammonites Sowerbyi, to shew septal outlines (Zittel, after Steinmann and Döderlein) | 584 |
| [307]. | Suture-line of Pinacoceras (Zittel, after Hauer) | 584 |
| [308]. | Shells of Hastigerina, to shew the “mouth” (Brady) | 588 |
| [309]. | Nummulina antiquior (V. von Möller) | 591 |
| [310]. | Cornuspira foliacea and Operculina complanata (Brady) | 594 |
| [311]. | Miliolina pulchella and linnaeana (Brady) | 596 |
| [312], 3. | Cyclammina cancellata (do.), and diagrammatic figure of the same | 596, 7 |
| [314]. | Orbulina universa (Brady) | 598 |
| [315]. | Cristellaria reniformis (do.) | 600 |
| [316]. | Discorbina bertheloti (do.) | 603 |
| [317]. | Textularia trochus and concava (do.) | 604 |
| [318]. | Diagrammatic figure of a ram’s horns (Sir V. Brooke) | 615 |
| [319]. | Head of an Arabian wild goat (Sclater) | 616 |
| [320]. | Head of Ovis Ammon, shewing St Venant’s curves | 621 |
| [321]. | St Venant’s diagram of a triangular prism under torsion (Thomson and Tait) | 623 |
| [322]. | Diagram of the same phenomenon in a ram’s horn | 623 |
| [323]. | Antlers of a Swedish elk (Lönnberg) | 629 |
| [324]. | Head and antlers of Cervus duvauceli (Lydekker) | 630 |
| [325], 6. | Diagrams of spiral phyllotaxis (P. G. Tait) | 644, 5 |
| [327]. | Further diagrams of phyllotaxis, to shew how various spiral appearances may arise out of one and the same angular leaf-divergence | 648 |
| [328]. | Diagrammatic outlines of various sea-urchins | 664 |
| [329], 30. | Diagrams of the angle of branching in blood-vessels (Hess) | 667, 8 |
| [331], 2. | Diagrams illustrating the flexure of a beam | 674, 8 |
| [333]. | An example of the mode of arrangement of bast-fibres in a plant-stem (Schwendener) | 680 |
| [334]. | Section of the head of a femur, to shew its trabecular structure (Schäfer, after Robinson) | 681 |
| [335]. | Comparative diagrams of a crane-head and the head of a femur (Culmann and H. Meyer) | 682 |
| [336]. | Diagram of stress-lines in the human foot (Sir D. MacAlister, after H. Meyer) | 684 |
| [337]. | Trabecular structure of the os calcis (do.) | 685 |
| [338]. | Diagram of shearing-stress in a loaded pillar | 686 |
| [339]. | Diagrams of tied arch, and bowstring girder (Fidler) | 693 |
| [340], 1. | Diagrams of a bridge: shewing proposed span, the corresponding stress-diagram and reciprocal plan of construction (do.) | 696 |
| [342]. | A loaded bracket and its reciprocal construction-diagram (Culmann) | 697 |
| [343], 4. | A cantilever bridge, with its reciprocal diagrams (Fidler) | 698 |
| [345]. | A two-armed cantilever of the Forth Bridge (do.) | 700 |
| [346]. | A two-armed cantilever with load distributed over two pier-heads, as in the quadrupedal skeleton | 700 |
| [347]–9. | Stress-diagrams. or diagrams of bending moments, in the backbones of the horse, of a Dinosaur, and of Titanotherium | 701–4 |
| [350]. | The skeleton of Stegosaurus | 707 |
| [351]. | Bending-moments in a beam with fixed ends, to illustrate the mechanics of chevron-bones | 709 |
| [352], 3. | Coordinate diagrams of a circle, and its deformation into an ellipse | 729 |
| [354]. | Comparison, by means of Cartesian coordinates, of the cannon-bones of various ruminant animals | 729 |
| [355], 6. | Logarithmic coordinates, and the circle of Fig. 352 inscribed therein | 729, 31 |
| [357], 8. | Diagrams of oblique and radial coordinates | 731 |
| [359]. | Lanceolate, ovate and cordate leaves, compared by the help of radial coordinates | 732 |
| [360]. | A leaf of Begonia daedalea | 733 |
| [361]. | A network of logarithmic spiral coordinates | 735 |
| [362], 3. | Feet of ox, sheep and giraffe, compared by means of Cartesian coordinates | 738, 40 |
| [364], 6. | “Proportional diagrams” of human physiognomy (Albert Dürer) | 740, 2 |
| [365]. | Median and lateral toes of a tapir, compared by means of rectangular and oblique coordinates | 741 |
| [367], 8. | A comparison of the copepods Oithona and Sapphirina | 742 |
| [369]. | The carapaces of certain crabs, Geryon, Corystes and others, compared by means of rectilinear and curvilinear coordinates | 744 |
| [370]. | A comparison of certain amphipods, Harpinia, Stegocephalus and Hyperia | 746 |
| [371]. | The calycles of certain campanularian zoophytes, inscribed in corresponding Cartesian networks | 747 |
| [372]. | The calycles of certain species of Aglaophenia, similarly compared by means of curvilinear coordinates | 748 |
| [373], 4. | The fishes Argyropelecus and Sternoptyx, compared by means of rectangular and oblique coordinate systems | 748 |
| [375], 6. | Scarus and Pomacanthus, similarly compared by means of rectangular and coaxial systems | 749 |
| [377]–80. | A comparison of the fishes Polyprion, Pseudopriacanthus, Scorpaena and Antigonia | 750 |
| [381], 2. | A similar comparison of Diodon and Orthagoriscus | 751 |
| [383]. | The same of various crocodiles: C. porosus, C. americanus and Notosuchus terrestris | 753 |
| [384]. | The pelvic girdles of Stegosaurus and Camptosaurus | 754 |
| [385], 6. | The shoulder-girdles of Cryptocleidus and of Ichthyosaurus | 755 |
| [387]. | The skulls of Dimorphodon and of Pteranodon | 756 |
| [388]–92. | The pelves of Archaeopteryx and of Apatornis compared, and a method illustrated whereby intermediate configurations may be found by interpolation (G. Heilmann) | 757–9 |
| [393]. | The same pelves, together with three of the intermediate or interpolated forms | 760 |
| [394], 5. | Comparison of the skulls of two extinct rhinoceroses, Hyrachyus and Aceratherium (Osborn) | 761 |
| [396]. | Occipital views of various extinct rhinoceroses (do.) | 762 |
| [397]–400. | Comparison with each other, and with the skull of Hyrachyus, of the skulls of Titanotherium, tapir, horse and rabbit | 763, 4 |
| [401], 2. | Coordinate diagrams of the skulls of Eohippus and of Equus, with various actual and hypothetical intermediate types (Heilmann) | 765–7 |
| [403]. | A comparison of various human scapulae (Dwight) | 769 |
| [404]. | A human skull, inscribed in Cartesian coordinates | 770 |
| [405]. | The same coordinates on a new projection, adapted to the skull of the chimpanzee | 770 |
| [406]. | Chimpanzee’s skull, inscribed in the network of Fig. 405 | 771 |
| [407], 8. | Corresponding diagrams of a baboon’s skull, and of a dog’s | 771, 3 |
“Cum formarum naturalium et corporalium esse non consistat nisi in unione ad materiam, ejusdem agentis esse videtur eas producere cujus est materiam transmutare. Secundo, quia cum hujusmodi formae non excedant virtutem et ordinem et facultatem principiorum agentium in natura, nulla videtur necessitas eorum originem in principia reducere altiora.” Aquinas, De Pot. Q. iii, a, 11. (Quoted in Brit. Assoc. Address, Section D, 1911.)
“...I would that all other natural phenomena might similarly be deduced from mechanical principles. For many things move me to suspect that everything depends upon certain forces, in virtue of which the particles of bodies, through forces not yet understood, are either impelled together so as to cohere in regular figures, or are repelled and recede from one another.” Newton, in Preface to the Principia. (Quoted by Mr W. Spottiswoode, Brit. Assoc. Presidential Address, 1878.)
“When Science shall have subjected all natural phenomena to the laws of Theoretical Mechanics, when she shall be able to predict the result of every combination as unerringly as Hamilton predicted conical refraction, or Adams revealed to us the existence of Neptune,—that we cannot say. That day may never come, and it is certainly far in the dim future. We may not anticipate it, we may not even call it possible. But none the less are we bound to look to that day, and to labour for it as the crowning triumph of Science:—when Theoretical Mechanics shall be recognised as the key to every physical enigma, the chart for every traveller through the dark Infinite of Nature.” J. H. Jellett, in Brit. Assoc. Address, Section A, 1874.
CHAPTER I INTRODUCTORY
Of the chemistry of his day and generation, Kant declared that it was “a science, but not science,”—“eine Wissenschaft, aber nicht Wissenschaft”; for that the criterion of physical science lay in its relation to mathematics. And a hundred years later Du Bois Reymond, profound student of the many sciences on which physiology is based, recalled and reiterated the old saying, declaring that chemistry would only reach the rank of science, in the high and strict sense, when it should be found possible to explain chemical reactions in the light of their causal relation to the velocities, tensions and conditions of equilibrium of the component molecules; that, in short, the chemistry of the future must deal with molecular mechanics, by the methods and in the strict language of mathematics, as the astronomy of Newton and Laplace dealt with the stars in their courses. We know how great a step has been made towards this distant and once hopeless goal, as Kant defined it, since van’t Hoff laid the firm foundations of a mathematical chemistry, and earned his proud epitaph, Physicam chemiae adiunxit[1].