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 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