None
Thus, the first class has 6.25% purely dominant in both characters; the second class, 12.5% purely dominant in one character and hybrid in the other, and so on. Recalling that hybrid zygotes produce somas with the dominant character, it follows that the progeny appear as follows: Ratios A. dom. + B. rec........... 18.75% 3 A. rec. + B. dom.......... 18.75% 3 A. dom. + 5. dom.......... 56.25% 9 A. rec. + B. rec........... 6.25% 1 This result again agrees with experiment. The resulting mixture of characters in tri-to poly hybrids may be likewise predicted, by extending the principles already laid down. MEASURE OF DISSYMMETRY IN ORGANISMS. A Dissymmetry-Index, 3, measuring the average degree of asymmetry in the right and left organs of bilateral organisms, has been proposed by Duncker (1903). First, a series of integral differences —3, —2, —1, 0, 1, 2, 3, 4, etc., between the right and left-side measurements of the organ in question is made, and the frequencies of each integral difference (reckoning to the nearest integer) is found. The average of the difference series is the difference of the averages of the right- and left-side measurements, and the standard deviation of the difference is given by in which the subscripts, refer to the bilateral series of which the asymmetry is to be found, and r is the coefficient of correlation between the two sides. Let d' represent any positive differences in the series, and d' any negative differences; and let /, /, //, etc., represent the frequencies of the negative difference, classes, and //', /', etc., the frequencies of the positive difference classes. Then the asymmetry-index CORRELATED VARIABILITY. 61 Example. Absolute difference between dextral (d) and sinistral (s) lateral edges (L) of carapace of right-handed fiddler-crabs — Gelasimus pugilator (Yerkes, 1901; Duncker, 1903) d=Ld-Ls: -10 Results. The literature references are to the Bibliography which follows this chapter, in which the titles are arranged by author and date. GENERAL. EXPOSITIONS, ADDRESSES, ETC.: Amann, '96; Ammon, '99; Camerano, '00, '01, '02; Davenport, '00, '00d, Olb; Duncker, '99b; Eigenmann, '96; Galton, '01; Gallardo, '00, '01, '01, '01; Ludwig, '00, '03; Redeke, '00; Volterre, '01. TEXT-BOOKS: Galton, '89; Bateson, '94; Duncker, '00; Pearson, '00; Vernon, '03. METHOD: Camerano, '00; Engberg, '03; Fechner, '97; Galton, '89, '02; Heincke, '97; Johannsen, '03; Pearson, '94, '95, '96, '97, '97b, '02m, '02n, '03e; Pearson and Lee, '00; Sheppard, '98, '98b, '03; Verschaffelt,' Wasteels, '99, '00; Yule, '97, '97b, '00, '00b, '03. VARIABILITY. General. Frequency polygon, its significance; its dependence on time, place, and conditions: Burkill, '95; Kellerman, '01; Tower, '02; Shull, '02; Yule, '02; Johannsen, '03. Proper value of ratio of first to second prizes: Galton, '02; Pearson, '02; Pearson, '02; Duncker, '00b; Davenport, '00e. Mutations: Bateson, '94; Howe, '98; deVries, '01-' 03; Weldon, '02°. Individual vs. specific variation: Brewster, '97, '99; Field, '98; Mayer, '02; Davenport '03. Variability independent of sexual reproduction: Warren, '99; Pearson and others, '01 c, pp. 359-362. Relative variability of the sexes: — in man, Pearson, '97; Brewster, '99; Pearl, '03; in crabs, Schuster, '03. Relative variability of primitive and modern races: — in man, primitive races less variable: Pearson, '96, p. 281; Pearson (and others), '01 c, p. 362. Man. Stature. — Seriation for adults of different races: Bavarians, Ammon, '99; United States, recruits, Baxter, '75, Pearson, '95, p. 385; various, Macdonell, '02; English middle upper classes, Galton, '89, Pearson, '96, p. 270; Germans, Pearson, '96, p. 281; French, Pearson, '96, p. 281; Cambridge University students, Pearson, Lot. Engl. upper middle class 1 683 69.215" ±. 066 2.592" ±.047 do. husbands. 200 69. 135" ±.126 2.628" ±. 089 3.66 Cambridge Univ. students 68. 863" ±.054 2.522" ±.048 cm. English fathers 1078 171.95 6.81 3.99 English sons... 1078 174.40 6.94 3.98 U. S. recruits 25878 170.94 6.56 3.84 N. S. Wales, criminals.... 2862 169.88 6.58 3.80 Frenchmen 284 166.80 6.47 3.88 English criminals 3000 166.46 6.45 3.88 French, Lyons 166. 26 ±.53 5.50 ±.37 Germans 390 156.93 6.68 4.02 in. Engl. upper middle class? 652 64.043 ±.061 2.325 ±.043 do. Wives. 200 63.869±.110 2. 303 ±.078 Cambridge Un. students? 63. 883 ±.130 2.361 ±.092 3.69 French, Lyons?.. 154.02 cm. ±.52 5 5.45 ±.37 Seriation at different ages: British infant at birth, Pearson, '99; school children, Bowditch, '91; St. Louis schoolgirls, Porter, '94, Pearson, '95, p. 386; Australian adult whites, Powys, '01. STATISTICAL METHODS. Lot. Average. New-born infant, British $. 20. 503 ±. 028 in. 1. 332 ±. 020 20.124 ±.025 1.117 ±.018 St. Louis schoolgirls 118.271 cm. 2.776 Australian whites: Age, Years 20-25 25-30 30-40 40-50 50-60 Average. 66.95 67.30 67.15 66.91 66.74 60 & over 66.26 62.50 62.76 62.44 62.96 62.22 61.31 2.475 2.562 2.587 2.618 2.633 2.365 2.432 2.383 2.555 2.591 2.300 $ 3.70 3.81 3.86 3.91 3.95 4.04 6.500 5.849 3.79 3.87 3.69 4.06 4.16 3.75 Weight. — Seriations at different ages, British: Infants, Pearson, '99; University students,  Univ. students, $ 152. 783 ±.35 16. 547 ±.25 10.83 Skull. — Cephalic index: Bavarians, Ranke, '83; 6800 20-year old Badeners, working class, Ammon, '99, p. 85; various races, Pearson, '96, p. 230, Macdonell, '02. Lot. n Bavarian peasants 100 Baden recruits 6748 Modern Parisians French peasants 53 Cambridge students 1000 Criminals (British) 100 Brahmans of Bengal 100 Whitechapel English 107 Maquada race Skull capacity: coefficients of variability. Fawcett and Lee, '02. Lot. $ Andamanese 5. 04 Ainos 6.89 Negroes 7.07 Low-caste Pun jabs 7.24 Parisian French 7. 36 Kanakas 7. 37 17th Century English 7. 68 A C 83.41 3.58 4.29 81 .15 3.63 4.48 79.82 3.79 4.74 79.79 3.84 4.81 78.33 2.90 3.70 76.86 3.65 4.75 75.77 3.37 4.44 74.73 3.31 4.43 72.94 2.98 3.95 Lot. $ 9 5.59 Naquadas.... 7 72 6.92 6.82 Germans . 7.74 8.19 6.90 Egyptian mummies., . 8.13 8.29 8.99 Polynesians . 8.20 5.55 7.10 Italians 8 34 8.99 6.68 Modern Egyptians. . 8.59 7.17 8.15 Etruscans .. 9.58 8.54 STATISTICAL BIOLOGICAL STUDY. 65 Various cranial dimensions, Lee and Pearson, '01. Other Organs. — Coefficient of variability of bones of skele- ton of French and Naquada (C. of limb-bones, 4.53-5.57), Warren, '97; appendicular skeleton, Pearson, '96; finger- bones, Lewenz and Whiteley, '02; seriation of position of spinal nerves, Bardeen and Elting, '01; various organs in diverse races, Brewster, '97, '99. Mammalia. Relative variability of specific and generic characters in various mammals the former being greater, Brewster, '97; seriation of number of Miillerian glands in Sus scrofa, n, 2000; A, 3.501 ±.025; a, 1.6SO±.018; C, 48.0, Davenport and Bui- lard, '96. Aves. Seriations of various proportions of N. A. birds, Allen, '71; characters of Lanius ("shrike") and its races, Strong, '01; Lot. n A a C Shrike, length L. wing $ 168 99.06mm. 2.74mm. 281 ' ? 112 97.98 2.64 2*69 tail length 4 141 101.57 3.48 343 ? 95 99 55 3.63 3.65 bill length, $ 164 12.01 0.71 589 " " ? 112 11.71 0.63 5^35 " depth, a 126 9.27 0.42 457 ? 85 8.95 0.41 4.61 melanism of crown, $ 144 83.57% 3.0% 358 ? 99 83.66 3.19 3.81 '" upper tail-coverts i 142 53.13 15.42 2902 1 ? 104 47.98 18.99 39^58 Curvature of cuimen 29.94° 2.74° 9. 15 Eggs, proportions: Passer domesticus, Bumpus, '97, Pear- son, '02e; various species, Latter, '02. Av. Length, Length, mm. Breadth, mm. Species. Bird, n A a C A a C Cuckoo in. 14 243 2° 40 1. 059 4. 72 16.54 .650 3 93 Blackbird 10 114 29. 44 1. 357 4 01 21 73 !787 3 62 Song-thrush .... Starling. 9 8-8.5 151 27 27 29 ,44 78 0 1. 999 097 3, 3 .04 08 20.69 21 76 .516 .423 2. '50 1 94 Yellowhammer.. Tree-pipit Meadow-pipet..  20 19. 21 21 20 55 01 72 .82 .32 .12 .22 0. 0. 1. 1 0 682 698 250 195 05 .810 ,857 3. 3 6. 5. 4 4 17 49 37 47 92 .02 24 16.04 15.09 14.56 15.34 14.73 15 43 .405 .449 .561 .525 .415 .477 2'53 2.97 3.84 3.38 2.81 3 09 Linnet... 5.5-6 65 17 .14 0, 598 3. .49 13.33 .358 2^69 66 STATISTICAL METHODS. Amphibia. Seriations of variations in position of pelvic girdle in Necturus, Bumpus, '97. Pisces. Geographical races: in Leuciscus, Eigenmann, '95; in adjacent lakes, Moenkhatis, '96; in schools of herring, Heincke, '97; in flounders, Bumpus, '98; in mackerel, Williamson, '00. See under Local Races. Various species: Pimephales fin-rays and scales of lateral line, Voris, '99; Zeus faber, an ancestral Pleuronectid, has its plates symmetrical in only 23.6% of the individuals, Byrne, '02; dimensions of 141 PetromyzorT, Lonnberg, '93. Tracheata. Lepidoptera. — Seriations of wing dimensions of Thyreus abotti. Field, '98; number of "eye-spots" on wing of Epinephele, Bachmetew, '03; number of spots on different species of the genus Papilio, Mayer, '02; breadth of wing, '985 Strenia clathrata C=4.57, Warren Aphidce. — Asexually produced offspring show an average variability of 60% that of the race, Warren, '02, p. 144; seriation of fertility, empirical mode =7 young, Warren, '02, p. 133; reduced variability of the earlier generations, because they include only such as can produce fertile offspring, Warren, '02. Dimension. Grandmothers. Children. Frontal breadth 2.28mm. 6.07% 2.96mm. 8.26 Length R. antenna 7.36 8.77 10.94 12.97 Lengthantenna Frontal breadth Myriapoda, — Lithobius: seriations of length of adults, C, for 4's= 10.97;?'s= 11.25; number of prosternal teeth; of antennal joints; of coxal pores in which C varies from 9.9 to 15.4, Williams, '03. Crustacea. Podophthalmata. — Seriations of 12 dimensions of right-handed and left-handed lt fiddler-crabs, Gelasimus pugilator, C varies from 7.0 to 11.1, Yerkes, '01; relative variability of male and female Eupagurus prideauxi from deep and from shallow water. Schuster, '03; forehead breadths of Carcinus moenas, Weldon, '93, Pearson, '94; various dimensions, Cranston, Weldon, '90; length of rostrum, Palaemon Serratus, Thompson, '94, Pearson, '94; number of rostral teeth of Palaisinonetes, Weldon, '92b, Pearson, '95, Duncker, '00. Lot. A, mm. n, mm. C, % Eupagurus, short edge of R. chela: $ deep water 9. 708 ±.085 2.76 28.5 $ shallow water 10. 272 ±.075 2.59 25.2 $ deep water 7. 400 ±.033 1.06 14.3 $ shallow water 7.485 ±.029 1.02 13.6 Eupagurus, long edge of R. chela: $ deep water 17. 97 ±.14 4.73 27.8 $ shallow water 18. 68+. 13 4.38 23.5 $ shallow water 14.14 ±.06 1.67 11.9 $ shallow water 13. 97 ±.05 1.82 13.0 Eupagurus, carapace length: $ deep water 8. 59 ±.05 1.67 19.4 $ shallow water 7. 54 ±.03 0.94 12.5 $ deep water 7. 12 ±.03 0.86 12.1 Palaemonetes vulgaris, dorsal spines 8.28 0.81 9.83 ventral spines. 2.98 0.45 15.03 Palaemonetes, varians, dorsal spines. 4.31 0.86 20.00 ventral spines. 1.70 0.48 28.26 Amphipoda. — Seriations of lengths of body, of second antennae, and of ratio of second antennae to body-length, Smallwood, '03. Annelida. Chicopoda. — Teeth on jaws of Nereis virens. Right: A = 10.055 ±.045, o= 1.339 ±.032, (7=13.3%; Left: A = 10.00 ±.044, <7=1.306 ±.031, (7=13.1%, Hefferan, '00. Brachiopoda. Seriation of widths breadth, width of sinus -f- depth, number of plications on ventral and dorsal valves in sinus and on fold, Cummings and Mauck, '02. Bryozoa. Number of spines on statoblasts of Pectinatella magnifica. A = 13.782 ±.031, o= 1.318 ±.022, C=9.57 ±.16, Davenport, '00. Moll u sea. Gastropoda. — Frequency polygons of ventricosity, weight, and index of Littorina littorea for 3 British and 10 American localities — greater variability in America. Index: <7=2.3%, B=2.6%, Cj = 3.0%, Bumpus, '98, Duncker, '98; critical, Bigelow and Rathbun, '03. Serrations of length, ratio of diameter to length, ratio of aperture to length, apical angle, number of whorls, color of aperture lip, and depth of suture between whorls in Nassau, Dimon, '02; seriations of shell-index and spinosity of lo in different parts of a river system, Adams, '00; variability of adult Clausilia laminata less than that of young, 15:13, ascribed to periodic selection, although average size not altered, Weldon, '01; variability of bands of Helix nemoralis in one spot of America, Howe, '98; in different localities near Strasburg, Hensgen, '02. Lamellibranchiata. — Seriation of number of ribs of Cardium, Baker, '03; Pecten; ray-frequency, Lutz, '00, Davenport, '00, '03 a '03b; change in proportions with age, acquisition of new symmetry about transverse axis; definition of form units from different localities, Davenport, '03, '03b. Lot. Number of Rays. Pecten irradians' A a C Cold Spring Har., L. I., R. valve 17. 353 ±.018 0.876 ±.013 5.05 ±.07 Cutchogue, L. I., R. valve 16.534 ±.034 0.852 ±.024 5.32 ±.36 Cold Spring Har., L. valve 16.790 ±.022 0.916 ±.015 5.46 ±.09 Cutchogue, L. valve 15.954 ±.105 0.881 ±.075 5.52 ±.49 Pecten opercularis: Eddystone, R. valve 17.478 ±.029 1.000 ±.020 5.72 ±.12 Irish Sea, R. valve 18.101 ±.029 1.074 ±.021 5.93 ±.11 Firth of Forth, R. valve 17.673 ±.027 1.117 ±.019 6.32 ±.11 Pecten gibbus Tampa, Fla., R. valve 20.512 ±.030 0.991 ±.021 4.83 ±.10 Pecten ventricosus: San Diego, Cal., R. valve 19.495 ±.087 0.885 ±.019 4.55 Eclimidermata. Seriation of ray-frequency in starfish, Crossaster papposus: A = 12.391, C=0.788, 0=6.36%, Ludwig, '93b. Coeleiterata. Scyphomedusce. — Seriation of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; empirical mode=8, genital sacs, M'=4, range, 2-10, Browne, '95, '01. Hydromedusce. — Seriation of number of radial canals, gonads, gastric lobes, and tentacles of Gonionemus, Hargitt, '01; radial canals and lips of Pseudoclytia pentata, Mayer, '01, Davenport, '02; radial canals, etc., of Eucope, Agassiz and Woodworth, '96. STATISTICAL BIOLOGICAL STUDY. Paramecium recently divided, Simpson, '02; seriation of diameter of Actinospherium and number of cysts and nuclei in body, Smith, '03; outer and inner diameters of shell of 502 Arcella vulgaris, Pearl and Dunbar, '03; various diatoms, Schroter and Vogler, '01. Lot. A a C Paramecium, length n 229.05 19. 15 8.36% breadth 68.13 9.16 13.44 index 29.91 4.03 Arcella, outer diameter 55.79±.17 5.73±.12 10.27±.22 inner diameter 15.91±.07 2.17±.05 13.66±.30 Plants. GENERAL. — Multimodal polygons especially frequent in plants, Ludwig, '97; critical, Lee, '02; Pearson, '02. RAY-FLOWERS IN COMPOSITE. — Seriation of ray-frequency of Coreopsis, de Vries, '94; of Senecio nemorensis, S. fuchsii, Cent urea cyanus, C. jacea, Solidago virga aurea, Achilla mille-folium, Ludwig, '96; ray-frequency in Chrysanthemum, Ludwig, '97C, Lucas, '98, Tower, '02, Pearson and Yule, '02; Helianthus, Wilcox, '02; Bellis perennis, Ludwig, '98; Arnica montana, Ludwig, '01; Aster, Shull, '02. Num. Ray-flowers. A o C Aster shortii 14.000±.068 1.526±.048 10.90 A. novaj-anglise 42.874±.302 6.308±.213 14.71 A. punicens 36.672±.107 4.480±.076 12.22 OTHER SERIATIONS OF FLORAL ORGANS: Ranunculus bulbosus, de Vries, '94. Pearson, '95; calyx, coralla, stamens, and pistils of Ficaria verna, Ludwig, '01; number of Ficaria pistils, early flowers, A = 17.448, a= 3.89; late flowers, A = 12.147, <r=3.88; number of stamens, early, A = 26.731, <y=3.298, MacLeod, '99, Weldon, '01; number of petals of Caltha palustris, de Vries, '94; number of calyx parts and petals of Trollius europseus and number of fruits per head of Ranunculus acris, Ludwig, '98b, '00b; number of seeds per capsule-compartment of Helleborus foetidus, Ludwig, '97. Cruciferae. — Number of flowers, Cardamine pratensis, empirical modes at 2, 5, 8, 11, 13, 16, 19, 22, not in Fibonacci series, Vogler, '03. Papaveraceae. — Number of floral organs in Papaver, Mac- Leod, '00; number of sepals and petals in the lesser Celandine, various species, Pearson and others, '03. Caryophyllacece. — Number of stamens in Stellaria media, varies with season and position on plant, Burkill, '95; number of anthers in 44,542 flowers of Stellaria media — a complex polygon due to effect of age and environment, Reinohl, '03. Sapidacece. — Number of compartments in fruit of Acerpseudoplatanus, de Vries, '94. Leguminosce. — Number of blossoms in clover plants, Type I: (7=2.788, de Vries, '94, Pearson, '95, p. 402; number of elevated flowers in blossoms of Trifolium repens perumbellatum, de Vries, '94; floral organs of Lotus uliginosus, L. corniculatus, Medicago saliva, M. falcata, Ludwig, '97; flowers per head of Lathyrus, Ludwig, '00b. Rosacew. — Number of stamens of Prunus spino, a and C. sanguinea, Ludwig, '01; sepals of 1000 Potentilla lormentilla and petals of 4097 Potentilla anserina, de Vriep, '94. Cornacece. — Number of flowers in head of Cornus mas and C. sanguinea, not in Fibonacci series, Vogler, '03. Capri foliacece. — Number of petals of 1167 Weigelea amabilis, de Vries, '94: number of flowers in inflorescence and number of petals on flower of Adoxa moschatellina, Whitehead, '02. Dipsacc B. — Number of flowers per head in Knautia arvensis, maximum at 64, Vogler, '03. Composite. — Number of male and female flowers in umbel of Homogyne, Ludwig, '01. Primulacece. — Number of flowers per umbel, Primula, multimodal, Ludwig, '97, '98b, '00; rays in Primula farinosa, Vogler, '01. STATISTICAL BIOLOGICAL STUDY. Scrophulariacece. — Number of parts in peloria of Lenaria spuria, Yost, '99; number of stamens, Digitalis, Gallardo, '00. Orchidacece. — Extremes in variability of number of spots on flower, Chodat, '01. LEAVES. — Seriation of numbers of paired leaflets of Pirus acuparia, Fraxinus excelsior, Senecio nemorencis, and Polemonium, Ludwig, '97, '98b. Length and breadth of leaves of Fagus silvatica and Carpinus betulus, Ludwig, '99. Leaf dimensions, Sanguinaria, Liriodendron, Ampelopsis, andilanthus (n, small), Harshberger, '01. Number of side ribs on leaves of Fagus silvatica, Carpinus betulus, and Quercus monticola, Ludwig, '99; on leaves of beech, Pearson, '00; leaves of mulberry, Fry, '02; dimensions of Typha leaves, Davenport and Blankinship, '98; pine needles, Ludwig, '01; from various branches of Pinus silvatica, Lee, '02. Lot length of pine needles A mm. a mm. a mm. C Pinus silv., lower branches. 22. 163 db. 048 4. 474 ±. 034 20. 19 " Branches. 26. 524 ±.055 5. 167 ±.039 19.48 " upper branches. 25. 949 ±.062 5. 858 ±.044 22.59 Fruit. — Number of ears in head of Agropyrum repens and Brachypodium, Ludwig, '01; of the grass Lolium, Ludwig, '00b; fruits per head of Ranunculus acris Ludwig, '00b; number of seeds per capsule-compartment, Helleborus, Ludwig, '97; fruit length, Oenothera Lamarckiana, and Helianthus, de Vries, '94; dimensions of beans in masses and in successive generations of same family, Johannsen, '03. BRYOPHYTA. — Seriations of length of capsule-stalk, Bryum cirratum, Amann, '96; parts in sexual organs of Marchantea and Lonicera, Ludwig, '00b. SOME TYPES OF BIOLOGICAL DISTRIBUTIONS. General. — Pearson, '95 'Old. a modified by selection, Reinohl, '03. Type I. Petals of 222 flowers of Ranunculus bulbosus, de Vries, '00b. Pearson, '95, p. 401. Number of glands of fore legs of swine, Davenport and Bullard, '96, Pearson, '96, p. 291: a=. 311 ±.016. STATISTICAL METHODS. Fertility (percentage of births with one year of marriage) of wives at different ages, Powys, '01. Rays in dorsal fin of Pleuronectes 5 , Duncker, '00. " " anal " " " ?, " " Type IV. Stature of St. Louis schoolgirls, Pearson, '95, p. 386. a=- 0.489. Number of teeth, Palsemonetes varians Plymouth, Pear- son, '95, p. 404. a= 0.134. Stature of Australian whites, Powys, '01. Rays in dorsal fin of Pleuronectes, ? , Duncker, '00. " " anal " " i( & " ll " " pectoral " " " $ " " Type V. Number of lips of medusa, P. pentata, Mayer, '01, Pearson, 'Old. a=.549. Normal. Stature, U. S. recruits, Baxter, 75, Pearson, 95, p. 385. Ray frequency, Pectens, Davenport, '00, '03b. Skewiiess. GENERAL. — Mathematical Analysis. — Pearson, '95, 'Old, '02f, '02^, '02ra. Biological Interpretation.— Davenport, ;01b, 'Olc. Quantitative Results. Numerous cranial characters, Naquada race, Fawcett, '02. Nearly always -K Num. lips of medusa, P. pentata (Mayer, '01; Pearson, '01(i) + .549 Num. Miillerian glands, legs of swine (Pearson arid Filon, '98). . . + .311 Num. dorsal teeth, Palsemonetes varians (Pearson, '95) + . 130 Num. rays, Pecten opercularis, Irish Sea (Davenport, '031')- ..... + .087 Eddystone (Davenport, '03h) . . . . + .080 " hooks on statoblasts, Pectinatella (Davenport, '00e) + .077 Weldon's crab measurements, "No. 4 " (Pearson, '95) + .077 Num. rays lower valve, Pecten irradians, L. I (Davenport, '00C)+ .023 " " " " P. opercularis, F. of Forth + .007 ' upper valve, P. irradians (Davenport, '00C) db .000 Height, British criminals (Macdonell, '02) — .023 Baxter's height of U. S. recruits (Pearson, '95) — .038 Porter's height of 2192 St. Louis schoolgirls (Pearson, '95) — .049 Head breadth, British criminals (Macdonell, '02) - .051 STATISTICAL BIOLOGICAL STUDY. Index of Littorina, Casco Bay (Bumpus. '98) +.13 Index of Littorina Newport (Bumpus. '98) +.068 Humbertshire (de Vries, '99) +.068 21-rayed Chrysanthemum (de Vries, '99) +.068 Selected 12- (and 13-) rayed Chrysanthemum (de Vries, '99) +.068 Rays  '011).. —.03 "Short-horned" short-horned...+.48 Complex Distributions. Bimodal Polygons. — Discontinuity in hairiness of Biscuit, Saunders, '97; of Lychnis, Bateson and Saunders, '02, Weldon, '02C. Length of cephalic horns of rhinoceros-beetle, and forceps length of male earwigs, Bateson, '94; explanation of di-morphism, Giard, '94. Multimodal Polygons. — Modes fall in Fibonacci series, Ludwig, '96, '96b, '96C, '97, '97C Modes of Chrysanthemum segetum at 13, 21, de Vries, '95. Opposed to Fibonacci series, complex polygon due to lack of homogeneity, Lucas, '93, Shull, '02, Pearson, '02, Reinohl, '03, Vogler,' CORRELATION. General and Method. — Galton, '88, '89, Pearson, '96, Yule, '97, '97b; spurious correlation, Pearson, '00C, Pearson and Lee, '00, Yule, '00, '00b, '02; index not constant in related races, Weldon, '92, Pearson, '96, '98b p. 175, '02n p. 2, Davenport, '03b. Man. General — Galton, '88; British criminals, various dimensions, r=.13 to.84, Macdonell, '02. Skull — Correlated with cranial capacity in living persons, Lee and Pearson, '01; breadth and length, Naquada, Bavarians, French, Pearson, '96, p. 280; N. A. Indians, Boas, '99; various dimensions, Aino and German, Lee and Pearson, '01; Naquadas, Fawcett and Lee, '02. With civilization, woman's correlation tends to gain on man's, Lee and Pearson, '01, Pearson, '02n. Lot. Breadth and Length: German, '49.05 Smith Sound Eskimo 47 Aino, '43.06 Aino, '37.07 German, '29.06 Modern Bavarian peasants 28.06 Naquada race 27 Sioux Indians. 24 Modern French (Parisians) 05.06 Shuswap Indians 04 Lot. Capacity and length 89 ±. 01. 66 ±. 05 11 breadth 56±.05.50±.07 height 54±.05.52±.07 Length and height 50±.05.35±.07 Breadth and height 35 ±. 06. 18 ±. 08 Cap. and ceph. index -.31 ±.07 -.25±.09 German: Capacity and breadth 67 d=.04.70±.03 11 length 51±.05.69±.04 Height 24±.06.45±.05 Cap. and ceph. index 20 ±. 06 -. 03 ±. 07 Breadth and height 07 ±. 06. 28 db. 06 Length and height 10±.07.31 ±.06 Skeletal. — Rollet, '89; stature correlated with length of long bones, reconstruction of stature of extinct races, Pearson, '98b; various coefficients of correlation, Pearson, '99, '00, p. 402; in hand-bones, Whiteley and Pearson, '99, Lewenz and Whiteley, '02. STATISTICAL BIOLOGICAL STUDY. Lot. Right and left femur 95 Metacarpals, ii and iii digits right 94 First joints, iv digit, R. and L. hands 93 First joints, ii and iii, right 90 Metacarpals, ii and v digits, right 89 Femur and humerus 84 to. 87 Femur and tibia 81 to. 89 First joints, ii and v, right 82 Stature and femur 80(?) to. 81(? ) Stature and humerus 77(?) to. 81(? ) Stature and humerus 77(?) to. 81(? ) Humerus and ulna 75 to. 86 Humerus and radius 74 to. 84 Radius and stature 67 ( « ) to 70( a ) Clavicle and humerust 44 to. 63 Forearm and stature 37 Clavicle and scapula 12 to. 16 Stature and cephalic index —.08 Various: Pearson, '99; intelligence not correlated with size or shape of head, Pearson, '02. Weight and length of new-born infant $ 644 ±.012 Weight and stature of Cambridge (Engl.) students, $.486 ±.016 Breadth of head (reduced to 12th yr.) and intelligence, youth 084 ±.024 Length of head (reduced to 12th yr.) and intelligence, youth 044 ±.024 Cephalic index and intelligence, youth 045 ±.024 Breadth of head and ability, adults 045 ±.032 Cephalic index and ability, University men 031 ±.035 Length of head, University men 031 ±.035 Vaccination and Recovery. — Pearson, '00C; Macdonell, '02, '03. r=.23 to.91. Assortative Mating. — Pearson, '96, '99b, '00, Pearson and Lee, '00. Stature of husbands and wives r—.093±.047 ditto, another determination r=.28 ±.02 Eye-color, husbands and wives r=.100 ±.038 Age at death of consorts r=.22 76 STATISTICAL METHODS. Lower Animals. ANTIMERTCALLY SYMMETRICAL ORGANS: Paired organs. — Number of Milillerian glands on R. and L. fore legs of swine, Davenport and Bullard, '96; R. and L. fins of fishes, Duncker, '97, '00; number of coxal pores on R. and L. legs of the centipede Lithobius, Williams, '03; R. and L. dimensions of Gelasimus, Yerkes, '01, Duncker, '03; number of teeth on R. and L. vials of Nereis, Hefferan, '00; breadth of R. and L. valves of Pecten, Davenport, '03b; skeletal spicules on R. and L. half of Echinus larva. Subject and Relative. Length R, and L. sides of carapace, Gelasimus 947 ±.003 M meropodite, first walking leg 918 ±.005 Breadth R. and L. valve of Pecten opercularis, Irish Sea...858±.006 Num. of teeth R. and L jaws of Nereis 820 ±.008 Fin-rays R. and L pectoral, Acerina 710 Coxal pores R. and L. 14th pair legs, Lithobius 69 ±.02 13th pair legs, Lithobius 69 ±.029 13th pair legs, Lithobius 58 ±.039 Other antimeric organs: Num of dorsal and ventral spines, Palsemonetes vulgaris (Duncker) OQb) 380±.019 Num. of lips and canals of the medusa, Pseudoclytia (Mayer, '01); Davenport, '02) 325 ±.019 SECONDARILY ANTIMERIC ORGANS. — (Median organs in animals that lie on one side.) Num. of dorsal and anal fin-rays in flounder, 651 Length antero-posterior and dorso-ventral diameters, Pecten. 970 ±.001 Unsymmetrical paired organs. — Pleuronectes, Duncker, '00; Gelasimus, the fiddler-crab, Yerkes, '01, Duncker, '03. Length of meropodite,  i.026 Num. rays R. and L. pectoral fin, flounder, Pleuronectes, $.594 of dorsal fin-rays at which lateral line ends, R. and L. Pleuronectes, $467 Num. rays R, and L. ventral fin, Pleuronectes, $243 METAMERICALLY REPEATED ORGANS. — Fin-rays of fishes, Duncker, '97; coxal pores centipede, Williams, '03; segments of shrimp Crangon, Weldon, '92.  pores of centipede, Williams, '03; length of carapace and of chela in Euphorbia, "hermit-crab," Schuster, '02; diameter of cell and body length, Daphnia, Warren, '03; cross correlation in teeth on jaws of Nereis, Hefferan, '00; various characters of the mud-snail, Nassa, Dimon, '02; circumference to number of spines, statoblast of Bryozoa, Davenport, '00; diameter of body of the Heliozoan Actinosphaerium Echorni and the number of cysts and of nuclei, Smith, '03; inner and outer diameters and color of the shell of Arcella, Pearl and Dunbar, '03. Organs. Carapace length and chela length, Eupagurus, $9389 ± 0036 Diameter of body of Actinospherian and num. of nuclei. 854 ± 017 Inner and outer diameter shell of Arcella 836 ±.007 Diam. of body of Actinosphasrium and num. of cysts. 769 ±.026 Wing length and tail length, Lanius 569 Diam. of cell and body length, Daphnia, hatching to 3d molt 551 Diam. of cell and body length, Daphnia, 3:1 to 4th molt 393 Diam. of cell and body length, Daphnia, after 4th molt. 248 Num. coxal pores, R. anal and L. 12th seg., Lithobius. 427 ±.046 Frontal breadth and antennal length (Warren, '02) 320 ±.032 Coxal pores, R. 14 The leg and body length, Lithobius...308 ±.059 Num. rays dorsal fin and end-point of L. lateral line, Pleuronectes, $-. -208 Outer diameter and color Arcella 012 Num. dorsal spines and L. pectoral rays, Pleuronectes..004 STATISTICAL METHODS. Organs. Body length and number antennal joints —.013±.067 Circumference of statoblast and number spines, Pectinatella. —.092 ±.006 Num. R. definite teeth and L. indefinite, Nereis —.524 ±.023 Carapp-ce length and chela index, Eupagurus —.522±.022 Num. of cysts and their diam., Actinosphserium —.669±.040 Plants. Between various parts of flowers, Ludwig, '01. Floral parts. — Stamens and pistils of Ficaria, MacLeod, '98, '99, Ludwig, '01, Weldon, '01, Lee, '02; rays and bracts and rays and disc florets of Aster, Shull, '02; various organs on Lesser Celandine, Pearson and others, '03. Organs. Num. rays and bracts. Aster 856 to.799 stamens and pistils Ficaria ranunculoides, early..507 ±.031 late 749 ±.015 rays and disc florets, Aster 574 to.353 petals and sepals Ficaria verna +.34 to —.18 stamens and pistils, Celandine 43 to.75 petals and petals, Celandine 38 to.22 petals and petals, Celandine 35 to.19 sepals, Celandine 25 to.03 stamens and sepals, Celandine 06 to.02 Other parts. — Size of leaves of same rosette of Bellis perennis, Verschaffelt, '99; various pairs of dimensions of fruits and leaves, Harshberger, '01; parts of Syndesmon, Kellerman, '01. HEREDITY. General. Treatises.— Galton, '89, Pearson, '00. Classification. — Galton, '89, pp. 7, 12, Pearson and Lee, '00, pp. 89, 91, 98. Law of ancestral heredity. — Galton, '97, Pearson, '98; estimate of heredity from a single ancestral generation, Pearson, '96, p. 306. Inequality in parental transmission. — Father prepotent in sons; mother in daughters, Pearson and Lee, '00, p. 115; heredity weakened by change of sex, Pearson and Lee, '00, p. 115, Lutz, '03. STATISTICAL BIOLOGICAL STUDY. Inheritance of Eye-color, Home, son; daughter; father; mother. (Average of rg/ and rdn) Parental grand-parental inheritance, average. No. of Changes of Sex. 0 .530 .370 .347 .459 .300 .222 .296 .145 Parental. Exceptional fathers produce exceptional sons at a rate three to six times that of non-exceptional fathers and exceptional pairs at ten times the rate of non-exceptional pairs, Pearson, '00C, pp. 38, 47. Cor. Reg. Longevity: r PXy Father and son (Beeton and Pearson, '99) .12 *' adult son (Beeton and Pearson, '01) .135 .10 " adult dau. "  (Pearson and Lee, '00) 55 to .44 Stature, English middle class: Father and son (Pearson, '96, p. 270) 396 .352 •• dau. " " " -360 .419 Mother anjd son " " " 302 .269 " dau. " " " 284 .275 Head index, N. Amer. Indian: Mother and son (Pearson, '00, p. 458) .370 " dau. " 300 Coat-color, thoroughbred horses: Sire, foal (Pearson. '00, p. 458) Dam, foal " 527 Fertility : Mother and daughter, British upper class Father and son, -051 ± -009 Mother and daughter, British peerage .210 Father and son, Mother and daughter, landed gentry Father and son -116 r P Frontal breadth, Hyalopterus (Warren, '02) Length R. antenna, Hyalopterus ' Ratio: R. antenna + frontal breadth (Warren, '02) . .. Ratio- Length protopodite-J- length body, Daphnia (Warren, '02) 466 -619 80 STATISTICAL METHODS. Graiidpareiital. Coat color, thoroughbred race-horses „ " Basset hounds Frontal breadth, Hyalopt3rus, Aohidse (Warren, '02) Length, R. antenna, Aphidae (Warren, '02) Ratio R. antenna -4- frontai breadth, Aphidse (Warren, '02 Ratio Length protopodite -r- length body, Daphnia (War- ren. '02) Gr'dson and gr'df.. homo male line (Pearson, '96) " " " female l>ne (Pearson, '96). Ortgr'dson and grtgr'df. homo $ line .339 .113 .321 .177 .231 .269 .269 .192 .295 Eye-color, home,  (Simpson, '02). 664 Horse, coat-color (Pearson, Lee, and Moore), average of 3 sets. 633 Man, forearm, English (Pearson, 'Olc) 542 Hound, coat-color, Bassett (Pearson and Lee, '00) 526 Man, eye-color, English (Pearson, 'Olc). Average of 2 sets 475 Pectinatella, statoblast hooks (Pearson, '01 c) 430 Man, stature Average of 3 sets. 403 Pectinatella, statoblast hooks (Pearson, '01 c) 317 Longevity, British peerage (Pearson, '01) 260 Quakers, "197 Average of 23 sets 476 Mean of 42 fraternal correlations (Pearson, '02k) 495 Some mental characteristics, inherited exactly like physical characters (Pearson, 'Ole): Conscientiousness.. 593 Popularity 504 Self-consciousness.. 592 Vivacity 470 Shyness 528 Intelligence 456 Average of 6 507 STATISTICAL BIOLOGICAL STUDY. 81 Theoretical coefficient of correlation between relatives. — Pearson, '00, Pearson and Lee, '00. Blended Alternative Inheritance, ance. Offspring and Parent 3000. 5000 grandparent 1500.250 great-grandparent 0.0 great-grandparent 0.0 Brothers 4000.4 to 1.0 Half-brothers 2000.2 to 0.5 Uncle and nephew 1500.250 First cousins 0.0 First cousins 0.0 Third cousins 0.0 Third cousins 0.0 Homologous, Oll; criticism, Bateson, 0.0; reply, Pearson, 0.0; rejoinder, Bateson, 0.0; correlation between differentiated homologous organs, Pearson, 0.0. Lot. Ceteract, Somersetshire Hartstongue, Somersetshire Shirley poppy Chelsea Character. Lobes on fronds Stigmatic bands Var. to rar. of Race. 78 79 79 Correlation. 631 .630 .615 .611 .599 .591 .570 .562 .549 .533 .524 .466 .416 .405 .400 .396 .374 .355 .273 .190 .183 .173 .457 English onion. Hampden Veins in tunics Holly Dorsetshire Soanish chestnut, mixed Beech, Buckinghamshire Papaver rhooas, Hampden . Prickles on leaves . Veins in leaves . Veins in leaves Stigmatic bands . 80 . 81 . 82 . 83 84 . 85 . 85 . 89 , 91 92 92 93 93 96 98 98 98 87.4 Mushroom Hampden Grill indices Papaver rhos, Quantocks Shirley poppy, Hampden Spanish chestnut, Buckinghamshire Broom, Yorkshire Ash. Monmouthshire Papaver rhos.  localities . Leaflets on leaves . Prickles on leaves . Leaf indices Nigella hispanica Slough . Seeded seed -capsules. .Seg. of seed-vessels.... . Members of whorls. Malva rotundi folia, Hampden Woodruff, Buckinghamshire Mean of 22 cases . . ,. Bands of capsules of Shirley poppies, msan of 8 crops (Pear- son, and others, '02) 498 Mean of 39 cases of homotyposis (Pearson, '02' ) 499 82 STATISTICAL METHODS. Mendelism. General Statement.— Mendel, '66, de Vries, '00, '00b, '00C, '03, Correns, '00, Davenport, '01, Bateson, '02, Castle, '03; critical, Weldon, '02, '03, Pearson, W. Plants.— Correns, '00, '00b, '01, '02-'02C, '03-'03C, de Vries, '02, '01-'03, Bateson and Saunders, '02 Animals. — Echinoids, Doncaster, '03; poultry, Bateson and Saunders, '02; mice, Darbishire, '02, '03, '03b, Castle, '03b, Bateson, '03b; rabbits, Woods, '03. Telegoiiy. No evidence of, in human statures, Pearson and Lee, '96. Fertility. Inherited in man and race-horses, Pearson, Lee, and Bram- ley-Moore, '99; greater fertility in poppy of seeds from cap- sules with a high number of stigmatic bands, Pearson, '02; fertility of medusae with symmetrical bands exceeds that of the unsymmetrical as 3 to 4, Mayer, '01. SELECTION. General. — Intensity of selection connotes a lessening tf correlation, Pearson, '02d, p. 23; mediocre individuals not the fittest to survive, Pearson, '02n, p. 50. Man. — 50% to 80% of human death-rate selective, Beeton and Pearson, '01. Other Animals. — Annihilation of the extremes in the. spar- row, Bumpus, '99; percentage death-rate of families of Aphids has inverse correlation with length of antenna of mother (r= -.201 ±.084), with frontal breadth of mother (r= —.184 ±.084), and with number in newly born brood (r= -.188 ±.084); in Carcinus moenas, Weldon, '95, '99; in Clausilia, Weldon, '01. Plants. — Transformation of skew frequency curve to a sym- metrical one by selection, de Vries, '94, '98; shifting of the mode by selection, de Vries, '99. Sexual. — Pearson, '96: A a Stature of husbands, inches 69.136.126 2.628.089 Males in general 69.215 ±. 066 2. 592 ±. 047 Wives 63.869 ±. 110 2.303 ±.078 Adult females in general 64. 043 ±.061 2. 325 ±.043 See also Correlation: Assortative mating (p. 75). DISSYMMETRY. The following values for A have been determined by Duncker, '00 and '03: STATISTICAL BIOLOGICAL STUDY. 83 Pleuronectes flesus L., 1060 R.-eyed and 60 L.-eyed: Right- Left-eyed, eyed. Num. of pectoral divided rays 997 —.983 Total num. pectoral rays 604 —.583 Num. of ventral divided rays 326 —.374 Total num. of ventral fin-rays 019 —.083 Gelasimus pugilator Latr. (fiddler-cnJt)). Right- Left-handed, handed. Lateral edge of car Appace 838.793 Length of meropodite, first ambulacral appendage..813.872 Length of meropodite, of carpopodite, and of pro-podite of chelse, all 1.00 1.00 Num. of rays on R. and L. pectoral fins, Acer ina —0.111 " glands on wrists of swine.0053 DIRECT EFFECT OF ENVIRONMENT. Animals. — Aphids reared in successive generations in increasingly unfavorable conditions have reduced dimensions, Warren, '02: Grandmother. Grandchildren. Frontal breadth, Aphid. A = 37. 56 33. 93 Length of R. antenna. A = 83. 91 76. 59 Ratio 5-*. A = 22.46 22.57 K. A. Depauperization of mud-snail, Nassa, in diluted sea-water, Dimon, ;02. Plants.— Conditions of life affect number of floral parts in poppy, de Vries, '99, MacLeod, '00, Pearson and others, '03; number of ray-flowers of Primula farin osa increases with moisture, Vogler, '01; empirical mode in number of anthers in Stellaria in poor environment is 3; in good environment 5, Reinohl, '03; leaf-blade smaller in light than in shade, MacLeod, '98. LOCAL RACES. General. — Davenport and Blankenship, '98, Davenport, '99. Pisces. — Leuciscus from different altitudes, Eigenmann, '95; herring from different sea-areas distinguishable, Heincke, '97, 98; mackerel from three Scotch localities differ, Williamson, '00; fin-rays of Pleuronectes from New England shore, Bumpus, '98: Wood H oil. Waquoit. Bristol, R.I. Dorsal fin-i ays. A = 66. 1 Invertebrata. — Mean and variability of deep-and-s shallow-water Eupagurus differ, Schuster, '03; proportions, variability, and correlation coefficients of Pecten opercularis differ at Eddystone, Irish Sea, and Firth of Forth, Davenport, '03b. Plants. — Lesser celandine, Pearson and others, '03. USEFUL TABLES. Probability Integral. — Area and ordinate of normal curve in terms of abscissa, Sheppard, '93, '03; abscissa of normal curve in terms of ordinate, Sheppard, '93; abscissa and ordinate in terms of difference of area, Sheppard, '03; abscissa of normal curve in terms of class index, Sheppard, '03; abscissa of normal curve in terms of class index, Sheppard, '03. Probability of fitted curve being the true one: Elderton, '02. Table of 4/ — I 2d%, for different values of I, Elder- ton, '02. Table of Iog 10 (+#)— x Iog 10 e for various values of a*, for use with curves of Type III. Tables for calculating probable error, Sheppard. Table of values of 1— r2 and \/l— r2 for all values of r from 0 to 1 proceeding by hundredths, Yule, '97. Probable errors of r for all values of n, Yule, '97. BIBLIOGRAPHY. Note. — An effort has been made to include all recent works containing usable quantitative data in botany and zoology; but the literature on the mathematical treatment of statistics and that affording data in anthropology are by no means completely listed. ABBREVIATIONS. The following names of journals often referred to have been much abbreviated: Amer. Nat. = American Naturalist. Ber. d. deutsch. bot. Ges. = Berichte der deutschen botanischen Gesellschaft. Biom. = Biometrika. Bot. Centralbl. = Botanisches Centralblatt. Phil. Trans. = Philosophical Transactions of the Royal Society of London. Proc. Roy. Soc. = Proceedings of the Royal Society of London. The references are scattered through fifty-seven periodicals. ADAMS, C. C. '00. Variation in lo. Proc. Amer. Assoc. for the Adv. of ScL, XLIX, 18 pp., 27 plates. 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A Statistical Study of the Variations in the Formation and Position of the Lumbo-sacral Plexus in Man. Anatom. Anz., XIX, 124-135, 209-238, Mar., Apr. BATESON, W., '89. On some Variations of Cardium edule apparently Correlated to the Conditions of Life. Phil. Trans., 1889 B., 297-330, PI. 26. BATESON, W., '94. Materials for the Study of Variation. London and New York, xvi-f-598 pp. BATESON, W., '01. Heredity, Differentiation, and Other Conceptions of Biology: a consideration of Professor Karl Pearson's paper "On the Principle of Homotyposis." Proc. Roy. Soc., LXIX, 193-205. BATESON, W., '01. Heredity, Differentiation, and Other Conceptions of Biology." and E. R. SAUNDERS, '02. Reports to the Evolution Committee — Report I. Royal Society. London: Harrison & Sons. 160 pp. BATESON, W., '02. Mendel's Principles of Heredity. Cambridge [Engl.]: Univ. Press. 212 pp. BATESON, W., '03. Variation and Differentiation in Parts and Brethren. Cambridge [Engl.]: J. and C. F. Clay. BATESON, W., '03. 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Biom., I, 90-108, Oct. BUMPUS, H. C., '97. The Variations and Mutations of the Introduced Sparrow. Biol. Lect. Woods Roll, 1896, 1-15. BUMPUS, H. C., '97. A Contribution to the Study of Varification. Jour. of Morphol., XII, 455-480. Pis. A-C. BUMPUS, H. C., '97. A Contribution to the Study of Varification. Jour. of Morphol., XII, 455-480. Pis. A-C. BUMPUS, H. C., '97. 98. The Variations and Mutations of the Introduced Littorina. Zool. Bull., I, 247-259. BUMPUS, H. C., '98b. On the Identification of Fish Artificially Hatched. Amer. Nat., XXXII, 407-412. 