None
Consequently, in the long run, we shall have of all the zygotes, d + 5%d, d + 25%r, r, or 50% of the zygotes hybrid and 50% of pure blood, and of the latter half exclusively maternal and half paternal. But since the soma developed from the hybrid germ-cell has the dominant character, we shall have 75% of the cases with the dominant character; 25% " recessive and this agrees with various empirical results, of which the following from Correns is instructive. A cross was obtained between a variety of pea with a green (g) germ and one having a yellow (y) germ. Yellow is dominating. COERELATED VARIABILITY. Gen. 1. 31 y (hybrid) peas produced 12 plants; these bore: Gen. 2. 775 y (hybrid + y) peas (=75-8%) 24 plants were produced: 7 g (pure-blooded) peas (=24.2 20 plants bore: 670 green peas. 7 (33%) pure-blooded hybrids, blood, because they are because they bore: bore: Gen. 3. 292 y peas 462 y peas 149 g (hybrid + y) (pure-blooded) peas (=76.4%) peas (=23.6%) It is clear that if this process of crossing of the hybrids continues, the proportion of hybrids to the whole population will diminish; for the share of pure-blooded forms breeds true; while the originally equal share of hybrids is repeatedly halved. If the hybrid is crossed with one of the parents instead of with another hybrid, we will get (1) (d+r}d=d,d+d,r, and (2) (d+r}=d, r+r,r). In (1) all of the progeny will appear of the In (2) one-half will appear of that type. This again agrees with experiment. Second Case. The two parents differ in respect to two characters — case of dihybrids. Imagine a lot of ripe germ cells with the antagonistic qualities of any pair separated according to the second principle stated at the outset. A indicates the one pair of qualities and B the other; then we shall have nine classes of zygotes, the proportion of each of which is as follows: A. 25%d,d B. Q.25%d,d; 12.5%d,r; 6.25%r, r. A. 50%d,r B. 12.5%d,d; 25%d,r; 12.5%r, r. A. 25%r, r B. G25%d,d; 12.5%d,r; 6.25%r, r. 60 STATISTICAL METHODS. 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,  rec. + B. dom 18.75% 3 A. rec. + B. 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 DISSYMETRY 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 & represent any positive differences in the series, and 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. 3 = 310X1 + 23X2 + 3X3 = 365,.£(/') = 336. 1, -?(/") = 1. n=400. M_336X365-lXl_ 122639 A 400X366 01, 'Olb; 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, '00, 'Old, '02, W, '02, '02, '03, '02, '03, '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; Decker, '00. STATISTICAL BIOLOGICAL STUDY. 63 Coefficient of variability; significance: Pearson, '96; Brewster, '97; Duncker, '00. Mutations: Bateson, 94; Howe, '98; deVries, '01-'03; Weldon, '02. Individual vs. specific variation: Brewster, '97, '99; Field, '98; Mayer, '02; Davenport '03b. Variability independent of sexual reproduction: Warren, '99, '02; Pearson and others, '01 c, pp. 359-362. Relative variability of the sexes: — in man, Pearson, '97C; 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; Cambridge University students, Pearson, '99. Lot. Engl. upper middle class $ do. husbands. Cambridge Univ. students English fathers 683 200 1078 1078 A 69.215" ±.066 69. 135" ±.126 68. 863" ±.054 cm. 171.95 174 40 a !.592" ±.047 5. 628" ±.089 2 522" ±.048 cm. 6.81 6.94 3.99 3.98 U. S. recruits N. S. Wales, criminals 25878 2862 284 170.94 169.88 166.80 6.56 6.58 6.47 3.84 3.80 3.88 English criminals 3000 166.46 166.26 6.45 5.50 3.37 3.88 390 156.93 6.68 4.01 English upper middle class? do. wives. Cambridge Un. students? 652 200 in. 64. 043 ±.061 63.869 ±.110 63.883 ±.130 154.02 cm. ±.52 in. 2.325 ±.043 2.303 ±.078 2.361 ±.092 5.45 ±.37 Serration at different ages: British infant at birth, Pearson, '99; school children, Bowditch, '91; St. Louis schoolgirls, Porter, '94, Pearson, '95, p. 386; Australian adult  20.124±.025 St. Louis schoolgirls 118.271 cm. Australian whites: a C 1.332±.020 6.500 1.117±.018 5.849 2.776 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 2.682 2.365 2.432 2.303 2.555 2.530 2.530 2.300 3.70 3.81 3.86 3.91 3.95 4.04 3.79 3.87 3.69 4.06 4.16 3.75 Weight. — Seriations at different ages, British: Infants, Pearson, '99; University students, Pearson, '99; 5552 Englishmen, Sheppard, '98. Lot. Average. a C New-born infants, $ 7.301±.0241b. 1.144±.017 15.66% ? 7.073±.021 1.006±.015 Cambridge 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. 280, Macdonell, '02. Lot. Bavarian peasants 100 83.41 3.58 4.29 Baden recruits 6748 81.15 3.63 4.48 Modern Parisians 79.82 3.79 4.74 French peasants 55 79.79 3.84 4.81 Cambridge students 1000 78.33 2.90 3.70 Criminals (British) 100 76.86 3.65 4.75 Brahmans of Bengal 100 75.77 3.37 4.44 Whitechapel English. 107 74.73 3.31 4.43 Maquadarace 72.94 2.98 3.95 Skull capacity: coefficients of variability. Fawcett and Lee, '02. Lot. $ Andamanese 5.04 5.59 Amos 6.89 6.82 Negroes 7.07 6.90 Low-caste Punjabs 7.24 8.99 Parisian French 7.36 7.10 Kanakas 7.37 6.68 17th Century English. 7.68 8.15 Lot. $ Naquadas 7.72 6.92 Germans 7.74 8.19 Egyptian mummies 8.13 8.29 Polynesians 8.20 5.55 Italians 8.34 8.99 Modern Egyptians 8.59 7.17 Etruscans 9.58 8.54 STATISTICAL BIOLOGICAL STUDY. 65 Various cranial dimensions, Lee and Pearson, '01. Other Organs. — Coefficient of variability of bones of skeleton of French and Naquada (C. of limb-Taones, 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 Müllerian glands in Sus scrofa, n, 2000; A, 3. 501 ±.025; a, 1.6SO ±.018; C, 48.0, Davenport and Bui-lard, '96. Aves. Serrations of various proportions of N. A. birds, Allen, '71; characters of Lanius ("shrike") and its races, Strong, '01; Cui 112 141 95 164 112 126 85 144 99 142 104 ' tail length $ bill length, $ depth, $ melanism of crown, $ upper tail-coverts $ vature of culmen.. A a C 99.06mm. 2.74mm. 2.81 97.98 2.64 2.69 101.57 3.48 3.43 99 55 3.63 3.65 12.01 0.71 5.89 11.71 0.63 5.35 9.27 0.42 4.57 8.95 0.41 4.61 83.57% 3.0% 3.58 83.66 3.19 3.81 53.13 15.42 29.02 47.98 18.99 39 58 29.94° 2.74° 9.15 Eggs, proportions: Passer domesticus, Bumpus, '97, Pearson, '02; various species, Latter, '02. AT. Length, Length, mm. Breadth, mm. Species. Bird, A C A C in. Cuckoo 14 243 22.40 1 .059 4.72 16.54 .650 3.93 Blackbird.... 10 114 29.44 1 .357 4.61 21.73 .787 3.62 Song-thrush.. 9 151 27.44 0 .999 3.64 20.69 .516 2.50 Starling 8-8.5 27 29.78 1 .097 3.68 21.76 .423 1.94 Yellowhammer 7 32 21.55 0 .682 3.17 16.04 .405 2 53 Tree-pipit.... . 6.5 27 20.01 0 .698 3.49 15.09 .449 2 97 Meadow-pipet. . 6 74 19.72 1 .250 6.37 14.56 . Hotfte-sparrow (English) 6687 21.82 1 1.95 5.47 15.51 3.38 House-sparrow 6687 21.32 1 1.05 4.92 15.34 Hedge-sparrow 6687 26 20.12 0 857 4 24 15 43 4477 3.09 Linnet 5.5-6 65 17.14 0 5.598 3.49 13.33 '358 2.60 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, Moenkhaus, '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 Petromyzon, Loiinberg, '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, 98 Strenia clathrata C=4.57, Warren, '02. Aphidce. — Asexually produced offspring show an average variability of 60% that of the race, Warren, '02, p. 144 Serration 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. Children. a C 2. 96 mm. 8. 26 10.94 12.97 1.84 7.82 Myriapoda, — Lithobius: seriations of length of adults, C, for $'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 "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 Dimension. Frontal breadth Grandm a 2. 28 mm 7.36 others. Ratio-Length antenna Ratio-Frontal breadth 1.23% STATISTICAL BIOLOGICAL STUDY. 67 Mean, Weldon, '93, Pearson, '94; various dimensions, Cranston, Weldon, '90; length of rostrum, Palcemon serratus, Thompson, '94, Pearson, '94; number of rostral teeth of Palcemonetes, Weldon, '92b, Pearson, '95, Duncker, '00. Lot. A, 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 13. 97 Eupagurus, carapace length: $ deep water 8.59½.05 1.67 19.4 $ shallow water 7.54½.03 0.94 12.5 $ deep water 7.12½.03 0.86 12.1 Palsemonetes vulgaris, dorsal spines 8.28 0.81 9.83 ventral spines. 2.98 0.45 15.03 Palsemonetes, 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. Chcetopoda. — Teeth on jaws of Nereis virens. Right: A=10.055½.045, a =1.339½.032, C=13.3%; Left: A=10.00½.044, C=1.306½.031, C=13.1½, Hefferan, '00. Brachiopoda. Sedation of width - breadth, width of sinus - 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 = 13.832.031, <r= 1.318 ±.022, C= 9.57±.16, Davenport, '00. Mollusca. Gastropoda. — Frequency polygons of ventricosity, weight, and index of Littorina littorea for 3 British and 10 American localities — greater variability in America. Index: <r.e=2.3%, M=2.7%, (7.5%, (7.5%, Bumpus, '98, Duncker, '98; critical, Bigelow and Rathbun, '03; variations 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, '93; 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, '03b; change in proportions with age, acquisition of new symmetry. About transverse axis; definition of form units from different localities, Davenport, '03, '03b. Lot. Pecten irradians Cold Spring Har., L. I., R. valve Cutchogue, L. I., R. valve Cold Spring Har., L. valve Cutchogue, L. valve Pecten opercularis: Eddystone, R. valve Irish Sea, R. valve Firth of Forth, R. valve Pecten gibbus Tampa, Fla., R. valve Pecten ventricosus: San Diego, Cal., R. valve Number of Rays. A C 17. 353 ±.018 0.876 ±.013 5.05 ±.07 16.534 ±.034 0.852 ±.024 5.32 ±.36 16.790 ±.022 0.916 ±.015 5.46 ±.09 15.954 ±.105 0.881 ±.075 5.52 ±.49 17.478 ±.029 1.000 ±.020 5.72 ±.12 18. 101 ±.029 1.074 ±.021 5.93 ±.11 17. 673±.027 1.117±.019 6.32±.11 20.512 ±.030 0.991 ±.021 4.83 ±.10 19.495 ±.087 0.885 ±.019 4.55 ±.10 Echiodermata. Seriation of ray-frequency in starfish, Crossaster papposus: A = 12.391, C= 0.788, v=6.36%, Ludwig, '9Sb. Coeleiiterata. Scyphonidae. — 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. Lot. A a C Pseudocyltia, num. radial canals 5.004±.094 0.441 8.81 lips 4.868±.012 0.556 11.4 Protista. 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 vulgar. Is, Pearl and Dunbar, '03; various diatoms, Schroter and Vogler, '01. Lot. A C Paramecium, length 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  '00b; Arnica montana, Ludwig, '01; Aster, Shull, '02. Num. Ray-flowers. A a C Aster shortii 14. 000 ±.068 1.526 ±.048 10.90 A. nové-anglise 42.874 ±.302 6.308 ±.213 14.71 A. prenanthoides 38.080 ±.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=3.8; number of stamens, early, A = 26.731, a= 3.761 and late, A = 17.863, a= 3.298. MacLeod, '99, Weldon, '01; number of petals of Caltha palustris, de Vries, '94; number of calyx parts and petals of Troll. Ius europa?us 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, MacLeod, '00; number of sepals and petals in the lesser Celandine, various species, Pearson and others, '03. Caryophyllaceae. — 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: o= 2.7 88, 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. corniculus, Medicago saliva, M. falcata, Ludwig, '97; flowers per head of Lathyrus, Ludwig, '00b. Rosacece. — Number of stamens of Prunus spinor a and Cra- taegus, Ludwig, '01; sepals of 1000 Potentilla tormentilla and petals of 4097 Potentilla anserina, de Vrie?, '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 ama- bilis, de Vries, '94: number of flowers in inflorescence and number of petals on flower of Adoxa moschatellina, White- head, '02. Dipsacce. — Number of flowers per head in Knautia arven- sis, maximum at 64, Vogler, '03. Composite. — Number of male and female flowers in umbel of Homogyne, Ludwig, '01. PrimulacecB. — Number of flowers per umbel, Primula, multimodal, Ludwig, '97, '98b, '00; rays in Primula farinosa, Vogler, '01. STATISTICAL BIOLOGICAL STUDY. 71 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 aucuparia, Fraxinus excelsior, Senecio nemorencis, and Pole- monium, Ludwig, '97, '98b. Length and breadth of leaves of Fagus silvatica and Carpinus betulus, Ludwig, '99. Leaf- dimensions, Sanguinaria, Liriodendron, Ampelopsis, and Ailanthis (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 silvestris, Lee, '02. Lot, length of pine needles A mm. a mm. a mm. C Pinus silv., lower branches. 22. 163 ±. 048 4. 474 ±. 034 20. 19 "middle 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, '94, 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, Duncker, '00. 11 "anal " "?, Type IV. Stature of St. Louis schoolgirls, Pearson, '95, p. 386. a= -0.489. Number of teeth, Palsemonetes varians Plymouth, Pearson, '95, p. 404. a= -0.134. Stature of Australian whites, Powys, '01. Rays  p. 385. Ray frequency, Pectens, Davenport, '00, '03b. Skewness. GENERAL. — Mathematical Analysis. — Pearson, '95, 'Old, '02, '02m. Biological Interpretation. — Davenport, 'Olb, 'Olc. Quantitative Results. Numerous cranial characters, Naquada race, Fawcett, '02. Nearly always +. Num. lips of medusa, P. pentata (Mayer, '01; Pearson, 'Old) + .549 Num. Miillerian glands, legs of swine (Pearson and Filon, '98). . . + .311 Num. dorsal teeth, Patemonetes varians (Pearson, '95) + . 130 Num. rays, Pecten opsrcularis, 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  .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. 73 Index of Littorina, Casco Bay (Bumpus. '98) + .13 Index of Littorina Newport (Bumpus. '98) + .25 Humber " " + .048 " " So Kincardineshire (Bumpus '98). + .068 21-rayed  (de Vries, '99) +1.9 Rays  of wings of long-winged chinch-bug (Davenport, 'Olb). . . — .43 " " " " short-winged chinch- bug ' ...+ .44 Length horns rhinoceros-beetle, long-horned (Davenport, 'Olb). . — .03 " " short-horned " .. + .48 Complex Distributions. Bimodal Polygons. — Discontinuity in hairiness of Biscu- tella, Saunders, '97; of Lychnis, Bateson and Saunders, '02, Weldon, '02°. 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, '97b, '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, Lee, '02, Reinohl, '03, Vogler, '03, Vogler, '03. CORRELATION. General and Method.— Galton, '88, '89, Pearson, '96, Yule, '97, '97b; spurious correlation, Pearson, '97; non-quantitative characters, Pearson, '00C, Pearson and Lee, '00, Yule, '00b, '02; index not constant in related races, Weldon, '92, Pearson, '96, '98b p. 175, '02" 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, '02. 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 peasants 13.09. British Columbian Indians & 08. Modern French (Parisians) 05.06. Shuswap Indians 04. Lot. Capacity and length 89.01. 01. 66. 01. 05. " breadth 56.05. 50.07. " height 54.05. 52.07. Length and height 50.05. 05. 35.07. Breadth and height 35.06. 06. 18.08. Cap. and ceph. index 31.07. German: Capacity and breadth 67.04. Length 51.04. Length 51.05. 05. 69.04. " length 24.06. 05. 45.05. Cap. and ceph. index 20.06. Breadth and height 07 ±. 06. 28 ±. 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 96 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(5) Stature and humerus 77(«) to.81(5) Stature and tibia 78(«) to.81(5) Humerus and ulna 75 to.86 Humerus and radius 74 to. 84 Radius and stature 67 (?) to. 66 Clavicle and humerus 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 $6 44 ±.012 " 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. ANTIMERICALLY 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 " 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 686 ±.029 12th pair legs, Lithobius 58 ±.039 anal pair legs, Lithobius 575 ±.039 Other antimeric organs: Num. of dorsal and ventral spines, Palaemonetes vulgaris (Duncker, '00&) 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.) Number 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, R. and L. chslse of Galasimus 754 ±.014 Carpopodite, R. and L. chslse of Gelasimus 698 ±.017 Number of rays  Cottus 11C coxal pores II. anal and 14th segment, Lithobius 440 R. 13th and 14th segments, Lithobius 722 II. 13th and 12th segments, Lithobius 464 Length carapace and post-spinous portion rostrum, Crangon 81 tergum VI abd. seg., Crangon 09 tergum VI and telson, Crangon 11C MIXED AND CROSS CORRELATION. — Length of wing and tail of Lanius "shrike," Strong, '01; in fishes, Duncker, '97, '99; proportions of aphids, "plant-lice," Warren, '02; length of carapace and of chela in Eupagurus, "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, Nassau, Dimon, '02; circumference to number of spines, statoblast of Bryozoa, Davenport, '00e; 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 shell 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 Actinosphaerium 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 Dianx. of cell and body length, Daphnia, 3J 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. 14th 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, r 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 Carapace 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 4-. 34 to —. 18 stamens and pistils, Celandine 43 to.75 petals and petals, Celandine 38 to.22 petals and petals, Celandine 35 to.19 Stamens and 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, 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; daughter; mother; mother. No. of Changes of Sex. Parental Average  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: Father and son (Beeton and Pearson, '99).12 " adult son (Beeton and Pearson, '01). 135 " adult daughter " " 130 Mother and adult son " " 131 " eye-color (Pearson and Lee, '00) 55 to.44 Stature, English middle class: Father and son (Pearson, '96, p. 270) 396 " daughter 4I " 360.419 Mother  " 300 Coat-color, thoroughbred horses: Sire, foal (Pearson. '00, p. 458).517 Dam, foal " " " 527 Fertility: Mother and daughter, British upper class.042±.010 Father and son, 44 ".051 ±.009 Mother and daughter, British peerage.210 Father and son, " ".066 Mother and daughter, landed gentry. 105 Father and son, ".116 Frontal breadth, Hyalopterus (Warren, '02).335.359 Length R. antenna, Hyalopterus (Warren, '02)...439.539 Ratio: R. antenna H- frontal breadth (Warren, '02)...439.539 Ratio: Length protopodite -4- length body, Daphnia (Warren, '02) 466 Grandparental. Coat color, thoroughbred race-horses Basset hounds Frontal breadth, Hyalopterus, Aohidse (Warren, '02) Length, R. antenna. Aphidse (Warren, '02) Ratio R. antenna -T- frontai oreadth, Aphidae (Warren, '02) Ratio Length protopodite -H length body, Daphnia (Warren, '02) Stature. Grayson and gr'df.. h^mo male line (Pearson, '96) f envile line (Pearson, '96). Ortgr'dson and grt gr'df. homo 3 line 2 " " " Eye-color, homo, f., grandfather, and son (Blanchard, '03) fVmt". fir^rco ** ** ** " '* .339 .113 .321 .177 .231 .27  m., horse, " homo, " " dau. horse, " homo, f., grandmother, and son horse, " homo, " " dau. horse, " homo, m., ' son horse, " homo, " horse, " dau. .421 .324 .380 .360 .372 .359 .297 .311 .272 .309 .221 .204 .262 261 .318 239 Fraternal. r Daphnia, length of spine (Warren, '99; Pearson, 'Olc) 693 Aphis, antennal length (Warren, '02) 679 frontal breadth (Warren, '02) 666 Paramecium, index of just separated fission pairs (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 cephalic index, N. A. Ind. " " Average of 3 sets. . .403 " longevity, Quakers (Beeton and Pearson, '01) 332 " temper, British (Pearson, 'Olc) 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 be- tween relatives. — Pearson, '00, Pearson and Lee, '00. Blended Alternative Inherit- Inherit- ance, ance. Offspring and Parent 3000 . 5000 " grandparent 1500 .250 " great-grandparent 0750 .123 " " gt.-gt.-grandparent . . . .0375 " " nth order grandparent . 6X(|)n Brothers 4000 .4 to 1 .0 Half-brothers 2000 .2 to 0.5 Uncle and nephew 1500 .250 First cousins 0750 First cousins once removed 0344 Second cousins 0172 Third cousins : 0041 Homotyposis. . Correlation in non-sexual reproduction, as in production of homologous undifferentiated physiologically independent parts, Pearson, 'Olc; criticism, Bateson, '01; reply, Pearson, '02s; rejoinder, Bateson, '03; correlation between differen- tiated homologous organs, Pearson, '02e. % Var. to p. Lot. Character. Var. of, C°rre- Race. latlon Ceteract, Somersetshire Lobes on fronds 78.631 Hartstongue, Somersetshire Sori on fronds 78.630 Shirley poppy, Chelsea Stigmatic bands 79.615 English onion. Hampden Veins in tunics 79.611 Holly Dorsetshire Prickles on leaves 80.599 Soanish chestnut, mixed Veins in leaves 81.591 Beech, Buckinghamshire Veins in leaves 82.570 Papaver rhoeas, Hampden Stigmatic bands 83.562 Mushroom, Hampden Gill indices 84.549 Papaver rhoeas, Quant ocks Stigmatic bands 85.533 Shirley poppy. Hampden. Stigmatic bands 85.524 Spanish chestnut, Buckinghamshire Veins in leaves 89.466 Broom. Yorkshire Seeds in pods 91.416 Ash. Monmouthshire Leaflets on leaves 91.405 Papaver rhoeas. Lower Chilterns. Stigmatic bands 92 Ash, Dorsetshire Leaflets on leaves.... 92.396 Ash, Buckinghamshire Leaflets on leaves.... 93.374 Holly Somersetshire Prickles on leaves.... 93.355 Woodruff, Buckinghamshire Members of whorls.... 98.173 Malva rotundifolia, Hampden Seg. of seed-vessels.... 98.183 Woodruff, Buckinghamshire Members of whorls.... 98.173 Mean of 22 cases 87.457 Bands of capsules of Shirley poppies, man of 8 crops (Pearson, and others, '02) 498 Mean of 39 cases of homotyposis (Pearson, '02) 499 Mendelism. General Statement. — Mendel, '66, de Vries, '00, '00, '00, '03, Correns, '00, Davenport, '01, Bateson, '02, Castle, '03; critical, Weldon, '02, '03, Pearson, '03b. Plants.— Correns, '00, '00b, '01, '02-'02C, '03-'03C, de Vries, '02, '01-'03C, Bateson and Saunders, '02. Animals. — Echinoids, Doncaster, '03; poultry, Bateson and Saunders, '02; mice, Darhishire, '02, '03b, Castle, '03b, Bateson, '03b; rabbits, Woods, '03. Telegony. No evidence of, in human statures, Pearson and Lee, '96. Fertility. Inherited in man and race-horses, Pearson, Lee, and Bramley-Moore, '99; greater fertility in poppy of seeds from capsules 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 of 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 sparrow, Bumpus, '99; percentage death-rate of families of Aphids has inverse correlation with length of antenna of mother (r= —.201 ±.034), 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 symmetrical one by selection, de Vries, '94, '98; shifting of the mode by selection, de Vries, '99. Sexual. — Pearson, '96: 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 44 adult females in general 64. 043 ±. 061 2. 325 ±. 043 See also Correlation: Assortative mating (p. 75). DISSYMMETRY. The following values for & 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-cush). Right-handed, handed. Lateral edge of carapace 838.793 Length of meropodite, first ambulacral appendage 813.872 Length of meropodite, of carpopodite, and of pro-podite of chelae, all 1.00 1.00 Num. of ray son R. and L. pectoral fins, Acerina —0.111 Glands on wrists of swine 053 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 A = 22.46 22.57 xv. 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 farinosa 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 Holl. Waquoit. Bristol, R. I. Dorsal fin-rays. A = 66. 1 Baltic, M'=39, southern North Sea 4H, Plymouth 44, Duncker, '99. Fish in similar and adjacent lakes belonging to different drainage-basins have marked difference in scales on nape, number of fin-rays and of dorsal spines, Moenkhaus, '96. 