None
Consequently in the long run we shall have of all the zygotes 25%d, d + 50%d, r + 25%r, r, or 50% of the zygotes hybrid and 50% of pure blood, dnd 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% " " " " M 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. CORRELATED VARIABILITY. 59 Gen. 1. 3en. 2 Gen. 3. 31 y (hybrid) peas produced 12 plants; these bore: 77.5 y (hybrid + y) peas ( =75.8%) 247 g (pure-blooded) 21 plants were produced: peas ( =24.2%). 7 (33%) pure- 14 (66%) hybrids^ blooded y, because they 20 plants bore : because they bore: bore : | 292 y peas 462 y 149 g 670 green peas. (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)r=d, r+r,r. in (1) all of the progeny will appear of the dominant type. 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. G.25%d, d; 12.5%J, r; 6.25%r, r. A. B. I2.5%d, d; 25%d, r; 12.5%r, r. A. 25%r, r B. 6.25%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, 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. + 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 DISSYMMETRY IN ORGANISMS. A Dissymmetry-Index, 3, measuring the average de- gree 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 'cor- relation between the two sides. Let df 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-L8: -10123 /: 1 63 310 23 3 2X<f) = 310X 1 + 23X2 + 3X3=365, J(<T) = 1, ^ (/") = !; n=400. w_ 336X365-X1 ^ 400X366 ~ 146400 62 . STATISTICAL METHODS. CHAPTER V. SOME RESULTS OF STATISTICAL BIOLOGICAL STUDY. It is hoped that the following analysis of the literature, although not complete, will prove suggestive and otherwise useful. Numerical results are occasionally given. These are intended to be used in making comparisons with numerical results obtained in the same field and thus to assist in the interpretation of such 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, '00b, '01, '02; Davenport, '00, '00d, Olb; Duncker, '99b; Eigenmann, '96; Galton, '01; Gallardo, '00, '01, 'Olb; Ludwig, '00, '03; Redeke, '00; Volterre, '01. TEXT-BOOKS: Galton, '89; Bateson, '94; Duncker, '00; Pearson, '00; Vernon, '03. MHTHOD: Camerano, '00; Engberg, '03; Fechner, '97; Galton, '89, '02; Heincke, '97; Johannsen, '03; Pear- son, '94, '95, '96, '97, '97b, '98, '00°, 'Old, '02C, '02*, '02*, '02m, '02n, '03e; Pearson and Lee, '00; Sheppard, '98, '98b, '03; Verschaffelt, '95; 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, '02k. STATISTICAL BIOLOGICAL STUDY. 63 Coefficient of variability; significance : Pearson, '96; Brew- ster, '97; Duncker, '00b; Davenport, '00e. Mutations: Bateson, '94; Howe, '98; deVries, '01-' 03; Weldon, '02C. Individual vs. specific variation: Brewster, '97, '99; Field, '98; Mayer, '02; Davenport '03*>. Variability independent of sexual reproduction: Warren, '99, '02; Pearson and others, '01', 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: Bavari- ans, Ammon, '99; United States, recruits, Baxter, '75, Pear- son, '95, p. 385; various, Macdonell, '02; English middle upper classes, Galton, '89, Pearson, '96, p. 270; Germans, Pearson, '96, p. 278; French, Pearson, '96, p. 281; Cam- bridge University students, Pearson, '99. Lot. Engl. upper middle class 1 do. husbands. Cambridge Univ. students English fathers. n 683 200 1078 A 69.215" ±.066 5 69. 135" ±.126 2 68 .863" ±.054 I cm. 171.95 a 5.592" ±.047 5.628" ±.089 2 522" ± .048 cm. 6.81 C 3.66 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.. .. Frenchmen 2862 284 169.88 166 . 80 6.58 6.47 3.80 3.88 English criminals 3000 166 . 46 6.45 3.88 166. 26 ±.53 5.50± .37 Germans 390 156 . 93 6.68 4.02 Engl . upper middle class ? do. wives. . .. Cambridge Un. students ? French. Lvons S .. 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 3.69 Seriation at different ages: British infant at birth, Pearson, '99; school children, Bowditch, '91; St. Louis schoolgirls, Porter, '94, Pearson, '95, p. 336; Australian adult whites, Powys, '01. 64 STATISTICAL METHODS. Lot. Average. a C New-born infant , British 3 . 20 . 503 ± . 028 in . 1 . 332 ± . 020 6 . 500 ?. 20.124±.025 " 1.117±.018 5.849 St. Louis schoolgirls 118.271 cm. 2.776 Australian whites: Average. a C Year's * ? * ? * ? 20-25 66.95 62.50 2.475 2.365 3.70 3.79 25-30 67.30 62.76 2.562 2.432 3.81 3.87 30-40 67.15 62.44 2.587 2.303 3.86 3.69 40-50 66.91 62.96 2.618 2.555 3.91 4.06 50-60 66.74 62.22 2.633 2.591 3.95 4.16 60 & over 66.26 61.31 2.682 2.300 4.04 3.75 Weight. — Seriations at different ages, British: Infants, Pearson, '99; University students, Pearson, '99; 5552 Eng- lishmen, Sheppard, '98. Lot. Average. a C New-born infants, $ 7 .301± .0241b. 1.144±.017 15.66% ? 7.073±.021 1.006±.015 14.23 Cambridge Univ. students, $ 152 . 783 ± . 35 16 . 547 ± . 25 10 . 83 ?125.605±.77 14.030±.57 11.17 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. n A a C 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 .... . 56 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 Maquada race 72.94 2 .98 3 .95 Skull capacity: coefficients of variability. Fawcett and Lee, '02. Lot. 5 ? Lot. i \ ? Andamanese 5 .04 5.59 7.72 6. .92 Ainos 6.89 6 .82 Germans . .. 7. 74 8 .19 Negroes 7 .07 G .90 Egyptian mummies.. 8. 13 8 .29 Low-caste Pun jabs .. 7 .24 8 .99 Polynesians. 8. 20 5 .55 Parisian French 7 .36 7 .10 Italians .... 8. 34 8 .99 Kanakas 7 .37 6 .68 Modern Egyptians. .. 8. 59 7 .17 17th Century English. 7 .68 8 .15 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, 4.58-5.57), 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, 1.680±.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 Shrike, length L. wing $ ......... 168 " ? ......... 112 tail length $ ............. 141 " bill length, $ ? 95 164 112 ............ " depth, $ ............ 126 ? ............ 85 melanism of crown, $ ..... 144 " " ? ..... 99 " upper tail-coverts $ 142 " ? 104 Curvature of culmen .............. Eggs, proportions: Passer domesticus, Bumpus, '97, Pear- son, '02e; various species, Latter, '02. 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 Species. Cuckoo Av. Length, Bird, in. 14 243 Blackbird Song-thrush . .. Starling ... . 10 . 9 . 8-8.5 114 151 ?7 Yellowhammer. Tree-pipit 7 6.5 32 ?7 Meadow-pipet. House-sparrow (English) ....  Length, mm. Breadth, mm A a C A a C 22 .40 29.44 27.44 29.78 21.55 20.01 19.72 21.82 1.195 5.47 15.51 .525 3.38 1 1 0 1 0 0 1 .059 .357 .999 .097 .682 .698 .250 4.72 4.61 3.64 3.68 3.17 3.49 6.37 Ifi 21 20 21 1(3 15 14 .54 .73 .69 .76 .04 .09 .56 .650 .787 .516 .423 .405 .449 .561 3 3 2 1 2 2 3 .93 .62 .50 .94 .53 97 .84 21.32 20.12 20.22 17.14 1.05 0.810 0.857 0.598 4.92 4.02 4.24 3.49 15.34 14.73 15.43 13.33 .415 2.81 .477 3.09 .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, 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, Lonnberg, '93. Tracheata. Lepidoptera. — Seriations of wing dimensions of Thyreus abbotti. Field, '98; number of "eye-spots" on wing of Epi- nephele, Bachmetjew, '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; 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 offsprmg,War- ren, '02. Dimension. Grandmothers. Children. a C a C Frontal breadth 2.28mm. 6.07% 2.96mm. 8.26 Length R. antenna 7.36 8.77 10.94 12.97 . Lengthantenna x 23% 5.67 1>84 7.82 Frontal breadth 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. Podophihalmata. — 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 STATISTICAL BIOLOGICAL STUDY. 67 moenas, Weldon, '93, Pearson, '94; various dimensions, Cran- gon, Weldon, '90; length of rostrum, Palsemon serratus, Thompson, '94, Pearson, '94; number of rostral teeth of Pakemonetes, Weldon, '92b, Pearson, '95, Duncker, '00. Lot. A, mm. a, mm. C,% Eupagurus, short edge of R. chela: $ deep water 9.708±.085 2.76 28.5 t shallow water 10.272±.075 2.59 25.2 ? deep water 7.400±.033 1.06 14.3 5 shallow water 7.485±.029 1.02 13.6 Eupagurus, long edge of R. chela: t deep water 17. 97 ±.14 4.73 27.8 * shallow water 18. 68+. 13 4.38 23.5 9 deep water 14.14±.06 1.67 11.9 ? shallow water 13.97±.05 1.82 13.0 Eupagurus, carapace length: $ deep water 8.59db.05 1.67 19.4 t shallow water 7.54±.03 0.94 12.5 $ deep water 7. 12 ±.03 0.86 12.1 PalsBmonetes 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. Chcetopoda. — Teeth on jaws of Nereis virens. Right: A = 10.055±.045, a= 1.339 ±. 032, C=13.3%; Left: A=10.00± .044, o= 1.306 ±.031, C=13.1%, Hefferan, '00. Bracliiopoda. Seriation of widths breadth, width of sinus -f- depth, num- ber 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, <r= 1.318 ±.022, C= 9.57 ±.16, Davenport, '0CK Mollusca. 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%, 68 STATISTICAL METHODS. <J4=2.7%, Cj5=2.6%, (7.4 = 3.0%, Bumpus, '98, Duncker, '98; critical, Bigelow and Rathbun, '03; seriations 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 Nassa, Dimon, '02; seria- tions 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 Car- dium, Baker, '03; Pecten; ray-frequency, Lutz, '00, Daven- port, '00, '03, '03b; change in proportions with age, acquisi- tion 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±.ll Firth of Forth, R. valve 17.673±.027 1.117±.019 6.32±.ll 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 ±.10 Echiiiodermata. Seriation of ray-frequency in starfish, Crossaster papposus: A = 12.391, C=0.788, v=6.36%, Ludwig, '98b. Coelenterata. 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 Wood worth, '96. STATISTICAL BIOLOGICAL STUDY. 69 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 vulgaris, Pearl and Dunbar, '03; the diatom Syndes- mon, polygon varies with season and year, Kellerman, '01; other diatoms, Schroter and Vogler, '01. Lot. A a C Paramecium, length /i 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; Pearscn, '02h. RAY-FLOWERS IN COMPOSITE.- -Seriation of ray-frequency of Coreopsis, de Vries, '94; of Senecio nemorensis, S. fuchsii, Centurea 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, '9Sb; Soli- dago serotina, Ludwig, '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. novje-angliae 42.874±.302 6.308±.213 14.71 A.punicens 36.672±.107 4.480±.076 12.22 A. prenanthoides 28.080±.107 4.070±.077 14.52 OTHER SERIATIONS OF FLORAL^ ORGANS : Ranunculacece. — Petals, 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, o= 3.89; late flowers, A = 12.147, <r=3.88; number of stamens, early, A = 26.731, a= 3.761 and late, A = 17.863, G= 3.298, 70 STATISTICAL METHODS. 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 Ranun- culus acris, Ludwig, '9Sb, '00b; number of seeds per capsule- compartment of Helleborus foetidus, Ludwig, '97. Cruciferw. — Number of flowers, Cardamine pratensis, em- pirical modes at 2, 5, 8, 11, 13, 16, 19, 22, not in Fibonacci series, Vogler, '03. Papaveracece. — Number of floral organs in Papaver, Mac- Leod, '00; number of sepals and petals in the lesser Celan- dine, various species, Pearson and others, '03. Caryophyllacece. — Number of stamens in Stellaria media, varies with season and position on plant, Burkill, '95; num- ber of anthers in 44,542 flowers of Stellaria media — a com- plex polygon due to effect of age and environment, Reinohl, '03. Sapidacece. — Number of compartments in fruit of Acer pseudoplatanus, 'de Vries, '94. Leguminosce. — Number of blossoms in clover plants, Type I: a= 2.788, de Vries, '94, Pearson, '95, p. 402; number of ele- vated flowers in blossoms of Trifolium repens perumbellatum, de Vries, '94; floral organs of Lotus uliginosus, L. cornicu- latus, Medicago saliva, M. falcata, Ludwig, '97; flowers per head of Lathyrus, Ludwig, '00b. Rosacece. — Number of stamens of Prunus spino: a and Cra- tsegus, Ludwig, '01; sepals of 1000 Potentilla tormentilla and petals of 4097 Potentilla anserina, de Vries, '94. Cornacece. — Number of flowers in head of Cornus mas and C. samguinea, 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. Compositce. — 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. ?1 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, '93; pine needles. Ludwig, '01; from various branches of Pinus silvestris, Lee, '02. Lot, length of pine needles A mm. a mmf 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; num- ber of seeds per capsule-compartment, Helleborus, Ludwig, '97; fruit length, Oenothera Lamarckiana, and Helianthus, de Vries, '94; dimensions of beans in masses and in succes- sive 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 Billiard, '96, Pearson, '96, p. 291: a=.311 ±.016. 72 STATISTICAL METHODS. Fertility (percentage of births with one year of marriage) of wives at different ages, Powys, '01. Rays in dorsal fin of Pleuronectes s , 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. " tl anal " " " s " " il " pectoral " " " S " " Type V. Number of lips of medusa, P. pentata, Mayer, '01, Pearson, 'Old. a=.549. Norigal. Stature, U. S. recruits, Baxter, 75, Pearson, 95, p. 385. Ray frequency, Pectens, Davenport, '00, '03b. Skewness. GENERAL.— Mathematical Analysis. — Pearson, '95, 'Old, '02f, '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, Palsemonetes varians (Pearson, '95) + .130 Num. rays, Pecten opercularis, Irish Sea (Davenport, '031') + .087 Eddystone (Davenport, '03b) .... + .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)4- .023 41 " " " P. opercularis, F. of Forth + .007 " " upper valve, P. irradians (Davenport, '00C) ± .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 Pectenirradians, fossil, Va oldest (Davenport,  of long-winged chinch-bug (Davenport, '01*>). . . — .43 44 " " " short-winged chinch-bug " ...+ .44 Length horns rhinoceros-beetle, long-horned (Davenport, 'Olb). . — .03 44 " " '* short-horned 4* .. + .48 Complex Distributions. Bimodal Polygons. — Discontinuity in hairiness of Biscu- tella, 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, Lud- wig, '96, '96b, '96C, '97, '97b, '97C Modes of Chrysanthemum segetum at 13, 21, de Vries, '95. Opposed to Fibonacci series, complex polygon due to lack of homogeneity, Lucas, '98, Shull, '02, Pearson, '02**, Lee, '02, Reinohl, '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, '00, '00b, '02; index not constant in related races, Weldon, '92, Pearson, '96, '98b p. 175, '02n p. 2, Daven- port, '03b. Man. General. — Galton, '88; British criminals, various dimen- sions, r=.13 to .84, Macdonell, '02. Skull. — Correlated with cranial capacity in living persons, Lee and Pearson, '01 ; breadth and length, Naquada, Bavari- ans, French, Pearson, '96, p. 2SO; N. A. Indians, Boas, '99; 74 STATISTICAL METHODS. various dimensions, Aino and German, Lee and Pearson, '01; Naquadas, Fawoett and Lee, '02. With civilization woman's correlation tends to gain on man's, Lee and Pearson, '01, Pearson, '02n. Lot. r 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. r& r? Aino: Capacity and length 89 ± . 01 . 66 ± . 05 " 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 db . 04 . 70 ± . 03 " length 51±.05 .69±.04 " " height 24±.06 .45±.05 Cap. and ceph. index 20± .06 - .03± .07 Breadth and height 07 ± . 06 . 28 ± . 06 Length and height - . 10± .07 .31 ± .06 Skeletal— RoUet, '89; stature correlated with length of long bones, reconstruction of stature of extinct races, Pear- son, '98b; various coefficients of correlation, Pearson, '99, '00, p. 402; in hand-bones, Whiteley and Pearson, '99, Lewenz and Whitelev, '02. STATISTICAL BIOLOGICAL STUDY. 75 Lot. r 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 S0(*) to .81(5) Stature and humerus 77 ( ? ) to . 81( * ) Stature and tibia 78(«) to .80(«) Humerus and ulna 75 to .86 Humerus and radius 74 to .84 Radius and stature 67 (?) to 70(a) 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 3 644 ± . 012 ' " " " 9 622±.013 Weight and stature of Cambridge (Engl.) students, $ . . . .486± .016 »«»•« •• » ? 721 ±.026 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 005 ± .024 Breadth of head and ability, adults 045± .032 Cephalic index and ability, University men 031 ± .035 41 " " length of head, University men — .086± .033 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 Miillerian 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; num- ber of teeth on R. and L. jaws 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. r 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 44 4> 4< " " "  Other antimeric organs: r Num. of dorsal and ventral spines, Palsemonetes 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.) r Num.  Pecten . 970 ± .001 Unsymmetrical paired organs. — Pleuronectes, Duncker, '00; Gelasimus, the fiddler-crab, Yerkes, '01, Duncker, '03. Length of meropodite, R. and L. chelae of Galasimus 7 54 ±.014 44 '* carpopodite, R. and L. chelae of Gelasimus 698 ± .017 44 4< propodite, R. and L. chelae of Gelasimus 473 ± .026 Num. rays R. and L.  lateral line ends, R. and L. Pleuronectes, $ 467 Num. rays R. and L. ventral fin, Pleuronectes, $ 243 STATISTICAL BIOLOGICAL STUDY. 77 METAMERICALLY REPEATED ORGANS. — Fin-rays of fishes, Duncker, '97; coxal pores centipede, Williams, '03; seg- ments of shrimp Crangon, Weldon, '92. Num. dorsal spines and soft fin-rays, Acerina — .379 " " " Cottus 110 " coxal pores R. anal and 14th segment, Lithobius 440 R. 13th and 14th segments, Lithobius 722 R. 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 — . 11 MIXED AND CROSS CORRELATION. — Length of wing and tail of Lanius " shrike," Strong, '01; in fishes, Duncker, '97, '99; pro- portions of aphids, "plant-lice," Warren, '02; coxal pores of centipede, Williams, '03; length of carapace and of chelae in Eupagurus, "hermit-crab," Schuster, '02; diameter of cell and body length, Daphnia, Warren, '03; cross correla- tion in teeth on jaws of Nereis, Hefferan, '00; various char- acters of the mud-snail, Nassa, Dimon, '02; 'circumference to number of spines, statoblast of Bryozoa, Davenport, '00*. diameter of body of the Heliozoan Actinosphserium 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. r Carapace length and chela length, Eupagurus, £ 9389 ± 0036 " 9 .8626±.0080 Diameter of body of Actinospherian and num. of nuclei .854 ± . 017 Inner and outer diameter shell of Arc'ella 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 Diaro. of cell an/1 body length, Daphnia, 3d 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 Ccxal 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. .001 78 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. r 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, Celandine 38 to .22 " pistils 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 peren- nis, Verschaffelt, '99; various pairs of dimensions of fruits and leaves, Harshberger, '01; parts of desmid, Syndesmon, KeUeraian, '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; esti- mate 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, '03t STATISTICAL BIOLOGICAL STUDY. Inheritance of Eye-color, Homo. «, son; d, daughter? /.father; m, mother. Parental I AVrge?f^and;^ - I rsmandrdf.. rdf rsjjr anc* rdmm rs/m' rd& rdmf> rsmm ' • r«m/' rdfm • Great-grand-parental inheritance, average , .. Grand- parental No. of Changes of Sex. .530 .370 .347 .459 .300 .222 .296 .145 .038 Parental. Exceptional fathers produce exceptional sons at a rate three to six times that of non-exceptional fathers and ex- ceptional pairs at ten times the rate of non-exceptional pairs, Pearson, '00C, pp. 38, 47. x y Cor. -Reg. Longevity: r pxy Father and son (Beeton and Pearson, '99) .12 " ** adult son (Beeton and Pearson,  (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) .517 Dam, foal " -527 Fertility : Mother and daughter, British upper class .042 ± . 010 Father and son , . . 05 1 ± . 009 Mother and daughter, British peerage .210 Father and son, -066 Mother and daughter, landed gentry . 105 Father and son -116 r f> Frontal breadth, Hyalopterus (Warren, '02) .335 .359 Length R. antenna, Hyalopterus " .427 .507 Ratio: R. antenna -^frontal breadth (Warren, ''02) . . . .439 .539 Ratio: Length protopodite -*- length body, Daphnia (Warren, '02) , 466 .619 80 STATISTICAL METHODS. Graiidparental. Coat color, thoroughbred race-horses " " Basset hounds Frontal breadth, Hyalopterus, Aphidse (Warren, '02) Length, R. antenna, Aphidae (Warren, '02) Ratio R. antenna -s- frontal breadth, Aphidse (Warren, '02) Ratio Length protopodite -r- length body, Daphnia (War- ren. '02) [. Stature. Gr'dson and gr'df.. homo male line (Pearson, '96) female line (Pearson, '96).. Ortgr'dson and grtgr'df. . homo $ 1;«~ 339 113 321 177 231 .269 .192 .295 27 .5] line Eye-color, homo, f., grandfather, and son (Blanchard, '03) Coat horse. *' "  m., horse, " homo, " ' dau. horse, " homo, f ., grandmother, and son horse, " homo, " ' dau. horse, " homo, m., horse, " homo, " ' dau. horse, '* .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°) 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): 'Consciousness 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(i)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 Homoty posts. Correlation in non-sexual reproduction, as in production of homologous undifferentiated physiologically independent parts, Pearson, 'Olc; criticism, Bateson, '01; reply, Pearson, '02* ; rejoinder, Bateson, '03; correlation between differen- tiated homologous organs, Pearson, '02e. Lot. Ceteract Somersetshire %^ Character. V Lobes on fronds. /ar. to ar. of Race. . 78 78 79 79 80 81 82 83 84 85 85 89 91 91 92 92 93 93 96 98 98 98 Corre- lation. .631 .630 .615 .611 .599 .591 .570 .562 .549 .533 .524 .466 .416 .405 .400 .396 .374 .355 .273 .190 .183 .173 Hartstongue, Somersetshire Shirley poppy Chelsea . ... .Sori on fronds Stigmatic bands English onion. Hampden Holly Dorsetshire .Veins in tunics Prickles on leaves. Spanish chestnut, mixed Boech Buckinghamshire. . Veins in leaves Veins in leaves. Papaver rhoeas, Hampden Mushroom Hampden . .. . Stigmatic bands .... Gill indices. Papaver rhoras, Quantocks Shirley poppy. Hampden Spanish chestnut, Buckinghamshire Broom Yorkshire . Stigmatic bands .... .Stigmatic bands. . .. Veins in leaves ..... Seeds in pods Ash, Monmouthshire Papaver rhoeas. Lower Chilterns. .. Ash, Dorsetshire Ash Buckinghamshire Holly. Somersetshire Wild ivy, mixed localities Nigella hispanica, Slough .Leaflets on leaves. .. .Stigmatic bands . Leaflets on leaves. .. . Leaflets on leaves . Prickles on leaves. . .. . Leaf indices. Seg of seed -capsules Malva rotundi folia, Hampden. . .. Woodruff, Buckinghamshire . Seg. of seed-vessels. .. . Members of whorls .. Mean of 22 cases 87 .4 .457 Bands of capsules of Shirley poppies, mean 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, '031'. Plants.— Correns, '00, '00b, '01, '02-' 02°, '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 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 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 44 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 & 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-crt,b). Right- Left- 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 rays on R. and L. pectoral fins, Acerina —0.111 " " glands on wrists of swine .0053 DIRECT EFFECT OF ENVIRONMENT. Animals. — Aphids reared in successive generations in in- creasingly 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 .TV. 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, Wil- liamson, '00; fin-rays of Pleuronectes from New England shore, Bumpus, '98: Wood Holl. Waquoit. Brfstol, R. I. Dorsal fin-iays. . . A = 66 , 1 65 . 2 64 . 9 Anal " ... 4 = 49.7 48.6 48.7 84 STATISTICAL METHODS. Number of fin-rays of Pleuronectes flesus from Western Baltic, Af'=39, southern North Sea 41£, 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. Invertebrata. — Mean and variability of deep- and shallow- water Eupagurus differ, Schuster, '03; proportions, variability, and correlation coefficients of Pecten opercularis differ at Eddy stone, 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, '98, '03; abscissa of normal curve in terms of ordinate, Sheppard, '93; abscissa and ordi- nate in terms of difference of area, Sheppard, '03; abscissa of normal curve in terms of class index, Sheppard, '98. Probability of fitted curve being the true one: Elderton, '02. Values of log ] ^i/— e~^2 [ for various values of f. Elderton, '02. Table of log —. - ^ — -. - . Elderton, '02. & n(n — 2)(n — 4) . .. /2 7*00 i o Table of A/ — I e ~ *x d%, for different values of 7, Elder- ton, '02. Table of Iog10 (l+x)— x log,0 e for various values of x, for use with curves of Type III. Tables for calculating probable error, Sheppard, 798. 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. BIBLIOGKAPHY. 85 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 Lon- don. The references are scattered through fifty-seven periodi- cals. ADAMS, C. C. '00. Variation in lo. Proc. Amer. Assoc. for the Adv. of Sci., XLIX, 18 pp., 27 plates. AGASSIZ, A., and W. McM. WOODWORTH, '96. Some varia- tions in the Genus Eucope. Bull. Mus. Comp. ZooL, XXX, 123-150. Plates I-IX. Nov. ALLEN, J. A., '71. On the Mammals and Winter Birds of East Florida, etc. Bull. Mus. Comp. Zool., II, 161-450. Plates IV-VIII. AMANN, J., '96. Application du calcul des probability a 1'etude de la variation d'un type vegetal. Bull, de 1'Herb. Bossier. IV, 578-590. AMMON, OTTO, '99. Zur Anthropologie der Badener. Jena: G. Fischer, 707 pp, 15 Tab. BACHMETJEW, P., '03. Ueber die Anzahl der Augen auf der Unterseite der Hinterfliigel von Epinephele jurtina L. Allgemeine Zeitschr. f. Entomologie, VIII, 253-256. BAKER, F. C., '03. Rib Variation in Cardium. Amer Nat., XXXVII, 481-43S, July. 