None
If now mongrels are crossed haphazard, a male cell may unite with either a female cell or with a female cell; likewise a male cell may unite with a female cell or with a female cell. Consequently, in the long run, we shall have of all the zygotes, 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 germ and one having a yellow germ. Yellow  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,r, and (2) {d+r)r=={i, 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. 6.25% d, d, 12.5% d, r; 6.25% r, r. A. 60% d, r B, 2.b%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-polyhybrids may be likewise predicted, by extending the principles already laid down. Measure op Dissymmetry in Organisms. A Dissymmetry-IiideXy a, measuring the average degree of asymmetry in the right and left organs of bilateral organisms, has been proposed by Dimcker (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 Od = ^ a^ + a^ — 2ra^a ii» 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 /j", /', etc., the frequencies of the positive-difference classes. Then the asymmetry-index 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-U: -10 12 3 /: 1 63 310 23 3 i'(d0 = 310X1 + 23X2+3x3=365, 2'(/0«33a 2'(d") = l, i'(/0 = li n=400. xd COBBELATED VABIABILITY. NATIONAL 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, '00, '01, '02; Davenport, '00, '00, '01; Duncker, '99; Eigenmann, '96; Galton, '01; Gallardo, '00, '01, '01; Ludwig, '00, '03; Redeke, '00; Volterre, '01. Text-books: Galton, '89; Bateson, '94; Düsseldorf, '00; Pearson, '00; Vernon, '03. Method: Camerano, '00; Engberg, '03; Fechner, '97; Galton, '89, '02; Heincke, '97; Johannsen, '03; Pearson,  '97; Duncker, '00; Davenport, '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, 'Ol', 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), 'Ol', p. 362. Man. Stature. — Seriation for adults of different races: Bavarians, Anunon, '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, '99. Lot. A C Engl, upper middle class 4 683 69.215 ±.066 2.592" d:.047 do. husbands. 200 69.135"±.126 2.628"±.089 3.66 Cambridge Univ. students 68.863" ±.054 2 522" ±.048 cm. 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 6.50±.37 Germans 390 156.93 6.68 4.02 in. in. Engl, upper middle class 9 652 64.043 ±.061 2.325 ±.043 Cambridge Univ. students? 63.883 ±.130 2.361 ±.092 3.69 French, Lyons 9 154.02 cm. ±.52 5.45 ±.37 Seriation at different ages: British infant at birth, Pearson, '99; school children, Bowditch, '91; St. Louis schoolgirl, Porter, '94, Pearson, '95, p. 386; Australian adult whites, Powell, '01. STATISTICAL METHODS. Lot. Average. New-born infant, British S. 20. 503 ±. 028 in. 9. 20.124±.025 1.332±.020 1.117 ±.018 C 6.500 5.840 Ob. JUNIOR B Australian A>lX\J%JHm IB- whites: ' XJ .O.^1 X MUH, «. 1 f VI t Age. Years Average. S 9 i a 9 i C 9 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 2.682 2.300 4.04 3.76 ( 1.144± .017 15 .66% 1.006± .015 14 .23 16.547 ± .25 10 .83 14.030 ±. .57 11, .17 Weight. — Seriations at different ages, British: Infants, Pearson, '99; University students, Pearson, '99; 5552 Englishmen, Sheppard, '98. Lot. — Average. New-born infants, i 7.301 ±.024 lb. 9 7.073±.021 Cambridge Univ. students, S 152.783 ±. 35 9 125. 605 ±.77 Skidl. — 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 Bavarian peasants 100 Baden recruits 6748 Modern Parisians French peasants 56 Cambridge students 1000 Criminals (British) 100 Brahmans of Bengal 100 Whitechapel English 107 Maquada race 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 Skull capacity: Lee, '02. Lot. Andamanese Ainos Negroes How-caste Punjabs.. Parisian French 17th Century English. coefficients of variability. Fawcett and S 9 Lot. S 9 5.04 5.59 Naquadas 7.72 6.92 6.89 6.82 Germans 7.74 8.19 7.07 6.90 Egyptian mummies 8.13 8.29 7.24 8.99 Polynesians 8.20 5.65 7.36 7.10 Italians 8.34 8.99 7.37 6.68 Modern Egyptians 8.59 7.17 7.68 8.15 Etmscans 9.58 8.54 STATISTICAL BIOLOGICAL STUDY. 65 Various cranial dimensions, Lee and Pearson, '01. Other Organs. — Coefl&cient of variability of bones of skeleton of French and Naquada (C. of limb-tones, 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 Müllerian glands in Sus scrofa, n, 2000; A, 3.501 ±.025; a, 1.680 ±.018; C, 48.0, Davenport and Bullard, '96. Avcs. Serrations of various proportions of N. A. birds, Allen, '71; characters of Lanius (** shrike") and its races, Strong, '01; Lot. n A o C Shrike, length L. wins J 168 99.06 mm. 2.74 mm. 2.81 *? 112 97.98 2.64 2.69 tail lengths 141 101.57 3.48 3.43 *? 95 99 55 3.63 3.65 bill length, i 164 12.01 0.71 5 89 •• •• 9 112 11.71 0.63 5.35 depth, i 126 9.27 0.42 4.57 9 85 8.95 0.41 4.61 *• melanism of crown, i 144 83.57% 3.0% 3 58 5 99 83.66 3.19 3.81 " upper tail-coverts i 142 53.13 15.42 29 02 *?, 9 104 47.98 18.99 39.58 Curvature of culmen 29.94 2.74 9.15 Eggs, proportions: Passer domesticus, Bumpus, '97, Pearson, '02; various species, Latter, '02. Av. Length, length, mm. Breadth, mm. Species. Bird, n A 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 14.56.561 3.84 House-sparrow (English) 6 687 21.82 1.195 5.47 15.51.525 3.38 House-sparrow.. 6 26 20.12 0.810 4.02 14.73.415 2 81 Robin 6 57 20.22 0.8.57 4.24 15.43.477 309 Linnet 5.5-6 65 17.14 0.598 3.49 13.33.358 2 69 67 STATISTICAL METHODS. Amphibia. Sedations 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, B3mie, '02; dimensions of 141 Petromyzon; Lonnberg, '93. Tracheata. Leindoptera. — Seriations of wing dimensions of Thyreus abotti. Field, '98; number of eye-spots on wing of Epinephele, Bachmetjew, '03; number of spots on different species of the genus Papillio, Mayer, '02; breadth of wing, 98 i Strenia clathrata C=4.57, Warren, '02. Aphides. — 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 Ratio : ^°^^, T^ Tl X 10.. 1. 23% 5.67 1.84 7.82 Frontal breadth Myriapoda. — Lithobius: seriations of length of adults, C, for 3's= 10.97; «'s= 11.25; number of prostemal 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 moenas, Weldon, '93, Pearson, '94; various dimensions, Cranston, Weldon, '90; length of rostrum, Palaemon serratus, Thompson, '94, Pearson, '94; number of rostral teeth of Palaemonetes, Weldon, '92, Pearson, '95, Duncker, '00. Lot. A, mm. a, mm. C, % Eupagurus, short edge of R. chela: i deep water 9.708±.085 2.76 28.5 i shallow water 10.272±.075 2.69 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: i deep water 17. 97 ±.14 4.73 27.8 i shallow water 18. 68+. 13 4.38 23.5 « deep water 14.14±.06 1.67 11.9 9 shallow water 13. 97 ±.05 1.82 13.0 Eupagurus, carapace length: i deep water 8.59±.05 1.67 19. 4 i shallow water 7.54±.03 0.94 12.5 9 deep water 7.12±.03 0.86 12.1 Pabemonetes 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. 48 28.26 Amphipoda. — Seriations of lengths of body, of second antennae, and of ratio of second antennae to body-length, Smallwood, '03. Annelida. Chobtopoda. — Teeth on jaws of Nereis virens. Right: A — 10.055 ±.045, (7=1. 339 ±.032, C=13.3%; Left: A = 10.00 ±.044, a=1.306 ±.031, C=13.1%, Hefferan, '00. Brachiopoda. Seriation of width -t- 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. 14 = 13.782.031, C = 9.57.16, Davenport, Mollusca, Gastropoda. — Frequency polygons of ventricosity, weight, and index of Littorina littorea for 3 British and 10 American localities — greater variability in America. Index: ap=2.3%, 68 STATISTICAL METHODS. 7^=2.7%, CB=2,e%, C = 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 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 Cardiimi. Baker, '03; Pecten; ray-frequency, Lutz, '00, Davenport, '03, '03, '03"; change in proportions with age, acquisition of new synametry about transverse axis; definition of Form units from different localities, Davenport, '03, '03. 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 Cutcheline, 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 20.12 ±.030 0.991 ±.021 4.83 ±.10 Hclii Oder iiiata. Seriation of ray-frequency in starfish, Crossaster papposus: 14 = 12.391, C= 0.788, i;=6.36%, Ludwig, '93^ Coelenterata. ScyphomediiscB. — Seriation of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; Serration of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; Serration of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; Serration of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; Serration of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; Serration of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; Serration of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; Serration of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; Serration of number of tentaculocysts of Aurelia aurita: n=3000, empirical range 4-15; Serration of number of tentaculocysts of Aure empirical mode=8, genital sacs, Af'=4, range, 2-10, Browne, '95, '01. Hydromedusas, — 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. 19.15 8.36% 9.16 13.44 4.03 5.73±.12 10.27±.22 2. 17 ±.05 13.66±.30 STATISTICAL BIOLOGICAL STUDY. Lot. A a C Paeudocyltia, num. radial canals 5. 004 ±. 094. 441 8.81 lips 4.868±.0l2 0.556 11.4 Protista. Paramecium recently divided, Simpson, '02; seriation of diameter of Actinospherimn 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, Schrdter and Vogler, '01. Paramecium, length n 229.05 breadth 68.13 index 29.91 Arcella, outer diameter 55.79 ±. 17 ** inner diameter..... 15.91 ±.07 Plants. General. — Multimodal polygons especially frequent in plants, Ludwig, '97; crlticaJ, Lee, '02; Pearscn, '02; Pearscn, '02; Ray-flowers in COMPOSIT-fi. — Seriation of ray-frequency of Coreopsis, de Vries, '94; of Senecio nemorensis, S. fuchsii, Centurea cyanus, C. jacea, Solidago virga aurea, Achilla millefoUum, Ludwig, '96; ray-frequency in Chrysanthemum, Ludwig, '97°, Lucas, '98, Tower, '02, Pearson and Yule, '02; Helianthus, Wilcox, '02; Bellis perennis, Ludwig, '00; Arnica montana, Ludwig, '01; Aster, Shull, '02. Nimi. Ray-flowers. A Aster shortii 14.000±.068 A. novsB-angli£B 42.874 ±. 302 A. punicens 36.672±.107 A. prenanthoides 28.080±. 107 Other Seriations op Floral Organs: Ranunctilacece. — Petals, Ranunculus bulbosus, de Vries, '94, Pearson, '95; calyx, coralla, Stamens, and pistils of Ficaria vema, Ludwig, '01; number of Ficaria pistils, early flowers, A = 17.448, <j= 3.89; late flowers, A = 12.147, <7= 3.88; number of stamens, early, A = 26.731, <7= 3.761 and late, -4 = 17.863, <7= 3.298. C 1.526± .048 10.90 6.308i: .213 14.71 4.480i: .076 12.22 4.070± .077 14.52 .»:; itttti 70 STATISTICAL METHODS. MacLeod, '99, Weldon, '01; number of petals of Caltha palustris, de Vries, '94; number of cal}^ parts and petals of Trollius europseus and number of fruits per head of Ranunculus acris, Ludwig, '93, '00; number of seeds per capsule-compartment of Helleborus foetidus, Ludwig, '97. Cruciferw. — Number of flowers, Cardamine pratensis, empirical modes at 2, 5, 8, 11, 13, 16, 19, 22, not in Fibonacci series, Vogler, '03. Papaveracece. — 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, Reindhl, '03. Sapidaceae. — Number of compartments in fruit of Acerpseudoplatanus, de Vries, '94. Leguminosae. — Number of blossoms in clover plants, Type I: cT= 2.788, de Vries, '94, Pearson, '95, p. 402; number of elevated flowers in blossoms of Trifoliiun repens perumbellatiun, de Vries, '94; floral organs of Lotus uliginosus, L. comiculatus, Medicago saliva, M. falcata, Ludwig, '97; flowers per head of Lathyrus, Ludwig, '00. Rosaceae. — Number of stamens of Prunus spinofa and C. sanguinea, Ludwig, '01; sepals of 1000 Potentilla tormentilla and petals of 4097 Potentilla anserina, de Vries, '94. Comaceae. — Number of flowers in head of Comus mas and C. sanguinea, not in Fibonacci series, Vogler, '03. Caprifolaceae. — 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, Dipsacola. — Number of flowers per head in Kautia arvensis, maximum at 64, Vogler, '03. Compositae. — Number of male and female flowers in number of Homogyne, Ludwig, '01. Primula. — Number of flowers per umbel. Primula, multimodal, Ludwig, '97, '98, '00; rays in Primula farinosa, Vogler, '01. STATISTICAL BIOLOGICAL STUDY. Scrophularia. — Number of parts in peloria of Lenaria spuria, Yost, '99; number of stamens, Digitalis, Gallardo, '00. Orchidaceae. — Extremes in variability of number of spots on flower, Chodat, '01. Leaves. — Serration of numbers of paired leaflets of Pirus acuparia, Fraxinus excelsior, Senecio nemorencis, and Polemonium, Ludwig, '97, '98. Length and breadth of leaves of Fagus silvatica and Carpinus betulus, Ludwig, '99. Leaf dimensions, Sanguinaria, Liriodendron, Ampelopsis, and Ailanthus (n, small), Harshberger, '01. Number of sicjfe 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. 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 22.69 Fruit. — Number of ears in head of Agropyrum repens and Brachypodium, Ludwig, '01; of the grass Lolium, Ludwig, '00; fruits per head of Ranunculus acris, Ludwig, '00; number of seeds per capsule-compartment, Helleboris, Ludwig, '97; fruit length, Oenother A. 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, '00". SOME TYPES OF BIOLOGICAL DISTRIBUTIONS. General. — Pearson, '95 '01. a modified by selection, Reindhl, '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. 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 i , Duncker, '00. *' ''anal '' '' '* ?, " " Type IV. Stature of St. Louis schoolgirls, Pearson, '95, p. 386. a= -0.489. Number of teeth, Palaemonetes 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 '* " " '' pectoral " " " « " " Type V. Nimiber 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, '03^. Skcwness. General. — Mathematical Analysis. — Pearson, '95, '01*, '02', '028r, »02«». Biological /nterpre^a/icm.— Davenport, '01»>, 'Olc. QuarUitaiive Results, Numerous cranial characters, Naquada race, Fawoett, '02. Nearly always +. Num. lips of medusa, P. pentata (Mayer, '01 ; Pearson, '01**) + .649 Num. MliUerian glands, legs of swine (Pearson and Filon, '98). . . + .311 Num. dorsal teeth, Palasmonetes varians (Pearson, '95). ...*.... + . 130 Num. rays, Pecten of)ercularis, Irish Sea (Davenport, 'OS"*) + .087 Eddy stone (Davenport, '03'») .... + .080 " hooks on statoblasts, Pectinatella (Davenport, *00') + .077 Weldon's crab measurements, "No. 4 " (Pearson, '95) + .077 Num. rays lower valve, Pecten irradians, L. I (Davenport, '00* )+ .023 •• " •• ** P. opercularis, F. of Forth + .007 " " upper valve, P. irradians (Davenport, '00«) ± .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 2l-rayed Chrysanthemum (de Vries, '99) .'— . 13 13- •• •* " *• •* + .12 Selected 12- (and 13-) rayed Chrysanthemum (de Vries, '99) +1.9 Raysof Pectenirradians, fossil, Va oldest (Davenport, '01^) .... — .22 • •• •• youngest... -.16 recent. N C - .09 " •• •• •• recent, LI +.023 Length of wings of long-winged chinch-bug (Davenport, '01^). . . — .43 •* •• •* short-winged chinch- bug " ** ...+ .44 Length horns rhinoceros-beetle, long-homed (Davenport, '01^). . — .03 •• short-homed " " .. + .48 Complex Distributions. Bimodal Polygons. — Discontinuity in hairiness of Biscuit, Saunders, '97; of Lychnis, Bateson and Saunders, '02, Weldon, '02. Length of cephalic horns of rhinoceros-beetle, anc, forceps length of male earwigs, Bateson, '94; explanation of di-morphism, Gird, '94. Multimodal Polygons. — Mode  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. r Breadth and Length: German, 49.05 Smith Sound Eskimo 47 Aino, 43.06 Aino, 9.37.07 German, 29.06 Modern Bavarian peasants 28.06 Naquada race 27 Sioux Indians 24 Modern French (Parisians) 05.06 Modem French (Parisians) 05.06 Shuswap Indians 04 Lot. r? Aino: Capacity and length 89.01.66.09 Thigh breadth 56.05.50.07 Thigh 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 —. 25.09.09 German: Capacity and breadth 67.04.70.04 Thigh length 51.05.69.04 Thigh 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. — Rollet, '89; stature correlated with length of long bones, reconstruction of stature of extinct races, Pearson, '98; various coefficients of correlation, Pearson, '99, '00, p. 402; in hand-bones, Whiteley and Pearson, '99. Lewena and Whiteley, '02. STATISTICAL BIOLOGICAL STUDY. 75 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(9) to. 81(6) Stature and humerus 77(«) to. 81(6) Stature and tibia 78(0 to. 80(6) Humerus and ulna 75 to. 86 Humerus and radius 74 to. 84 Radius and stature. 67 («) to 70(«) 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 S 644d:.012 Weight and stature of Cambridge (Engl.) students, S....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 length of head. University men 031.035 Vocalization and Recovery. — Pearson, '00'; Macdonell, '02, '03, '03, '03 to '91. Assortative Mating. — Pearson, '96, '99', '00, Pearson and Lee, '00. Stature of husbands and wives 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 Müllerian glands on R. and L. fore legs of swine, Daliport 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. vessels of Nereis, Heflferan, '00; breadth of R. and L. valves of Pecten, Davenport, '03; skeletal spicules on R. and L. half of Echinus larva. Subject and Relative. Lengeth R. and L. sides of carapace, Gielasimus 947 ±.003 meropodite, first walking leg 948 ±.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 58 ±.039 Other antimeric organs: Num of dorsal and ventral spines, Palsemonetes vulgaris (Duncker, '00b) 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 dorsalis and anal fin -rays in flounder, $651 Length antero-poaterior 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. chelse of Galasimus 754 ±. 014 "carpopodite, R. and L. chelse of Gelasimus 698 ±.017 "propodite, R. and L. chelse of Gelasimus 473 ±.026 "of dorsal fin-rays at which lateral line ends, R. and L. Pleuronectes, J 467 Num. rays R. and L. ventral fin, Pleuronectes. i 243 "Metamerically repeated organs. — Fin-rays of fishes, Duncker, '97; coxal pores centipede, Williams, '03; segments of shrimp Crangon, Weldon, '92. Num. dorsal spines and soft fin-rays, Acerina —.379 Cottus lie "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 rostnun, 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; proportions of aphids, "plant-lice," Warren, '02; coxal pores of centipede, Williams, '03; length of carapace and of chelse 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 Echomis and the number of cysts and of nuclei. Smith, '03; inner and outer diameters and color of the shell of Arcella, Pea, and Dunbar, '03. Organs. Carapace length and chela length, Eupagurus, i.9389:t 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 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. 14th leg and body length, Lithobius....308 ±.059 Num. rays dorsal fin and end-point of L. lateral line, Pleuronectes, i 208 Outer diameter and color Arcella 012 Num. dorsal spines and L. pectoral rays, Pleuronectes..004 T:>-t 78 STATISTICAL METHODS. Organs. r Body length and number antennal joints —.013±.087 Circumference of statoblast and number spines. Pectinatella — t:>-t 78 STATISTICAL METHODS. Organs. r Body length and number antennal joints —.013±.087 Circumference of statoblast and number spines. Pectinatella — t:>-t 78 STATISTICAL METHODS. Organs. r Body length and number antennal joints —.013±.087 Circumference of statoblast and number spines. Pectinatella — t:>-t 78 STATISTICAL METHODS. Organs. r Body length and number antennal joints —.013±.087 Circumference of statoblast and number spines. Pectinatella — t:>-t 78 STATISTICAL METHODS. Organs. r Body length and number antennal joints —.013±.087 Circumference of statoblast and number spines Nore. R. definite teeth and L. indefinite. Nereis —.524 ±.023. Carappace 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 Astor, Shull, '02; various organs on Lesser Celandine, Pearson and others, '03. Organs. Num. rayB and bracts. Aster 856 to.799 Stamens and pistils Ficaria ranunculoides, early.... 507 ±.031 late 749±.016 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 petals, 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. Inequity 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. Inheritance of Eye-color, Home. No. of Changes of Sex. son; d, daughter; /. father; m, mother. 2 Averaoe of r.^ and f ^^ .530  '99) adult son (Beeton and Pearson, '01) adult daughter Eye-color (Pearson and Lee, '00) 55 to 44 Stature, English middle class: Father and son (Pearson, '96, p. 270) dau. Mother and son Head index. N. Amer. Indian: Mother and son (Pearson, '00, p. 458) dau. Head index. N. Amer. Indian: Mother and son (Pearson, '00, p. 458) Dam, foal Fertility: Mother and daughter, British upper class Father and son, " Mother and daughter, British peerage Father and son, " Frontal breadth, Hyaloptenis (Warren, '02) Length R. antenna, Hyaloptenis Ratio: R. antenna + frontal breadth (Warren, '02)  .300 .517 .527 .042± .010 .051 ± .009 .210 .066 .105 .116 P .335 .359 .427 .507 .439 .539 .466 .619 80 STATISTICAL METHODS. Grandparental Coat color, thoroughbred race-horses 339 Basset hounds 113 Frontal breadth, Hyalopterus, Aphidse (Warren, '02) 321.269 Length, R. antenna, Aphidse (Warren, '02) 177. 192 Ratio. R. antenna + frontal breadth, Aphidse (Warren, '02) 231.295 Ratio. R. antenna + frontal breadth, Aphidse (Warren, '02) [.27.5] Stature. Gr'dson and gr'df.. homo male line (Pearson, '96) I99 • female line (Pearson, '96), 089 Grtgr'dson and grtgr'df.. homo i line " " \ 105 •• ..I. ». Q «. «t 4* ftai Eye-color, homo, f., grandfather, and son (Blanchard, '03) .421 Coat horse, ** »» «» t. ' it • ,i ' .324 Eye homo, ** '* dau. •« «* .380 Coat horse, ** •« it «« «* .360 Eye homo, m.« *' son «« »* .372 Coat horse, '* *• »» »• *• .359 Eye homo, ** •* dau. «• •» .297 Coat horse, ** •« «* «« *« .311 Eye homo, f., grandmother, and son •• •• .272 Coat horse, ** it II »• •• .309 Eye homo, ** " dau. «• M .221 Coat horse, ** tt tt «• • « .204 E.ye homo, m., " son •• • » .262 Coat horse, " *t *( »« • « .261 Eye homo, *• ** dau. «• •• .318 Coat horse, *' •• •» •• •• .239 Fraternal. Daphnia, length of spine (Warren, '99; Pearson .*01«). • • •. Aphis, antennal length (Warren, '02) 679 Frontal breadth (Warren, '02) 666 Parallel, index of just separated fission pairs (Simpson, '02) 664 Horse, coat-color (Pearson, Lee, and Moored, average of 3 sets 633 Man, forearm, English (Pearson, '01) 542 Hound, coat-color, Bassett (Pearson and Lee, '00) 526 Man, eye-color, English (Pearson, '01) 526 Man, eye-color, English (Pearson, '01) 332 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, '01) 317 ** longevity, British peerage (Pearson, '01) 260 Quakers " " 197 Average of 23 sets 476 Mean of 42 fraternal correlations (Pearson, '02') 496 Some mental characteristics, inherited exactly like physical characters (Pearson, '01): Conscientiousness 593 Popularity 504 Self-consciousness 592 Vivacity 470 Shyness 528 Intelligence 456 Average of 6 507 STATISTICAL BIOLOGICAL STUDY. Inheritance, ance. Offspring and Parent 3000.5000 "grandparent 1500.250 "great-grandparent 0750.123 "great-grandparent 0375 "great-grandparent 0375 "nth order grandparent. 6X(i)^ Brothers 4000.4 to 1.0 Half-brothers 2000.2 to 0.5 Uncle and nephew 1500. 250 First cousins 0750 First cousins 072 First cousins 072 Third cousins 0041 Homology. Correlation in non-sexual reproduction, as in production of homologous undifferentiated physiologically independent parts, Pearson, '01; criticism, Bateson, '01; reply, Pearson, '02; rejoinder, Bateson, '03; correlation between differentiated homologous organs, Pearson, '02. Velt. of Porro- Race. 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 80.699 Spanish 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, Quantocks Stigmatic bands 85.533 Shirley poppy, Hampden Stigmatic bands 85.624 Papaver rhoeas, Lower Chiltems Stigmatic bands 85.624 Ash, Dorsetshire Leaflets on leaves 91.416 Ash, Monmouthshire Leaflets on leaves 91.405 Papaver rhoeas, Lower Chiltems Stigmatic bands 92.400 Ash, Dorsetshire Leaflets on leaves 92.396 Ash, Buckinghamshire Leaflets on leaves 93.374 Holly, Somersetshire Prickles on leaves 93.355 Wild ivy, mixed localities Leaf indices 96.273 Nigella hispanica, Slough Sees of seed -capsules 98.190 Malva rotundi folia, Hampden Sees of seed -vessels 98.183 Woodruff, Buckinghamshire Members of whorls 98.173 Lot. Character. Var. of Mean of 22 cases 87.4.457 Bands of capsules of Shirley poppies, mean of 8 crops (Pearson, and others, '02) 498 Mean of 39 cases of homotypons (Ftan, '02).499 STATISTICAL  '02, '03, Pearson, '03''. Plants.— Correns, '00, '00, '01, '02-'02c, '03-'03S de Vries, '02, '01-'03, Bateson and Saunders, '02. Animals. — Echinoids, Doncaster, '03; poultry, Bateson and Saunders, '02;  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 unsjnnmetrical as 3 to 4, Mayer, '01. SELECTION. General. — Intensity of selection connotes a lessening of correlation, Pearson, '02, p. 23; mediocre individuals not the fittest to survive, Pearson, '02, 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 ±.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 83rm-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 2.592d:. 047 "wives 63.869.110 2. 303d: 078 "adult females in general.. 64. 043 ±. 061 2. 325 ^. 043 See also Correlation: Assortative mating (p. 75). DISSYMETRY. The following values for 3 have been determined by Duncker, '00 and '03: Pleuronectes flesus L., 1060 R.-eyed and 60 L.^yed: 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-cr.b): 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 chelffi, all 1.00 1.00 Num. of rays on R. and L. pectoral fins, Acerina —0.111 Glands on wrists of swine 0.0053 DIRECT EFFECT OF ENVIRONMENT. Animals. — Aphids reared in successive generations in increasingly unfavorable conditions have reduced dimensions, Warren, '02: Grandmother. Grandchildren. Frontal breadth. Aphid.. 1 = 37. 56 33. 93 Length of R. antenna.... A = 83. 91 76. 59 Ratio 1^' A = 22.46 22.57 R. 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 Hole. Waquoit. Bristol, R. I. Dorsal fin-iays... il = 66.1 65.2 64.9 Anal **... A = 49.7 48.6 48.7 _Ui-V •«...-*- 84 STATISTICAL METHODS, Number of fin-rays of Pleuronectes flesus from Western Baltic, M'=39, southern North Sea 41i, 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. InvertebrcUn. — Mean and variability of deep- and shallow water Eupagurus differ, Schuster, '03; proportions, variability, and correlation coefficients of Pecten opercularis differ at Eddystone, Irish Sea, and Firth of Forth, Davenport, '03. 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, '98; abscissa and ordinate in terms of difference of area, Sheppard, '98; abscissa of normal curve in terms of class index, Sheppard, '98. Probability of fitted curve being the true one: _ Elderton, '02. Values of log \ Xv—^~^^ ^^^ various values of x^- _ Elderton, Table of log —, for different values of Elderton, '02. Table of log —, for different values of Elderton, '02. Table of log, for different values of x, for use with curves of Type III. Tables for calculating probable error, Sheppard, '98. Table of values of 1— r^ and \/l— r^ for all values of r from to 1 proceeding by hundredths. Yule, '97. Probable errors of r for all values of n. Yule, '97. BIBLIOGRAPHY. BIBLIOGRAPHY. 