th Sap nth nl te ln ey ts ide ih i ny Ve Ys at ee) ee ag wae ; py ny cn 7 f a a) i= fi ni, _ See : ni 7 | a) i if] 7 ¥ E val y i " { a vy -: ' ‘ - i oH - eae 7 7 “ ’ i] [ u se ' ' % Oy t - M ' Dp: : 7 ¢ F ine a "4 a _ A i] re nh rel eh Pay eau Aan mh) yi ay ri, Fi Cares Vor a rea 4 hy Oia eK A A JOURNAL FOR THE STATISTICAL STUDY OF BIOLOGICAL PROBLEMS FOUNDED BY W. F. R. WELDON, FRANCIS GALTON ano KARL PEARSON EDITED IN CONSULTATION WITH FRANCIS GALTON AND IN COLLABORATION WITH C. B. DAVENPORT W. R. MACDONELL W. PALIN ELDERTON RAYMOND PEARL § BY KARL PEARSON VOLUME VI Marcu 1908 ‘tro Marcu 1909 GENERAL INDEX, VOLS. I TO V CAMBRIDGE AT THE UNIVERSITY PRESS LONDON: FETTER LANE, E.C. (C. F. CLAY, Manacer) And H. K. LEWIS, GOWER STREET EDINBURGH : 100, PRINCES STREET NEW YORK: G. P, PUTNAM’S SONS BERLIN: A. ASHER AND CO. LEIPSIC : BROCKHAUS BOMBAY AND CALCUTTA: MACMILLAN AND CO., LIMITED [All rights reserved] 206164 ~ ee - i ~ i ' : ‘ ’ . ah o i hoe wy ale - >" = 4 ‘ 1 , Cambridge : PRINTED BY JOHN CLAY, M.A. AT THE UNIVERSITY PRESS. ; F . ci I : hee ae 594,057 XIII. CONTENTS. Memoirs. The Probable Error of a Mean. By “SrupEentr” Split-Hand and Split-Foot Deformities, their Types, Origin and Transmission. By THomas Lewis, M.D., D.Sc. and DENNIS EMBLETON . On the Generalised Probable Error in Multiple Normal Correlation. By Karu Pearson, F.R.S., and ALiIcE LEE, Sc.D. On the Inheritance of the Deformity known as Split-Foot or Lobster- Claw. By Karu Pearson, F.R.S. On a Determinantal Theory of Inheritance, from Notes and Suggestions by the late W. F. R. Weldon. By Karu Pearson, F.R.S. Pigmentation Survey of School Children in .Scotland. (a) Committee and Grants (b) Report. By J. F. TocuEr Variation, Development and Growth in Holothuria floridana, Pour- talés. By CHartEes Lincotn Epwarps Probable Error of a Correlation Coefficient. By “STUDENT” Zur Frage vom viergliederigen Tarsus der Blattidae und der Regene- ration der Fiisse derselben. Von Tu. S. ScHTSCHERBAKOW Some Statistical Observations on Termites, mainly based on the work of the late Mr G. D. Haviland. By Ernest Warren, D.Sc. Note on the Skin-Colour of the Crosses between Negro and White. By Karu Pearson, F.RS. . ' Ueber die Liangenvariation der Coniferennadeln. Von A. HEYER . Statistical Study of Anti-typhoid Inoculation. By G. D. Maynarp PAGE lv XIV. XV. XVI. Contents PAGE On the Frequency Distribution of Phagocytic Counts. By M. GREEN- woop, Junr. and J. D. C. WHITE . ‘ : ; . 376 A Biometric Study of the Blood Beueee of the Common Tadpole By Karu Pearson, F.R.S. : 402 Data on Variation in the Comb of the Domestic Fowl. By Raymonp PEARL, Ph.D., and Maup DEwITT PEARL . 420 Miscellanea. Some Notes on Interpolation in n-dimensional Space. By W. Pauin ELDERTON : : : : : 94 Note on the Relative Variability of the Sexes in Carabus auratus, L. By H. G. Krirs . 103 Variation in Flower-heads of Gaillardia aristata. By W. W. Roppins 106 The Effect of Errors of Observation upon the Correlation Coefticient. By J. A. Cops 109 On Heredity in Sex. Remarks on Mr Cobb’s Note. By Karu PEARSON, F.R.S. . . 109 On the Influence of Double Selection on the Variation and Corre- lation of two Characters. By Kari PrEARson, F.R.S. 111 On certain Points concerning the Probable Error of the Standard Deviation. By RAYMOND PEARL, Ph.D. : : 112 Addendum to Memoir: “Split-Hand and Split-Foot Deformities.” By Tuomas Lewis, M.D. ; 117 On a Formula for Determining T[ (# + 1). EDITORIAL . ins On the Inheritance of the Sex-Ratio in the Thoroughbred Racehorse. By Davip Heron, M.A. ; 120 Note on Inheritance of Brachydactyly. By THomas Lewis, M.D.. 327 Note on Inheritance in Man. By Karu Pearson, F.R.S. BT Fecundity of Swine. By FRANK M. SurrFace, Ph.D. . 433 The Frequency Constants of a Variable Zee mY By RayMonpD PEARL, Ph.D. ‘ ; 437 The Correlation between a Variable and the Deviation of a Dependent Variable from its Probable Value. By J. ArrHuR Harris, Ph.D. 438 Notices and Bibliography ; : : 4 : ; . 128, 444 Plate I. Plate II. Plates IIT.—VII. Plate VIII. Plate IX. Plate X. Plate XI. Plates XIIT.—XVI. Plates I. and II. Plates IIT.—XV. Plates XVI.—XX. Plates XXI.—XXVI. Contents Plates. Part I. Genealogical Tree of the “G” Family (Split- Foot) ; ; : Photographs of Hands and Feet of members of G-family (Split-Foot) . Skiagrams of Hands and Feet of G-family Family Tree, Inherited Lobster-Claw . Diagrams illustrating defective hands of Lobster-Claw Family Diagrams illustrating defective feet of Lobster- Claw Family Photograph of Handsof Motherand Daughters, Lobster-Claw Family ; ‘ Skiagrams of Hands and Feet of Lobster- Claw Family Parts II. anp III. . Maps of Scotland, showing the Pigmentation districts Maps of Scotland, illustrating the distribution of Hair and Eye Colour Diagrams, illustrating the Local Differences of Hair and Eye Colour in the Counties of Scotland Maps of Glasgow, illustrating the distribution of Hair and Eye Colour in Glasgow and Environs . . to face p. 74 74 78 78 137 232, 232 vi Contents Part III. Plate I. Colour Variation in the Young of Holothuria floridana, Pourtalés . : : . . to face p. 300 Plate II. Colour Variation in the Adult of MHolothuria floridana, Pourtalés. : ; 3 , » 3800 Plates III—V. Papilla, pedicel, and calcareous spicules of Holo- thuria floridana, Pourtalés . : ; : » 300 Folding Plate. Holothuria floridana, Pourtalés . ; : $ ee: Part IV. Photographs of Negro and White Crosses. , E 5 ; ye 800 SPECIAL SUPPLEMENT TO VOL. VI. Pigmentation Survey of School Children in Scotland. Appendix to Report. By J. F. TocHErR . : (Separate pagination) pp. 1—67 Erratum. On p. 119, line 19, for “Since log ae~* = '848,4081,” read “Since log 2e-* = 3:526,3058.” % * S1YOS 4 a _ Sra Vis Partick. ‘March 1908 BIOMETRIKA A JOURNAL FOR THE STATISTICAL STUDY OF BIOLOGICAL PROBLEMS | A FOUNDED BY W. F. R. WELDON, FRANCIS GALTON ann KARL PEARSON EDITED athe IN CONSULTATION WITH FRANCIS GALTON : AND IN COLLABORATION WITH ecb. DAVENPORT: W. R. MACDONELL ~ .W. PALIN ELDERTON RAYMOND PEARL , BY _ KARL PEARSON - CAMBRIDGE AT THE UNIVERSITY PRESS LONDON; CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, FETTER LANE (C..F. CLAY, Manaczr) ‘ ano H. K. LEWIS, GOWER STREET NEW YORK: G. P. PUTNAM’S SONS LEIPSIC: BROCKHAUS BOMBAY AND CALCUTTA: MACMILLAN AND CO., LIMITED . Entered at the New York: Post Office as Second Class Matter. Price Ten Shillings net. [Issued April 18, 1908] The publication of a paper in Biometrika marks that in the Editors’ opinion : fa , it contains either in method or material something of interest to biometricians. 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Now any series of experiments is only of value in so far as it enables us to form a judgment as to the statistical constants of the population to which the experi- ments belong. In a great number of cases the question finally turns on the value of a mean, either directly, or as the mean difference between the two quantities. If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty :—(1) owing to the “error of random sampling” the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals. It is usual, however, to assume a normal distribution, because, in a very large number of cases, this gives an approximation so close that a small sample will give no real information as to the manner in which the population deviates from normality: since some law of distribution must be assumed it is better to work with a curve whose area and ordinates are tabled, and whose properties are well known. This assumption is accordingly made in the present paper, so that its conclusions are not strictly applicable to populations known not to be normally distributed; yet it appears probable that the deviation from normality must be very extreme to lead to serious error. We are concerned here solely with the first of these two sources of uncertainty. The usual method of determining the probability that the mean of the popula- tion lies within a given distance of the mean of the sample, is to assume a normal distribution about the mean of the sample with a standard deviation equal to s/Vn, where gs is the standard deviation of the sample, and to use the tables of the probability integral. Biometrika v1 1 bo The Probable Error of a Mean But, as we decrease the number of experiments, the value of the standard deviation found from the sample of experiments becomes itself subject to an increas- ing error, until judgments reached in this way may become altogether misleading. In routine work there are two ways of dealing with this difficulty: (1) an experiment may be repeated many times, until such a long series is obtained that the standard deviation is determined once and for all with sufficient accuracy. This value can then be used for subsequent shorter series of similar experiments. (2) Where experiments are done in duplicate in the natural course of the work, the mean square of the difference between corresponding pairs is equal to the standard deviation of the population multiplied by 2. We can thus combine together several series of experiments for the purpose of determining the standard deviation. Owing however to secular change, the value obtained is nearly always too low, successive experiments being positively correlated. There are other experiments, however, which cannot easily be repeated very often; in such cases it is sometimes necessary to judge of the certainty of the results from a very small sample, which itself affords the only indication of the variability. Some chemical, many biological, and most agricultural and large scale experiments belong to this class, which has hitherto been almost outside the range of statistical enquiry. Again, although it is well known that the method of using the normal curve is only trustworthy when the sample is “large,” no one has yet told us very clearly where the limit between “large” and “small” samples is to be drawn. The aim of the present paper is to determine the point at which we may use the tables of the probability integral in judging of the significance of the mean of a series of experiments, and to furnish alternative tables for use when the number of experiments is too few. The paper is divided into the following nine sections : I. The equation is determined of the curve which represents the frequency distribution of standard deviations of samples drawn from a normal population. II. There is shown to be no kind of correlation between the mean and the standard deviation of such a sample. III. The equation is determined of the curve representing the frequency distribution of a quantity z, which is obtained by dividing the distance between the mean of a sample and the mean of the population by the standard deviation of the sample. IV. The curve found in I. is discussed. V. The curve found in III. is discussed. VI. The two curves are compared with some actual distributions. VII. Tables of the curves found in III. are given for samples of different size. VIII and IX. The tables are explained and some instances are given of their use. X. Conclusions. By STUDENT 3 Section I. Samples of n individuals are drawn out of a population distributed normally, to find an equation which shall represent the frequency of the standard deviations of these samples. If s be the standard deviation found from a sample 2, 2,...7, (all these being measured from the mean of the population), then S(a’) ais (* =) = 2 cy) - 8 (a’) = 2S (x22) n n n? n 2 s n Summing for all samples and dividing by the number of samples we get the mean value of s? which we will write s’, ee Mpy _ fly (mn — 1) a 9 2 n ne WW where p, is the second moment coefficient in the original normal distribution of x: since 2, 2, etc., are not correlated and the distribution is normal, products in- : , : 28 (aa) . volving odd powers of «, vanish on summing, so that — @ a) 55 equal to 0. n If M;’ represent the R' moment coefficient of the distribution of s? about the end of the range where s? = 0, F (n—1) My’ = pp. ——— . Again eye jae . (Stay 2 n ze (° oy _ 28 (a?) € )y - ay n n n nv S(t) 25 (et). 29 es) 4S (ara) S (a7) — eG 2 a _ ees 4 n n n n n 6S (#2a," ; : ACE ae terms involving odd powers of 2, etc., which will vanish on summation. Now S(a,‘) has n terms but S(aa,2) has 4n(m—1), hence summing for all samples and dividing by the number of samples we get = 2 a MP PED 2 aye OD n n° = CS Os Ms i Sug” —1) ar F n n = fe — an — 1} + (n—-1) {n?— 24 3}. n WwW Now since the distribution of # is normal, u, = 3p”, hence . (n—1) F ,(n—1)(n4+1) Nite ae {8n —3 4+ n?—2n+3} =p, a 1—2 4 The Probable Error of a Mean In a similar tedious way I find: My ne —1)(m+ were) ne and We = ua —1)(m+1)(r+3) Qt 5) ni The law of formation of these moment coefficients appears to be a simple one, but I have not seen my way to a general proof. If now M;, be the R moment coefficient of s? about its mean, we have jee = (Gray -a(@7 1b) = 4,2 8 —1) nm” HO ee 24 n® n n° nr .— 1 Meal =] a ) in? + 4n+3—6n+6—n24+ 2n— 1} =8 atte ) ne | B rien ine M,= = 2 (y —1)(n4+ 1) (v4 3)(n 4+ 5) — 32 (n— 1 — 12(n — 1)? —(n — 1) e(n—1 ; ie ule ) (w+ 9n? + 23n + 15 —32n4+32—12n?4+24n—12—n?+3n?—3n+1} n _ 12pst (n — 1) (n +3) - n' ; ie eas _M, _3(+3) Se sey Ker a a hr * 28,38, -6 =~. (6 (n +3) - 24-6 (n—1)} =0. Consequently a curve of Professor Pearson’s type III. may be expected to fit the distribution of s*. The equation referred to an origin at the zero end of the curve will be a — Creme M, _ A4u2(rn—1)n? nn M, 8n2p,3(n — 1) = 4 n—1 n—-3 BS pee Ole eo where y= and y = Ca 2 ge ee | which will give the distribution of s’. co n-3 NX The area of this curve is of x? e@ *dx=TI (say). 0 By StrupENt 5 The first moment coefficient about the end of the range will therefore be rc N-l Ne Qu n-1 NX> w= ca | n-3 _ nx Sie =O = Pe Ty eee 4 Fs F c| e® ¢ mde al x? e =| o| Ppt ® @ de nN The first part vanishes at each limit and the second is equal to 0 — a ame el i Ser ae and we see that the higher moment coefficients will be formed by multiplying : n+1 n+3 successively by art! ones ,, M,, ete. Hence it is probable that the curve found represents the theoretical distribu- tion of s?; so that although we have no actual proof we shall assume it to do so in Hs, ete., just as appeared to be the law of formation 2) 7 what. follows. The distribution of s may be found from this, since the frequency of s is equal to that of s? and all that we must do is to compress the base line suitably. Now if y, = $(s") be the frequency curve of s° and GS TOY yp 2 are ae: then yd (s") = yds, or yds =2y,sds, Yo = 2sy,. j Sicekie oe Hence Wat 2CS(6)i 2 es is the distribution of s. , This reduces to te Ose ots, na Hence y= Aa”~e 2% will give the frequency distribution of standard devia- tions of samples of n, taken out of a population distributed normally with standard deviation «. The constant A may be found by equating the area of the curve as follows :— Area = A | v0 D nas na® ) nD Tee lar: (Let I, represent | xP e do 0 oc _ ne? van o (n—38)(n—5)...4.20, n according as n is even or odd. Ca dace - But ue [ @ 2tdu = ss J0 Qn ca nz? 9 227 4=a 2 : ea (tag ert I o~ and J, is | xe *"dza=|——e =—, JO) nN 2-0 n Hence if n be even, Area A SS SSS Se ; w (o\"> (n—38)(n—5)...3.1 = = 2 ( ) 2\n and if n be odd Area A> 7 ne eaea (n—3)(m—5)...4.2 c 2 n Hence the equation may be written jmp raf E(t te Bie oem Y= ay = 5) RESIN ail) ee (n even N aN _nae? = 7. ae — 2 n—2 Qo? I~ (u=8)(n—5)...4.2 ( ) ane a" (n odd) or (oma where WV as usual represents the total frequency. Section II. To show that there is no correlation between (a) the distance of the mean of a sample from the mean of the population and (b) the standard deviation of a sample with normal distribution. (1) Clearly positive and negative positions of the mean of the sample are equally likely, and hence there cannot be correlation between the absolute value of the distance of the mean from the mean of the population and the standard deviation, but (2) there might be correlation between the square of the distance and the square of the standard deviation. Let Ti (Hy and s?= S@) _ (Hey : ut n n Then if m,’, M/ be the mean values of wu? and s?, we have by the preceding (n—1) bs part M,' = p. =a and m,' = - By StTupENtT ff Now ws? = S (a) (* a) Ra eS n 7 n Fe (F eo +2 S (#12). S (a,’) = S (a!) n n nt 6a~a2 : . f é — wien other terms of odd order which will vanish on summation. n Summing for all values and dividing by the number of cases we get pigy ol) n n—1 Ryeowce + mM, = = + py ies ) == 3 py n? n? n » where R,2,. is the correlation between w? and s*. v—1 —1 -—1 Rego sy ar py —- ps ue ) {3 -n— 3} = Be a a 7 Hence Ryzgoywog = 0 or there is no correlation between wv and s°. Section III. To find the equation representing the frequency distribution of the means of samples of n drawn from a normal population, the mean being expressed in terms of the standard deviation of the sample. ns? C -53 : : eg Soe es We have y=—— s"e *” as the equation representing the distribution of s, oO the standard deviation of a sample of n, when the samples are drawn from a normal population with standard deviation o. Now the means of these samples of n are distributed according to the equation van 18 SS 20? ’ V2 o and we have shown that there is no correlation between aw, the distance of the mean of the sample, and s, the standard deviation of the sample. Now let us suppose # measured in terms of s, 2.e. let us find the distribution of z=~. 8 If we have y, = $(#) and y, = (z) as the equations representing the frequency of x and of z respectively, then Yan = dz = Y, 2 ; ie Yr = SY . * Airy, Theory of Errors of Observations, Part 11. § 6. 8 The Probable Error of a Mean a 02 2 NVis Hence y=———e Qa is the equation representing the distribution of z for samples of » with standard deviation s. Now the chance that s lies between s and s+ds is: ioe (6) ns” 52 9 20 ds o”1 “BAC Ge | aS sr @ 202 ds 0 which represents the V in the above equation. d Hence the distribution of z due to values of s which lie between s and s+ds is ns? (1+27) stds (J re _ns?(1+2?) “ym (stds os We gre 20? ds Ue | ste 20? ds aq oof 2ar 27 J y ee EEE EEEEEEEE SEE e CO C _ ns 2 _ ns? | a sre 20 ds o| gr @ 2o? ds G 0 and summing for all values of s we have as an equation giving the distribution of z a ns? (1+2?) n a Lan s-| ste ds 27 5 02 o aes) ns gn? en 202 ds / 0 By what we have already proved this reduces to ln-2 n- 4 5 2if n be odd, Y= = ) UD eels Tae eS n— 4 4 i ea ea 8 3 ie -9 Cl a )) 2 -2 and to y T (1+2°) ? if n be even. Since this equation is independent of o it will give the distribution of the distance of the mean of a sample from the mean of the population expressed in terms of the standard deviation of the sample for any normal population. Section IV. Some Properties of the Standard Deviation Frequency Curve. By a similar method to that adopted for finding the constant we may find the mean and moments: thus the mean is at Toe N—2 eae: (n—2) (n—4) See , which is equal to Goa) eel ar (if n be even), (n—2)(n—4) 38 To. 01 G=s@lnn2 we aii (if n be odd). By STuDENT ce) The second moment about the end of the range is Li (n = ae dias a n : The third moment about the end of the range is equal to dae saa ; y ea =o’ x the mean, The fourth moment about the end of the range is equal to Ino _ (nu —A(n +1), ae coe oO. ies n” : , D If we write the distance of the mean from the end of the range ~? and the Jn moments about the end of the range 1, r., ete. Do _n-1 De C= 2 Ve oo, wBR=—, w= Eni Nn n Jn nv From this we get the moments about the mean then y= o Pe WD by 5 (n JP), se if , CO oir: , Q) mmr Ls 2 et 2a 48h, o Ge ps = 75 (— 1 — 4D'n + 6 (n— 1) D?- 3D} = “pt — L— (3 Dt — 2n + 6)}. It is of interest to find out what these become when n is large. In order to do this we must find out what is the value of D. Now Wallis’s expression for 7 derived from the infinite product value of sin w is eee Or et (20)? 19437752... (n= I) 7 g (2u + 1)= If we assume a quantity 0 (= Uy +o + ete.) which we may add to the 2n+1 in order to make the expression approximate more rapidly to the truth, it is easy 1 1 to show that 6 = — a+ 16, ~ ete: and we get l ) 2? 4°. 6... (2nyP T 1?.3?.5? 2. Qn =—1) 7 (2 wi 1 Y. ES Coys Ti pease 2 Ilb6n ) a : ' o,o1 From this we find that whether ” be even or odd D? approximates to n— 5 + 8n when n is large. * This expression will be found to giye a much closer approximation to 7 than Wallis’s, Biometrika v1 ‘x 10 The Probable Error of a Mean Substituting this value of D we get | aaa a2 (1 =| — EN Qn" 16n2 oe ( ae i T ) pe on 4m]? oo 4n? Bs Ent 2n V6n7/ Consequently the value of the standard deviation of a standard deviation which we have found Caf) becomes the same as that found for the normal 1 2, Pepi 420 Ve 4n curve by Professor Pearson (¢//2n) when n is large enough to neglect the 1/4 in comparison with 1. Neglecting terms of lower order than - we find 2n—3 1 1 er aay 8.=3(1-5,)(1 +55). Consequently as n increases 8, very soon approaches the value 3 of the normal curve, but 8, vanishes more slowly, so that the curve remains slightly skew. Diacram I, Frequency curve giving the distribution of Standard Deviations of samples of 10 taken from a normal population. 9 = N 10? 2 = SS pA as he = ae 27, Teaoe) Ge mdi Equation y= 7 1:6 N/ = te al : i i 1-4 1g Is 1: 21%) <— ta iS N e (ox ] 'S | . | ra iS i pee Gs ies N ! ig ‘oe a y/ ieee! S aM fi ' ‘S Ay aie il ie lo “150 Diagram I shows the theoretical distribution of the s.D. found from samples of 10. < = 10.22 N18 (2a aoe 1.35 souN. (9,08 SECTION V. Diane .— if n be even n—-2 n—4 1 y i n Some properties of the curve y= (Glee) @. | Or GO| 5 if n be odd n—2 n— 4 p= 3 OSD affords an easy way of drawing the curve. Also dz = d@/cos? 6. Writing z= tan @ the equation becomes y= etc. x cos” @, which By SrupENtT 11 Hence to find the area of the curve between any limits we must find n—-2 n-4 ; ——. , _.... ete. X [cose n-3 n—5 ‘ = este ie se ... eb” ee | cos” 4 0d + eoaie cu at n—-3 n—5 \n—2. n—2 me s a= iy peereuc, [ cos" 6d0 + ae en ... ete. [cos”-? @ sin 8], n-5 n-T7 n-38 n-5 ; and by continuing the process the integral may be evaluated. For example, if we wish to find the area between 0 and @ for n=8 we have Obeset 2. Mie |e. area= 5.3.4 -7 | cos 6dé 5 a 5) =5--.| Beoiot. =) = cosh e Sine > TT 0 5.3 7 gv 2 : 1 ‘ i Ae, , : = ey eee cos? 9 sin € +—.=.— cos’ @sin 6, Tv 3° °T Oe TTg and it will be noticed that for n=10 we shall merely have to add to this same : eG wate. 2 Sk expression the term 75 y+ 7 008 é sin 0. The tables at the end of the paper give the area between — % and z (or — 5 and @= tan 2) ; This is the same as 5+ the area between 06=0, and @=tanz, and as the whole area of the curve is equal to 1, the tables give the probability that the mean of the sample does not differ by more than z times the standard deviation of the sample from the mean of the population. The whole area of the curve is equal to Tv 7+ saa GO, >< | : cos”? 6dé, n—-2 n—4 n—-3°>n-5 t and since all the parts between the limits vanish at both limits this reduces to 1. Similarly the second moment coefficient is equal to a Peni — A p= Oy ee 4 ... ete. X [ ~ cos”? 6 tan? 0dd » n—-2 n—4 sige 2 = ... ete, x | (cos"— @ — cos” 6) dé us 2 n—3 n—5 n—2 1 Tob SoS 12 The Probable Error of a Mean Hence the standard deviation of the curve is 1/¥n—3. The fourth moment coetticient is equal to += n—-2 n-4 2 ; =) ... etc. Xx | cos” @ tant 6dé n—-3 n—5 a T n-2 n—4 _ ee EF 3 =—.. =~ ++. etc. X (cos”°@— 2 cos”*@ + cos” 6) dé n—-3 n—5 mu 5 n—-2 n-4 2(n—-—2 3 = (aa [jo ee n—-3 n—-—5 n—-—3 (n — 3) (n — 5) The odd moments are of course zero as the curve is symmetrical, so 0 oe 3(n —3) = 2 3+ a n—5 n—od Hence as » increases the curve approaches the normal curve whose standard deviation is 1/Vn — 3. 8, however is always greater than 3, indicating that large deviations-are more common than in the normal curve. ; N 8 6 2 Diacram II. Solid curve y=5 X= pegs eos!” 6, x/s= tan @. ‘ oOo 7 A J7 -N ~je 4 Broken line curve y= -e “*, the normal curve with the same s.p. See 1:5$ 1:0S “5S Os 5S Distance of mean from mean of population I have tabled the area for the normal curve with standard deviation 1/V7 so as to compare with my curve for »=10*. It will be seen that odds laid according to either table would not seriously differ till we reach z=°8, where the odds are about 50 to 1 that the mean is within that limit: beyond that the normal curve gives a false feeling of security, for example, according to the normal curve it is 99,986 to 14 (say 7000 to 1) that the mean of the population lies between — 0 and + 1°3s whereas the real odds are only 99,819 to 181 (about 550 to 1). * See p. 19. By StTupDENtT 13 Now 50 to 1 corresponds to three times the probable error in the normal curve and for most purposes would be considered significant ; for this reason I have only tabled my curves for values of n not greater than 10, but have given the n=9 and n= 10 tables to one further place of decimals. They can be used as foundations for finding values for larger samples*. The table for n=2 can be readily constructed by looking out @= tan z in Chambers’ Tables and then ‘5 + 6/7 gives the corresponding value. Similarly 4 sin 6+°5 gives the values when n= 38. There are two points of interest in the n =2 curve. Here s is equal to half ; : 8 the distance between the two observations. Uae 7 so that between +s and 4 a u or half the probability, ie. if two observations have been made Tv 4 and we have no other information, it is an even chance that the mean of the (normal) population will lie between them. On the other hand the second moment coefficient is —s lies 2 x +2 15 ~| : tan? Odd = be jan é-— a| =, T T 7 or the standard deviation is infinite while the probable error is finite. Section VI. Practical Test of the foregoing Equations. Before I had succeeded in solving my problem analytically, I had endeavoured to do so empirically. The material used was a correlation table containing the height and left middle finger measurements of 3000 criminals, from a paper by W. R. Macdonell (Biometrika, Vol. 1. p. 219). The measurements were written out on 8000 pieces of cardboard, which were then very thoroughly shuffled and drawn at random. As each card was drawn its numbers were written down in a book which thus contains the measurements of 3000 criminals in a random order. Finally each consecutive set of 4 was taken as a sample—750 in all—and the mean, standard deviation, and correlation+ of each sample determined. The difference between the mean of each sample and the mean of the population was then divided by the standard deviation of the sample, giving us the z of Section ITI. This provides us with two sets of 750 standard deviations and two sets of 750 z’s on which to test the theoretical results arrived at. The height and left middle finger correlation table was chosen because the distribution of both was approximately normal and the correlation was fairly high. Both frequency curves, however, deviate slightly from normality, the constants being for height 8, = 0026, £,=3'175, and for left middle finger lengths 8,=-0030, 8,=3°140, and in consequence there is a tendency for a certain number of larger standard deviations to occur than if the distributions were normal. This, however, appears to make very little difference to the distribution of z. * E.g. if n=11, to the corresponding value for n=9, we add 2x%x8x4xeos’ sind: if n=13 we add as well x3x8x#x4x4cos!0@ sin 6 and so on. + I hope to publish the results of the correlation work shortly. 14 The Probable Error of a Mean Another thing which interferes with the comparison is the comparatively large groups in which the observations occur. The heights are arranged in 1 inch groups, the standard deviation being only 2°54 inches: while the finger lengths were originally grouped in millimetres, but unfortunately I did not at the time see the importance of having a smaller unit, and condensed them into two millimetre groups, in terms of which the standard deviation is 2°74. Several curious results follow from taking samples of 4 from material disposed in such wide groups. ‘The following points may be noticed : (1) The means only occur as multiples of °25. (2) The standard deviations occur as the square roots of the following types of numbers n, n +19, n+ °25, n+ °50, n+ °69, 2n+°75. (3) = > Sa) ~ a ony . a : nz of prandard 5 m 5 5 ° 5 alten pe a x a is es me 2 ia deviationof; & 8 $ 5s | + = + Ho eh Sei eae |e 2 + ~e |} | O88 population | S [4 |e jo | = ‘2 © |r |olagie/n{/ele; zis io {ss : | Sa ek Sh iid ost IWR neeseellea ote | | Calculated | | | | frequency | 14 |103| 27 |453| 645 | 784 | 87 | 88 |S1$| 71 |58 | 45 | 33 | 23 | 15 | 93 | 5$| 7 Observed at | frequency | 3 |14$) 244 | 374] 107 67 73°) 77 77h | 64 | 524) 493) 35 | 28 | 125 | 9 |114! 7 | | | = = . | | 3 ! ee a | | | | | i Difference | +14) +4| —23| -8/ +423) -114] -14| -11] —4| —7/-53)+43) 42/45 -24) -3}.4+6| 0 | | | | ; whence x?=48:06, P=-000,06 (about). In tabling the observed frequency, values between ‘0125 and ‘0875 were included in one group, while between ‘0875 and (0125 they were divided over the two groups. As an instance of the irregularity due to grouping I may mention that there were 31 cases of standard deviations 1:30 (in terms of the grouping) which is :5117 in terms of the standard deviation of the population, and they were therefore divided over the groups ‘4 to °5 and ‘5 to 6. Had they all been counted in groups °5 to “6 x? would have fallen to 29°85 and P would have risen to ‘03. The y? test presupposes random sampling from a frequency following the given law, but this we have not got owing to the interference of the grouping. When, however, we test the z’s where the grouping has not had so much effect: we find a close correspondence between the theory and the actual result. There were three cases of infinite values of z which, for the reasons given above, were given the next largest values which occurred, namely +6 or —6. The rest were divided into groups of ‘1; ‘04, (05 and ‘06, being divided between the two groups on either side. The calculated value for the standard deviation of the frequency curve was 1 (+017) while the observed was 1:039. The value of the standard deviation is really infinite, as the fourth moment coetficient is infinite, but as we have arbi- trarily limited the infinite cases we may take as an approximation from 1 4/1500 which the value of the probable error given above is obtained. The fit of the curve is as follows :— 16 The Probable Error of a Mean Comparison of Fit. Theoretical Equation: y == cos'6, z= tan 0. ‘ ate re = _ wD | WWD 9 WwW WD iS IP aXe, toy WwW WD Sf = ies) Ss Ss [aoe aes > Seek Se = | 2 | = | Say Sy) ~s 1 ON i aa ™ ™ Bare | paee! i a Sy) Sa) S| ep ar ie a a baal a ear | et | i Seen er =e | 2 a lage eee i tS Scale of 2 | = = Sie nS AP) | es » B58 | aS g 2 2) mn) s a wD IW | 1 ak toy Key WD wD | Io Ve wD 1D Ney 35) i S S57) XS r NS > ~ ~ | = RS Ss WD Ss o n . is ry ~ . . . . . | 7 | . = = os 89 RQ | oN | \ oN ™ NR 2 S ya | | | ar ar | S) a | leu 3 | | sie) || ate ar || Calculated | | | | | frequency | 5 | | Observed | | | frequency | 9 | 144|11$| 33 | 433] 703 1193] 151% | 122] 674 | Difference +4) +5 | 14| -1 | +3 | +103) +3) -11 whence y?=12°44, P="56. This is very satisfactory, especially when we consider that as a rule observa- tions are tested against curves fitted from the mean and one or more other moments of the observations, so that considerable correspondence is only to be expected ; while this curve is exposed to the full errors of random sampling, its constants having been calculated quite apart from the observations. Diacram III. Comparison of Calculated Standard Deviation Frequency Curve with 750 actual Standard Deviations. 100 ai catharsis] 80 60) 40 Frequency per ~sthe 20 1 6-2 3 <4 1-5 -6 +7 <8 =O) 4-9 (1-1 1:05 VR edeAD AR eRe 4270 1:8) 129190 0-12. OlO SRORAROI 5) Scale of Standard Deviation of the Population The left middle finger samples show much the same features as those of the height, but as the grouping is not so large compared to the variability the curves fit the observations more closely. Diagrams III.* and IV. give the standard devia- tions and the 2’s for this set of samples. The results are as follows :— * There are three small mistakes in plotting the observed values in Diagram III., which make the fit appear worse than it really is. 1 KY By STUDENT ajdups ayy fo uoymraag pvpunig fo ovo¢ ‘sasvo Qc) Jo afduies yengoe ue YIN ‘ (+1) = = fi aamo Xouonbary [woyatoayy ayy jo uostavdwiog ‘AT NVYOVIG 6- Biometrika v1 18 The Probable Error of a Mean Mean value of standard deviations ; calculated 2:186 + 023 . FF . observed 2:179 Difference =— ‘007 Standard deviation of standard deviations :— Calculated °9224 + 016 Observed ‘9802 Difference = + ‘0578 ; : ee ‘ : 16 x 750 we Comparison of Fit. Theoretical Equation: y= ———ae °°. N20? mil, , olu le |) so Stare | Scale interms | ~ 2 % tS | 9 N ce) a | eS ie a a a Sikes of standard } es los 5 5 S S 5 at 5 ° ° } } } o |e deviationof | S | 5 wo | 4 | 45 = | 2 a = ic & aS 45 aS 42 a 5 g al} population |S] |e |e |e) se jo] = | © | a | so | om | 1 emcees . , [oN | 4 N = —_ _ a | i | Calculated frequency | 14 | 10$ | 27 | 453 | 643) 783 | 87 88 814 | 71 | 58 | 45 | 33 | 23 | 15 93) 53] 7 Observed frequency | 2 | 14 /273/ 51 |644/ 91 | 944 | 68} | 654 | 73 | 484 | 404 | 423 | 20 | 293 | 12 | 5 | 72 | | | Difference | +3 | +31 +4| 4+53| — | +123|.4+74| —19}| —16| +2|—9n| —4h) 0R )3 eye eeu whence x?=21°80, P='19. Calculated value of standard deviation 1 (+017) Observed 982 hl 2? ” Difference =— ‘018 Comparison of Fit. Theoretical Equation: y= 2 cos!@, z= tan 0. ito is 5 | —ed| Xs) S S 3 3 19 | 9 pa | 6 toy toy SS Fue 3S Sa) & N N ‘. | ae aa ea S = | ~ sy] os SD Po} Pp beepere poh bp | ry ae ae ee a eee Scaleofz|4@)/¢/|2g|2|]28] 8 18|s1|-98 |-s 1212 \2ealgeme a Vey Vey LS eS) | wD vey toy Wa i ates We wD | © XS) es SPANPSAR |r Nee (Ok | Ee OLeewt he eee ell ee Pees ee | = © SP) RQ ™ eaten ented QQ | ce ee ee peice | ES Calculated | | | | frequency | 5 | 93) 13} | 344 443) 78 |119]}141/119 | 784} | 443) 343 | 182 | 93 | 5 Observed | _ | | frequency | 4 |155] 18 | 333) 44 | 75 |122/138)120$) 71 |464) 36 | 11 | 9 6 ees | Pe | 2 all | | <—il | [esas os | | | | _ Difference —-1'4+6 443) -1 =} —33) 43] -3/ +15) -7$) 42 413] -23| -$/ 41 | | | | whence x?=7°39, P=-92. A very close fit. We see then that if the distribution is approximately normal our theory gives us a satisfactory measure of the certainty to be derived from a small sample in both the cases we have tested; but we have an indication that a fine grouping is of advantage. By STUDENT 1) If the distribution is not normal, the mean and the standard deviation of a sample will be positively correlated, so that although both will have greater variability, yet they will tend to counteract each other, a mean deviating largely from the general mean tending to be divided by a larger standard deviation Consequently I believe that the tables at the end of the present paper may be used in estimating the degree of certainty arrived at by the mean of a few experiments, in the case of most laboratory or biological work where the distribu- tions are as a rule of a ‘cocked hat’ type and so sufficiently nearly normal. = odd 3 ac x ry 5) tan—!z Srotion VII. ‘ables of “~~ ~ i We . cos" 6 dd n—-3 n— my Al -5 = .— neven 2 l & for values of n from 4 to 10 inclusive. 7 pe Together with —— | e = dx for comparison when n= 10. V2arJ - 2% | For comparison :(=2) n=4 n=5 n=6 n=7 n=8 n=9 n—10 (= fi > | Rn) = | ‘1 5633 “5745 5841 5928 6006 | -60787 | 61462 ‘60411 2 6241 6458 6634 6798 6936 | “70705 | *71846 “70159 3 6804 "7096 *7340 "7549 7733 | *78961 | *80423 ‘78641 “4 “7309 ‘7657 *7939 8175 8376 | 85465 | -86970 85520 2) ‘7749 8131 *8428 8667 *8863 | *90251 | -91609 ‘90691 6 8125 8518 8813 “9040 9218 | -93600 | -94732 94375 ail *8440 *8830 ‘9109 9314 9468 | 95851 | -96747 ‘96799 8 ‘8701 ‘9076 9332 9512 9640 | -97328 | -98007 98253 og) 8915 "9269 9498 9652 ‘9756 | 98279 | :98780 99137 1:0 ‘9092 "9419 | "9622 ‘9751 9834 | ‘98890 | -99252 99820 | 11 9236 95387 | “9714 9821 ‘9887 ‘99280 | *99539 99926 12 9354 | -9628 | -9782 ‘9870 "9922 | -99528 | °99713 99971 13 9451 ‘9700 | *9832 ‘9905 | ‘9946 | -99688 | :99819 ‘99986 14 9531 ‘9756 | -9870 9930 ‘9962 | -99791 | -99885 ‘99989 15 9598 ‘9800 | ‘9899 9948 ‘9973 | -99859 | -99926 99999 16 9653 | *9836 +9920 ‘9961 9981 99903 | °99951 IEG ‘9699 | -9864 | ‘9937 ‘9970 ‘9986 | -99933 | -99968 1°8 ‘9737 9886 -9950 9977 9990 | -99953 | *99978 19 ‘9770 | 9904 ‘9959 9983 "9992 | 99967 | *99985 2°0 ‘9797 9919 9967 9986 9994 | -99976 | -99990 2°1 9821 9931 9973 ‘9989 ‘9996 | -99983 | -99993 2°2 9841 9941 9978 9992 ‘9997 | 99987 | -99995 2°3 9858 9950 “9982 9993 9998 | :99991 | -99996 2°4 ‘9873 9957 “9985 "9995 "9998 | -99993 | -99997 2°5 ‘9886 9963 9987 ‘9996 "9998 | -99995 | -99998 2°6 9898 9967 ‘9989 “9996 ‘9999 | -99996 | -99999 2°7 9908 9972 ‘9991 | +9997 "9999 | 99997 | -99999 | 2°8 9916 ‘9975 9992 | -9998 ‘9999 | -99998 | :99999 2°9 9924 9978 | :9993 | +9998 9999 | 99998 | :99999 | 3°0 9931 | -9981 :9994 9998 — "99999 | = — = 20 The Probable Error of a Mean Section VIII. Laplanation of Tables. The tables give the probability that the value of the mean, measured from the mean of the population, in terms of the standard deviation of the sample, will lie between — 0 and z. Thus, to take the table for samples of six, the probability of the mean of the population lying between — © and once the standard deviation of the sample is °9622 or the odds are about 24 to 1 that the mean of the population lies between these limits. The probability is therefore (0378 that it is greater than once the standard deviation and ‘0756 that it lies outside + 1:0 times the standard deviation. Section IX. Tllustrations of Method. Illustration I. As an instance of the kind of use which may be made of the tables, I take the following figures from a table by A. R. Cushny and A. R. Peebles in the Journal of Physiology for 1904, showing the different effects of the optical isomers of hyoscyamine hydrobromide in producing sleep. The sleep of 10 patients was measured without hypnotic and after treatment (1) with D. hyoscyamine hydrobromide, (2) with L. hyoscyamine hydrobromide. The average number of hours’ sleep gained by the use of the drug is tabulated below. The conclusion arrived at was that in the usual dose 2 was, but 1 was not, of value as a soporific. ; Additional hours’ sleep gained by the use of hyoscyamine hydrobromide. Patient 1 (Dextro-) 2 (Laevo-) Difference (2-1) I. + 67 +1°9 +12 2 —16 + °8 + 24 3. — 2 +11 +13 4. —12 ae +153 5 -—1 - il 0 6. +3°4 + 44 +1:0 7. +3°7 + 55 +18 8. + 8 +16 + 8 a: 0 + 4°6 +46 10. + 2°0 + 3°4 +14 Mean + °75 Mean + 2°33 Mean + 1°58 S.D. 1:70 S. D. 1:90 S. D. 117 First let us see what is the probability that 1 will on the average give increase of sleep; i.e. what is the chance that the mean of the population of which these +°75 T70 = ‘44 and looking out z="44 in the experiments are a sample is positive. By STUDENT oA table for ten experiment we find by interpolating between 8697 and ‘9161 that °44 corresponds to ‘8873, or the odds are ‘887 to ‘113 that the mean is positive. That is about 8 to 1 and would correspond in the normal curve to about 1‘8 times the probable error. It is then very likely that 1 gives an increase of sleep, but would occasion no surprise if the results were reversed by further experiments. If now we consider the chance that 2 is actually a soporific we have the mean increase of sleep = 13 or 1:23 times the s.p. From the table the probability corresponding to this is ‘9974, 1e. the odds are nearly 400 to 1 that such is the ease. This corresponds to about 4:15 times the probable error in the normal curve. But I take it the real point of the authors was that 2 is better than 1. This we must test by making a new series, subtracting 1 from 2. The mean value of this series is + 158 while the s.D. is 1:17, the mean value being + 1°35 times the sD. From the table the probability is ‘9985 or the odds are about 666 to 1 that 2 is the better soporific. The low value of the S.D. is probably due to the different drugs reacting similarly on the same patient, so that there is corre- lation between the results. Of course odds of this kind make it almost certain that 2 is the better soporific, and in practical life such a high probability is in most matters considered as a certainty. Illustration II. Cases where the tables will be useful are not uncommon in agricultural work, and they would be more numerous if the advantages of being able to apply statistical reasoning were borne in mind when planning the experi- ments. I take the following instances from the accounts of the Woburn farming experiments published yearly by Dr Voelcker in the Journal of the Agricultural Society. A short series of pot culture experiments were conducted in order to deter- mine the causes which lead to the production of Hard (glutinous) wheat or Soft (starchy) wheat. In three successive years a bulk of seed corn of one variety was picked over by hand and two samples were selected, one consisting of “hard” grains and the other of “soft.” Some of each of these were planted in both heavy and light soil and the resulting crops were weighed and examined for hard and soft corn. The conclusion drawn was that the effect of selecting the seed was negligible compared with the influence of the soil. This conclusion was thoroughly justified, the heavy soil producing in each case nearly 100 per cent. of hard corn, but still the effect of selecting the seed could just be traced in each year. But a curious point, to which Dr Voelcker draws attention in the 2nd year’s report, is that the soft seeds produced the higher yield of both corn and straw. In 22 The Probable Error of a Mean view of the well-known fact that the varietves which have a high yield tend to produce soft corn, it is interesting to see how much evidence the experiments afford as to the correlation between softness and fertility in the same variety. Further, Mr Hooker* has shown that the yield of wheat in one year is largely determined by the weather during the preceding harvest. Dr Voelcker’s results may afford a clue as to the way in which the seed is affected, and would almost justify the selection of particular soils for growing seed wheat +t. The figures are as follows, the yields being expressed in grammes per pot. Year 1899 1900 1901 ee _ : (ae ae . Standard | Average | Deviation| 7 Soil Light | Heavy) Light | Heavy| Light | Heavy Yield of corn from soft seed 7°85 | 8:89] 14°81] 13°55!| 7°48 1 15:39] 11°328 Re hard ,, 7:27 | 8:32 | 13:81) 13:36°)7-97 | 13:13.) 10:643 Difference... sae .. | €°58 | +°57|/4+1:00} +:'19 | — 49 |4+2°26] +:°685 ‘778 88 Yield of straw from soft seed | 12°81 | 12°87 | 22°22 | 20°21 | 13°97 | 22°57 | 17°442 . - hard ,, | 10°71 | 12°48 | 21-64 | 20°26 | 11°71 | 18°96 | 15°927 Difference... soe ... | +2710) +°39 | +°78} —:05 |4+2°66 (+3°61 +1°515 1261 1:20 | | If we wish to find the odds that soft seed will give a better yield of corn on the average, we divide the average difference by the standard deviation, giving us z='88. Looking this up in the table for n=6 we find p=‘9465 or the odds are 9465 : 535, about 18:1. Similarly for straw z= 1:20, p ="9782, and the odds about 45: 1. In order to see whether such odds are sufficient for a practical man to draw a definite conclusion, I take another set of experiments in which Dr Voelcker com- pares the effects of different artificial manures used with potatoes on the large scale. The figures represent the difference between the crops grown with the use of sulphate of potash and kainit respectively in both 1904 and 1905. ewt. qr. Ib. ton cwt. qr. Ib. 1904 +10 3 20:+1 10 1 26 19095 + 6 0 3:4 1332S * Journal of Royal Statistical Society, 1907. + And perhaps a few experiments to see whether there is a correlation between yield and ‘ mellow- ness’ in barley. (two experiments in each year). By STUDENT 23 The average gain by the use of sulphate of potash was 15°25 ewt. and the S.D. 9 ewt., whence, if we want the odds that the conclusion given below is right, z=1°7 corresponding, when n= 4, to p= ‘9698 or odds of 32:1; this is midway between the odds in the former example. Dr Voelcker says ‘It may now fairly be concluded that for the potato crop on light land 1 cwt. per acre of sulphate of potash is a better dressing than kainit.’ As an example of how the tables should be used with caution, I take the following pot culture experiments to test whether it made any ditference whether large or small seeds were sown. Illustration ITT. 111899 andin 1903“ head corn” and “ tail corn” were taken from the same bulks of barley and sown in pots. The yields in grammes were as follows: 1899 19038 Large seed ...... 13°9 73 Small seed ...... 144 87 +5 +°6 The average gain is thus ‘55 and the s.p. ‘05, giving z=11. Now the table for n=2 is not given, but if we look up the angle whose tangent is 11 in Chambers’ tables, __tan?ll 84° 47’ [soe 1p aso so that the odds are about 33:1 that small corn gives a better yield than large. These odds are those which would be laid, and laid rightly, by a man whose only knowledge of the matter was contained in the two experiments. Anyone con- versant with pot culture would however know that the difference between the two results would generally be greater and would correspondingly moderate the certainty of his conclusion. In point of fact a large scale experiment confirmed the result, the small corn yielding about 15 per cent. more than the large. I will conclude with an example which comes beyond the range of the tables, there being eleven experiments. To test whether it is of advantage to kiln-dry barley seed before sowing, seven varieties of barley were sown (both kiln-dried and not kiln-dried) in 1899 and four in 1900; the results are given in the table. It will be noticed that the kiln-dried seed gave on an average the larger yield of corn and straw, but that the quality was almost always inferior. At first sight this might be supposed to be due to superior germinating power in the kiln-dried seed, but my farming friends tell me that the effect of this would be that the kiln-dried seed would produce the better quality barley. Dr Voelcker draws the conclusion “In such seasons as 1899 and 1900 there is no particular advantage in kiln-drying before sowing.” Our examination completely justifies this and adds 24 The Probable Error of a Mean “and the quality of the resulting barley is inferior though the yield may be greater.” Price of head corn in Value of crop per lbs. head corn per acre cod ts. str > ERR f 240) pets shillings per quarter ewts. straw per acre in shillings * acre N. K.D | K.D. | Diff. JN. K.D.) K. D. Diff. }N. K. D.| K. D.| Diff. JN. K.D.| K. D. | Diff. —— | ot (ees CS pee Neca = = aoe ,; 1903 | 2009 | +106 264 264 0) 194 25 +53 1403 152 +113 1935 | 1915 | — 20] 28 261 | —12] 223 240 | +12) 152h aieiaa 79 1910 2011 +101 294 283 —] 23 24 | +1 1583 161 +24 18994 | 2496 2463 — 33] 30 29 =i 23 28 | +5 2044 | 199} | —5 2108 | 2180 | + 72] 273 ype ex 224 921 | 0 162 164. | +2 | 1961 | 1925 | - 36] 26 26 0 19% 193 | —} 142 139} | —23 2060 | 2122 | + 62 29 26 —3 244 224 — 27 168 155 —13 | 1444 1482 + 38 294 28) -—1 15} | «(16 +4 118 1174 | -4 cen 1612 | 1542 | - 70] 284 meer 18 174 | -3 PS | ie Paye | 1316 | 1443 | +127] 30 209 leat 14} 15g} +14 | Joo | 1162 | 47 1511 1535 | + 24] 283 28 | <2 17 17s ee 120 120% || +2 = ; — — — — Average | 1841°5 | 1875°2 | +33°7] 28:45 27°55 | —"91f 19°95 | 21°05) 41°10] 145°82 | 144-68 | +114 Standard ) | ee | "7 | 9-96 6 Deviation) = 63°1 - sack el Roy = — | 2:25 = — | 6:67 Standard Deviation - -- 22°3 — -— 28 — — 80 _ _- 2°40 +,/8 * Straw being valued at 15s. per ton. In this case I propose to use the approximation given by the normal curve with standard deviation ——— 2 /(n — 3) the ditference divided by 7a: The probability in the case of yield of corn per aud therefore use Sheppard’s tables, looking up 223 or the odds are about 14:1 that kiln-dried corn gives the higher yield. =1:51 in Sheppard’s tables. This gives p= ‘934, acre is given by looking up Similarly = 3:25, corresponding to p=‘9994,* so that the odds are very great that kiln-dried seed gives barley of a worse quality than seed which has not been kiln-dried. Similarly it is about 11 to 1 that kiln-dried seed gives more straw and about 2:1 that the total value of the crop is less with kiln-dried seed. * As pointed out in Section V. the normal curve gives too large a value for p when the probability is large. I find the true value in this case to be p="9976. It matters little however to a conclusion of this kind whether the odds in its favour are 1,660:1 or merely 416; 1. By STUDENT 25 SECTION X. Conclusions. I. Accurve has been found representing the frequency distribution of standard deviations of samples drawn from a normal population. II. A curve has been found representing the frequency distribution of values of the means of such samples, when these values are measured from the mean of the population in terms of the standard deviation of the sample. III. It has been shown that this curve represents the facts fairly well even when the distribution of the population is not strictly normal. IV. ‘Tables are given by which it can be judged whether a series of experiments, however short, have given a result which conforms to any required standard of accuracy or whether it is necessary to continue the investigation. Finally I should like to express my thanks to Professor Karl Pearson, without whose constant advice and criticism this paper could not have been written. Biometrika v1 4 SPLIT-HAND AND SPLIT-FOOT DEFORMITIES, THEIR TYPES, ORIGIN, AND TRANSMISSION™. By THOMAS LEWIS, D.Sc. M.D. etc. and DENNIS EMBLETON, B.A., M.R.GS. ete. (From University College Hospital.) CONTENTS. PAGE Introductory . : : : : : 26 Detailed Account of ihe Determines of the ns q” Fammilee : : 27 Types of Split-foot, their Terminology, and the Nature of the Oe: Bones é 36 Origin and Transmission of the Deformity ; ; : : : 2 2 43 (a) General. : : : : ; : : : : : : 0 43 (b) Maternal impressions : : 6 : : : : 44 (c) Origin in an acquired lesion (extmteene) 5 3 , : : : 44 (d) Arrests of development. : 3 : : : : 5 oe 45 (e) Atavism . : 2 : : : 3 ; 45 (f) Origin as a result of Pereterine pendieioas : : : : : 2 46 (g) Origin as a “sport” : 48 (hk) Transmission of “ ete diary Split. (on ‘ ate nT eval the rolntion of its mode of transmission to Mendelism . : : : : : 50 Summary and Chief Conclusions . : : : : : : : : : 56 Bibliography . : : ; , : ; : : ; : : : : 56 Explanation of Plates . . : : : : . c . : : 58 Introductory. THE deformity presented by the family described in this communication is one of exceptional interest and has so far received little attention. Accounts of it, of a brief and scattered nature, sometimes with figures, are to be found in the works of many of the well-known teratologists, such as Geoffroy Saint-Hilaire, Ammon, Forster and Otto. In a Japanese temple an image of it has assumed, states Perthes (p. 136), the dignity of a god; a cloven hoofed deity. * To this paper, written in November 1907, a short postscript, dated March 2nd, 1908, has been added. It will be found in the Miscellanea of this number. Biometrika, Vol. VI. Part I. : oN 9 Se eee . \ 1 oe bine Ales ‘ . x . Biometrika, Vol. VI, Part | Fic. 10 Fic. 12 Fic. 13 Plate IV Biometrika, Vol. VI, Part | Plate V Fie. 14 Fia. 16 Fic. 17 Plate VI Biometrika, Vol. VI, Part | Fic. 19 Fic. 18 21 Te Pr Fira. 20 Biomeirika, Vol. VI, Part I Plate VII Fic. 24 Fic, 25 — a - eS ¥ a é 7 7 4 re mad 5 vad! = 4 T if) \ - = « 2 . T. Lewis anpD D. EmBLETOoN 33 Left hand. This is the most malformed of the series (Fig. 17). There are three heavy metacarpals articulating with the trapezium, os magnum and unciform bones. They probably represent the 3rd, 4th and 5th metacarpals. From the 4th springs a bone resembling a phalanx which articulates with the outer side of a welded mass of bone which itself springs from the head of the 5th metacarpal. The welded mass is 2 inches long and about 1 inch broad, It lies in the line of the metacarpal, from which it springs. At the free end of the mass are two terminal projections resembling short horns. The inner bears two small nodules of bone and a double nail. The outer has no nail. Between it and the inner are two small nodules of bone. There is thus evidence that the mass as a whole represents the portions of at least the inner three fingers. The feet. There is one digit on each foot in the position of the 5th toe. Each bears three phalanges. The metatarsal at its base is thick and articulates with the whole of the anterior surface of the cuboid. The base of the 1st metatarsal is represented on both sides, and on the right probably the base of the 3rd also. (V, 25.) Miscarriage, 4 months pregnancy. The mother states that the child had one finger and one toe on each limb, (V, 27.) L. A. (1885, single, suffering from tuberculosis of the lungs). Right handed. Screening of all extremities. Right hand. This is almost perfect but shows contractures, the thumb is small, the index finger is flexed. There is skin union of the 3rd and 4th fingers and slight bony union of the terminal phalanges. The bones are otherwise normal. Left hand. The 1st metacarpal is surmounted by a small nodule of bone only. The 2nd metacarpal has one complete and a second incomplete phalanx. The remaining three fingers are normal. Between the 2nd and 3rd fingers is a small piece of bone about 14 cm. long, thin and narrow. It is on a level with the Ist phalanges and has the shape of a diminutive phalanx. Right foot. On the inner side of the cleft the Ist toe is complete. On the outer side the inner toe is complete and to its inner side is a mass of bone obviously representing the 3rd and 4th metatarsals. Left foot. On the inner side of the cleft the 1st toe is complete. On the outer side the 5th toe has metatarsal only. The 4th metatarsal has one complete and one incomplete phalanx, it is united at its base with the remains of the 3rd metatarsal. (V, 28.) H. A. (1887- approx. 1895). Tubby states that this child had two fingers on each hand and two toes on each foot. (V, 31.) J. A. (approx. 1892-1897). We are indebted to St Thomas’s Hospital for notes of this child*. Right hand. The thumb is not represented. The 5th finger has a full complement of phalanges. The 2nd, 3rd and 4th metacarpals are poorly developed and have no phalanges. Left hand. Much the same as the right, but has two sets of phalanges for 4th and 5th fingers. Right foot. Great and little toes only, of which the metatarsals are alone perfect. The cleft extends to the articulation between the metatarsal and the internal cuneiform. Left foot. The same as the right, but the great toe has the stump of a metatarsal only. (V, 36.) M. A. (approx. 1902-1905). The mother states that there was the usual deformity of the feet, each having two toes. The hands are said to have had one finger each, * The notes are ward notes, there was no screening. Biometrika v1 5 34 Split-Hand and Split-Foot Deformities (V, 38.) J. A. (1906—1906). Screening of extremities. The child was born by the vertex, forceps were used and labour was prolonged. The after-birth was normal and there were no signs of adhesions or amputated digits. The post-mortem some months later was not obtainable. Right hand. The five metacarpals were present though the Ist was small and bore no phalanges. The 2nd, 4th and 5th fingers had complete bones. The 3rd metacarpal had a phalanx double at its distal end and this in turn bore two complete sets of phalanges. The 2nd, 3rd and 4th fingers, namely four sets of phalanges, were united by skin (cp. Left hand of H. G. (V, 7)). Left hand. This was normal. The feet. The deformity was typical, the feet having each two toes, separated by wide clefts. The increased thickness of the Ist and 5th metatarsals and the general conformity of the foot to the type in other members of the family is of interest in that it indicates that little of the permanent adult deformity is due to use. (V, 39.) E. W. G. (1886, living). Right handed. All extremities screened. Right hand. Precisely similar to the left hand of R. E. G. which is figured (Fig. 7), except that its epiphyses are joined and that the 3rd metacarpal has no head. Left hand. This is the same as the right but it has the head of the 3rd metacarpal. The feet. The 1st and 5th toes are present with the full number of bones. The clefting is deep and the tarsus disturbed. There is welding of the remains of the 2nd and 4th metatarsals to the adjacent bones. (V, 40.) E. M. G. (1888, living, single). Ambidextrous, Skiagraphy of all extremities. Right hand, Fig. 13. There is no trace of the bones of the thumb. The remaining meta- carpals are present. The 3rd bears a half phalanx. From the distal end of the 4th a large complex cross-bone extends to the head of the 5th, articulating with it and the conjoined bases of the two phalanges, presumably those of the 4th and 5th fingers. The united phalanges are separate at their distal ends, and bear, the inner one, the outer two phalanges, the latter united. We are inclined to the view that the 1st phalanx of the 5th finger is represented in the inner end of the cross-bone. Left hand, Fig. 12. The base only of the 1st metacarpal is present. The 2nd meta- carpal is thin and like the 1st bears no phalanges. The remaining metacarpals are present and of them the 4th and 5th have the full complement of phalanges, the two sets syndactylised by skin. From the head of the 3rd metacarpal a curved cross-bone proceeds to the metacarpo- phalangeal joint of the 4th finger. Right foot, Fig. 15. On the inner side of the cleft is the 1st metatarsal bearing two phalanges. On the outer side are the 4th and 5th metatarsals, carrying between them two sets of united phalanges. The clefting is deep and causes some displacement and modification of the tarsus. Left foot. This is practically identical; the middle cuneiform appears to be welded to the base of the 4th metatarsal. (V, 41.) R. E. G. (1890, living). Right handed. Skiagraphy of all extremities. hight hand, Figs. 4 and 7. The thumb is entirely absent. ‘The 2nd metacarpal misses its distal end, the remainder are complete. The 5th finger is complete, the base of the 1st phalanx has a double articulation, the one facet for the metacarpal the other for the cross- bone which extends from this joint to the head of the 4th metacarpal. Left hand, Figs. 4 and 6. This is similar, except that the 2nd metacarpal is represented by its base only. Right foot, Figs. 5 and 9. There are the usual two toes and deep clefting. The outer toe has two phalanges, the inner two irregular ones. The base of the 4th metatarsal is represented. — T. Lewis AND D. EMBLETON - 35 The middle cuneiform appears to be absent, while the external seems to be welded to the cuboid. Left foot, Figs. 5 and 8. This is similar, but the base of the 4th metatarsal is welded to that of the 5th. (V, 42.) J. T. G. (1892, living). Right handed. Skiagraphy of all extremities. Right hand, Fig. 19. The thumb is not represented. The four outer metacarpals are present, the 2nd being thin. The 4th and 5th have complete sets of phalanges. 9.27011, aye alone dealt with. + It is true that examples of split-foot and polydactyly of the hands are reported in three successive generations, yet in no case are the deformities identical. T. Lewis AnD D. EMBLETON 51 The partial suppression of deformity in one generation has been referred to in dealing with atavism, but the latter, even if applicable as a term, offers no reasonable explanation of the phenomenon. It might be supposed that this partial “latency” could be brought about by the intervention of other characteristics which might themselves be transmitted*. As it is only in exceptional cases that the deformity of a parent is a gauge, and even then a by no means strictly accurate one, of the malformation which will appear in the offspring; and as at the same time the deformities in both parent and offspring, as in all members of a family, may be said to have been cast in the same mould, there is strong presumptive evidence that the inheritance depends on the transmission of some common factor. That representatives of the deformity are not transmitted in detail is obvious, for no two individuals have as yet been reported in any family in which the deformities were identical. Also in view of these multiple variations, it appears inconceivable that the originating factor is a recurring variation in the representatives of the hand or foot in the germ cells. It seems far more probable that a funda- mental factor, which influences the ultimate general conformation of the affected parts through their normal representatives, is at fault, that it is transmitted, and that its interaction with these representatives varies slightly in quality and quantity in different individuals and generations; and that the varying interaction is produced by the interference of factors which may or may not be transmitted, such as those which may be conceived to account for the partial latency above mentioned. Such an hypothesis would not only offer a rational explanation of partial latency, but would render the quadruplicity of this and many other deformities less inexplicable; at the same time accounting for the marked tendency to symmetry which usually exists. The hypothesis is in accord with the observations of Weismann on the subject of polydactylism (cp. Wilson and Windle also). Whatever view be taken it is difficult to avoid the conclusion that in spite of the variation in individual deformities, there is a common factor and fundamental scheme in transmission, both as far as hands and feet are concerned. Before passing to the inheritance of the deformity as a whole there remain two considerations; the first in connection with sex preponderance, the second with twins. In Bédart’s short family there was a predominance of the female sex in the proportion of 2 to 1, though taking deformed and undeformed together the male element was in the ascendant. In Mayer’s report there is a male excess in the proportion 6 to 1 (Fig. 2). Apart from these examples sex plays no part in transmission, and therefore requires little comment. There have been in all four cases of twins. In two of these’ ", where the twins were heterologous, the female was in each unaffected. In a third instance (V, 38, 34), two children of opposite sex were normal. Lastly of Mayer’s homo- logous twins (Fig. 2, III, 6, 7), arising from a deformed father, one only was deformed. Interest attaches itself to this case in view of the opinion that certain * A phenomenon related to if not identical with the ‘‘ cryptomerism” of Mendelians. 7—2 or 2 Split-Hand and Split-Foot Deformities homologous twins result from the fission of a single ovum. We can only conclude that in the case of Mayer’s twins such an origin is highly improbable. RECESSIVE DOMINANT HOMOZYGOTE HOMOZYGOTE R. l| rAEAEYN HOMOZYGOTE HETEROZYGOTE % 99009 9 4 550d 56d9 Fia. 2. Fia. 3. Fic. 2. The figure illustrates the deformities of a family of hereditary split-foot described by Mayer (loc. cit.). The arrangement and signs correspond to those of Fig. 1. The family is of special interest as it shows:—marked dominance of the deformity: offspring from two wives by the original deformed member: male predominance: inheritance of type (II, 2 and 3, III, 10 and 11): and homologous twins of which one is deformed (III, 6 and 7). Fic. 3. Diagram illustrating Mendelism as applied to human sports. The horizontal and oblique lines are to be interpreted as in Figs. 1 and 2. Each individual is represented by a double circle, the outer representing the appearance of the individual (black deformed and white normal), the inner circle divided by a vertical line the nature of the gametes. Homozygotes are consequently represented uniformly in black or white; heterozygotes with the outer ring black (signifying the actual deformity and illustrating the dominance of the same) and the inner ring half black and half white, to denote the potential deformities of the gametic cells. In the figure a recessive and dominant homozygote are supposed to be crossed, producing heterozygotes only, one of which is shown. This individual is then crossed with a normal or recessive homozygote with the production of equal numbers of homozygotes and heterozygotes. Of these offspring one of each variety is crossed with a normal homozygote. The figure shows that from heterozygotes when crossed with normal individuals an equal number of deformed and normal offspring are to be expected. We now come to a subject of considerable interest and importance, in the discussion of the transmission of the deformity as a whole. There appears to have been of late years a growing feeling that slow or continuous variation is insufficient to account for the origin of widely differing species (cp. Lock), and a tendency to attribute such species to discontinuous variation or sport. The essential con- sideration in view of the possibility of a new species originating in a sport, is the stability of the particular deformity in its transmission. Weismann stated that there is no difficulty in understanding the gradual swamping of sports, when it occurs, and even went so far as to assert that it is inevitable in the absence of inbreeding. But Weismann based his statements chiefly on theoretical con- siderations, and the “id” hypothesis in its application to sport characters is perhaps no longer free from doubt. In the recent revival of Mendelism a great many new observations have been made into the subject of “hybridism.” The investigations have been made for the most part upon the vegetable and lower T. Lewis AnD D. EmBLETON 53 animal kingdom, and the term “hybrid” is now given wider scope. Bateson in a recent communication has suggested the applicability of Mendelian laws to hereditary pathological and teratological conditions. In the ensuing paragraphs the applicability of these laws to hereditary split-foot will be examined ; for if the cross between a deformed individual and a normal one is to be designated as a hybrid, and if the transmission of any deformity can be shown to proceed along Mendelian lines, the question of permanent stability of that deformity upon transmission may be considered as settled in the affirmative, and the possibility of a human sport originating a species, in the wide sense of the term, will be past denial. According to the Mendelian doctrine animals and plants cannot be considered, from the point of view of heredity, as “units,” but as composites of separate characters. If as a result of the crossing of two individuals, bearing separate types of a single character, these types segregate independently in the offspring, they are termed “allelomorphs” and may be expected to obey certain fixed laws. A fundamental proposition of Mendelism states that it is impossible for the same gamete to carry more than one member of the same pair of allelomorphs. Again, one allelomorphic character may show dominance to the other member of the pair, in which case the result of the cross between a “dominant” and “recessive” allelomorph will be the appearance of offspring all bearing the dominant character™. The offspring will nevertheless produce an equal number of gametes carrying dominant and recessive characters. Such offspring are termed “ heterozygotes,’ as opposed to those arising from the union of like allelomorphic gametes, which are termed “homozygotes.” When a heterozygote is produced by the union of a dominant and a recessive allelomorph, and is crossed with a homozygote resulting from the union of two recessive allelomorphs, homozygous offspring bearing the recessive character and heterozygotes bearing the dominant character will be produced in equal numbers. This principle is illustrated in the accompanying diagram (Fig. 3). From this necessarily short account} it may be gathered that when dealing with allelomorphic characters an abnormal offspring cannot arise from recessive homozygotes, and that in a family tree arising from an abnormal ancestor the deformity may be expected to be stable. It also follows that the abnormal offspring of one normal and one abnormal parent is a heterozygote. We have seen that there is reason to believe that a sport in all probability arises as the result of the union of a normal and an abnormal gamete. It may be therefore assumed, if Mendelism is to apply, that the original sport is a heterozygote, an assumption which Bateson appears to have made. From this it follows that if a family is in agreement with Mendelian laws the total number of deformed and undeformed offspring from deformed parents should be equal. * Tf the sport character is recessive, it can never appear in the family unless there is intermarriage. + Which for simplicity takes no account of “latency.” 54 Split-Hand and Split-Foot Deformities The counts for split-foot families are as follows :— Parker and Robinson’s...16 deformed and 16 normal. QUES ais vest teweueciinestiiee 44 deformed and 32 normal. Hotherby's...:5.22/s5-0s00 16 deformed and 10 + normal. IMaWOnisc.gr cncseenastin ea 12 deformed and 6 normal. Thus there is a greater dominance* of the deformed than is to be expected, though several of the families are fairly in agreement with the rule. But we have now to proceed a little further. It has been stated that the original sport should be a heterozygote, but in the family of Mayer (Fig. 2), all the members of the second generation show the dominant character, namely are deformed. On Mendelian principles this would be brought about if the original sport were a homozygote. But if this is assumed there is every reason to assume that every original sport of the sort is a dominant homozygote also, and this cannot be allowed, as were it so all children of the second generations should be invariably deformed, which they are not. Moreover it is the rule in these families for an excess of deformed individuals to show itself in the first generation, and this is the case also with the majority of deformities of the hands or feet which run through long families ft. Lastly if Mendelian proportions are to hold good they must not only hold good in every family of the particular deformity examined, but they must above all hold good for each succeeding generation, for upon this depends entirely the question of stability, which is the chief point at issue. In families showing split-foot the following figures are shown :— Parker & Robinson’s Ours Fotherby’s Mayer’s D. N. D. N. D. N. D. N. D. N. Ist gen.{ ... 1 6 1 0 1? 2 1? 2 —= || — 2nd gen. 9 4 11 3 1? 2 6 0 27 7 3rd gen. 7 12 13 5 2 2+) 5 6 27 25 4th gen. ... - 17 22 9 3 1 0 27 25 5th gen. ... — a= 1 2 4 5 — = 5 7 Totals... 86 64 D.=deformed, N.=normal. An examination of these figures shows a decided tendency for the deformity to die out. In view of this and of the hyperdominance of the deformity as a whole, * A dominance which has already been noted by Bateson in many families. + Families illustrating ‘‘ latency,” are not here considered. + For convenience sake, the numbering of generations in this table does not correspond with that given in Fig. 1. T. Lewis AND D. EmMBLETON 55 the evidence points to the conclusion, despite the apparent segregation, that the transmission of hereditary split-foot is not governed by Mendelian laws. We have not yet seen a family tree of fair proportions which shows this adherence to Mendelism*. The family trees given by Bateson tend to show the same diminution in the proportion of affected to non-affected offspring in succeeding generations. In concluding this paragraph it may be said that evidence has not yet been produced which warrants the statement that any human sport is trans- mitted along the lines of Mendelism. Passing back to the original question, we find that the evidence of stability which Mendelism might have given is not forthcoming and that when the figures are taken on their own merit, they uphold the view expressed by Weismann that swamping of transmitted sports will eventually take place. As Weismann stated for polydactyly, that no family deformity has been traced through six generations, so might the same statement be made for hereditary split-foot, but the statement of Weismann no longer holds good+ and there is no reason to disbelieve that the deformity of the “G” family will assert itself for several if not many more generations. Given the factor of inbreeding a split-foot race might quickly arise. In this connection the family quoted by Windle after Devay is of interest (Linnean Soc. Trans.), for it shows the development of a polydactylous race in an isolated village. Deformities may die out in one of several main ways. The deformity may be so gross as to render life impossible. Lesser grades of malformation though compatible with extrauterine life may predispose to early death, or handicap the individual in obtaining the necessaries of life. Other deformities, from their tendency to disfigure, may hinder mating. Others may render procreation impossible. Of these none, so far as can be seen, influence to any extent the prolificacy of individuals suffering from hereditary defects of the digits. In Devay’s family there appears, upon the introduction of new blood, to have been a gradual diminution in the severity of the individual lesions as they passed through succeeding generations. The same tendency was considered by Fotherby and Mayer to be present in their families, but the evidence in these last cases is inconclusive. The extermination of hereditary split-foot takes place by a pro- portionate decrease in the number of deformed offspring, arising from deformed parents, from one generation to the next. To what this diminution is due is a question to which at present no answer is forthcoming, but the fact as it stands is directly opposed to the supposition that human sports or their originating factors may be regarded as unit characters, transmitted along those definite lines which certain natural characters in animals have been shown to be inherited. * Though we have searched a large number. + Families of eight generations have been reported. 56 Split-Hand and Split-Foot Deformities Summary and Chief Conclusions. 1. A family containing 44 deformed members is placed on record. Of these 17 are described in detail. 2. Of the many varieties of split-hand and split-foot, one is most prominent and is of sufficiently common occurrence to merit the name “ hereditary split-foot.” A general account of it is given and reasons assigned for considering it a deformity sur generis. 3. It usually affects the four extremities and shows great variability in all families in which it occurs. The types of deformity of the hands and feet are discussed and their relationship shown in different individuals and in separate families. 4. All the cases of symmetrical split-foot, which have been found, have been included in the bibliography. Of these over 167 occur in families in which other members are similarly affected; the remaining 13 are isolated. Nevertheless there is reason to believe that they are all of the same nature. 5. ‘The deformity consists mainly of an ectrodactyly, but is frequently associated with various grades of syndactyly and polydactyly. 6. The deformity has its origin in a “sport,” which takes place in the parental germ cells or their precursors, probably in the latter. —— 7. ,’). Further: zda,dx,... da, will equal N i (Chiko pee representing the frequency due to n independent variates. eX dX dX, Cat adn; 60 Generalised Probable Error in Multiple Normal Correlation The ellipsoid in n-fold space can be reduced to a sphere by proper squeezes in the directions of its principal axes, and accordingly its volume can be found from The volume of a sphere in n-fold space that of a sphere in n-fold space. _ Qn Gr (/1)” : Bak eee ye BSNS, ge (+1) n ale Sar = , if m be odd. Hence the volume of an ellipsoid in n-fold space Pp P 2 Oh; Wes cs. Om (A/a) © - = 1.2-3...4n , if n be even, 22) aotty...An(Vry = ae ney ts , if n be odd. Applying these to our special cases we have for the volume of correlation ellipsoid, V: Qn ea aes nX” (/70)” i Ve oe , if n be even, 4 (n+1) > ve eee _& Di Dosen Va , if n be odd. 18) Boca Ht Thus for the two cases: = ORD Dae te OND) emmy Cet) tee ee 3 (n-+1) SS SS n—1 n—i = 2 Die so+ Bn dx (4/77) Gucddy: Li, Dina Now the total amount of frequency between two contour ellipsoids is z6V, and accordingly the frequency inside a given contour ellipsoid y is given by: and I.=| 2dV N i Aacniae eae ie aa ——___—__—_——— ? n—1 or 9 : [i 2.4.6...n—2 NS x x ) =,/2 ie a 7s gfe x" dy, for w odd. 71.3.5...n—2Jo . 1 : Np 3t? 7, Let bn (&) = = |. ae dx be defined as the “incomplete nth normal moment function.” Then NV Qar pn (x) G I, /N = SAC ener if n be even, Zn (x) : me Se paige sles Now 1,/N is the chance of an observation falling inside the contour yx, and 1—J,/N the chance of its falling in the fringe outside this contour. a K. PrarRson AND A. LEE 61 We see accordingly that the chance of an outlying observation being reasonable or not,—the observation consisting of a complex of n variates,—can be readily found, if the incomplete normal moment functions have once been tabled, and the constants of the correlation surface be known. These incomplete normal moment functions serve a variety of purposes which will be developed in later papers. The present paper merely refers to the means they provide of determining the probability of any observation lying outside a given contour ellipsoid, i.e. there being any “fringe” beyond this value of y. In Table I. pp. 66, 67 the values of m, («) = fn (x)/{(n — 1) (n — 3) (n— 5)... 1}, if n be even, and = fn (x)/{(n— 1) (n— 38) (n— 5)... 2}, if nm be odd, are tabled for values of # from 0 to 5 proceeding by tenths. They were calculated in the following manner. Let a 7S —hau? Ve —iy2 \&% ae x _ gr walle Ne one es aia Mee «hal sense ned if n be even, pee set yee cage Qn =e \1+ 5 tog do: ag eT , if n be odd. Then: Mn = $(1—q,), if n be even, =a/ (1-4) if n be odd. The even series involve the probability integral which was taken from Sheppard’s Tables (Biometrika, Vol. 1. p. 182). Consequently the even series may have an error of unity in the seventh figure. It is hoped that arithmetical blunders have been avoided, but the labour has been very considerable and some blunders may have escaped notice. If we make 1,/N =4, we find the contour ellipsoid within which half the frequency lies. In other words an observation is as likely to lie inside as outside this contour ellipsoid. The corresponding value of y may be spoken of as the “generalised probable error.” Since the first 10 incomplete moment functions have been calculated it is possible to determine the generalised probable errors for 1 up to 11 variables. These are given in the table on the next page. Of these, the first is very familiar. The second was first given in Bravais’ classical memoir (Mém. prés. par divers Savans Etrangers, T. 1x. 1846, pp. 255— 332). The third professes to be given by Czuber, Theorie der Beobachtungsfehler, S. 404, but I do not agree with his results. The value 1°53817 was given by me in College Lectures in 1896. The remainder have, as far as I know, not hitherto been published, although they have been for a considerable time in use in my Biometrical Laboratory. 62 Generalised Probable Error in Multiple Normal Correlation - Table of Generalised Probable Errors. Nome ot Probable Error 1 0:674,4895 2} 1°177,4062 a 1°538, 1667 4 1°832,1239 o 2°086,0146 6 2°312,5982 if 2°519,0869 8 2°710,0022 9 2°888,3962 10 3056, 4366 11 3°215,7402 The method of calculation was as follows: If » be even we have from the equations on p. 61: Ope ps = = 11994711. If n be odd: a = 25, since [,/N =}. The problem therefore resolves itself into an interpolation in the tables. Let y be the required argument of the table and « the corresponding value of mp_,; let a, #,, be the two values in the table immediately below a, and a, a, immediately above ; then the formula _2(e-m) (ea) (w- 2) (& — &1) (® — L2) (€) — #3) (& — &y) (@ — a2) (@ — #5) (&, — Xo) (®%, — Ly) (#4, — 23) _ (@ = &) (@& — %) (@ — &) ) (3 — Xp) (@p — 2) (#3 — @2) was used to find y, i.e. a cubical parabola was passed through the four points. The accuracy of a variety of other interpolation formulae was found to be less. y= tts} Having found the values of the first eleven probable errors, an empirical formula was then sought which would closely express them, and which accordingly might be used for extrapolation. The form of curve finally adopted was that found by adding the ordinates of a line to that of a logarithmic curve. Its equation, after the adjustment of its constants by the method of least squares, was: P.E. = — (067,769 + :071,986n + 2°308,272 logy, (994,484 + n), giving the probable error in terms of the number of correlated variables n. Of course we must not expect such an arbitrary formula to be true to more than some four figures. As a matter of fact in fitting it only the values from 3 to 11 were taken. The following give the calculated and actual values: K. Prarson AnD A. LEE 63 n Calculated * Actual 1 “696 674 2 1176 1177 3 1°537 1°5388 4 1°832 1°832 5 2°087 2°086 6 2°314 2°313 v 2°520 2°519 8 2°710 2°710 9 2°888 2°888 10 3°055 3°056 11 3°215 3°216 12 3°367 == 13 3°513 — 14 3°654 — Lo 3°791 — It appears accordingly probable that our formula up to possibly n=15 or more will represent the probable error with not more than ‘001 error. The extreme divergence for the case of n=1 is noteworthy, and seems to place this result on a different footing to the others. The general agreement is shown graphically in the diagram on p. 64. The general use of the table provided will be obvious, it enables us to tell the probability of any outlying individual really being a member of a population of which the constants are known. Thus one may look forward to the day when the biometric constants of a race being sufficiently well known, it may be possible to tell from a complex of five or six characters whether a skeleton or a skull may be reasonably supposed to have belonged to a member of that race. At present the labour of calculating the correlation coefficient-determinants and their minors stands in the way of much work in this direction, when we wish to advance beyond two or three characters. The incomplete normal moment functions provide us with a method of determining, theoretically at least, the constants of a truncated normal distribu- tion. The method is as follows. Let NV be the total frequency, o the standard Mean of Tail <—ho>< y' > * For plotting the curve we have also the ordinates *3710, ‘0276, —:0733 for n=4, 0-1, 0, respectively. 64 Generalised Probable Error in Multiple Normal Correlation Diagram for value of probable error for x Variables. [EES SE Nau Atk AE coh HHEAUEAILE LN a | = Se yO Oe OS se SS Qi Nia ai as LOL ajquqgoig fo apnzuboyy Sie - —_ its) a --92 Number of Variables K. Prarson anp A. LEE 65 deviation, and / the distance from the mean at which the distribution is truncated. Then the frequencies of the shaded part are known, but V,/ and o are unknown. Let n be the known total frequency of the tail, »,’ the distance of its centroid, or mean, from the ‘stump,’ v,’ the second moment of the tail about the stump, and ¥ the standard deviation of the tail, of course about its mean; then vy, and vp,’ (or > = Vp/ — v2), are known from the observations. Now nv,’ is the pth moment of the tail about its stump and ) N os 1 - ue e “(x—h)?dax , WW, = — ‘p V2Qara0lh No? co = = | e7 #*" (a — NW)? da’, if a’ =a/c, h' =h/o, V20 h’ = No? (a, (h’) — ph py a(l’) + P u ao hi? wy. (h') — ete.) 5 where p, (h’) is the incomplete normal moment function of the pth order. Repre- senting it by yw,’ for brevity, we have NG, TW, —Note = pg, ); nvy = No? (pw, — 2h’, + hp,’). Hence we find ee —— — (g N —ea fy )| fy fig) -e es oes (1). Now yf, is a known quantity, being the ratio of the squared standard deviation of the tail to the squared distance of its mean from the stump. Accordingly if the value of Wy, be tabled to each h’, then,—p,’ being known from a table of the probability integral, and py,’ and yp,’ from tables of the incomplete normal moment functions—we shall be able to find h’ from the known value of Ww. In the next place: IVE Muliity Conte noes accasa ves Mtawe smite, anaes 12 (2) will be known from the probability integral table of 4’ as soon as h’ is known. Lastly : Ce My, —— ley Va Wg ivaaea nae seesesavwasteceks (3). Or, if W.= py (uy — ho’) be tabled for values of h’, o will be given at once in terms of v,. Then h=/h’o is determined, and the constants of the complete normal distribution found from the constants for the truncated tail. We require accordingly tables of y, and w,. It was found impossible to calculate these with sufficient accuracy from the usual 7-figure tables of the probability integral and the new tables of the normal moment functions. When h’ gets at all considerable wy, and yy, depend on the differences of very small quantities. Accordingly p,’ and yp.’ were calculated de novo, and owing to the kindness of Mr Sheppard an unpublished 9-figure table of the probability integral calculated by him was used. Even thus, it has not been considered desirable to give the table to more than three decimal figures. Biometrika v1 9 66 Generalised Probable Error in Multiple Normal Correlation TABLE I. Values of the Incomplete Normal Moment Function py (a). A. Odd Moments my (#) = pn (@)/{(n —1) (n — 3) (n — 5)... 2}. x my (x) ms, (a) | Ms (x) mz (x) Mg (x) 0:0 ‘0000000 “0000000 ‘0000000 “0000000 ‘0000000 O'1 ‘0019897 *0000050 “0000000 ‘0000000 “0000000 O32. ‘0078996 ‘0000787 “0000005 ‘0000000 “O00V0000 0°3 0175545 *0003920 ‘0000059 ‘0000001 *0000000 Or4 ‘0306721 *0012105 ‘0000821 *0000006 “0000000 Od ‘0468770 ‘0028688 ‘0001183 *0000037 ‘0000001 06 ‘0657177 ‘0057372 “0003390 ‘0000151 “0000005 0'7 ‘0866883 ‘0101861 ‘0008146 *0000493 “0000024 0°8 *1092507 0165494 *0017172 ‘0001350 ‘O000086 0-9 *1328570 0250925 0032702 *0003242 *0000259 1020) "1569716 ‘0359862 ‘0057399 ‘0006988 ‘0000687 IEA *181090] "0492895 “0094199 0013795 *0001634. 1:2 ‘2047562 °0649423 0146092 *0025293 *0003549 1:3 ‘2275737 ‘0827672 °0215865 0043539 0007135 Ih "2492148 "1024819 ‘0305828 ‘0070957 0013414 15: *2694247 1237174 *0417570 0110219 °0023776 126) *2880214 "1460428 -0551764 0164068 “0040005 eT *3048932 *1689923 ‘0708039 ‘0235098 0064248 1°8 *3199921 *1920929 0884945 °0325513 0098944 1°9 *3333265 *2148899 *1080009 ‘0436894 “0146688 2-0 *3449513 *2369694 *1289874 *0569995 "0210055 cl *3549587 °2579749 *1510502 ‘0724606 0291380 BS, 3634677 ‘2776192 1737425 *0899486 0392533 O-8) *3706152 *2956902 ‘1966019 "1092390 *0514703 24 *3765478 *3120515 ‘2191769 *1300173 °0658224 Zo) *3814140 3266380 2410506 *1518971 *0822459 26 *3853593 *3394489 ‘2618602 °1744437 *1005767 Oy *3885213 *3505370 *2813106 *1972006 *1205553 2°8 *3910268 *3599983 *2991823 *2197160 "1418391 29 *3929897 *3679593 *3153329 2415682 *1640231 30 *3945104 3745671 3296946 *2623860 *1866637 oul, *3956755 *3799784 *3422662 "2818638 *2093055 BI *3965582 *3843517 *3531029 *2997718 *2315079 33 *3972197 *3878403 *3623049 *3159582 ‘2528687 34 *3977101 *3905878 *3700046 °3303476 *2730432 35 *3980696 3927244 *3763548 *3429335 °2917571 3°6 *3983304 *3943653 *3815183 *8537687 *3088145 Bu, *3985175 *3956099 3856585 | °3629529 *3240979 ons 3986503 °3965425 *3889331 *3706199 *3375646 39 *3987436 *8972329 3914881 | °38769253 3492376 40 *8988085 *3977378 *3934552 =| = *8820351 3591947 41 *3988530 *3981028 3949499 | -3861165 *3675554 42 *3988833 *3983635 *3960708 3893304 3744677 43 *3989037 °3985475 *3969007 *3918258 | 3800964 Ah *3989173 *3986759 *3975073 °3937367 *3846117 Uo *3989263 *3987645 *3979452 *3951801 “3881809 46 *3989321 *3988248 *3982573 °3962557 *3909614 ye] 3989359 “3988656 *3984770 *3970466 *3930967 48 *3989383 *3988927 *3986298 *3976205 *3947135 49 *3989398 3989106 | °3987348 *3980315 *3959207 or? *3989408 3989222 | ‘3988061 | -3983221 *3968097 oro) *3989423 *3989423 *3989423 *3989423 *3989423 ee K. Prarson AND A. LEE TABLE I.—(continued). B. Even Moments my (av) = py (x)/{(n — 1) (n— 8) (n—5)...1}. Hi My (wv) my (x) mg (x) mag (x) Myo (x) 0-0 “0000000 “0000000 “0000000 “0000000 “0000000 Ovl 0001325 “0000002 “0000000 “0000000 “0000000 0-2 ‘0010512 “0000084 “0000000 “0000000 “0000000 03 0034951 0000626 “0000008 “0000000 “0000000 O-4 0081136 0002572 “0000058 “0000001 “0000000 O'5 0154298 ‘0007604 ‘0000270 “0000008 “0000001 O'6 0258121 *0018200 0000925 0000037 “0000001 0-7 0394585 0037575 0002588 0000139 0000006 O's 0563914 ‘0069507 0006223 0000437 “0000025 0-9 0764632 0118045 0013297 ‘0001177 “0000086 10 09938740 ‘0187171 0025857 0002812 0000251 JERI "1246965 0280428 0046525 “0006094 “0000658 1:2 1519070 °0400559 ‘0078427 *0012160 0001558 IEE 1804203 0549214 0125028 0022617 0003386 Ld 2096248 0726741 0189894 0039577 0006842 1°5 2389164 0932091 0276408 0065653 ‘0012964 16 2677274 "1162835 0387442 0103869 0023209 Ley *2955511 1415300 0525059 0157516 0039494 HS: 3219594 "1684803 0690258 0229926 0064207 UD) 3466134 1965937 0882796 0324204 *0100147 2-0 *3692680 2252921 “1LIO1113 0442938 0150415 21 3897700 2539927 1342371 ‘0587910 0218224 2:2 *4080525 2821413 "1602593 0759866 ‘0306667 2°3 4241237 *3092387 1876903 0958345 0418437 24 4380556 3348616 *2159821 1181613 0555560 2°5 *4499695 "3586763 *2445598 1426700 ‘0719132 2°6 4600231 3804450 2728554 "1689546 0909136 27 4683965 “4000247 3003387 "1965228 “1124320 2°8 “4752816 “4173616 3265431 2248263 1362197 2:9 “4808719 432.4798 3510842 2532933 1619132 30 4853546 “4454679 "3736720 2813629 "1890538 31 4889053 4564647 “3941138 3085150 °2171145 32 4916838 4656432 4123121 3342962 2455315 BB 4938321 “4731975 4982552 3583379 2737379 ah 4954736 4793298 "4420056 3803672 *3011962 BS 4967130 4842409 4536843 “4002102 3274261 36 4976381 4881218 4634555 “AL77877 3520261 a7 4983205 4911484 “4715111 *4331061 3746880 3S 4988183 4934784 4780568 “4462441 3952025 a9 “4991771 4952491 4833001 4573366 4134583 40 "4994330 4965779 4874418 4665592 "4294345 41 4996133 4975627 4906683 4741120 4431886 42 4997391 4982835 4931479 4802063 "4548407 4B 4998258 4988045 4950279 4850521 4645574 44 4998849 ‘4991766 4964343 4888500 4725352 45 4999247 4994392 “4974729 "4917846 ‘4789861 46 4999512 4996222 4982298 “4940207 4841246 Ai 4999688 4997483 “4987744 4957010 4881574 4s “4999802 4998342 *4991613 4969464 4912765 49 4999876 “4998919 4994326 "4978572 “4936544 50 4999923 4999303 *4996206 4985144 “4954417 eo 5000000 “5000000 “5000000 “5000000 “5000000 9—2 6 — 68 Generalised Probable Error in Multiple Normal Correlation TABLE II. Values of the Functions Wr, and wv, required to determine the Constants of a Normal Frequency Distribution from the Moments of its Truncated Tail. h’ ua Yo h’ aN pr O-l "588 1311 1°6 “787 92°358 0°2 “605 1°371 HON, "796 2°437 O°3 "622 1°432 1'8 “804 2°517 O-4 638 1°495 1°9 813 2°598 0°5 653 1°560 2:0) "820 2°679 0°6 ‘668 1°626 pay | "828 2°762 Os ‘682 1°693 22 *835 2°845 0°8 696 1°762 Os. "842 2°929 0-9 “709 1°833 a4 “848 3°013 1:0 22 1°904 2:5 *854 3°098 Lieiy, Tod. 1:977 26 “860 3°184 1°2 ‘746 2°051 2:7 “866 3°270 se ADIL 2°126 2°8 “871 3°357 Ly ‘767 2°202 2:9 “876 3°445 Ls) weet 2°280 30 “880 3°532 This is quite sufficient for practical purposes, for the difficulties of practice do not arise from the paucity of figures in this table, but from quite other considera- tions, now to be described. In the first place, when we have a truncated distribu- tion like that indicated in the above figure, the group of maximum frequency is at one end of the distribution, and any variation in this frequency widely modifies not only { but 1’. Thus the probable error of random sampling in the “stump” group is very influential. Next, the frequency is almost certain to be given in definite ranges, and the correction of the raw moments for such a case with the maximum frequency group at the terminal is tedious even if it can yet be considered satisfactorily determined. Thus in actual statistics, I have found that truncating at different frequency groups much modifies the values of the unselected frequency constants. For these practical reasons no very great number of decimal places is needful in y, and y,. I think, however, the tables may be of service in determining the constants of the untruncated distribution to a first approxi- mation, especially if the final values of those constants be based on truncating at two or three points and averaging the results. Further they may serve to give the first idea of the root of the nonic required when we break up a distri- bution into two components, the constants of one component being indicated by the tail of the frequency on that side. I have to thank Dr A. Lee for the laborious arithmetic involved in the preparation of the tables accompanying this paper. A further use of the incomplete normal moment tables in evaluating the incomplete B- and I'-functions will be considered in another paper. ON INHERITANCE OF THE DEFORMITY KNOWN AS SPLIT-FOOT OR LOBSTER-CLAW. By KARL PEARSON, F.R.S. (1) My attention was drawn at the beginning of 1907 to the existence of a family in which “ split-foot” or “lobster-claw ” was an hereditary deformity. I was unaware at the time that Dr Thomas Lewis and Mr Dennis Embleton were at work on a much more elaborate study of the same subject based on quite different material, and when I did know I did not hand over my material to them, as I ought properly to have done, because I wanted to ascertain independently to what extent simple Mendelism really applied to an obviously inherited and fairly simple human deformity. I wanted to convince myself that Mendelism does or does not apply to such cases, by handling the material myself and investigating by all the means at my disposal the authenticity of the records. At the same time my readers will suffer from having nothing like the completeness of detail in my case which may be found in the earlier paper of this number. The members of the family are scattered through an agricultural district some distance from London, and I could only afford the cost of bringing three members up to London for radiography. In this matter I must mention my deep indebted- ness to Miss C. O. Stevens not only for much aid in following up the family history from the clue she first reported to me, but also for the arduous task of piloting the strangers through the sights of the Metropolis. To Dr Mackenzie Davidson I owe the further big debt that, in the interests of science, he gave up a large portion of his valuable time to preparing by stereoscopic radiography no fewer than 22 negatives of the feet and hands of these three individuals. Only a few of these radiograms are reproduced in this paper, but the variety of positions taken, as well as the stereoscopic nature of the pictures, has enabled my colleague, Professor Thane, to give a very complete account of the hands and feet of these three individuals. The ever ready aid given by Professor Thane to biometric inquiry would be very inadequately expressed by a few lines of thanks in a single biometric memoir. It would indeed be impossible from Professor Thane’s account of these three cases to predict the precise nature of the deformity—the presence or absence of bones—in other members of the family who have not been radiographed. No 70 Inheritance of Deformity known as Split-Foot or Lobster-Claw great faith is to be put in the family record of the number of perfect fingers or toes possessed by dead or living members. The list given on pp. 74, 75 must only be trusted for such obvious and gross variations in the nature of the deformity as supernumerary digits or syndactylised fingers. The importance of the accurate description of each individual member, however desirable, is less, after the work of Messrs Lewis and Embleton; their memoir fairly indicates the range of types to be expected. These types are largely represented in the members of my family who have been more fully examined ; there are certain additional types also. It is clear that what they and I are dealing with is an hereditary deformity of the hands and feet, with a definite, if remarkably wide, field of variation. Lastly, I have most heartily to thank Mr J. H. Astbury, whose intimate know- ledge of the district and its inhabitants has been most helpful to me in my inquiries. (2) Before turning to more definite details as to the present family, I should like to mention the existence of a similar family, with names Bell and Agnew, at Whithorn, Wigtownshire, some 50 years ago. An old man told my informant that a boy with deformed hands was a descendant of the “Cleppie Bells.” This was a family, one of which had assisted as Sheriff’s officer at the drowning of the Wigton Bay martyrs in 1685. On that occasion the officer Bell said to a young maid, Margaret Wilson, “ Will you not say: God bless King Charlie, and get this rope from off your neck?” “God bless King Charlie, if He will,” she responded. Whereupon he said “Clep down among the partens and be drowned.” Thus he was called “Cleppie Bell,” and his descendants have ever afterwards suffered from a deformity of the hand, although sometimes a generation is missed over. It is true that the term “clepped” in Scotland refers to webbed, but the reference to the lobsters suggests “lobster-claw” deformity, and one phase of this, the syndactyly, might easily be described as fingers grown or webbed together. The boy referred to above became a sailor and was last seen in Glasgow 20 years ago. No stress whatever can be laid on such a tale as this, but it is interesting as pointing to the existence in Scotland* of a deformed hand inheritance for nearly two hundred years, and the information might be followed up by any one coming across Scottish cases of either webbed hands or lobster-claw. This is the only case I] have met with in which there is any statement that deformed offspring were born from undeformed parentst. Throughout both my family and that of * Messrs Lewis and Embleton state that their family originated in Scotland. + This follows also from the somewhat different version given in Sir Andrew Agnew’s The Heredi- tary Sherifis of Glasgow, Edinburgh, 1893. We read in Vol. 1m. p. 142; ‘Still more grotesque is the tradition of the ‘Cleppie Bells.’ A constable who was held to have carried out his orders unfeel- ingly, as he fastened the women to the stakes, was asked how the poor creatures behaved when the cold wave roared and foamed about their heads. ‘Oo,’ he replied jocularly, ‘they just clepped roun’ the stobs like partens, and prayed.’—-Soon after Bell’s wife was brought to bed, when the howdie exclaimed in horror: ‘The bairn is clepped!’ (i.e. the fingers grew firmly together). Another child was born, and yet another, and as each little wretch in turn was seen to be ‘clepped’ the most incredulous were convinced it was a judgment of Providence.—We have been gravely assured that within the memory of man a female descendant of the bad constable on giving birth to a child, was horrified by the exclamation, ‘ The bairn is clepped.’” Plate VIII Biometrika, Vol. VI, Part | ‘piooad ou ‘YQIIG 4B pad ‘FT pue g ‘I Jo Wortpuos Jo pxodat ON 4 OeQuQa Oududerd a a 2 OH OF Os Guu GuGuQuQsOs @ O@ "O10 AL SSS) SISSY SWZ ~e QrQu didn QecQur debe der On Oss 2OudordaQes @ babe 2@or St Or. @ xz O22 @ 2002 ss PS es @x Ou bu @ Os omer @ 6 S ‘ CMVIQ YALSHOT,, CELIVAHNE “GAUL, ATV K. PEARSON 71 Messrs Lewis and Embleton undeformed members give rise only to undeformed offspring. It is not possible to say whether the deformity really is latent or not, there have been no cousin marriages to form even a rough test of latency. The absence of cousin marriages of any kind compels us to consider “ lobster- claw” as a dominant character, and after the ancestress I. 2 of my pedigree, who may in Mendelian terminology possibly have been a homozygote, all the descendants must be looked upon as heterozygotes. On this assumption all normal individuals are recessive, and the fact that normal individuals from tainted stocks do not have deformed offspring meets with a ready explanation. It is this noteworthy point not only in the present family, but in Lewis and Embleton’s family, in Drinkwater’s Brachydactylous Family and in Nettleship’s Night Blind Family, which is the main-stay m these cases of the Mendelian theory. It is perfectly true that it would flow from other hypotheses, for example from the assumption that the gamete was not pure, but that dominance flowed from a numerical preponderance of allogenic determinants*. Such a theory could only be tested by inbreeding. For the sake of science, therefore, if not for local well-being, it is desirable that marriages between the normal members of these stocks should occur, and this even in sufficient numbers to test whether there are really latent tendencies to the deformity in normal members of the stock. Should this not prove to be the case, the non-marriage of the deformed members would be sufficient to check the spread of the deformity. Obviously a determi- nantal theory not based upon the pure gamete would further account for the occasional and rare appearance of the deformity in a child of normal parents. Mendelism must assert in a case like the present where the character must be dominant, that such an appearance is a mutation or sport. (3) Since the deformity must be looked upon as dominant in the Mendelian sense, it follows that on the average half the offspring of a deformed parent ought to be deformed. We have data for such families in three generations, and the following results flow from them : Families Totals N=Normal ‘ eae | D= Deformed 1 2 | 3 4 i | No D) |) No Da) N...Dw|) Ni De |-N. Dd.) N: D: Il. Generation 4 4 = | = = <= 4 4 III. Generation 5 5 OG | a — — eal TV. Generation 0 3 Ot | wo ns 3.0 5 10 Totals acs | = = 14 25 * See the paper in this number of Biometrika on p. 80. 72 Inheritance of Deformity known as Split-Foot or Lobster-Claw The amount of material here is not very great, but, as far as 1b goes, it does not support the conclusion that for the tainted families the abnormal members are relative to the normal fewer in number. It seems rather to indicate that in the last generations the abnormal have been twice as numerous as the normal. My data are, however, far less numerous than Messrs Lewis and Embleton’s. Leaving out their two doubtful cases, I find (Biometrika, Vol. vi. Plate I) that they have 82 normal to 43 abnormal members in the families of their stock with deformed parents. I shall confine my attention to their stock and my stock, because I feel in my own case the confidence of the personal collector, and am sure that a number of individuals have not been omitted or wrongly classed; and because I realise in their case also that Messrs Lewis and Embleton have examined their stock with the special view of testing definite ratios, The families of other observers may have been carefully worked out, but the importance of complete enumeration has only been recognised since it has become desirable to test Mendelian theory. Examining the data from the statistical standpoint, I draw attention in the first place to the first family of the third generation. This family should approxi- mate to 3 normal to 3 deformed, but every member born was deformed. The odds against a run of six deformed are 63 to 1, if the chances of normality and of lobster-claw are equal. The odds against a deviation as great as 25 to 14 from a ratio of equality are 14 to 1; the odds against Messrs Lewis and Embleton’s ratio of 43 to 32 are about 9 to 1; the odds against such an excess as is represented by our combined results 68 to 46,—a ratio corresponding to 3 to 2 instead of 1 to 1,—are more than 49 to 1. Now this excess of the abnormal in any de- formity like the present ought to be admitted, if it actually exists, for it is not only opposed to simple Mendelism, but its bearing on Eugenics is of the greatest importance. While I have found the like excess in other cases, it does not appear to be true for all deformities. Thus, from the pedigree plate in Mr Nettleship’s admirable paper on Night Blindness*, I deduce the following results : | Abnormal Normal seneration III. 10 6 Generation IV. 15 43 Generation V. 26 | 29 Generation VI. 30 51 Generation VII. ih 55 Generation VIII. 14 36 Generation IX. 9 11 Totals 131 | 931 * Ophthalmological Society’s Transactions, Vol. xxvu1. pp. 269-291. K. PEARSON 73 The odds against such a deviation from equality are enormous, i.e. about 10,000,000 to 1. But it will be noted that the abnormal members are largely in defect. Mr Nettleship himself remarks that this deficiency may probably be explained by unavoidable imperfections in the record, especially in the earlier generations. The excess of normals, however, has been more than maintained in the recent generations ; and if, in defending the Mendelian ratio of equality, we impugn the record on the ground that members of the stock are ashamed to own their defect and screen it, what then becomes of the evidence it undoubtedly provides for Mendelian theory in the “invariable continuity of descent of the disease in the affected branches, and its permanent disappearance from all other divisions of the genealogy”? The screening of the disease must clearly have become an hereditary character, and the above evidence of segregation would be worthless. This principle of segregation is so vital, is such a wonderful, and I am inclined to say, glorious addition to our knowledge of heredity, that I am inclined in these cases of family abnormalities to defend Mendel against Mendel, or to preserve Mendelian segregation at the expense of Mendelian ratios. We have seen that the odds against a ratio of 3 to 2, which is the combined result of our split-foot families, are very slight, and this applies equally to the case of Night Blindness, where a random sample deviating as much as the present one from the ratio of 3 to 2 would occur once on the average in 6 or 7 trials. There is an additional point also to be noted. The Curé of Vendémean, according to Mr Nettleship, states that if the original night-blind individual, “the Jean Nougaret of 1637 could reappear to-day, except for a few individuals recently established in the district, all could salute him as their ancestor” (loc. cit. p. 288). IRf this be true, then the Mendelian ratio to be expected is more than 1 to 1, for the husband or wife of the night-blind individual would, in certain cases, be screening their own defect, and the offspring ought to have been night-blind in the ratio of 3 to 1. On the whole, while these cases give very definite evidence of the segregation factor, they do not seem to me to favour the segregation in rigid Mendelian proportions. (4) When we turn to the actual nature of the deformity in the case I am dealing with, we find all the principal types observed by Messrs Lewis and Embleton recur, with one exception which may exist, but owing to the few individuals who have been radiographed, this cannot be asserted. I refer to the existence of cross bones (Biometrika, Vol. v1. p. 41). On the other hand, indi- viduals exist showing syndactyly and polydactyly; gross deformity, several “ fingers ” placed promiscuously on a large misshapen “hand”; or branching fingers which, without careful radiographic examination, it would perhaps be hard to classify as polydactyle or misplaced. The usual type of hand is to outward appearance, the hook-like form of my Plate XI, but the degree of defectiveness in the bones of the hand, even as affecting the carpus, may vary widely. In one case (II. 3) the hands were perfect but the feet deformed. There seems to be some evidence that in the younger generations the defectiveness is increasing; thus all the children of I. 6 had two- Biometrika v1 10 74 Inheritance of Deformity known as Split-Foot or Lobster-Claw toed feet, but the children of IIT. 21 are one-toed, with one exception, who has one two-toed foot, and the other one-toed. In this family as distinct from that of Lewis and Embleton the defectiveness in the foot may reach the tarsus. Contractions of the fingers and toes, these being flexed towards the centre of the member, are common. The following is a rough external account of the deformity of the individuals in the pedigree : List of deformed members of the Stock. I. 2. Ann J. Nothing known of her parents ; said to have had a brother and sister but no record of their condition to be found. She had one finger only to each hand, but the 1st and 5th toes on both feet. Died at 77. There was no consanguinity between I. 1 and I. 2. II. 6. Two fingers on right hand, one finger and thumb on left; Ist and 5th toes on each foot. No consanguinity with wife II. 5. Cause of death, asthma. II. 10, II. 13. Deformed, both hands and feet. II. 3. Hands perfect, both feet only Ist and 5th toes. Husband II. 4 not related. III, 21—24, 26, 27 are children of II. 6 above. III. 21. One finger to each hand, and Ist and 5th toes. Subject to fits. Unrelated to husband, III. 20, See Plates XI, XII, XIII and XV, Fig. vii. III. 22. Right hand six fingers, the supernumerary beyond the little finger; left hand five fingers, all deformed and bent at angles to palm of hand. 1st and 5th toes on each foot. Dead. III. 23. Both hands one finger, both feet 1st and 5th toes. Diseased arm bone. III. 24. Right hand ring and little fingers, but these united together ; left hand two bent fingers and thumb. Ist and 5th toes on each foot. III. 25. Right hand two fingers only ; left hand two fingers and thumb; both feet 1st and 5th toes. III. 26. One finger on each hand ; 1st and 5th toes on each foot. III. 4, 5, 7, 9 and 14 are children of II. 3. No details except that both hands and feet are affected. In the fourth generation, we have first children of III. 21. IV. 19. Both hands and feet affected ; 5th toe only. Married, no offspring at present. IV. 20. Both hands and feet affected ; 5th toe only ; stillborn. IV. 21. Only 5th toe on each foot ; little finger on each hand. Has had one or more fits, Plates XI, XIV and XV, Fig. viii. IV. 22. Both hands and feet affected ; 5th toe only; weakly constitution. IV. 23. One finger on each hand. 1st and 5th toes on right foot, 5th toe only on left foot. See Plates XI and XVI. TV. 24? Expected Birth*. IV. 18 has also a weakly constitution though hands and feet are normal. Of the descendants of II. 3, the grandchildren through III. 7 and III. 8 (who are unrelated) are : IV. 4. Ring and little finger only, joined together on each hand. 1st and 5th toes on each foot. TV. 5. One little finger only on each hand ; 5th toe only on each foot. IV. 6. One little finger only on right hand; thumb and little finger on left hand; 1st and 5th toes on each foot. * Born as this proof goes finally to press; a girl deformed in both hands and feet. Thus the improbability of the Mendelian quarter is greater than that given above. Biometrika, Vol. VI, Part | MoTHER’s HANDS. Ta. RiGHT HAND Lert HAND LUNAR SCAPHOID TRAPEZOID PYRAMIDAL PISIFORM T wauv2viaw TT 11510 ELDER DAUGHTER. Richt HAND Lert HAND LUNAR LUNAR SCAPHOID SCAPHOID__ TRAPEZOID TRAPEZOID OS MAGNUM. TRAPEZIUM TRAPEZIUM Lond A T Wadd vowLaw TL i19ia OieiT OL PYRAMIDAL, oS MAGNUM Plate NormMaAL Hanpbs. Richt HAND Lerr HAND LUNAR LUNAR SCAPHOID SCAPHOID PYRAMIDAL PISIFORM UNCIFORM, OS MAGNUM PYRAMIDAL PISIFORM. UNCIFORM OS MAGNUM TRAPEZOID TRAPEZIUM I L916 YOUNGER, DAUGHTER. Ti RicHT HAND Lert HAND 1 FA Lunar LUNAR SCAPHOID SCAPHOID. fe ERAN IO LUNCIFORM OS MAGNUM PYRAMIDAL. PISIFORM UNCIFORM, eed be TRAPEZOID TRAPEZOID. Oe ACU i TRAPEZIUM TRAPEZIUM as METACARPAL tp r i fe Re Pe f j 1 7 7 4 z > “= - ‘ - \ : 7 : . +86 a - _ — Biometrika, Vol. VI, Part | MoTHER’S FEET. Ta: RIGHT FOOT LEFT Foot TALUS TALUS = CALCANEUM CALCANEUM CUBOID. NAVICULAR NAVICLILAR _ — CUBOID EXTERNAL MID-CUNEIFORM = ip-CUNEIFORM EXTERNAL CUNEIFORM CUNEIEORM INTERNAL INTERNAL. CUNEIFORM, CUNEIFORM [ ivsevivisw al ta zy al \s xt oe | \E el ft co = a 3 ws é 2no 2 2nd 3rd 3rRo DB) ELDER DAUGHTER.. IVs. RIGHT Foor LEFT Foot TALUS TALUS = = CALCANEUM CALCANEUM CUBOID, NAVICULAR NAYICULAR CuBOID EXTERNAL MID-CUNEIFORM MID- CUNEIFORM EXTERNAL CUNEIFOR CUNELFORM INTERNAL INTERNAL CUNEIFORM CUNEIFORI METATARSAL I Norma FEET. Rigut Foor LEFT Foot — TALUS TALUS CALCANEUIA_ CALCANEUM CUBOID. NAVICULAR NAVICULAR — CLUBOID EXTERNAL__ MID-CUNEIFORM = MID-CUNEIFORM EXTERNAL CUN EIFORN CUNEIFORM INTERNAL INTERNAL CUNEIFORM CUNEIFORM 5 He 2no is P 2ND YYouNGER DAUGHTER. V7. RiGuTt Foor Lert Foor == TALUS VA Sie eee CALCANEUM____ CALCANEUM CUBOIDES = NAVICULAR NAVICULAR CuBOID EXTERNAL EXTERNAL CUNE!FORM WIO-CUNEIFORM MID-CUR EIFORM CUNEIFORM INTERNAL \NTERNAL CUNEIFORM CUNEIFORM Iw) Heyy iv METATARSAL IL 2np SrRo Plate X ‘ g = ~ ~ . , I, me ' " it . ad ; ; . . = 3 ‘ : . , . . c ree ri bs . f { Sy : ‘ > * - £. 1 7 ? i t * x K. PEARSON 75 Of the other two grandchildren of II. 3, belonging to the deformed group, IV. 7 and IV. 15, I only know that both feet and hands are deformed. Attention must be drawn to the fact that the deformed individual III. 5 has had three children all normal, and to the fact that the deformed individual III. 24 has had three children born dead, of whom nothing is known as to presence or absence of deformity. (5) Of the three individuals III. 21 and her two daughters IV. 21 and IV. 23, aged respectively 10 and 24 years, the following account has been drawn up by Professor Thane from Dr Mackenzie Davidson’s radiograms. In the list below a plus sign marks the presence of the corresponding bone, the dot its absence. In the diagrams of Plates IX and X the defectiveness of the bones of the hands Elder Younger 4 Mii Daher | Date noire | Eee | Zoungme Age 37 ee tee WI. 21 | "Tv. 21 IV. 23 Hands Age 10 Age 23 Feet | | | | Right} Left | Right | Left | Right | Left Right | Left Right| Left | Right | Left ay 2 =e eee 2 _ | Scaphoid as ar ° aE ° e | Calcaneum +f de a ae ate ae | Lunar aso |} ar a ote te ° e | Talus... + + + + + 4 Pyramidal...) + +r ar oF + + | Navicular ay |) ae +. + 4b 4h Pisiform . + dt e e ° ° Intl. Cuneiform + | + | + ae ah ° Trapezium ... toy) at e e ° e Mid. Cuneiform | + | ay) e ° e ° Trapezoid ... + + e e ° ° Extl.Cuneiform | + sits e ° e ° Magnum ... + ae +? + + + | Cuboid soll) ae) + au + + Unciform ... fs + au 4b a + | Metatarsall...} + | 4+ e e ak e Metacarpal 1 e ° e e ee ; De os ° | e e ° e ° aS 2 + + e e e | e “ By oe e e e e ® ° “4 3; + | + | + | + | 4?) 4 » 4.4.| © . ° ° ° : a 4; + | + | + + +) + oe oh ce + + + | + + . 5 ay = ar ar ieee: Digit eee -b + e e + e Digit 1 ° ° ° ° ° ° 2 ph. | 2 ph. 1 ph. ” 2 ° ° ° ° ° ° fused ” 3 e 0 e e e | e ” Qe e e e | e e e of 4 ° e e e e | e 5 She e e e | e ° e ” 5 ar ar ae ar a ar a 4.. e MW ee HO e e 3 ph. | 3 ph. | 3 ph. | 3 ph. | 3 ph. | 3 ph _ 5. + of + | + + + | 3 ph. | 3 ph. |?2 ph.| 2 ph | 1 ph. |2 ph. and feet is indicated by noting the presence of bones by shading in each case, the unshaded bones are absent, a key figure indicates the bones of the normal hand and foot*. These figures show nothing of the contracted and distorted form of the original members, for which the reader is referred to Plates XII to XVI which give a few of the radiograms of these three cases. It is fairly possible by the shadow of the fleshy parts and the aid of Plate XI to reach a reasonable appreciation of the actual appearance of the living individuals. The nature of the deformity in these limbs is a partial suppression of the digits, together with reduction (absence or fusion) of certain associated carpal or * Owing to an oversight of the draughtsman, the names of the bones were inserted on all the figures; it seemed better to leave the redundancy than to go to the labour of redrawing the plates. 10—2 76 Inheritance of Deformity known as Split-Foot or Lobster-Claw tarsal elements in the more pronounced cases. The bones of the forearm and leg are normal in their disposition as far as they appear in the photographs. In the mother, ITI. 21, the left hand has a well-developed carpus which may be regarded as normal, while in the right hand the distal row of the carpus shows only three bones, the outermost of which probably represents the fused trapezoid and trapezium. In both hands the fifth digit (little finger) is well developed; the whole thumb is missing, as are also the phalanges of the index, middle and ring fingers, those digits being represented only by the metacarpal bones, of which the proper second (that of the index finger) is the smallest, and indeed in the right hand is reduced to a small piece of bone corresponding to the basal portion only of the normal bone. In the left hand of the daughter, IV. 21, there are three bones in the proximal row of the carpus, the pisiform being as yet unossified, two only in the distal row, magnum and unciform, the three inner metacarpal bones, diminishing in size from the fifth to the third, and the normal three phalanges of the little finger. Sup- pressed are the two outer bones of the distal row of the carpus, trapezium and trapezoid, the first and second metacarpal bones, and the phalanges of the thumb, index, middle and ring fingers. The right hand shows a greater degree of reduction, the scaphoid being suppressed in the proximal row of the carpus, while in the distal row there is only one bone representing the fused magnum and unciform, and the third metacarpal is smaller than in the left hand. IV. 23 has only three carpal bones, pyramidal, magnum and unciform, in each hand, but she is still too young for ossification to have started in the others; the fourth and fifth metacarpal bones are fairly well developed; the third metacarpal is small, in the right hand merely a nodular vestige of the basal portion; the phalanges of the little finger are present and of good size. The malformation of the hands consists therefore of suppression or reduction of parts proceeding from the radial (thumb) side towards the ulnar (little finger) side, and carried to the greatest extent in the young child, IV. 23. The feet are not so homogeneous as the hands, and fall into two well-marked groups. In the one, comprising the two feet of the mother and the right foot of the younger child, IV. 23, the three middle digits are suppressed, including meta- tarsal bones and phalanges, while the first and fifth are fairly well developed, especially in the mother. The tarsus may be regarded as complete in the mother, only in the right foot the number of elements is apparently reduced by the fusion of the internal and middle cuneiform bones; while in the right foot of IV. 23 the middle and external cuneiform bones are missing, but it may be that they are still in the cartilaginous stage, ossification not having yet begun. The two feet of IV. 21 and the left foot of IV. 23, which constitute the second group, are also very much alike. Here the inner four digits are suppressed, and only the fifth (little) toe is represented. In all the talus, caleaneum and cuboid of the tarsus are well developed, the navicular is ossified (just beginning to ossify in K. PEARSON 1h IV. 23)*, and the external and middle cuneiform are wanting, while a rudimentary internal cuneiform is present in both feet of IV. 21; that this is not seen in IV. 238 is again possibly due to delayed ossification. Hence the second group differs from the first in the suppression also of the first digit, and probably a concomitant reduction of the tarsus. The close resemblance of the condition in this second group to that exhibited by the hands is obvious. All through the deformity is greater in the children than in the mother. In the hands, IV. 23, the younger daughter, shows greater degree of reduction than IV. 21. The small number of carpal bones in IV. 23 is to be explained how- ever by the fact that the child is too young for ossification to have begun in the missing elements. The same consideration will account for the absence of the pisiform in LV. 21. This does not apply to the metacarpal bones. In the feet there is a difference on the two sides. The left foot is slightly more reduced in IV. 23 than in IV. 21; whereas the right foot is much more defective in IV. 21, IV. 23 having the first digit fairly well developed. In all three the right hand shows a greater degree of reduction than the left, expressed in the condition of the metacarpal bones. In the mother the left foot may be regarded as being slightly more reduced, as indicated by the fusion of the internal and middle cuneiform bones. In 1V. 21 the reduction is slightly greater in the right foot than in the left; whereas in IV. 23 the left foot is the most reduced of the whole series, while the right foot has a well developed metatarsal and phalanx to both great and little toes. (6) I have delayed referring to my final criticism of the application of Mendelian conceptions to cases of abnormality like the present, until I had placed before the reader the above accurate account of the nature of the defect in two or three individuals. But having done so it seems to me that a very difficult question has to be answered. What in a case like this of split hand and foot is the Mendelian unit character? What are the allelomorphs whose combined absence or combined presence is impossible in the zygote? We can understand what is meant when an organ is said to be yellow or white, rough or smooth, however much we may wish for the use of a quantitative scale of such characters. We can understand what is meant by the presence or absence of a given individual bone, say the second phalanx of the fifth digit. But in a case like the present we are concerned not with a simple unit of any kind, but the absence of a complex of even as many as 60 bones situated in four different parts of the body. In other cases 10, 20 or 40 bones may be wanting or incompletely developed. It is true that these parts are highly correlated, but as we have seen, deformity of the feet is not always accompanied by deformity of the hands. Can we look upon the character here as built up of a series of coupled characters representing the system of bones we have referred to? If so, how can we explain the variety of detail which is to be found within the same family? How shall we account for other * It is interesting to the anatomist to note that the tuberosity of the navicular bone has a distinct centre of ossification in both feet of IV. 21. 78 Inheritance of Deformity known as Split-Foot or Lobster-Claw families in which mere syndactyly or polydactyly occurs, or again in which club-foot alone is inherited? It appears to me that in a case like the present we cannot possibly speak of the presence or absence of a unit character, there must be an inertia or weakening of some development-controlling determinant. I will not venture to call it an absence of such a determinant, because its range varies so widely from individual to individual. If we use the word absence we must make the full control depend on the presence of a large number of units, and there must be—as for example in the reducing division—some process by which a random number of these are cast out. Even with this interpretation we are really thrown back on quantitative degrees in the controlling factor. These control units cannot be specific, for if they were associated with special bones, it is not easy to under- stand how a bone occurring in parent and grandparent* could disappear in the zygote resulting from a normal union. The problem has been forced on me recently from the practical side in studying cases of human degeneracy with correlated defects, and although I have thought over it carefully I can see no daylight theoretically in these questions of correlated physical or mental defects —defects having a considerable range of variation, but peculiar to certain stocks —except from the assumption of development-controlling units or determinants. These determinants may be more or less definitely associated with certain portions of the body—hands and feet, or eyes for example—but the total number rather than any specific character of each must determine in every individual case the extent of defective development. Whatever the modus may be, i.e. whether the determinantal system be quantitatively continuous or consist of discrete units, I venture to suggest that it is rather in the direction of inertness in controlling determinants than in the hypothesis of a definite allelomorphic character in the Mendelian sense that we must seek for light on the inheritance of physical or mental degeneracy or deformity in man. The complexity and variety of the deformity in many of these cases is too great for us to attribute it to a single allelomorph, and there is thus no obvious reason for anticipating a simple Mendelian ratio. (7) On the subjects of my present study a few general remarks may be made. They show remarkable aptitude in the use of their misshapen hands. At school the children hold their own with normal scholars in writing, drawing, and even needlework. The family rather resent anything in the shape of pity. One of its men expressed himself as follows: “Bless ’e, sir, the kids don’t mind it. They never had the use o’ fingers and toes, and so they never misses em.” One of the girls with the 5th digit only on each hand is learning dressmaking as a pursuit. In Messrs Lewis and Embleton’s family the gait appears to be normalt, but I should hardly say that this describes those members of the present family that I have seen. One who has long been acquainted with them writes: * Bug. the first digit of the foot existing in III. 21 and II. 2 disappears in the offspring of a marriage of III. 21 with a normal, as in IV. 21. + Biometrika, Vol. vt. p. 28. Biometrika, Vol. VI, Part | Plate XI Hands of Mother (ILI. 21) and Daughters (1V. 21 and LY. 23) —— “« : th Plate XII Biometrika, Vol. VI, Part | u “OL MOTA JUOT ‘(IZ “TIT) ey,oTY Jo yoo 1 org a De ae e 43 4 ‘ ‘ . i Plate XIll Biometrika, Vol. VI, Part | AL ‘OLY AMOIA OpIg ‘(1G TIT) toyzo]Y Jo yoo WE ‘OL + 2 ¢ ‘ ‘ Ns \ 1 tr ‘ ’ > * aig e 4 - t Fi = A } : x : Oy," 7 x : i ' , : ; ‘ 7 : - * : P 5 ? . ‘ + boas : + ‘ + 2 . > ' ‘ ~ an ‘ iN =4 “a « ; Bate 48 i Plate XIV Biometrika, Vol. VI, Part | Fig. v Fic. vi Front and side views Feet of elder Daughter (IV. 19). amuse Biometrika, Vol. VI, Part | Plate XV Fig. vii Hands of Mother (III. 21) Fia. viii Hands of elder Daughter (IV. 19) Oo Biometrika, Vol. VI, Part | Plate XVI Fia. ix Hands of younger Daughter (IV. 23) Fig. x Feet of younger Daughter (IV. 23) - a : f a a“ on : a yt di - bd ® e . va 1 - Dy re f . - 5 ane . — ‘ K. PEARSON 79 “Their feet lack the natural spring of the normal foot and their gait is therefore very ungainly, being assisted by a peculiar swing of the arms, much as a normal person would walk on heels alone. This is of course a great drawback, but not such as to incapacitate them from earning a living.” Turning to a further point we note that the deformed members seem to have no reduced fertility, nor do they appear to have difficulty in finding normal husbands or wives. On this account there is some concern at the perpetuation of the deformity in the district. Physically we may perhaps detect in some members signs of degeneracy, but they cannot be said as a rule to have weak constitutions. Intellectually the children take high rank in intelligence, or perhaps it would be better to say in “cuteness.” Thus physically handicapped it would perhaps be unreasonable to expect in all members the highest social qualities, and assuming the stock to have been initially good, it may be doubted whether the deformity permits its members to select the physically and mentally fittest of normal mates. The stock is sufficiently extensive now to intermarry, and should it be ostracised might do so, a result which would have much scientific interest ; but which might lead to the perpetuation of a split-foot race. Eugenically the problems associated with the family are not only scientifically difficult but practically serious; we live no longer in an age when the need for perfect hand and foot in the struggle for existence preserved the race from the perpetuation of a deformity. How is pro- tection now to be maintained? In view of possible future legislation, it would seem for national purposes desirable that stocks of the present type should be kept under observation and careful records preserved of the history of all their branches. One of the most urgent social necessities is that every birth certificate should be associated with a medical certificate of the normality or abnormality of the child registered. A separate filing of the abnormal cases would not only keep the scientist in touch with important material, but provide the legislator with data whereby to appreciate the extent to which the suspension of natural selection is racially deleterious. ON A MATHEMATICAL THEORY OF DETERMINANTAL INHERITANCE, FROM SUGGESTIONS AND NOTES OF THE LATE W. F. R. WELDON. By KARL PEARSON. (1) Introductory. In the memoir of Weldon’s life published in the last volume of this Journal* occurs the following paragraph referring to the year 1905: “In the summer the present writer was at East Ilsley, some seventeen miles from Oxford, and there was cycling out several times a week ; the writer’s chief work was on other than biometric lines and broken by other claims on his time, but there was steady joint work on the determinantal theory of inheritance as outlined by Weldon, and it is hoped that it is sufficiently advanced to be completed and published.” That hope is not wholly fulfilled. My mathematical draft of the theory was finally taken by Weldon from Ilsley to Oxford to be rewritten with proper biological terminology, and to have erroneous developments marked for reworking; this revision never appears to have been accomplished, and beyond my attempt at mathematical interpretation of Weldon’s ideas, which I knew to be inapplicable at certain points, and his letters and a notebook full of numerical illustrations due to an earlier period of the same year, I have practically nothing to guide me in reconstructing Weldon’s theory. The possibilities before me were threefold, to allow the matter to drop, to wait till I could find a cytologist with an interest in and a knowledge of the theory of chance at all comparable with Weldon’s before going further, or lastly to publish what I could put together on my own responsibility. I have adopted the latter course, not because I am unconscious that I am likely to blunder, but because the material may at some time prove sufficiently suggestive to a reader with competent knowledge to cause him to take up the subject on broader and more effective lines, than I can pretend to do. Accordingly for all that is suggestive or valuable in the present discussion Weldon is responsible. My contribution is solely the mathematical analysis, and even here directly, and by force of numerical illustration, he had gone a con- siderable way independently. Any defects in terminology and misstatements of cytological facts are mine alone. * Vol. v. p. 46. K. PEARSON 81 In starting his investigations Weldon proceeded on very general lines, which it may be well to indicate. He was not inclined to accept the theory of unit characters, of allelomorphs and of pure gametes as capable of fully describing even the inheritance of the simplest characteristics. At the same time he recognised the importance of the segregation first pointed out by Mendel in the offspring of hybrids, though even here he was not prepared to make the segregating classes so distinct and so wanting in continuous variation, as some Mendelians have held them to be. He was convinced that in a sufficiently general theory of inheritance some place must be left for a normally arising percentage, however small, of variants, specially related to the distant ancestry. He was thus seeking for a mechanical explanation of latent characters, or in other aspects of reversions and even mutations, In starting his work Weldon was perfectly catholic as to the possibility or not of paternal and maternal chromosomes retaining their individuality from the moment of fertilisation up to the reducing division of the germ cells. He did not consider this point as at present absolutely settled by the cytologists. While the retention of individuality immensely simplifies the analysis, this did not deter Weldon from investigating at great length the numerical results flowing from supposing an interchange of chromomeres at every mitosis. The following rough notes of January 2, 1905, express the ideas then in his mind; it must be remembered that they were not written for publication, but as suggestions for his own work. 1. It is, I think, evident, from the facts of regeneration, that the theory of a nucleus as composed of specific organic determinants is hopeless, It is also evident from the behaviour of eggs, such as those of Ctenophora, that a special structure leading to determinate fate of special portions, may exist in the cell body. 2. The above facts do not invalidate conception of nuclear elements as a series of stirps, in Galton’s sense, each containing something capable of exciting the development of any of the somatic characters, according to its position in the organism. 3. It seems necessary to regard a stirp as capable of exciting, not only somatic characters like those of its parents, but characters like those of its more remote ancestors under certain circumstances. 4, It is evident, from the facts of growth and regeneration, that the characters of any one stirp which become active in any one generation are determined by the position of that stirp with reference to the rest,—i.e. by a process of the same nature as Mendelian “dominance.” 5. In an individual of pure race, the stirps will each contain the present and ancestral characters of that race. Assuming equality of numbers in germ cells which can fertilise each other (about which there is no real knowledge) the hybrid zygote should contain two sorts of stirps in equal numbers, each representing the race-characters of one parent. It seems possible on this assumption to develop a theory of nuclear division, which may give Mendel’s results without eliminating ancestral influence,—i.e. without a theory of the “pure” gamete. 6. Such a theory would start by taking “chromomeres” as units. A chromosome of n chromo- meres becomes entangled in the nuclear network: say there are in the zygote 2m chromosomes, there will be 2mn chromomeres in the resting nucleus. Before division these will be gathered into 2m groups for an ordinary mitosis, into m groups for a maturation mitosis,—the maturation division being afterwards heterotypic. Biometrika v1 11 82 On a Mathematical Theory of Determinantal Inheritance Weldon first proceeded on the basis of the non-individuality of the paternal and maternal chromosomes, and supposed a chance distribution of the chromomeres in ordinary mitosis. He investigated the problem with great wealth of numerical illustration and with a variety of hypotheses as to segregation. He concluded : “Tt seems clear that such forms of segregation as I have assumed during nuclear division will not lead to a separation of zygotes into classes sufficiently sharp for Mendelian purposes, unless some persistence of effect from one mitosis to another be assumed.” j He accordingly turned to the other extreme hypothesis, ie. that from the moment of fertilisation up to the reducing division of the germ cells paternal and maternal chromosomes retain their individuality. It is clear that this assumption disregards the reticulated stage of the chromosomes so far as its bearing on heredity is concerned. Weldon did not, however, reach the standpoint of the individual persistence and identity of the chromosomes during the reticulated state owing to a bias in favour of one or other theory. He recognised by extended numerical investigation of a number of cases that, if the chromomeres are the bearers of hereditary properties, interchange of chromomeres during ordinary mitosis was incompatible with any definite segre- gation in the offspring of hybrids. Throughout the theory hereinafter developed, the persistency of the individual chromosome up to the reducing division will be supposed to hold. The evidence in favour of this persistency is far from negligible, but it is hardly as complete as some Mendelians are inclined to believe. It is here accepted as a working hypothesis with the view of ascertaining whither it leads. That no hypothesis was found numerically workable and consistent with segregation phenomena, neither proves that such a hypothesis does not exist, nor’ demonstrates the universal truth of segregation. It merely indicates that in the present state of our knowledge we shall be most likely to reach suggestive and test results, if we follow up the idea of individuality in the chromosomes up to the reducing division, (2) Let us suppose that each somatic cell consists of 2g chromosomes, effective with regard to any one inherited character*, and that each such chromosome contains p determinants on which the nature of this inherited character depends. If we start with a cell belonging to an individual of pure race we may suppose these p determinants alike, and the 2q chromosomes identical in character. We may speak of this first group of determinants as protogenic determinants and the corresponding chromosomes as protogenic chromosomes. Taking a cell belonging to an individual of a second pure race, it will also contain 2q chromosomes built up of p determinants. These may be termed the allogenic chromosomes and allogenic determinants. Suppose q protogenic chromosomes to be contained in a germ cell after the reducing division, and let them join with q allogenic chromosomes in a germ cell of the second race to form a zygote. Then whatever fusion of the * The whole number of chromosomes may be anything larger than 2q. K. PEARSON 83 nuclei may take place in the process of fertilisation, if we suppose the chromosomes to retain their individuality, there will be no interchange of chromomeres or their determinants between the allogenic and protogenic chromosomes in the zygote. Ordinary mitosis will now take place and somatic cells be indefinitely multiplied without interchange of determinants. Each hybrid cell will contain 2¢ chromosomes, q with p protogenic and q with p allogenic determinants. The nature of the somatic characters of the hybrid will not be determinable in any way unless we have some theory as to whether the protogenic or allogenic determinants are dominant, or blend, or learn by experiment or observation that they give rise to certain characters which may differ from those of either pure race. We have a hybrid somatic cell in which there is a balance in number of the two types of determinants. As long as each ordinary mitosis divides equally the number of each kind of determinant in this heterogenic cell, it will not matter whether we suppose individual chromosomes to consist solely of determinants of one race, or each chromosome to have p protogenic and p allogenic determinants. The important point is that this equality of division should be maintained up to the reducing division. We shall now suppose that on the reducing division the protogenic and allogenic chromosomes fuse and interchange determinants, i.e. there is a random selection of p determinants out of the total 2p, p protogenic and p allogenic determinants. This is equivalent to drawing p balls out of a bag containing p black (=protogenic) and p red (=allogenic) balls*. Or, the distribution of frequency of the several heterogenic chromosomes which contain p, p—1, p—2, p — 3,... protogenic determinants is given by the successive terms of : p! P p(p—1))? (p—1)(p-—2))}? a Gpyi 1 + pil po) +{? Ec 2 % +] Reerereate (11). It is obvious that these terms are proportional to the squares of the binomial coefficients (1 + 1)?. If we take a second heterogenic cell and give it a reducing division, the frequency of the protogenic determinants in the resulting germ cells will be also given by (ii). Fertilisation of a heterogenic germ cell of gq chromosomes by a second will lead to the somatic cell of the offspring of the ‘hybrids.’ This somatic cell contains 2q chromosomes each containing p determinants, and the frequency of the number of protogenic determinants in these chromosomes will be given by the expression {on E + p+ jee + 2 Cowes AG a + |p Git (2p)! 1.2 ee * Tt is well known that the chances of drawing r, r—1, r—2,r—3... black balls out of a bag con- taining u black and v red balls are the successive terms of the series : u! (u+v—-r)! eee DG = Uy v (v—-1) (u+v)!(u-7r)! u-7r+1 1.2 (w-r+1) (w—-7r4+2) ) = 2) —_v(v-Y(-2) | a ; (i) A) (w-7r+1)(w—r+2)(w-—r4+3) 0" ees (poe : 84 On a Mathematical Theory of Determinantal Inheritance this is raised to the power of 2g, since the two hybrid or heterogenic germ cells have the same constitution of chromosomes. Now several possibilities arise at this stage of the development of the theory: Suppose we have only a single chromosome in the germ cell, or two in the somatic cell, then p =1 gives us the following condition of affairs: 4 of the zygotes would consist of two chromosomes both with protogenic determinants, one-half of two chromosomes one with a protogenic and one with an allogenic determinant, and one-quarter with allogenic determinants alone. This is I take it pure Mendelism. The single determinant is the unit character and the protogenic and allogenic determinants are the allelomorphs. But a difficulty occurs in the fact that we must content ourselves with two chromosomes for most cases of inheritance. If we accept De Vries’ view of an interchange of chromomeres bearing the determinants occurring at random between paternal and maternal chromosomes at the reducing division, then to reach pure Mendelism we must assert that only two chromosomes in the somatic cell, one in the germ cell, contain the inheritance factor for any character, and that this factor is built up of a single determinant. If we suppose for example that all the chromosomes, say 2g of them carry the determinant, then our distribution would be ($ + 4)*%, and it is clear that a homozygote would only result among the crossings of hybrids in a percentage far below the simple Mendelian 25. Thus De Vries’ explanation appears to involve the narrow differen- tiation of the chromosomes, two only being concerned with any single character ; or if more or all of them are to contain the determinant of any one character, then there must be some special mechanism to insure that all chromosomes at the random interchange of determinants before the reducing division interchange in precisely the same manner. We are not compelled to assume such a mechanism, which there is at present no cytological evidence in favour of, until it has been demonstrated that the experimental destruction, or observed absence of one or more chromosomes in a cell involves no loss of any series of characters. If a perfect zygote should develop from two germ cells, when half the nucleus of one has been removed, the problem of how De Vries’ suggestion could lead to Mendelism would have to be further considered. Meanwhile let us proceed on the assumption, that there exist not a single Mendelian unit but p determinants for the character either in a single chromosome of the germ cell, or in g “tuned” chromosomes. The distribution of protogenic determinants in the two, or the 2q “tuned,” chromosomes of the somatic cells of the zygote will be given by the system of chances involved in the series ety 5 B0 Gor prurins (BPSD) gent POMP rag} The symbols 7 and a here refer to protogenic and allogenic determinants ; the chance of s protogenic and s’ allogenic determinants occurring in the two chromosomes (s + s’= 2p) or in the “tuned” qg pairs of chromosomes, being given by picking out the numerical coefficient in the above expansion of 7a", I illustrate this on the first four cases. K. PEARSON 85 Casel. p=1. 1 oes 2 ok oS 2 ag (™+%) ='257r? + 50a +250, m 25 °/, Dominance of protogenic determinants, amr 50°/, Balanced heterogenic determinants, a@ 25 °/. Dominance of allogenic determinants. In this case it will be seen that the dominance of either determinant means a pure cell. The case is that of simple Mendelism and is the basis of a “pure gamete” theory. Case2. p=2. 2! 2 2)2 Gp {ar ar Ara ar ary”. This gives wT 860278 ‘ ; ; = 25 °/, Dominance of protogenic determinant, Ta 22:22 ma? 50:00 =50°/, Balanced heterogenic determinants, 5 ma 22-29 = 25 °/, Dominance of allogenic determinant. O° at 2°78 This case is of peculiar interest ; we get absolutely the Mendelian percentages, if the somatic character follows the preponderance of a given pure race determinant, using preponderance here in a simple numerical sense. Further, the protogenic 25 per cent. would apparently breed true to the somatic character of the pure protogenic race, if the somatic character of the balanced heterozygote were, as is occasionally asserted to be the case, indistinguishable from that of the protogenic race. The peculiar suggestiveness of this result lies in the exact Mendelian properties arising on a simple view of dominance apart from any hypothesis of the pure gamete. There exists a latent allogenic determinant in the heterogenic chromosome of a large percentage of the 25 per cent. with dominant protogenic character. This, if judicious cross-breeding were adopted, might be rendered manifest in some, if only a small number, of the grandchildren of the offspring of the hybrids. Case 3. p=8. (3!) (6) (7? + 97r?a + Ora? + a?) m 025 °/. mai 4°50 °/,- 29°5 °/, Dominance of protogenic determinant, ma? 2475 °/. ma’ 41:00 °/,; 41 °/, Balanced heterogenic determinants, mast 24°75 °/ mo? 450 °/, + 29°5 °/, Dominance of allogenic determinant. Ee OZD. 86 On a Mathematical Theory of Determinantal Inheritance Here, if the balanced heterogenic group be classed with the protogenic group, we should have the ratio 70°5 to 29°5, and most readers will remember worse experimental Mendelian quarters than this. The illustration shows that it is quite possible to get numbers approaching the Mendelian when there really exists a considerable variety in the determinantal constitution of the cells in which the protogenic race is dominant. Case 4. p=4. SU {wr + 167° a + 36770? + 1670? + at}? (8 Py 00T TT . m 0-020 °/, ma? 24163 °/, ma 0653 °/, Tot 6694 °/, ma 6694 °/, me’ 0653 °/, moe 24163 °/, a 0:020)7/6 mia 36939 °/, Thus we see that there would be 31°5 °/, with dominance of protogenic deter- minant, 37 °/, with balanced heterogenic determinants and 31°5 °/, with dominance of allogenic determinant. The distribution is diverging considerably from the simple Mendelian quarter and approaching much more nearly a normal distribution (or binomial distribution) in the protogenic determinants. No special stress is laid on the above examples, I have only taken them to indicate, how simple Mendelism passes when we increase the number of deter- minants concerned from a pure gamete theory to one in which we have dominance with closely Mendelian proportions, but diversity of gametic constitution in the dominant quarter, which might not cease to be latent for two or more generations. Again, on still further increasing the number of determinants, we pass to what is clearly a close approximation to the normal curve of distribution. It seems desirable, therefore, to investigate further the general theory of p determinants each occurring in two or in 2q “tuned” chromosomes. (3) Returning to the fundamental formula (11), which gives the distribution of protogenic determinants in the chromosomes of the germ cell, we note the complexity of the analysis required to deal further with it in its present shape. But we see that it is formed by the squares of the terms of a symmetrical binomial. Now for p even moderately large this binomial is extremely close to a normal curve, and accordingly the squares of the ordinates of this curve will represent extremely closely our series. But the squares of the ordinates of a normal curve are themselves ordinates of a normal curve. Thus the normal curve* which fits closely (4+4)? is y= e~ 2”'le” where o=Vi (pte, 20 and cis the unit of plotting. Very frequently V}pc is taken for o, and p being * Phil. Trans. Vol, 186, A, p. 355. K. PrArRson 87 large, there is no sensible difference. Since y xc gives approximately the ordi- nates of 9 +1)?, we may expect 2” (p |)? (2p)! Or, supposing p moderately large and using Stirling’s Theorem, we may anticipate that the terms of (ii) will be given fairly well by 1 ate ee ee errr en iv). V2r Vine? ay) This is a normal curve of standard deviation Vipc, and accordingly it must y’c to give the terms of (ii). again be closely given by the binomial (§ + Lye? I find that the areas of (iv) give (ii) closely, but that if we work with ordinates we get a better result from V1(p+4).c as the standard deviation of the normal curve, ie. neither using p nor p+1, but the mean of these values. The following table illustrates the closeness of approximation for p=12: Normal curve A " Accurate values Areas Ordinates from (ii) (b+4)2? (c =N tp =1:22475) [o=N2 (p+4) =1-25] 0000 0000 0000 0000 ‘0001 0000 ‘0001 ‘0001 0016 ‘0000 ‘0020 0019 ‘0179 0156 ‘0185 ‘0179 0906 0937 ‘0897 ‘0887 ‘2320 2344 ‘2306 2318 3156 3125 ‘3181 3191 2320 ‘2344 2306 2318 ‘0906 0937 0897 ‘0887 ‘0179 0156 0185 ‘0179 ‘0016 ‘0000 0020 0019 0001 ‘0000 0001 ‘0001 0000 ‘0000 ‘0000 ‘0000 It is clear that for all practical purposes the normal distribution, and even the simple binomial, may replace the expression in (ii) for the distribution of determinants in the heterogenic chromosome when p is as large as 12. The errors of the actually available samples, 500 to 1000 at most of each generation, will be well within the errors of random sampling. Even if p=4, the agreement between (ii) and (4 + 4)? is not wildly out: 0143 ‘0000 2286 "2500 5143 5000 2286 2500 0143 ‘0000 88 On a Mathematical Theory of Determinantal Inheritance In fact it would often be extremely difficult to distinguish between (i1) for p=4and a true +, 4 and } system of frequency. For example, in any breeding experiment yet made we may well doubt whether it has been on a scale sufficient to distinguish between 51 and 24 per cent. as compared between 50 and 25 per cent. We are therefore justified in replacing (ii) by a normal curve for practical purposes. If we calculate areas we may take its standard deviation Vip; if we calculate ordinates we shall get a somewhat better result from Vi(p+3), but for p as large as 12, the results will agree within the errors of random sampling for practical series. We have now found a fairly simple analytical form for the distribution of determinants in the chromosome of a gametie cell of the hybrid. The probability that the chromosome of the gametic cell of the hybrid will have a number of determinants of protogenic character lying between $p + a/c and 4p+(w+ 82)/c is PaaS gS IES (iv) bis. WA wee e ese rercorsesesereses ie ine The close resemblance of this result to (4 + Ly? shows that the variability of the chromosomes in the number of protogenic determinants is practically confined to the range of }p to $p. More accurately, only two individuals per thousand would have more than }p+%p protogenic determinants. Now the gametic cells of both hybrid parents will have a distribution of this character, and supposing random mating among the hybrids, the frequency of protogenic determinants in the zygotes will be given by a normal curve of standard deviation > where S=1pc+4pe, or L=V5p.c. Thus the frequency with which p+s protogenic and p—s allogenic deter- minants occur in the somatic cell chromosomes of the offspring of the hybrids is given by the normal curve - 21 1, 4eiapey) Y* lin Tipe where s=2/c. (4) We have now to determine the constitution of the gametic cells of the offspring of the hybrids or to take away by the reducing division p determinants at random from p+s protogenic and p—s allogenic determinants. The result is reached at once by substituting in (i) of p. 83 the valuesu=p+s, v=p—s,r=p. But the complexity of the result would be great (for general theoretical purposes apart from special numerical illustration) if we did not use some close-fitting continuous curve for the series. Such a curve is provided for in my memoir “On Skew Variation in Homogeneous Material*.” In the notation of that memoir we find ; _@{1+pyr—-s il : 2, = ares a , Bi=0; Bs see oe sete lee (vi), * Phil. Trans. Vol. 186, A, p. 361. K. PEARSON 89 and hence the differential equation to the curve i i Se y da Bi + Bae + Bx? becomes simply LCS bee AGH ea) EU Reena ee terse (vil). yde tell+py—s} +a Whence, integrating, we find 1 OO eT + pi} +a PF Here « is measured from the modal value which is clearly the same as the mean, and corresponds to a length }(p+s)c, or to the number 3(p+s) of protogenic determinants. Further, y, will be a function of s which remains to be determined. Pe De ee (viii), Let n, be the total frequency corresponding to somatic cells of the offspring of the hybrids, i.e. to the cells before the reducing division. We must have ei +o 5, - +00 da Ns = ot L= Yo wo (Ag + ayer? where A,?= $e? {(1 + p)?—s*}. Let c=), tan @, then +30 oy | cos” Od0 2g?" Tv -3 Or Yo—Ne eh tap, where ae sin? dd®¢ is a well-known integral. 0 __ NsAgPH Voy (AZ + gi) PH But «is measured from $(p+s)c the mean value of protogenic determinants in the gametic cells of the offspring of the hybrids. Let us write «=—4sc + &, then Thus (viii) becomes err ee Yfke (1 +p’) + B= cE} To find n;, we must note that it is defined by the strip yd’ of a normal curve eee a (x) pa, SS Ae abe) = —— _ —— @ 3 Y Van Vipe where a/c =s, for this is the distribution for the somatic cells of the offspring of the hybrids. Thus the frequency for the germ cells of the offspring of the hybrids of chromo- somes with 4p + &/c protogenic determinants arising from offspring of hybrids with somatic cells with chromosomes with p+ ’/c protogenic determinants is given by the surface f all Ee ema ez) a {ho2 (1 + ptt Ee af}? tt Biometrika v1 iP) /2 r2 ; Z= a re (x1), 90 On a Mathematical Theory of Determinantal Inheritance where z is a function of p, but not of w. This is nothing else than the correlation surface between the number of protogenic determinants in somatic cell chromosomes of the offspring of the hybrids and the number of protogenic determinants in the germ cell chromosomes of the same individuals. (xi) is again somewhat complex, but it will suffice to reduce it for most practical purposes to a normal correlation surface. Thus 2 (1+ p)*) 1/(1+p) eds prt eyrtt=ned serie ph] pe FPF ={(e(14 pyri Stet} approximately. 2 Similarly we have p+ p+h fo Oe eet pity = ac (ip) {1 - sao | eth mentee where m = (14+ p)?/(4 + p). Thus the correlation surface, if z,/ be a new function of p only, is given by a Pw a? gage Om geh(ped) "Ape? Voge sen tieecsosene enema (xii). Writing this in the form {a!2/Z%, — 2Rs,gox'E/ Zs, Zg, + 7/27 Go rd g=2e “1-F sg, we easily find aa bare Correlation between somatic and gametic ~ V3 fe +p ay =! cells of offspring of hybrids. = V3 Nie ptl p+: p+: sp+3 2 (Standard deviation of somatic ea “RR 4 p ptt p+l ~ | cells of offspring of hybrid. See pel a eres deviation of gametic cells of Vp? +: +intl offspring of hybrid. Thus we find V3 e P Rs.g, Xg,/—q Npe 2s,/3Npe 2 5108 11632 1:0290 4, 5423 10865 1:0206 6 5537 1:0590 10157 20 ‘5773 1:0000 1:0000 It will be noted that as p increases the correlation rapidly approaches the value ‘5773 and the variability of the gametic and somatic chromosomes the values af Vpe and 4Vpce. Thus we see that, according to the theory here developed, the chromosomes of the somatic cells are absolutely more variable in the ratio of 1 to ‘866 than those of the gametic cells. But, if we deal K. PrARsSon 91 with their relative variabilities as measured by their coefficients of variation, the gametic cells are more variable in the ratio of 1:73 to 1. The regression of the gametic chromosomes on the somatic chromosomes gives us the value a5 a Vpe/(4Vpc)=4, or 5 is the value this regression takes even when p is a small number. Thus, while there is no variation in the somatic cells either of the pure races or of the hybrids, and accordingly while it is impossible to find a correlation between somatic and gametic cells for these generations, its value being indeterminate, we see that as soon as we reach the offspring of the hybrids, a sensible and definite correlation exists, and this correlation has a value which may be suggestive for other forms of enquiry. The present writer is fully aware that a variety of other mathematical theories of the broad facts of cytology may be developed, and as our knowledge increases more ample theories, consonant possibly with a wider range of facts, will probably be invented. But he believes that the present theory is the first to show that there will be a definite correlation between the deter- minantal structure of the chromosomes in the somatic and in the gametic cells, and that its value will not improbably be found to be about ‘5. Looked at from this standpoint the somatic cell precedes the germ cell of the individual, and the somatic cell might, under the proper stimulus, give rise to a germ cell. These germ cells are not of one type; they are variable, but correlated with the originating somatic cell. It is difficult, if we look at matters for the time being from this aspect, to find any basis for a “continuity of the germ plasm.” Every reducing division may produce a new germ cell, and the whole group of germ cells is relatively more variable than the somatic cells from which they arise. The link between the two is one of correlation and not causation, a result produced by the random partition in the reducing division. (5) I now turn to the somatic cells of the grandchildren of the hybrids, i.e. the children H, of the offspring H, of the hybrids H. Le, . 9 : Let Date be the number of protogenic determinants in the chromosomes of the somatic cell of the first parental H,, and }p + &,/c be the number of protogenic determinants in the chromosome of the gametic cell of this parent. Let p + a,/c, and $p+ &/c be the corresponding quantities for the second parent and let us suppose the matings among the A, absolutely random. Then the number of protogenic determinants in the two chromosomes of the somatic cell of the off- spring H, is p + (+ &)/c=p+s’”, say. We require to find the correlation surface between s’” and s’ and s” (or a/c and ~,/c) or the deviations from the mean p of the protogenic determinants in the offspring H, and the two parents H,. Let us write n = &, + &, and since when p is only moderately large we have seen that p +1 and m =(p+1)/(p+4) may be practically replaced by p, we shall write for (xii) Boat a2) ao =o, 3 3 3 Zi Ce a tcp gc*ps 92 On a Mathematical Theory of Determinantal Inheritance Accordingly the chance from parental somatic cells lymg between a, and x,+ 8x, and w, and w,+ 6x, of getting gametic cells respectively between &, and £,+ 5£, and &, and &,+4 6£, is measured by - 8 ( £7 1+ 2q 6 (x Lie baat (&? af = 8 (a & +o &) + ( 1 2+ ao") } dax,da,dé,dé,, where Z, is a constant depending on p and c only. Write for &, — &, and the chance becomes 1 -$ ep {8 (2&,? — 2nE, + 4?) — 8 (mx, + (ty - &}) &) +6 (x, + 2,?)} Loe dax,dax,dn dé. Now integrate this expression throughout the range of values of & and we shall have the triple correlation surface connecting 2, 2, and ». In order to do this we must make the result a perfect square in &. We thus find Ze x16 (E&— [+3 (ty —2)))? +49? +5 (ay? + 0?) ~ 4 (ary +p) + Bary xy} dé,dnda,di, Integrating throughout the range of &, we only modify the constant Z, without changing the terms in 7, 7,, or v7. Thus the frequency surface is finally of the form: 4e2p ee *y te%p = 4c2%p ~— Sep c*p Faia ae nay Z Qnty 2a i= nents Let r be the correlation between chromosome in the parents’ and in the offspring’s somatic cells, then: The correlation of 7 with either 2, or #,=~r, and the correlation of a, and in (1) Let o, and o, be the equal standard deviations of a, and a; o, of 7. Then the bracket term ought to be equal to : == {2 a a2(1 — r?) a aP(1—1?) 2nayr 2nar i ea Hence we deduce: 1 1 4 1 1l1-r 5 1 r 2 ‘i 1 1 oe 1—2r ep’ o21—2r i ep’ a0, 1 —2r° = Cp’ op 1—2r° a ep? The second and fourth equations give us r’=1/6, agreeing with the value obtained from the first, second and third. The first and second then give of=cp and of= c'p. 2 2 2 Oy Oy 0301 O30) Oy Thus finally we have: Variability of the somatic cells in H, or in the offspring of hybrids = $c,/p. Variability of the somatic cells in H, or offspring of H,=3 kcy/p. Correlation of the somatic cells in parents H, and offspring H, = = 4082. Regression of the filial on the parental somatic cells = *5000. These results seem to be of not a little interest. They indicate that if two pure races be crossed, the variability in protogenic determinants of the chromosomes of the somatic cells will be still increasing to the third generation, Le. 1t 1s 1:225 times as great in the H, generation as in the H, generation. The correlation, K. PEARSON 93 however, is rapidly assuming a value very close to those which have been deter- mined biometrically for large populations mating at random, and the regression has already reached that value °5*. It is noteworthy that the regression of the gametic cell of an individual on the somatic cell of that individual is identical in value with the regression of the somatic cell of the offspring on the somatic cell of the individual. (6) I have not thought it worth while at present to proceed with further reducing divisions, although the results would not be without interest as determining the rate at which a stable population was established after crossing two “pure races,” owing to the cessation of change in the variability of successive generations, and to the corresponding equalisation of correlation and regression. The present investigation suffices to show that we fairly rapidly approach the biometrically observed condition of things, even if we start with two pure races, and this result will be shown on another occasion to be experimentally verified. It may, of course, be said that the hypothesis which makes the inherited character depend on p unit determinants in the paternal and maternal chromosomes, separated into two moieties at random in the reducing division, is not the only conceivable one. This is fully admitted, but by working it out as a first and not unreasonable hypothesis, we have reached a number of suggestive points. We see that Mendelian dominance and the Mendelian quarter may arise in cases where there is no pure gamete, and that the discovery of a latent character may need several generations of breeding. Further we sce a continuous transition from simple Mendelism, through various phases of pseudo- Mendelism to distributions closely following the normal curve. We notice also that if we increase the number of determinants on which a character depends, we very soon, even if we start with two pure races, reach by hybridisation and crossing of the hybrids a population closely following the correlation found biometrically for large groups mating at random. If the hypothesis here dealt with were correct, it would follow that the Mendelians were merely working at one end of the scale, the biometricians somewhat further down. At present interesting problems which suggest themselves are: the possibility of in any way correlating the somatic and the resulting gametic cells; the existence or not of ratios actually or nearly Mendelian, but where the apparent homozygotes do not breed true; lastly, the investigation of whether or not the values of parental correlation hold closely when we have bred for only a couple of generations from the hybrids of two pure stocks. With regard to this last problem, we may hope shortly for light; Mendelian literature for the careful reader may provide answers, perhaps, to the second. At present it does not seem needful to defend the assumptions upon which the present theory is based. It suffices that it is sufficiently wide as it stands to cover the Mendelian and the biometric views. It has been expounded here on account of its suggestiveness. What there is of good in it is Weldon’s; where it may blunder is where I have failed to correctly interpret by word or symbol his ideas. * The fact that there is in this case a difference between the correlation and regression depends upon the variability of the somatic cells of the two generations not yet being equal. MISCELLANEA. I. Some Notes on Interpolation in n-dimension Space. By W. PALIN ELDERTON. 1. Introductory. The main idea of this paper is summed up in the principle, or the extension of the principle, that in certain cases the use of linear second differences will give a better result than the use of two-variable first differences, e.g. three points in the table chosen on a straight line may give a more accurate interpolation than the four “nearest” points. The usual formulae of interpolation assume that we require to find from tabulated values of w, a value of the function corresponding to a certain value of # not among the tabulated cases. In some circum- stances we have to deal with a function of two variables, and it was recently shown by Mr John Spencer* that in certain circumstances the simple one-variable interpolation formulae could be used. This saves a great deal of work in practice, and in the examples dealt with it was found to give accurate results. The object of the present paper is to supply a general method and to show that it is not necessary to limit the number of variables to two. Before proceeding to the subject itself it will be well to outline the alternative methods available. The most usual practice in two-variable interpolation is to interpolate between four values ; thus if v3 is required and wp, %1, %o and zw, are given, then vw, is found from wp and wp, and uw, from wo, and wy, and then wv. from vw, and uw . Graphically these processes might be represented by the following diagram, in which the dots show the positions of the given values, the crosses the positions of the interpolated values, and the lines connecting the points indicate the values used in each interpolation. Of course to give the values in a figure we should have to erect perpendiculars to the surface of the paper. r y=1e See) y=8 S y=0 e—— x ° z=0 1 Fie. 1. The general solution in terms of differences is obtained by expanding the right-hand side of Ung = ( a5 A,)" a a A,) U0» * John Spencer, ‘‘Some practical hints on two-variable interpolation,” Journal of the Institute of Actuaries, Vol. xu. pp. 293 et seq. Miscellanea 95 but it is, I think, better to use coefficients* instead of differences, just as one does when employing Lagrange’s formula in the ordinary one-variable interpolation, and with the help of auxiliary tables such as those of Mr Herbert H. Edwardst very accurate results can be easily obtained. If however the intervals by which the given table of the function proceeds are different from those adopted by Mr Edwards, a large amount of arithmetical work is necessary. It is however worth while to recapitulate the method and increase the number of the independent variables from two to m. Assuming that we require to find ws. (n); then by Lagrange’s interpolation formula we have Upst... =T0 Most... HP Uist... F Pe Mose. CtC., where 7, 7... are numerical coefficients depending on the number of terms and the value of 7. And similarly Usrt...= So Uort... E81 Ure... F 82 U2rt...5 Uys... = to Mors... FA Uors... + C2 Mors... and so on; hence Upst...=7080 Co. Moo .. + 7OS0L «+. Yoo... + ete. =S (Mi Setr e+ Una... where S stands for the summation of all combinations of h, 4, 7... for all values from 0 upwards. The calculation of all the 7,, s,, 4... terms is done directly from Lagrange’s formula and is simple though laborious, and the remainder of the work is mechanical. When the function only depends on two variables the interpolation involves fairly heavy arithmetic if only three values are given to both / and 4, while if there are three variables the work could only be completed in two or three hours, and it is therefore clear that if the ordinary one-variable interpolation formula could be used we should save a great deal of arithmetical work. The ideas underlying the two methods can be seen graphically. A Fic. 2. In this figure a surface ACKG represents w,,, 80 that when «=0, y=2, Uz has the value represented by the height A, and when #=1, y=1, wz, has the value represented by E. Now if we require to find w».,., we can approximate to the surface by the (1+A,) (1+A4,) method or by the Lagrange coefficient method and hence find the particular height we require, or we can choose the positions of two or more values so that the straight line passing through them also passes through the point v=:2, y='4 and then interpolate by the one-variable formulae between the values of the function corresponding to the points’ on this straight line. In fig. 2 the line joining =0, y=0 to v=1, y=2 passes through #="2, y="4 and by interpolation between B and G we can therefore approximate to w»,4. The dotted lines show the process. * W. Palin Elderton in Biometrika, Vol. mu. Part 1. + Journal of the Institute of Actuaries, Vol. xu. pp. 289—293. 96 Miscellanea 2. The Interpolation Line Method. We may now attack the theory of this second method in greater detail. Let us assume that from the following tabulated terms it is required to find Ub, kyl? U0,0,0,...9 Una, ty. U2, 28, Wty ...9 etc., Ud, 3, t,...9 Ur, 28, 2t,...9 U2r, 38, 38, ..9 etc., etc., etc. This scheme is general and there is no loss of generality in assuming that the interpolated values are for integers, ie. if the function is tabulated for 7=0, 5, 10, etc., y=0, 8, 16, etc., z=0, 2, 4, etc., the interpolated values required would be for x=1, 2, 3, 4, etc., y=1, 2, 3,..., 2=1, 3, 5, ...; because if fractional values are required we can assume that the ’s, y’s, 2’s, etc. proceed by larger differences. : ( Now in order to get w, we take z and use the formula (1+A)" w=, or we can take i and h k use (1+A’)27 wyj=u,, Where A=u,—Up and A’=%z,—uy. Again to get w,., we take (14+ A)s up or k (1+4’)2s up or etc., where A and A’ have similar meanings. But if ss be used for a two-variable, then the interpolated function found could be Ue eet and therefore in order to get terms from which interpolation can be made we ath, yt—s 5 h must use, not wo, Ure, etc., but wo, Ura, 98) 80 that when we take (1+Aq)ra Uzy We Shall get w,. It is fairly clear that if we can fix either ra or s8 the other can be obtained easily, and a little consideration of the way the ra and sf arise will show the reader that the term can be fixed by the least common multiple of 2, 7, & and s. A numerical example will make this clearer. Let wo,0, 5,8, %40,16, etc. be given and assume that we require v3; then the L.c.M. of 2, 3, 5, 8 being 120 we must interpolate between Uo,oy Uso,120) V%160,240) «--» for having fixed the 120, the proportion to be taken is 735=7y and 2x40=80. If a third variable is introduced the same method can be used, and if in our last numerical example we take w,0,0, %s,8,10) %10,16,20) --- a8 given, and require w,3,7, we can use U0, 0,09 240,360,840) %480,720,1680, etc. The numerical work would be as follows in an imaginary example: . , Uo, 0,0 = 4872 — 2760 +1656, Uo40, 360, 840 = 2112 — 1104, W480, 720, 1680 = 1008. Us, 3,7 = 4872 — zig. 2760 —4. zh 448. 1656 = 4832. There are, of course, many objections to such a method in practice when it entails differences in the independent variable, such as 240, 360 and 840, but it can often be simplified considerably ; for instance, in the last example, if we imagine the given values to extend to negative values of a“, y and z, we can start from w5,9,39 and seek wo,3,7;. We notice that our fractions are now 3, 3, ~ and the L.c.m. is reduced to 120. The terms to be used are w5,0,10, “—115,120, -110 and W235, 240,230) and the value of 237 is U5, 0,10 + xy (%—15, 10, -110 — Ms, 0,10) 3+ xo + 34 (Second diff). In this way we can sometimes diminish the range of values considerably. Even here however a large table would be required for practical work, but it must be borne in mind that a three- variable table is very seldom made, and a two-variable table is frequently simplified by both the xs and y’s proceeding by the same difference. The difficulty is however always present to some extent and it would be impossible to find values of wu corresponding to a number of decimal places in w, y, ..., though the method might even in these cases be of help as a rough check. Miscellanea 97 Graphically these examples can be shown very simply by the following figures. Using dots to show the position of given values, then, if the required value is 2#2,g, we join (0, 0) to (2, 6) and produce it till it passes through another point (w’, y’), then we can interpolate for w,_ between U0,0) Ux',y’y Urx', 2y’» ete. y=16 @ © y=8 @ e y=6 y=0 ° e ° r=0 2 3 6 9 Fia. 3. In a similar way if there are three variables the following diagram may be constructed, in which dotted lines show those parts of the figure that would not be visible if we had a solid, and the dots show the positions of given values ; the “line of interpolation,” as it might be called, is OB. In fig. 2 we have represented the surface by giving the heights of the ordinates at the given points, and the same could have been done in fig. 3, but it would have been impossible in fig. 4 Fia. 4, Biometrika vr 13 98 Miscellanea because as we are there dealing with a third-dimension body we should require a fourth dimension in order to enable us to represent the values of w,,, as well as their positions. For the same reason we cannot give a graphical illustration of interpolation with four variables. 3. Some particular cases. It will probably be useful to give the “interpolation-lines ” in the case of a function of two variables where the values proceed by small differences. We shall assume that only integral values are required, and in our diagrams a heavy dot will stand for the position of a given value and a small dot for the position of a value obtained by interpolation, while the lines show the “interpolation-lines.” Difference in # =3. ” » ¥ =3. Fia. 5. In this case the line between AB is an obvious interpolation, and similar lines will be neglected in other diagrams ; in fact there is only one “interpolation-line,” since AC and BD are the same in principle; they have merely different starting-points. Difference in # =4. ” » Y = 4, Fic. 6. Miscellanea 99 In this case there are only two “interpolation-lines,” viz. BH and AC, for CH is the same as BE and HD, BF and CG are all the same as AC with different starting-points ; in fact we can in general deal with any half quarter of the square BCHH (i.e. half of any one of the triangles formed by two diagonals and a side) and use the results as applicable to all cases. Example. If we wish to interpolate for w,; we should take one quarter of the way between U,o and ws,4; if a third term were required we should take either w,3 or w_g,4, and the latter would generally be preferred as it is nearer the value required. Difference in 7 =5. ” » Y =o. Fic, 7. This is a very common case and there are only two necessary “interpolation-lines.” It will be noticed that there is sometimes more than one line that could give the interpolation, but I have shown the one most likely to give a good result. Difference in w =3. ” vo ¥ =2. Fic, 8, 13—2 100 Miscellanea In this case in order to obtain an interpolated value for w2,; we require 2,9, %e,4 and w_¢-4; clearly a less useful tabulation than differences of 3 in both w and y, and not much improvement (sometimes it is worse) than differences of 4 in both # and y. The lesson to be learnt from this is that if one can choose one’s differences in tabulation it is best to take the same difference in both # and y. Difference in 2 =10. ” » ¥ =10. The diagram in this case becomes rather troublesome, but the following table answers the same purpose. ee ; 4 y Interpolate between faking 10 Dea where n is 1 1 0, Oand 10, 10 I 1 1 2 0, Oand 10, 20 II 1 | 1 3 0, Oand 10, 30 III 1 1 4 10, 10 and —20, -10 IV 3 1 5 0, - Qandi. 10; 50° V 1 2 2 0, Oand 10, 10 I 2 2 3 0, Oand 20, 30 IV 1 2 4 0, Oand 10, 20 II 2 2 5 0, Oand 20, 50 VI 1 3 3 0, Oand 10, 10 I 3 3 4 0, 10and 410, -10 II 3 3 5 0,-10 and 10, 40 V 3 4 4 0, Oand 10, 10 I 4 4 5 10, -10 and -10, 40 VI 3 5 5 0, Oand 10, 10 I 5 This would of course be applicable where one decimal place is required and the tabulation is for integral values, but as will be noticed immediately, the number of independent “ interpolation- lines” (see Roman numbers) is very great, and it is not very difficult to show that the decimal system is by no means the best method of tabulating functions. We shall however return to this after showing the application of the above diagrams to numerical work. 4. Numerical Examples. The following table gives the values of a function of three- variables, which will enable us to give a few examples. 2=45 «x=50 “2=55 x= 60 y y y y Zz 10 15 20 25 10 15 20 25 10 15 20 25 10 15 20 25 30 5 | 7°24] 9°51] 12°74) 17°71) 5°74] 7°39| 9°60] 12°74) 4°69] 5°93] 7°53) 9°65] 3°95] 4:94] 6:14] 7-66 9°71 | | 10 | 16°06 | 21:04 | 28°20} 39°36 | 12°70 | 16°27 | 21°11 | 28°11 | 10°34 | 13°01 | 16°45 | 21:13 | 8-69 | 10°77 | 13°33 | 16°62 21°19 | 15 | 26°76 | 35-03 | 47°09 | 66:18 | 21:08 | 26°94 | 35-01 | 46°90 | 17-09 | 21°41 | 27-06 | 34:94 | 14°30 | 17°61 | 21°74 | 27°23 | 34°97 20 | 39°73 | 52°12 | 70°49 |100-00 | 31°13 | 39°81 | 51°99 | 70-27 | 25°09 | 31°39 | 39°84 | 51°84 | 20-86 | 25°61 | 31°70 | 39°95 | 51°74 Miscellanea 101 Let us first find a value for v=45, y=17, z=12; this only involves two variables, and fig. 7 tells us to interpolate between 45, 10, 5 and 45, 15, 10, ete.; hence the interpolated value required is obtained by ordinary interpolation in the following way : A A2 A3 7°24 13°80 12°25 13°61 21°04 26°05 26°86 47:09 52°91 100°00 therefore value is 7:244-1°4 x 13°80 ee 12°25 — a 13°61 = 29°13, while with only three terms we should have obtained 29°89. If we had used the ordinary double- interpolation method with the terms 21:04, 28°20, 47°09 and 35:03, we should have obtained 30°28, and as the true result is 29°48, we have in this case obtained a better approximation by the “interpolation-line” method. The data are not good for interpolation because the differences do not decrease, but this is no disadvantage for our present purpose. As a second example we will take 7=60, y=18, z=11, and we can use 14°30, 13°33 and 9°71 and obtain 14:30 —°8 x ‘97 se x 2°65 = 13°73, and the true value is 13°69. Two terms only would have given 13°58. With a little practice the values to be used can be easily picked out. We will take as our final examples two three-variable cases. To obtain v=49, y=18, z=14 we can use 45, 20, 10 and 55, 15, 20 and take two-fifths of the difference, i.e. 28°20+2 (31°39 — 28°20) = 29°48, or we can use 50, 20, 15 and 45, 10, 10 thus getting 31°21 while if we add 55, 30, 20 which is 70°02 we get 29:93; the true value is 30°31. To obtain v=52, y=14, z=14 we can use 50, 10, 15 and 60, 30, 10 and obtain 21°10, or we can take 50, 15, 15 and 60, 10, 10 but the former is distinctly preferable and if we add the term 70, 50, 5 which is 17-63 it becomes practically exact. The latter arrangement, however, shows the method at its worst. The differences run extremely awkwardly and the interpolation by first differences leads to an untrustworthy result. When using the “interpolation-line” method we are, as it were, picking out a level piece of ground on our surface before interpolating ; if we choose an uneven piece of ground, ie. if the differences are large, the result will be inaccurate. 5. Connection of Method with the Construction of Tables. An interesting point of some practical importance may now be examined. If we were to make a new two-variable table, what would be the best interval to use if we intended to apply the “interpolation-line” method ? We must clearly use an interval so that the terms used in the interpolations are not far apart, and in order to answer the question it becomes necessary to consider what intervals are most satisfactory from this point of view. We will first see how the various interpolations can be built up and will take the interval 5 to start with. The terms we require to find by interpola- tion are 1,1; 1,2 and 2, 2, because 1, 3 is just the same as 1, 2 but with a different starting point, for it is merely distance 1, 2 from the given term 0, 5. There are therefore only two lines necessary, one symbolised by 1, 1 and showing interpolation between terms like 0, 0 and 5, 5, and the other by 1, 2. The former gives 2, 2; we should have to take two-fifths of the distance between the 0, 0 and 5, 5 given terms instead of the one-fifth that gave 1, 1. Now let us take 7 as an interval, The terms wanted are 1,1; 1,2; 1,3; 2,2; 2,2; 3,3. The 1, 1 line gives 1,1; 2,2 and 3,3; and the 1, 2 line gives 1, 2 and 2, 4, but the second of these is the same as 2, 3 with a different starting-point, and we only therefore require two lines, The idea is easily continued, 102 Miscellanea and it follows that if we use a prime number (p) as our interval, we get with each interpolation Pp- 5) a é 1 : line cases; but as we require ie ele cases in all, the number of interpolation-lines required is 3 (P5741). This gives the following table : or — — — ow fod aI —4 wo) Interval 2 3 No. of lines 1 1 2 2 3 4 5 5 Turning from prime numbers to those containing factors we find at once that many more lines are required. Thus we have already seen that an interval of 10 calls for no fewer than six interpolation-lines, and the intervals of 6 and 8 will both be found to require four. The interval 9 requires three lines. Let us now compare the 11 interval with the 8 and 10 intervals and see which is the best grouping. Interval 11. Ordinary interpolation Line 1, 1 Line 1, 2 Line 1, 3 gives gives gives gives 0, 1 1,1 th 1h 3} 0, 2 2,2 9g, 4 2, 6=2,5 0,3 3, 3 3, 6=3, 5 3, 9=3, 2 0, 4 4,4 4, 8=4,3 4, 12=4, 1 0, 5 5, 5 5, 1O=5, 1 5, 15=5, 4 Average interval in interpolation in # = 8°25 ” ” ” ” » ¥ =194 Maximum interval in aise 3 | ” ” ” y =33 Interval 10. Ordinary interpolation Line 1, 1 Line 1, 2 Line 1, 3 Line 1, 4* Linel,5 Line 2,5 gives gives gives gives gives gives gives 0,1 Hee 1,2 1,3 1, 4 1,5 2, 5 also by 1, 2 i 3 2,6=2,4;. ? =2,2 0, 2 2, 2 2, 4 , 6=2, poe ethers 2, 8=2, 0, 3 3, 3 3, 6=3, 4 3, 9=3, 1 3, 12=3, 2 3, 5 6, 5=4,5 0, 4 4,4 4, 8=4, 2 0, 5 5,5 which has already been obtained Average interpolation interval in « = 85 or 95 ” ” ” yy Y =235 or 22°5 Maximum interval in ee %=20 y =50 ” ” ” * 2,3 would give the same results and the averages resulting in each case are given. Miscellanea 103 Interval 8. Ordinary interpolation Line 1, 1 Line 1, 2 Line 1, 3 Line 1, 4 gives gives gives gives gives 0, 1 Theil 1, 2 il; 3} 1, 4 0, 2 2, 2 2,4 2, 6=2, 3 0, 3 3,3 3, 6=3, 2 0, 4 4,4 Average interval in) # = 571 ” ” ” y =13-71 Maximum interval in « = 8 ” ” » ¥ =382 The interval 9 gives quite a good result, certainly better than 8, but considering the fewer number of values that would be required 11 seems preferable to either, and it is far better than the common decimal interval. When the number representing the interval has factors the “interpolation-lines” do not give as many values as they do when a prime number is used because, owing to the factors, there is repetition. 6. Conclusions. The conclusions to which these notes lead us would seem to be (1) that interpolation can be effected by means of the ordinary one-variable formulae in n-dimension tables ; (2) that the method can give reasonably accurate results ; (3) that if the intervals can be chosen, (@) the same interval in all the variables will generally be better than different intervals even if the latter are rather smaller, and (b) the interval should be given by a prime number. II. Note on the Relative Variability of the Sexes in Carabus auratus, L. By H. G. KRIBS. (From the Zoological Laboratory of the University of Pennsylvania.) The majority of biometrical investigations, which have been made regarding the comparative variability of the sexes as such, seem to have been confined to the human species*. Many observations have been made among lower organisms however, on the existence and variability of secondary sexual characters, or those morphological differentiations, apart from the sexual organs per se, by which the male is easily distinguished from the female of the same species. The possible significance of secondary sexual characters for evolution was first pointed out by Darwint, as suggested by the disproportionate development of these characters in the males and females of the same species where sexual dimorphism is present, and by the difference in behaviour seemingly correlated with it. The data furnished by Darwin covered a wide range in the animal kingdom, and his conclusions have received very general acceptance. One conclusion reached by Darwin was that in a bisexual species the female ordinarily lies closer to the morphological norm of the species than the male, and that her contribution in reproduction is inherently conservative and tends to maintain the organic stability of the norm. The male, on the other hand, was thought to vary considerably more about the species, norm. {* The relative variability of the sexes has been dealt with in crabs, wasps, toads and a variety of other published cases, not hitherto collected together, but all tending in much the same direction as in Carabus auratus. Ep.] + Descent of Man, Chap. YIII. 104 Miscelianea Entirely lacking in definite quantitative evidence in its favour, this general point of view regarding the relative variability of the sexes has been widely prevalent among biologists. Now it is obvious that if this generalization is a valid one the general principle involved should find expression, in some measure at least, in all sexual organisms. Whether it does or not, may be determined in a perfectly definite way by application of modern biometrical methods to the analysis of data collected by actual measurement of various characters in individuals of the two sexes. Asa small contribution toward such data, [ have determined the chief variation constants of some very carefully collected material presented by Dr A. Porta*. The published data give measurements of fifteen similar characters of 84 males and 84 females of the beetle Carabus auratus, L. The characters measured were the following: (1) Length of body. (2) Maximum breadth of body. (3) Length of head. (4) Width of head. (5) Length of prothorax. (6) Width of prothorax. (7) Length of antenna. (8) Length of first four joints of antenna. (9) Length of anterior leg. (10) Length of median leg. (11) Length of posterior leg, (12) Length of tarsus of anterior leg. (13) Length of mandible. (14) Length of elytra. (15) Length of first joint of antenna. The measurements are expressed in millimetres, In the table presented herewith, we have given, in the first column, the mean of each several character with its probable error. In the second column are likewise arranged the standard deviations from the mean of each character with their probable errors. In the third column are given the coefficients of variability and their probable errors. From the evidence of the means of the fifteen characters measured, four—the length of posterior leg, length of anterior leg, length of tarsus of anterior leg, and total length of antenna —are so nearly equal in length that any difference is more than covered by the probable error. These characters can hardly be held to possess any secondary sexual significance. In these four characters, whose mean size is the same in both male and female, there is, furthermore, no evidence that one sex varies any more than the other. In the case of the anterior leg, the female shows a slight tendency to vary more than the male. This difference is not significant, however. In all the other characters measured the mean is distinctly larger in the female than in the male, and we may safely assume that these differences represent a greater or less degree of secondary sexual differentiation. In four of these characters—length of first four joints of antenna, length of prothorax, length of head, and width of body—the female shows a higher index of variability than the male. In none of these, however, is the higher rate of variability of real significance, as in no case does it exceed double the probable error. In the seven remaining characters the male shows a tendency to be more variable than the female. In four of these—length of mandible, length of first joint of antenna, length of body, and width of prothorax—the excess of variability is so slight as not to be appreciable. It is much more than offset by the size of the probable error. In the last three characters the male is probably significantly more variable than the female. In the length of elytra, length of median leg, and width of head, the excess of variability in the male is practically three times the probable error for the same. On account of the small numbers of individuals taken in each case little emphasis can be laid upon the details of the results noted. It is worthy of consideration, however, that the four characters of equal size in each sex are equally variable, and that in the eleven remaining characters when there is a difference in size between the two sexes, only three show a greater variability in the male than in the female. The general conclusion can only be, that, so far as the present data indicate, there is no uniform tendency for the individuals of one sex to be more variable than those of the other sex in the beetle, Carabus auratus, L. * Porta, A., ‘‘Le Differenze sessuali secondarii quantitative nel Carabus auratus, L.” Bull. Soc. Entom. Ital. Ann. 34, 1902. Miscellanea 105 TABLE I. Character Mean S. D. C. of V Length of body ... 3 22°506 + ‘077 1:041 + 054 4°62 + 24 9 22°851+ ‘081 1°095 + ‘057 4°40 + 123 Difterence 345 +°112 ‘054 + ‘078 22 + °33 Width of body ... g¢ 8:9944-030 | 4104-021 | 4-564 -24 910-176-038 | “5214-027 | 5124-27 Difference 1'182 + :048 "111+ °034 56+ 369 | Length of head ... gd 3°750 + 020 270 +014 7°20 + °38 Q 4:0364-023 | “318+°017 | 7894-41 Difference “286 + °030 048 + 022 69 + *56 P | Width of head ... 3 3°152+:°015 *199 + :010 6°30 + °33 9 3:°396+°011 - "145 + 008 4°25 + °292 | Difference 244 + -019 054+ °013 2°05 + -40 ¢ Length of prothorax gd 4°589+:018 248 + 013 5°40 + -28 | 2 4:946+ 021 289+ ‘015 5°84 + °30 Difference 357 + 028 041 + :020 “44+ 419 | Width of prothorax 3 6°693 + 024 322+ °017 4°82 + 25 2 7:292+ 024 332+ ‘017 4°55 + °24 Difference 599 + :034 010 + 024 27 £°35 ¢ _ Length of elytra o are! d 14:411+ 051 693 + 036 4°80 + 25 | io) 16-066 + -047 639 + :033 3°98 + 21 Difference 1°655 + ‘069 054+ :049 82+ °33 Length of anterior leg 4 15°613+°051 698 + ‘036 4°47 + °39 | 9 15°589 + 056 766 + 040 4°92 + 26 | Difference 024 + ‘076 O68 + *054 "45+ 479 | Length of median leg ... 3 17°857 + 071 965+ °050 | 540+ °28 f°) 18°304 + 057 774+ 040 423+ "22 | Difference "447 + ‘O91 191 + :064 117+ 364 | Length of posterior leg oy 3 247423 + 081 1-099 + 057 4514 "24 | 2 24°423 + 080 1-088 + *057 4:46 + 23 Difference ‘000 + *114 011+ :081 05+ 33. | Length of tarsus of anterior leg | S$ 5176+ -029 3°980 + 021 7°68 + *40 © 5176+ :029 3°980 + :021 7°68+ °40 Difference “O00 + °041 000 + *030 00 + 57 | | Length of antenna | 13°750 + 046 629 + 033 4°58 + °24 9 13°685 + :046 619 + 032 4°52 + 24 Difference 065 + ‘065 010 + 046 06 + °34 g Length of first four joints of d 5°329+°017 232 + ‘012 4°36 + °23 antenna as ee io) 5 *483 + °020 269+ 014 4°90 + -26 Difference 154+ 026 037 + °019 54+ °35 9 Length of first joint of antenna d 2°063 + °010 128 + ‘007 6°10 + 32 Q 2°128+ -009 122+ 006 Se Bynes 30 Ditterence 065 + 013 006 + -009 874444 Length of mandible 3g 3304+ °015 *208 + -011 6°30 + °33 2 3°607+°015 °205 + ‘O11 5°63 4 "29 Difference *303 + ‘021 ‘003 + ‘016 67+ °44¢ Biometrikavr 7 14 106 Miscellanea III. Variation in Flower-heads of Gaillardia Aristata. By W. W. ROBBINS. This conspicuous Composite has flower-heads about 6 cm. broad with purplish-brown centres and bright orange rays. In some heads a part of the rays are of the usual length and colour but tubular (Torrey, vi. 190, 1906) as was noted by the writer in a previous paper. During the summer of 1907 from July 17 to August 14 a collection of 500 flower-heads was made from localities in the neighbourhood of Boulder. Gaillardia aristata commonly grows in loose soil where there is not much water. About one-half of the flower-heads studied were, however, collected at an altitude of 9000 feet, from plants growing in an aspen grove. These plants were well-developed and the rays larger than those in plants found growing in the open. Other than this no special variation has been noted in the rays of plants growing in different altitudes and habitats. Records were made of the number and character of all the ray-flowers in each head studied. A part of the data appear in the following table. yo eee 3 y 5 | 6 7 8 | he _.¢| Number of | Percentage | Percentage Percentage Number of | Nanbecter | Ae he haaes heads with of heads of heads of heade! rays ina Henan ail the vayetallithe rays mixed ligu- withall the) with all | with mixed head eniat ys | fabal late and rays ligu- | the rays | ligulate and ae sha (| late tubular | tubularrays | 9 1 1 | O 0) 100 0) 0 | 10 8 5 | 0 3 62 0 38 11 23 16 ®) 7 69 0) 31 Le | 33 27 0) 6 8] 0) 19 3 123 95 1 27 lene 09 21°9 | 14 | 53 40 1 12 75°4 2 22°6 15 47 31 1 15 65°9 2°2 31°9 16 | 55 41 1 13 74°5 1:9 23°6 17 ‘45 33 0) 12 73 0) 27 18 33 21 0) | 12 63 0 37 188) 21 14 1 | 6 66°6 4°9 28°5 | 20 21 10 O ll 47 0 53 21 8 7 0) 1 87 0) 13 22 13 6 1 6 46°1 6°8 46°1 23 5 2 0 3 40 0) 60 2 4 1 0) 3 25 0) 75 25 1 0 0 1 O 0) 100 26 2 0 0 2 | 0 0 | 100 27 (0) (0) 0) 0) O 0) 0) 28 3 0 0) 3 0 O 100 33 ] 0) O 1 0 0 100 | 500 350 6 144 70 1:2 28°8 To illustrate what the table shows the 13-rayed head may be taken as an example. Columns 1 and 2 show that of the 500 heads examined 123 had 13 rays in a head. Column 3 shows that 95 of these had all ligulate rays ; Column 4 shows that 1 had all tubular rays; Column 5 shows Miscellanea 107 Various forms of ray-flowers seen in the flower-heads of Gaillardia aristata x 1}. that 27 had mixed ligulate and tubular rays. Columns 6, 7 and 8 deal with percentages ; it is seen that 77:2 is the percentage of 13-rayed heads with all ligulate flowers ; 0°9 the percentage of 13-rayed heads with all rays tubular, and 21°9 the percentage of 13-rayed heads with mixed tubular and ligulate rays. It is seen that when the number of rays in a head is large both ligulate and tubular rays are apt to occur. While with fewer rays in a head there are some instances in which all the flowers are tubular and many in which all are ligulate. The normal head has all ligulate rays, but a percentage of 28°8 heads with mixed ligulate and tubular rays shows a strong tendency to vary from this normal. The accompanying curve of variation for the number of rays is computed from columns 1 and 2 of the foregoing table. It includes all rays without regard to their form. There is a well-developed mode at 13 and the usual skewness to the right which may be expected in all such studies as the present one. The 500 flower-heads examined had a total of 7709 rays. The larger part of these rays were three-lobed and ligulate but some had as many as six lobes and a single specimen had only one lobe. In the following table the records for all of these flowers are tabulated. It includes therefore both ligulate and tubular rays. It will be seen from the table on p. 108 that while the ligulate rays have as a rule three lobes, the tubular rays are more often four-lobed. The percentage of ligulate rays decreases and the percentage of tubular rays increases with an increase in the number of the lobes. 14—2 108 Miscellanea 130 - SRR Se . meas) ah Eee Number of heads ig cl salle mabe ees (el a RS ‘a i) 2 4 8 O 12 14 #%16 18 20 22 24 26 Number of rays in a head Record of 7709 Ray-Flowers in 500 Flower-Heads. f, Ligulate | f, Tubular | °/,Ligulate | °/, Tubular Z ee | ee -— i pear l-lobed flowers ... st 0 100 0 2-lobed flowers... 193 0) 100 0 3-lobed flowers... 5908 146 98 2 4-lobed flowers... 893 296 75 25 5-lobed flowers... 78 | 183 | 30 70 6-lobed flowers... 0) | Tal 0) 100 _ | ew 7073 | 636 92 8 Summary. The normal flower-head of Gadllardia aristata has 13 three-lobed ligulate rays. Variation from the normal, however, is common and occurs in the number and form of the rays and in the number of lobes in a ray. The tendency to vary is toward a flower-head having a larger number of rays, mixed ligulate and tubular, the latter being four-lobed. A few heads are found with all the rays tubular. UNIVERSITY OF COLORADO, BovuuprEr, Coto. [It is worth noting that the Fibonacci mode series (see Biometrika, Vol. 1. p. 306), namely, 5, 8, 13, 21, 34..., is not represented in the sub-modes of Gaillardia aristata ; and, except for the primary mode 13, there is no evidence in favour of the Fibonacci doctrine from the data. Ep.] Miscellanea 109 IV. The Effect of Errors of Observation upon the Correlation Coefficient. By J. A. COBB. S (xy) Noxoy observation. If we assume all the 2’s and y’s to be subject to errors a, 8, with standard S (vy) No The correlation coefficient 7= , where the values of w and y are unaffected by errors of deviations g,. o,, the errors of w and y in every pair being independent: will become a“) yo fo) 5) S(wta)(y+B)) _ S (ay) NAV (62+ 022) (opt oy2) NV (02 + 02,2) (64? + oy) a Oy Vy = Oxy So = hy @ r V(o2+o2, ) (vy +o,,”) ; r In the special case where o,=0, and o;,=0,,, becomes The correctness of 2 : x Ox +0z," determinations of correlation coefficients has often been considerably affected by the neglect of this point. The question of the inheritance of sex-ratio is an interesting one in this connexion. The sex-ratio of an individual is the value which the ratio of male to total births in his fraternity would tend to assume if his fraternity were infinitely large. The standard deviation of error of sex-ratio due to taking small families is approximately fi where m is the number of the family and p, g the ratios of male and female respectively to the whole in all the families. The total standard deviation of the sex-ratio in families of the same size is due to the deviation ie i and to o,, the variability of the sex-ratio of families. Therefore 2_ PY o7p= n= = i om? where go is the total observed standard deviation. I have in this way calculated o,, from various data, and it turned out to be between ‘03 and ‘04. Now in the case of families of nine children tf ='028. So if the observed sex-proportion is used in forming a correlation table between the sex-ratios of parents and offspring in families of nine, the resulting correlation coefficient must Oo. +1 2 be multiplied by — = ne of parents and offspring. =24 to give the true correlation between the sex-ratios V. On Heredity in Sex. Remarks on Mr Cobb’s Note. By KARL PEARSON, F.R.S. Mr Cobb’s point is an important one, though as a statistician I am never convinced by unpublished statistics which are said to give a certain result. But Mr Cobb’s criticism would I think apply to all correlation treatment of inheritance. If we take the male offspring of a father of definite arm-length, their mean based upon four or five cases may differ very widely from the mean of all the offspring the father would have, if we supposed him capable of an indefinite number of offspring. In the same way he himself is only a single random sample from an indefinitely great array which might theoretically be attributed to his parents. I do 110 Miscellanea not see that there is anything more of the nature of “an error of observation” in taking the actual sex-ratio of the offspring as a somatic character, than in taking the actual stature or actual arm-length of the offspring. Neither represents the actual gametic character, if what is meant by that is the mean value for an indefinite number of offspring. What the biometrician is concerned with is the relation between the somatic character as actually observed in one generation and again in the next, and for the sex-ratio this relationship is practically zero. In the case of the sex-ratio the variability o,, noted by Mr Cobb is not a variability due to error of observation, but a variability characteristic of the species itself being determined by its fertility. According to Mr Cobb it is so great that it renders it impossible to determine for the sex-ratio any relation between the somatic character in parent and offspring. Is this more than a biometrician means when he says that there is no inheritance of the sex-ratio? No process, for example, of selecting families, giving many sons, would alter the sex-ratio, because the mean sex-ratio of families sprung from families with few and families with many sons is sensibly the same. I am not certain, however, that the numerical example given by Mr Cobb, i.e. Pa = 028, is correct. For, if be really an inherited character it may take all values from 0 to 1, and accordingly we shall not get the proper value of this expression by putting p=q=H, the value which gives the maximum value of pg, but by putting pq its actual observed mean value in man; this reduces Mr Cobb’s multiplying factor to about a fifth of the value he assumes for it, and such a factor, if it were correct, would not influence the general conclusion. But Mr Heron has applied several further tests to his own data. It will be remembered that for the Whitney data in his memoir on sex inheritance Mr Heron took the sex-ratios in two generations of families having four or more members, the correlation for 2197 families was found to be °02+‘01. From the same data Mr Heron has picked out the 420 families with eight or more members, the correlation is now ‘01+°03. Instead of increasing as it ought to do, on the assumption of Mr Cobb, it has got still more insignificant. But Mr Cobb’s note suggests a point which it seemed well worth while working out. If there be no correlation the resulting standard deviation of the material ought to be exactly what would be obtained on the theory of pure chance, i.e. there would be no variation due to heredity superposed on this. Mr Heron has investigated this point for 496 families given by my schedules and for 2305 families taken from the Whitney data. Suppose we take all the n, families of s members ; let mm, be the mean number of males, o, the standard deviation of this array, then m,/ng and o,/nr; Will be the mean and standard deviation of the sex-ratios of this array of families of s members. Let p be the mean sex-ratio of the whole series of families and o the standard deviation, then shane) a i Now o,/ns is what Mr Cobb puts op, and he makes this differ from his pq/m, so that he obtains a quantity o,, which is the variability of the sex-ratio, if the families were indefinitely great, and upon this he tells us the true heredity depends. Accordingly if o, be a reality the value found for o? by putting m,/ns=p and o,/n,=pg/n ought to be less than the actually determined value of o?. Mr Heron finds the following results : Value of o? Pearson’s Schedules Observed ‘1944 Calculated +1946 Whitney Family _ ‘2079 s "2086 In both cases the calculated value is insensibly greater than the observed. In other words o, raust be imaginary, or rather within the limits of the probable error it is zero. Shortly, of any individual had an indefinitely large family, the ratio of the sexes would not differ from that of the Miscellanea 111 general population, or there is no variability in the sex-ratio due to individuality. All the variation observed is actually due to the random sampling involved in taking small families. It appears to me therefore that Mr Cobb’s note is of value, as it enables Mr Heron to confirm his results from another standpoint. For practical purposes the main problem is: Are the actual sex-ratios in parent and offspring related? The answer is: Not sensibly. Mr Cobb suggests that this result is only due to the apparent family not representing the gametic reality. This raised the question of whether any individuality at all exists for the sex-ratio. The answer appears to be none, because the standard deviation observed is precisely that which would be found were the sex-ratio for any individual that due to a random selection from the general population of a group equal in number to his family. VI. On the Influence of Double Selection on the Variation and Correlation of two Characters. By KARL PEARSON, F.R.S. In a memoir published in the Phil. Trans. Vol. 200 A, pp. 1—66, I have dealt with the problem of the influence of selecting g characters on the variability and correlation of n—q non-selected characters*. My present problem is somewhat different, and as the solution provided has been in use, and given in lectures for some years past, it may be desirable to publish it. There are two correlated variables, 1 and 2, with standard deviations o, and gy, and correlation 72. In entering up a record a selection is made of the variable 1, so that its mean is shifted to m, and its standard deviation to s,; let p;=s,/0;. In entering for the variable 2, a selection is made so that its mean is shifted to m, and its standard deviation is changed to sy; let py=so/o9. As illustration suppose cards formed of characters in parent and offspring ; we pass through the cards, putting a red line through every card not one of the selected parents; we pass through them again and put a blue line through every card not one of the selected offspring; the result is that cards may be thrown out because they carry a red line or a blue line or because they carry both. The problem is what are the standard deviations 3, and 3, and the correlation Rj» of the material left after this double selection, If we assume the material normal the following values are readily found by considering the probability of selecting a definite individual pair 21, X to be of the form 9 . vy — m4)? L — Mg)? eel vy2 QWrayte Ly? ae = a ( ae 9 Ton 5) = - 2 e 2s,” e 289" const. x e 12 OL alee) Le ort Canna x wy CAugusts a a 1 S ‘Ithe Biggl} Hebrides Muck LITTLE 2-—~ /Buddon, Ness Lex of Tay ¥ St Andrews Colonsay Oronsay P_ a i 4 ae v ecbles ; a drvine é a WMilmarnock Muirkirks Sid é i aS oJ Siburgh o* ePiinida Adsa Roe RY , Lockerbie Malewelltown o> Dumfries LZ Stranraer 3 yeW"l GTOW Nao Por Pee istownl eS c i Luce Bay f . ‘Burrow H4 Mull) of Galloway / R/S H s 5 Long .W.of Greenwich 4 W.&AK Sohnstan Limited Edmiburgh 4 Loudon. M Biometrika. Vol. VI. Part II. Plate II. - Pa AL eat ea S —_ = Fa wy ae A 2a, oe ae | ye O—~ Ng: ee ae fe f Pt ya y oak / es: % ie tes Pod re la d 1C At T HONE SS A } fo t H @) / . ae a @) Z 8 “a Sh (‘08 ass THERLAND ‘\ : | is a ~ ps rg | ; } 5 3S eS ee lV yf ) ¢ \ ) => STS wot (02) ; ‘Me ‘ . CN 2» €; Con 4 ( ! ie i ) aN = ee =. ta Fy — | ay ] — _ ve vy F 5 / : i } x \ " | %) | My | | i i a why : FOR F R . ie TU es SP ww 3 ? \ a ¢ 7 on 4 D oa @) a ut \ Jos }. if @ ~~ } (38) aie (58) ‘ = ea akc yy yo f Tek e, bein & ie et Te a fms mia BN ew ty, HANS (62) @ » UNG)? mpg Ng 8) > 48) wet iS oS 3: at wpatice Go)44 om Lt CN jf ‘a ) Sgt ¢ +4] Cx Ino TON’ Z ARMS Sy iS ea egies 13 ©) ® @y NGF DIN BURGH ‘ edi ! aaa Gs)" Dae ? (47) Nf x I Bai \ ae Nee 2D @®%o ae waa teas ea reo K dy SA Vege OOR! Hagen’ & , fy 5 XY © a ee (ius) @ SE we nes ue u \ as { \ 29) 9 Sey f ow NS eS 5) = ek ( bates) }} \ ez, A NS Pm > \ ( @ = \ NEN g N (ans & a (a) ” Q) ? ASELKLR K or 3 a ©®C™~ [h@ ) 103) i a ee M\ rd Z ROXBURGH / ee 2 A \ / Ge) aa Ge Fad pi we J Sy 7 / SU) ‘ig \ os i acd ) x (36 Oo u M F R iE s Lied / ay 38) @) No y “ es Vv ay = ) f apwnicts, 2s rd - \ Annee tineeupenient |G) { ck \ = I ny \ (34 ) ( NE \ SS —~ ke, \ \ wiGtow wv Pa A Ge a ees i. nny 4 es / \' SY % MICH \ + a i 7 ii ‘ wd J. F. Tocurr 137 be seen later, these two methods were adopted by the Committee and employed by the author as convenient and desirable ones for the purpose of analysis. At this stage, however, Mr John Gray suggested “the natural subdivision of the country into river basins, as it is well known that watersheds, when they form mountain ranges even of moderate size act as racial barriers.’ The view was expressed by him that “if the ordinary subdivision into counties were adopted, we should have in many cases to include populations with quite different character- istics in the same division and valuable ethnic distinctions would be lost in taking an average.” The suggestion seemed a good one as a means of determining the differences between the populations in the various river basins. Also, when the population in each river basin is subdivided into districts, we have the means of determining whether any one district significantly differs from another in that basin. But this method of grouping is neither superior nor inferior to any other method of grouping populations in adjacent areas, as all that can be said in each case is that, conformably to size of sample, the population differs or does not differ from another population or from the general population of the country. Thus counties and groups of counties are quite convenient groups for the statistician to deal with, and since this method of grouping is well known to the public, it has a slight advantage over any other. Again, one must remember that no one method of grouping will solve all the problems the anthropometrician desires to solve. For instance, one may wish to contrast a city population with its environs; a mining population with a rural one; or a coast population with an adjacent inland population. Thus special groupings are frequently necessary. In a small country like Scotland the river basins are exceedingly small, compared with the great basins on the continents of Europe, Asia, Africa and ' America. Besides, one has in Scotland a population the vast majority of the members of which speak one language and which has bred intraracially for gene- rations. It therefore did not seem to the writer to be likely that grouping by river basins alone would yield all the information obtainable as to the distribution of colour, but the general idea of basins was kept in view in constituting the groups intermediate between parishes and counties, namely, districts. Thus a satisfactory solution of the area problem was found, since all the groupings discussed, namely schools, parishes, districts, counties and river basins, were and are available for statistical analysis. The writer proceeded to carry out the district* system of grouping, com- mencing with the county of Lanark. Altogether 110 districts were thus consti- tuted, the task of locating schools on the maps being an exceedingly laborious one indeed, so that much time was consumed in the construction of the districts. The Key maps opposite page 137 (Maps I.f and II.) show in a general way the * The special district grouping has been used by the writer to determine urban, suburban and rural differences and, as already stated, is the basis of Mr Gray’s memoir. Of course the maps constructed by him show the districts graded and do not show the actual numerical district averages as given in tables supplied to him. + For names of the Divisions see Explanatory Note, p. 148, Biometrika v1 18 138 Pigmentation Survey of School Children in Scotland location of these districts, while their exact relationship to counties is given in the following table (Table III.). TABLE III. Counties (with Districts). Aberdeen, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87. Argyll, 100, 101, 102, 108, 104. Ayr, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36. Banff, 85, 86, 87, 90,91. Berwick, 39, 42. Bute, 103, 104. Caithness, 97, 98. Clackmannan, 51. Dumbarton, 10, 12, 19, 22, 101, 105, 106. Dumfries, 35, 36, 37. Edinburgh, 44, 45, 46, 47. Elgin, 88, 89, 90, 91. Fife, 50, 52, 58, 54, 55, 56, 57. Forfar, 64, 65, 66, 67, 68, 72, 73, 75, 76. Haddington, 48. Inverness, 89, 91, 92, 93, 94, 99, 100, 107, 108. Kincardine, 72, 73, 74, 75,79. Kinross,57. Kirkcudbright, 33, 34,36. Lanark, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Linlithgow, 48, 49. Orkney, 109, 110. Nairn, 89, 90. Peebles, 41. Perth, 51, 57, 58, 59, 68, 69, 70, 71, 76. Renfrew, 14, 16, 17, 18, 19, 20, 21, 23, 24. Ross and Cromarty, 93, 95, 96, 99, 108. Roxburgh, 37, 38, 39. Selkirk, 38, 40. Shetland, 110. Stirling, 10, 12, 59, 60, 61, 62, 63. Sutherland, 95, 96. Wigtown, 32, 33. This completed the work of organization, and the writer at once proceeded to carry out the survey. On the afternoon of the 7th December, 1903, the schedules, with instructions, leaflets stating fully the object of the survey, circular letters to teachers and addressed return envelopes* were sent out from Peterhead to 3329+ different school establishments in Scotland. At the same time an explanatory letter, setting out the objects of the survey, and the nature of the results expected to flow from the data about to be collected, was sent to all the leading daily and weekly newspapers in the country. Public attention was thus at once directed to the scheme approved of and circulated by a Committee which had for two of its members Professor (now Principal) Sir Wm. Turner, and Professor R. W. Reid, well known University teachers, and notable for their contributions in the domain of anatomical and anthropological science. ‘The fact of having two such experienced and distinguished men associated with the survey, actively promoting it and directly recommending it to the teachers, has meant everything to the success of the undertaking, and has translated it from a desirable and important scheme on paper to an accomplished fact. The author can never sufficiently thank Sir Wm. Turner and Professor Reid for their solid backing of the survey, their hearty cooperation during the entire period from its inception until now, and for their uniform courtesy and kindness during the entire course of the many interviews the author has had with each. The proposed survey was widely noticed by the daily press, was favourably commented on and strongly recommended to the notice of the teachers. * These envelopes were addressed to 36, York Place, Edinburgh, when by arrangement with the Post Office, they were, as received, immediately sent on to Peterhead. The writer’s examining work took him frequently to Edinburgh and permitted of this arrangement being carried out. On his own behalf and that of the Committee he has cordially to thank Mr J. Rutherford Hill and his staff for providing a collecting centre for the Returns and for the trouble and care taken in sending them on to their present resting place. + This was the apparent number of schools at the time. Several of these were afterwards found to be merged in other schools while a few were found to be extinct, J. F. Tocuer 139 Meantime, in order to have the returns systematically arranged for inspection and tabling, two large cases (9’ x 7’) having 120 compartments were made ready and put in the writer’s laboratory. Of the compartments, 110 were prepared for the special reception of the returns by districts, but of course each return envelope had printed and written on it the name of the school, parish, district and county to which it referred, for immediate identification. The remaining compartments were reserved for incomplete returns. A special case with county compartments was prepared to deal with the separate correspondence and a series of despatch boxes was obtained to hold and systematise the tabled data. These, with a typewriter, constituted the equipment for the survey. Everything was now ready for action. On the 8th December, one day after the issue of the schedules, the first group of returns—5 in number—was received. After this a steady flow of returns came by each post. Within a fortnight, 366 had been received, and by the beginning of the last week of December the author was able to submit his first Interim Report to the Royal Society, stating that over 700 had been returned. Hundreds of letters had meantime been received asking for additional schedules and_ for explanation as to what appeared doubtful to the teachers making enquiries. These were all promptly answered, and as a result of the experience gained with those returns already sent in, an additional explanatory circular was sent out to those schools from which returns had not yet been made. This circular made clear doubtful points with regard to (1) classification of boys and girls, and (2) the method of recording relationships. The circular had the desired effect of obviating any further difficulties in making the observations. A steady stream of returns came during the early months of the year 1904. Each return was at once acknowledged and the teacher making the return thanked on behalf of the Committee. The response of the teachers was remarkable. The vast majority of them made the returns in an evidently painstaking and careful manner; and a great many of them, besides, wrote explanatory letters as to relationships, ancestry and probable racial mixture of their groups. The author was kept employed acknowledging these, and in replying to the hundreds of additional letters of enquiry during the first nine months of the year. In order to keep the scheme fully before the teachers, a reminder circular was issued in April to those schools from which no returns or acknowledgments had been received, This had the effect of bringing in a larger proportion of returns during the month of April. The rate steadily decreased until November, when only 3—the last included in the analysis—came in by post and were acknowledged. The following table (Table IV.) shows the actual numbers received during each month and the rate of return per cent. per month. Altogether, 2695 returns were however received, but of these 407 were in- complete in certain particulars. Over 500 schools therefore made no return. The following table shows only the number of schools from which complete returns were received. With regard to the incomplete ones, either the names, ages, sex or 18—2 140 Pigmentation Survey of School Children in Scotland TABLE IV. Table of Returns Received. Year Month Number received | Per cent. 1903 December 817 35°71 1904 January 548 23°95 5 February 344 15°04 5 March 146 6°38 3 April 270 11°80 m May 84 3°67 i June 22 96 55 July 22 96 . August 25 =: 1:09 s September 5 22 October 2 09 mi November 3 13 Totals — 2288 100-00 colour characters singly or jointly with one another were wanting. These schools have not been dealt with in this memoir. The data proper therefore consisted of fully complete returns from 2288 schools containing the records of the names, ages, sex, fraternal and cousin relationships, and colour characters of 257,766 boys and 244,389 girls, a total of 502,155 children. Although there was a good deal of further correspondence with the teachers, only a few more returns were received after November, 1904. These have not been included in the district analysis which was in operation before the returns were received but have been included in the division, county and general analyses*. The work of classification and tabling, which was commenced as soon as practicable, was soon in full operation. The response of the teachers had been remarkably enthusiastic and complete. The survey was an accomplished fact. On behalf of the Committee the writer begs to acknowledge its great obliga- tions to the teaching profession in Scotland for so promptly responding to the invitation of the Committee to carry out the desired observations. The writer also wishes to record his personal sense of indebtedness to the teachers and to ‘thank them very cordially for all the pains and trouble they have taken in making the elaborate returns so vital to the success of the scheme. The credit of the accomplished survey is undoubtedly due to the teachers. Without the recognition * The late returns came from the counties of Lanark, Renfrew, Banff, Elgin and Inverness and belonged, in the district scheme, to the first, fourth, eighteenth and ninety-first districts. The total results of observations for these districts are however given in the Appendix tables and not the slightly smaller figures on which the district analysis was made. The figures for the later returns are also of course given along with the others under their respective parishes and counties and were included in all analyses except the district one. The only points therefore to be noted are (1) that the district analysis is based on the slightly smaller general totals and (2) that, in the analysis of Districts I., IV., XVIII. and XCL., the late returns (not to hand at the time of analysis) are excluded. J. F. Tocuer 141 by them of the importance of this scientific investigation, their cordial cooperation and most painstaking and laborious setting down of all the minute details required from each school, the survey would have been still in the limbo of fancy, to remain there until the census office should have the power to deal with the matter, along with the present ordinary details of this important statistical department. Only when the recording of measurable and non-measurable cha- racters comes to be included in the census, and is dealt with officially, will the importance of much voluntary pioneer work by the teaching profession be fully recognised. (4) The Problems to be discussed. Before proceeding to make a brief statement of the analytical methods employed and to follow with a general discussion of the resulting classified data, it seems desirable at this stage to enumerate the problems germane to the survey. (a) The first problem clearly is: How are the children distributed with respect to the various colour classes, what is the proportion of children found in each class, and how does the general distribution among the classes compare with those of the continental countries already surveyed ? The answer to this problem is given (a) in Table XIII., where the general distribution and the percentages of the colour classes are given, and (8) in section (12), where the results are compared with those of continental countries. (b) The second problem deals with relative local differences in each colour class. Considering each colour class or category separately, one must ask, by how much does each locality in Scotland (division, county or district) differ from the remaining population? In other words, is the distribution of colour uniform throughout Scotland, and if not by how much does the proportion for each class in each locality differ from the proportion which would occur on an even distribu- tion of the school population over the whole country? This amount when found for each locality is termed the relative local difference and the complete solution of the problem is reached when significant relative local differences are determined, and separated from those relative local differences which are fair samples of the general population. This problem is dealt with under section (6). (c) The third problem is one bearing on the general resemblance of local populations to the general population. Here hair colour as a character is con- sidered as a whole in each locality, all the classes constituting the character being considered together. Similarly eye colour as a character is considered as a whole in each locality. The distribution in each locality of the classes constituting each character is compared with the corresponding general distribution of the classes for the same characters which is found for the whole country. Considering, in this manner, hair colour collectively or eye colour collectively, do or do not local populations resemble the general population? If local populations do not resemble the general population how far do the actual local frequencies as a whole differ from the corresponding frequencies which would occur on an even distribu- 142 Pigmentation Survey of School Children in Scotland tion of the population throughout the country? In other words, if divergencies from this even distribution occur, what is the relative degree of divergency for each locality? This is, in short, the third problem which is discussed in sec- tion (7). (d) The degree of local segregation of each of the colour classes constitutes the fourth problem. If the population is not evenly distributed with respect to the colour classes, which class shows the greatest degree of isolation into separate groups? This can be determined by considering successively the nature of the distribution of relative local differences of each class collectively and without reference as to where each local difference occurs. That is to say the relative local differences of each class are successively considered interlocally as a whole and the variability of each distribution determined. The greater the variability of the distribution of relative local differences for a class the more uneven will be the distribution of the class throughout the country, and the greater will be its massing into groups, and thus the greater will be the local segregation of the class. ‘This problem is considered in section (8). (e) It is important from the eugenic standpoint to know whether pigmenta- tion is associated in any way with disease, inherited or non-inherited defects, race, or with density, fertility or other characters of the population. These problems are considered in section (9). (f) An interesting problem which is concerned with sexual differences is considered under section (10). The problem may be divided up into three parts. 1. In what respects, if in any, do the constants found for boys and girls differ ? 2. Are there any significant pigmentation differences between boys and girls? 3. What is the average resemblance between the male and female factors of the population ? (g) The next problem is one concerning urban and suburban populations. The questions may be put. 1. Are there any significant differences between the purely urban and the suburban and rural populations, and if so in what respects do they differ? 2. What differences occur (a) within each urban population (ve. intralocally), and (8) between different urban populations (¢.e. interlocally), and are these differences environmental, racial or both? This problem is dealt with in section (11) with special reference to Glasgow and its environs. (hk) A further problem which is of importance turns on the point as to whether hair and eye colours are independent variables or whether they are dependent. It is desirable therefore to know what degree of association, if any, exists between hair and eye colours. If association is found to exist does the relationship found agree or differ with that indicated by former surveys of adults and children. This problem is considered among others in section (12). (¢) The pigmentation data present other problems for solution, such as whether brothers and sisters or cousins resemble one another to any degree in hair and eye colour. These problems are not dealt with in this memoir. J. F. Tocuer 143 (5) Methods Employed to Determine Significant Differences. In making a survey of the measurable physical characters of a population one has not only to ascertain the type and variability of each character but also to consider the relationship of each local group to the general population*. Thus, in the recent investigation on the inmates of asylums it is shown that several physical types exist among the Scottish insane, and that, whether they differ or not from the sane population, local asylum groups generally do not resemble the general insane population. But non-measurable characters can scarcely yet be dealt with in the same way. It has not been found possible up to the present time, for instance, to determine the value of the character, hair colour, just because no quantitative scale based on experience has yet been devised on which to plot the observations in an orderly way indicating increase or decrease of intensity of colour. It is not clear whether such a scale is possible. Experimental work has just been undertaken by the writer which may throw some light on this point. But while hair colour cannot yet be represented on a scale of intensity of colour such as stature or head length, it can be quite properly dealt with under well defined classes or categories. As already explained, the limits of these classes have been defined in the analytical table given in each schedule. What statisti- cians have here to consider therefore are the frequencies of the various classes individually and collectively without reference as to whether the classes can be arranged on a scale showing grades of intensity of colour. This has been done on a moderate scale for adults+, and it may be well to restate here the methods employed before proceeding to state the results of the analysis. A population of NV individuals is to be considered, each of which possesses the character X. The character X is not measurable but can be divided into m classes. Let s, s,...5 be the classes and let the class frequencies for the whole population be respectively ¥5,, Ys,++- Ys, The population is divided into groups of magnitude n, and each group is observed and classed with respect to the character X. In making the observations, the probability that any person observed (if the operation is a random one) belongs to class s is y,;/N =p, and the probability of the person not belonging to that class, but to one of the others is (l1—p)=q. If the groups are samples drawn from the general population purely at random, the frequency for the class s for each of the groups is therefore equal to ny;/N = np =y,, which is thus for the class s the most probable number likely to be drawn in this way; or is, shortly, the theoretical class frequency. It is necessary to consider what would happen if the whole population was observed in unselected groups at random for the following reason. If the observed class frequencies in the various geographical areas actually differed insignificantly from the theoretical class frequencies then it would be clear that the population was evenly distributed with respect to the character. Thus, so far as this character is * Tocher: Biometrika, Vol. v. Part 111. pp. 315 et seq. + Tocher : Biometrika, Vol. v. Part 111, pp. 335 et seq. 144 Pigmentation Survey of School Children in Scotland concerned, it would be a homogeneous population. Heterogeneity must be sought for in other characters. If all the physical characters showed homogeneity then it would be clear that one had a common race to deal with. But if, with respect to the character X, the observed and theoretical class frequencies appeared to differ significantly, then the population would not be evenly distributed with respect to X. Instead, there would be excess frequencies in some classes and frequencies falling quite short of theory (7.e. the proportional even distribution) in others in various localities or groups. One would then have to ascertain whether the significant differences were racial or due to other influences. The question now is: How can one determine whether any difference between observation and theory is significant or not? In other words, if y,” = observed class frequency, how can one measure the significance of y;’— y,;? Pearson* has pointed out that the distribution of such differences as y,” — y;, 1f occurring at random, takes the form of the hypergeometrical series DN CoN = 1) (ON = te) qN OWN = Ds( None ty, eee n(n—1) gN (qN —1) +f, 1.2 (pN-—n+ 1)(pN—n+2)* and he has shown that the standard deviation of the distribution is given by n—-1 Ly -y,) => J nq (1 — iN 7) ° The areas on either side of the ordinate which divides the distribution at the abscissal value (ys” — y,’)/Wnpg (N — n)/(N — 1), are proportional to the probabilities of greater or lesser values than the particular value found occurring in future samples. The areas can be determined when the form of curve is known. In the great majority of cases in this survey, the values of n although fairly large are but small fractions of V, and p is not very small. In such cases the hypergeometrical distribution closely approximates the normal curve, the constants 8, and £, being respectively 0 and 3 within the limits of their probable errors. The modal value of the distribution is the nearest whole integer to cy SS +1). stitch + differs insignificantly from the mean, ng. Thus the asymmetry and leptokurtosis are insignificant and therefore the probability of greater or lesser values than that found occurring in future samples can be dotennine! from the tables of the probability integral. In certain cases the fraction 7 is an appreciable one, and in these the asymmetry and leptokurtosis are both significant. In certain other cases p is rather small. In these cases the inioepreeaian of the value of the standard deviation given, which in itself is correct, requires considerable modification because the hypergeometrical series can be no longer * Pearson: Biometrika, Vol. v. pp. 173—175, J. F. Tocuser 145 satisfactorily represented by the normal curve. The tables of the probability integral are therefore not applicable and do not give the probabilities. They can be found however when the type and the constants of the curve which fits the hypergeometrical distribution have been determined. Tables* for these extreme cases are in the course of production, but they involve laborious calculation and it may be some time before they are ready. Accordingly special stress must not be laid on the differences found where the value of p is such as to give a significantly asymmetrical distribution of samples from which the probabilities of greater or lesser values in future samples are found. The form in which each difference has been expressed and studied requires notice. It is obvious that, in considering differences and their standard deviations, one may take the observed absolute numbers and expected absolute values—that is, in the notation herein used, y,’ and y,;. Again one could take the observed and theoretical percentages—that is the difference 100 {(y,.”/n) —p}; or reckoning ys in each case as 100, one could take the difference as 100 {(y,”/y;’)— 1}. Now it is easy to see that Vnpq(N —n)/(N—1), reckoned as a percentage, is 100 Vpg (N — n)/n(N —1), the standard deviation with which 100 {(y,”/n) —p} has to be compared. Expressed as a coefficient of variation, it is also easily seen to be 100 Vg (NW — n)/np (N — 1), the variability constant (decreasing as n increases) with which 100 {(y,”/ys.)— 1} has to be compared. Thus there are for selection, according to convenience, in the statistical analysis, the three ratios (1) (ys” —ys’)/V mpg (M — n)/(N — 1). (2) 100 {(ys’/n) — p}/V1002pq (NV — n)/n (N = 1). (3) 100 {(ys”/ys’) — 1}/100Vq (W — n)/np (N — 1). It is perfectly obvious that the above ratios, applied to the data, will give identical results. These ratios will, throughout this memoir, be called relative local differences (RLD), this term being the one introduced by the writer in a previous investigation to denote the local differences in the physical characters of the Scottish insane+. In determining relative local differences, the first expression, which deals with the absolute figures, has been the one used, the calculations having been performed in duplicate. Since the percentages in district groups have been calculated, it was found convenient to use the second form in cases where it was necessary to compare certain of these districts with the general population. The following table (Table V.) constructed to illustrate, by means of maps, the relative local differences in the physical characters of the Scottish insane + will be used throughout the memoir both in the text and in the maps, and defines the terms used to indicate the significance or non-significance of the observed results. From what has already been said, these relative local differences when n is fairly * Biometrika, Vol. v. p. 175. + Tocher: Biometrika, Vol. v. Part 111. pp. 317—318 ; also Table VIII. of that memoir. Biometrika v1 19 146 Pigmentation Survey of School Children in Scotland TABLE V. Class Ranges. RLD. The value found compared with the value for Suecitie Ter Range of Class in the general population is Pee ese Class terms of (ys = Ys [2 (yy"-Y,') Very much smaller ; nd ane ... | Distinctly Micrometropic -—4 —3°5 upwards Probably significantly less... ... | Probably Micrometropic —3 —2°5 to—3°5 Less but not quite acess less .. ... | Mesometropic -2 —155 to—2°5 Very slightly less ne : cae ... | Mesometropic jal —0°5 to—1°5 Quite insignificantly different Ae ... | Mesometropic 0 05 to - 05 Very slightly greater ... ... | Mesometropic 1 05 to 15 Greater but not quite significantly oreater ... | Mesometropic 2 15 to 2°5 Probably significantly preater noe ... | Probably Megalometropic 3 25 to 35 Very much greater... ae 580 ... | Distinctly Megalometropic 4 3°5 upwards large, but small compared with V and p is not very small, are evidently the abscissal values of the normal curve whose equation is These conditions exist for the majority of cases, and here therefore, for any individual result, the probabilities of greater or lesser values can be readily calculated. But in cases where asymmetrical curves result owing to n/N being appreciable, or p small or both, the probabilities, as already stated, cannot be found from the tables of the probability integral, and thus the specific term applied to any class within the range of which the relative local difference falls, may or may not apply in such cases. The terms* denoting the significance of the results in the table of class ranges (Table V.) are therefore intended to be strictly applicable only to relative local differences which are abscissal values of a normal curve, and are applicable to those which are abscissal values of a distinctly asymmetrical curve only as a first approximation. With this reservation those relative local differences which fall beyond +2 and —2 may possibly or even probably be significant, those falling beyond + 3 and —3 may probably be significant, while those falling beyond + 4 and — 4 may be regarded as distinctly significant. (6) Relative Local Differences geographically considered. Indindual differences of each class. (Problem 6b.) I. Eaplanatory and Introductory. In studying the individual relative local differences of each class (that is the individual relative differences, whether the divisions, counties, districts or other * Tocher ; Biometrika, Vol. v. p. 318, J. F. Tocuer 147 smaller areas are considered) the following plan will be followed with respect to Scotland geographically. The distribution of each class with respect to the eight great divisions of Scotland, as understood by the Registrar-General and used in the census and other official reports, will first be considered. Then the county distributions will be noted and finally the distributions with respect to the smallest unit—the district—will be dealt with. Thus the reader (1) will get an appreciation of the nature of the distribution in general terms, 7.¢. the significant inter-divisional differences will be determined and pointed out; (2) will learn how far counties differ from one another, thus enabling the reader to note intra- divisional as well as inter-county differences ; and finally (3) will see what localities influence the various county and divisional differences, thus detecting differences occurring within each county—that is, the significant intra-county or purely local differences. It should be noted that the frequencies of the various classes of a character such as hair colour or eye colour are correlated. Thus an excessive frequency of one class would point to a defect in the frequency of one or more of the other classes. Before describing the various differences, it will be useful here to show the total frequencies of each class and their percentages for the whole of Scotland. These are as follow (Table VI.): TABLE VI. Colour Distribution of Scottish Children. Hair Eyes Fair Red |Medium| Dark avers Blue Light |Medium| Dark Totals Boys A | 64312 | 14162 | 111569} 64511 | 3212 | 37788) 78140] 84334) 57504} 257766 o 24°950 | 5°494 | 43-283 | 25-027 | 1°246 | 14°660 | 30°314 | 32°717 | 22°309 | per cent. Girls A | 67036 | 12435 | 99873] 62073 | 2972 | 36347 | 74068 | 78357 | 55617 | 244389 » B | 27°430 | 5:088 | 40°866 | 25°399 | 1:216 | 14°873 | 30°307 | 32°062 | 22°758 | per cent. r Boys A and Girls A=total frequencies of each class for whole of Scotland for boys and girls respectively. Boys B and Girls B= percentages of each class for whole of Scotland for boys and girls respectively. The following tables (Tables VII., VIII. and IX.) give the values of the relative local differences for hair colour and eye colour of both boys and girls, These differences, classed as described in Section 5, are shown in the maps, named in the course of the descriptions of the differences in each colour class in this section (Maps ITI. to XL.), and are the basis of the following remarks: 19—2 148 Pigmentation Survey of School Children in Scotland TABLE VII. Relative Local Differences. Values of (ys” — | 4/ m4 i! = =a} ; Divisions. BOYS. | | | Hair Eyes Division Fair Red ‘Medium Dark ee Blue Light |Medium| Dark I. 2°24 1:96 | —6°31 2°91 4:08 6°58 | —4°68 03 | — °46 IT. 4°36 | — °56| —9°98 5°66 6°60 12°92 05 — 5°67 | —4°64 IIL. 2°13 6°08 | —2°57 | —1°69 | —2°73 3°69 | —1°56 2°15 | —3°83 IV. 1°25 | —2-99 1°64 | —1°83 1:08 4°33 | —5°82| — +50 3°31 V. — ‘567 | —2°95 | —4°67 6°67 3°09 | — 1°27 5°48 | —1°74| -—3°01 VI. — 8°48) —1°70 7°58 95 | — ‘96 | —14:°38 1:96 4°78 4°66 VII. 3°63 1°60 3°88 | —7°87 | —4°03 1°22 1°55 | —2°73 33 VIII. 3°13 | — °38| —1°79| — *19| —2°68 | 2°48 2°23 | —2°20 |} —2°09 GIRLS. Hair Eyes Division ; | Fair Red | Medium; Dark ee Blue Light | Medium | Dark I. 7°20; — ‘70| — 4°61 | —2°49 2°70 719) —2°77| —3°22 52 Il. 4°08 | —1°15 | —10°18 5°33 9°98 14°25 | -1:08| ~—7:10 | —3°01 II. 8:12 516 | — 4°92 | —5:06 | -—1:28 4°48 | —2°10 2°36 | —4:13 IV. 4°02 | —1°01} — 1°85 | —1°61 32 1°36 | —6°50 “75 5:14 V. | — *24] —2°80| — 2°09 3°33 2°78 | — 1°35 6°81 | —2°80 | —3:20 VI. —19°99 | —1°46 12°60 7°69 | —2°73 | —11°32 ‘14 5:03 3°85 VIL. 5°68 1°27 1°43) —7°03| —4°15|] -— °85 2°41 | — °33 | -1°55 VILL. 7°62) — *50} — 4°68 | —2°55 1°10 1:27 4°38 | —3°54 | —1°94 Explanatory Note on the “ Divisions.” (See Map I.) I.=Northern Division (Sutherland group). II. =North-Western Division (Inverness group). IIL. = North-Eastern TV. = East- Midland V.= West-Midland VI.=South- Western VII.=South-Eastern VIII. =Southern (Aberdeen group). (Perth group). (Argyll group). (Ayr group). (Lothian group). (Dumfries group). J. F. Tocuer 149 TABLE VIII. Relative Local Differences. Counties. BOYS. Hair Eyes Fair Red Medium} Dark | ey Blue Light | Medium | Dark Aberdeen Co. ... 33 3°55 | -— ‘27 | —2°27 1°52 6°56 | —1°27 | 2°38 | —6°86 Aberdeen City... | — 1:04) 3°55 07 ‘40 | —5'12] — 5°86 147) 171) 1:45 rgy . | — ‘81| — -81| —7:°59 | 9:40 2°02} — °47 5°27 | —1°08 | —4:21 | Ayr 5:89 | — ‘77| —3°81 | —1:02] — °38 6°91 3°26 —5°60 | —3'15) Banff 1°56 3°84) —1:20 | —2°03| — ‘69 1:10 —4:02 1°48 | 1°84} Berwick 5°72 -—1°01) —4°38 | — °39 85 1°64 3°06 | —2°60 | —1°85 Bute we | — 4°56 “59 2°57 64 2°57) — 4°33 2°56 1:03 | -— °31 Caithness ae 18} 1:12) —3:25 1°52 5°54 | — 2°90) —2°21 1:98 | 2°68 Dumbarton ane 3°07 | —2°38| — 2°50 68; 1:41} — 1°27) 4:29) -3:16 | — -09 Dumfries aes 2°93 | —2°83 159 | —2°40) —3°34] — 3:15 3°36 | 2°69 | —4:06 Edinburgh Co. ... 3°10) 12 114 | —3°79 | —2°63 628) — 84 = 2-54 | 1:55 Edinburgh City ... 3°19) — -45| — -62 | -1-66| —2:29 1°30] —1:10| —4-84 | 5°57 Leith .. | — 2°45} 1°46] 3°32 | —1:18| —3°64/ — 8:94] 3°84]; 2°36 70 Elgin & Nairn ... 6°15 “61 | —3°44 —2°47} - 21 8°82 | —3:°27| —2:02 | -1°61 FifeK.&C. ... 1:26) —2°61 2°40 | —2°32) —1:18| — 1:48] —1°58 3°19 | — ‘64 Forfar os b4 06 58 | — 66] — 2°23 8:12 | —3°52| —4°74 2°33 Dundee . | — 3°77) — 733 4:00 | — ‘99 1°37 — ‘81 } —5:92 2°30 4°21 Haddington | — °48 114 aay |) eile} |) leis} 5:20 | -1:26) —1:09 | —1°80 Inverness Be 2°17| — °83) - 7:00 5:23 4:08 8°82 | — *55| —4:79 | -—1°48 Kincardine .. | — cll] — °16| —3:05 3°98 | —1:16} — 1:20 3°47 | —1:25 | —1°41 Kirkcudbright ... | — 2°02 ‘70 | — 2:04 4°32 | — 1°33 1:93) 1°30 | —2°86 Oils) Lanark one 1°62) — ‘08 ‘25 | —5°34| — ‘71] — 9:04 1°34 6°76 | —1:42 Glasgow ... | —12°00| —1:16| 7°36 4°57) —1°52| —18°55 1:04 4°95 9°03 Govan .. | - 780} — 80} 7°64 | — ‘54 05; — 09) - 27) —2°31 2°98 Linlithgow cs 1°37 2°14) 2°78 | —5°50| - 64); — 84) 3°01 45 | —3:'12 Orkney uae 33-9 | = 2:26 | = 34 38 3°71 | 31 1°62 | — 5°33 Perth Hee 4:29 | —2°38 — 4°52 98 4°53 3°30 | — °34| —3:08 1°04 Renfrew .. | — 3°78) — *43| 3°56 | — °47 1°54 ‘92 | —2°61/ 1°61 29 Ross & Cromarty 3°96 | 06 ~—6:'99 2°67 519 9°29 | 64) —3:13 | —5:07 Roxburgh eee 4°33 1°25 | —1:99 | —2°59| — 49 4°54 | "74 | —5:29 1°28 Selkirk & P. ... | — *82 64) 5:95 | —6:19| — 50 1:24) —2°88|; 2:96 | —1°20 Shetland nee 1°84 1°88 | —2°87 | “Qi 95 11°74) —5:06 |) -3°81 | — ‘09 Stirling -- | — ‘90} —2°13| - +28 2°08 1:02 1:05 — ‘08 28 | —1:12 Sutherland ow. | — ‘94 2°20) —4:44 4°84 10 3°24 —3:05 — :93 1°66) Wigtown is “45 1°39 | —2°30 1°22 “92 3°74 | —2°34] — °382 | — 24 150 Pigmentation Survey of School Children in Scotland TABLE IX. Relative Local Differences. Counties. GIRLS. Hair Eyes | | Fair Red | Medium| Dark ete Blue Light | Medium} Dark Aberdeen Co. 5°19 1:49; —2°34 | — 4°11 2°72 4°36 alii 52 | —4°46 Aberdeen City — +33 2°37) — ‘1l 53 | —5°05 |} — 2°78) —1:21 3°65 | — °38 Argyll = 76) =. 1S || 16-44 591! 4:26 56| 4:20; -1°17 | —3°78 Ayr 5°61 | — 67) — ‘75 | — 4:14} —1°67 7°66 1:24} —2°82 | —4°71 Banff 4°75 5°58 | —2°05 | — 4°92 | —1°79 1:14 | —3-00 1°30 87 Berwick 5°67 | — ‘07| —3:26 | — 1°86) — :97 1°29 2°75 | —1°92 | —1°96 Bute — 1:16 52] —1:03 | 2°03 19) — 2°91 2°50 1:42 | —1°85 Caithness 1:94) —1:18| —1°94 | — :08 3°47 | — 1:27 704) — °89 2°03 Dumbarton 1°88 —2°54| —2°67 2°09 116] — 2°42 6:93 | —3°80 | —1°31 Dumfries vs 6°59 —1-11} —2°00 | — 3°92) — -10| — 2°47 3:14 1:77 | —3°30 Edinburgh Co. ... 5°88) 2°73 1:73 | — 8°52 | —3°38 3°84} — 40 00 | —2°83 Edinburgh City .... | — 1°84) -— *51 56 1°03 2°00} — +34} —1°02| —2°83 4°55 Leith ee 18) — *43 176 | — ‘91| —4:18} — 8°32 4°32 4:09 | —2°22 Elgin & Nairn ... 5°39 ‘43 | —3°66 | — 1°87 1:03 6:95 | — 4°60 54 | —1°46 Fife K. & C. 7°57 | —2°43 |) —2°21 | — 2°84} —4°79| — 1:94) —2°36 2°49 1°46 Forfar “72 114 34 | — 1:96 1:05 4:96 | —3°21 | —4:91 4°78 Dundee — 595/| — -12 3°18 2°08 1°97] — 2°16 | —6°32 4°49 3°77 Haddington 3°59 54) —2:47 | — °83] —1°31 3°34 1:25 | —2°48 | —1°44 Inverness ‘92 | —1°22|} —7:30 5°74 8°68 10°71 | — -01} —8:04 | -— °138 Kincardine aaa 4°38} 1:48) —4:55 | — 33 “94 191 4:06} —2°77 | —2°99 Kirkeudbright ... 1-41 | — °72| —2°14 1:21 51} — 90 4°65 | —2°55 | —1:49 Lanark 2°44) 1:07 1:24 | — 3:14} —5:18} — 5:24 1:58 2°73 | — °32 Glasgow —24°17 | —1°938 9°85 14°28 1°40 | —14°61 | —2°16 6°62 7°40 Govan — 12°50 | ‘09 9°53 2:22} — *84| — 2°07 1°39 | —2°35 2°86 Linlithgow 4°95 62 | — ‘97 | — 3°63 | —2°64 “49 168} — °58 | —1°61 Orkney 4°87 | — -27| —2°96 | — 2:29) — -06 4°01 “16 69 | —4°35 Perth 3°72 | 20 | —4°47 15 3°95 2°93 | — *58| —1°82 ‘17 Renfrew .. | — 8°37 | —1°38 4°51 3°61 2°16} — 2°90 | —1:46 2°69 1:08 Ross & Cromarty 4°83 — 38| —6°89 1°69 5°28 | 9:24 | —1°51 | —1°87 | —4:11 Roxburgh 4:45 1:54) 2°40" | — "2:81 “75 | 2°43 ‘70 | —4:07 171 Selkirk & P. - 61 ‘71) 4°85 | — 4:96} —1-00 34 | — 1°62 2:90 | -1°75 Shetland 4°57 89 | —3°24 -— 1:77 1°18 9°73 | —4°56 | —3°32 43 Stirling — 79) —2°25 3°33 | — 1°81} — ‘01 55 ‘65 | — °86 | — °22 Sutherland 3°58 | — -44] —2-03 | — 1:20 18 4°26 | —2°25 | —3°74 3°01 Wigtown 1°42) — °34 |} —2:98 1°74 1°38 5:26 | — -46| —3°87 34 II. Differences in Hair Colour. Hair colour of both sexes will first be considered. (a) Fair Hair. (Maps III., IV., XXI., XXII. and XXXIX.) The North-Western, South-Eastern and Southern divisions are significantly fair haired, or, using the term for significant excess of a class, these divisions are megalometropic both for boys and girls. divisions in a way more readily understood geographically, the Inverness group of counties, the Border counties and the Lothians have the greatest excess of fair hair (f and 2) compared with the general population. Naming the The distributions for J. F. Tocuer 151 boys and girls, however, appear to be different. The results for girls show that the whole of Scotland, excepting the West-Midland and South-Western divisions, are megalometropic or conversely—the Argyll and Lanark groups are micro- metropic, the proportion of fair hair in these divisions or groups being significantly less than that of the general population. Looking now at the inter-county and intra-county (district) differences it is seen that any megalometropic character in the Northern division is due to Orkney and Shetland and only very slightly to the east coast of Caithness. The following counties north of the Forth are signifi- cantly fair haired: viz. Stirling, Perth, Inverness, Ross, Cromarty, Nairn, Elgin and Banff. These are distinctly Highland counties or counties on the Highland line. Examining the districts it is seen that the region of the Cromarty Firth, the region immediately south of the Moray Firth, South Perthshire, South Forfar, except Dundee, the Isle of Lewis, Dunfermline district and the Trossachs, are the specific localities north of the Forth which are significantly fair. Skye and the adjacent mainland are also moderately fair. South of the Forth, Dumbarton (north of Glasgow), Ayr (south of Glasgow), Midlothian and the Border counties are megalometropic. Lanark, excluding Glasgow, is probably megalometropic. The specific localities significantly fair or megalometropic, south of the Forth, are North Ayr, North Lanark, Midlothian, Berwick and a portion of Roxburgh. On the whole the county distributions for boys and girls correspond. Haddington, Fife and Linlithgow are significantly fair haired counties in the girl population. In view of the fact that significant excess appears in so many large areas, one must enquire where the micrometropic population is. The most outstanding cases are the cities of Glasgow, Dundee, Leith and Greenock. The relative difference in Glasgow is so great (RZD =— 12:00 and — 2417 for boys and girls respectively) as to point to exceptional circumstances with respect to this great city. The colour distribution is entirely different from any other part of Scotland. A sepa- rate section will therefore be devoted to Glasgow and to problems bearing on the relationship between density of the population generally and colour. Aberdeen city is like the general population, while Edinburgh is significantly fair haired, slightly more so than the surrounding population. Hawick, Airdrie, Dunfermline, Forfar, Hamilton, Dumbarton and Perth are megalometropic towns; Stirling, Kirkcaldy, Rutherglen, Montrose and Peterhead are micrometropic; while Paisley, Kilmarnock, Ayr, Arbroath, Inverness, Falkirk, Dumfries, Dysart and Galashiels are mesometropic, 2.e. these towns are like the general population. Generally speaking, excess of fair hair is found both in the Highlands and the Lowlands in Scotland, but it cannot be said that this class is characteristic of either—the distribution is far from uniform. In the Highlands, fair hair is more characteristic of the boundaries than of the heart of the Highland country. The Moray and Cromarty Firths, Hast Perthshire, the Trossachs, Dumbarton, Lewis, and East Caithness encircle and are mostly part of the Highlands, and these districts are significantly fair populations. The Borders, North Ayr, and parts of Lanark and Midlothian, as against Galloway, Selkirk, Peebles, Glasgow, and the region 152 Pigmentation Survey of School Children in Scotland surrounding Glasgow, are fair Lowland districts. Orkney and Shetland are both significantly fair, the only distinguishing feature in hair colour among the popu- lation of these islands. (8) Red Hair. (Maps V., VI, XXIII, XXIV. and LX.) Significant excess of red hair is confined (/ and $) to the North-East division ; there is a possible significant excess for boys also in the Northern and South-Eastern divisions. The counties of Aberdeen and Banff stand out clearly as having the greatest excess in the North-Eastern division; Midlothian, Roxburgh, Orkney and Shetland (for boys); Linlithgow and Sutherland (for girls) are also megalometropic. Proportions slightly above the average occur in Haddington, the Borders, Galloway, Arran and Caithness (#*), and in Haddington, Lanark, Peebles, Selkirk, Arran, Forfar and TABLE X. County Specification. Fair Hair. Both Sewes. The sign ¢ indicates boys only; and 9, girls only. Megalometropic Mesometropic Micrometropic Distinctly Probably Probably Distinctly Ayr Dumbarton g Aberdeen City Dundee Berwick Dumfries ¢ Argyll Glasgow Elgin & Nairn | Edinburgh Co. ¢) Caithness Govan Perth Edinburgh City §| Leith Renfrew Ross & Cromarty | Orkney ¢ Forfar Bute ¢ Roxburgh Inverness Banff 9 Kirkcudbright Aberdeen ? Lanark Dumfries ? Selkirk & Peebles Edinburgh Co. 9 Stirling Fife Wigtown Haddington ? Aberdeen ¢ Kincardine 9 Banff ¢ Linlithgow ? Fife K. & C. g Orkney ? Haddington ¢ Shetland ? Kincardine ¢ Sutherland ? Linlithgow ¢ Shetland ¢ Sutherland ¢ Bute ? Dumbarton ? Edinburgh City 2 Kincardine ($); but in none of these cases can the differences be said to be at all significant. Only on the border of the North Highlands is there even the slightest excess of red hair. J¢ is quite clear that the population north of the Grampians and east of the Caledonian Canal is the only one in Scotland where red hair persists quite above the average. Special notice of this peculiarity is taken in a later section. J. F. Tocuer 153 TABLE XI. County Specification. Red Hair. Both Sexes. The sign ¢ indicates boys only; and 9, girls only. Megalometropic Mesometropic Micrometropic Distinctly Probably Probably Distinctly Banff Edinburgh Co. ? | Argyll Dumfries ¢ Aberdeen Co. ¢ Ayr Fife K. & C. ¢ | AberdeenCity 3 Berwick Dumbarton ? Bute Caithness Lidinburgh City Leith Elgin & Nairn Forfar Dundee Haddington Inverness Kincardine Kirkcudbright Lanark Glasgow Govan Linlithgow Orkney Perth Renfrew Ross & Cromarty Roxburgh Selkirk Shetland Stirling Sutherland Wigtown Dumbarton ¢ Edinburgh Co. g Aberdeen Co. ? Aberdeen 9? Dumfries ? Fife K. & C. (y) Medium Hair. (Maps VIL, VIIL, XXV. and XXVI.) Excess of medium or brown of various shades is peculiar to the Scottish Midlands, there being corre- sponding defects in the north, the Borders and Galloway. The East-Midland, South-Western and South-Eastern populous divisions show for boys significant excess. In only one division—the South-Western—is there significant excess among the girls. Among the counties, Renfrew, Selkirk and Peebles are megalo- metropic for both sexes; Stirling and Midlothian for girls only; Linlithgow, Fife, Dumfries and Haddington for boys only. Glasgow, Dundee and Leith are megalometropic towns. As will be seen later, brown or medium hair is characteristic of densely populated parts. Biometrika v1 20 154 Pigmentation Survey of School Children in Scotland TABLE XII. County Specification. Mediwm Hair. Both Semes. The sign ¢ indicates boys only; and 9, girls only. Megalometropic Mesometropic Micrometropic Distinctly Probably Distinctly Probably | Glasgow Bute ¢ Aberdeen Co. Shetland Argyll | Govan Leith g Aberdeen City Caithness ¢ Inverness | Renfrew Linlithgow g | Banff Elgin & Nairn ¢ | Perth Selkirk & Peebles | Dundee ? Dumfries Kincardine ¢ Ross & Cromarty Dundee g Stirling ? Edinburgh Co. | Berwick 9 Ayr 3 Edinburgh City | Dumbarton ? Berwick ¢ Fife K. & C. Wigtown 2 Sutherland ¢ Forfar Elgin & Nairn ? Haddington Kincardine 9 Kirkcudbright Lanark Orkney Roxburgh Dumbarton ¢ Stirling g Wigtown ¢ Ayr 9 Bute ? Caithness ? Leith Linlithgow @ Sutherland ? (8) Dark Hair. (Maps IX., X., XXVIII. and XXVIII.) The distribution of dark hair is very striking. Significant excess is found in the entire west of Scotland, and compared with the general population there is a corresponding significant defect of this class in the east. The Northern, North-Western and West-Midland divisions (¥) and the North-Western, West-Midland and South- Western divisions (?) are distinctly megalometropic. The South-Western division for boys shows slight excess. Examining the counties, it is seen that Sutherland, Ross and Cromarty, Inverness, Argyll and Kirkcudbright, all in the west, are for boys megalometropic. Kincardine (") is the sole eastern megalometropic county. Significant excess among the girl population occurs only in the counties of Ross and Cromarty, Inverness, Argyll, Renfrew and Wigtown. There is only a slight excess in Kirkcudbright. Examining the districts it is seen that Mull, Jura and the portion of the mainland opposite is the most significantly dark population of Scotland. Then follow the remaining portion of Argyll, the western portions of Inverness, Ross and Cromarty (excluding Skye) and Sutherland. Although Ayr- shire (‘) is not megalometropic, the southern portion below Ayr itself is, the district analysis showing significant excess in the Doon region and also in the southern portion of Galloway (Wigtown and South Kirkcudbright). The district J. F. Tocurr 155 analysis shows the same restricted nature of the distribution in the girl popu- lation. Wigtown is the only portion of Galloway with excess. The extreme north of Ayrshire (and not the south as among ,’), and an isolated portion on the Moray Firth (Dornoch and Tain) are also dark-haired districts. Dundee, Edinburgh and Aberdeen show among the girls a slight excess of dark hair, Dundee being the most marked. Summing up the results for this class, 7 7s found that the Highlands, Galloway and the city of Glasgow are the populations which show significant excess of dark hair. There is therefore clearly a sharp distinction geographically, and, as will be shown later, racially in the distribution of this class of hair colour. The east, excepting the slight excesses in Edinburgh and Aberdeen cities (2), a small portion of the coast-line north of Montrose and Donside (() is characterised by a significant defect in the expected proportion of dark hair compared with what would occur on an even distribution of that class throughout the whole country. TABLE XIII. County Specification. Dark Hair. Both Sees. The sign ¢ indicates boys only; and Q, girls only Megalometropic Mesometropic Micrometropic Distinctly Probably Probably Distinctly Argyll Ross & Cromarty ¢ | Aberdeen City Roxburgh — | Edinburgh Co. Inverness Berwick Fife 2 Linlithgow Glasgow Bute Lanark 9? Selkirk & Peebles Kincardine ¢ Caithness Lanark ¢ Kirkcudbright ¢ Dumbarton Aberdeen Co. 9 Sutherland ¢ Edinburgh City Ayr ? Renfrew 9 Leith Banff ? Elgin & Nairn Dumfries ? Forfar Dundee Haddington Govan Orkney Perth Shetland Stirling | Wigtown Aberdeen Co. ¢ Dumfries ¢ Fife K. & C. ¢ Renfrew ¢ Kincardine @ Kirkcudbright ? | Ross & Cromarty ? | Sutherland 9 156 Pigmentation Survey of School Children in Scotland (ce) Jet Black Hair. (Maps XI, XII, XXIX. and XXX.) In a general way, the distribution of jet black hair resembles that of dark hair. While this however is the case, the jet black class seems to be more scattered than the dark-haired class. Taking the divisions first, the Northern, North-Western and West-Midland divisions are clearly megalometropic both for boys and girls. The North-Eastern, South-Eastern and Southern (), the South-Eastern and South-Western (?), are micrometropic; the remaining divisions are fair samples of the general population— they are mesometropic. Surveying the counties, it is seen that the excess in the Northern division is due to Caithness; the excess of the North-Western division is equally divided among the respective counties, while the excess of the West- Midland division is due to Argyll and Bute and slightly to Dumbarton. In the South-Western division, although itself meso- ($) or micrometropic (*), the county of Renfrew stands alone in showing significant excess of this class. The East-Midland and North-Eastern divisions are not at all uniform in their distri- bution of jet black hair. Thus (f and 2) Perth resembles the contiguous county of Argyll in showing excess; only the eastern portion (~“) is micrometropic. Among girls, Fife is the only eastern county in this division which is micro- metropic. The other eastern counties and Dundee show a slight excess over the general population. Aberdeenshire (but not Aberdeen city) stands out as mega- lometropic, although the North-Eastern division itself is either meso- ($) or micrometropic (f‘). Taking now a more detailed view of the distribution locally, one notes that, starting from John o’ Groat’s, excess of jet black hair runs along the coast to Inverness, where it leaves the coast and permeates the upper regions of the Findhorn, Spey and Donside. A slight excess is found along the Buchan coast. It is absent again until the Forfar and Fife coasts are reached, when again slight excess is noticed. It is in defect south of the Forth on the coast- line. Running inwards from Fife and Forfar the excess increases and reaches a maximum in North Perthshire, where it unites with the excess in the Spey valley and the slight excess of Donside. Southwards from Perthshire it reaches Stirling, Dumbarton, and a portion of Renfrew. Northwards it runs through Inverness, part of Ross, and on to Skye and Lewis. It avoids the main portion of Argyll where there is great excess of dark hair, but affects the portion con- tiguous to Skye and Inverness, 7.e. the mainland to Ardnamurchan Point, and the Isles of Mull, Tyree, Coll and Rum. An isolated spot occurs in Wigtown (¢), and in North Ayr and the contiguous portion of Lanark (¥*). A general wew of this class, small numerically, shows that jet black hair, like dark hair, 1s characteristic of Highland counties, but that the distribution is not so restricted as in the case of dark. There is a greater scatter in the distribution for boys than in the corre- sponding distribution for the girl population. J. F. Tocurr 157 TABLE XIV. County Specification. Jet Black Hair. Both Sexes. The sign ¢ indicates boys only; and 9, girls only. Megalometropic Mesometropic Micrometropic | Distinetly | Probably Probably Distinctly Inverness Bute ¢ Ayr Edinburgh Co. | Aberdeen City Perth Aberdeen City 9 | Banff Dumfries ¢ | Leith Ross & Cromarty | Caithness @ Berwick Linlithgow ? Fife K. & C. ¢ Caithness ¢ Dumbarton Lanark 9? Argyll ? Edinburgh City Elgin & Nairn Forfar Dundee Haddington Kincardine Kirkcudbright Glasgow Govan Orkney Renfrew Roxburgh Selkirk & Peebles Shetland Stirling Sutherland Wigtown Aberdeen Co. ¢ Argyll ¢ Fife K. & C. g Lanark ¢ Linlithgow ¢ Bute @ Dumfries ? III. Differences in Eye Colour. (a) Blue Eyes. (Maps XIII, XIV., XXXI. and XXXII.) The general percentage for blue eyes among boys is 14°66 and among girls is 14°87. The greatest excess is found in Shetland and the smallest percentage in Glasgow. Noting first the general distribution it is seen that the north is distinctly the blue-eyed region. The Northern, North-Western, North- Kastern (f and $) and East-Midland () are significantly blue-eyed. The South-Eastern (¢/) and Southern (f° and ¢) show slight excess. The South- Western (f° and $¢) is distinctly micrometropic—there is quite a deficiency of blue eyes in this division compared with the general population. The West- Midland division is only slightly micrometropic. Examining the county distri- butions, one finds that Orkney, Shetland and Sutherland (but not Caithness) are significantly blue-eyed ; all the counties in the North-Western division (f and ?) are also megalometropic; in the East-Midland division, Perth and Forfar (but not Kincardine, the coast, Dundee and Fife) are also quite significant in their 158 Pigmentation Survey of School Children in Scotland excess of blue eyes. Midlothian and Haddington (South-Eastern division) show significant excess; Berwick (*) only a slight excess. Wigtown and Roxburgh (of the Southern division) and only Ayr (South-Western division) are megalo- metropic counties with respect to blue eyes. On the county basis of analysis, the tract of country stretching from Fife through the Midlands to Dumbarton and southwards through Stirling, Linlithgow, Lanark, Renfrew, Peebles, Selkirk, Kirkcudbright and Dumfries, is characterised by a deficiency (in many localities highly significant) of the blue-eyed class of children. Argyll alone of the Highland counties shows no bias in favour of blue eyes; it is like the general population. Examining the distribution from the results of the district analysis it is seen that there is no significant excess on the east coast except in the Elgin district. Inwards from Elgin, north to Sutherland, west to Lewis, south to the border of Argyll and North Perthshire, and east through the Spey region to West Aberdeen- shire, blue eyes is quite in excess of the general population both for boys and girls. The excess is small in Mid Perthshire, increases in the south of the county and diminishes rapidly in passing into Stirlingshire and the populous region between the Forth and the Clyde. Turning eastwards, the excess becomes sig- nificant in North-East Lanarkshire and the neighbourhood of Linlithgow. In the Lothians, the excess found there by the county analysis is shown by the district analysis to be fairly evenly distributed. No great city shows excess of the blue-eyed population. On the contrary, there is a significant defect in each, “TABLE XV. County Specification. Blue Eyes. Both Sexes. The sign ¢ indicates boys only; and 9, girls only. Megalometropic Mesometropic Micrometropic Distinctly Probably Probably Distinctly Aberdeen Co. Perth Argyll Caithness ¢ Leith Ayr Sutherland ¢ Banff Dumfries ¢ Lanark Edinburgh Co, Haddington 2 | Berwick Aberdeen City 2 | Glasgow Elgin & Nairn Dumbarton Bute @ Aberdeen City g Forfar Edinburgh City | Renfrew ¢ Bute 3 Inverness Fife K. & C. Orkney Dundee Ross & Cromarty Kincardine Shetland Kirkcudbright Wigtown Govan Haddington ¢ Linhthgow Roxburgh ¢ Selkirk & Peebles Sutherland 9 Stirling Renfrew 3 Caithness 9 Dumfries ? Roxburgh ? J. F. Tocuer 159 excepting Edinburgh (f and ), and Dundee (#), which approximate the general population in distribution. Looking at the distribution of blue eyes in the division and county maps, it seems a very wide one. That is, geographically considered it is wide, but it must of course be kept in mind that the areas shown are very sparsely populated. The populous area between Edinburgh and Glasgow and the populous centres are mainly defective an blue eyes. Thus the question of density again arises. It will be seen later that just as fair hair is negatively correlated to density so also are blue eyes. (8) Light Eyes. (Maps XV., XVI, XXXIII. and XXXIV.) The proportion of light-eyed children in the general population is 30°314 per cent. for boys and 30°307 per cent. for girls. The West-Midland division (that is, the Argyll group) stands out prominently as the only division where significant excess of light eyes occurs both among boys and girls. The Southern or Galloway division is also significant for girls, while the South-Eastern or Midlothian division (f and ?), Galloway (*), the South-Western (¥*) have a moderate but not a significant TABLE XVI. County Specification. Light Eyes. Both Sexes. The sign ¢ indicates boys only; and 9, girls only. Megalometropic Mesometropic | Micrometropic Distinctly Probably Probably Distinctly Argyll Berwick Aberdeen Co. | Elgin & Nairn ¢ Dundee Dumbarton Dumfries Aberdeen City Renfrew ¢ Shetland Leith Ayr ¢ Caithness | Selkirk & Peebles ¢} Banff g Kincardine ? Bute ¢ Edinburgh Co. | Sutherland ¢ Forfar ¢ Kirkcudbright 2 | Kincardine ¢ | Edinburgh City Banff 9 Elgin & Nairn ? Linlithgow ¢ | Fife K. & C. Forfar 9 Haddington Inverness Lanark Glasgow Govan Orkney Perth Ross & Cromarty Roxburgh Stirling Wigtown Kirkeudbright g Ayr 2 Bute ? Linhthgow @ Renfrew ? Selkirk & Peebles ? Sutherland ? 160 Pigmentation Survey of School Children in Scotland excess of this class. It is seen from the county analysis that Argyll and Arran account for the excess in the West Midland division (f and $), Dumbarton also contributing in the case of the girl population. Taking the more local view revealed by the district analysis, it is found that the excess in Argyll thins off through Inverness to Ross, where it disappears. It extends eastwards and north- wards through Mid Perthshire and over to Deeside and the Kincardine coast. All these are thinly populated districts. In the populous districts between Edin- burgh and Glasgow excess appears sporadically here and there. It runs from Glasgow and Greenock through Renfrew, North Ayr to Kirkcudbright and South Dumfries, a slight break occurring in the district inland from the town of Ayr. Finally, south of the Lothians, a tract from Peebles to Berwick shows moderate excess. Passing from the purely local distribution to the distribution in a general sense, it is quite clear that the light-eyed class is more characteristic of the south than of the north. The excess is more marked in the girl population. Renfrew, Selkirk and Peebles are the exceptions. These counties are slightly micrometropic, or, compared with the general population, the proportion of the light-eyed class is scarcely so great, although not significantly less. (vy) Medium Eyes. (Maps XVII, XVIII. XXXV. and XXXVI.) Turning now to the mixed class of eye defined as medium, it is found that there is 32°72 per cent. of this class for boys and 32°06 per cent. for girls in the general popu- lation. The only division in Scotland where this class is in significant excess is the populous South-Western division or Lanark group of counties. This result is found for both boys and girls. The North-Eastern division or Aberdeen group shows a moderate excess (f and $), but the excess is not greater than could quite possibly occur in making a random selection of the same number from the general population. Examining the distribution with respect to counties, it is seen that Lanark (excluding Glasgow), Dumfries, Selkirk and Peebles—just those counties deficient in all the other classes (excepting Dumfries which has also excess of light eyes)—are the megalometropic counties of this class. These counties are all contiguous and the result is common to both boys and girls. The counties of Fife and Aberdeen and the cities of Dundee and Aberdeen have also an excess of medium eyes (f and ¢). Caithness (¥“) and the Orkney Islands show a moderate excess of the class. Taking the local distribution, it is found that West Renfrew, North Lanark stretching into Stirling, Selkirk and the town of Dumfries, are the areas where the greatest excess is shown in these counties. West Fife in Fifeshire, the southern portion of the Buchan coast in Aberdeenshire, account for the moderate excess found in these counties. The coast from John o’ Groat’s to Banff, with one or two local exceptions, shows an excess of the medium class. Taking a general view of the distribution of medium eyes, it ts seen that excess of the class is restricted to an area commencing with Fife and extending right to Dumfries through Lanark. The other regions of excess are more or less detached from this region. County Specification. J. F. Tocuer TABLE XVII. Medium Eyes. Both Sexes. The sign ¢ indicates boys only; and @, girls only. 161 Megalometropic Mesometropic | Micrometropic Distinctly Probably | Probably Distinctly = | | = Glasgow Selkirk & Peebles | Aberdeen Co. | Kirkcudbright Forfar Lanark ¢ Dumfries ¢ Argyll | Berwick ¢ Inverness Aberdeen City 2 | FifeK.&C. g — Banff Dumbarton ¢ Roxburgh Leith 2 Lanark 9? | Bute Edinburgh Co. ¢ | Ayr g Dundee @ Renfrew @ Caithness | Perth ¢ Edinburgh City g | Elgin & Nairn Ross & Cromarty ¢ | Shetland ¢ Haddington Ayr ? Dumbarton ? Govan | Edinburgh 2 Sutherland ? Linlithgow Kincardine 9 | Wigtown ? | Orkney Shetland ? . Stirling Aberdeen City g Leith g | Dundee g | Kincardine ¢ Renfrew ¢ Sutherland ¢ Wigtown ¢ Berwick ? | Dumfries ? Edinburgh Co. ? Fife 9 Perth ? | _ Ross & Cromarty 9 | (5) Dark Eyes. (Maps XIX., XX., XXXVII. and XXXVIII.) The per- centage of dark eyes in the general population of boys is 22°31; in the general girl population it is 22°76. The distribution of dark eyes from the point of view of the ‘division’ analysis shows excesses in the South-Western or Lanark division and the East-Midland or Perth-Forfar division. The buffer county of Stirling, belonging to the West-Midland division, resembles the general population. The North-Western, West-Midland and North-Eastern divisions are all distinctly micro- metropic (both ~ and $¢) for this class. The other divisions are slightly micrometropic or are mesometropic. Examining the results of the county analysis it is noted that Dundee city and Forfar county are responsible for the significant excess in the East-Midland division, while Glasgow alone is responsible for the excess In the South-Western division. Outside these divisions there is a probably significant excess in the counties of Caithness and Sutherland. A slight excess occurs in Banffshire as also in the county of Roxburgh. Taking a local view it is found that an excess occurs in the south and east of the county of Lanark, in South Ayrshire, East Fife and the neighbourhood of Perth, besides the cases just mentioned. The most striking feature in the distribution of dark eyes is the Biometrika v1 21 162 Pigmentation Survey of School Children in Scotland fact that excess is in the main confined to the great cities. These cities are deficient in blue eyes. There does not seem to be any great bias in favour of or against light and medium eyes, but there does seem to be a bias in favour of dark as against blue in the chief cities of Scotland. TABLE XVIII. County Specification. Dark Eyes. Both Seaes. The sign ¢ indicates boys only; and 9, girls only. Megalometropic Mesometropic Micrometropic Distinctly Probably Probably Distinctly | Edinburgh City | Govan Aberdeen City Ayr 6 Aberdeen Co. Dundee Caithness g Banff Linlithgow ¢ Argyll Glasgow Sutherland 2 | Berwick Dumfries ? Orkney Forfar ? Bute Edinburgh Co. ? | Ross & Cromarty Dumbarton Kincardine @ Dumfries ¢ Leith Ayr @ Elgin & Nairn Fife K. & C. Haddington Inverness Kirkcudbright Lanark Perth Renfrew Roxburgh Selkirk & Peebles Shetland Stirling Wigtown Edinburgh Co. ¢ Forfar ¢ Kincardine ¢ Sutherland ¢ Caithness 9 Linlithgow 9? (7) The General Resemblance of Local Populations to the General Population. I. Introductory. II. Hair Colour as a Character, all Classes constituting the Character being considered together. III. Eye Colour as a Character, all Classes constituting the Character being considered together. I. Introductory. (a) Class frequencies constituting a character are here con- sidered as a whole for each locality (division, county or district), that is to say, intralocally and collectively, and compared with the proportional class frequencies of the general population. (8) As an alternative method, leading to the same result, class frequencies collectively of one locality are compared with the class frequencies collectively of the remaining population and the extent of divergency of the local population measured, J. FE. Tocuer 163 In the previous section the difference between each local group and the general population, z.e. the (RZD)’s for each colour class, were detected and discussed. In doing so, the significance or non-significance of these differences for each local group (division, county or district) was determined for each colour class or category. It has been noted that for each class of hair colour or of eye colour, many localities exhibit significant differences from the general population. In others the dif- ferences may be insignificant, while in a few localities the differences may be considerable although not quite significant. But it is possible that a locality may exhibit a difference or differences almost or just significant for one or more colour classes and yet, when the differences of all the classes constituting the character (either hair colour or eye colour) in any one locality are considered collectively, these differences as a whole may quite conceivably occur even if the locality in question were a fair sample of the general population. A comparison between the entire pigmentation of each local group and the entire pigmentation of the general population is therefore necessary, in order to detect what local groups really diverge and what local groups do not diverge significantly from the general popu- lation, for the two characters under consideration, namely, hair colour and eye colour. In other words, the degree of general resemblance of local populations (firstly in hair colour and secondly in eye colour) to the general population is to be determined. Such a determination can be made at least in two ways, and has already been made in the pigmentation of one fairly long series, namely, the Scottish Insane. (a) One can observe for each locality how closely the observed frequencies of the various classes of hair colour or eye colour as a group correspond to their respective theoretical frequencies—the theoretical frequencies meaning of course, as already noted, those which would be got if, for each locality, the frequencies of the various classes constituting the character were proportionally the same as the frequencies found in the general population The probability that differences in the class frequencies would arise at random in any locality as great as, or greater than, the observed set of differences in class frequencies, can be found by evaluating _,/ 2? - Vs 2-4 & Mere 4 Me ) Paa/2 fe PX aN oee Luaiea De coe © wae ce (ns) if n’ be even, and - ht ( 2 x! x5 . oe aes ) Pie Eo ae woe aig) a DUA Gh. (w= 8) if n’ be odd, where n’ =” +1 classes in the series constituting the character, m, = theoretical frequency of any class, m,’ = observed frequency of any class and x? —§ (ane My 164 Pigmentation Survey of School Children in Scotland This is Pearson’s test of goodness of fit* and is applicable, in the manner above stated, to the present data. (8) One can determine the divergency in hair colour or eye colour of any locality from the remaining population by measuring how far the local group deviates from being a random sample of the general population. This can be done by forming a divergency table and evaluating the mean square contingency coefficient which measures the degree of departure of the local group from complete resem- blance to the general population, or the degree of relative divergency of the local group. Such tables+ have already been formed for the purpose of determining the relative divergency of the local insane from the general insane population with respect to pigmentation. In a divergency table two groups of the population are _ dealt with, the local group and the remaining population, but of course the number of classes is not limited. In this investigation the number of classes is small, five for hair colour and four for eye colour. The frequencies for a particular class, S, of the two groups form a column of the table, while the frequencies of all the different classes of either group form a row of the table. If y? = the total square contingency coefficient and y?= 8 a aad ; n=number in any local group and My N = total population, then the relation y? = a x” holds between y? and ’; or x’ is a fraction of the total square contingency, being, as seen in the working, a partial summation of y”. The mean square contingency coefficient is of course eee ae Caf ey: Since y’ has already been calculated, the above formula need not be used. In terms of x? rae ee x 0=0=4/y¥— and is readily obtained. Since Q measures the divergence of a local group from the remaining population, it is called the divergency coefficient. The probable errors of Q have not been evaluated, except in one or two instances. It is sufficient to note that any value of @ > 008 in the present series is probably significant. The values of @ and log P have been calculated for all the forms of local groups, namely, divisions, counties and districts, and are given in the following tables (Tables XIX., XX., XXI. and XXII.). These two sets of constants have been classed, the classification being the same as that previously adopted for the pig- mentation of adultst. As may be seen from the maps, Class O with values of log P< 3 and Q < ‘008 is the non-significant class, the localities belonging to this class being similar on the whole to the general population. * Phil. Mag. Vol. 1. pp. 157—175, July 1900. + Tocher: Biometrika, Vol. v. pp. 333,334. For theory and probable errors see Pearson, Biometrika, Vol. v. pp. 198—203. + Tocher : Biometrika, Vol. v. pp. 335—340. J. F. Tocuer 165 II. Hair colour. (a) Divisions. Considering first the divisions it is seen on referring to the table (Table XIX.) and maps (Maps XLI. and XLII.) that the East-Midland division resembles the general population in hair colour, both boys TABLE XIX. Divergency in Hair Colour and Kye Colour. Divisions. Hair HKyes Division of Boys Girls Boys Girls Scotland Log P Q Log P Q Log P Q Log P Q 1 10°3 0143 12°3 ‘0160 117 0143 12°8 0152 g 28°9 0231 39°5 ‘0281 37°2 ‘0265 44°1 ‘0296 oI 9°8 ‘0141 19°5 ‘0210 54 0104 liad 0123 4 2-1 ‘0076 3°8 ‘0083 9°8 ‘0137 9°2 ‘0146 0} 12°8 ‘0157 59 *0103 64 70110 93 ‘0139 6 11°3 ‘0188 47-0 ‘0380 28°8 “0286 18°5 0237 if 15:7 ‘0180 14:4 ‘0181 2°7 ‘0058 Tl 0052 8 3°6 ‘0080 12°9 ‘0158 3°4 ‘0077 52 0103 and girls, more than in any part of Scotland. The Southern division (¥*) and the West-Midland division (?) approximate more closely to the general population in the distributions of hair colour than the remaining divisions. All the other divisions diverge widely from the general population. The divergency is greatest in the North-Western division for both sexes. This is clearly due to the excesses of dark, jet black and fair hair in this division and the comparative absence of medium. Red hair is only slightly in defect in the division. (8) Examining the general distributions in the county groups, it is noted that the eastern counties generally can passably be described as samples of the general population. The Northern Isles (¥), Aberdeen (), Kincardine (*), Forfar (f and ¢), excluding Dundee, Fife (¥*), Haddington (¥*), Stirling, right to Dum- barton in the West (f and ¢), and also Lanark (¢"), excluding Glasgow, show, by their divergency coefficients being small, < ‘008, that their populations approximate the general population in hair colour, Kirkcudbright and Wigtown in the extreme south are also like the general population. The rest of Scotland shows great divergency from the general population in its distribution of hair colour. For instance the north-west region, owing to both its darkness and fairness, and the south-east region contiguous to the Border, owing to its fairness and brownness, are widely divergent. Can any reason or reasons be assigned why certain counties or areas are more like or more unlike the general population than others ? References to the maps (Maps XLIII. to XLVI.) and to the following table (Table XXIII.) show that at least for the boy population the counties which show 166 Pigmentation Survey of School Children in Scotland least divergency for hair colour are just those counties densely populated, Lanark, Stirling and the like. It must be remembered that the four great cities, Glasgow, Edinburgh, Dundee and Aberdeen, are excluded from the county analysis. Three of these, Glasgow, Dundee and Aberdeen, show significant divergency, that of Glasgow being very great. Edinburgh, however, resembles the general population. Now if an urban population consisted of persons coming from all parts of the country indiscriminately, each group in the densely populated area would be a fair TABLE XX. Divergency in Hair Colour and Eye Colour. Counties. Hair Eyes Counties Boys Girls Boys Girls Log P Q Log P Q Log P Q Log P Q Aberdeen Co. 3°2 “0084 56 ‘0105 16°8 0174 611 0114 Aberdeen City 73 0123 67 0114 75 0116 31 "0083 Argyll Q1°5 0201 12s ‘0159 7:4 0115 54 ‘0100 Ayr 8:0 ‘0118 WES 0126 15-2 0173 15°9 0173 Banff 4:7 0088 14:7 0169 30 0080 2°5 0061 Berwick ie 0120 6:1 0116 3°1 0079 3°9 0070 Bute 5:4 0101 15 0045 6:0 0091 3°2 0080 Caithness 89 0124 Beil 0086 4:5 0085 12 0046 Dumbarton 3°1 0084 aoe 0085 41 0090 10°2 "0142 Dumfries 6-7 0109 9°5 0138 74 ‘0115 5'8 ‘0096 Edinburgh Co. ... 5:7 0100 20°6 0201 81 0125 46 0088 Edinburgh City... | 3-7 | -0077 T1 | 0056 99 | 0128 | 60 | -0095 Leith City ~...| 54 | 0102 | 48 | -o090 | I7-3 | ‘0179 | 18-4 | -o189 Elgin & Nairn ... 8°7 0125 62 0116 18-0 ‘0175 12°4 0154 Fife K. & C. 3°6 “0080 15°5 ‘0179 23 "0064 48 0073 Forfar 1°4 0047 14 0048 AN 0181 13°7 "0159 Dundee City 4-4 | -0093 72 | -0126 99 | -0127 | 12:9 | O152 Haddington ea "0054 3°6 “0080 6°7 0103 e320 "0082 Inverness 14-9 0163 27°6 0233 17:0 0180 30°8 0241 Kincardine eae 3:0 0085 6:9 0109 3°9 “0069 6°9 0105 Kirkeudbright ... 4:4 “0092 1:3 “0050 2°3 0062 5°9 0095 Lanark : 16 0043 76 0128 19:2 0200 68 0111 Glasgow 29°5 0248 1200 0510 71'3 0381 49°8 0324 Govan 16°9 0176 34:0 "0265 2-2 0064 3°4 0078 Linlithgow 6°2 0114 737 0120 3°4 0075 14 0042 Orkney EP) 0069 5:9 ‘0100 9:0 0118 6°5 0108 Perth 10°5 0142 7:4 0124 3°0 0072 2°4 0063 Renfrew ae 4°8 ‘0089 15:3 ‘0180 -2°9 "0080 _3°5 ‘0077 Ross & Cromarty 14°3 0167 15°6 70175 | Q1°5 0197 19°8 0192 Roxburgh wi 4:1 0095 5:5 0104 | 85 0121 45 "0088 Selkirk & Peeble 10-7 0139 7-9 0118 35 0074 1253 0064 Shetland 23 0067 56 0103 31°6 0237 22°7 0205 Stirling 2°8 “0060 3°9 0076 1°8 0027 19 0021 Sutherland 79 0116 2°1 0073 46 “0084 7:0 0120 Wigtown 12 "0052 2°4 0067 31 0078 74 0118 J. F. Tocurr 167 TABLE XXI. Divergency in Hair Colour. Districts. Naa Log P Class Nae bor Log P Class of — of SSEEACE Boys Girls Boys | Girls a ier Boys Girls Boys | Girls 1 3°58 2°13 ) (0) 57 5°52 4°86 I i 2 12°87 7:32 | III | Il 58 1°64 1°88 0 0 3 5-90 3°79 I 0 59 7:28 5°65 II I | 4 2°46 1:87 0 0) 60 4°73 4°49 I I | 5 4:17 4°24 I I 61 3°36 4°51 0 I 6 1°79 2°55 0 0 62 2°21 4°39 0 I tf 119 1:30 0 0 63 1-02 3°19 0 0 8 2°33 2°07 0 0 64 3°48 4°47 0 I 9 5°42 1°64 I 0. 65 211 4°46 0 I 10 7°65 4°50 Il I 66 4°66 6°06 I I 11 775 2°43 Il 0 67, 68 6°55 4°56 | I I 12 4:29 2°56 I 0 69 2-26 2°04 0) 0 13 44:88 | 146°66 | VIL | VII 70 7:06 16°75 II V 1h 3°83 3°18 0 (0) 71, 76 10°48 5:38 | Ill | I 15 4°63 8°84 I II | 143 3°57 2°52 0 0 16 3:58 2-06 0 07 13 i-32 1°25 0 (0) 17 1-94 2:97 0 0 th 3°37 6°91 0 I 18 5°65 7°84 I Il 5 1-62 3°48 0 0 19, 20, 22 1°54 2°62 0 0 WHE 7°43 6°76 Il I 21 1:09 2°95 0 0 78 2°64 113 0 0 23, 30 8:40 2°04 II 0 x9 2-50 2°97 0 0 24 801 13°17 II | IV 80 5:08 10°45 I | Ill 25 3°60 115 0) 0 81 1:10 118 0 0 26 3°88 819 0 II 2 117 1:03 0 0 a7 1:14 9°77 0 II 83 2-03 4°39 0 I 28 9-05 5°89 Il I 8h 4°46 4°18 I I 29 1:13 2°40 0 0 85 4°55 684 | I I 31 5-09 1:95 I 0 86 1°54 3°46 0 0 BD. Ss 3°61 2°06 0 0 87 3°55 7°86 0 Il 3h 3:02 1:48 0 0 88 14°73 7°64 IV | Il 35 1°52 1°89 ) 0 89 3°54 1°34 0 | O | 36 1°36 8°32 0 II | 90 3°72 8°52 0) II | Sie 7:09 8°67 Il II | 91 14°45 12°61 IV | Ill 38 | 5-16 3°20 I oO | 2 252 3°92 0 (0) 39 | 1:35 2°33 0 0 93, 94 6°75 8°16 I Il 40 5:26 4°49 I I | 95 10°65 3:23 | IIL! o 41 5:06 3-01 I 0 96 7°56 6°86 | Il I 42 701 cot es || AB et 97 T7715 10:85 0) Vo} 43 1:05 3°62 0 0) 98 3°10 2°77 0 0 4h 3°78 1:08 0 0 99 14°78 15°76 | IV | IV 45 Biol 4°92 I I 100 11:10 Toy | TIL) Vi | 4G 2-03 6°95 0 I 101 5:83 3°98 I () Ai 2:06 15°87 0 | IV 102 15°65 4:99 | IV I 48 4°72 2-00 I 0 103 2°56 4°93 0 I 49 601 8-06 iis ee 104 5°17 1:12 I ) 50 3°18 1°89 0 0 105 7-91 12°67 II | Ill 51 3°80 3:14 0) 0 | 106 3°47 4°45 0 I 52 | 7°34 16:33 II V 107 2:23 3°88 0 0 53 3°02 548 0 I 108 3°87 3°79 0 0 54 1-02 4°73 0 I 109 2-23 5°88 0 I 55, 56 4°63 6°53 I I 110 2°31 5°62 0 I Scale of Divergency classes is given on the Divergency Maps (Maps XLIII. e¢ seq.). Pigm entation Survey of School Children in Scotland TABLE XXII. Divergency in Eye Colour. Districts. | 9 2 Number ns Class Number x Che of of Dae Boys Girls | Boys Girls esas! Boys Girls | Boys | Girls 1 78 2°3 0) 0) ov 58°2 55°6 TT See 2 189°7 76:2 | VII| V 58 73 3°5 0 0) 3 | 18°7 24°2 I I 59 49°2 17°8 Il 0) 4 52 22°92. | O I 60 21°5 20°9 I I 5 10°9 Cal O 0 61 37°8 34:5 Il Il 6 63°4 51°7 Iv | Ul 62 19°8 21°8 I I dé 25°9 11-3 |-I 0 63 13°9 4:4 0 0) ro 43°3 21:9 | II I O4 35°0 38°2 Il II 9 40°9 Spy} | IU I 65 38°8 23°2 Il I 10 18°4 6°0 I 0) 66 40°3 53°2 II | Ill itil | 31°6 44°5 1 a 67, 68 44°2 38°4 II II 12 | 37°9 45°7 II II 69 22:4 15°3 I 0) 13 270°0 198°5 | VII | VII 70 39°0 60°5 II | Ill 14 7:3 3°7 0) 0) 71, 76 25°8 23°3 I I 15 42°6 30°7 II I 72 7:0 9°5 0 0 16 19°4 27°9 I I 73 5:7 21°3 0 iL iy 10°2 18°2 0) 0) Th 2°4 14:2 0 0 18 10'9 17°4 0) 0) ie 11°9 77 0 0) 19, 20, 22| 29°1 47°2 I U 1H 32°3 16:2 I 0 a1 4:9 17°0 0 0) 78 23°5 25°0 I I 28, 80 56°5 42°5 Ill II 79 28°4 25:7 I I 24 5°9 3°6 0) 0) 80 53°4 57°9 III | Ill 25 13°1 9°8 0 0 81 18°9 14°6 I 0) 26 19°5 29°9 I I 82 13°4 66 0 10) 27 17°3 14°4 0) @) 8&3 49°1 16:0 | Ill 0) 28 32°9 45°4 I II 8h 20°4 9°4 I 0 29 56°0 45°9 Ill | I 85 36°0 51°9 Il | Ul 31 9-2 45 0 0) 86 9°2 30°1 0) I 32, 33 24°3 42°1 I II 87 12°6 15°6 0 0) 34 12°9 20°3 0) I &8 | 10774 74°8 VI | IV 35 52°4 25°1 Ill I 89 18°8 13°7 I 0) 36 17°8 26°6 O I 90 83°6 13°4 Vv 10) 37 12°6 7°3 Oo | O 91 55°5 60:2 III | II 38 9°3 8°4 10) 0) 92 21°0 15:0 I 0) 39 56°7 iyi Ill O | 98, 94 124°8 112°3 | VII | VII 40 45°0 21°6 II I 95 75 1-7 0 0) 41 8:0 8-2 0) 0 | 96 43°7 59°7 II | Ill 2 177 15:07) 200) 0 | 597 25-0 ci i 0 3 27°7 16°2 I 0 98 16 71 0 (0) 4A 40°6 20°4 Il I 99 24°8 39°0 I II 45 80°2 851 V | V 100 15°7 6°3 0 0) 46 9-1 1°8 0) 10) 101 24°7 13°8 I 0 df 44°4 23°5 1 102 79°1 35°2 V II 48 44°2 12°9 II 0) 103 24°4 4°] I 0) 49 422 | 399 | II | II 104 153 | 122 | 0 | O 50 13°3 23°0 0) I 105 31°7 26°2 I I 51 12°5 17°6 O O 106 35°9 47°8 II | Ill 52 10°6 26°0 0) I 107 10°7 34:5 0) II 538 7:0 114 #O O 108 50°2 47°8 Ill | Il 54 13°9 6:0 0) 0) 109 35°5 28°9 II I 55, 56 6°2 19°5 0) I 110 144:0 102:°0 | VII} VI J. F. Tocurer 169 TABLE XXIII. Persons per Counties considered Square Mile Average Density of Population in non-divergent counties (Boys)... 291 ” ” ” ” (Girls) ee 263 Average Density of Population, taking the 33 counties of Scotland ... | 256 sample of the whole country. If, however, there were special causes leading persons belonging to one or more of the colour classes to congregate in certain areas to the exclusion of others, the groups in the densely populated areas would tend to diverge from the form of distribution found to hold for the whole country. The densely populated counties of Forfar, Fife, Stirling, Dumbarton and Lanark (excluding Glasgow), are fair samples of the boy population, and therefore in these densely populated areas no special causes are likely to be found to exist tending to change the distribution of hair colour. The same can be said of the girl populations of Forfar, Stirling and Dumbarton. But the still denser centres, namely the great cities, are different, excepting Edinburgh, which is quite like the general popula- tion, for both boys and girls. The cities of Aberdeen, Dundee and particularly Glasgow, densely populated centres, diverge largely from the general population, for some reason or other. What special cause or causes are in operation which make the chief cities, excepting Edinburgh, unrepresentative ? Two suggest them- selves. (1) One would expect great seaports to differ if foreigners and others (Irish, etc.) of non-Scottish origin, who on an average differed in their colour characters from the general Scottish distribution, settled in these places, (2) Another special cause would clearly exist in the case where a country popula- tion contiguous to a large town differed largely from the general population, their influx thereby changing the character of the town population—a population which otherwise should be a fair representation of the whole country. It will be seen in a later section that the facts support the foregoing propositions at least in the special case of Greater Glasgow, which contains within its bounds one-fifth of the whole population of Scotland. (y) Divergency in hair colour in district groups will now be briefly considered. It has just been stated that of the great cities Glasgow stands out as by far the most divergent, Aberdeen, Dundee and Leith following, while Edinburgh is quite passably a sample of the general population and is thus for hair colour a repre- sentative sample of all parts of Scotland. Kirkcaldy, Perth, Inverness, Ayr, Kilmarnock, Montrose, Stirling, and other smaller towns moderately resemble the general population. Examining now the country districts, it is seen that by far the most divergent area is along the seaboard of the west (see Maps XLVII. and XLVIII.). This area contributes largely to the divergency of the north-west by its blackness, darkness and fairness, as revealed by the division and county analyses, and has the following boundaries. It commences in the north-west of Ross, is Biometrika v1 22 170 Pigmentation Survey of School Children in Scotland bounded by Strath Glass eastward, includes Skye in the west and terminates in Islay and Jura for boys and Mull for girls. This is of course the heart of the Gaelic speaking region. The region of the Caledonian Canal is less divergent than the west, but passing over to Perthshire, East Inverness due again to excess of fair and jet black, and Moray due to fair, the divergency increases. The divergency of the population eastward of this diminishes but it is still high in Donside in Aberdeenshire. Travelling southwards, it again reaches a maximum in the region of Dunkeld and eastward towards the coast, but excluding it, due again to blackness and fairness. As already pointed out in the county groups, the east coast is not very divergent, Fife being the most divergent portion of the coast-line. The region around Dunfermline, due to a large excess of fair, is widely divergent, as also is Midlothian from the same cause. Berwick, north of the Tweed, is a divergent population, but Roxburgh, south of the Tweed, is very like the general population. From Berwick the divergency follows the Tweed and passing through Selkirk and Peebles reaches the Solway Firth, where it again turns in a north-western direction ($), avoiding Galloway which, as has been already pointed out, passably resembles the general population. The divergency ($) maintains the same degree in Ayr (north) as in Dumfries, but excepting a portion south of Ayr burgh the whole of the south-west population of boys is fairly homogeneous. As shown by the district grouping the local populations of boys which passably resemble the general population, are the regions of West Caithness, the south coast of the Moray Firth, excepting Elgin, the Deveron Valley, the Ythan valley; Deeside, Kincardineshire, the south-west of the Firth of Forth, the south-east of Fife, the Lothians, the Teviot valley and the south-west of Scotland—that is, west of Peebles and Dumfries, and south of Renfrew and North Lanark. Speaking generally of the boy population, the populous area commencing in the north-east and ending in the region of Glasgow, i.e. in the northern portion of the south-west (including most of the intervening area), is the least divergent area for boys. The north-west and south-east are the most divergent—the north-west mainly because of its darkness, and the south-east mainly because of its fairness. The divergency of the girl population is different in some respects. Only a small portion of the coast near Inverness is non-divergent instead of the larger tract for boys. The Lothians, a considerable portion of Dumfries, the northern part of Kirkcudbright and Ayr north of the burgh are all more divergent than the boy population and do not passably resemble the general population as the corre- sponding groups for boys do. The northern portion of Argyll and the southern portion of Inverness are non-divergent girl populations, the corresponding boy populations being much more divergent. On the whole the non-divergent girl groups are more isolated from one another than the boy groups, and the separation of the population (excluding certain towns) diagonally into an east-north-east and midland non-divergent population and a west-north-west and east-south-east divergent one is not so apparent. In a general way one can see that the district groups confirm the results of the county analysis. One can see from the district J. F. TOCcHER TABLE XXIV. Divergency in Hair Colour. ilgial Not Significant or Scarcely Probably Significant or Quite Significant. Widely Divergent. Significant. Class 0 Classes I and II Classes III and upwards : ‘ : Divergence is Division Division Divergence is mainly Division mainly due to due to excess of PRON East-Midland North-Eastern (¢) | fair, red | Northern fair, jet black, Southern (3) West-Midland (? ) dark, jet black dark (4 ) North-Western fair, dark, jet black South-Eastern fair, red (3) medium (0) South-Western medium, dark North-Eastern (@ ) | fair, red West Midland (¢) | dark, jet black Southern (? ) fair County County County Orkney & Shetland (¢) fair | Orkney & Shetland (@ ) | fair Fife (¢ ) fair Aberdeen (¢) red Aberdeen (¢ ) red, jet black Banff (9? ) fair, red Kincardine (3) Kincardine (? ) fair Selkirk (3) medium, red Forfar Lanark (@ ) fair Peebles ( 3) medium, red Fife Caithness (3) fair, jet black Ross & Cromarty | fair, dark, jet Stirling Kirkcudbright (4) red _ black Dumbarton Bute (¢) medium, jet black | Inverness jet black, dark, Lanark ( ¢ ) Sutherland (¢) dark, jet black fair Wigtown Elgin fair Argyll dark, jet black Haddington Banff ( ¢) fair, red Perth (2) fair, jet black Caithness ( ? ) Aberdeen City red, dark Glasgow medium, dark Kirkcudbright ( ¢ ) Dundee medium, dark, black | Govan medium Bute (¢ ) Leith medium Sutherland (9 ) Berwick fair, medium Edinburgh City Roxburgh fair Dumfries fair, medium Ayr fair Selkirk (? ) medium, red Peebles (? ) medium, red Perth (?) fair, jet black District or Area District or Area District or Area Caithness inland Lower Spey, Findhorn & Deveron Valleys, except Elgin Deeside Kincardine coast Esk Valleys Loch Earn Falkirk region (¢) Haddington coast Teviotdale Galloway & Clyde Valley to Ayr Coast (¢) Galloway & South Ayr(?) Upper Spey region parallel to Caledonian Canal, east- wards & northern portion of Argyll (¢) Towns :—Edinburgh Kirkcaldy Perth Inverness Ayr Kilmarnock Montrose Stirling donian Canal (¢) Leith Hamilton Dundee Central Buchan Stirling South Forfar Loch Leven district South-East Fife Selkirk Banff and Aberdeen Coast The district parallel eastward to the Cale- Upper Tweeddale, Ettrick and Yarrow region Seaboard on west coast from Suther- land to Mull, bounded by Strath Glass and Cale- donian Canaleast- wards Caithness Seaboard to Black Isle Upper Spey and Findhorn Valleys Region South of the Forest of Athol Donside ( @ ) Dunkeld region Dunfermline region Glasgow Greenock dark, jet black (fair slightly) fair, dark, jet black fair fair, jet black fair fair, black fair dark, medium dark 172 «Pigmentation Survey of School Children in Scotland maps (XLVII. and XLVIII.) that the denser midland and east coast areas are well mixed samples of the population. Over the whole of Scotland about 60 of the separate district groups are quite representative of the general population, repre- senting a total of 114,482 boys in the boy population of 257,766, or 44°4 per cent., and 97,839 girls in the girl population of 244,389, or 40 per cent. The results of the divergency analysis for hair colour can now be summarised. Taking large samples of the population (i.e. the divisions) to remove merely local differences and to some extent the effect of unequal density, thus getting a general view, it is seen that the populous East-Midland division is a fair representation of the general population for hair colour of both boys and girls. The Southern division is so for girls only. The fairly populous North-Eastern division diverges mainly because of its fair-haired and red-haired population ; the less populous West- Midland division because of its dark population. The other divisions are widely divergent for several reasons. The divergencies of the Northern and North and North-Western divisions are accentuated by their being comparatively small samples separated geographically from the rest of the population, and are not like the rest of the country because of their excessive fairness and darkness. Taking smaller samples of the population (counties, cities and districts) it is seen that populous counties are fairly representative of the general population ; many populous districts also are; but the great cities (excluding Edinburgh which is representative of the population) are divergent. There are elements present in the urban populations which make them unrepresentative of the general population. Certain outlying sparsely populated districts, particularly on the west coast, are also divergent and unrepresentative. The cause or causes of the divergency in the populations affected will be considered in the next section. III. Lye Colour. (a) Divisions. The Southern and South-Eastern divisions (f and ¢) are the most representative of the general population. These popula- tions are passable samples of the general population. Next in order are the North- Eastern, East-Midland and West-Midland divisions. Then follow the Northern— due to excess of blue eyes, and the South-Western—due to excess of medium and dark ; and lastly the most divergent of all, the North-Western, whose divergency is also mainly due to the excess of blue eyes. (See Maps XLIX. and L.) (8) Counties. Examining the county divergencies it is seen that, in the boy population, and taken in the order of greatest divergency to least divergency, the following counties diverge greatly from the general population owing to excess of blue eyes, namely: Orkney, Shetland, Ross, Cromarty, Inverness, Elgin, Nairn, Aberdeen and Forfar. Ayr in the south greatly diverges owing to excess of both blue and light eyes, and Lanark greatly diverges owing to a large excess of medium eyes. The divergencies in all the foregoing cases are very great. Among the still significantly but less divergent counties are the Lothians and Roxburgh (excess of blue eyes), Dumfries (excess of light and medium), Argyll and Dumbarton perhaps (excess of light eyes). The non-divergent regions are somewhat isolated from one another; they are Banff and Kincardine in the north; Perth, Fife, Stirling, J. F. Tocuer 173 Dumbarton, Renfrew and Linlithgow, all contiguous—that is, practically the whole of the Scottish Midlands ; Berwick, Peebles and Selkirk, contiguous in the south- east, and finally Kirkcudbright and Wigtown in the south. The girl population shows on the whole equal divergencies in the northern counties already mentioned, divergencies which are due to excess of blue eyes; in Ayr the divergency is almost entirely due to blue eyes and scarcely any to light eyes as among the boy population. The divergency in Lanark is only just significant and is due to excess of both medium and light eyes. Wigtown and Kirkcudbright are both significantly divergent, due in the case of Wigtown to excess of blue eyes and in the case of Kirkcudbright to excess of light eyes. Galloway therefore differs distinctly in its boy and girl distributions of eye colour. The non-divergent regions or rather the non-significantly divergent regions in the girl population for eye colour are as follows: Caithness and Banff in the north ; Perth, Linlithgow, Stirling, North Lanark and Renfrew all contiguous; and Ber- wick, Selkirk and Peebles also contiguous near the Border. (y) Districts. Looking at the district results, they confirm the county analysis and also the conclusions arrived at with respect to hair colour. The populous Midlands, namely, North Lanark, Perth, Stirling, Dumbarton, Fife and portions of the east coast (i.e. Forfar and north-east Aberdeenshire, and from Nairn to Caithness) are all comparatively representative of the general population in eye colour. Thus while Glasgow itself is divergent, the great part of the environs is not. Such populous centres as Greenock, Kilmarnock, Falkirk, Ayr, are scarcely significantly divergent. Edinburgh, Dundee and Aberdeen cities are significantly divergent. In Aberdeen it is due to excess of medium, in Dundee to excess of dark and medium and in Edinburgh to excess of dark alone. It is seen, just as in hair colour, that the very sparsely populated regions and the very thickly populated areas are the most divergent. But while all the sparsely populated regions diverge on account of excess of blue eyes, all the very densely populated areas diverge because of excess of light, medium or dark. It is to be expected that Dundee would have a fair proportion, or even excess, of dark eyes, since the country adjacent to the city, namely, Perthshire and Forfarshire, are the only counties in Scotland showing excess of this class. The reason for the excess in Edinburgh is not so apparent, unless the migration from these counties to the capital is greater than from the rest of the country. The foreign population, as will be shown later, is significantly associated in general with dark eyes, but on examining the returns, it has been found that foreigners are not present in Edinburgh in sufficient numbers to affect the distribution of dark eyes in the school population there. With Glasgow or certain districts of the western city, the case is different, as will presently be shown. Forfarshire and Perthshire people are perhaps likely to have migrated to Edinburgh in greater numbers than people from other parts. This would account for the excess. The excess of medium eyes in Glasgow may be partly accounted for by a greater proportion of migrants from Lanarkshire, Dum- fries, Peebles, Selkirk and Fife, all counties with a distinct excess of this class, 174 Not Significant or Scarcely TABLE XXV. Divergency in Eye Colour. Probably Significant or Quite Pigmentation Survey of School Children in Scotland Widely Divergent. Significant. Class 0 Significant. Classes I and II Classes III and upwards Se = = { Division Division Due to Excess of Division Due to Excess of South-Eastern Northern blue North-Western blue Southern North-Eastern | medium & blue | South-Western medium East-Midland dark & blue West- Midland light County County Due to Excess of County Due to Excess of Banff Sutherland blue, dark Shetland blue Caithness Aberdeen blue, medium Ross & Cromarty | blue Kincardine Argyll light Inverness blue Perth Dumbarton light Elgin & Nairn blue Stirling Midlothian blue Forfar blue & dark Dumbarton Roxburgh blue (and dark) | Lanark (¢) medium Govan Dumfries light Ayr blue & light Renfrew Orkney blue Glasgow medium & dark Linlithgow Aberdeen City | medium Leith light & medium Selkirk Dundee City medium & dark Peebles Edinburgh City | dark Berwick Kirkcudbright Wigtown Bute Haddington Fife Kinross & Clackmannan District or Area District or Area Environs of Glasgow Renfrew including Greenock Kilmarnock Ayr Parts of North Lanark Falkirk area Environs of Edinburgh Fifeshire generally except Loch Leven area North Forfar Area from Buchan coast to Spey Valley Dornoch and Tain region Caithness inland North and South Uist Mull and adjacent mainland South Ayrshire Dumfries North Kirkcudbright | South Roxburgh Peebles Berwick Parts of North Lanark and North Ayr Midlothian except near Edinburgh South Fife (¢ ) Dundee Most of Perthshire Edinburgh City Aberdeen City Galloway Linlithgow area Skye and the adjacent mainland, north and south Orkney Remaining environs of Glasgow Irvine Roxburgh Outskirts of Perth city Donside Part of Buchan coast Lewis North Dumbarton District or Area Due to Excess of North-East Lanark, Carluke region Elgin district Spey Valley Black Isle Glen Urquhart region Islay & Jura Shetland Glasgow blue blue blue blue blue light blue medium & dark J. F. Tocurer 175 Whether migrants from these counties partly account for the excess of medium eyes in Glasgow or not, excess of medium eyes is associated with densely populated centres and is accordingly dealt with in the section discussing the relationship between density of population and colour. It should be finally noted that the very sparsely populated regions, all of them having an excess of blue eyes, are inhabited by a people who have been undisturbed by any recent immigrations and who most probably are descendants of a race long resident in the country. The accompanying table (Table X XV.) gives a synopsis of the results respect- ing the relative divergency in eye colour, in the divisions, counties and districts respectively. (8) Class Segregation. The Nature of the Distribution of Relative Local Differ- ences of each Class considered collectively and interlocally, without reference as to where they occur geographically, and the Degree of Segregation of each Class determined. I. Interlocal Constants. It has been shown (Section 6) that, in each colour class, differences occur throughout the country in localities (specifically pointed out, in each case, in the section referred to), which are distinctly significant. Positive differences, much in excess of the expected, occur in contiguous areas, indicating a differentiation for each class more or less from the remaining population. That is, the existence of these individual local differences proves that the population is not an evenly distributed one with respect to the colour class or classes under consideration. It is true that many of the differences could quite well occur at random and therefore that many localities resemble the general population with respect to one or more classes. But those larger differ- ences, reckoned significant owing to the great odds against their occurring at random, quite upset the proposition that the distribution of the class over the whole country is a random one. Having indicated the localities where individual significant differences occur (thus proving segregation) and also those where non- significant differences occur, the differences for each class collectively will be considered without reference as to where they occur geographically in order to compare the degrees of segregation of the classes. It will then be seen which class has the greatest geographical separation. It is therefore necessary to provide a measure of local segregation, that is to say, one must have a single common measure, for each class, of the extent of the deviation from a uniform distribution of persons belonging to the class over the whole country. This measure is easily obtained when it is remembered that the relative local differences are all the local differences reduced to a common scale by dividing each difference by its standard deviation. Since this is the case, if the differences are such as would arise from a uniform distribution of the persons belonging to each class all over the country , these differences as a series would of course form a normal distribution with a mean value h=0 + ae and a standard deviation s=1+ To) )? where q is vq the number of groups (either counties, districts, or units of area) considered. Thus 176 =Pigmentation Survey of School Children in Scotland h and s are interlocal constants. This test of the degree of homogeneity of a class or character in a population scattered over a wide area has already been’ applied by the writer, the constants for both measurable and non-measurable characters being determined*. If then a population is non-segregated with respect to any class (that is, if persons belonging to the class are well distributed over the country) the interlocal constants h and (s—1) will be both equal to zero within the limits of their probable errors, and the segregation of a class will increase as these constants become greater and greater. The following table (Table XX VI.) gives the values of the interlocal constants for both the boy and girl populations, the distributions considered being those of the relative local differences arrived at from the county data—that is, with the county as the unit of area. Table XXVII. is one in which the classes are arranged in the order of the significance from lesser to greater segregation. II. Significance of the Constants. These results show how decided the devia- tions are from purely uniform distributions of the class populations. It is seen that the blue-eyed class and the fair-haired class are both highly separated geo- graphically from the general population. The separation is greater in the case of fair-haired girls than in the boys of the same class. The deviation from a random distribution for boys and girls is of the same order in the other colour classes. TABLE XXVI. Interlocal Constants. Colour Segregation. (This table shows that a grouping of children of the same class occurs no matter what class is selected. The figures show the relative extent of the segregation of the classes.) h=mean of the series of relative local differences, boys or girls, for each colour class. s=standard deviation of the series of relative local differences, boys or girls, for each colour class. ; Sm=standard deviation, as above (boys). sp=standard deviation, as above (girls). Boys Girls | Colour s-l s-l h (s—1) THe h (s —1) ees Sm — Sf Fair Hair e's °45 | 2°75 | 34:12 114 | 5°14 | 63°77 | —2°39 Red Hair Tee 18 69 8°56 ‘09 “56 6°95 13 Medium Hair ... | — °57 | 2°82 | 34°86 | — -81 | 2°90 | 35°98 | — -:09 Dark Hair ... | — 04] 2°24 | 27°79 | — °39 | 2:95 | 36°60 | — ‘71 Jet Black Hair ... 20 | 1:36 | 16°87 32 | 1:93 | 23°95 | — -57 Blue Eyes os 1°17 | 5:02 | 62°28 1:02 | 4°12 | 51°12 90 Light Eyes .. | — 09] 1°78 | 22°08 13 | 1°85 | 22°95 | - ‘07 Medium Eyes ... | — °51] 2°09 | 25°93 | — °59 | 2°15 | 26°68 | — -06 Dark Eyes ee eS BRU ail, |) Srapalish | 3 cats) |) itl |) PeBies0) 24 * Biometrika, Vol. v. pp. 323—327. J. F. Tocuer 17 Red hair is the only class which shows a moderate approach to uniformity of distribution, but even in this class the deviations are 7 and 84 times their probable errors for boys and girls respectively. There is, however, a decided approach towards an even distribution of this class over the whole country compared with all the other classes. But for the probably significant excesses in the north-east TABLE XXVII. Segregation in Colour. (This table shows that children with red hair are the most uniformly distributed class, while fair haired blue eyed children are not well distributed throughout the country. They have a tendency to occur in groups and show therefore the greatest segregation.) i eepaae ae MOG: Interlocal constant is Class of Category Significant ... | between 0 and 1:0 Red Hair ¢ and 2 Pee : Se (Jet Black Hair g and 9 Very significant 33 3 1:0 and 2:0 ‘Light Eyes ¢ 9 Dark Eyes 9 ae Eyes g Medium Eyes g 2 Highly significant ... = 2-0 and 3°0 Dark Hair ¢ and 9 Fair Hair ¢ Medium Hair ¢ 9 Excessively great ... | above 3:0 Fair Hair 9 Blue Eyes g ? of Scotland and the neighbourhood of Edinburgh as shown in the class analysis (Section 6), the distribution of the class of red-haired persons would be fairly uniform. The chance against meeting a schoolboy of this class in travelling over Scotland is about 17 to 1. One would have to note at random the colour characters of at least 18 people on an average in order to have one of this class in the group. But the chances are slightly lower in Aberdeen and Banff and Mid- lothian. They fall to about 14 to 1 against. The chance against meeting a person of the jet black class is much smaller, about 99 to 1, but the chances vary more as one moves from place to place. In certain places it is as small as 400 to 1. The chance against meeting a person of the dark class or of the fair class is about 3 to 1 and of the medium class about 3 to 2 and so on. The point is that while one can state in a general way the chances for or against a Scottish child belonging to any one of the hair and eye colour classes, these chances vary largely from district to district. The question may be asked, What is the typical Scotchman like? One cannot answer that question offhand from the present data, which deals with school children only. It must be remembered that there is a change in hair colour and eye colour in passing from childhood to manhood. Hair colour generally becomes darker more or less with age. A fair- haired boy or girl may or may not become a fair-haired man or woman, but there is a tendency to become darker. A measure of the change, from Prussian and British data by Pearson*, and by the author+ from the Aberdeenshire data, shows * Pearson: Biometrika, Vol. ut. p. 161. + Biometrika, Vol. y. pp. 389—341. Biometrika v1 23 178 Pigmentation Survey of School Children in Scotland that the correlation between age and hair colour is quite appreciable. On the assumption that the rate of change of hair colour and eye colour with age is not likely to vary appreciably in passing from one district to another, the author determined the probable distribution of the colour of the adult population of Scotland. The result was published in the same memoir*. Using the result together with the percentage results for the whole of Scotland for boys and girls as found from the present data, the following table (Table XXVIII.), constructed as a probability table, gives the chance of a person of Scottish nationality possessing any one of the following characteristics :— TABLE XXVIII. The Probability of the Person belonging to any one of the following Colour Classes is Boys Girls Colour Adult Scotland Range in Scotland Range in Population | Generally Counties Generally Counties From To From To Hair: Fair fe “115 250 291 ~| 314 ‘274 243 344 Red sad 042 055 7046-069 051 041 068 Medium... 559 433 373 495 “409 356 “474 Dark 284 250 187 | 308 254 194 291 Jet Blackj ** 7 013 008 024 012 002 026 Eyes: | Blue 278 147 103 259 148 118 252 Light es ae 303 227 337 303 241 348 Medium... 459 =| 327 ‘279 344 321 266 358 Dark so 263 "223 174 "244 228 159 263 With regard to the juvenile population, the above table shows that one can hardly say any particular eye colour is typical of Scotland. There is a bias in favour of light and medium eyes. Brown hair is the most likely colour for a child to possess. Fair and dark are equally likely hair colours in the juvenile population. Medium eyes and brown or medium hair are more typical of the adult population. Summarising the results of this section, it has been found possible to classify the degrees of segregation of the colour classes—a segregation already proved, although its amount was not revealed in any one case in considering the individual differences. It has now been shown that segregation of certain classes from others exists, The greatest segregation from others (or congregation as a class) is shown * Tocher: Biometrika, Vol, vy. pp. 339—341, J. FE. Tocuer 179 in the case of blue eyes, the interlocal or segregation constants (s—1) being 5°02 and 4:12 respectively (see also Diagrams VI. and XV.). The odds against an even distribution of persons belonging to this class is thus enormously great, as also are the odds against persons of the fair-haired class being evenly dis- tributed (see Diagrams I. and X.). The difference in the segregation of the boys and girls is marked. Medium hair and dark hair are approximately equal to fair hair (f) in their divergence from uniformity of distribution (Diagrams III, TV., XII. and XIII.), and then follow medium and dark eyes (Diagrams VIII, IX., XVII. and XVIITI.), and with slightly less segregation still, ight eyes (Diagrams VIL and XVI), and jet black hair (Diagrams V. and XIV.). Finally, in the case of red hair the interlocal constant shows persons belonging to this class to be the most evenly distributed one throughout the country (Diagrams II. and XI.). In no case, however, can the exact probability of an individual belonging to any particular class be predicted with accuracy, just on account of the uneven nature of the distribution of persons belonging to the class. It falls finally to be noted here that the differences for each class have been considered collectively, without reference as to where they occur geographically or as to whether the differences for boys and girls occur together in the same place. This point is specially dealt with in another section, where a measure is given of the agreement of the sexes in colour characters. The most striking result in this section is that bearing on red hair, Its distribution is so markedly different from the rest of the classes as to attract attention. The occurrence of red hair in Scotland either (a) is independent of race, or (8) is one of the effects of blending of races—perhaps widely divergent races, or (vy) is an abnormal condition in hair colour and deserves the attention of the physiologist and pathologist. (9) Peculiarities in the Distribution of Colour in Scotland. I. General. An examination of Table XXIX. will show how far the distri- bution for boys and girls differ, and also what excesses for hair colour and eye colour occur together. It should be noted that this does not necessarily mean that a particular combination (e.g. fair hair and blue eyes) is in excess. This can be accurately determined only by comparing the excess frequencies of the particular combinations found in the localities under consideration with the pro- portional frequencies of the same combinations in the general population. The statistical labour involved in such an analysis would be very great and could not be attempted by the writer until the present analysis had been completed. Besides, no funds were available to defray the considerable additional expense which would have been incurred in providing for clerical assistance in tabling the combinations and otherwise completing the statistical analysis. Thus, the results of the present investigation are those flowing from individual classes and only indirectly from combinations. 23—2 180 Pigmentation Survey of School Children in Scotland The table (Table XXIX.) shows that in the girl population of the entire north, excess of blue eyes and fair, dark and black hair occurs together. Excess of blue eyes, although common to the entire north for the boy population, is associated with great excess of fair hair only in the North-Western division, and with excess of red hair in the North-Eastern division, which excess is also TA BEE Sox: Excess positive Frequencies* peculiar to each of the eight great Divisions of Scotland. B=Boy Population. G=Girl Population. Division Colour i II Ill IV V VI | VII VIII Hair: | Fair .. | BG BG BG G —— = BG BG Red see | — —_— BG B = Medium ... == = = B = BG B = Dark avs B BG = = BG G — — Jet Black ... | BG BG == = BG = = — Eyes: Blue | BG BG BG B B Light ee | BG | B BG | BG Medium wf oS — BGS | = 7) =— BG — — Dark | | BG | — BG == = | | | characteristic of the girl population in that division. The characteristic feature of the East-Midland division is that it possesses both an excess of blue eyes and an excess of dark eyes. There is an excess of fair hair (?), and a defect of red hair (g), but otherwise the hair distribution does not markedly differ from the general population. The West-Midland population differs quite sensibly from the East-Midland. The characteristic feature of the West-Midland population is that excess of light eyes occurs with excess of both dark and jet black hair. The South-Western division with its dense urban populations is quite different from the Southern and South-Eastern divisions. The South-Western population has an excess of medium hair occurring with excesses of medium and dark eyes, while the remaining Southern population is characterised by an excess of fair hair only. The Southern division (2) has the excess of fair hair occurring with excess of light eyes. The question may well be asked: What can one learn from all this maze of detail as to the significant differences in the distributions of the various colour classes? Are they racial differences or differences due to other factors? One * In some cases the excess positive frequencies are not quite significant (see tables of relative differences, Table VII.). J. F. Tocuser 181 cannot in this memoir enter into a general discussion as to the origin and racial characteristics of the Scottish people. This memoir is concerned only in eluci- dating the nature of the colour characteristics of Scottish children for the purpose of assisting those engaged in studying racial and social problems and problems in heredity. Such peculiarities as may assist this study may therefore be noticed in detail. II. Red Hair. A striking peculiarity in the distribution of red hair has already been noted in the last section. The class is almost uniformly distributed throughout Scotland. Three probable causes of its occurrence were stated in the section referred to. Whether any of these are valid must be determined by investigation, but the fact remains that the distribution of the class widely differs from the distributions of the other classes. The occurrence of red hair is certainly not confined to modern times, neither is it peculiar to any social circle. It has occurred in the past as a becoming feature in princes and among the people. It is an inherited trait in many distinguished families. Is it that here one has a case of exclusive inheritance, and therefore that cases of red hair occurring in families none of the parents of which belong to the class, are reversions? Such observations as have been made point to this conclusion, but a larger mass of data is wanted to prove or disprove this view. It is a curious circumstance that significant excess of the class should be found occurring in the historic home of the opponents of Agricola. The solitary reference of Tacitus to the red-haired Caledonians who inhabited Scotland north of the Grampians deserves a passing notice. Taking the general impression of Tacitus as indicated in his statement “ Namque rutilae Caledoniam habitantiam comae, magni artus, germanicam originem asseverunt” to mean that the northern Scottish people in his time were mostly red-haired in our sense and appeared to have a North European origin, it is perfectly obvious that the North of Scotland has changed most markedly, as one should expect it would have, in the long interval between his time and the present day. Not more than 5:49 per cent. and 5:09 per cent. respectively of the boy and girl populations of Scotland are red-haired. It is curious to note, however, that the greatest excess of red hair from this proportion is found in the region of Scotland north of the Grampians. While this is the case one must remember that the actual proportion of red- haired persons anywhere in the north is really a small one. Only a small pro- portion, ranging from 5 to 7 per cent., taking fairly large areas, is at the present day red-haired. But if the observation of Tacitus has any truth in it at all, is it fair to infer, since hair colour is an inherited character, that this small class has for a considerable portion of its ancestry the race found in North Britain in later Roman times? One must not come to the hasty conclusion that there was in reality an exclusively red-haired race in Scotland or anywhere else. Indeed, no such exclusive race now exists. But at the present time one finds red hair occurring in all the North European races more or less. That is to say, the 182. Pigmentation Survey of School Children in Scotland English, Irish, French, German, Danish, Dutch, Belgian, Norwegian and Swedish speaking peoples, at least, have all of them certain proportions of the red-haired class in their respective populations. It thus appears that in every Northern race there is likely to be a certain proportion of the red-haired class. A moderate proportion (5 per cent.) is found in Scotland generally, and all one can meantime say therefore is that it is a characteristic of one-seventeenth of the population of the north-east of Scotland to have red hair; or that that population, observed in early time to have red hair, has a significant excess of that class over the general proportion found in the country at the present time. Ill. Relationship between Gaelic speaking Population and Pigmentation. As already indicated, one cannot open a discussion as to the origin, distribution and characteristics of the Keltic and non-Keltic portions of the population. Nothing germane to this investigation would be solved by it. Authorities differ greatly as to the facts. One could by an analysis of the colour characters of the popu- lation with respect to surnames, Highland, Lowland and otherwise, throw a little light on that portion of the Keltic problem bearing on colour. This has already been done by the writer for the populations of Aberdeenshire of 1696 and 1896*, and he proposes at some future time to table the data now collected for the whole of Scotland in a similar way. What can be done, however, is to investigate the characters of the Gaelic speaking portion of the population as com- pared with the non-Gaelic speaking and greater portion, and note whether they are really different or not. Here one is on safe ground. The problem of the ethnic descent of the Gaelic speaking and non-Gaelic speaking portions of the popu- lation the writer leaves untouched. But he proposes to note whether there is any particular association of colour with the Gaelic speaking population. In the Report on the Scottish Census of 1901+, the number of “Gaelic and English ” speaking persons above three years of age is given for each division of Scotland. The percentages of Gaelic and English speaking persons in the eight divisions of Scotland can thus be found and compared with the corresponding percentages for hair colour and eye colour found from the results of this survey. The corre- lation coefficients were determined in the following manner :—Let «#, = deviation from mean percentage of the Gaelic speaking population; #,= corresponding deviation from the mean percentage of children belonging to any colour class , o,=standard deviation of percentage of the Gaelic speaking population; o, =standard deviation of the percentage of children belonging to colour class s; and N = number of the divisions into which Scotland is divided; then the corre- lation coefficient 1s: _ Layay ~ Noyoo’ and determines the degree of association or correlation between the Gaelic speaking population and the colour class s. Taking as an example s=jet black hair, the following table (Table XXX.) was formed :— * British Association Report, Cambridge, 1904, p. 707. + Eleventh Decennial Census of the Population of Scotland with Report, Vol. 1. Table XV. p. xxviii. r J. F. Tocuer 183 TABLE XXX. Gaelic speaking . Division | Population Jet pines Hair vy) 2 i N. 4°82 30 II. NW. 39°17 79 Ill. NE. — 9°30 _ 95; Vv. WM 1°73 -08 VI. SW. — 8°57 _ +20 An inspection of this table reveals the fact that in every division where there is an excess of the Gaelic speaking population there is an excess of the jet black class, and vice versd. The values of the correlation coefficient 7 and its probable error in the particular case when r=0, or Ey», have been evaluated for all the colour classes and the Gaelic speaking population with the following result (Table XXXI.). The ratio 7/#,,..) shows how much the correlation found exceeds the probable error when 7 is equal to zero. TABLE XXXI. Correlation of Hair and Eye Colours with Gaelic speaking population. Colour Class r ee Evo | Fair Hair ee 3482 ies Red Hair fos — 3027 —1:19 Medium Hair ... — 8663 — 3°40 Dark Hair co *8126 3°19 Jet Black Hair ... ‘9581 3°76 Blue Eyes or 8663 3°40 Light Eyes a5 — 1248 —0°49 Medium Eyes ... — °8760 —3:44 Dark Eyes Fes — 6387 —2°51 This result is of some importance. It shows definitely for the first time the general nature of the colour characters of the Gaelic speaking as against the non-Gaelic speaking population of Scotland. It proves that the proportion of dark-haired and jet black-haired persons is far greater among the Gaelic speaking than among the non-Gaelic speaking population. In technical language, dark hair and jet black hair are positively correlated to the Gaelic speaking population. The association is clear, and the result ought to be of assistance to the student of the Keltic race. The above table also shows that blue eyes are associated with the Gaelic speaking population, the association being slightly 184 Pigmentation Survey of School Children in Scotland greater than in the case of dark hair, and nearly as great as in the case of jet black hair. The odds against a less correlation than that found are so great as to warrant the conclusion that blue eyes are far more common where Gaelic is spoken than where it is not. Medium eyes are distinctly correlated negatively to the Gaelic speaking population. One may safely conclude that medium eyes are rarer in Gaelic speaking regions than in the rest of the country. Medium hair, and in a lesser degree dark eyes, are also negatively correlated to the Gaelic speaking population, the correlations being appreciable in each case, but fair hair, red hair and light eyes are present in practically the same proportions in both the Gaelic and non-Gaelic speaking populations. Thus, on a direct survey of the Gaelic speaking population, one would expect the group to be much darker in hair colour and more blue eyed persons would be expected among the Gaelic speaking than in the remaining population, the excess being accompanied by lesser proportions of medium hair and medium eyes and also dark eyes. No sensible differences would be expected in the fair-haired, red-haired, and light-eyed classes compared with the general population. The definite relationship between the Gaelic speaking population and certain colour classes now established, enables one to interpret more fully the meaning of the significant differences in the western portion of Scotland. In Table XXX. it is seen that the North-Western, West- Midland and South-Western divisions are the only ones in which there is an excess of Gaelic speaking persons over the general average. In these divisions about 65 per cent. in Sutherland and about 50 per cent. in each of the counties of Ross and Cromarty, Inverness and Argyll speak Gaelic. So far as hair colour is concerned, all these counties show great excess of dark and jet black hair. This excess is therefore due mainly to the Gaelic speaking populations in these counties. Light eyes, although in excess in Argyll, are neither peculiar to the Gaelic speaking population nor to the non-Gaelic speaking population, since the value of the correlation coefficient is a very small one. The one group is likely to have as large a proportion of light eyes as the other. But blue eyes are associated even more intensely with Gaelic speaking people than dark hair, and this class is in excess in Sutherland, Ross and Cromarty, Inverness and the Western Isles. A fairly large proportion of the dark-haired Gaelic speaking people have therefore blue eyes. In these counties, however, fair hair is also in excess, and since the Northern Isles, Orkney and Shetland, are characterised by a large excess of fair hair and blue eyes and by an exceedingly small proportion of Gaelic speaking people, one would infer that blue eyes are largely associated with fair hair in the non-Gaelic portion of the population of these counties as well. Thus these counties consist of a mixture of fair-haired, blue-eyed, or blonde non-Gaelic speaking popu- lation (or if Gaelic speaking, at least of non-Keltic origin) and a dark-haired Gaelic speaking population. The distribution of eye colour in this latter population is unknown, but all classes of eyes are most probably represented, a fairly large proportion of blue eyes being quite certain. J. F. Tocuer 185 IV. Relationships between Pigmentation, Density of Population, and Foreigners. In the Census Report already referred to, the number of persons per square mile is given for each of the eight chief divisions of Scotland*. The means are at hand therefore to compare the density of the population with pigmentation. With regard to the foreign element, one would naturally come to the conclusion without examining the actual data that foreigners are likely to be found in the more densely populated areas of the country. Business leads them to where the industries are and therefore to where closely packed populations reside. It is desirable therefore that any correlation existing between the two should be measured. The association has been measured from two sets of data. The degree of correlation has been determined (1) between foreigners and density (number of persons per square mile), and (2) between foreigners and the number of families (a) living in one and two rooms, (8) living in three to nine rooms, and (y) living in ten rooms and upwards. The correlation coefficients were calculated from the following table (Table XXXII.) :-— TABLE XXXII. Number of families living in (per 1000 of each division) Division | Persons per square mile | One and Three to Ten rooms two rooms | nine rooms | and upwards I. 31 535°'8 440°4 22°5 II. 23 490°9 468°3 40°6 Il. 127 394°3 569°4 36°3 IV. 166 549°8 419°0 roll We 87 552°5 408 °6 38°8 VI. 827 686°4 296°2 | 17°3 VII. 363 530°7 422-1 | 47°2 VIII. 62 | 376°'9 562°9 | 60°2 | | | The following table (Table XX XIII.) gives the population, the number of foreigners, and the number per 1000 of the respective populations, of each division in Scotland :— TABLE XXXIIL Divisi Pp lati Wovel Number of Foreigners | Deviation from mean | ivision opulation oreigners per 1000 per 1000 | I. 112175 147 1°3105 — 1°6643 Il. 166554 124 0°7445 — 2°2303 III. 460941 621 13472 —1°'6276 IV. 665215 1515 2°2775 —0°6973 We 348585 1044 2°9950 0:0202 VI. 1862775 15062 8:0858 5°1110 VII. 662415 3888 58694 2°8946 VIII. 1934438 226 1'1683 —1°8065 1 * Eleventh Decennial Census, Appendix Tables, p. xxxv. Biometrika y1 24 186 Pigmentation Survey of School Children in Scotland The last column in above table has of course to be compared with each of the values for the various classes of hair colour and eye colour and with the density figures. The values of 7, the correlation coefficient, and 7/#, are given in the following tables (Tables XXXIV. and XXXYV.): TABLE XXXIV. Foreigners and Density. Correlation between r ws EE Foreigners and Density 508 ace ae ase Sb es 9456 37°46 ns and Number of families in 2 rooms and less ... ode “7555 7°38 5 and Number of families in 3 to 9 rooms ee we | — 77793 — 8°32 9 and Number of families in 10 rooms and upwards... |—°3362 -1:°77 These results are interesting. They show that foreigners tend (1) to reside in most densely populated areas, (2) to reside in districts where families live in one room or two rooms, and (3) not to reside as a rule in districts where families live in three to nine rooms. There is not a very decided tendency against their residing where families live in large houses with many rooms. The following are the results of the comparison between foreigners, density and pigmentation : TABLE XXXV. Correlations between Density of Population, Foreigners and Pigmentation. Density Foreigners Colour r a r f Ev=0) Ey=o) Hair: Fair ee — 805 3°16 —°788 3°09 Red Ane — 001 “005 —°093 37 Medium ... ‘716 2°81 “757 2°97 Dark ae — 195 id. — 243 95 Jet Black ... — 460 1°81 — 497 1:95 Eyes: Blue rn — 612 2°40 — 668 2°62 Light nee 090 BY) ‘219 *86 Medium cate *560 2°19 "523 2°05 Dark ais 533 2-09 514 2-02 The striking feature in the above table is the great similarity in the results in comparing foreigners with pigmentation and density with pigmentation. The results show the futility of attempting to draw any conclusions as to the probable predominant colour classes of foreign immigrants from these tables since the J. F. Tocuer sey correlation between foreigners and density is exceedingly high. It is certainly the case that foreigners coming into this country live in districts in Scotland having on an average distinctly greater proportions of medium haired, medium eyed and dark-eyed persons among their number than that found for the general population. But these are just the classes which are in excess in densely populated parts, and foreign immigrants reside for the most part in these denser centres. One cannot therefore say from the foregoing whether the foreign immigrants have large pro- portions of these classes among their number or not. It is not known what the proportions are. It has simply been proved that they are associated with densely populated centres in Scotland. The colour characters of the immigrants themselves must be investigated. The effect of the foreign element in the population will be considered in detail in the special section on Glasgow and environs. The subsection can be summarised as follows: country tend {Populated} excesses are found of the «Medium Eyes Rosen on reaching this Densely ) where (among school children) (Medium rt fo) to reside in Areas following classes, namely : pst Eyes Immigrants V. Relationship between Pigmentation and the Death Rate. It is stated by Pearson* that there is a positive correlation between fairness and disease in child- hood. It has long been known that there is a correlation between density of population and the death rate not due directly or mainly to the crowding of persons together but to the association with density of filth, poverty, drunkenness and the like. Russell has shown the correlation between the size of house and the general death rate+. Newsholmet pointed out in 1891 that the true test of density is a statement of the number of persons living in each occupied room. Applying any test of density, the correlation between it and the death rate is high, using Scottish figures. Taking for instance the number of persons per square mile, the correlation TABLE XXXVI. Correlation between Density of Population and Death Rate in Scotland. Disiaen Deviation from mean number Deviation from mean of persons per square mile Death Rate I. —179°75 —1:240 Il. —187°75 — ‘078 IIL. — 83°75 —1:012 IV. — 44:75 138 V. — 123°75 — ‘975 VI. 616°25 2°450 VIL. 152°25 Bills) VIII. — 148°75 — ‘297 * Pearson: Biometrika, Vol. 111. p. 465. + Russell: Proceedings of Glasgow Philosophical Society, Nov. 1888. + Newsholme: Journal of Royal Statistical Society, Feb. 1891, 24—2 188 Pigmentation Survey of School Children in Scotland was found to be r =‘9125 from the accompanying table (Table XXXVI.). Diagram XIX. shows graphically the connection between density and other characteristics in the population. Thus the association is very high. It will be of interest now to note what relationship, if any, exists between colour and the death rate. The following results were obtained (Table XXXVIL). TABLE XXXVIL. Correlation between Death Rate and Pigmentation. : oy d E@=0) Hair: Fair re — 806 —3:'16 Red ane = Bye) — 1°36 Medium... ‘567 2293 Dark Saat 064 G5) Jet Black ... — 252 — 99 Eyes : Blue one — 488 —1°91 Light hee 226 *89 Medium ... "284 111 Dark ane *410 1°61 This result, a positive correlation between the death rate and medium hair, and another between death rate and dark eyes, was to be expected, since density is similarly associated with colour. The denser the population is the greater is the death rate; the denser the population is the greater is the excess of medium hair; therefore the greater the excess of medium hair, the greater the death rate. (1) Is it to be concluded that medium haired or dark-eyed people are less virile and cannot stand the strain of city life? (2) Must one say that the blue-eyed fair- haired classes have been all killed out in densely populated areas since they have less resistive power and it is now the turn of the darker section of the population who now presumably show greater mortality? (3) Or must it be said that the conditions of town life are such as to cause a larger section of the fair-haired class to become so much more sensibly darker in towns than in rural districts so as to be classed as medium or brown? There is a darkening in the fair-haired class with age; that much is well known. Is the darkening more intensely operative in towns, and why? (4) If not, can any explanation be offered as to why medium hair colour is associated positively with density and thus with the death rate—why a proportion of medium haired persons much above the average live in more densely populated parts (and are thus of the poorer class) where mortality is higher than the average? An attempt will now be made to answer these questions so far as they can be answered, seriatim. VI. The probable Cause of the Association of the Medium or Brown Haired Class with Density of Population. It cannot be said from the data of this survey J. F. Tocuer 189 what colour class is more virile than another or whether there is any difference among the classes. Is such an hypothesis necessary ? This question is put, because it can be quite easily seen that if there is a large proportion of the medium class living in very densely populated areas, deaths among medium haired persons will be more frequent there than in the rest of the country. But this does not explain why medium haired persons are in excess in densely populated parts. No reason is known why darkening with age should be more intense in densely populated centres, but it is a possible explanation of the excess of medium in these centres and the hypothesis should be proved or disproved by observation. If there was any special force tending to send medium haired and dark-eyed persons in from the country to towns, that would explain the excess. But no such force is known to exist. If foreign immigrants had a high percentage of medium hair this might be a factor, but foreigners coming into this country are, on an average, DIAGRAM XIX Relationship between Density and the other characteristics of the Scottish Population DENSITY OF POPULATION DEATHS BIRTHS PER => <. PER 100 FAMILIES AAP IO IS Lata 1000 SQUARE MAILE. GAELIC SPEAKING POPULATION FOREIGN IMMIGRANTS 190 Pigmentation Survey of School Children in Scotland darker-haired* than the Scottish population. With a less proportion of medium hair than that occurring in this country, the foreigners—a handful compared with the total population of towns—could have no effect in this direction. They are likely, from actual observations, to have an effect in very densely populated areas in the direction of darkness of hair and dark eyes. If Irishmen and Englishmen were browner-haired on an average than Scotchmen, and if it was proved that a high proportion of them lived in densely populated areas of Scotland, this would be an important factor and a probable explanation. It is true that, at any rate in Glasgow, the Irish are found in large numbers, but from the results of this survey (see Glasgow section—lIrish children) and the results given by the pioneer observer of colour in this country, Beddoet, Irishmen have no greater proportion of the medium class on an average than Scotchmen. Beddoe’s statistics for England have also been tabulated and a general percentage evaluated. The English appear on an average to be no browner-haired than the Scot. Both indeed seem likely to have a less proportion of this class. Pearson’s statistics for English boys show that they are fairer than Scottish boys. There seems however to be a higher proportion possessing jet black hair. The following table (Table XXXVIII.) shows the colour distributions of English, Scottish, and Irish populations, as at present known. TABLE XXXVIII. Hair Eyes Fair | Red | Medium| Dark | ,1°%, | Blue | Light | Medium | Dark (1) Irish 10°4 4°6 33°4 40°5 | 11°0 — 66°5 14°7 18°6 (2) English, North of England 21°3 | 5:8 416 | 286 | 26 | — | 60°5 14:7 24°7 (3) Scottish Adults, Probable Distribution... 115 | 4:2 55°9 28-4 — — | 27:8 45°9 26°3 (4) Scottish Boys, Actual Ob- servation 25°0 | 5:5 43°3 25°0 13 | 14°7 | 30°3 32°7 22°3 (5) Irish Boys, Glasgow || eee sel 35:1 33:1 4-6 | 21°2 | 26°0 | 28:4 | 24-4 (6) English Boys see .. | 83°5 | 4:1 34:0 26°5 1°9 — | 41°5 37°0 21°6 The figures for the Irish and English populations are derived from Beddoe’s tablest. The figures for Scottish adults are the author’s, deduced from results from the Aberdeenshire adults and Scottish school children}. The figures for Scottish boys are from the present data; those for Irish children are also from the present data. Pearson’s figures are taken from the Fourth Huxley Lecture §. The table is not intended to represent the actual distributions for the three king- doms, but merely to show that the excess of medium hair found in Scotland is not * See actual results in section on Glasgow; also Livi and others on Italians, Jews, Russians, etc. + Beddoe: Races of Britain, pp. 188, 189; and pp. 160 et seq. { Biometrika, Vol. v. pp. 341, 342. § Journ. Anthrop. Instit. Vol. xxx1. 1903, pp. 214, 215. J. F. Tocuer 191 likely to be from Irish or English sources. The presence of neither foreigners, Irishmen, Englishmen, nor of brown-haired immigrants from rural districts at home (although they might contribute a little) can explain the excess of medium hair. None of these groups are likely to have contributed; it has been proved, in short, that they do not. Having considered among others the effect of the presence of persons of a non-Scottish origin—the effect of a section of the popu- lation proved to be present whose origin is forth of Scotland—and shown it to be inappreciable or non-operative, one must conclude that the cause has an internal origin and is not derived from an external source. It must be some- thing operating within the Scottish population itself. What factor is operating within Scotland producing an excess in densely populated areas of the various shades of brown hair classed as medium ? One or more of at least three factors might possibly operate and provide the explanation. (A) Darkening among the fair-haired might occur earlier in towns and might be more intense. No grounds exist for this explanation. It is purely hypothetical and requires investigation. (B) The medium class might be the most fertile. Since this class is correlated with density of population, since the lower classes live in the densely populated areas, and since it has been shown that the lower classes are the most fertile, one might conclude that the medium class is the most fertile of the fertile lower classes. If true, this would explain the excess. (C) The excess might be due to the effect of blending of the fair and dark classes of the population. With regard to (A) until observations from towns and rural districts, bearing on this, are calculated, the truth or otherwise of the hypothesis cannot. be verified. The pigmentation survey returns contain no data capable of furnishing the means of testing this hypothesis. (B) The probability of the medium haired class being the most fertile. Com- paring the number of births per 100 families (calculated from the figures of the Census Report—the only data at present available to estimate the relative fertility in the various divisions of Scotland) with density of population, the value of the correlation coefficient was found to be Te Ip EL, E yao) That is to say, births per family are greater in number in more densely populated areas than in sparsely populated parts*. Of course this does not give the measure of true fertility. To get this, one would require to get a return of the number of wives for each division, whose ages are within the childbearing range, and compare r='782 + 093; and — thus = 8°44; and =o 0c. * On the other hand on comparing the number of families per 1000 of the population with density of population the correlation was found to be negative (r= —-6109--1495), This does not necessarily mean that in towns the families arelarger. The large population of young men and women employed in industries and otherwise and drawn from less densely populated areas contribute largely, if not mainly, to the result. 192 Pigmentation Survey of School Children in Scotland this with the number of births in each division. The value, r = ‘782, cannot be taken as the true measure unless the ratio of the number of possibly fertile wives to the number of families is quite approximately the same in each division. The correlation, however, between the number of births per family and density of population is so high as to warrant the conclusion that fertility is really greater among the inhabitants of densely populated areas. Since the more densely populated centres are occupied by the lower classes, this is tantamount to saying that the lower classes are more fertile than the remaining section of the population, a conclusion already reached by several observers. Let now the number of births per family, in each division, be compared with the pigmentation data. The following results were obtained : TABLE XXXIX. Correlation between Pigmentation and Births per Family. r Col P ; olour ? Hee Hair: Fair nee — 936 —3°'67 Red es — 043 —0:17 Medium... STAT 2°85 Dark es — 059 — 0:23 Jet Black ... — 504 —1:98 Eyes: Blue ies — "775 —3:'04 Light ae 386 1°51 Medium ... ‘671 2°63 Dark Sar "292 1:15 These results show that the number of births per family is greater where there are excesses of medium hair and medium eyes and is much less in regions of excess of fair hair and blue eyes. Now these results are similar to those obtained in comparing density of population with pigmentation except that dark eyes are significantly associated with density, but not with the birth rate per family. Thus the lower class population is associated with a higher birth rate per family and with an excess of medium hair and medium eyes over the general population. Is one to say that the medium haired, medium eyed classes are as a whole more fertile over the whole country; or are only those sections of them living in more densely populated parts (i.e. working class sections of these classes) the more fertile? That question cannot be answered from the present data, but it can be said that the medium haired, medium eyed and populous lower classes are more fertile than the remaining population, and this factor is probably operating in favour of producing distinct excess of these classes in the more densely populated areas of Scotland where they are found. (C) The probability that excess of medium hair in dense centres is due to blending. Consider first a population consisting of more or less isolated groups of J. F. Tocuer 193 fair-haired and dark-haired people living in sparsely populated regions. The chances of conjugal union of persons of the same colour class, if the mating occurs at random or is pangamic, are greater than if they lived all together as one group in a densely populated town. In the past, more unions between persons of the dark-haired class (for instance, in the west coast) were likely, on the assumption that mating occurred purely at random, to occur than between them as a class and the fair-haired class. Similarly, isolated groups of the fair-haired class would have more unions among themselves than with the smaller dark-haired groups. On the other hand, however, wherever towns sprang up, the different classes would be brought more in contact with one another and the chances of union among all classes with one another would be greater. But does mating actually occur purely at random ? That is to say, taking the character here considered, hair colour, does the fair-haired class, for instance, select mates indiscriminately from the other classes or do they tend to mate more with members of their own class? Similarly, taking eye colour, what is the nature of the mating? Pearson* has shown that, for certain measur- able characters, like tends to mate with like; that is, assortative or homogamic mating exists. For eye colour he has shown that both homogamic and preferential mating exist. Can one say with respect to hair colour whether the mating is homogamic, preferential or pangamic? In the past, with isolated groups and with the clan system in vogue, endogamic mating would certainly exist and be a power- ful factor in determining the prevailing colour characters. Thus one would expect at the present day to find a section of the population in the Highlands with characters distinctly different from another section, and this, one finds, is the case. Different race or clan groups have married within the race or clan and retained the ancestral characters. But endogamic mating can now no longer be a powerful factor, except im isolated cases, since greater intermixture and greater dispersal of the population now occur than was ever possible in the past. Retaining this form as possibly contributing, and remembering that mating of unlikes (conjugal union of say a member of the jet black class with a member of the fair-haired class) is also quite possible, the five possible forms emerge, namely : Homogamic =like with like ; Endogamic =members of the same clan ; Preferential =preference for a certain colour ; Heterogamic= mating of unlikes; and Pangamic =random. Now while it has been shown that inheritance of eye colour is more of the exclusive form than of the blended form, is it more likely that hair colour (except perhaps red hair which has been already noticed) is a case of blended rather than of exclusive inheritance? As yet there are no statistics from which the intensity of blending can be directly proved or disproved. One can only advance the theory that blended inheritance prevails largely in hair colour, and see whether it explains the excess of medium hair in densely populated centres. Blended inheritance in * Pearson and Lee: Biometrika, Vol. u. pp. 357—462; and pp. 481—498; and many others. Biometrika v1 25 194 Pigmentation Survey of School Children in Scotland hair colour certainly exists, although no statistics are forthcoming to prove its intensity. The average observer will have noticed that the offspring of parents, one fair and one dark, are not uniformly fair and dark, but have also on an average among their number members of the brown-haired or medium class. What the proportions of each are, on an average, will be revealed by observation. What form the distribution takes does not affect the argument. Granted that pangamic mating (not excluding other forms) now exists for hair colour among the Scottish people and granted blended inheritance as probably occurring as one of the results, and the phenomenon of regression will appear in hair colour. The colour of future generations of offspring will tend to become brown-haired and in a few generations a brown type will be established breeding true to itself. Thus in densely populated areas where greater opportunities for random mating exist, a greater proportion of medium hair will arise, granting blending of hair colour as an appreciable factor, but not of course debarring exclusive and even particulate inheritance as operative as well. This alone, or together with the suggested greater fertility of the medium haired class, would explain the excess of medium hair found in densely populated areas particularly in and around Glasgow, an excess which is not explainable by the presence of non-Scottish or Scoto-Keltic elements in the population. As has been said before, it cannot be proved from the present data what is the cause of the excess, and the foregoing is only the probable explanation. The proof or otherwise of the validity of the theory will be forthcoming when the results of direct observations on parents and offspring have been made, tabulated and analysed. VII. Colour classes which are associated geographically. (a) Hair classes which are associated with one another.—The theory that brown hair is really a blend of fair and dark is supported by the fact that throughout the country excess of the class is not generally associated with excess of other hair colour classes. In order to determine the extent of the association of excesses and otherwise of the various colour classes, the percentages of all the classes were compared with one another and the correlation coefficients determined. The following table (Table XL.) gives the numerical values of the correlations of each class with all the other classes. One must be careful as to the meaning of the result. Association of excesses of fair hair and blue eyes (a positive correlation) does not necessarily mean from this portion of the analysis that the blonde type predominates in the region of excess. All the analysis tells one is that regions of excess of fair hair are also regions of excess of blue eyes. This will be evident when one considers the other associations with fair hair. Examining the table it will be seen that regions of excess of jet black hair are also generally regions of excess of fair and dark, This combination could not obviously occur in the same person. Regions of excesses of fair and dark indicate the presence of two types—a heterogeneous and not a homogeneous population. On the other hand, examine the column indicating the associations with excess of medium hair. acess of medium hair as a rule is associated with excess of no other colour class, The negative correlations J. EF. Tocner 195 show that regions of excess of medium hair are not regions of excess but of defect of dark and jet black hair. This would seem to indicate a greater approach towards fusion of the fair and dark types in more densely populated centres and the consequent gradual disappearance of these types to form the medium (brown or dark brown) type. There is no bias for or against the presence of red as a class with excess of medium hair. acess of red hair is found as a rule only in regions where the proportion of the dark-haired class is well below the average. A slight excess of fair is associated with excess of red. The probable reasons for these positive and negative associations will not be further entered into here. Sufficient evidence has not yet been accumulated to explain the differences with regard to pigment and matrix in human hair*. The present grouping of the shades into five classes is based on the general appearance of hair in the mass. The problem generally is one on inheritance, but the material to solve the problem comes from divers sources, chemical, microscopical, biological, statistical. Until - this material is collected and dealt with, no explanation of any great weight from a scientific point of view can be given, particularly as to the shades of red hair, although several quite plausible theories can quite easily be advanced. One must therefore be content to state the bare facts as they emerge from the statis- tical analysis. It does not appear to be an insoluble although perhaps it is a somewhat difficult problem. When more light is obtained the explanation will be forthcoming. (8) Hye classes associated with one another.—Excess of dark eyes in densely populated centres. The only class which is not positively associated significantly with any other class is the class of light eyes. Excess of light is negatively associated with blue and dark. Where light eyes are in excess, blue and dark eyes are not likely to be so, but the reverse; there is likely to be a defect of these classes. Excess or defect of light eyes is not connected with any excess or defect of medium eyes. Excess of blue eyes is as a rule associated with defects in the frequencies of the other classes of eye colour. Excess of dark eyes accompanies excess of medium and defect of the other two, light and blue. So that, broadly speaking, it is found that excess of blue eyes is found alone, excess of light eyes is found alone and excesses of dark eyes and medium eyes occur together. This is an interesting result, since it has been shown by both Galton and Pearson that exclusive inheritance prevails in the dark-eyed class. That is to say, the offspring for example of parents one dark-eyed and the other light-eyed or blue-eyed are, as a rule, either dark-eyed or light-eyed or blue-eyed. Medium eyes do not usually appear from such unions. There is no evidence as yet as to the blending or otherwise of the three classes, blue, light and medium. But since the offspring of parents, one dark-eyed and the other medium eyed, are likely to be either dark- eyed or medium eyed, unions among the two classes for gencrations would have no appreciable effect on the eye colour of the offspring, and therefore, as the results of * The chemical and microscopical aspects of the problem of hair colour will be dealt with by the author in another memoir. 196 Pigmentation Survey of School Children in Scotland this investigation show, one would still have the two classes, just as though there Pearson* has shown that preferential mating is likely to be operative against the dark-eyed class and he also shows from Galton’s data that they are more fertile under their present environment than say the light-eyed. The results of the present analysis do not tend to confirm this (see Table XXXIX.), but it must be remembered that the comparison was not made between births with respect to possibly fertile wives had been no intermarriages in these classes at all. and pigmentation, but between births per family and pigmentation. Thus, with TABLE XL. Association of Colour Classes in the same Regions. Values of 7 the correlation coeflicient. Hair Eyes Fair | Red | Medium | Dark eee Blue Light | Medium| Dark ; | Fair ee i 3074 | —°6916 | —-0867 3733 ‘7207 | — 3044 | — 5786 | —°4233 | Red 5 || <— 1 ‘0873 | —°5881 | — 3414 0324 | — 3966 3858 "0022 |Medium ...| — — 1 — 6459 | — -9039 | — -9431 2273 8563 6874 | Dark Ser - 1 8443 5075 1166 | — °6295 | — 5110 Jet Black ... = — *8728 | — 2565 | — °8211 | — -5200 Blue ; — — 1 — -4329 | —°8226 | — 5429 |Light ...| - = a 1 | —-0905 | —-4290 | Medium = == = 1 6991 Dark = =a aes a 1 TABLE XLI. Classes, eacesses of which are found together in the same regvons. Hair Hyes Fair | Red | Medium | Dark a Blue | Light | Medium | Dark Hair: Fair = te = = ae at = = = Red + - + c= Medium — = ae + Dark é dt db Jet Black aE = = ae = ate = = a0 Byes: Blue ab = = a aL Light = = Medium = db dk = = = == == 4 Dark = = de ae =e The rows or columns show for any one class what other classes are associated with it. * Pearson: Phil. Trans. Vol. 195, pp. 79—150; and Grammar of Science, 1900 ; page 428. J. F. Tocuer 197 the proper data, it is possible that the positive association may become a significantly positive one. Since excess of dark eyes in the Scottish population has been here shown to occur in densely populated parts, the dark-eyed class here at any rate belongs largely to the poorer section of the population. But the lower classes are more fertile than the upper classes. If the dark-eyed portion of the lower classes is more fertile than the remaining portion, and if a selective death rate does not operate against the dark-eyed, this would go far to explain the excess of dark eyes in densely populated parts not explainable by the presence of foreigners or of migrants from contiguous rural areas. VIII. Relationships between Pigmentation and Physical and Mental Defects. In a recent memoir*, already referred to, it was shown, using the division analysis results of the present data, that cases of insanity were in excess of the mean in areas where there was an excess of light eyes in the population. The enquiry has been extended in order to note whether excess of any particular hair colour or eye colour is associated with physical or mental defects such as blindness, deafness and imbecility. The following results were obtained, the results for insanity cases being included. The figures used in comparing the results were taken from the Census Report 1901. TABLE XLII. Relationships between Pigmentation and certain Defects or A ffections. Hair Colour. Fair Red Medium Dark | Jet Black Defect or Affection = r r if T . ae P Le E r E(=0) E\r=0) E\r=0) Ky =0) E(r=o) Insanity ... | —°024] — -10| —-582| —2-98| —-128| — -50| -340] 1:33] 084 | -33 Inbecility or Feeble- mindedness “608 2°38 | —°213| — °83| —:942 | —3-69 672 2°63 | °893 | 3°50 Blindness 565 2°22 “006 ‘02 | — °868 | —3°40 546 2°14) 885 | 3°47 Deafness “300 1:18 054 ‘21 ) —°707 | —2°77 572 2°24 | -789 | 3°10 Deaf and Dumb “126 “49 | 148 58 | —'1386 | — °53 | —:026] — *10] °273 | 1:07 Eye Colour. Blue Light Medium Dark Defect or Affection ie = P hel aeee r pe Apt! ears E\r=0) E\r=0) | E(r=0) E(r=0) | | alta Insanity ... | —°072| — +28 695 2°73 | —°322 | — 1°26 | —°482 | —1-°89 | Imbecility or Feeble- | mindedness 841 3°30 | —°253 | - ‘99 | —°753) —2°96| —-547 —2:15 | Blindness 951 3°73 | — °464 | —1°82 | —-775 | —3°04 | —-442 | — 1-73 | Deafness 819 | 3:21 | —°386 |) —1°51 | —°609 | —2°39 —:489 —1:92 Deaf and Dumb 309 «1:21 | — 453) —1'78| —°118 — -46 149 58 | * Biometrika, Vol. v. p. 342. 198 Pigmentation Survey of School Children in Scotland These results show that the distribution of cases of mental affection differs from those of the three other classes of defects. Excesses in the number of cases of imbecility, blindness and deafness occur in regions of excess of blue eyes and dark and jet black hair. From the results of the enquiry into the relationship between the Gaelic speaking portion of the population and pigmentation, it was shown that these were the classes correlated positively with excess of Gaelic speaking people. The correlation between this portion of the population and the four groups were accordingly calculated when it was found to confirm the conclusion that the Gaelic portion was correlated positively to those groups as expected, as the following table (Table XLIII.) shows: TABLE XLIII. Relationship between the Gaelic speaking Population and Defects. Defect or Affection Value of r d E(r=0) Deaf see *865 3°39 Blind Ler "884 3°47 Imbeciles eee “788 3°09 Deaf and Dumb ... 295 1°16 From whatever cause, therefore,a significantly greater number of cases of imbecility, blindness and deafness occur in Gaelic speaking regions than occur throughout the country in general. Emigration of the fitter portion of the inhabitants from the west in greater proportion than from other parts of Scotland would explain the occurrence of larger proportions of cases of defect in the Highlands. It must not be concluded therefore that Gaelic speaking Scots on an average are in any way inferior physically to Lowland Scots—perhaps the reverse is the case—or that a really higher proportion of defects exist among the race or races which speak the Gaelic language. (10) Degree of resemblance between the Boy and Girl Populations in each of the Colour Classes. It has been seen in a general way that the boy and girl populations agree in many localities in showing excess or defect frequencies in the various classes compared with the general population, and in several cases it was found that the populations differed, excesses in one sex being associated with defects in the other and vice versa. It is necessary therefore that the difference between the two populations generally should be measured. It will be seen then which of the classes shows the greatest agreement and which the greatest difference, or whether there is any appreciable ditference in the extent of association or independence of the two sexes as separate populations. (a) The degree of resemblance between the boy and girl populations in the same localities was determined, using in the first instance the percentage figures as J. F. TocuHer 199 found for the eight great divisions of Scotland. If «, = deviation from the mean percentage of any class in any division for boys, a= the corresponding deviation from the percentage in the same division for girls, o,, and oy the standard devia- tions of the respective percentage distributions, LLin By r= Nomoy and measures the general degree of resemblance between the boy and girl populations in the same division. (8) In the second instance the values of the relative local differences found for counties and cities were used. If /,, =the relative local difference of any class for boys, and ly = the corresponding relative local difference of the same class in the same locality for girls, then —_ Lin by Noi, olf and is a measure of the general resemblance between the boy and girl populations on the county and city basis of grouping. (y) In the third instance the counties alone were used, the cities being included in their respective counties while percentages were used as the basis, just as in the case of the great divisions. The following results were obtained : TABLE XLIV. Degree of Resemblance between the Boy and Girl Populations. Values of r Values of r Values of r Colour percentages | Counties and| Percentages Divisions Cities—-RLD. Counties Hair: Fair on 83 83, 63 Red es 73 68 “49 -Medium ... 93 87 o7f! Dark ae 72, 68 2 Black ae *89 a7Al O75} Average... 82 75 66 Eyes: Blue oi ‘99 95 92 Light eae 92 86 82 Medium ... 85 83 ‘79 Dark ets ‘91 ‘91 “91 Average... 92 “89 "86 These results show that on an average any excess or defect in the boy population from the general mean in any locality is accompanied in about 70 to 90 per cent. of the cases by a corresponding excess or defect in the girl population and vice versa. The agreement is least in the case of red hair. 200 Pigmentation Survey of School Children in Scotland It may be of interest to point out that Tschepourkowsky has determined the mean resemblance between man and woman to be about ‘8, the characters studied interracially being stature, relative arm length, cephalic index and four other measurable characters*. (11) The Colour Characteristics of the Population of Greater Glasgow and Environs. I. Introductory.—Tables of classified data. The city of Glasgow deserves special investigation for many reasons. (1) By far the largest in Scotland, the second city of the Empire contains one-fifth of the total population of the country. (2) Glasgow and the immediately adjacent counties, that is, Lanark, Renfrew, Ayr, Dumbarton and Stirling, contain one-half of the whole Scottish population. (3) Not only are these counties the most densely populated ones, but Glasgow itself greatly exceeds any Scottish town in the density of its population. (See Table LIII.) (4) The Census shows it to contain a much larger proportion of foreigners than any other town in Scotland. The Gaelic speaking population owing to its proximity to the Highlands is well represented. Ireland is also well represented. (5) Finally, it has been shown from the results of the present analysis that the great western city diverges in an extreme degree from the rest of Scotland not only in the distribution of hair colour of its school population but also in the distribution of eye colour, both for boys and girls. The following table (Table XLV.) shows the observed and expected results for Glasgow and Govan and Glasgow proper, the expected results meaning of course those which would occur on an even distribution with respect to colour of the whole of the school children throughout Scotland. TABLE XLV. Glasgow and Govan. | | Hair Byes Result Fair | Red | Medium| Dark | p)°t, | Blue | Light | Medium] Dark _ Observed ... |17809| 4179 | 36528 | 21809 | 965 | 9941] 24661 | 27021 | 19667 | Expected -.. |91267| 4308 | 34240 | 20478 | 997 |11986| 24644 | 26325 | 18335 | The observed result | compared with the | 3458 | 129 2288 1331 32 | 2045 17 696 1332 | expected oneis... | less | less | greater | greater | less | less | greater | greater | greater * Biometrika, Vol. 1v. pp. 161—168. J. EF. Tocuer 201 TABLE XLV.—(continued). Glasgow Proper. Hair Tyes Result Fair | Red | Medium| Dark ae Blue | Light | Medium| Dark Observed ... | 12734] 2984 | 25967 16042 716 | 67386 17634 19802 14271 Expected ... | 15290| 3094 | 24606 14734 719 | 8628 | 17714 18934 13167 The observed result | compared with the | 2556 | 110 1361 1308 3 1892 80 868 1104 expected one is... | less | less | greater | greater | less | less less | greater | greater | From the foregoing table it is seen that there are about 3500 less than the expected number of fair-haired children, about 2300 more medium haired and over 1300 more dark-haired. There are 2000 less blue-eyed children than expected, about 700 more medium eyed and over 1300 more dark-eyed children. Such differences, even with the large numbers dealt with in Glasgow, have a definite significance and are not differences which would occur in making a random draw of the same numbers from the general population. In the county and district analyses, Glasgow has been treated as a unit. The city has been contrasted as a whole with the neighbouring counties and also with the immediately surrounding population, a population which has been divided up into districts. In both cases, it has been shown to be unlike those outside popula- tions. It seems highly desirable therefore to examine Glasgow from the inside in order to see what is the cause of the great difference; whether, analysed intra- locally, the population of the city is different in different parts of the city; and whether these various divisions agree with or differ from the surrounding sub- urban areas. Under the School Board of Glasgow the city is divided into ten educational districts. The accompanying table (Table XLVI.) gives a list of the districts and their respective schools: In order to have approximately equal numbers in the various areas dealt with by the author, Calton, Camlachie and Bridgeton were grouped into one pigmenta- tion district; Tradeston, Gorbals and Hutchesontown, three other educational districts, were grouped into another pigmentation district. The following pig- mentation districts were also constituted for the environs of Glasgow: North Suburban, South Suburban, Kast Suburban and West Suburban. The following table (Table XLVII.) shows how the pigmentation groups of Greater Glasgow were made up, while the succeeding table (Table XLVIII.) shows the actual frequencies of the various classes for these districts. The results of the analysis of these figures Biometrika v1 26 202 * 0 ST > OT YS 90 PO * ph SONOS OS OC Coa * G0 ST > Ot 98 PO Educational District. I. Awnprrsron DistTRICT. Bishop Street. Finnieston. Overnewton. Anderston. Kelvinhaugh. Kent Road. Glasgow High School. Washington Street. I Dobbie’s Loan. Henderson Street. Rockvilla. Milton. Garnetbank. Glasgow High School for Girls. Kay. Oakbank. Grove Street. Woodside. St George’s Road. Springbank. Napiershall. Pupil Teachers’ Institute. Dunard Street. Willowbank. Woodlands Institute School (for Children). Mitron District. ITI. Kennedy Street. Springburn. Keppochhill. Freeland. Martyrs’. St David’s. Townhead. Elmvale. Provanside. Hydepark. St Rottox District. IV. Dernnistoun District. Wellpark. St Rollox. Dovehill. Dennistoun. Whitehill. Alexander’s. Petershill. Rosemount. Pigmentation Survey of School Children in Scotland TABLE XLVI. Name of School. 9. *10. sali *k * OK ok * DAD OUP ww bo Cripple SO Educational District. SA ESI EECA) So) Name of School. Alexandra Parade. Golfhill. Haghill. V. Catton District. Tureen Street. St James’s. Calton. VI. Thomson Street. Barrowfield. Parkhead. Camlachie. Campbellfield. Annfield. Newlands. Quarry brae. CAMLACHIE DistTRICcT. VII. Rumford Street. Hozier Street. John Street. Springfield. Dalmarnock. Queen Mary Street. Strathclyde. Special School for Cripple Children. BRIDGETON DISTRICT. VIII. Traprston District. Centre Street. Crookston Street. Shields Road. Sir John N. Cuthbertson. Scotland Street. IX. GorsBats District. Greenside Street. Abbotsford. Gorbals. X. HurcHEesontown Districr. Rose Street. Camden Street. Oatlands. Mathieson Street. Wolseley Street. Adelphi Terrace. Hayfield. * No returns were received from these schools. J. F. Tocuer 203 are given in Tables XLIX. and L. (Table XLIX. Relative Local Differences and Table L. General Divergency). The results are also shown diagrammatically in Maps LV. to LXXVIII. TABLE XLVIL Name of Pigmentation Groups Pigmentation Group embraces I Anderston The Wards of Anderston, Broomielaw, Sandy- ford, Exchange, Blythswood, part of Park II. Milton... The Wards of Cowcaddens, Park (part of), Woodside (part of) III. St Rollox The Wards of Townhead, Cowlairs (part of), Springburn (part of) IV. Dennistoun _... es oe ... | Dennistoun Ward V. Calton, Camlachie and Bridgeton ... | The Wards of Calton, Whitevale, Milend, and Dalmarnock VI.‘ Tradeston, Gorbals & Hutchesontown | The Wards of Kingston, Gorbals and Hutchesontown VII. South Govan ... All the Govan School Board area south of the river VIII. Partick i nae Partick ; Kelvinside Ward IX. South Suburban District The Parishes of Eastwood, Cathcart, Ruther- glen and Cambuslang X. North Suburban District The Parishes of Cadder, New Kilpatrick, Old Kilpatrick and Baldernock XI. East Suburban District The Parishes of Bothwell, Barony and Old Monkland XII. West Suburban District The Parishes of Renfrew and Abbey (Paisley Burgh and Paisley landward) II. Analysis of Glasgow Data. (a) General Divergency in Colour. (1) Degree of General Resemblance of the various divisions of Glasgow to the General Population in Hair Colour. It will be remembered that in the district analysis, the 13th district, Glasgow and Govan, exhibited the excessive divergencies from the general population as represented by log P = 44°8 for boys and log P = 146°6 for girls. In the county analysis the chief cities were treated separately from the counties and Govan was separated from Glasgow, when it was found that the values of log P fell—that is, less divergency was exhibited for Glasgow and Govan separately than for Glasgow and Govan together. Still the significance of the divergency was very great. Log P (boys) for Glasgow proper was 29°5 and for Govan 16:9. For girls the values were 1200 and 34:5. much more divergent than Govan. Glasgow proper is thus From the analysis of Greater Glasgow and environs, one is able to locate the areas of greatest divergency. Of all the pigmentation groups, the sixth group (Tradeston, Gorbals and Hutchesontown) stands out the most divergent in hair colour for both boys and girls. South Govan and Anderston follow a long way behind. From the fact that there is a large excess of medium and dark hair in the girl population, Calton, Camlachie and Bridgeton as a group is as greatly divergent as South Govan, but the boy population is quite a good sample of the 26—2 204 Pigmentation Survey of School Children in Scotland TABLE XLVIILI. Frequencies of the Colour Classes in the various Divisions of Glasgow. BOYS. Hair Eyes Totals Fair | Red | Medium | Dark ae Blue | Light | Medium | Dark Anderston 717 199 1654 960 | 34 414 | 1197 1073 880 | 3564 Milton ... 1161 322 2411 1322 51 626 | 1634 1739 1268 | 5267 St Rollox | 741 160 1378 710 15 313 955 1028 708 | 3004 Dennistoun .| 825 196 1552 870 34 402 | 1082 1166 827 | 3477 Bridgeton Group | 18320 | 286 | 2518 | 1448 | 61 605 | 1597 | 2088 | 1343 | 5633 Tradeston Group 1122 | 282 | 2842 | 1749 | 107 527 | 1829 | 2136 | 1610 | 6102 Partick is 932 224 1947 986 49 723 | 1234 1251 930 | 4138 Govan South ... 1054 | 266 2408 1304 67 628 | 1554 1669 1248 | 5099 South Suburban Area 970 | 247 | 19386 | 1170 | 34 634 | 1283 | 1425 | 1015 | 4357 East Suburban Area 1373 | 293 2681 1493 | 68 732 | 1745 | 2178 1253 | 5908 North Suburban Area | 981 | 267 2082 1121 39 505 | 1406 1566 1013 | 4490 West Suburban Area (Paisley), 864 | 182} 1477 787 | 75 496 | 983 | 1128 783 | 3385 | 7 Totals 12060 | 2924 | 24886 | 13920, 634 | 6605 | 16499) 18442 | 12878 | 54424 GIRLS. Hair Eyes Totals Fair | Red | Medium | Dark ee Blue | Light | Medium | Dark Anderston 681 172 | 1479 1005 43 470 979 1092 839 | 3380 Milton 1149 283 2168 1482 58 654 | 1633 1599 1254 | 5140 St Rollox 8386 163 1601 1007 46 421 | 11038 1235 894 | 3653 Dennistoun ‘ 729 143 1422 834 43 384 924 1141 722 | 3171 Bridgeton Group 1242 | 289 | 2586 | 1643 |] 50 630 | 1679 | 2117 | 1384 | 5810 Tradeston ase 1190 | 272) 2807 | 1873 | 88 640 | 1865 | 2134 | 1591 | 6230 Partick : 870 205 1721 1025 48 708 | 1159 | 1107 895 | 3869 yovan South ... : 1051 249 2344 1321 51 545 | 1593 | 1640 1238 | 5016 South Suburban Area 1000 189 1821 1106 | 32 528 | 1309 1362 949 | 4148 East Suburban Area .. 1448 | 306} 2294 | 1369 | 52 673 | 1577 1963 1256 | 5469 North Suburban Ar ea 1080 220 1825 1095 29 532 | 1389 1364 964 | 4249 West Suburban Area (Paisley) 811 | 173 | 1389 857 | 76 497 | 949 | 1031 829 | 3306 Totals 12087 | 2664 | 23457 | 14617] 616 | 6682 |16159}| 17785 | 12815 | 53441 J. F. Tocuer 205 TABLE XLIX. Relative Local Differences. Greater Glasgow and Environs. BOYS. Hair Hyes Fair Red | Medium | Dark fee Blue | Light |Medium} Dark + Anderston — 671 25) 3°80 2°65 |—1:60|— 517 4:29) —3°35 3°44 Milton — 4:93} 2°01 3°69 12 |—1:86 |-— 5°75 114 “46 on St Rollox — ‘'36|/— -40} 2°88 —1:78 |—3:°73|— 6°61 1:78 1°76 1:67 Dennistoun ... - 1°68 38) 1°63 — ‘O1)/—1:45)— 5:20) 1:05 1°08 2°10 Bridgeton Group — 2°66}-1°38) 2°18 118|--1:14|-— 841)—3°24) 7:03} 2-79 Tradeston Group —11°99| —3°01 5°26 6°63 | 3°58|/—13°46|— -58 3°85 Tere Partick — 3°64/— 22 4:94 —1:80/-— °39 5'16/— -69| —3°44 26 South Govan .. (— 13|— +87 5°74 ‘91 ‘42 |— 4°78 26 "02 3°75 South Suburban Area |— 4°13 52) 1°55 9°80}-2°81)/— ‘21/—1:°25| — 02] 1°58 East Suburban Area |— 3°07|—1°81| 3°30 43 |— ‘69)/-— 4:99] 1:31 6°87 |—2°06 North Suburban Area |— 4°84] 1°36} 4°22 — ‘10|—2°32|- 6°52 1:48 3°11 “41 ; West Suburban Area *78|— -29 ‘42 |—2°41)/-—5:09|/-— -01|/-—1°62 ‘57 | 1:16 GIRLS ; Hair Hyes Fair Red | Medium | Dark | ee Blue | Light )Medium} Dark | Anderston — 955!/— ‘00| 3°44 5°83 33 )— 1:59 -1-71 ‘Ol 2°88 Milton — 8:24 1337) 1°93 5°72 |— ‘54/— 4375 2°30} —1°48 2°83 St Rollox — 620/—1°74| 3°66 3:03 | 27!1— 5°73\-— :15 Wks} 2°49 Dennistoun : — 5°64 |)—1°'50 4°58 WPily ‘76 | — 24K) | 4°76 ‘Ol Bridgeton Group —10°47/-— -41| 5°71 511 |—2°47|- 8°73|}-2:38| 7:23} 1:95 Tradeston Group —14:93 - 2°63} 6°81 857) 1:48)-10°33/-- 65) 3°76] 5:30 Partick ae — 6°95 60} 4°61 | E517) 18 6:04 — *48) — 4°63 56 South Govan ... | - 1039 )— -41] 8°53 154|/—-1:°26]/— 8:05] 2-26 ‘97 | 3:28 South Suburban Area |— 4°84/—1°58] 4:01 1:89 |—2°61]— 3°91| 1-76 1:08 18 East Suburban Area |— 1°60] 1°72| 1°64 |-— °63|—1:°77)— 5:39 /-—2°40 6°14 37 North Suburban Area |— 2°97) +26] 2°78 56 —-3:17|/— 434) 3°41 06 |— ‘11 West Suburban Area |— 3°76) +38] 1°35 70) 5°77 Hy | — 2-02 -—1:08| 3:20 | | 206 Pigmentation Survey of School Children in Scotland TABLE L. Divergency in Hair Colour and Kye Colour. Greater Glasgow and Environs. | Hair Eyes Boys Girls Boys Girls | Log P Q |Log P Q LogP| Q Log P Q Anderston 10°7 | 0139 | 20-6 | 0201 | 11°5 | 0143} 2-2 | 0066 Milton 62 | °0114| 15:0 | 0179) 8-9 | -0119| 6:8 | 0106 St Rollox 45 | 0090) 9-6 | -0137|) 9°3 | 0130] 8-9 | 0122 Dennistoun ... 1-3 | :0150| 8:9 |-0127| -6°7 | -0104) 7-5 <||-0117 Bridgeton 2°3 | ‘0069 | 25°4 | 0226 | 22°2 | -0204 | 22-2 | -0210 | Tradeston | 36°3 | 0263 | 52-6 | 0321 | 44:2 | 0286 | 25-0 | -0224 Partick 55 | -0101 | 10:8 | 0143) 60 | -0110| 10-9 | -0137 Govan a | 11-0 | 0150 | 25-2 | 0226 6-2 | 0109 | 14-4 | -o166 South Suburban Area | 5:2 | -0105]) 7-1 | 0125} -1°6 | 0034] 3:1 | 0081 | East Suburban Area... | 3°4 | ‘0081 | 2°7 | -0063 | 12°6 | -0149 | 11-2 | :0149 North Suburban Area ... | 7°8 | 0116] 4°5 | 0093) 9:2 | 0131] 5:5 | -0099 West Suburban Area 6°7 | 0109} 9°8 | 0135, 1°6 | 0085} 4:0 | -0069 general population—there is no great excess or defect in any of the classes. Milton, the north suburbs and west suburbs are about equally divergent for boys, and show a fall as compared with those just mentioned. Then follow Partick, St Rollox and the south suburbs. These show a distinct approach to uniformity of distribution and resemble the general population. Finally the boy populations of the adjacent areas of Calton, Camlachie, Bridgeton, Dennistoun and the east suburbs are fair samples of the general population. Of all the pigmentation groups, only the population of the east suburbs among the girls show resemblance to the general population. As indicated by the boy results, the east end of Glasgow is thus the least divergent and the adjacent southern area—Tradeston, ete.—the most divergent. (2) Hye Colowr. On examining the results for eye colour, it is seen that Tradeston, Gorbals and Hutchesontown again come out most divergent. Clearly there are elements in this population of a different character from the population in general. Calton, Camlachie and Bridgeton are also very divergent. South Govan follows in the decreasing scale, then Anderston and the other groups. The south and west suburban areas are quite like the general population, but the east suburban group, partaking of the character of the east end of the city, is as divergent as Anderston, a populous centre. Thus the special features of the divergency analysis of the component parts of Greater Glasgow are that (1) the eastern portion of the city is quite like the general population in hair colour but is most unlike in eye colour; (2) the suburban areas are much liker the general population than the purely city areas; J. F. TocuHer 207 (3) in several cases the divergencies for the boy and girl populations are unequal. When this is the case, the girl population has the greater divergency. (8) Individual Classes. (1) Hair Colour. The relative local differences have in all cases been calculated and show definitely the cause of the divergencies in each pigmentation group. It will be recalled that fair hair is in defect in the city generally. The difference between the city and the general population is very great, 12 and 24 times the standard deviation of sampling of the differences for boys and girls respectively. There is a distinct fall in the magnitude of the difference in taking Glasgow to pieces. Still in no case is fair hair in excess in the city. There is only a slight excess in the west suburban group. Tradeston is prominent in the magnitude of its negative difference, and resembles the figure for Glasgow generally. South Govan and Anderston, also in the heart of the city, follow with large differences. Milton and the three suburbs, north, south, and east, differ in a moderate degree, while St Rollox, Dennistoun and Bridgeton for boys are passable as samples of the general population, such negative differences as they show being quite possible in a draw from an evenly distributed population. In the girl population, however, only the four suburbs are passable as representative of the general population. All the city groups differ widely from the general average. In a word, one or two of the northern areas in Glasgow possess the average proportion of fair hair and are thus somewhat like the suburbs, but the densely populated areas in the city generally are awanting in the proper proportion of the fair-haired class. There are slight excesses of red hair in Milton, Partick and the north, east, and south suburban groups, but in none of the cases are the excesses significant. Thus the uniformity of the distribution of this colour class is shown to exist practically all over the country, the north-east of Scotland being the exception. No grouping occurs to speak of in the densely populated city of Glasgow and no defect in the frequency of this class occurs to an extent in the least significant. Town and country are thus much alike with regard to this class. Medium or brown hair however occurs in quite excessive frequencies in several of the city groups, but is less frequent in the suburbs generally. In the west sub- urban area, Paisley and Renfrew, the proportion is quite an average one. Tradeston, Gorbals and Hutchesontown (f and $); Calton, Camlachie and Bridgeton (2); and South Govan (f and ¢) are the areas of greatest excess of the various shades of brown constituting the medium class. Dennistoun (¥*) and Milton (@) are fair samples of the general population in this class. In the dark-haired class, Tradeston, Gorbals and Hutchesontown again stand out. The greatest excess of this class is found over the area of these three divisions. Anderston and the south suburban group for boys show perhaps significant excess, but the differences in the other groups although positive are not significant. In the suburbs generally there are less dark-haired children proportionally than in the heart of the city, and the northern portion of the city itself has a less proportion than the southern and eastern portion, With regard to the small class of jet black haired persons, 208 Pigmentation Survey of School Children in Scotland Tradeston, Gorbals and Hutchesontown are the only divisions of the city which show significant excess. Excess occurs outside the city only in one suburban group, that of the west, Paisley and Renfrew. (2) Hye Colour. The blue-eyed class, much below the average for Glasgow as a whole, shows significant negative differences in all the divisions and groups excepting the Partick and Kelvinside group, which shows a decided excess. Light eyes are in excess only in Anderston, the heart of the city, and in the north suburban area. There is a slight excess among girls in the South Govan group. Medium eyes are in excess in the east of Glasgow and in defect in the west. Starting in the north suburban area, the excess appears in St Rollox, Dennistoun and the Bridgeton group and finally in the Tradeston group. Govan, the south and west suburbs are like the general population. The defect is greater in Partick. The distribution of dark eyes is interesting on account of the fact that excess in Scotland generally is limited, when a large number of cases is considered, to one region of Scotland, that of Perthshire and Forfarshire. The only suburban area showing excess of this class is the west (Paisley and Renfrew) for girls. There is a slight excess in the boy population of the south suburban area. In the city, Partick is different from the rest of the population in that it possesses the average number—it is quite like the general population for this class, All the other divisions and groups show excess of dark eyes. It is most marked in the Tradeston group, the excess there being highly significant. South Govan follows and then Anderston and Milton. The excess is significant for boys in the Bridgeton group. but not quite significant among the girls of that group. (y) General view. The predominant colours of each of the divisions of Glasgow can now be stated. They are given in the following two tables. Table LI. shows significant positive differences only and these are classed so as to show the intensity of the excesses. Table LIL. is a condensation of Table LI. and gives a brief specification of each division. Taking a general survey of the pigmentation distribution of Greater Glasgow as shown by an analysis of its divisions and the environs, one sees that the excesses of medium and dark hair and medium and dark eyes (found in considering Glasgow as a unit) are not evenly distributed over the city and suburbs. It is however the predominant feature of the more densely populated and larger portion of the city to be brown or dark in hair colour and medium or dark in eye colour. This of course but confirms the general result in comparing density with pigmentation. There are some interesting features in the colour distribution which deserve special mention. The occurrence in certain parts of Glasgow of excesses of classes generally deficient in the city (either with or without the prevailing colours) is striking. Why, for instance, should Anderston have an excess of light eyes in the boy population? Why should Milton be the only district having even a slight excess of red hair ? Why should the Tradeston group be the only one in the city having an excess of the jet black class, and be otherwise so very divergent as it has proved to be? Why should Partick be the only division in Glasgow having blue eyes in excess, J. F. Tocuer 209 TABLE LI. Specification of the Greater Glasgow Population. (Only significant positive relative local differences shown.) BOYS. Anders : St | Dennis- | Bridgeton | Tradeston re South ; : ton Milton Rollox| toun Group Group Partick Govan 8. 8.) E. 8.) N. 8./ W.8. Fair a5 —= = = = Re = 7 Red — 2 — — — = == _ ==) Se ce | Medium 4 4 3 — — 5 5 6 —|— 4 — Dark tS. 3 — 6 — — 3 — | — | — Jet Black... — — — — — 4 “= 5 General Diver- gency for 3 1 1 0 0 7 1 3 1 0 2 1 hair colour Blue = = = = a a 5 —_ os Hipeeeer.||| teas jill Lene Light 4 — — = — — = = SS) | Ss | = Medium — — _— — 7 4 — — — 7 3 — Dark Re 3 33 — = 3 7 — 4 — = == = General Diver- gency foreye 3 2 2 1 i 7 1 1 0) 3 2 0 colour r GIRLS. d | iS) D Brid Trad South Anders- | ,,. t ennis- | Bridgeton | Tradeston : outh | y fon Maes Reliox| tan Group Group Partick | Goyan| 5: 5. |B. S.|N.S.| W.S Fair = — — — = = = — = | = | = | = Red = = — = = = = = a 2 _ — Medium 3 —— 4 4 6 7 5 9 4 — 3 — Dark 6 6 3 — 5 9 — — — | Jet Black — — —_— — — — — 6 General Diver- gency for 6 4 2 2 qf a 3 7 2 0 1 2 hair colour Blue — = — = — — 6 — —}/—|]—]— Light = = = = = = 5 = Medium = = = 5 7 4 = — — 6 _ = Dark ibs 33 3 = — a 5 = 3 = = -_ oa General Diver-) gency for eye 0 1 2 2 7 7 3 4 0 3 1 1 colour f Differences between 2°5 and 3°5 are here class 3; between 3°5 and 4°5 class 4; between 4°5 and 5°5 class 5 and so on. The object is to show the degrees of difference even in significant cases. In the general analysis of the whole country, all differences above 3°5 are shown as one class. In the maps however all differences above 3°5 are included in class 4, to be in conformity with the general scheme. Biometrika y1 27 210 Pigmentation Survey of School Children in Scotland TABLE LIL. Boys Girls Hair Eyes | Hair Eyes Anderston ... | Medium, Dark Light, Dark Medium, Dark | Dark Milton ... | Slightly red, Medium | Dark | Medium Dark St Rollox ... | Medium — Medium, Dark — Dennistoun ... -- — Medium Medium Bridgeton Group — Medium Medium, Dark | Medium Tradeston Group | Medium, Dark, Black | Medium, Dark | Medium, Dark | Medium, Dark Partick ... | Medium Blue Medium Blue South Govan ... | Medium Dark Medium Dark South Area... | Dark — Dark — East Area ee -—— Medium Red Medium North Area... | Medium Medium Medium Light West Area ... | Jet Black — Jet Black — the only excess in hair colour (scarcely significant) being that of the dark class? Finally there is the general problem of the colour characters of Glasgow. Why should this population differ so markedly in pigmentation from the general popu- lation of Scotland? This problem will now be solved as far as it can be solved from the data of the survey and other available information. III. Specific Elements in the Glasgow Population, causing Divergency. (a) Introductory. In one of the previous sections (Section 9) it was proved (1) that excess of blue eyes, dark hair, and jet black hair, are associated with regions of excess of the Gaelic speaking population; and (2) that excess of medium or brown hair, medium eyes and dark eyes are associated with more densely popu- lated regions, which in turn are also regions of excess of foreigners. ‘This means, briefly, that blue eyes, dark, and jet black hair are probably typical of Gaelic speaking people* although of course all the other classes are represented in this population, and that brown hair is typical of densely populated areas which in turn have a proportion above the average of foreign immigrants. (B) The Gaelic Speaking Population. Taking the Gaelic speaking population first, there is undoubtedly a large Scoto-Keltic or Highland element in Glasgow. At the last Census, no fewer than 18,279 persons could speak Gaelic and English in the city proper. This is equal to 9 per cent. of the total Gaelic speaking population. Taking Glasgow, Govan, Kinning Park and Partick, that is Greater Glasgow (without the environs), the Census shows that nearly 24,000 or 11°7 per cent., or more than one-ninth of the whole Gaelic population, is concentrated in the great western city. Ananalysis of the Census returns further shows Kelvinside, with 64 per cent.; Tradeston (Kingston Ward), with 5 per cent.; Milton (Park Ward), * Gaelic speaking people are not associated with dense areas as a whole. The correlation js negative, r= —°39+°2, The association with sparsely populated parts is therefore not very high, J. F. TocuHrr 211 with 4°9 per cent.; Anderston, particularly Sandyford Ward, with 4°8 per cent., to be quite in excess of the general average for Greater Glasgow, which is 2°6 per cent. of the whole population of the city. Govan is also in excess, having 4°4 per cent. of Gaelic speaking people in its population. One seems justified in inferring that such a population distributed over Glasgow would have a marked effect on the nature of the distribution of colour. Since Glasgow is significantly darker than the general population, since dark hair is significantly associated with the Gaelic speaking population, and since at least one-ninth of the whole Gaelic speaking population resides in Greater Glasgow, the conclusion is inevitable that the Gaelic speaking portion contributes largely to the significance of the excess of dark hair. It is not contended that this is the whole cause of the significant excess, but it is a prominent factor. But it may be argued that blue eyes are in defect in Glasgow generally and since blue eyes are also associated with Gaelic speaking people, their presence does not seem, on this hypothesis, to affect the character of the distribu- tion. The answer is: it must be borne in mind that the combination of blue eyes and fair hair in one person, that is the blonde type, is in great defect in Glasgow, thus diminishing the proportion of blue eyes to a great degree. There are also large excesses of dark eyes to which it will presently be seen the foreign element contributes. These and other factors prevail over the Gaelic factor and the theoretical excess of blue eyes is converted into an actual deficiency in this class, with one exception only. This exception is the Kelvinside and Partick group. Here a highly significant excess of blue eyes appears with an excess of dark hair, thus revealing the presence of the Gaelic speaking portion as one of the pre- dominant causes of the divergency in these districts, for it has already been observed that in Kelvinside alone 6°4 per cent. (the highest percentage in any district in Glasgow) of the population speak Gaelic. Presence of excess of light eyes among boys in Anderston deserves notice. While it has been observed that excess of blue eyes is associated with the Gaelic speaking portion generally, it must be noted that Argyll has in its rural population 62 per cent. of Gaelic speaking people and has a large excess of light eyes. Excess of this class is therefore a characteristic of a section of the Highlands as it has been shown also to be of Ayr and Galloway which are closely allied in blood to the Highlands as it formerly was in language. It is highly probable that county immigrants and their descendants from Argyll, Ayr and Galloway, are at the present time in excess of the general proportion in Anderston generally, thus disturbing the balance in favour of an excess of light eyes in the boy population. In addition to this, there is the Irish element. Beddoe’s results, already quoted, show an excess of light eyes in the Irish compared with the Scottish figures of the present data. ‘I'he Gaelic element does not however account for excesses of medium hair and dark eyes in Anderston, although it would account for the excess of dark hair and light eyes. The general analysis shows Perthshire and Forfarshire to have significant excess of dark eyes, which has been suggested to account for the similar excess in Dundee and perhaps to some extent to explain the excess of the same class in Edinburgh. Are county immigrants and their descendants from these regions in excess also in Anderston 27—2 212 Pigmentation Survey of Schoot Children in Scotland and in Glasgow generally, for the excess of dark eyes is common practically over the whole of Glasgow although it is more highly significant in Tradeston, Govan, Anderston, Milton, and Bridgeton? I think this is unlikely. There must be some other factor or factors besides mere immigration from the Scottish Midlands. What are they ? (y) The Foreign Population of Glasgow. It was shown in the last section that the correlation between foreigners and density of population was very high. It was so high that on comparing foreigners and density of population separately with pigmentation, the same conclusion was reached for each. It could not however be said whether foreign immigrants were causing the excesses in the three classes named by their great numbers or whether the excesses were there independently of them, for, since foreigners came mainly to towns, it might be only through density as the common link that the correlation existed at all. The association between foreigners and density is however real. Foreign immigrants are likely to be found to reside in greater numbers in the most densely populated areas and in the smallest houses. Now it is very suggestive that, at the last Census, 9644 foreigners or 42°6 per cent. of the total number of foreigners in Scotland (22,627 in 1901) resided in Glasgow alone. It is also suggestive that of the great cities Glasgow is by far the most densely populated. The following table gives the relative densities of the chief towns in Scotland: TABLE LIII. Number of Persons per Square Mile in the Chief Towns of Scotland. Persons per Persons per igen Square Mile Hows Square Mile Pollockshaws ve 43,177 Coatbridge a 12,830 Greater Glasgow ... 39,331 Musselburgh er 12,826 Leith ae 33,787 Alloa het 12,661 Rutherglen aes 30,537 Kirkcaldy ee 12,515 Dundee sist 28,069 Barrhead ce 11,916 Johnstone ae 27,859 Dumbarton sas 11,387 Port Glasgow cs 24,289 Falkirk sak 11,223 Motherwell isle 21,978 Perth ch 11,031 Edinburgh ia 20,089 Peterhead wee 10,991 Greenock a 18,598 Inverness nan 10,514 Fraserburgh es 17,510 Galashiels Rae 10,085 Kilmarnock aes 17,125 Ayr te 9,177 Hamilton wee 15,750 Brechin ae 9,086 | Aberdeen ae 15,716 Stirling i 8,552 Clydebank vat 14,959 Dunfermline oe 8,016 Dumfries soe 14,726 Kirkintilloch nee 7,992 Wishaw as 14,535 Forfar a 7,444 Bo’ness a 13,889 Montrose ae 5,422 Airdrie Se 13,598 Renfrew a 3,742 Hawick ae 13,434 Irvine ate 3,429 Arbroath oe 13,075 Rothesay fs 2,461 J. EF. Tocner 213 TABLE LIV. Population in 1901 of the Chief Towns in Scotland arranged in the order of their magnitude. Town Population Town Population Greater Glasgow ... | 906,391 Stirling bop 18,403 Edinburgh oe 316,837 Hawick | 17,303 Dundee ee 161,173 Port Glasgow see -| 16,857 Aberdeen =e 144,117 Rutherglen vee. | 16,185 Leith ee 77,439 Galashiels = 13,615 Greenock te 68,142 Dumfries ee 13,092 Coatbridge se 36,991 Montrose oe 12,427 Kilmarnock | 34,165 Peterhead oe 11,794 Kirkcaldy Yes 34,079 Musselburgh ae 11,711 Perth ve 32,873 Alloa bi | 11,421 Hamilton Fee 32,775 Forfar i 11,397 Motherwell siete l| 30,418 Pollockshaws nea 11,183 Falkirk ara 29,280 Johnstone 600 || 10,503 Ayr Sco 28,697 Kirkintilloch saa | 10,502 Dunfermline aes 25,250 Barrhead tal 9,855 Arbroath oe 22,398 Irvine ase | 9,618 Airdrie — 22,288 Rothesay ae 9,378 Inverness oe 21,238 Bo’ness all 9,306 Wishaw ae 20,873 Renfrew scan 9,296 Dumbarton ve 19,985 Fraserburgh jo 9,105 Clydebank ate 18,670 Brechin ase 8,941 From the results found in ascertaining the degree of association between density and pigmentation, excesses of medium hair, medium eyes and dark eyes would be expected in Glasgow. But the most densely populated parts of the city have been proved to be likely to contain more foreigners than the less densely populated parts. Thus the greater the number of persons per square mile a popu- lation has, the greater will be the expected excess of the three classes associated with excess of foreign immigrants. Now the only large group which has the complete density-colour specification (and in the greatest excess) and which has the highest general divergency, is the group of divisions Tradeston, Gorbals and Hutchesontown. It is highly probable that the foreign element may be one of the factors in the divergency of this group—foreign immigrants may contribute to the excesses in one or more of the classes there. In order that an estimate of the probable number of school children of foreign parentage attending Glasgow schools might be formed, an enumeration of those possessing foreign surnames was made. At the same time the colour characters were noted and classified. Only those surnames which were unmistakably foreign were taken, so that the estimate is most probably below instead of above the actual figures. The following is the result of the enumeration for the various pigmentation groups of Greater Glasgow. The environs were not included. 214 Pigmentation Survey of School Children in Scotland TABLE LY. Children in each division having foreign surnames, per cent. of the total number Division or Group of children in Greater Glasgow having foreign surnames Anderston... wee ae ace sai 12°51 Milton ae me ae as fa 7°78 St Rollox ae oe i oe oe 1°28 Dennistoun ... Fae es a wee 7°98 Calton, Camlachie and Bridgeton ... es 3°85 Tradeston, Gorbals and Hutchesontown ... 59°21 South Govan... aoe aa ae a 6°50 Partick and Kelvinside _... Ae oa “89 Totals ee si see daa ae 100-00 This result is striking and confirms what has been said as to the Tradeston group. In two schools alone, Gorbals and Adelphi Terrace, about 500 children had distinctly foreign, mostly Jewish, surnames. The colour characters of these children were tabulated with the following result (Table LVL): TABLE LVI. Children with Foreign Surnames Gelour Gorbals Adelphi Terrace oe ouy per cent. per cent. Hair: Fair vee 3°14 8:00 Red vats 1:04 2°29 Medium Nee 37°98 26°29 Dark ae 53°31 56°57 Jet Black... 4°53 6°86 Eyes: Blue we 3-14 lier Light sis 17°42 17°71 Medium tie 21°25 18°86 Dark wee 58°19 61°71 In Gorbals Public School 41 per cent. and in Adelphi Terrace Public School 44 per cent. of the children of foreign parents had dark hair associated with dark eyes in the same individual. Thus the Jewish element alone in the Tradeston group is sufficient to account for the excesses in dark hair, jet black hair, and dark eyes, found in this populous district. It has been directly ascertained that the foreign element in the Tradeston group is largely made up of Jews of Russian and Polish origin. From the Census Report it is seen that of the whole number of foreigners in Glasgow, 60 per cent. J. F. Tocuer 215 are Russians and Poles; 15 per cent. are Italians; 10 per cent. belong to other races whose predominant hair colour is known to be brown or dark. Only 15 per cent. belong to Northern races or peoples likely to have a moderate or large pro- portion of the blonde type, namely, Germans, Swedes, Norwegians, Dutch and Belgians. Thus wherever foreigners congregate together in the city anywhere they are likely to increase the darkness of the population rather than otherwise. The general effect outside the Tradeston group may be small, since the foreign population is more scattered, and is in much smaller proportion consequently in every division but Tradeston and Gorbals. Any effect Italians have would be in the direction of excess of medium hair and dark eyes since Livi* has shown these are the typical classes among Italians, but there is no evidence of the concentration of members of this race as a group in the city*. (8) The Irish Population of Glasgow. The Gaelic speaking population has been shown to be likely to influence the colour distribution of Glasgow in the direction of excess in the dark and jet black haired classes and also probably in the blue-eyed and light-eyed classes. The divisions likely to be influenced have also been pointed out. But there is another very important element in the Glasgow population still to be considered. It is estimated by reliable authorities that there are about 100,000 Irishmen in Glasgow. Over 40,000 as a minimum are Protestantst. The proportion of persons of Irish origin in other parts of Scotland is very small. The effect of this large population, if its colour characters differed from those of the Scottish population, would be very great. In one of the previous sections (Section 9, Table XX XVIII.) it was pointed out from Beddoe’s figures that compared with Scotland, Ireland was likely to have much higher proportions of light eyes (light and blue, however ; Beddoe grouped both together as one class), dark hair and jet black hair. Beddoe’s figures of course refer to the adult Irish population. It therefore seemed desirable to get an estimate of the distribution of colour among Irish children. The colour characters of school children, stated by the teachers to be of Irish origin, in certain Glasgow schools were tabulated, when the figures given in the accompanying table (Table LVII.) were obtained. These figures confirm the conclusion from Beddoe’s results. Dark and jet black hair are both in excess compared with the Scottish population. The distribution therefore differs markedly from the general Scottish distribution. If children of Irish origin were present in a moderately large proportion in any of the districts, they would sensibly affect the colour distributions in the schools of Glasgow. In order to gain some information as to the number of children of Irish origin in each of the pigmentation districts of Glasgow, the author recently communicated with the headmasters who very kindly sent in a return showing the numbers approxi- mately of children of non-Scottish origin, in three classes: (a) foreign, (8) Irish, * R. Livi, Antropometria Militare, Roma, 1898. + Canon Ritchie has very kindly supplied me with figures from the Roman Catholic Clergymen of Glasgow which show that Italians are nearly in even proportions in the various divisions. + This estimate is based on figures supplied by Orangemen, through the kindness of Mr Hugh Berrie, Glasgow, 216 Pigmentation Survey of School Children in Scotland TABLE LVII. Colour Distribution of Children of Irish origin. Per Cent. Trish Adults Boys Girls Beddoe Hair: Fair ae 24°31 22°11 10°4 Red ase 4°53 5°09 4°6 Medium bas 40°32 35°13 33°4 Dark = 27:26 | 33-07 40°5 Jet Black... 3°58 4°60 11:0 Hyes: Blue at 22°53 21°23 66°5 Light > 26°52 26-03 | Medium mae 28°84 28°38 14°7 | Dark vate 22°11 24°36 18°6 | | (vy) English and Welsh. The following table (Table LVIII.) shows the percentages of each of the three classes based on the returns received. The author desires cordially to thank the teachers of Glasgow for supplying the additional information asked for—information which assists in the verification of some of the conclusions as to the cause of the great divergency of the population of Glasgow from the general population. TABLE LVIITI. Percentages of Children of Non-Scottish Origin. Glasgow Proper. Number of Children of Origin as noted below in Public Schools sending returns Division Per Cent. Per Cent. Per Cent, Foreign Trish English | Anderston... we iat Te aa 68 6°61 3°39 Milton mics ane ae aA abs 1:16 4:29 4:90 St Rollox nae Sas aa wae aes 67 7°99 6°42 Dennistoun ... aes ua wins sis 15 9°35 5°80 Calton, Camlachie and Bridgeton ... see "24 5°15 4°36 Tradeston, Gorbals and Hutchesontown ... 8:18 3°72 3°08 This table does not of course represent the absolute percentages of non-Scottish children in the above named divisions. Practically the whole of the children attending Catholic schools are excluded. The percentage of Irish school children in each division is really much higher. The above table merely shows the pro- portion in the public schools sending returns, The table serves its purpose as J. F. Tocuer re hig showing the large Irish element in the public schools of Glasgow—an element which, from the results of the analysis of the colour characters of Irish school children in Glasgow, tends to make the hair colour distribution of the western city darker than the remaining Scottish population. The school children of Irish origin have on an average 2 per cent. more of the dark-haired class (boys) and about 8 per cent. more in the girl population. A distinctly greater proportion belong to the jet black class among the Irish population, about 4 per cent., compared with 1} per cent. in the Scottish population. Although a greater proportion of the Irish population observed, compared with the general Scottish population, has blue eyes, this class does not appear in excess in any of the populous centres except Partick. Partick was not included nor was Govan in the investigation as to the number of school children of non-Scottish origin—an omission which the author regrets he made when the Glasgow teachers were invited to send the additional returns. Further work is contemplated on the Glasgow returns and an additional return is expected from many of the large Catholic schools. These schools have an attendance of about 20,000 children whose colour characters have not yet been observed. A very large number of these children are of Irish origin and a knowledge of their colour distribution will be useful. Of course since these children were not included in the present survey, they do not contribute to the divergency found for Glasgow. The results of this subsection show that children of Irish origin clearly affect the nature of the distribution of colour in Glasgow. They tend, as the Scoto- Keltic and the foreign populations do, to create an excess of dark hair and jet black hair. The Irish population does not appear to affect the eye colour distri- bution of Glasgow sensibly. It may however do so. Other factors which have not yet been discovered may be operating to obscure the effect of the Irish element on the distribution of eye colour in the western city. The association of excess of dark hair, jet black hair, blue eyes and light eyes with the Scoto-Keltic and Irish populations is a striking feature in these results. The results but confirm the common origin of the two peoples—their association as determined by language, by history and by tradition. IV. Summary of this Section. (1) The general analysis reveals Glasgow to diverge largely from the general population both in hair colour and eye colour. (2) Further analysis shows the divergency to be due to excesses of the medium and dark haired classes and the medium and dark eyed classes, and to defects of the fair-haired and blue-eyed classes. (3) Analysis of the divisions into which Glasgow is divided brings out the fact that the excesses are not uniformly distributed over the city. No excess of the fair-haired class appears in any quarter of the city, but certain districts, St Rollox (¥), Dennistoun ("), and the western suburban area (Paisley) have about the average proportion of this class. Milton, the Cowcaddens district, is the only one showing excess—a slight one—of the red-haired class. Excess of medium hair in varying Biometrika v1 28 218 Pigmentation Survey of School Children in Scotland proportions occurs in every district of the city. In St Rollox, Dennistoun, Calton and Bridgeton, the excesses are not so marked in the boy population. Excess of dark hair is characteristic in a marked degree of Anderston and Tradeston, Gorbals and Hutchesontown. In other densely populated centres the girl population also shows excesses of this class. Jet black hair is in excess in the Tradeston group. Blue eyes is in excess only in the Partick group; light eyes in Anderston ; medium eyes in Dennistoun and the Bridgeton and Tradeston groups; dark eyes in Anderston, Milton, Govan and the Tradeston group. (4) The environs of Glasgow diverge in a much less degree from the general population. The population is not so dark as in the city. (5) The deficiencies in the blue-eyed and fair-haired classes are due to the presence of a complex group which, with a darker colour specification, creates deficiencies in these classes. This complex group includes Highland, Irish, and foreign populations. (6) It cannot be said from the data whether these classes (fair hair; blue eyes) are less fitted for town life or whether this theory would account for any of the low percentages of these classes. The low percentages are on the other hand explained by the presence of the darker Scoto-Keltic and non-Scottish elements. (7) The Scoto-Keltic, Highland or Gaelic speaking population appreciably affects the distribution of colour and helps to explain excesses in dark hair and light and blue eyes. (8) The Irish population, a very large one, also helps to explain the large excesses in dark and jet black hair and probably light eyes where they occur. (9) The foreign element helps largely to explain why Tradeston and Gorbals diverge so widely from the rest of the population. The presence of other non- Scottish groups in this part of the city is probable. (10) The country north-east and almost contiguous to Glasgow might con- tribute in some degree to excess of dark eyes, since these parts (Stirling, Perth, etc.) have an excess of this class in their own populations. The greater fertility of the lower classes, and of the dark-eyed portion particularly, might contribute to explain the excess of this class. (11) Excess of medium hair and medium eyes cannot be accounted for by the presence of a Scoto-Keltic element or of a non-Scottish element or by the migra- tion of excesses of Scottish members of these classes from rural districts to the city. Excesses of these classes are not found to any extent outwith densely populated centres. (12) The excesses may be due to blending of fair and dark populations or to greater fertility of the medium classes, or to both these causes, J. EF. Tocuer 219 (12) Comparison with other Data. I. Scottish Data. (a) Hast Aberdeenshire Children in 1896. The only data of a similar character with which any of the results of the present survey can be at all compared are the East Aberdeenshire results of 1896 published in a preliminary paper by the author in 1897*. Owing to slightly different ranges in some of the classes however the results are not directly comparable, as printed, with the results for East Aberdeenshire in 1903, when the general pigmentation survey was carried out. Fortunately in 1896, the teachers were asked not only to record the colour with reference to the classes then adopted but also to note where possible, and always if in doubt, the probable sub-class from a series of stated sub- classes, similar to Broca’s scale. Thus the author has been able to retabulate where necessary the results of 1896 and, as far as possible, place the children in the classes as specified in the analytical tables of the present survey. The first survey, it has been found, had a wider range of medium and a slightly wider range of red. With respect to the eye classes, the blue and light-eyed class of 1903 corresponds pretty closely to the light-eyed class of 1896. The following table (Table LIX.) shows the relative differences in the classes between the two sets of observations. To be more specific, the table shows the difference per cent. (or d) in each class compared with the probable error of the percentage difference, that is, compared with Ey = 67-449 Je 42a mon where in this formula, p = a3 q=(1—p); y= observed frequency of the class in TABLE LIX. Relative Difference between East Aberdeenshire in 1896 and 1903. (Boys and Girls.) d Colour EB, Hair: Fair ane Leia Red aes — 2°05 Medium wes — 6°79 Dark ius 6°28 Eyes: Light re 6-29 Medium awe —1°74 Dark ae —3°78 * Tocher: Trans. Buchan Field Club, Vol. tv. pp. 137—152. 28—2 220 Pigmentation Survey of School Children in Scotland the first sample; m=number in first sample, p’= a (1—p’)=q; y’ =observed frequency of the class in the second sample; n=number in second sample; N = total children in first sample; and WV’ = total children in second sample. The negative sign indicates that the proportion of the class considered was less in 1903 than in 1896 and the positive sign that it was greater. The above results seem to indicate that the school population of East Aberdeenshire became darker haired to an extent which must be reckoned significant, and lighter eyed to an extent also significant in the eight years’ interval. Making allowance for any difference in method of observation, and comparing parish with parish, the results are however very similar. The difference lies chiefly in the results from the two towns in the division, Peterhead and Fraserburgh. (8) Scottish Adults—The Insane. The colour results of the survey of asylums in Scotland are not directly comparable, since the observations were made on adults and since the group is a selected one and is not truly representative of the general population. All one can do is to note in a general way the agreement or otherwise of the two sets of data. The author has not found it possible to spare the time to estimate from the juvenile data the probable distribution of the ordinary adult population in each division or to deal in further detail with the colour characters of the insane. Moreover it seems more desirable—more satis- factory—to wait until the adults of the normal population are directly surveyed. Instead of the promised detailed comparison between the two sets of data, it seems sufficient to point to the leading features. Both sets of data agree in showing less divergency in densely populated parts. The excess of dark hair in the west found for the asylum population has been amply confirmed by the results of this survey. The region of excess of dark eyes in the asylum population has proved to be the same region for the general school survey. Perthshire, Stirling and Forfar are the counties constituting this region. The excess of medium hair is in both associated with density. The proportions of fair hair and red hair are small compared with the juvenile population. Excess of light eyes is somewhat similarly distributed, but is not so much south-west as the juvenile distribution. The region of excess of red hair is quite the same. Briefly, while it would be useless to compare the relative frequencies of the two sets of data for the reasons already stated, still when the local class frequencies of each set are compared with each set’s own general population, they show on the whole the same significance. It has been shown that the colour distribution of the insane population as a whole cannot represent the general distribution of the sane in one important particular, namely, in the frequency of the light-eyed class. Regions of excess of insanity from the general average are associated with regions of excess of light eyes, thereby increasing the proportion of light eyes in the general insane population beyond the expected amount for the general adult sane population*. * Biometrika, Vol. v. pp. 298—850. J. F. Tocuer 221 (y) Scottish Adults—Beddoe’s Observations. The figures of the pioneer observer Dr Beddoe are useful, indicating as they do the predominant classes in various localities in Scotland. The samples of the population observed by Beddoe are usually small and in many cases they are too local to give an idea of the dis- tribution of the surrounding area. His classes do not all correspond to those of the present data, and since adults and not children were observed by him one is farther debarred from attempting to compare directly the relative frequencies of his classes in various localities with those from this survey. The proportion of red hair generally found by him appears to be slightly higher than that found by the teachers of Scotland among the children. The excesses however appear in the same districts. He shows excess of dark hair in the same western regions of the country. The proper time to enter into a discussion of Dr Beddoe’s results is when a survey of the colour characters of the adult population has been completed and the results tabulated and analysed. II. Foreign Data. (a) The Actual Data. The results of this survey will now be compared with the results of the surveys of the colour characters of children which have been carried out in Germany, Switzerland and (partially) in England, and with the results of the surveys of the colour characters of the adult popu- lations of Sweden and Italy (military data). The following table (Table LX.) gives the percentages of the classes in each of the countries named, the school figures for Scotland being given alongside for comparison. TABLE LX. Hair HKyes : 4 Nature of | sUOTALY ay Population | l 7 — Fair | Red | Medium | Dark | Light | Medium) Dark Virchow... | Prussia ... se ... | Children 72°4| 3 26°0 13 | 42-9 || 32°6 24°5 Beddoe ... | Switzerland ass 52°9 | 2-9 38°9 bes Retzius ... | Sweden ... ee ... | Adults 75°3 | 2°3 21°6 8 | 66°7 28°8 | 45 Livi 560 |) 12h aaa ae ... | Military 8:2 6 60°71 311 | 10°3 20°6 | 69°1 Ammon... | Baden... ack ... | Adults ANG. | Ue7 38°6 181 | 64:4 229 | 127 Tocher ... | Russian Jews in Glasgow | Children | 5°1 | 1°2 334 59°7 | 19°8 | 21°1 | 59°71 Pearson ... | England wee ... | Boys 33°5 | 4:1 | 34:0 28°4 | 41°5 37°0 | 21°6 Tocher ... | Scotland oe ... | Boys 24°95 | 5:49 | 43°28 | 26°28 | 44:97 | 32°72 | 22°31 9 sa0 5) ee =. |) Gurls 27°43 | 5:09 | 40°87 | 26°62] 45°18] 32:06 | 22°76 | (8B) Comments. The first fact worthy of notice is that Scotland occupies an inter- mediate position between the extreme northern race (Germany) and the extreme southern one (Italy) in the matter of pigmentation. The northern German race has about 72 per cent. of the fair-haired class; the Italian race about 60 per cent, of the brown-haired class and 31 per cent. of the dark-haired class. Scotland has about equal proportions of fair and dark; about one-fourth of the school population is either fair-haired or dark-haired; the remaining belong to intermediate classes which include the shades of brown and red. Now if a pure race of the blonde 222 Pigmentation Survey of School Children in Scotland type is defined as meaning a population which has been isolated and has bred within itself in an environment unsuitable for the production of hair pigment for a sufficient length of time to ensure that every individual will be fair-haired, it is obvious none of the northern races are pure races of the blonde type. They have relatively large sections in their respective populations which are pigmented. Similarly if by a pure race of the dark-haired type is meant a population which has bred within itself in an environment suitable for the production of hair pigment for a sufficient length of time to ensure that every individual was uniformly pigmented dark, it is clear the southern Italian race is not a pure race of the dark-haired type. The Italian people are largely of the brown or intermediate type (about 60 per cent.); 31 per cent. or nearly one-third are dark; about 8 per cent. are fair. If all the races of mankind were uniformly pigmented or non-pigmented, hair colour would cease to be one of the tests of race. But this is not the case and the problem is: how far can one use colour as a test of race or of racial purity ? One must in the first place consider whether in conjugal unions between the fair and dark types blended or exclusive inheritance holds, or whether both exist. It is clear from observation that blended inheritance does exist for fair and dark hair colours, the shades of brown being the blend. What is wanted is a measure of the blended inheritance in this case. From observation it is possible that exclusive inheritance exists in the case of red hair. But the main point here is that, in hair colour, one has a problem in blended inheritance. Now granting equipotency of the two types, fair and dark, and random mating with respect to hair colour as well as other forms of mating as probable, and it is obvious that varying proportions of fair, dark and the shades of brown hair will occur in the population of a country according to the proportions of the fair and dark types originally settling in that country. Is anything known of an exact nature as to the distribution of colour in the offspring of fair and dark parents, i.e. of parents one dark and one fair? Insufficient data exist to show the exact nature of the distribution. A large number of carefully made observations are required. Individual cases can be cited. (A) Dark-haired, and (B) fair-haired, have a family of five. One is fair, one is dark, three are medium. All are children, but the oldest, classed medium, is getting darker and will probably be dark. To be accurate one must compare the colour of the parents when they were children with the colour of the offspring as children; or the colour of the parents with the colour of the offspring as adults. Can it be said that the most probable distribution of colour in the offspring of such parents, granting blended inheritance and equi- potency in determining pigment, is, in say a family of four, 1,2, 1; one fair-haired, two medium and one dark-haired? The object of science is to give a shorthand description of the facts. In this case the expanded binomial (4+ 3) is put forward tentatively as the shorthand description. If true it is a problem like deter- mining the number of times two heads, one head and no heads, will turn up in spinning two coins together. The most probable distribution in this case is, 1, 2, 1. Can hair colour in Scotland be cited as an example of this simple binomial distri- bution, similar to the Mendelian example in the crossing of peas? This has to J. F. Tocuer 223 be determined. What the writer wishes to lead up to is this. In Scotland the distribution of colour is roughly, 1 fair, 2 mixed, and 1 dark. Is it fair to infer that the original elements of the Scottish population were fair-haired and dark- haired races in approximately equal proportions? Proof is wanting but the distribution is suggestive. From our knowledge of the distribution of eye colour in Scotland, it is unlikely that although there were fair-haired and dark-haired races, the two elements were entirely blonde and brunette—the blue-eyed fair- haired type, and the dark-eyed dark-haired type. It cannot be shown from the data what proportion of the dark-haired element was of the brunette type or what proportion was of the type found in the Gaelic speaking population, the blue or light-eyed dark-haired Keltic type. Who were our ancestors of the brunette type? Were they of the Mediterranean or Danish type or both? The fair-haired element probably was made up of the blonde type, Scandinavians and others of Germanic stock who, history tells us, came to our shores in bygone centuries and who fought, struggled, settled and made Scotland—the Scotland of the dark-haired Kelt—their home. Together with the darker elements they may have united and appear to be now uniting to form a blend—the Scottish type—one which in physical characters has proved itself vigorous and which, considering mental characters, has been at least relatively as productive of men of ability as any in the British Isles. Ill. Zhe Data bearing on correlation, and comparison with similar data. (a) General. Hitherto, throughout the entire course of this investigation, the author has been considering hair colour and eye colour separately—taken one at atime. It is obvious however that an account of the colour characters of the Scottish children would be incomplete which did not include an investigation on the two taken together as found occurring in each individual. It is one of the disadvantages of a private investigation as compared with an official one carried out by a Department of the State, that an adequately paid staff is not available to tabulate the enormous mass of data, the complete analysis of which is necessary before a full account can be given of all the facts which flow from the results and which lie hidden until the tabulation has been made. Although the author has been continuously engaged in the tabulation and numerical treatment of the returns so kindly made by the teachers voluntarily more than four years ago, he has been able only to complete the investigation in so far as it refers to the separate colour characters. The large mass of data bearing on fraternal and other relationships lie practically untouched. The tabulation of the combinations of the two characters has still to be made, except for one or two districts. The author has complete confidence that not only will he be able to get the funds necessary for clerical assistance to tabulate these important data, but that he will be personally given sufficient time to do the work. The correlations between hair and eye colour when such data are tabulated and the values of the correlations evaluated for each locality will be of great value. Not only will the predominant types in each district be determined but the relative homogeneity 224 Pigmentation Survey of School Children in Scotland of each group will be accurately ascertained. Again, there are the colour characters of groups of families as revealed by surnames to be considered. A tabulation and analysis of the colour characters of surname groups for each surname would show whether they were really associated, like family groups, or were merely samples of the general population. The degrees of resemblance of brothers and sisters would be determined on numbers hitherto undealt with and would confirm or otherwise the measures found from the numerically smaller English data. Finally, the degrees of resemblance between the various kinds of cousins, an investigation suggested to the author by Professor Karl Pearson, await determination*, and the determination cannot be made until the almost overwhelming mass of data bearing on cousinships has been also tabulated. (8) Comparisons. The correlation between hair and eye colour has been determined, the contingency method being used, for one Scottish group, namely, 19,279 school children of the city of Aberdeen, and also for 1000 children taken at random from the entire pigmentation data. The following two tables give re- spectively (Table LXI.) the results of the observations of hair and eye combinations in the city of Aberdeen, and (Table LXII.) the values of the contingency coefficients. The author’s results for other Scottish populations and those from British and continental returns are given alongside for the purpose of comparison. TABLE LXI. Hair and Eye Table. 19,279 Children in the City of Aberdeen. Hair. | | Fair Red | Medium Dark Jet Black | Totals [een See eee | | | | | : | Blue 56H 1105 131 | 885 | 348 1 2470 2 | Light .. | 2285 405 2434 851 9 5984 =| Medium ... 1208 360 3242 | 1601 29 6440 Fl Dark ...| 366 | 209 | 1621 | 2094 95 4385 | Totals .. | 4964 1105 8182, 4894 |, 134 19279 These results show, if it is a mark of racial purity of any race to have its individuals all of one hair colour and of one eye colour, that the Prussian school children are relatively more homogeneous than the Scottish school children, and that the latter in turn are more homogeneous than the British schoolboys generally, since the value of the correlation is lowest in the case of the Prussian children and highest in the case of the British schoolboys. It may be here noted that if two races, one of the blonde type and one of the brunette type, were present in a population in equal proportions, the degree of correlation between hair colour and eye colour would be equal to unity. On the other hand, (1) the * The author intends to hand over the classified data on cousinships to Professor Pearson as soon as they have been abstracted and tabulated. J. F. Tocrer 225 TABLE LXII. Correlations. Hair and Eyes. Population en aal Returns by Reference Scottish Children, General, 1903 ... a. "3453 J. F. Tocher | This Memoir Scottish Children, East Aberdeen, 1896 ... “3802 R +5 Scottish Children, Aberdeen a City, I 1903... “3361 = - British Schoolboys sins ‘ i "4203 K. Pearson | Biometrika, Vol. 11. p. 461 Prussian Children ... a ai re 2714 R. Virchow iS = Jewish Children ws aa a ae 3381 : . _ Adult Scottish Population ... ac ies “3673 J. F. Tocher | Biometrika, Vol. v. p. 339 Male Asylum Inmates ne see + 3039 5 55 _ Female Asylum Inmates... re ae 2994 . a - Swedish Conscripts ... ine eee a 2495 G. Retzius Biometrika, Vol. ut. p. 461 Italian Conscripts ... e352 ah er, 3091 R. Livi 35 . Baden Conscripts... a ae sai 3540 O. Ammon 5 5 Mean of above values wa Ae aoe 3312 nee ee ee more this population in time and through intermarriage was thoroughly crossed, or (2) the nearer this population came to consist of members entirely of either race, the smaller would be the value of the correlation and the nearer 1t would approach to zero. Looked at from this point of view, a large value for the corre- lation would mean heterogeneity in that population and a small value greater homogeneity. Judging from the above results, the correlation between hair and eyes does not appear very close in any of the countries) With more local groups it is probable that in countries like Prussia and Italy less association would be found. In the further investigations on the data of this survey, it will be interesting to find what values the correlation coefficients take in the various districts ; particularly (a) in those where one type has been found to be predominant, and (8) in those sparsely populated parts where two diverse types were found. (13) Summary of the Results. I. The general result of the Pigmentation Survey of School Children in Scotland shows that, of the 502,155 children surveyed, about one-fourth are fair- haired, one-fourth dark-haired, and nearly one-half belong to two intermediate classes embracing the various shades of brown or medium and red hair. The pro- portion of the brown or medium class in the boy population is about 43 per cent., and in the girl population 41 per cent. The class embracing the various shades of red hair constitutes about 5 per cent. of the population. In the dark-haired group there are two classes—a large class with dark brown hair approaching to black, Biometrika vr 29 226 Pigmentation Survey of School Children in Scotland and a small class with jet black hair. This latter class constitutes only 1} per cent. of the total population. The girl population contains a higher proportion of the fair-haired class than the boy population, over 27 per cent. as against 25 per cent. There is a correspondingly less proportion of the medium or brown- haired class in the girl population. The cause of this difference is not quite apparent. It should be remembered that the children surveyed are those of school age—a fairly wide range, from 6 to 18—and that hair colour in children gets visibly darker as the children get older. If the children were classed according to age and their colour characters tabulated, it would be ascertained whether or not the difference was due to an earlier darkening in hair colour among the boy population, or whether the boy population was really significantly darker in hair colour. from infancy than the girl population. From the results of observations of the physical characters generally of both sexes, a really significantly darker boy population from natural causes is improbable. It should moreover be remembered that, in determining hair colour, boys and girls are not judged exactly under the same conditions. Hair colour in girls is generally judged from long tresses. These are usually absent in boys, whose hair colour is judged from the shorter mass. Besides, girls’ hair frequently shows extreme variety of tint from tip to root. Another possible explanation is the stimulus given to the increase of pigment by hair cutting in the boy population. This explanation requires verification from observations, (a) on a population of children in which the conditions are the same, and (@) on the adult population. The results of the observations on eye colour show that over 22 per cent. (nearly one-fourth) of the school children of Scotland have dark brown or dark eyes, and over three-fourths of the population possess blue, light or medium eyes. About 15 per cent. possess pure blue eyes, 30 per cent. light eyes, and about 32 per cent. (nearly one-third of the population) possess eyes of the mixed type —the varieties classed as medium eyes. Comparing these general results with the results of similar surveys in foreign countries, it is seen that they differ markedly in many respects. In Northern Europe, between the same latitudes as Great Britain lies from Frankfurt, Prague and Cracow in the south to Christiania, Stockholm and St Petersburg in the north, one finds a heterogeneous population in which the fair-haired class pre- dominates. In Prussia alone, 72 per cent. or nearly three-fourths of the children are fair-haired. In Sweden, a similar proportion of the adults are fair-haired. In Schleswig, 80 per cent. of the children are fair-haired; in Saxony, 69 per cent. Germany, south of Frankfurt and Coburg, is distinctly darker than the northern and larger portion. But even in South Germany the proportion of the fair-haired class far exceeds that found in Scotland. In Alsace and Lorraine the proportion is 47 per cent.; in Baden 58 per cent.; in Wiirtemberg 62 per cent.; and in Bavaria 54 per cent. The difference in the distribution of eye colour is not so marked. Prussia is somewhat similar to Scotland in its eye colour, the proportions being in Prussia 43, 33 and 24 as against 45, 33 and 22 in Scotland for light, J. F. Tocuer oi medium and dark eyes respectively. Germany as a whole has a significantly greater proportion of dark eyes than in Scotland, 32 per cent. as against 22 per cent. Scotland does not resemble Italy in any respect, except that in both medium is the predominant class in hair colour. In Italy, however, the proportion 1s significantly greater, 60 per cent. as against 43 per cent. in Scotland. Nowhere on the Continent does one find a distribution of hair colour similar to Scotland, It remains to be seen, when observations are made on English, Welsh and Irish children, in what respects these will differ from the results for Scottish children as shown by this survey. The difference between Pearson’s series of 4000 children and Scottish children is not very great. II. The results of this survey show that the distribution of colour is by no means uniform throughout Scotland. On the contrary, there are well-defined areas where the proportions of the various classes exceed quite significantly the pro- portions which would occur if the population were as evenly distributed throughout Scotland as, say, the grain of a cornfield is sown by the farmer. In this example, the distribution of the grain is not absolutely uniform, but the farmer succeeds in preventing excessive deposits of grain in one part and meagre deposits in another. An enumeration of the number of seeds in each square yard, and an analysis of the numbers would show that the intention had been to make a uniform distri- bution. No such uniform distribution of the population of Scotland is found when the population is considered in sections as represented by the various colour classes. This is quite apart from the density of the population, which is well known to be very far from being uniform. The proportions of the various classes quite exceed in the expected values in many localities. Excesses of blue eyes and fair hair occur mainly in the north of Scotland and are common for both sexes to Orkney, Shetland, the isle of Lewis, Ross, Cromarty, Elgin, Nairn and Perth, and portions of Stirling, Forfar and Fife; also to Ayr and portions of Renfrew and Lanark in the west and Berwick in the east; in all representing only about 1,000,000 of the population ; that is, about one-fifth of the whole population of Scotland has a significantly greater proportion than the average of the fair-haired and blue-eyed classes, the excesses being common to both sexes. In the girl population the distribution of excess of both classes is greater ; it extends to a population of nearly two millions in the case of fair hair and to about a million-and-a-half in the case of blue eyes. The distribution of red hair is fairly uniform throughout Scotland. The region of marked excess for a large area is the north-east of Scotland. Isolated cases of excess occur in Sutherland and in the north-east of Lanarkshire. Excessive proportions of medium or brown hair occur in Glasgow, Govan, Dundee, and in the counties of Renfrew, Selkirk and Peebles. The excess in Leith for the boy population is also probably significant, as also the excesses in the counties of Stirling (girls), Linlithgow and Bute (boys). Excess of this class (see VII.) is peculiar to densely populated districts. Excess of dark hair is peculiar to the west of Scotland, the only eastern county showing excess of this class (boys only) being the small county of Kin- 29—2 228 Pigmentation Survey of School Children in Scotland cardine. The counties of Inverness and Argyll, and the city of Glasgow, show excess of this class for both the boy and girl populations. Kirkcudbright and Sutherland (boys), and Renfrew (girls), also show significant excess. The west is also the region of excess of jet black hair, a small class numerically. Altogether there are only about 6000 children out of a total of over 500,000 who possess jet black hair. The excess is common to both sexes in the counties of Perth, Inverness, Ross and Cromarty. Caithness (boys) and Argyll (girls) also show significant excess. Excess of blue eyes has already been stated to be common to the north. Significant excess of light eyes is common to Argyll and Dumbarton in the west and to Leith in the east. Kincardine and Kirkcudbright both show significant excess of this class in the girl population. Significant excess of medium eyes is peculiar to the great cities, Glasgow, Aberdeen (girls), Leith (girls), and Dundee (girls); and to the county of Lanark generally. Significant excess of dark eyes is also peculiar to the great cities, Glasgow, Edinburgh and Dundee. The county of Forfar shows significant excess for the girl population. Ill. Many parts of Scotland quite resemble the general population in hair colour and eye colour. These parts are usually densely populated. Notable exceptions occur. Glasgow is the striking example. The presence of non-Scottish elements and of excess of the Highland element makes Glasgow unrepresentative. The populous East-Midland division is most representative of the general popu- lation in hair colour. The populous counties, Forfar, Fife, Stirling and Dumbarton, and the city of Edinburgh are fairly representative of the general population. The counties which diverge largely in hair colour from the general population, and have therefore non-representative populations, are Ross, Cromarty, Inverness and Argyll, the divergency being common to both the boy and girl populations. The divergency in the case of Argyll is due to excess of dark hair and jet black hair, and in the other cases to excesses of both fair and dark. The divergency in the north-east of Scotland is due to excess of red hair and fair hair. The sea- board on the west coast from Sutherland to Mull is highly divergent, due to significant excess of dark hair and jet black hair. In eye colour, the Southern and South-Eastern divisions are the most representative; the North-Western and South-Western the most divergent. Orkney, Shetland, Sutherland, Ross, Cromarty, Inverness, Elgin, Nairn and Forfar all diverge because of excess of blue eyes; in Sutherland and Forfar excess of dark eyes also contributes to the diver- gency. In the cities of Glasgow and Dundee, the divergency is due to excess of medium and dark eyes; in Aberdeen to medium; and in Leith to light and medium. The counties of Argyll, Dumbarton and Dumfries in the west diverge because of excess of light eyes; and Ayr because of blue and light. The isle of Lewis diverges because of excess of blue eyes and the isles of Jura and Islay because of excess of light. These islands contribute largely to the divergency of their respective counties, Inverness and Argyll. IV. It has been proved (see II. and III.) that excesses in the various classes, or positive differences much in excess of the expected, occur all over the country, J. FE. Tocuer 229 frequently in contiguous areas, thus indicating a differentiation for each class from the general population. In measuring the degree of geographical separation or local segregation for each class, it has been proved that the blue-eyed and fair-haired classes have the greatest degree of local segregation. The segregation of these classes from the others is excessively great. Children belonging to these classes are congregated more in sparsely populated regions than in densely populated or moderately populated parts. The medium haired and medium eyed classes show the next greatest degree of local segregation. Children of these classes are congregated more in towns and in densely populated parts. The other classes all show a high degree of segregation except the red-haired class, which is almost uniformly distributed throughout the country. But for the regions of excess in the north-east of Scotland and in one or two other isolated and much smaller areas the distribution of this class would be practically uniform. This fact suggests that the occurrence of red hair (a) is independent of race, or (8) is one of the effects of blending of races, perhaps widely divergent races, or (vy) is an abnormal condition in hair colour and deserves the attention of the physiologist and pathologist. The statement of Tacitus as to the red-haired Caledonians points at least to the fact that red hair was a trait among the inhabitants of the north of Scotland in earlier times, and it is a striking circum- stance that excess of this class is found in the region referred to by him. V. It has been found that regions of excess of the dark-haired, jet black haired and blue-eyed classes are associated with regions of excess of the Gaelic speaking population, The measure of the association is given. This association was to be expected, seeing that these classes occur in excess in western counties, where the population is bilingual and where Gaelic is the mother tongue of a large proportion of the inhabitants. A typical Scoto-Kelt is therefore blue-eyed and dark-haired, but the light-eyed dark-haired type is also common in Argyll and its Isles. It will be seen later (X VI.) that there is a similar Irish type. VI. It is proved that foreign immigrants tend to reside in the most densely populated areas in Scotland and in districts where families live in one or two rooms. The children of foreign immigrants have an effect,—scarcely an appre- ciable one,—on the population of Scotland as a whole, but in certain very densely populated parts they have a distinct effect. For example, it is shown that in certain divisions of Glasgow, Tradeston and Gorbals (see XVI.), the proportion of school children of foreign origin is so high as to change completely the nature of the distribution of hair colour and eye colour. VII. It is proved that densely populated regions are positively correlated with excesses of the following classes: medium hair, medium eyes and dark eyes. The more densely populated a region is the greater will be the proportions of these classes in the population, and conversely, the more sparsely populated a region is, the smaller on an average will be the proportion of the classes just named. 230 Pigmentation Survey of School Children in Scotland VIII. It is well known that mortality is higher in more densely populated regions than others. It has been proved (see VII.) that certain classes are more characteristic of crowded areas than others. It is therefore to be expected that these classes would be positively correlated with the death rate. It is shown that an increase in the proportions of medium hair and dark eyes is associated with an increase in the death rate. This does not necessarily mean that persons belonging to these classes are less virile but simply that a large proportion of them live under conditions which are productive of a higher mortality. A direct investiga- tion to determine whether any colour class is associated positively with a high death rate is desirable. IX. It is shown that neither the Highland, Irish, English nor foreign elements in the population account for the high proportion of medium hair found in all densely populated regions. These elements however (excepting the English) where present, tend to increase the proportion of dark and jet black hair. X. It is proved that the number of births per family is greater on an average in densely populated parts, and, as a consequence, that the number of births per family is greater where there are large proportions of medium hair and medium eyes. The lower classes are found in the denser centres. Thus it is likely that the medium haired, medium eyed lower classes are on an average more fertile than the remaining population. Here again a direct investigation is desirable. XI. The main cause of the large excess of medium hair in densely populated parts probably arises from the blending of colour in the offspring of fair-haired and dark-haired persons: it is pointed out that blended inheritance exists in hair colour and what is wanted is a measure of its intensity. In densely populated areas, greater opportunities for intermixture of races occur, and it is shown (II. and III.) that in the large sparsely populated districts fair hair and dark hair, indicative of at least two different types, occur in excess, while in the urban regions these excesses mainly disappear and excess of medium hair appears. XII. The excess of dark eyes in urban areas does not appear to be explainable in the same way. It has been suggested that exclusive inheritance in eye colour may be one of the causes of the excess in these areas. In the offspring of dark- eyed and blue-eyed parents it is possible that reversions may occur, maintaining the dark-eyed type. XIII. The extent of the association of the colour classes geographically has been determined. One of the main results shows that as a rule medium hair is associated geographically with no other hair colour and goes to confirm the theory that medium hair is a blend. Thus it is to be expected that the proportion of this class will increase, tending to make the hair colour of the Scottish people more and more uniform. Excess of red hair is found as a rule only in regions where the proportion of dark hair is well below the average; a slight excess of fair is associated with excess of red. There is no positive association geographically of ny | J. F. Tocuer 231 any class with light eyes. Excess of blue eyes occurs alone, but excesses of dark eyes and medium eyes as a rule occur together. XIV. It has already been shown elsewhere by the author that where there is an excess of light eyes in the population the number of cases of insanity is above the average and wice versa. It is now shown here that a greater number of cases of imbecility, blindness and deafness occurs in regions where blue eyes, dark and jet black hair are in excess. It has been already pointed out (see V.) that these classes are associated with the Gaelic speaking population. A direct determination of the relationship shows that significantly greater numbers of cases of these defects occur in Gaelic speaking regions than throughout the rest of Scotland. This is most probably due to the greater rate of emigration of the fitter portion from, and the relative absence of immigration to, the Highlands. XV. The degree of resemblance between the boy and girl populations has been determined. It is found that positive and negative differences in the boy population are mainly associated with positive and negative differences in the girl population in the same regions. The resemblance is least in the red and dark- haired classes and greatest among the medium-haired and blue-eyed classes. The resemblance is closer in eye colour than in hair colour. XVI. Glasgow so greatly diverges from the general population in hair colour and eye colour that it has been made the subject of a special investigation. The various municipalities constituting Greater Glasgow, as well as its environs, have been included in che investigation. It is shown that the Highland, Ivish, foreign elements all contribute to increase the proportion of the dark-haired classes. Tradeston and Gorbals have greater proportions of dark hair, jet black hair and dark eyes, mainly due to the large foreign element present in these populous divisions. The detailed analysis shows that the immigrants are of Russian origin and this is confirmed by direct enquiry. More than 500 Jewish children attend school in these divisions. Dark hair, jet black hair, dark eyes are the leading classes in this population. The Highland and Irish elements are found all over the city. It is shown that the Irish resemble to a great extent in colour characters the Highland population. Both contribute very largely to the excess of dark hair. Medium hair is in excess all over the city, as expected, since this class is associated with density and since Glasgow contains a greater number of persons per square mile than any other part of Scotland. The high proportions of these classes (dark and medium) cause a corresponding defect in the proportion of fair hair in Glasgow. Only in one or two divisions, St Rollox, Dennistoun, and the Paisley district, does the proportion of fair hair approach the average for Scotland. In all the other divisions fair hair and blue eyes are distinctly below the average. It cannot be said from the results of this survey whether fair-haired and blue-eyed children are less fit for town life than the other classes, but the defect in fair hair at least is quite explainable on the ground that the proportion is disturbed (a) by a darker Scoto-Keltic or Highland element, (@) by a darker Trish element, (y) by a darker foreign element and (6) by the effects of blending of 232 Pigmentation Survey of School Children in Scotland fair and dark producing the various shades of brown classed as medium. All these contribute to the result and, taken together as a whole, are sufficient to cause the defect in the proportion of fair hair. Hntia non sunt multiplicanda. It is probable that the country north-east and contiguous to Glasgow may contribute to the excess of dark eyes, but it is also probable, since the lower classes are more fertile, since dark eyes are associated with density, and since it has been shown elsewhere that dark eyes are associated with greater fertility, that greater fertility may contribute to produce the excess found in Glasgow. XVII. The population of East Aberdeenshire which was surveyed in 1896 has possibly become slightly darker in hair colour and lighter in eye colour in the eight years’ interval. The change does not appear to have taken place in the rural districts but is more likely to have taken place in the two towns, Peterhead and Fraserburgh. XVIII. The regions of excess and defect in hair colour and eye colour as found in surveying the Scottish insane correspond in many cases to similar regions as found by this survey. In others they do not agree. This arises mainly from (a) the fact that the insane are a somewhat selected population, (@) the fact that they are adults and not therefore directly comparable and (vy) the fact that the numbers are small compared with the numbers in this survey. XIX. Several of Dr Beddoe’s results have received confirmation, but the remarks on the Scottish insane (see XVIII. above) apply to his observations. His results are not directly comparable. XX. The degree of association between hair colour and eye colour found from the results of this survey corresponds very closely to the values already found from other British and from foreign data. XXI. The results of this survey point to the conclusion that there are at least five types in Scotland. (a) One whose colour characters are dark hair and dark eyes; (8) dark hair and blue or light eyes; (y) fair hair and blue eyes; (6) a fourth type probably a product of two or more of the foregoing possessing medium hair (and perhaps dark hair) and medium eyes; (e) a fifth type, possessing red hair associated mainly with medium eyes, is also present in small proportions (about 5 per cent.) and is also probably a product of two or more of the other types. These may be named respectively (a) the Dark European type (examples of subtypes: (1) Mediterranean, (2) Danish); (@) the Scoto-Keltic type; (y) the Scandinavian or Germanic type; (6) the Scottish type; and (e) the Caledonian type. Biometrika. Vol. VI. Part II. Plate III. Il oV IV A pena i siramadeangis Black =Excess Fair Hair. Boys — Divisions. Black =Excess Red =Defect ane ri 2. Red ~=Defect White = Neutral eee | =o White = Neutral —065 to—16 Mi oY | 406 t 06 VI oU +O06to 16 15to 26 25to 36 3:5 upwards Red Hair Girls — Divisions. Red Hair Boys — Divisions. Black = Excess Black = Excess Red = Defect Red = Defect White = Neutral White = Neutral Biometrika. Medium Hair Boys — Divisions. Black = Excess Red =Defect White = Neutral Dark Hair Boys — Divisions. Black = Excess Red = Defect White= Neutral Vol. VI. Part II. — 35 upwards —25 to—35 —15t—-25 —05to—15 +05 to—O5 +O05to 15 15to 25 25 to 35 3:5 upwards Dark Hair Girls — Divisions. Black = Excess Red = Defect White = Neutral Plate IV. 2) eee re Biometrika. Vol. VI. Part II. Plate V. SCALE —_ |Jdet Black Hair Reto: Class | Girls - Divisions. 7 Black =Excess _g |Red =Defect 9 White = Neutral Jet Black Hair Boys — Divisions. Black = Excess Red = Defect White = Neutral —3°5 upwards —25 to— 35 —15 to —- 25 —05 to—15 +05 to— 05 +05to 15 15to 25 25to 35 3:5 upwards Blue Eyes Girls — Divisions. Black = Excess Red = Defect White = Neutral Blue Eyes Boys — Divisions. Black = Excess Red = Defect White= Neutral Biometrika. Vol. VI. Part II. Plate VI. Light Eyes Boys — Divisions. Black = Excess . Black = Excess Red = Defect _ ee Ursa) = Defect ‘ = to— 35 White = Neutral Sito Ons —05 to—15 XVII +05 0 -OS +05 to 15 15 to 26 25to 35 3:5 upwards Medium Eyes — : Medium Eyes Boys — Divisions. he Girls — Divisions. Black = Excess é Black = Excess Red = Defect ‘ ‘ Red = Defect White = Neutral White = Neutral Biometrika. Dark Eyes Boys — Divisions. Black =Excess Red =Defect White = Neutral Fair Hair. Boys— Counties. Black = Excess Red = Defect White= Neutral Vol. VI. Part II. —3°5 upwards —25 to—35 —15to—25 —05 to—15 +05 to— 05 +05to 15 15to 25 25to 35 3°5 upwards Dark Eyes Girls — Divisions. Black = Excess Red = Defect White = Neutral Fair Hair. Girls —Counties. Black = Excess Red = Defect White = Neutral Plate VII. Ga Biometrika. Red Hair Boys— Counties. Black = Excess Red =Defect White = Neutral Medium Hair Boys — Counties. Black =Excess Red +=Defect White = Neutral Vol. VI. XXIII Part 11, = SCALE, —— R. L. D. Class —3°5 upwards —25 to—35 —15 to—-25 —05to—-15 +05 to-O5 +05 to 15 15 to 25 25to 35 3:5 upwards Red Hair Girls — Counties. Black = Excess Red = Defect White = Neutral Medium Hair Girls — Counties. Black = Excess Red = Defect White = Neutral Plate VIII. “a a ” ” Biometrika. Vol. VI. Part II. Plate IX. XXVIII Dark Hair Boys — Counties. Black = Excess Red =Defect White = Neutral -R.L.D. Black = Excess Red = Defect White = Neutral — 35 upwards —25 to—35 —15 to— 25 —05 to—-15 +056 to— O05 +05 to 15 15to 265 25to 365 35 upwards Jet Black Hair Girls — Counties. Black = Excess Red = Defect White = Neutral Jet Black Hair Boys — Counties. Black = Excess Red = Defect White= Neutral Biometrika. Vol. VI. Part II. Plate X. XXXII Blue Eyes Boys — Counties. Black = Excess a Red =Defect s Be sell White = Neutral See wXY —-05to—15 XXXII eon eae +O05to 15 15t0 25 25to 35 3:5 upwards Black = Excess = Defect Light Eyes Light Eyes Boys — Counties. p Girls— Counties. Black = Excess Black = Excess Red =Defect Red = Defect White = Neutral White = Neutral Biometrika. Vol. VI. Part II. Plate XI. Medium Eyes Boys — Counties. Black = Excess — 35 upwards Red = Defect —25to—35 Black = Excess Red =Defect White = Neutral Ein te a White = Neutral —05 to—15 XXXVII +05 to—O5 XXXVIII +05to 15 15 to 25 25to 35 3:5 upwards Dark Eyes ft Boys — Counties. ~ Y Girls — Counties. Black =Excess Black = Excess Red =Defect Red = Defect White = Neutral White = Neutral Biometrika. Vol. VI. Part II. Plate XII. fi) ° . n e e ” oleae Fair Hair. =~ | ee scare —_ Red Hair. fo) Boys— Districts. S ~, Toe Black = Excess é i 2. Red = Defect 7) 8 chss. [Boys —Districts, , 0.) Black = Excessf\) ; i.{]Red = Defect f ij, |White= Neutral 1 Ql Wl ~ White = Neutral © to (iv t) a tO) ied Iioeed ae 8] Shall SI ol ol rl Ol on Hair Colour. Hair Colour. Local Divergencies. y Local Divergencies. Boys— Divisions. Girls—Divisions. Biometrika. Vol. VI. Part II. Plate XIII. XLIV. |Hair Colour. . |Local Divergencies. ;|Girls —Counties Hair Colour. Local Divergencies. Boys—Counties. XuVE u ws ell A eA I Ol & wl ol Lat (abel | eo ool eal < Density of Population in Non-Divergent Counties. Density of Population for each county in Scotland. Persons per square mile, Persons per square mile. - : e i rt { ‘ 2 ‘ , = = are DF i 1 , 7 ‘ \ 2 ‘ - wes : 7 — 7 Ss : 7 ; 1 ; i - a ‘ i , i : = ~ . : - 4 : . ow | . 7 w . . ts ' - Biometrika. Vol. VI. Part II. Plate XIV. XLVII. = = 2 ts Hair Colour Local Divergencies | Boys —Districts 456] 1 |( )|Boys—Districts es Eye Colour Local Divergencies 4 Girls —Districts ’ 7 4 ‘ ° ; j ch - ‘| as 7 7 rf as . fl - = ! ” ' 7 oh 1 Ei _ : 7 ie a a ’ [ ‘ i . LS >. . a - i * Pi ” . : 7 } r a : : : ; : , : oe) , . ' ae : : i : i re Biometrika. Vol. VI. Part II. Plate XV. Eye Colour. Local Divergencies. Boys— Divisions. . |Local Divergenciés. .. |Girls—Divisions. , upwards, Eye Colour. Local Divergencies. Boys—Counties. Eye Colour. Local Divergencies. Girls —Counties. Plate XVI. Vol. VI. Part Il. Biometrika. | =| - | z © 1 | : é il it | | | s s | | | 9 9 | | + 1 L L L 8 8 t 6 6 He t or or LCA BAIN 03 1 LEA QAIND 04 zx ce =h uonjenby iL 1 It et 2 ioions ? vonenby It \ YMIVH WUvd t j on YVIVH WOAICHWN et skog — sanunos L | | skog — saiunos saduaIayI [PI0T Hh et saouasayiq, [vo07J et aane[ay jo uonnqmisig we aanepayYy jo vonnqisiq | ; T bas ' cae; AI NYYOVIG II] WYYOVIG | | ' | iets ee ee i= gf _ s- 9- 2- g- z r vs pe | (aa) - \ | \ | z y ] 7 z \ | | | | A \ | ' | (ae e | \ | | é ® | | 5 i 7s | T 9 : I } lt i t e) = L 4 ij L \ i \ 1 | | 8 ‘ 4 + | 8 \ | | 6 ‘ ; + ' 8 rer Lo QaIn2 03 i i or CIB oe uonjenby 4 : ot up LEA _ 3AIND 0} (Ajunor v \ i ech = ce vonenby a spuasaiga aavnbs yovsz) 4 | 11 \ YMIVH Gay oy YVIVH UVa | at skoq — saiunosy shogq — sarunosg Val saouriafiq, [Roo] SI Sous, [Loo7T Ht _—— sl aanepay jo uonnqiasig DANL[IY yo uoNNquas \ eT . l u J ar ut : 'd ‘ $I I] Wvuoviq ] WYUDVIG Plate XVII. Part Il. Biometrika. Vol. VI. LZ = =f one YIVH MOVIE Lal s[4tp — saljunoy saouaayiq, [eI0'T JAQR[IY jo uonngWastcy IA WYUOVIG 2xry-9 PAIN 03 uonenby YVIVH NOVI LAL skoq — saijunog saouasayIq [e907] aanrpyY jo voNnqysig, A WVUOvVIG Plate XVIII. Vol. VI. Part Il. Biometrika. a JAIN 03 ce uonenby UIVH WAVG sj4ip — sajunoy Sad [PIO'T aanyay jo uonnqimisiq XK WYUDVIG 2zve_o = YWIVH WOIdAW s]4ID — saunos saousIayIq, [eo0T XI WVvaDvId LTA fr 28in> 03 ce uonenby sanjay jo vounquasiq LEA = aAINI OF 2ey-9 ce el uorenby WIVH dday s}4Ip — sanunos SaIUAIFFIG [e207 aanerjay jo uonnqiuysig IIA WVYOVIG DAINI 0} zz 4-9 “ee uorjenba MIVH UiVA s|4ID — saiunos saoudtof{id [e907 DANE[OY jo uonnqtysiqd IA WVYYOVIG Plate XIX. Vol. VI. Part Il. Biometrika. = 5 | | | | i | LEA =; QAiIN2 03 ee =" uonenby SHAY WAV ssoq — sanunos saduatayiq [e207 aaneay jo vounqiasiq AIX WVYOVIG zzr¥_F LEA QAIND 03 22 y¥-9 ce =f uonenby SHAq WOAIGHUW ssoq — sanunosy saouaiayiq [vI0TJ aanreay jo uornqiuasiqd HIX Wr¥ovid CITT \ \ | H 1 | r2¥-9 ce =f uonenby SHAQ LHOITI skoq — sainunos saduatayiq. [vo0'T aaneaYy jo uonnqisiq IX Wvudoviqd LEA aAin? 03 ze¥_9 “ee uonenby 4 SHAY ANT skogq — saijunosy saouaIayiq, [vI0'T aanepay jo vonnquasiq IX Wvyoviqd Plate XX. Part Il. Biometrika. Vol. VI. sAle [OY Jo uonnqliysiq IHIAX WVaoOVIG | 6 or LA — fr 2Asn2 03 1 i Cue aAINd 03 22¥-9 “eg. a uonenby 1 if It zx ce uonenby y q SHAD WAV 1 af | zt SHAY WOIdCHW s]4ID — sarunos eae, s|41p — sanunog sa0uslayIq, [e207 r TH el saouaiayiq, [PI0T sAlefay jo uoOHNqyAsiC, IAX Wvuovig LTA — fp 288m 03 2ry-9 “Ce — uonenby SHAH LHOIT s|]4ID — saijunosy SaoUdIafIC jeooT dANRIY fo uolNniysiqd IAX W¥¥dvVIG €t cas “£Z sontin ame SHAT ANT s|]4ID — sanunog saouaiayfIiq] [P90] aanrjay jo vounqisiqd AX WYYOVIGd Plate XXI. Part II. Vol. VI. Biometrika. ‘moog eAq ul Kouessealg—syaly “INO[OD sey ul AouasI0AIg TITAT AVIV *SUOJIAUT pue MOSSEL Jo}voIy ae: —S[ly ‘suodIAUy pue Mossepy J TAT IV eae are edt) ‘anojo9 eAq ul Aouass Ad IN | 100 (09 10 | On bo to) = “dNo[oD arey ul Aouesuearg ealq—shog TIAT SVN —skog ‘suodiAuq pue Mosseyy Ja}veds) “AT AVIV Plate XXII. spieadn Gg 1 GS dey pyy —sf[dty ‘“suodIAUWT pue MOSSEL) da}eody : : poy — shog “SUOJIAUT pues MOSSEL) dayeody ‘TEXT dV ‘IXT dYW QO} spsemdn al Bs) MH ia} Ay aa S Oo > 3 4 q YY vo = aS ea) S IVY IeJ—sp) ‘suodiaAug pue Mosse[y Jayeouy ; dey atey—skog ‘suouiauq pue Mosseyy seyeody ‘XT dW XIT 4VQq Plate XXIII. Vol. VI. Part II. Biometrika. dey ydeVq — Sty dey WNIPeR| —s[uty *SUOJIAUG PUB MOSSIN JojBeIy “TAX IV ‘SUOJIAUq pue Mogseyy Je}eodt) ‘AIXT IV dey yseq —shog ajeyH UINnIpey, —sfog *SUOUIAUY PUv MOSSEID Jo}veIN ‘AXT 4¥N “SUOIIAUT pue MOSSEIN Ja}ved4) TIIXT AV Plate XXIV. Vol. VI. Part II. Biometrika. sokq on[g—sdly ‘SuouIAUA PUue MOSSEL Ja}KeI5 qyeH Hoel JeL “XXT dC SHI) ‘suod{Aug pue Mogse]y Ja}Bedy ‘THIAXT dV spsemdn C.g GSE 3C% Go AGT GT 23¢0+ GO-92¢C0+ GT-—190-— G3 -—-9 GT— GE-— 1 C-%8-— spsemdn G.g — sek onjg—sAog ‘suouiAug pue MoSsely Jo}eodN “XIXT 4VV aey yoVlg yer—shog ‘suowjAUg pue MoOssE[y Ja}e0Iy TIAXT dV / ‘ : - if ‘ f a : i ce Le ‘a Pe ps " a x coe ’ = e : ; : “2 eign = i : Plate XXV. Vol. VI. Part II. Biometrika. sefq wnNIpep — sui sek 14311 — SIM1D ‘suOJIAUq pUe MOSSEID Ja}Bedy AIXXT 47¥W ‘suOJIAUg PUB MOSSEI JoBedy ‘TIXX1 4VN spsemdn ce 0 GS 91 02 QO} o 3) oO spsemdn v € G T 0 T z € v sefq wnipeyy — sfog ‘THXXT AVI soky 343r] — shog “SUOUIAUT PUB MOSSE] Ja}vedy GY ‘SUOQJIAUY pus MOSSEL) Joz8Od ‘TXXT dV Plate XXVI. Vol. VI. Part II. Biometrika. if vauy, wysynans HLnos vauVv J . Nvsungns dnowo VaIYV N Ph NOLTVS vaynsns1sva “ss, ‘vaguv NvsZngns HLYON (HIAXXT @2PF yuM asvdusod) spasy upgingns Suimoys ‘doy day *“SUOJIAUY PUB MOSSE Jo}VI19 THAXXT 4VW ‘SUOJIAUg pue MOSSE] Jo}eeIy TAXXT IV sekq yleq—saiy 77a MHL08 ONVIMNOW O10 spsemdn C.g GE 3G6 GE 1GT 0160+ a1G¢O+ 2¢-0= b 1G .T— Gos 1 GS spsemdn c.g — sokq yaeq—shog HOONNOWUVO ONWISNGWY ADtetved dnowo NOLqWS paaanae “so” ‘NOLO274L3H8 TIHAWYA w3aavo WOIMLVdTIM MAIN WOIWAVETIX GI0 MOONUBOIVE saysiipd Buidjjno pup Surdnos8 4719 Suimoys ‘doy hay ‘SUOIIAUY PUB MOSSEL JO}veIy ‘TIAXXT AVN "SUOJIAUT PUB MOSSETD 19}BOID “AXXT 4VW fs ~ < = J. F. TocuHer 233 MAPS. Pi. PL I. Key Map, Districts and Counties. I. XLIV. Hair Colour, Local Diver- Il. 5 Divisions, Counties and gencies, Girls, Counties. XIII. Chief Towns. I. XLV. Density of Population in Non- Divergent Counties. 3 DIvistons. XLVI. Density of Population for IIT. Fair Hair, Boys. Ill. each County in Scotland. __,, IV. * Girls. 55 XLVII. Hair Colour, Local Diver- V. Red Hair, Boys. a gencies, Boys, Districts. XIV. VI. = Girls. ; XLVIII. Hair Colour, Local Diver- VII. Medium Hair, Boys. IV. gencies, Girls, Districts. " VIII. 5 Girls. ; XLIX. Eye Colour, Local Diver- IX. Dark Hair, Boys. 3 gencies, Boys, Divisions. re Xx. ‘ Girls. 5 L. Eye Colour, Local Diver- XI. Jet Black Hair, Boys. V. gencies, Girls, Divisions. s5 XII. 5 Gils. 5 LI. Eye Colour, Local Diver- XIII. Blue Eyes, Boys. % gencies, Boys, Counties. XV. XIV. 3 Girls. 5 LII. Eye Colour, Local Diver- XV. Light Eyes, Boys. VI. gencies, Girls, Counties. XVI. ‘5 Girls. 5 LIII. Eye Colour, Local Diver- XVII. Medium Eyes, Boys. % gencies, Boys, Districts. % XVIII. A Girls. 9 LIV. Eye Colour, Local Diver- XIX. Dark Eyes, Boys. VIL. gencies, Girls, Districts. XX. _ Girls. % LV. Glasgow. Boys, Divergency in hair colour. XXTI. CouNrIES. LVL. », Girls, Divergency XXI. Fair Hair, Boys. oe in hair colour. i XXII. “ Girls. 5 LVI. » Boys, Divergency XXIII. Red Hair, Boys. VIII in eye colour. 5 XXIV. 39 Girls. A LVILI. » Girls, Divergency XXYV. Medium Hair, Boys. Ps in eye colour. 5 XXVI. - Girls. a LIX. » Boys, Fair Hair. XXII. XXVIII. Dark Hair, Boys. IX. LX. » Girls, Fair Hair. 5 XXVIII. 5 Girls. 4 LXI. » Boys, Red Hair. ‘ XXIX. Jet Black Hair, Boys. 3 LXII. » Girls, Red Hair. + XXX. ¥ Girls. 5 LXII. ,, Boys, Medium Hair, XXIII. XXXI. Blue Eyes, Boys. Xx. LXIV. » Girls, Medium Hair. _,, XXXII. Girls. 5 LXV. » Boys, Dark Hair. .; XXXITI. Light Eyes, Boys. > LXVI. ,,_~—- Girls, Dark Hair. 7 XXXIV. _ Girls. : LXVII. ,, Boys,Jet Black Hair. XXIV. XXXV. Medium Eyes, Boys. XI. LXVIII. ,, Girls, Jet Black Hair. ,, XXXVI. 55 Girls. 3 LXIX. 4, Boys, Blue Eyes. ¥ XXXVII. Dark Eyes, Boys. 3 LXX. » Girls, Blue Eyes. . XXXVIIL. 5 Girls. FA LXXI. ,, Boys, Light Eyes. XXYV. XXXIX. Fair Hair, Boys, Districts. XII. LXXII. ,,. Girls, Light Eyes. 7 XL. Red Hair, Boys, is LXXIII. ,, Boys, Medium Eyes. ,, XLI. Hair Colour, Local Diver- LXXIV. ,, Girls, Medium Eyes. _,, gencies, Boys, Divisions. __,, LXXV. ,,_ Boys, Dark Eyes. XXVI. XLII. Hair Colour, Local Diver- LXXVI. ,,. Girls, Dark Eyes. % gencies, Girls, Divisions. _,, LXXVII. ,, Key Map. rr XLII. Hair Colour, Local Diver- LXXVIII. ,, Key Map with Sub- gencies, Boys, Counties. XIII. urban areas. a Biometrika v1 30 234 I. Il. IIL. IV. XIV. XY. XVI. XVII. XVIII. Pigmentation Survey of School Children in Scotland DIAGRAMS. Distribution of Relatwe Local Differences. Pl. Boys, Fair Hair. XVI. IX. » Red Hair. 5 X. » Medium Hair. ¥ VI. » Dark Hair. x3 XV. 5 Jet Black Hair. XVII. XVI. » Blue Eyes. XIX. XVII. », Light Eyes. 3 XVIII. » Medium Eyes. 5 XIX. », Dark Eyes. 35 Girls, Fair Hair. XVIII » Red Hair. 3 TABLES. Page Analytical Table of Hair and XIX Eye Colours 132 Schedule ; : 134 XX. Counties (with Districts) 138 Returns Received . 140 XXI. Class Ranges . 146 Colour Distribution of Booteish XXII. Children 147 Relative Local ipteronces 148 XXIII. » ” ” 149 ” ” ” 150 XXIV. County Specification, Fair Hair, Both Sexes 5 its. County Specification, Red XXYV. Hair, Both Sexes 153 County Specification, meth Hair, Both Sexes 154 XXVI. County Specification, Dane Hair, Both Sexes . 155 XXVIL. County Specification, Jet XXVIII. Black Hair, Both Sexes 157 County Specification, Blue XXIX. Eyes, Both Sexes . 158 County Specification, Light XXX. Eyes, Both Sexes 159 County Specification, Median Eyes, Both Sexes 161 XXXI. County Specification, Dan Eyes, Both Sexes 162 » Light Eyes. » Medium Kyes. » Dark Eyes. Pi. Girls, Medium Hair. XVIII » Dark Hair. 5 , vet Black Hair. XVII. » Blue Eyes. XX. Relationship between Density and Other Characteristics in Population. See p. 189. Divergency in Hair and Eye Colour, Divisions Divergency in Hair and Hye Colour, Counties Divergency in Hair Colon Districts Divergency in Eye Colone Districts Comparative Population . Divergency in Hair Colne Divisions, Counties and Dis- tricts . Divergency in Eye Coleud Divisions, Counties and Dis- tricts . Interlocal Constanta Coloue Heterogeneity Heterogeneity in Colour Probability Table, Hair and Eye Colour Excess Positive Frequencies peculiar to great Divisions. Correlation Table, Gaelic Population and Jet Black Hair . Correlation, Hair end Byes with Gaelic pee a lation Densinies of the Page 165 166 167 168 169 171 174 176 177 178 180 183 183 J. F. TocuEr XXXII. Density of Population, Divi- sions . XXXIII. Foreigners in each great Di- vision XXXIV. Correlations, Foreigners and Density XXXV. Correlations, Density and Pig- mentation and Foreigners and Pigmentation : XXXVI. Density and the Death Rate . XXXVIIL. Correlations, Death Rate and Pigmentation : XXXVIII. Colour Distributions, Ivish, English and Scottish Adults XXXIX. Correlations, Births per family and Pigmentation : XL. Associations, Colour Classes in the same Regions. XLI. Classes, excesses of which are found together in the same Regions : XLII. Relationships Beiyean: Pig- mentation and certain De- fects XLII. Relationship Reuveen ths Gee lic speaking Population and Defects XLIV. Degree of Resemblaties te tween the Boy and Girl Populations XLV. Observed and zpened Re: sults, Glasgow and Govan XLVI. School Board Districts and Schools in Glasgow Page 185 196 198 199 200 202 XLVII. XLVIII. XLIX. LXI. LXII. 235 Page Pigmentation groups of Greater Glasgow 203 Frequencies of Colour Classes in Greater Glasgow . 204 Relative Local Differences, Greater Sa! and Envi- rons 205 Divergency in iar and Eye Colour, Greater Glasgow and Environs 206 Specification of the Gieater Glasgow Population 209 Condensed Specification of Greater Glasgow Population 210 Number of Persons per square mile in Chief Towns of Scot- land . 212 Population in 1901 of Chief Towns in Scotland 213 Foreign Surnames in Glasgow 214 Colour Characters of Foreign Immigrants in Glasgow 214 Colour Distribution of Chil- dren of Irish origin . 216 Percentages of Children of Non-Scottish origin . 216 Relative Difference between East Aberdeenshire in 1896 and 1903 : .. 219 Comparative Table, British and Foreign Data - 221 Hair and Eye Colour, City of Aberdeen : . 224 Correlation, Hair and Eyes, British and Foreign Data . 225 30—2 VARIATION, DEVELOPMENT AND GROWTH IN HOLOTHURIA FLORIDANA POURTALES AND IN HOLOTHURIA ATRA JAGER. By CHARLES LINCOLN EDWARDS, of Trinity College, Hartford, Connecticut. CONTENTS. Page I. Introduction . : 238 E. Pedicels and Papillae . A. History. Conclusions anounced a. Distribution per sq. cm. . in this Paper . : 238 b. Development and Appearance . B. Material and Methods of stnaee 239 c. Warts é : Il. Holothuria floridana Pourtalés . 241 1. Distribution of Warts : A. Body . : : : : . 241 2. Number of Warts on Sides of a. Form : : : : . 241 Bivium b. Size . : ; : . 241 d. Papillae around the Anusl 1. Length in cm. ; : . 241 Distribution of Papillae 2. Diameterincm. . ; . 241 around the Anus 3. Volume in cm? . 2 . 248 F. Thickness of Body-wall Bb. Development and Growth . . 243 G. Calcareous Spicules of the ia C. Colour. : 244 wall : : : a. Living and csale Snecinene 244 a. Tables 5 b. Methods of Determination . 244 1. Development of the Table ce. Colouration . : . 246 2. Structure of the Table . 1. Pedicels and Papiline : . 246 3. Variation in Crown and Ver- 2. Distribution of Colour on the tical Rods. Body : : . 247 b. Tables of Bivium and iene D. Tentacles and Auncalae : . 248 in H. floridana a, Symmetry in Arrangement of 1. Disc Tentacles and Ampullae . 248 2. Height Variations from the Sym- 3. Crown : : : metry of the Tentacles of c. Rosettes and Rosettes with the Mid-dorsal Interradius Holes in Relation to the Attach- ment of the Mesentery . 248 b. Number of Tentacles ; . 249 Variation in the Number of Tentacles and the Relation of those present to the Normal Symmetry . . 249 c. Branches on Tentacular Am- pullae and Variation in their Number ; 4 . 251 . Variation in Size of Mentnclea ~ vas) e. Development of Tentacles . 252 d. Perforated Plates 1. Development of the Parton rated Plate 2. Structure and Variation of the Developed Perforated Plates e. Number of Rosettes and Pee forated Plates f. Correlation of Rosettes and per forated Plates with Ad- vancing Age 262 263 263 ERRATA. P, 243. Table VI. Last column, the volume should be cubic mm. not cm.? as printed in text. P. 295. C. Additional Characters of H. floridana. Growth. The volume of the embryo in the first four lines of this section should be given in cubic mm. not em.? as printed in text. ro ree! 23; Ror yew isp fA A ape E GC. L. Epwarps H. Calcareous Spicules of the Ambu- lacral Appendages and the Dif- ferentiation of Pedicels and Papillae a. Form Suckers End-plates Supporting Rods 1. Dorsal . 2. Ventral. Association of Forms of ‘Aunbulae cral Appendages with Types of End-plates : f. Association of Suckers mith Types of End-plates g. Association of Supporting Rods with Types of End-plates h. Conclusions and Definitions The Calcareous Ring . Polian Vesicles Stone-canals and Madrepor ited Gonads Respiratory Trees The Enteric Canal Habitat : Hlolothuria atra Jiger . Body . a. Form b. Size. : 1. Length in cm. 2. Diameter in cm. . 3. Volume in cm.? B. Colour . a. Colouration 1. Pedicels and apis 2. Distribution of Colour on the Body : C. Tentacles and Ampullae a. Number of Tentacles Variation in the Number of Tentacles and the Relation of those present to the Normal Symmetry . b. Branches on Tentacular Am- pullae and Variation in their Number ‘ D. Pedicels and Papillae . a. Distribution per sq. cm. : b. Distribution of Papillae around the Anus E. The Body-wall Pe ee @ = fa goes tm PA Page 278 279 279 279 280 | 280 Bo ¢ Oo a. Thickness in mm. b. Pits . F. Calcareous a mrentes of the igekie wall . : ; : a. Tables b. Tables of Bivium a Aue in H. atra 1. Disc 2. Height . 3. Crown . : : : c. Rosettes and Rosettes with Holes . Number per sq. cm. Calcareous Spicules of the enna: lacral Appendages and the Dif- ferentiation of Pedicels and Papillae Form Suckers End-plates Supporting Rods Dorsal ; e. Supporting Rosettes ane sup porting Plates. Ventral . = f. Association of Form of Ambu- lacral Appendages with Types of End-plates in the Bivium g. Association of Suckers with Types of End-plates h. Association of Supporting Rods with Types of End-plates i. Conclusions and Definitions The Calcareous Ring . Polian Vesicles ‘ Stone-Canals and Mecroporites : Gonads Respiratory Trees The Enteric Canal Habitat Summary Characters separstng H. fort. dana Pourtalés (=H. mexicana Ludwig, HZ. africana Théel) from I, atra Jiiger Characters Common to itie TWO Species Additional Characters of H. for t- dana Additional Char Beles of H. atra Literature cited . Explanation of Plates 238 Holothuria floridana and Holothuria atra I, INTRODUCTION. A. History of the Subject. Conclusions announced in this Paper. Pourtalés, 1851, p. 12, described the Holothurid from the muddy flats of the Florida Keys as Holothuria floridana. This was recognized as a valid species by Selenka, 1867, pp. 324-6, Pl. 18, Figs. 47-50, but this author probably included part of H. atra Jager, 1838, pp. 22-3, Pl. 3, Fig. 2, in his foridana. After inves- tigating a good number of specimens from Florida and the Pacific Ocean, Selenka notes differences in (1) size of calcareous ring, (2) number of ventral pedicels in old individuals, (8) size of end-discs, and (4) number and size of stone-canals, but he concludes that such differences, being only of relative size and not of form, give no ground for specific separation. Semper, 1868, pp. 88, 92, 278-9, made of Selenka’s atra the variety amboinensis and gave the floridana of Pourtalés as a synonym of H. atra from Celebes described by Jager. Since then all authors have followed Semper in relegating H. floridana to the synonymy of H. atra. Ludwig, 1874, p. 101, described H. mexicana from one small specimen (6 cm. long), without gonads, in the Hamburg Museum under the rather indefinite locality-label of “ Mexico.” Clark, 1901, p. 258, identified specimens from Porto Rico as H. meaicana Ludwig. I have 10 of Clark’s specimens included in the series from which my statistics were taken and they are in all respects like the average H. floridana as determined in this paper. Heérouard, 1902, p. 8, identified 2 specimens from the Azores as H. meaicana, although in some doubt from the fact that the spicules had been dissolved. Clark, 1902, p. 530, places specimens from Clipperton Island under H. atra (Jager) but is “confident that no less than three distinct species are now included under that name.” Théel, 1886, pp. 174-5, Pl. 8, Fig. 7, described a single specimen from Simon’s Bay, Africa, as H. africana, and at the end of his description said, “The species in question is possibly identical with Ludwig’s Holothuria meaicana.” In view of the facts established by my studies, I believe we must confirm Théel’s suggestion in making H. africana and H. mewicana identical, and further that the species common from Florida to the Caribbean region is distinct from H. atra and there- fore, to designate it, the name H. floridana Pourtalés should be re-established (Edwards, 1905). The small individual described by Ludwig is, without doubt, a young H. floridana, and so H. mewicana Ludwig =(H. africana Théel) becomes a synonym of H. floridana Pourtalés. The validity of Semper’s variety amboinensis was questioned by Ludwig, 1883, and denied by Lampert, 1885, and Sluiter, 1902. The last author examined a series of 21 specimens from 12 localities, and found all the intermediate stages ©. L. Epwarps . 239 “ from H. atra to the variety amboinensis. My studies show that the characters - given for the variety have no validity. B. Material and Methods of Study. The material subjected to a statistical analysis for this paper includes 138 specimens from the collections of the U.S. National Museum, the Museum of Comparative Zoology, Harvard University, and my own series. For their courtesy in placing specimens in my hands for study, I desire to express my thanks to Dr Richard Rathbun, Assistant Secretary of the Smithsonian Institution, and Dr J. E. Benedict, Assistant Curator, Division of Marine Invertebrates of the U.S, National Museum; and to Dr Alexander Agassiz, Director, Dr W. McM. Woodworth, Assistant, and Dr H. L. Clark, Curator of Echinoderms, of the Museum of Com- parative Zoology, Harvard University. I would acknowledge my indebtedness to Dr Charles B. Davenport for his counsel, and also express my appreciation of the skilful and conscientious aid rendered by my assistant, Mr Hubert Dana Goodale. The various taxonomic characters have been analysed by the biometric methods whose development and application to biological problems are due so largely to the work of Francis Galton and Karl Pearson. In biometry it is important to separate the young specimens from the adult. In the Holothuroidea it is evident that both length and breadth combined in volume must be considered in judging the age. The formula, volume of cylinder = 7lr?, was adjusted to the more or less shrunken body of the alcoholic specimen and its natural departure from the cylindrical form, by the measurement of the volume of ten individuals in water displacement. It was thus found that the average actual volume is 50 per cent. of the volume estimated by the above formula. Hence I have used the formula we to deter- mine the approximate volume of the specimens studied. Mitsukuri, 1903, pp. 13— 19, concludes that individuals of Stichopus japonicus Selenka taken during the spring and early summer divide themselves into three lots; (1) the adult, (2) the second-year young and (8) the first-year young. From Mitsukuri’s tables, in which lengths and diameters are given, I find with the formula ae that the average volume of the “second-year young” of Stichopus japonicus is 113°99 c.c. Mitsukuri concludes “that Stichopus japonicus reaches the adult condition in two whole years” therefore the “second-year young,” while not sexually mature, are of adult rather than young size. The average volume of the “ first-year young” is 43°16 c.c. In H. atra and H. floridana I have included in the adult category all of 50 c.c. or greater volume™, realising that such an exact line of division is, to a certain extent, arbitrary, and yet that it is near enough to nature to give in a broad manner the average adult characters for comparison with those of the first-year young. Since it is possible that some of the specimens included in the class may * One specimen of H. utra, volume 49°46 c¢.c. is given as adult. 240 Holothuria floridana and Holothuria atra be slightly beyond the first-year I will use simply the general term young to designate the group. Mitsukuri, 1897, demonstrated that with advancing age the spicules in Stichopus japonicus change so much that “the form distinguished by Théel as var. typicus is only a stage in the growth of the species,” and from the results of my work I would emphasize Mitsukuri’s conclusion as to the important bearing such facts have upon the description of species and the classification of Holothuroidea. Ludwig, 1898, found in Phyllophorus urna that the spicules pass from an Elasipod larval stage to the typical generic type and then, in old age, to secondary rosettes. This author (1898a) also proved in Cucwmaria laevigata a change in the spicules with advancing age. Ostergren, 1898, believed that Holothuria aphanes represents the young of Holothuria impatiens. The spicules of the former type disappear in the larger specimens and then later are replaced by those peculiar to Holothuria impatiens. Of the 138 specimens available for this paper, 118 are H. floridana Pourtalés from the Bahamas, the Florida Keys, Tortugas, Cuba, Porto Rico, Haiti, St Thomas, Swan and Curacoa Islands, Caribbean Sea, and 20 are H. atra Jager from Zan- zibar, Mozambique, Arabian Sea, Marshal Is., Samoa, Society Is., Tahite and Hawaiian Is. After completing this study, I have examined specimens from the Galapagos Is. now in the collection of Dr H. L. Clark, which thus extends the range of H. atra across the entire Indo-Pacific Ocean. Simon’s Bay, at the Cape of Good Hope, the locality of Théel’s H. africana is beyond the reported limit of H. atra toward that of H. floridana. Adopting H. africana as a synonym of H. floridana it would be interesting to learn whether this species occurs at any places between the southern point of Africa and the Caribbean Sea. To facilitate comparison, under each character studied I have placed side by side the values for adult and young of the biometric constants, mean, standard deviation or index of variability, and coefficient of variation, each followed by its probable error (+) and at the end the total range of variation of the character. The formulae as given by Davenport, 1904, were used. For graduated variates and integral variates with a class range of more than one, the classes are named from their middle values. For graduated variates with a class range of one, or less than one, the classes are named from their minimum values. The adjectives dorsal and ventral refer to the bivium and trivium respectively. The data for H. floridana are presented first, then those for H. atra together with comparisons between the two species. In the summary are given the differential characters which define H. floridana Pourtalés and H. atra Jiiger and upon which I base the re-establishment of the former as a valid species. Finally there is a brief résumé of the additional facts concerning development, growth and variation in common for the two species and then such as are peculiar to each, ~~ a wi? we) ee | He a ae & as eh by | BO) ee / sy te ae coe aa lao } ay of We hee tm. | 9 BB yyy 3) at oer ae yy) 8 a . gf bby Oe nt a Sj e) | od oa ei 4 ) 6S oo & ar a ty ath | ee aa Re de: me ie eet a iL | ge Ti oe ee, Sones: oY ei, te 8 =) Be a of @ | of OR Or fee) oe |e Kota) Ph oR Ube os Ore é ha oe, rn | = ata ty Fe Bh eg de) “Tae & a a a a Lat be COL SS y heyy BT P echoe ) v x e 1 Rc! — a 2 Q' le te Se i OL ee -b.T Sel ATtOL ar «ot isl) EE ae te 0% of teed nent) aS Se eG en A fe oe | a! ee oe | ees > a eS ef c Og eh é aD fe | @ ee OT ef i og) ates a7) ut eh age MP 18 _ “ < " 7 Rearins yet} FOR ON a Se ob OR é | Oss ia = | @IVOl Sf. | & é ef Ore pi Ty Nae 8 ie rt) t | aa Oe | VE . og re f wise 1 Fo Te Mo 5 a a c Cf) | aT BS a rah B x 4 | é O£ wd 7 a a 3 = oe yas og Oe So | tae of é = Ai at Af Orb a Ge | Te | 6 = b Qt ors is areiee F igiasik Se — 5 | ne he ra dy Wel Pode G = e | Of oe Wy ey atthe |e - é OS. daoaes h ag it é ae Bl ere, Pye be |. 08 iy 18 ad Soe ee Mane. ee hae | "ee _ j | Of 4 eae a Sa IF & = a | oe oo Wi PRs |) re é e |, & Ort a GR Su i | Sari LFA ca | 2 Ala v ee OO EON te OF the Peer ee 0: ett: i MereOl auaresRe tod he I SUN | at i oebetet 1 OS Mpeg Gs ik She | ue e EN RECS? FO |) STOR NG, |) OMB | | IRN || AINE) we Ve | Med ng cea ab || @ 0" | 08T | leaky 4| Rate Ol We ee O08 a ec ) 1 eS a a eee na QL See eee Rem eas Pk tiene ae pa cl > ob 0g, ae a TO t» BS, 4] wet j ApoeT |) “08ch we Bk Fy Og SO Nite || BN | Aaa es ; navn ) geil rane nica mae nek, forsee ieee - er oe” er — alee eee | Taper Set Ne ete re | Og ae Dive dois ho SP [RO OF ora Me ae bf fi > pa) ies © ah 9 ig BiG oa 4 | 66 7 wl as Syaer | ek |) o& é af Oe § | Se Le BE Beta rae: |) tT ye es eas Bo) |p Rat) Sa e a. Ea é is Om | a yi) Ie) 148) Be Wn Nee {l y Py Peds) 8 x 3& ae oy | SS 4] OF @ 4) 8 2s08 OE ox it ve él roay | (Os , &T ~g | og ab F ON ae CT 5 — j a . =e _. —- fe cael a OGY | OF | 41 a a Oe hh a re && GE my Sea gt é Og Ob é £9 | R& | Ke a ee i =e awe aS) ws & | pa = = ROOT ae er | $e) 2 20Re Sa. ite 3 aD Pas iy Ye. Sc | Gf Ov 3 O08. 7 4 P08 Of | S| BI be cae Scant ie —- —— ! 4 3 ; v2) (O08 | eI 216 | | ae | (eh | 8d | DE 1 as eat ieee Adee er ae) Be ieee oe oa | = — — a { | ~ ice ail a ee ral { is | | fea VE SNE AEA SS CE Oe 0 De oe eee oe Vee esinogotbscn (e19ve8 wad (@\ athyt winor inert ont @ vet elonso-duede € SA out) Quit anosuole ,* et yeahs Bi dash worl shiovst basvisH add god “ecbuatie” odal obi 88--0\ 5 umneeeil dos, Inia AZS* « BBY CBG doo), ena0s ASG ag od eto S18 ewsbiol ws) spabinvlll ~e—fa) Qa E ee renee a Cit SenRAoN 82 M8). y eB Ao. dank ase So : somnay® ae eats derbies Diba wld, Lge lesth ity ge zeal LembitnA iA bits: bie as ea Dy "rid noe} ig ! Biometrika, Vol. VI, Parts Il and III TABLE L TH, floridana Pourtalés, Adult. i Pours Vestcues Sroxe Casars | Paptona:axp Parintae ; | — = | -| Nomen * Museum Nowpen Disruturios if Average Nostoen oF In Tofts In Tafts with Branched Vesioles Solitary ‘Total Number Length mm. Number Length PEN SQ. Cat. Thick- Wants: eet = ee = — = Sorinl | Length | Diameter | Volume | ness of | Sex = 5 | eas |S Pe eae || Ee Number Number | Namber of Branched | Simple , | mm. Number| of | Number |ofSimple| Branched | Number | | Vesicles ; Groups US. of | Vesicles! of | Vesicles | Vesicles | of Vesicles |Branches| and | Greatost | Least | Right | Left | Totals| Greatest | Average | Tentacles | of Anal | Dorsal | Ventral | National | Harvard | Edwards Tatts | ineach | Tufts | in each | in each |Branchos} Number | Nuaber | Number Branches! | Papillno Musoum Right)! Left pr poses | enor Vesicles |Branches| Vesicles | — — - == - ——— = i} = = = = 1 | 13 | 10 | 93 10 65 19 5 12 a7 = = 1 0 | 76 | 40856] 50 | 9] 0] oO = = = 1 13 1 2 13 15 37 a 3 ¢ ; 1 5 2 190 58 | 35100) 40 | 9] 15 | 17 1 : — — - = = — 3 8 — ~ 37 8 | Ran ES B 70 20 & 3 aL - 2 Sollesa loge Sassi ca all ell = = = = = = 1 nl RB 16 5 | 30 40 2 | 33 | 36 | 69 6 40 20 i 22 er || = = 3 ~ 1 2 = = = = = = = = — = = = = Sa | — 1 2 = = - _ = = || aul — — = — = a= | = if 18:3 so |1906| 50 |9} 0 | 0 1 = = = — = — 3 27 = 23 2 | 10)| 19 | 29 13 85 20 6 12 21 = = On 1 = = = = = =, a a = = se aes au = zt = pa BS ae | — as, — — = —_ — 1 = = = = = = = = = = = = || = = = = 1 — _ _ = — = = = = — = = — = = — = _ — }- Ss = 5 2 — _ = 1 5 = 6 5 ll 13 7 20 30 21 16 6 18 i — ob 6 160 ¥3 3 x | x 1 = ma = = = 1 5 - = 20 25 eal || 16 6 *5y ||| 18 5 16 V7 — = Oc 1 — = - — = - ~ = - — —|- = = a = = _ - 7 z = = - — - = 3 3 = a ld 2 10 15 wa 20 6 WW 23 = = Oe ae ao 5 Sls = = = = 1 1 = = wy | — |u| 2 9 6-0 20 5 1G BA = da Nl tos 26 |¢} x | x — 1 — 1 1 — = 2 4 2 6 19 4] as | 18 10 1-0 2 | 5 | 18 al = — 4b 1 1 = = = = = = = = || = = = = =A) = = = ye = = = — = 1 1 3 4 1 5 21 2 | 35 50 4 20 4 | 16 2 — | de x8 AS. a g _ e 2 2 1 = = 1 2 9 4 4 45 30 i 16 20 21 20 5 10 2 = dd = 3 3 = = = = = as ees = = = = | Be pat = = = = = ES 2 4 = — 1 1 = = = = = Ss = - - = = = = | Hell See 2 ee | Se alee all Sp | S| Sialtenllarelern less) ata lie re 4:5 | 120°88 g 5 6 1 2 = = = — 1 1 2 5 1 6 23 50 2 6 } 38 ay = = te ; = = = = = = 0 = = 8 1 8 6 45 5 ; | 33 | Soe 3 "bd ‘ea 1 2 = = = = = = 2 4 = Pa 3) || 13 8 45 15 32 Sill or 16 75 3 | x x 1 4 = = = = = _ 5 15 _ 31 2 15 16 80 12 35 1714 | -- — 1 6 _ — = = = = = = = = =| = = — = = == — _ _ dé | OT 35 é 6 4 4 2 — = = _- 1 3 31 58 8 | 66 22 1 42 8 oo 20 12 35 MW7i4 —_ =— t 3 _— = _- _ sf 5 — —- — — = — _ — _— — _ _ — — _— — 1 4 = = = = = = = = = = = = =| = = = = = | = 2 5 — = = = — = = =— = = _— —-/—|]-/]=— = — = = = = = = 17 23:8 an 167-1 45 6| * * 1 2 1 2 1 2 1 1 20 79 13 92 22 at 16 4 20 at 70 20 6 4 29 14715 _ = 2 3 = 1 1 1 1 — — = = = = |= = = = = 3 4 1 2 1 3 1 1 - —-|- = = | = = ~ 6 = — 1 4 c= a = = — = = =F = — = TT} = = = == = =a 1 7 = = — ~ = = = = — —|/=-|-|= = — = || = = 1s 221 39 40 3 7 6 1 5 1 1 1 i) 1 1 5 3 15 29 1 21 45 66 u 5 12 21 — =— Z 1 1 = = = iW Shad be tN eg P| ee we =e || = a = = 7 = oo}; o} — - - - - ~ _ - _ = - 23 22 1 | 56 | 37 | 83 7 50 22 5 15 30 = 1057 - | 29 es ; g u 7] = - 7 = - — — _ — | 0 98 1 s 6 | 14 7 55 18 | 5 14 29 = ‘a = a | 49 | 150-86 J\g] 7] 10) — = = _ = _ = — — | 19 13 8 | 10 6 | 16 5 40 20 4 12 33 = f = 22 . 12 6 7 =— = = = <= — = = = 2 30 = 10 6 | 16 9 oS 20 4 19 30 a ” _ 2 44 101-1 ¢ 23 38 eles x = = — = os = _ 1 1 = = Et = 9 4 13 6 5 20 i 16 0 = é Ss 0} o = = - = = = - 2 30 1 | 33 | 21 | 44 5 35 20 c 12 2 = 1 es ta i o | o = = - = - = — = = ul 58 3 | 90 | 44 | 83 10 8:0 20 5 16 22 592 - 42 1g] 0] o = _ _ = — 7 7 1 | wo 8 | 18 5 40 20 a |) Ke — = o| oo — - = ~ 3 3 = = 22 Bi) 10 5 | 16 3 5 2 | 6 10 7 - 7a $ 9 8 = = — — _ 1 1 - - ul —| 5 ad 7 i 1 |) a4 20 = ib 2 0 0 _ — - — = = 1 1 — _— 16 = 7 3 10 4 5 | at 22) _— Td — = — _ 2 — = oh 3 63 18 81 10 5 | 1 = — oils las = = = 1 4 22 1 4 6 1 a | 7 a | ay 9 nf = = 9] of] o _ = - = - — 7 9 — = 36 go | 21 5 5 12 7 “ — - ¢ — = = = = - 1 1 — — 23 = 33. 23 56 5 4 } 12 Ww ‘nh = = g ei i = — — = — = _ 4 = — 30 3 21 20 a 5 22 5 10 15 & _- - ay eee Miss = = — = — — 3 3 = = 21 eH eG 9] 1,37 4 19 5 10 26 | 16712 | — — | g|a]a _ = = = = = ~ = 9 40 1] 18 | 1 | 33 6 20 i 7 40 = i = eg} of] o - — — = = = 1 1 _ = 1 1| 7 8 | 15 8 19 5 18 a4 = = ¢| 0| 0 = = = = = = = = 7 4 2 | 46 | 18 | os 1 20 6) |) 16 28 = 7 = 3 x x 1 = = = = = 1 3 = 23 5 4 1 5 4 20 5 18 13 16721 = =_ ? x x —_— = — = = = = 1 1 — 28 — 18 21 39 5 18 4 2 16 16697 = = su | eX x = = = — _ — - 1 1 = = 1G — | 2 4 | 26 4 F 19 4 3 22 = = = Q| 1d] ga) — = = — — — 1 1 = 25 =| 0 4) 13 5 5 20 i 10 16 | 16698 = 0 9 8 5 {) mS — _ - _ 1 1 — 26 — 5 3 7 7 5 20 & 13 23 16699 7 _ ’ 6 |g| 8 | 10 = = — 1 1 = - 28 =| 15 |] n | 36 4 35 20 Cine! 1 | 16697 | — — Ab gd | 10 | 10 = = = = = = = 3 a _ — 32 3) 13 7 20 4 30 18 ay 9 16 3 — = ic 20 |9] 8! 6 = = = = — = = = = v —| 12 6 | 18 7 05 20 5 9 21 | 16892 |) = - aT 3:5) |NbGhll see il! x 1 3 — - = ~ 4 7 = = 38 i |) oe 9 | 92 6 5:0 20 5 9 19 | 16716 | — = is 70 | 9| 1a | 15 — — — - - - - 4 4 - 30 1 9 5 | 14 7 6-0 20 5 13 20 se = = 9 10 | 9] u 9 - ~ — - = = = = 1 = = = |=) a 3 iG 5 40 By) ot ||) 10 20 | 16699 | — - a0 = |2| 0] © = = ~ — a ~ — = = 6 58 1 | 37 9 | 36 10 70 20 |) id 39 = 1061 = a — |¢] 6] 5 - = - = — - — = = 12 40 he) SONI ahh | EM 10 70 20 i 22 32 = 614 = oe 20 a 0 " = = = = = = 2 2 = 26 10 6 5 11 5 45 19 6 16 20 — 405, = 53 15 o = = oa = = = 1 1 = _ 19 = 9 by || Tek 3 25 20 5 10 21 = 36 = bh 30 19) of of = 1 1 1 = on 15 1 16 19 Soy G is | ear lie37, 5 40 2 | 6G 13 25 | 19669 | — =! 55 a) Op = — = — = = 1 3 u 12 3 1s 16 1 {51 | 15 | 66 5 45 19) | 5 ub 18 = = 56 wo |g} o6] 5) — | — | — | = ~ == mM ow} Ss] = S|) apr) || 16 |i eszh||) ie . 20 iS} cea i] es » = as at 156 | 3| 0} © 1 2 - = = = — = 5 7 = = 7 Ue a en et 3 15 19 Ei || bl 1s n = = 58 26 |g] x | x = = = = = = = = 3 3 = = 10 8 | 29 | 98 | 67 id 35 20 4 6 4 = = = 59 LO) 91 cha ests 1 a - - - = _ 7 15 37 = = 22 1) }/783: | 20) | 43 13 65 20 5 13 30 | 19667 | — a 1 6 - = = - = — = = = = = |= == = = = = = = = = = 2 i - = - = - = = — — = = = = = - - co | 207 | Biby || ON kx ise — = = - - — = = 4 4 = = 14 Vf] a | 24 || 35 i : 20 5 13 23° | 19667 | — = Ol V5 | 75) 1692) (051 (0) }) — = = = — — 1 3 6 7 2 9 28 1} 52} 34 | 86 i 55 21 || om 18 | 19672 |) — = v2 | 149 60 |g} 0] 0 = - 1 1 1 1 2 4 7 6 13 19 1) 26 } 14 | 30 8 46 31 i 1 26 e = = 63 16-0 1-0 9] 0 0 = = = — — = |= = 12 12 = = 23 1 28 24 62 3 30 18 5 20 23 19673 _— - Gh 245 6-0 3) x x = = = = = = = = = = = 8 16 9 | 30 22) 62 8 70 20 i i 22 = 132 = 65 324 = 9] 0 oO = = = = = = = _ _ = 29 15 1 43 21 64 5 50 20 5 ug 2 — 74 = oo 327 = her) @ 0 = = = = = = = = = = — 14 iW 1] 35 | 38 | 73 8 70 19 c lL 27 = 74 = oF 200 Cadac |) 2 A a = = = = = = 4 13 — a 20 V] 16 |} 26 } 41 7 50 20 5 10 25 7501 — = os | 196 | BLO} Oa 2 = = = M | 8) =] = |] a 1} %8 | ai |i | 6 | 4s 20 2 Gi) oS il gm) = | = on 72 70 | 33097} 50 | 9] x x = = 3 = = = = = 13 13 = = 31 Giies | so |\ te a re = Fae llierg = = = = 70 | 162 | 73 | 33002} 70 |9] x | x 3 2 1 3 1 1 1 1 1B 31 2 33 16 1 | 24 | 39 | o3 $ 40 20 Cea enls) 2 Gr les = | 3 a ty ny L a B a El 2 33 Ww ie | 2 25 aig » = | 1 4 = = = = = = = = = = = = | Slice = = = = = aur = a u Md 36 73:29) 35 |g} 1 9 = = _ — = — = = 3 3 = = 18 2 7 6 | 19 6 55 20 a 19 36 a = = 72 | 14 | 72 | a1851] 6B |g] oO] Of} 1 2 —|- = = 1 1 10 4 6 20 73 1} 34 | 18 | 62 | 10 | oo 20 0 13 | ner | — = | | = — ad ae a cad ro = er = = ar = or = = =a 738 184 | GO | 36013/ 55 |g] 0] Oo a fe 1 a 2 — — 16 40 2 42 a7, 1} 26 | 30 | 46 9 Fi 21 A 12 26 jaz). = Salk 2 4 = = = = Sa SE ||| a ie = = = = = = = = 1 iy = = = = = = = = = | =- = = =| = = = = = = ze Ps | 1 Hiveee I = = = —_ = — — — —— _ = 1 Missing, + Undiflerentinted. x Trnces. d Some in bivium. i Indefinite, In a circle, In 40 the Polian vesicle arises from the right dorsal radial canal united. 11 has one stone-canal with 2 branches. 32 has an extra ventral tuft of 4 stone-eanals, 1—14, Bahamas, Abaco, Green ‘Turtle Cay ; 15—10, who presented theso specimens, collected in the Bahamas and since Clark, 1899, pp. 122—3, says Jf. floridana does not occur in the Bermudas, Key; 90-38, Babin Honda ; 9, between Salt Pond Key and Stock Ta; 40—49, Key West ; 60-59, Tortugas ; 64-03, Porto Rico; 64—58, 72—73, Curacoa I, ~ Originally 24, 25 and 61 wore identified us Milleria agussisii Selenka ; 50, 52, 53 and 64 as Holothuria floridana Pourtal’s; 64—03 as H. mexicana Ludwig, and the othors of the Harvard and U.S, National Musoums \ SUES es To face p. 239 2 = be _ 1 _ 7 o] ? 7 a - a ae 7 7 - a 7 = 4 7 1 - - [ae ati a me ; ——— i ———— 73 184 = =6:0 | 260°13 5°5 3 0 0 3 2 1 | | 1 3 4 | | 2 4 — | | 1 5 —_— | | ¢ Missing. + Undifferentiated. x Traces. dSome in bivium. 7 Inde united. JZ has one stone-canal with 2 branches. 32 has an extra ventral tuft of who presented these specimens, collected in the Bahamas and since Clark, 1899, Key ; 36—38, Bahia Honda; 39, between Salt Pond Key and Stock Is. ; 40—49, 72—73, Curacoa I. | Originally 24, 25 and 51 were identified as Miilleria agassizii Selenka ; 50, 52, | To face p. 239 | C. L. Epwarps Il. HOLOTHURIA FLORIDANA POURTALES. A. Body. a. FORM. 241 The cylindrical body tapers somewhat more posteriorly than anteriorly and is At the anterior end the mouth is ventral while the anus is terminal posteriorly. As the Holothurid pushes itself along over the slimy whitish coralline sand of the bottom, from the low tide mark to one, or a few fathoms, in depth, pieces of dead water-weeds, small shells and calcareous debris are caught up among the dorsal ambulacral appendages and flattened in the trivium upon which it generally creeps. serve as an excellent protective mask. b. SIZE. TABLE III. 1. Length in cm. Alcoholic specimens measured while straightened out on a table and placed between two glass plates. Adult Young Number of specimens... 73 45 Mean 5D tet esis 17°656+ °390 6694+ 344 Standard Deviation er 4°939+ °276 3517+ 240 Coefficient of Variation ... 29°972 +1°561 52°541+3°736 Range of Variation me 9—32°7 1°7—15°4 Selenka, 1867, p. 325, gives several individuals 35 em. long. TABLE IV. 2. Diameter in cm. Greatest obtainable taken with a pair of dividers. Adult Young Number of Specimens... 73 45 Mean tee areie wile 5149+ °120 1:983+ ‘071 Standard Deviation on 1512+ -084 “816+ °047 Coefficient of Variation ... 29°361+1°640 40°614+2'878 Range of Variation ads 3°2—8'3 6—3°4 Biometrika v1 31 Holothuria floridana 242 “Ia8Be VID “FT SB sdoyjo oy} ‘s9TeJINOg vunprluoy mr.UNYI0)I0FT 8B peyiyuapt AT[eUIsIIO o1eM 1E—eg ‘QoUSPIAOIG MON ‘neVsseN ‘ZS UOI}Ippe UL WNIAIG oY} UO s}IVM OABY 16 PUB 96 ‘T6 “68—L8 ‘TS ‘FL ‘ooeqy WOly T8—PL “eqny ‘eueaey “TT ‘LIT A : ‘seonq1oy, “OTI—FIT ‘qsom Aoy ‘eTI—g6 ‘soy Bova ‘6 ‘Aoy uerpuy ‘TE :oBIeT Aoy ‘06—gg ‘Ay syorTA ‘28 ‘epito,qT edeg ‘gg—eg : epuolg ‘gII—¢eg ‘semueqeg ‘SNIPeL [VsIOp YOVS JO WOISeL OY} UL MOI 9UO SLY QJ PUL SMO [BIO}L] WOT pus FYBIA oy} 09 “SOPOISOA § YIM 4yn} T SBY ETT PUB SopoIseA UBITOT GZ YHA 4jn} T SVY SIT “apis 4J°T oy uo Azoyuesoul ou} iIe9U ST O[DISOA ueBl[od ou} GL Ul ‘aqtugeputr 17 “AT[BsaIop eml0s p “So0ely X “poyeltyueteyipun + *SUISSTUL é = = = TI 8 G 0% G.F G SI | FP Il = 9 T x x $ 0:6 | #9-F€ 0-€ 8-6 SIL = = = 126 9T g 06 0-4 g GI |G L =a eI T 6 Gor | © 0-6 | &8- FZ 8-3 6-L LIL = 18g = 6¢ 61 G 0% 0-7 G 8 F PF j OT 8 8 OL | © 0-6 | OL-6L 0: LL 9IT = L8G aa #9 0€ g 0G 0-T T 8 g G = pp T 10 ont) G1 | 78 GL 0-7 GIL = L8G = 98 GS G 06 0-T 3G Sey, 6 6 6 z 8 6 £ 0:6 | #9-€T GZ 0-8 FIL = = G689T| 06 9T g IZ 0-€ g 6I | 9 I j &% 9 L 9 3 0-T | $6.48 8-3 LOL | &IT = = 6699T| &T ‘al 2 0G GZ g 9. | ¢ Il T 61 91 | & i 3 G.I | €0-0F €-& 9-01 | &@IT = — es GG Fe 9 61 0-T Sj 9 T G = a T IL | 6 ap @.T TI-6 0-3 9 IIT = = - 66 it F 0G 0-¢ € G T P = a 0 8 ¢ ar 0-1 1% GT 6 OIL = — y 61 ial g 0% 0-6 g 91 | ¢ II =a ra T x x + 0-T TL-€L $-G 9-9 60T = == GOLOT| 6% FI g 0z 0-3 G Glan, L T Il F F L 3 0-T L¥- TT 0-3 eh 80L = = ay 9& 8% z 0G 0-T T g T j = F T 8 2 é 0-T | 9F-0 8-0 8-1 LOL = = 9GG) OF 9% G 0% 0-T T 6 g F = j T g T é 0-T | S2L-0 0-T 6-1 90I = = i oF GE G 02 0-6 j 2 G SG aaa 9 T yy Or | + 0-T GFT LI 0-€ GOT = = a 09 FF 0 0z 0-T T ¢ jG € == g T F F é T-0 | 92-0 9-0 8-1 FOL = a 2 9¢ 0z g 0G 0-T T F j a = g T 0 0 é T-0 | 9F-0 8-0 8-T S0L = = ‘ 0g 9% F 61 0-1 I g T j = 3S T F g é T-0 | €F-0 8-0 LT GOL == = i: GP &@ ¢ 0% G.T j i} j G = g T 9 G ar F-0 | &3-3 ia 6:6 TOL = = ‘ FF 61 g 0% 0-T T v S jw = F T x + G-0 6&1 fle lt 8-3 00T = = i 8% 9T G 0% 0-1 T 8 G 9 = g T 8 G 3k 0-1 GL-€ 9-1 T-§ 66 = = 60L9T| Lz LT G 0% 0-3 € f € 57 = 9 T G L é ¢.0 | Ste GT 6-8 86 = = A 8% ial G 61 0-1 I P Sj j — 9 T 8 8 sf T-0 | 8T-& G.T 9-€ £6 = a 90L9T| Lz ST € 0% 0-€ P 9 € € == 6 T L 8 g 0-T | 01-6 LZ 9.¢ 96 = = = CP Ge i 0% 0-¢ i; F € T = é T (0) 0) 0-6 G6-F% 9.3 5-6 G6 = —— wt 0% al G 0z Gg F G j € oa GT T g L 3 0-T €0-12 1% 6-8 #6 = = 8699T | L1G 9T G 0% 0-€ € F T g —s 9 T or] It | 3 €-0 | 6L-8T 6-T 9-8 &6 = = GILIT| 8% ST PF 0z 0-€ € 16 | 6 ral = 9% T ol | FI | © C6 | $9-6E 8% 9-01 | &6 = = FILOT| SI aL 2 0% 0-6 G cI |8 L 8 eI € [AEa|) tele |) G6 | O8-LE CB FGI | 16 = = i eI LT G 0G 0-3 € 8 € G € G j 6 i) $ 10 | €0-¢ 9-1 0-¢ 06 = = a cg &@ G SI 0-1 6 Ot | 3% 8 = g T 8 i} s GT 68-8 FT 0-¢ 68 = = 99T9L| FT GG g 61 0. ¢ c&@ | IL | FT = S T Pp Pp 3 GG | GP-8 9-1 F8 88 aL = a a OL 2 0% G.F G IT |g 9 = OL I L L £ G6 | GG-9% ie T-8 £8 = 0&@ = OF 0% i 0Z G.T j 3 I T j 2 g OL | 8 é == 86-1 6-1 G.CT | 99 = 08% — 9 9% G 0% 0-1 T G T F Ii F F x x + 0-% 0-2 9-T 0-2 G8 = 699 = 89 0Z G 0% 0-€ g 6 g 9 = ial ii 8 9 £ 0-€ | 8e-L LT G.9 FS = 00% ae 61 0% G 0% 0-9 9 6I | Ff CT = 8 T x x 2 0-€ | 6F TE LG 0-IT | §8 — = GILPL| 8F FE g SI 0: 3G G 0 g T F fe G G £ 0-T 80-T LT €-% a) = = 8G jit G 0G C.F fi bi j G = oc T OT] ot | © 0-6 | §6-EE 0-€ 9.6 18 = _ “ &3 6 G 8T 0-¢ 9 Tt Mh OT FI eT G 6 6 3 GT G8. OF F-€ T-OL | 08 = = a CF 61 2 0G 0-¢ i hi | || € €T II al j G 0 £ GT GG- SE 9-2 .6 Z a= — 09 OF a 0G G.g F Ol | F 9 = II if 6 6 ’ ¢.0 | 88-41 G6 G9 8£ = = sf 821 OF ¢ 8T 0-€ g 6 F G al 1 9 et | + 1-0 | 26:6 eT ¥-F LL a= — i 8% II G 0G 0-9 L GL, 1g OL = 6Z T Gla \Ol ee GT €0- 88 6-3 0-01 | 92 = — 1p ST g 0% GF L OT | F 9 = LT T 0 i; 3 GT | 06-8T (Shite Leb CL = = SILbT| OF | AT G 0z 0-¢ f} F I ¢ eae ST T 6 OL | © 0-6 | TS-9T ¥- eb FL Terqua a | pestog | aseIiaay | 4ysayeary | TRIO], | WeT! WB | ysvoT | 4s9qvaIy WoT | dws te eee - SO[DISO A ee spreapy | PreaIeH | weruos ‘utd ‘bs | jo sapoequa, UU Ysa raquin “um Yysua'T pantie SHR AL xag | jo ssau Belted F AG) es bast bose ‘aims | der sunitea | ot cepa oe ggee | eae eed |e pue s[aoipag STVNV) @NOLY | “Buno x ‘saypynog puppwoy “A ‘TT ATAVIE C. L. Epwarps 243 TABLE V. ; alr? 3. Volume in cm3 v= om Adult Young Number of Specimens... 73 45 Mean cae esis ues 209°584 +13°185 12°506+ °645 Standard Deviation aD: 167°025+ 9°323 6511+ °463 Coefficient of Variation ... 79'679+ 4°450 52°07643°701 Range of Variation ss 51°04— 88464 *26—45°85 B. Development and Growth. During the summer of 1888 I reared the young of this species at Green Turtle Cay, Abaco, Bahamas, (Edwards, 1889)*. During the first 5 days the embryo TABLE VI. Yer 3 Reso ete Teac) pee | Vee Days Specimens Oe: mm. ( 5) ) 5 3 33. 28 ‘0102 a 3 “31 25 ‘0076 9 3 30 27 “0086 10 3 27 27 0077 11 6 “40 26 “0106 12 6 *A2 24 ‘0095 13 3 “47 23 ‘0097 14 8 “41 *20 “0064 15 3 37 18 “0046 18 8 34 “30 0120 19 3 34 33 0145 20 3 “42 30 ‘0148 22 6 36 32 0145 24 2 50 32 ‘O101 30 3 1:00 48 “0905 33 1 1:40 45 11138 40 2 1°65 65 ‘2737 42 2 2°00 68 3632 45 3 1°70 93 5773 49 2 2°30 68 “4176 51 2 2°10 “90 “6680 53 3 2°05 “72 4173 55 2 2°30 85 6525 67 1 2°30 90 ‘7316 71 2 2°95 95 1:0454 75 2 4:00 95 14175 87 2 2°30 “75 “5080 88 2 1:95 “85 3726 * The erroneous identification of this Holothurid with Miilleria agassizii Selenka was made, without reference to the taxonomic literature, from the label of a specimen in the biological museum of the Johns Hopkins University. Table I. in the present paper shows that three individuals were thus identified in the Harvard collections. Naturally such errors are due to the most superficial exami- nation. , 31—2 244 Holothuria floridana develops within the vitelline membrane. In the fourth day it has four tentacles and a budding posterior ventral pedicel (Edwards, 1907, pp. 775—776). In the sixth day after fertilization the embryo breaks its way through the slime covered egg membrane. The larval Holothurid has a primitive symmetry of five tentacles and one posterior ventral pedicel by means of which it creeps about. At times it is erect upon this posterior pedicel in a Hydra-like attitude. Then again it comes down on its tentacles while the pedicel is released from the bottom of the dish and waved aloft. It is nourished from the micro-organisms in the slime of the aquarium. ‘This slime is left at each change of water so that the algae and other protists multiply and thus furnish a good supply of food. Table VI. shows the growth in length*, diameter and volume of 89 of these very young individuals from the fifth, or last day within the vitelline membrane, to 88 days of age. In general there is a progressive increase in size up to 75 days. The diminution in volume of the individuals for 87 and 88 days undoubtedly indicates stunting from lack of food and other conditions in the small aquaria. Cc. Colour. a, LIVING AND ALCOHOLIC SPECIMENS. On July 11, 1891, at Harbour Island, Bahamas, the colours of 25 living speci- mens were determined by comparison with Ridgway, 1886. Besides the usual colours shown in the following analyses of alcoholic specimens, coral-red, scarlet and scarlet-vermilion were each found in two individuals and flame-scarlet in one. These colours have disappeared from the specimens which have remained in alcohol. Ludwig, 1889-92, p. 27, points out that certain pigments like yellow, yellowish-red and red are changed by alcohol. However, in the Holothurids considered in this paper the masses of pigment are so thick that in most cases, excepting those noted above, the colours here recorded for the alcoholic specimens may be accepted as about the same as those of the living individuals. Since ordinarily, for taxonomy, museum rather than living examples are studied it is certainly important to have the colours properly taken and recorded from alcoholic specimens, if it is not possible at the same time to have them for comparison from the animals while alive. b. MertHops or DETERMINATION. The colour was determined, on a clear day, with Ridgway, 1886, as the standard. In Tables VII. and VIII. a summary of the colouration and the distribution of the colours of the pedicels and papillae and the body is given for the bivium and trivium. The “stalk” is that portion of an appendage extending from the body- wall to within about ‘5 mm. from the distal termination where usually the “end” is marked off by a ring around the tip. In the absence of the ring the “stalk” extends to the sucker. Sometimes, especially dorsally, the appendages arise from * Measured from base of tentacles to proximal end of the posterior ventral pedicel. CG. L. Epwarps 245 slight elevations, “ warts,’ or in other cases from spots, or rings, differing in colour from the surrounding portions. For the body the mid-dorsal and lateral- dorsal regions correspond to the similar regions of the bivium. The trivium is often sharply marked off and occupies about two-fifths of the circumference of the animal. The mid-dorsal and lateral-dorsal regions are not always to be differen- tiated. Sometimes the differing lateral colour is along the dorsal edge of the side. “Dots” are minute bits of colour up to ‘2mm. diameter; “spots” are from ‘2mm. to lem. in diameter, while “blotches” are larger areas often extending over a considerable portion of the surface. Light colour like cream is often due to heaps of spicules visible through the skin. The colouration is very variable as given in Table VII. and represented in Plate II. for the adult and in Plate I. for the young. The general statement of colouration is given in a brief and untechnical form by grouping the following TABLE VII. = AMBULACRAL APPENDAGES Bopy Dorsal Dorsal Ventral Ventral Orici Mid- Lateral- Ventral Stalks Ends Stalks Ends a Dorsal Dorsal a a o ot coal ot o a a E ake BS ae E alo RS “Ihe & ae BS Shs & He cE She pee Regen ap =| On| = a8) = | 19 |) = ea.) = | Se | — | 90) — Colours } Adult, Browns ... | 67*| 73°7 | 674] 92-0 | 38>) 49-4 | 70°) 91:0 | 11 | 58°0 | 904) 79-1 | 106® | 72:1 | 56f| 56°0 Creams ...| 11 | 12°11] 5 | 69} 8|10°4} 4] 52} 1] 5:3) 10] 8-7] 24 | 16:4] 34 | 34:0 Specimens | Grays... | 13 | 14:3) — | — | 25] 325] 3] 39] 2/|105/ 14/123] 16/109) 8] 80 Black ...] —] — 1} 14) 1] 14) —]}] — 4/2170} — | — 1 a 1 1:0 White ...] -——-}| — |—] — 5 | 65) — | — 1} 53 —}— BO teal es ae ee iy ete | ea BG) 25) 5 | | op | Colours | Young, Browns ... | 408} 60°0 | 54"| 81:7 | 278] 43°5 | 49!| 89:0} 5j) 25-0 | 61% 38-7] 65! | 38°7 | 28 | 30°5 45 Creams ...| 19 | 28°4| 6] 9°0] 19 | 30°7| 5 | 971 1 | 5:0) 28 |17°9} 34 | 20°3} 27 | 2971 Specimens | White ...| 4] 6:0} —|]| — 6] 97/} 1) 18) —} — 4 | 2°5 5 | 30} 4] 43 Grays ...| 3] 45] 6] 91) 9/145] —] — 1] 5°0) 63 | 40-0} 61 | 36°5| 32 | 34°5 Black ...| 1 | 15} — | — 1 16/— ;} — | 13 /65°0/} 1 6 3 18); 2] 22 ® Dark tints; seal, clove, predominant. » Tints, well distributed ; seal, sepia and drab about alike. ¢ Tints, distributed; seal, clove, sepia and clay-colour well marked. 4 Dark tints ; seal, clove, Vandyke prominent. ©& Seal, clove, sepia, Prout’s, Broccoli, drab and cinna- mon prominent. ‘ Tints well distributed ; seal, clove, drab and cinnamon more pronounced. & Light tints; Prout’s and clay-colour prominent. » Light tints; cinnamon and especially clay-colour prominent. 4 Seal, cinnamon and clay-colour, * Tints well distributed ; seal, clove, sepia, Vandyke, Prout’s, Isabella and clay-colour the more prominent. ! Seal, clove, Prout’s, Isabella and clay-colour prominent. 246 Holothuria floridana TABLE VIII. Distribution of Colours on the Body expressed in Percentages. Mip-Dorsau Laterau-Dorsau VENTRAL | Whole ; Body Mixed Mixed Mixed Cees Uniform ee — 'Umitorm Uniform Ground | Markings Ground | Markings Ground | Markings 12°38 60°3» — -— 28 °8¢ -- a 57°54 — — Adult, | Browns — -- adead 53°8 — 81:0 50:0 — 53:1 57°71 73 Creams — — 23°7 19°2 = 13°9 20°8 — 43°8 14:3 Specimens | Grays — —- 3°6 26°9 — 3°8 29°2 _- 31 28°6 Black -— — -- — — 1:3 — — - — 4°4¢ — —_ = 66f —_ -—— 33°38 — _- Young, | Browns — 13°2 65°8 26°8 — 65:9 24°6 _ 42°4 14°3 45 Creams _- _ 18:4 28°1 _ 20°5 30°4 — 36°3 32°1 Specimens | Grays — _ 15°8 42°3 _ 91 40°6 a 21°3 39°3 Black — — — — — 4°5 — — — White — — _- 2°8 — — 4:4 — — 14°3 2 Mostly seal and clove-brown. » Mostly seal-brown. ¢ Seal-brown, lighter browns and 1 cream-colour. ‘ Lighter browns and creams. ¢& Prout’s brown and black. £ Isabella-colour and cream. £& Browns, creams, grays and 2 in black. colours so that the 25 tints from seal-brown to clay-colour are the “browns,” the 4 tints from cream-buff to cream-colour the “creams,” and the 9 tints from slate- colour to pearl-gray the “grays,’ while black and white stand independently. Browns: seal, clove, sepia, chocolate, Vandyke, bistre, walnut, burnt umber, olive, mummy, Prout’s, hair, Mars, raw umber, Broccoli, russet, tawny olive, drab, wood, cinnamon, écru drab, fawn-colour, Isabella-colour, ochraceous rufous, clay-colour. Creams: cream-buff, buff, buff-yellow, cream-colour. Black. Grays: slate-colour, slate-gray, gray, drab-gray, olive-gray, plumbeous, lilac-gray, lavender-gray, pearl- gray. White. c. COLOURATION. 1. Pedicels and Papillae. The dorsal stalks of the adult are chiefly dark brown while in the young the lighter browns prevail together with relatively more of the creams. In the ventral stalks of both adult and young the browns are less prominent than dorsally, and there is a marked increase in the grays and white. In the appendages all over the body the ends show a considerable increase in the browns over those characteristic for the stalks of the regions. In both adult and young the spots of origin are of a “dark” colour, either distinctly brown, or approaching black. C. L. Epwarps 247 The colours of the tentacles have not been separately tabulated. Usually the ends (distal branches) are darker than the stalks and show the general colour of the body. The stalks are sometimes whitish, or colourless, or again, more or less of the darker tints of the ends run down upon them. 2. Distribution of Colour on the Body. In Table VIII. it is shown that 12°/, of the adult and only 4°/, of the young are uniformly coloured. In all such cases browns and generally dark tints like seal and clove prevail. The mid-dorsal region is uniform in 60°/, of the adult, and in only 13°/, of the young. Here again are the browns exclusively. When the colours of this region are mixed the dark browns like seal, clove and Vandyke are predominant, with some intermixture of creams and grays, in both the ground- colour and the markings, of the adults. In the young, while the browns of lighter tints prevail in the ground-colour, the creams and especially the grays and white are in excess in the markings. The lateral-dorsal regions present much more variegation, since only 28°/, of the adult and 6°/, of the young are uniform and there is a decided turning to the lighter browns and creams. When the colours are mixed the browns still pre- dominate in the adult, although the markings are somewhat lighter, while in the young the ground-colour and markings are proportioned about as in the mid- dorsal with some increase of the creams. The ventral region in the adult shows a return to greater uniformity (57°5 °/,) but now the tints are among the lighter browns and the creams, while only 33 °/, of the young are uniform, with the browns, creams and grays about evenly re- presented. When the colours are mixed there is in the adult a decided increase of the creams in the ground-colour with more of the browns in the markings, while for the young in the ground-colour the creams, and especially the grays, increase, and in the markings the browns are equalled by white, each being only one-seventh, while the creams and grays make together five-sevenths, of the colouration. In the adult the percentage of creams is doubled from mid- to lateral-dorsal and again from lateral-dorsal to ventral, thus gradually changing the colour from the dark brown back to the lighter belly, but even here the browns are pre- dominant. In the young the increase in creams ventral is not so marked but, added to the very large percentage of grays over the whole body, gives the hght and variegated colouration which so generally strikingly characterizes the young of H. floridana and may lead one upon superficial examination to class such indi- viduals with H. grisea Selenka. Pourtalés, 1851, p. 13, noted that the young “are of a lighter colour than the old individuals.” Hérouard, 1902, p. 8, describes the colour, at the moment of capture, of one specimen as greenish, dotted with brown spots upon the back, while the ventral surface is uniform, and he describes another as having, in addition to the brown dots, spots more extended and of a lighter brown. Clark, 1901, p. 258, notes great variation in colour. In general in both adult and young, as graphically represented in Plates I. and 248 Holothuria floridana II. a, the ground-colour is marked with dots, spots, blotches, streaks, or more rarely rings, of different tints. Altogether the rings occur 37 times, 28 being in the browns and 9 in the creams. The party-coloured coats of these Holothurids are often very beautiful and sometimes present most fantastic combinations of nearly all the possible tints and shades of the browns, creams, and grays from black to white. D. Tentacles and Ampullae. Because of the great contraction of the anterior end of the body and of the retracted tentacles one is lable to make errors in counting tentacles even with the exercise of considerable care. After the first determinations, in working out the relation of these organs to the symmetry and the correlation of tentacles and ampullae, the various parts were spread out. In many cases a seeker was passed from ampulla to tentacle and in others Prussian blue was injected, either through the radial canal, or the ampulla. Thus, in several specimens, it was found that, in the previous count, short stumps of tentacles had been overlooked. a. SYMMETRY IN ARRANGEMENT OF TENTACLES AND AMPULLAE. Normally there are 20 tentacles arising from the radial canals and distributed evenly in the interradii as shown in Fig. A. See Plate V. Fic. A, represents the scheme for the symmetry in the arrangement of the tentacles, tentacle ampullae, dorsal mesentery, and calcareous ring. A dotted line indicates the median plane passing through the mid-ventral radius, the mid-dorsal inter- radius, and the attachment of the dorsal mesentery to the mid-dorsal interradiale. MVR, mid- ventral radius; RVR, right ventral radius; LVR, left ventral radius ; RDR, right dorsal radius, LDR, left dorsal radius, dl, d2, the tentacles dorsal, and vl, v2, ventral, rl, r2 right, and 11, 12 left, of the radius marked; OC, oral canal; OE, oesophagus; RC, radial canal; T, tentacle; TC, tentacle canal; TA, tentacle ampulla; R, radiale; IR, interradiale. Variations from the Symmetry of the Tentacles of the Mird-Dorsal Inter- radius in Relation to the Attachment of the Mesentery. The simplest pattern in asymmetry is where the number of tentacles is normal, and among those for the dorsal interradius one more than usual is found on one side or the other of the mesentery. Including this kind of asymmetry found in individuals having at the same time more or less than the normal number of tentacles, there are, in all, 27 cases in which the tentacles of the dorsal inter- radius are distributed as follows :— Number To Right To Left of Cases | of Mesentery | of Mesentery me 00 bo eS Re Wwe Ww me bb we ©. L. Epwarps 249 The mesentery is attached at the junction of the dorsal interradiale with the left dorsal radiale in 10 cases (15, 28, 35, 41, 45, 66, 68, 70, 73, 89) and with the right dorsal radiale in 1 (98); to the left side of the dorsal interradiale in 33, 37, and to the right side in 34; slightly to the left of the mid-line in 19, 20, 77, and to the right of the mid-line in 113. The attachment is very broad for about lcm. in 40. In 37 the dorsal interradiale is fused with the right dorsal radiale. One would anticipate that the displacement of the tentacles should be in the opposite direction to the displacement of the mesentery found in 14 of the above cases. Such a relation indeed is present in 11 of the 14 specimens. While the mean, in adult and young, is about the same, there is greater range and greater variability in the adult than in the young. b. NUMBER OF TENTACLES. TABLE IX. Adult Young Number of Specimens... 73 45 Mean 206 aba oe 19°709 + ‘064 19°756 + ‘064 Standard Deviation mee *808 + 045 642 + 025 Coefficient of Variation ... 4°099 + *229 3°229 + -229 Range of Variation 606 16—22 18—21 Variation in the Number of Tentacles and the Relation of those Present to the Normal Symmetry. Adult and young are tabulated separately but under this particular head they are treated as one group. Among the 30 varieties there is a decided tendency to reduction in the number of tentacles, since 23 individuals (76°6°/,) have less than the norm of 20 tentacles. It is well known that holothurians may lose one or more tentacles by accident, hence this excess in individuals with less than the norm probably represents such losses rather than congenital variation. This in- terpretation is also justified by the fact that in many cases of deficiency of tentacles the normal number, 20, of ampullae, is present. Of the 12 cases in the 19 tentacle class, 9 (75 °/,) have the tentacle absent in the trivium. Of the 10 cases in the 18 tentacle class, 3 lack the 2 tentacles in the trivium, 1 in the bivium, 4 lack 1 tentacle in each region and 2 are not deter- minable. Of the 23 cases in all, 15 (65°/,) have the tentacle deficiency in the trivium. Holothurid 5 with 16 tentacles, lacks the 4 of the left ventral interradius, v2, vl from the left ventral radius and 12,11 from the mid-ventral radius. In the Biometrika vr 32 Holothuria floridana 250 Jaquinyy 1810, “MOTINALAASIp JO UOTZVUIUAAEZep OJ poyepIqnuUr 003 pur [[vuIs At9A UoUIIOSdG + “poj}OU SVAL UOTJNGLAYSIP JOVXe OLOJoq SOT SepORQUAT, y — — 0 ia io | Ee a eS be iF ot S550) 1 | St ey 0 Suno x 0 64 | 6 T@ | 68 | G MIOONWNOOAr OO 99 9D “SID 1H 1) © wnpy T@ | GQ | GP | Tp 12.430 A -PIN [BAJUIA JOT [equa A IBS [es10ogd Ijory [Bstog yYsyyY Jaquiny [Rl4ag aay ‘9 Aq poyeorpur sniper repnoyaed ui saporyus) Jo souesqy ‘CA 981g) Y ‘Stq ut ueats Ayowus Jo owMayoOs oY} YA psoooe ut TONQIAySI(T ‘$9)9DJUAT, OC UDY? SSA2 YPM SU0o1INIWD Y X GTdvVL calcareous ring of this specimen (Fig. 96) the ventral and left ventral radialia are fused, the intervening left ventral interradiale being included in the composite piece. C. L. Epwarps 251 TABLE XI. Variations with more than 20 Tentacles. Distribution in accord with the scheme of symmetry in Fig. A. Presence of extra tentacle in particular radius given. ‘As Serial | Right Left | Right Left Mid- Total Be Number | Dorsal Dorsal | Ventral | Ventral | Ventral | Number 30 d3 = | = = = 21 61 = =e iW 28 od = 21 62 d3 = — — = 21 OE ere) eS vB | ne: = 21 19 —- | =— — d3, v3 — 22 34 — -- a3 v3 = 22 Young | 113 - d3 — — —- 21 In the 7 cases with more than the normal 20 tentacles there appears a slight tendency to the addition of extra tentacles dorsally. c. BRANCHES ON TENTACLE AMPULLAE AND VARIATION IN THEIR NUMBER. TABLE XII. Branches on Tentacle Ampullae. Distribution as in Fig. A. Number of branches in :— Serial | Right Left Right | Left Mid- Total Number | Dorsal | Dorsal | Ventral | Ventral | Ventral | Number | is sR eee | eee (ae ae 1 — v1 (2) -- v1 (1) — 3 2 — v1 (1) — | = — 1 Bs) — : air — — 21 (2) 2 1(1) | 7 | d1(7) Pe (3) a2 On tes 23 (v1 (2) 8) 8 — v2 (1) — — — 1 10 d2 (1) — — = 1 11 d2(1) — — — —_ 1 IS v2 (1) — —_ — — 1 16 — — d2 (1) — — 1 30 — — — —_ rl (1) 1 32 v1 (1) — — — — 1 33 —— vl (1) | v1 (1) — — 2) 35 — — vl (2) — — 2 37 dl (1) — — — — 1 63 v1 (1) d2 (1) —_ —_ — 2 67 — v2 (1) — — ~~ 1 70 — v1 (3) — — — 3 73 — dl (1) di (1) — — 2 32—2 252 Holothuria floridana In 18 individuals of Table XII. 27 of the tentacles have ampullae with branches. Of these, with origin as given in the Table, 18 have 1, + have 2 3 have 3, and 2 have 7 branches. ) In 16, d1 right dorsal radius arises under the mesentery, slightly toward the left and then passes over to the right. In 63, d1 right dorsal radius arises to the right of the mesentery and then passes beneath the mesentery to the left. The ampullae of 7 are rather remarkable in having altogether 23 branches and in that 2 (dl, right dorsal radius and d1; left ventral radius) have each 7 branches in the form of a tuft. The branches are found only in adults and so indicate one of the changes which may come with advancing age. d. VARIATION IN SIZE OF TENTACLES. Variations from the normal size of the tentacle may be classed as small and medium. 'The number of small tentacles present in Holothurids of my series are found to vary from 2 in 42, 60, 93, 95, 96 and 3 in 18, 108 to 5 in 33 and 6 in 7. In addition to the 6 in the last case there are 4 tentacles of medium size. A stump of a tentacle, lost by accident, is present in 1, 56 and 58 and 2 such stumps in 42. In most cases it 1s probable that small and medium sizes are stages in regeneration from the stumps of those lost by accident although, of course, it is possible that they are congenital variations in size. e. DEVELOPMENT OF TENTACLES. The completed study of the development of the ambulacral appendages necessitates some minor changes from my preliminary report (1907). The first 4 tentacles are found on the 4th day, when the embryo is still within the vitelline membrane. Represented in accord with Fig. A, Pl. V. the 4 tentacles arise from the radial canals as follows :—d1, left dorsal; d1, right ventral; r1, mid-ventral and d1, left ventral. The 5th, 11, mid-ventral, buds on the 4th day and thus completes the primitive symmetry. The 6th, d2, right ventral, has developed by the 40th day. From the 40th to the 49th days appear the 7th, d2, left ventral, the 8th, d1, right dorsal and the 9th and 10th, v1, of either right, or left, dorsal. If the 9th arises from the right, then the 10th comes from the left, dorsal, or vice versa. The 11th, 72, mid-ventral, buds on the 49th day. The 12th, /2, mid- ventral, appears on the 71st day, and the 13th, the last in my series raised from the embryo, is d2, left dorsal, and is developed by the 75th day. E. Pedicels and Papillae. It is often very difficult to differentiate papillae from pedicels both as regards their form and the presence, or absence, of calcareous end-plates (cf. Ludwig, 1889-92, pp. 100—110; Lampert, 1889, p. 821 and 1896, p. 53). ‘The whole ©. L. Epwarps 253 matter is of such interest and importance in the solution of the problems presented by the thesis of this paper that I have taken up the various elements in detail. TABLE XIII. a. DISTRIBUTION PER SQ. CM. Directly counted through an opening of 1 sq. cm. punched in a metal sheet. When the animal is sufficiently large an opening of 4 sq. cm. is used and the average sq. cm. obtained. On very sinall individuals the appendages are in distinct rows and an exact average per sq. cm. is impossible but the nearest number is given, although often obtained from a fraction of one sq. cm. and multiplied to the standard for comparison. In one case, 104, the sinallest young individual, this leads to an error, for it is credited with 44 dorsal appendages per sq. cm., when a count shows only 12 present in the dorsal region. Dorsau VENTRAL Adult Young Adult | Young = | Number of’ Specimens ... 73 45 73 45 Mean Bee ies ... | 18:096+ °279 | 20°667+ ‘876 | 25°288+ °675 | 35:°112+1°432 Standard Deviation a8 3°545+ °197 8717+ 620 8°550+ ‘477 | 20°147+1°432 Coefficient of Variation ... | 26°994+1°507 | 42°175+3°000 33°819+41°867 | 57°379+4:°179 Range of Variation ra 6—22 8—44 6—50 11—128 The above table shows that there are 1°6 as many appendages in the trivium as in the bivium in the adult, and 1'4 as many in the young, and that the young have a considerably greater standard deviation im both regions. There is a wide range of variation in the adult as well as in the young, and thus in some indivi- duals the appendages are scattered while in others they are closely crowded. The number per sq. cm. may vary more or less with the state of contraction of the specimens. The absolute number for the whole body in very small individuals is much less than in large ones, yet the number per sq. cm. may be relatively very large as in 77 which is 44 cm. long and has 128 ventral appendages per sq. cm. while the largest number found in any adult is 50 per sq. cm. in 23, which is 12 cm. long. Ordinarily the smaller number of appendages per sq. cm. in the adult demonstrates that the increase in number of appendages does not keep pace with the general growth of the body-wall. In 5 specimens the papillae, as defined on p. 267, were counted, yielding an average of ‘86 per sq.cm. In other words about 1 out of 16 of the dorsal appen- dages is a papilla. b. DEVELOPMENT AND APPEARANCE. The first pedicel is present as a bud from the posterior end of the mid-ventral radius of the 4th day embryo. The 2nd buds on the 7th day, the 3rd, on the 254 Holothuria floridana 22nd day, and the 4th on the 33rd day, all 3 from, and to the left of, the mid- ventral radius. On the 24th day the Ist pair of papillae bud ventral from the anterior ends of the dorsal radii and will become the first of the warts described below. On the 30th day the first pair of pedicels appear from the lateral-ventral radial canals, one on each side. Not before the 40th day does there appear a pedicel from the mid-ventral radius to the right. Gradually the number of ambu- lacral appendages increases until on the 75th day there are 30 developed pedicels and papillae and 68 buds, mostly arranged in rows along the radial canals. In the adult this arrangement in radial rows is obscured by the presence of fairly evenly distributed interradial appendages. The smaller young individuals, as Pourtalés, 1851, p. 12, remarks, show the radial rows more distinctly. In 3 of the smallest of the young of my statistical series the appendages were counted with the following result :— Serial | Vol | Mid- Right Left Right Left | Inter-radial N ha ofume | Ventral | Ventral | Ventral | Dorsal | Dorsal in Dorsal Totals 2 weGs Radius | Radius | Radius | Radius | Radius Region | 104 26a nee, 21 22 6 6 — 77 103 46 23 23 22 10 9 12 99 105 1:00 | ~~ 30 30 30 12 12 36 150 c. WARTS, Pourtalés, 1851, p. 12, noted that of the dorsal papillae the two rows situated near to the ventral surface, are always very conspicuous. “They are erectile, like the suckers, and possess a canal, which communicates with an internal vesicle.” I have adopted the name warts for the more or less prominent conical projections usually formed from an accumulation of rosettes, perforated plates and their developmental stages. The warts nearly always bear a papilla; occasionally more than one. They appear along the sides, having arisen from the right and left dorsal radii or sometimes they are scattered over the back. Being made of spicules, the warts are of light colour and generally stand out against the darker background. Where warts are not noted it is probable that some are present but obscured by an increased number of spicules in the skin, or by dark colour. TABLE XIV. 1. Distribution of Warts. I(t Right Right Left Scattered T and Left| Only Only | on Bivium races Adult 20 = oe 1 25 Young ... 35 1 P22 1 5 CG. L. Epwarps 255 These warts are much more prominent in the young for 97%°/, of this class show warts or their traces, as against 63°/, of the adult. Of those with warts, 80°/, of the young have them in the prominent right and left lateral rows, while this is true in only 27 °/, of the adult. TABLE XV. 2, Number of Warts on Sides of Bivium. ADULT Youne Right Left Right | Left Mean ... pee 5G 9°25 8°65 7°90 7°68 Range of Variation ... 5—15 5—19 1—14 3—12 | d. PAPILLAE AROUND THE ANUS. Selenka, 1867, p. 325, mentioned a crown of papillae surrounding the anus, and Théel, 1886, p. 216, described a specimen of H. meaicana Ludwig, as having the “anus with five minute groups of papillae.” TABLE XVI. Distribution of Papillae around the Anus. In Groups Age Number of Groups ree | Indefinite | Destroyed | Totals 0 | 1 | 2 oi Ty) 5 G Adult =. | 1 | 0 | 2 | 1 | 8 | 44) 12 4 12 1 73 VOUN Sees |) Ly) Om 0 | 1 4/31] 1 7 —- — 45 | From Table XVI. it is seen that in 60°-4°/, of the adult and 68:8 °/, of the young there are 5 groups of papillae around the anus. These groups may run into one another but their centres are always clearly marked. The anal papillae vary in length from ‘1 to 15mm. and have the supporting rods characteristic of papillae in general. F. Thickness of Body-wall. The much larger mean and range of the adult show, as one would naturally expect, that the body-wall (skin) becomes thicker with age. Not only is the adult body-wall nearly three times as thick as the young, but at the same time the standard deviation is nearly three times as much. 256 Holothuria floridana and Holothuria atra TABLE XVII. Determined by measuring in mm. the thickest and thinnest places along a ventral incision and then taking the average. Adult Young Number of Specimens... 62 44 Mean : eae 4°144+°195 1°495 + -084 Standard Deviation 2°974+ °138 *827 + (059 Coefiicient of Variation 54°876 + 332 5°527 + 397 Range of Variation 1:0—13°0 1—3°0 Naturally some individuals will die with the body-wall much more contracted than the average, and others with it much more expanded. Thus in 56 the body- wall is quite uniformly “thin” (‘3 mm.—1‘0 mm. thick) and in this one character the specimen is similar to H. atra. G. Calcareous Spicules of the Body-wall. These spicules are of three classes; tables, rosettes and perforated plates. They are not always distributed evenly throughout the body-wall but often in heaps and groups, which in some cases may be due to greater contraction in the regions where they occur. In general the spicules are more numerous in the trivium. At least in the young the spicules are being developed constantly, so that a more or less complete series of stages illustrating their development may be secured. The data were obtained from pieces of the body-wall of 2 or 3sq. cm. area taken from near the middle of the body, cleared in dilute potassium hydras and then, after dehydration by the alcohols, mounted from cedar oil into balsam. a. TABLES. The tables in H. floridana are like those of H. atra and so in the following general description of their development, structure and variation no attempt is made to keep separate account of H. floridana and H. atra specimens. The tables studied did not le near any appendage and so unquestionably belong to the body- wall. They are found in the superficial layer of the dermis. 1. Development of the Table. The developmental series represented by Pl. IV., Figs. 42—49, was selected from many individuals during the progress of this study. As shown by Diiben and Koren, 1844, this spicule begins as a cross-shaped body or as better expressed by Ludwig, 1889-92, pp. 45, 56, as a short rod with forked ends (Fig. 42). At the proximal end of each prong a vertical rod arises (Figs. 43, 44). The end of each C. L. Epwarps DAS prong forks (Fig. 45, a variate with 5 prongs and 5 vertical rods), and these branches grow toward one another while the vertical rods rise higher and the centre of the fundamental rod becomes elevated (Fig. 46). The outer branches grow together and unite to form the primary and peripheral holes of the disc, while the distal ends of the vertical rods are joined by transverse beams to build the crown, and then the teeth begin to appear (Fig. 47). Finally the last cross-beam is added to complete the crown and spire, the last peripheral branches fuse to form the disc, the teeth enlarge and the normal table is completed (Figs. 48, 49). 2. Structure of the Table. The typical table consists of a disc perforated by 4 larger, primary holes extending toward the centre alternating with 4 secondary holes of medium size in the periphery (Figs. 49, 64—97). Generally there are one or more (range 1—9) smaller tertiary holes in between the secondary and forming with them a peripheral circle (Figs. 57—62). The bars between the primary holes bend upward, so that the centre of the disc is elevated, and at the same time it supports a spire consist- ing of 4 vertical rods united distally by cross-beams to form a crown (Fig. 49). The crown bears at each of its 4 corners, 3 teeth; 2 horizontal, diverging at right angles, each continuing the axis of a cross-beam, and the 3rd perpendicular to the plane of the others (Fig. 75, the positions of the underlying vertical rods shown by dotted circles). 3. Variation in Crown and Vertical Rods. Among the 234 tables of H. floridana 5 have a triangular crown (Fig. 79) supported by 3 vertical rods; 5 have the crown arrested in development, the central hole not formed and with only 3 vertical rods (Fig. 80), and 4 have the normal 4 vertical rods but with the crown incomplete on one side. Three have spires with 5 vertical rods. The number of teeth varies from 6 to 16, the largest number being represented in Fig. 78. Sometimes odd teeth project from the middle of the cross-bars (Figs. 76, 77, 83). There are 5 crowns in each of which 1 tooth is bifid at the tip; 2 crowns with 2 teeth bifid; 1 crown with 6 teeth bifid; 1 crown with 7 teeth bifid and 1 crown with 1 tooth trifid.. Not included in the statistical series of H. floridana are several interesting variations. Fig. 81 shows a triangular crown without a central hole; Fig. 82, a partly formed crown hole; Fig. 86, an incomplete crown with 38 teeth bifid and 5 supporting rods; Fig. 87, a complete disc with 5 rods and no crown; Fig. 88, the disc, and Fig. 89, the crown, of a table with 7 rods; Fig. 90, from above and Fig. 91 from below, a depressed abnormal form. b. TABLES oF BiviuM AND TrRiviuM IN H. FLORIDANA. For the study of these tables data were taken from 14 Holothurids representing various places scattered over the Florida-Caribbean region. When possible the Biometrika v1 343} 258 Holothuria floridana measurements and counts were made from 10 tables in the bivium and 10 in the trivium of each specimen. Without attempting a study of the variation in the different parts of the table in individual Holothurids, the determinations for the species were made from the whole 130 dorsal and 104 ventral tables. TABLE XVIII. Tables of Bivium and Trivium. Disc Crown phagaes Number TO Height Number| Diameter Diameter | Diameter Kena of eet 18 of of Hole not includ- | including Moles Spines bod a Teeth a ing Teeth «| Teeth u Mean 5°746 907} 50210 54°150 12°177 7°220 18°720 38°590 + 149] + 091) + °351 + 529 |+ 064| + 140 | + *150 | + -106 Standard 2°523 1°883 | 5940 8945 1:078 2°340 2°5384 5°176 Deviation |+ *106)+ 079) + °248 + 374 |+ 045] + :088 + ‘158 22117, Coefficient of | 43°909 }199°21 | 11°839 16°510 8°849 32°41 13°510 13°420 Variation |+1°837|+ °833. + °490 + 690 |+ °370| +1°'36 + ‘570 + °570 Range of Variation | O—13 | O—10 | 35°2—67°2 | 32°3—72°6 | 8—16 | 3:°2—12°8 | 12°8—22°4| 25-6—54°4 Mean 4°654 346 42°539 45°610 11-692 6°560 18-750 35904 + 144; + ‘075| + °524 + ‘660 |+ (092); + ‘013 + °241 + ‘388 Standard 2°170 1°150 5342 9:934 1°394 1:920 2°400 6°012 Vv 1 Deviation |+ ‘091|}+ °044) + ‘140 + *465 |+ °065 + 092 + ‘115 + ‘281 entra! | Coefficient of | 46°617 |332°29 | 12°550 21°770 | 11°923| 29-260 12-800 16-740 Variation |+2°180| +1°554! + ‘590 +1:020 |+ °558| +1°400 + ‘610 + -780 Range of Variation | 0—10 1—6 | 32:°0—57'6 | 24°3—81°0 | 6—14 0O—9°6 9°6—22°4 | 22°4—51°2 I, “Dise: The form of the disc has the following distributions: dorsal ;—square, 81 (62°3 °/,) (Pl. IV. Figs. 54 and 66); irregularly square, 8 (6°2 °/,) (Figs. 53 and 73); round, 7 (5°4°/,) (Figs. 60 and 72); irregularly round, 12 (9°2°/,) (Figs. 62 and 74); irregular, 22 (16°9 °/,) (Figs. 52, 55 and 70): ventral ;—square, 58 (55°8 °/,); irregularly square, 14 (13°5 °/,); round, 3 (2°8°/,); irregularly round, 13 (12°5 °/,); irregular, 16 (15°3°/,). These types run into one another, and when the irregular variations are added to their respective types the form of the disc is practically the same in both bivium and trivium. The mean number of peripheral holes in the disc, in the dorsal tables, is 6*, with a range of 0—13; in the ventral, 5 with a range of 0—10 (Figs. 49—74). In the series of variates there is a typically symmetrical form with 4 secondary holes (Figs. 54, 64—67), one at the base of each vertical rod (Fig. 49). When * In the discussion of the tables the nearest whole numbers are used. C. L. Epwarps 259 more than the 4 secondary peripheral holes are present, the additional tertiary ones are usually smaller (Fig. 61). It is to be noted that an asymmetrical distri- bution of peripheral holes prevails. The mean number of spines on the disc is ‘9 in the dorsal tables with a range of 0—10 and ‘3 in the ventral, with a range of 0—6. With the mean less than 1 it is apparent that spines are not often found in any number. Sometimes the spines are large (Fig. 69), and again they may arise from a projection of some size (Fig. 68). Of the dorsal tables 22°/, bear spines while only 11°/, of the ventral are so characterized, and thus the possession of spines cannot be considered normal in the species. Hence, as a diagnostic character of Semper’s discarded variety amboinensis, the possession of spines on the disc has no significance. The mean diameter of the disc is 50 in the dorsal tables, with a range of 35 4—67 pw, and 43 pw in the ventral, with a range of 32 w—58 yu. 2, Height. The dorsal tables have a mean height of 54, with a range of 32 ~—72y; the ventral 454, with a range of 24y~—81y, and thus the dorsal tables are 20°/, higher than the ventral. 3. Crown. The mean number of teeth is 12 in the dorsal tables, with a range of 8—16, and 12 in the ventral, with a range of 6—14. The mean diameter of the hole is 7 in the dorsal crowns, with a range of 3u4—13; 7 in the ventral, with a range of Ow—l0y. In Fig. 76 this hole is large; in Fig. 79, small, while in some cases it is absent (Fig. 81). The mean diameter of the crown, not including teeth, is 19» in the dorsal tables, with a range of 13 ~—22 w; 19» in the ventral, with a range of 10 u—22 p; the diameter of the crown including teeth 39 in the dorsal tables with a range of 26 w—54 4; 36 in the ventral, with a range of 224—5ly. Taking one half of the difference between the two last determinations, the average length of the teeth on the crown is 10 in the bivium and 9 yw in the trivium. Thus from an examination of Table XVIII. it is found that the dorsal tables have more peripheral holes, spines and teeth, broader crown, larger crown-hole and longer teeth than the ventral tables, albeit the difference in some of these characters is very small. As shown by the standard deviations, the features of the disc are more variable in the dorsal tables, while the height and crown characters are more variable in the ventral tables. In the suckers of the dorsal pedicels are found what may be called reduced tables, in which only that central part of the disc immediately below and supporting the well-developed spire is present (Fig. 92). 33—2 260 Holothuria floridana c. ROSETTES AND ROSETTES WITH HOLES. Generally the rosettes are stellate of 3 or 4 broad rays, forked and rounded at the swollen ends (Figs. 29—31). Sometimes the central part is drawn out so that the spicule is irregularly H-shaped (Fig. 28), and then from this central bar additional projection may arise (Fig. 32). When some of the prongs of the forked ends grow together and fuse, the spicule comes under the class of rosettes with holes (Fig. 33). The average thickness of the rosette is 5 but often the centre is still thicker (10), giving a biconvex contour to the spicule as seen in profile. These spicules le in the dermis below the tables. They may be few and scattered but are, for the most part, densely crowded together in Beebe, often of irregular outline, or less frequently in rings. The determinations recorded in Table XIX. were taken from 10 specimens of H, floridana, 15 spicules from the dorsal region and 15 from the ventral, of each Holothurid, or from a total frequency of 150 dorsal and 150 ventral rosettes and rosettes with holes. In the bivium there are 141 (94°/.) rosettes and 9 (6°/,) rosettes with holes, and in the trivium 133 (89 °/.) rosettes and 17 (11 °/,) rosettes with holes. TABLE XIX. Rosettes and Rosettes with Holes. | RosEtrEes Rosetres witH Hoes Greater Smaller Number Greater Smaller Diameter Diameter of Diameter Diameter 7 M Holes be LK Mean 22030 18:090 2°556 26°800 21°470 +221 +°173 + +321 + ‘509 + °449 Standard Deviation ... 3°903 3°056 1°427 2°265 1:996 Dorsal ap Vila +123 an eps) + '356 ees Coefficient of Variation 17°700 16°910 55829 8°430 9°320 +°710 + *680 +8°876 +1°340 +1°480 Range of Variation 14°4—28°8| 9°6—24:0 | 1—5 | 24:0—28°8 | 19°2—24:0 Mean 20°470 17°010 3°353 27°450 21°530 +293 +161 + +258 + ‘768 + +506 Standard Deviation ... 3°814 2°748 1°577 4°693 3°093 Ventral +°158 +°114 | + :183 + 543 + 358 Coefficient of Variation 18°610 16°110 47°037 17°080 14°350 +°770 + ‘670 +5:441 +1:'970 + 1°660 Range of Variation 9:'6—28°8 | 9°6—24:0 1—6 | 19°2—33°6 | 14:4—24:0 In the bivium the mean dimensions of the rosettes are 224 x 18 and of the rosettes with holes, 274 x 21; in the trivium the rosettes are 204 x 17m and C. L. Epwarps 261 the rosettes with holes, 27 x 22u. The increased size of the rosettes with holes shows that they are older, and it is probable that most of them are developmental stages of the perforated plates. Comparing the rosettes in the bivium and trivium, it is seen that the mean number of holes in the former is less than 3 and in the latter more than 3. Corresponding to this increase in the mean number of holes, the greater diameter of the ventral rosettes with holes is 16°/, above that of the dorsal, while at the same time the standard deviations show that the size of these ventral rosettes is more variable and they have a greater range. Pourtalés, 1851, referred to the rosettes when he noted (p. 12) that “the skin contains small, caleareous bodies, of various forms, but mostly in that of an irregular cross, or star, the branches of which are bifurcated at their extremity.” d. PERFORATED PLATES. The determinations in Table XX. were made from 10 Holothurids, taking 15 plates in the bivium and 15 in the trivium of each, thus giving a total frequency of 150 dorsal and 150 ventral plates. In general the plates are more numerous ventrally than dorsally. TABLE XX. Perforated Plates. Dorsau : VENTRAL Mutat | sieength width | Somer) Length Width Holes be i Holes bi bi Mean ... aie rae 6°420 28°840 22870 6°515 26°510 21-130 ae) lla} + °204 + °262 ap “ilteil + °445 + ‘314 Develop- | Standard Deviation ... 1°539 2°461 Bieilis}s) 1°540 3°787 2°673 mental + ‘090 +144 +190 1128 + 314 a 222 Stages | Coefficient of Variation | 23-793 8°530 13°810 | 23-634 14290 12°630 +1°397 + °506 +°810 +1:°962 +1:190 + 1°050 Range of Variation ... o> 19°2—38°4 | 14°4 —28°8 4—8 19:°2—33°6 | 14:4—24°0 | Mean ... sats ... | 13°476 29-040 23°710 14°761 26°690 22460 + ‘216 + *207 +°192 + °244 ae OAlly + ‘170 Standard Deviation ... 2-932 2°819 2603 3°915 3°402 D235 Developed + +153 fay, +140 + ‘173 15) 120) Coefficient of Variation | 21°754 9°710 10°960 26°523 12°730 12°110 +1°132 +°513 +566 +1:170 + +560 + 530 Range of Variation ... | 9—21 | 24-°0—38-4 | 19°2—28°8 | 9—31 | 19°2—88-4 | 19°2—33°6 1. Development of the Perforated Plate. The plate begins as a rod with forked ends, the simple rosette, like Pl. IV. Fig. 28, of the same fundamental form (cf. Ludwig, 1889-92, p. 58) as the ‘ Anlage’ 262 Holothuria floridana of the table (Fig. 42) but with the central rod shorter and more slender and the prongs shorter, wider and thicker. The diverging branches of the prongs unite to form holes and thus is developed the 4-holed symmetrical Type a (Fig. 37) in which the 2 central holes are about twice the size of the 2 terminal holes. Of this type there are 2°/, dorsally and 6°/, ventrally. Plates of this stage in general have not the perfectly smooth contour of Fig. 37 but show one or more bifurcating branches which will unite to make 2 additional holes at each end and thus produce the 8-holed symmetrical Type b (Fig. 38). Eighteen per cent. of both the dorsal and ventral developmental stages are of Type b. The majority of Type b plates have the peripheral prongs indicating growth toward the complete plate, and also bars running into the larger central holes, as well as occasionally into the smaller holes (Fig. 38 a). Type a* with 4 holes asymmetrically distributed does not occur in the dorsal series but does in 6°/, of the ventral, and Type b* with 8 holes asymmetrically distributed is found in 5°/, of the dorsal and 15°/, of the ventral. Type c includes all of the plates with 5—8 holes indefinitely distributed, part of them showing the regular contour which might be taken to indicate a fully developed plate, and part of them with the prongs of growth of an incomplete plate. Type c constitutes 76°/, of the dorsal and 55°/, of the ventral plates. It is quite possible that many of these types, especially those with regular contours and of large size, are developed plates (“buttons”), but since Types a and b are clearly two well-marked develop- mental stages, I have included all plates with 8 or less holes in the same general group of perforated plates in the process of development. Their mean number of holes is about 6°5 both dorsally and ventrally, their mean dimensions 29 x 23 dorsally and 274 x 21m ventrally with practically no difference in the standard deviations in the two regions. 2. Structure and Variation of the Developed Perforated Plates. The plate becomes developed by the addition of more holes to Type b, while, with increasing age all of the holes may be gradually filled in with lime (Figs. 39, 40, 41). The mean number of holes is 13 dorsally and 15 ventrally and the mean dimensions 29 x 24 dorsally and 27 x 22 ventrally, with the standard devia- tions somewhat greater in the ventral region. 20°/, of the dorsal and 10°/, of the ventral plates have the peripheral projec- tions which indicate that additional holes may be in process of formation. Such a plate, much larger than the average, is shown in Fig. 34. In many cases a bar, or sometimes 2 or 3 may grow out into each of the 2 primary central holes (Fig. 34). The bar may grow through the hole, fusmg with the opposite wall, and thus forming 2 holes in place of the normal single hole. In the majority of these developed plates it is easy to trace the fundamental Type b (cf. Pl. VIII. Fig. 7, d, e of H. africana Théel, 1886). Sometimes the initial forked bar is much thicker than usual (Fig. 35) and after the fusion of the terminal branches the 2 primary holes formed are very GC. L. Epwarps 263 small (Fig. 36). With age the holes may become so much filled in with calcareous matter as to assume the form of pits (Fig. 41, where 11 of the 15 holes have become pits; indicated by the cross lines), Upon some of the plates are ridges and then the holes lie in the furrows between the ridges. The standard deviations given in Table XX. show that the developed plates are more variable than the undeveloped. A specimen from Key West, Florida, compared with specimens from Porto Rico and St Thomas, presents plates with more holes and at the same time has more plates with developmental branches which indicate that yet additional holes will be formed. An extended study of the perforated plates from the various localities would, without doubt, reveal interesting place modes. Théel, 1886, p. 215 (ef. also Clark, 1901, p. 258) in describing H. mexicana notes that “of the crowded plates two types may be observed, one more rounded, pierced with minute and commonly more numerous holes ; and the other irregularly rectangular, with fewer and larger holes.” The first of the two types of these authors I consider identical with the developed plate, and the second with the developmental stage 7'ype b described in this paper. Ludwig, 1874, in his original description of H. mexicana only mentions “numerous symmetrical perforated plates” but figures the two kinds (Taf. VII. Fig. 47a). These facts, together with the other points in agreement, establish my claim that H. meaicana Ludwig and H. africana Théel are identical with H. floridana Pourtalés, and therefore synonymous with the last-named species. e. NUMBER OF ROSETTES AND PERFORATED PLATES. In a piece of the body-wall of 1 sq. cm. area, the average thickness of the layer of spicules, extending through about + of the body-wall, was ‘82 mm. The spicules averaged ‘04 mm. long x 036 mm. wide x ‘005 mm. thick, giving a possible 145,000 spicules in 1 cu.mm., or 11,890,000 to 82 cu.mm., or 1 sq.cm. of surface. The spicules are packed densely in this layer, but a discount must be made for gaps as well as protoplasmic structures between the spicules. Even allowing this to be 50°/, there would be still over 5,000,000 spicules to a sq.cm. of surface in the crowded areas. f. CORRELATION OF ROSETTES AND PERFORATED PLATES WITH ADVANCING AGE. In order to determine whether the different classes of spicules are correlated with special ages of the Holothurid, 62 from the whole series of 118 specimens were carefully examined without, however, any attempt at a quantitative determi- nation. Hence the percentages given below are only approximate. A specimen usually shows a large majority of either rosettes or perforated plates but, at the same time, in each individual some examples, at least, of all classes of spicules occur, illustrating more or less completely the developmental series from the simple rod and x-formed rosette to the complete perforated plate. 264 Holothuria floridana The rosettes are specially abundant and thus characterize specimens 18, 26, 42, 47, 52, 53, 71, 75, 78, 80—86, 93, 95, 106, 113—118, twenty-five in all, of which eighteen, or 72°/,, are young as judged by the criterion of size (cf. pp. 239, 243). But of the other seven, four do not much exceed the limit for the young (50 c.c.) and the remaining three are considerably below 209°58 c.c., the average size of the adult. Allowing for a natural variation in which some young are larger than the limit I have assumed, it may be asserted that, for the most part, the rosettes are characteristic of young specimens. The perforated plates characterize 25 specimens, 15, 19, 21—25, 36—38, 51, 54, 55, 57-—67, 72, all of which are adult. So without question the perforated plates are characteristic of the adult. Four fully grown specimens 32, 50, 56, 69, have 90°/, perforated plates and 10°/, developmental stages, thus closely approaching the adult state. Holothurid 17, with 90°/, de- velopmental stages and 10°/, perforated plates, and 30, 31, 33, with 90°/, develop- mental stages and 10°/, rosettes, present such intermediate conditions as would be expected in occasional individuals. Specimens 44, 76, 79, 94, have 90°/, rosettes and 10°/, developmental stages, thus mostly presenting a young condition. Of these four, 44, an adult, has a volume much less than the adult average, while the other three are young but above the average for the young. Jn wew of these facts it is clear that the large majority of spicules in the young are rosettes and in the adult, perforated plates, while a number of specimens give the intermediate stages of the developmental series. Some rosettes and developmental stages may be found in any adult and some perforated plates in any young. Mitsukuri, 1897, discovered that, in Stichopus japonicus Selenka, with ad- vancing age the tables gradually degenerate “until in full-grown individuals, there are found nothing but small perforated plates, representing only a small central part of the basal disc and without any trace of the spire.” In H. floridana I have found correlated with advancing age a succession in the developmental stages of the perforated plate, but not a series of degenerative changes in the tables. H. Calcareous Spicules of the Ambulacral Appendages and the Differentiation of Pedicels and Papillae. The differentiation of pedicels and papillae is of primary importance. An exact definition of each of these two classes of ambulacral appendages is much needed. In such definitions the elements to be especially considered are (a) Form, (b) Suckers, (c) End-plates, and (d) Supporting Rods, together with the correlation of these elements. The end-plates and supporting rods are additional to the tables, rosettes and perforated plates described above for the body-wall, and found as well in the walls of the pedicels and papillae which are evaginations of the body-wall. From 9 holothurids 88 dorsal ambulacral appendages were taken, and from 3 other specimens, 50 ventral appendages. In a number of cases certain elements were not sufficiently clearly seen for accurate judgment and so are called “not determinable.” C. L. Epwarps 265 a. Form. The typical pedicel is cylindrical (Pl. III. Fig. 2), and the papilla conical (Fig. 1). In this species the form of the 88 appendages of the bivium studied is: cylindrical, 49 (55°7 °/,); conical, 4 (4°5°/,); not determinable, 35 (39°8°/,). In the trivium all are cylindrical. b. SUCKERS. The presence of a fundamental sucker is the chief and necessary character of the pedicel. In 73 (83°/,) of the dorsal appendages the sucker is present, in 2 (2:3 °/,) rudimentary, in 4 (45 °/.) absent and in 9 (10:2°/,) not determinable. In all of the ventral appendages a well-developed sucker is present. c. END-PLATES. With but one exception the ambulacral appendage has at least some trace of a perforated plate, or a rosette, as the end-plate. One dorsal case was not deter- minable. In the pedicel the end-plate is large and located in the base of the sucker (seen in profile in Plate II. Fig. 2). TABLE XXL. Diameter of End-plates in wu. Dorsau VENTRAL Type Type A B C D A B Gi Frequency... ... [41 (47°7°/,) | 86(41°9 °/,) | 8 (9°3°/,) | 1(1°1°/,)} 46 (92°/,) | 3(6°/.) | 1 (2°/.) Mean ... aor ate 540°953 354°677 182°380 90-000 701°260 | 288-000 | 210:000 +9°632 + 5°676 +5:°195 — +13°785 | +9°927 Standard Deviation ... 91°436 50°486 | 21°786 — 138°545 25°493 +6°811 +4:013 +3:°674 — + 9°743| +7°020 Coefficient of Variation 16°900 14°230 11°940 = 19°750 8°850 +1°270 +1°130 +2°020 = + 1:380] +2°430 Range of Variation ... | 485—750 225—420 120—195 — 450—975 | 255—315 The most completely developed end-plate I have called Type A. It is nearly circular and has numerous holes varying in size (Fig. 3). In some cases the holes are less uniform with larger holes toward the centre (Fig. 4). T'ype A has a mean diameter of 541 with a range of 435 w—750 4 dorsally. In the trivium Type A is larger, having a mean diameter of 701 with a range of 450 p—975 p. This type occurs in 48 °/, of the dorsal appendages and in 92°/, of the ventral. Type B (Fig. 5) has a mean diameter of 355 w with a range of 225 ~—420 uw dorsally and therefore it is something over half the size of Type A in this region. In Biometrika v1 34 266 Holothuria floridana the trivium Type B has a mean diameter of 288 w with a range of 255 w—315 mp. Type B occurs in 42 °/, of the dorsal appendages and in only 6 °/, of the ventral. Type C, with the smaller holes toward the centre (Fig. 6), or with larger, irregular holes (Fig. 7), in the bivium, has a mean diameter of 182 4 with a range of 120 ~—195 yp, and in the trivium occurs but once with a diameter of 210 p. The most degenerate form in this species is 7’ype D (Fig. 8) with a diameter of 90. It only occurs once dorsally and not at all ventrally. d. Supportine Rops. 1. Dorsal. In the dorsal appendages supporting rods are present in 14 (15°9°/,), absent in 44 (50°/.) and not determinable in 30 (34:1°/,). Those especially characteristic of the papillae (Figs. 10, 11, 12) form a series of rib-like structures, from rods only very slightly curved and with a few spines at each end (Fig. 10) to those more bowed and spinous with the ends slightly branched (Fig. 11). Occasionally a rod is found either straight, or curved, with the ends expanded and from 1 to several holes in addition to the spines and branches. Fig. 13 presents a rare variate in the form of a rosette with a few large holes. The tentacles have supporting rods similar to the series described above for the papillae. In the tentacles the rods are confined to the branched ends and are not found in the stalks. 2. Ventral. The ventral supporting rods (Figs. 20—22) are especially characteristic of the pedicels and so may be found with these appendages in the bivium. The most completely developed (Fig. 22) is a rod straight, or slightly curved, with a hole in each expanded end. Terminal prongs may grow out (Fig. 21), and then these may branch and their ends unite to form several holes at each end (Fig. 20). Connecting links (Figs. 18, 19) to the perforated plates (Fig. 17) of the body-wall can be found, lying particularly toward the base of the pedicel. So far these ventral supporting rods have not been found in their typical form in the dorsal pedicels. In some Holothurids they seem to be missing from the ventral pedicels. The curved rib-like rods of the papilla, in their typical form, are not found in the pedicel. e. ASSOCIATION OF ForMS OF AMBULACRAL APPENDAGES WITH TYPES OF END-PLATES. In the analysis of the characters of the pedicel and the papilla it is necessary to show which characters are associated together. The following data are from the dorsal region. Of the appendages with J'ype A of end-plate 32 (78°5°/,) are cylindrical, none conical and 9 (21:9°/,), not determinable. This type may be considered as typical for the completely established pedicel. The association of Type B is not determinable in 21 cases (58°3°/,), but since the remaining 15 (416 °/,) are with cylindrical appendages and none with conical, it may be C. L. Epwarps 267 assumed that this, like Z'ype A, is characteristic of the pedicel. Sometimes perhaps the presence of Type B may indicate that the pedicel is not fully developed. Type C, only found in 9°/, of the dorsal appendages, has a frequency of 2 (25°/.) in cylindrical, 2 (87°5 °/,) in conical forms, and 3 (37°5°/,) not determi- nable. This type may be taken as an intermediate stage. Type D occurs but once and then the form of its appendage is not deter- minable. f. ASSOCIATION OF SUCKERS WITH TYPES OF END-PLATES. Of the appendages with Type A end-plates 89 (95:1°/,) have suckers and 2 (49°/,) are not determinable and with Type B 32 (88°9°/,) have suckers, 1(4°9 °/,) has a rudimentary sucker, and 3(8°3 °/,) are not determinable. As none have them absent in these two classes and only 1 with Type B is rudimentary it may be assumed as the rule that Types A and B of end-plates are found in appen- dages having suckers. With Type C the suckers are present in 2 (25 °/,), rudimentary in 1 (12°5 °/,), absent in 3 (37°5°/,) and not determinable in 2 (25°/,) of the appendages. The one case with Type D is uncertain but probably has a rudimentary sucker. g. ASSOCIATION OF SUPPORTING RoDS WITH TYPES OF END-PLATES. Of the dorsal appendages with 7'ype A end-plates, supporting rods are present in 16 (39°/,), absent in 17 (41°5°/,) and not determinable in 8 (19°5°/,); with Type B they are present in 4 (11:1 °/,), absent in 17 (47:2 °/,) and not determinable in 15 (41°7°/.); with Type C they are present in 5 (62°5°/,), absent in 1 (12°5 °/,) and not determinable in 2 (25°/,); and in the only one with Type D, the rods are present. h. CONCLUSIONS AND DEFINITIONS. In the evolution by degeneration of the papilla from the pedicels the form has become conical with more and more pointed tip, the sucker rudimentary and finally lost, the end-plates smaller to vestigeal rosettes and supporting rods more frequent. The smaller diameter of the end-plates in the bivium, with the addition there of Type D, and more of Type C, indicates the greater progress of this evolu- tion in the dorsal region. The typical pedicel is cylindrical in form, with functional sucker, having end- plates of Type A in a large majority of the cases, the rest being of Type B, and dorsally with supporting rods more often absent than present. The typical papilla is conical in form, without sucker, having end-plates of Type D, or E, and with supporting rods present. 342 268 Holothuria floridana As a eonnecting link between the typical pedicel and papilla is an appendage not definitely cylindrical, or conical, with suckers either present, rudimentary, or absent, having end-plates of T'ype C. I. The Calcareous Ring. The typical radiale of the adult (Plate V. Fig. 93), is convex anteriorly and slightly concave posteriorly. The anterior half is somewhat expanded, the sides sloping in for about one-half the length when they become straight at the junction with the inter-radialia, At the middle of the rounded anterior margin of the radiale is the notch for the radial nerve. It is 1mm. wide, cutting into the piece for 4 of its length and slightly increasing in breadth toward the bottom. The surface rises up from the edge of the notch to a ridge along either side. These meet a similar ridge which arises from the posterior margin. In its greatest dimensions the radiale is about 6mm. long, 6 mm. wide, and 2mm. thick. In the young (Fig. 97) the radiale is more delicate, more regular in outline and with the median anterior notch V-shaped and decreasing in breadth toward the bottom. A variation (Fig. 94), not hitherto described, is often found in which there are two additional small notches cutting into the anterior margin, one toward each side. Sometimes only 1 of these notches may be found. This variate often occurs together with the normal form in the same animal. The interradiale of the adult (Fig. 95) has a concave posterior margin and the sides run in and forwards from the lines of junction with the radialia to the anterior rounded point, thus giving the piece a somewhat triangular form. Two ridges follow the sides to unite behind the anterior end. In the young (Fig. 98) the interradiale is more delicate and the anterior sides are deeply concave, thus leaving the median portion as a bold projection. In specimen 5 (which has only 16 tentacles) there is a fusion of the ventral and left ventral radialia and the intervening left ventral interradiale (Fig. 96). The dotted lines give the outlines of the attachment of the ventral and left ventral radial muscles. The increase in size of the pieces of the calcareous ring, as age advances, is demonstrated by the 3 following specimens; 94, about midway in the range of the young, 42, a small adult and 56, a fairly large adult :— SPECIMEN RapIALE INTER-RADIALE Number | Volume | Length | Width | Length | Width Serial ¢c.c. mm. mm. mm, mm. 94 21 2°8 2°8 1°6 1°5 42 59 4:0 3°8 2°5 2°5 56 485 5:0 4°8 3°6 3°6 ©. L. Epwarps 269 J. Polian Vesicles. As a general rule the Polian vesicles are club-shaped and may be simple or branched (Fig. B, S, Br), coming off from the water-vascular ring as solitary vesicles, or so close together that it is difficult to determine the separate origins of some, or all, of the vesicles of a group. RD RV Mv LV LD 4 N Ne A Ze JZIN Ae RStC \ ae Tuft BrTuft Fic. B. Water-vascular ring with Polian vesicles and stone-canals. M, Mid-dorsal mesentery. Radial canals; RD, right dorsal; RV, right ventral; MV, mid-ventral; LV, left ventral ; LD, left dorsal; R St C, L St C, right and left stone-canals; S, simple, Br, Branched, Br Tuft, tuft with branched vesicles. x 5}. Such a group, when made up of simple vesicles, I have called a tuft (Fig. B, Tuft). When some, or all of the vesicles, are branched and arise either from the base of one of the vesicles of the group (Br Tuft) or directly from the water- vascular ring, it is a tuft with branched vesicles. There are two principal groups of Polian vesicles in the region opposite the bases of the right and left ventral radial canals with small tufts and solitary vesicles in the ventral region between (Fig. B). Sometimes, as in 75 (Table IT.) a Polian vesicle may have its origin near the dorsal mesentery, and again they may come off from the entire extent of the water-vascular rmg. In 3 (Table I.) one Polian vesicle arises from a radial canal between the tentacle and water-vascular ring, and in 40 one large vesicle arises from the right dorsal radial canal just below the calcareous ring. The most interesting case is specimen 17, which has a total of 92 vesicles and branches of which 32 are solitary, and of these, 3 have each 1 branch. There are 9 tufts ranging from 2—7 vesicles in a tuft. In addition there are 2 tufts with branched vesicles; the first with 2 simple vesicles and 1 with 1 branch, 1 with 3 and 1 with 4 branches. 270 Holothuria floridana The branching of vesicles and the formation of tufts and tufts with branched vesicles are due to the continued growth and multiplication of these organs along with the growth of the adult Holothurid, for 36 °/, of the adult have tufts and tufts with branched vesicles, while only 4°/, of the young have tufts and none have tufts with branched vesicles. Ludwig, 1889-92, p. 113, gives H. mexicana and H. africana among the species in which several vesicles spring from a common stalk. Because of the variation in size of both vesicles and branches, in order to simplify the matter, in making Table XXII. I have grouped vesicles and branches together. TABLE XXII. Polian Vesicles. Aputt; 73 SPECIMENS Youne; 45 SpEcIMENS Number of Greatest Number Greatest Vesicles Length of Vesicles Length and Branches mm, and Branches mm, Mean aay ae ae 12°56341°263 | 25°4294+1:002 | 2°667+°321| 10°140+ -801 Standard Deviation Pep 15°774+ °893 | 12°058+ ‘687 | 2°494+°177) 6°822+ °506 Coefficient of Variation ... | 125°550+7°107 | 47°427+2°703 | 93°513+ °665 | 64°278+4°893 Range of Variation ae 1—92 8—73 O— 16 2—29 The mean number of Polian vesicles and branches is 13 with a range of 1—92, in the adult, and only 3 with a range of 0O—16 in the young. Eighteen per cent. of the adult have only 1 vesicle while 74 °/, of the young have 1, 12°/, have 2 and only 14°/, have more than 2 vesicles. The mean greatest length increased from 10mm. with a range of 2mm.— 29mm. in the young to 25mm. with a range of 8mm.—73mm. in the adult. These facts demonstrate that, as in the formation of branches and tufts noted above, the number of vesicles and branches and their length increase with the growth of the Holothurid. Ludwig, 1889-92, p. 114, notes that most species have only 1 vesicle in the beginning, and that there are only 3 families in which these organs fail to increase in number. It is possible that most authors do not include the branches in the number of Polian vesicles given. Lampert, 1885, p. 85, notes 2 branches on the Polian vesicles. Not counting the branches, from Table I. it is found that the mean number of vesicles in the adult is 11, the four largest numbers being 40, 41, 58 and 79. Lampert, 1885, p. 85, remarks that in H. mexicana the Polian vesicles are very inconstant and may be conceived of as in continuous multiplication. Ludwig, 1889-92, p. 115, gives the number of Polian vesicles in H. mexicana as 1—13. Théel, 1886, p. 175, in describing H. africana says: “The Polian vesicles are numerous, up to 12 or more, of unequal size and some of them carry small branches at their base.” From my series, as given above, the range of variation is greatly increased. ©. L. Epwarps 271 K. Stone-canals and Madreporites. As a rule the stone-canals appear in two tufts, one slightly ventral of the base of each dorsal radius (Fig. B, R St C and L St C). In some cases from 1—7 stone-canals are separated in a line extending to 10 mm. from the dorsal mesentery. D Fics. C—F. Stone-canals and madreporites. C, cylindrical ; D, spherical; EH, pear-shaped ; F, profile of HE. x54. In the majority of cases the madreporite is cylindrical (Fig. C), less frequently spherical (Fig. D), or pear-shaped (Fig. E). The head is compressed from side to side, presenting a narrow profile (Fig. F). Fics. G, H. Cylindrical madreporites. G, partly twisted; H, twisted in a spiral. x8. Often a cylindrical madreporite is tiisted upon itself (Fig. G), or even has as many as 4 or 5 turns of a spiral (Fig. H), and frequently the stone-canals are twisted. At times 2 madreporites are joined together. In 16, six such united pairs occur in the left tuft. In other individuals 3, 4 or 5 madreporites may be fused, 272 Holothuria floridana and Fig. I shows a monster composed of 6 stone-canals with the madreporites form- ing a common enlarged madreporic body, while the stone-canals are shortened and IX Fic. I. Six stone-canals with madreporites fused. x 54. independent except the middle two, which have grown together. Only one stone- canal was found with 2 branches. TABLE XXIII. Stone Canals. Aputt; 73 SPECIMENS Youne; 45 SPECIMENS Number | Number |Greatest| Average Greatest} Average | Length | Length Length | Length | Right Left Mota ees Haahad, Right Left |. Total ae manan, Mean ... . | 21°589 | 15°836 | 37°479 | 7:959 5°368 6°223| 3°556| 9°556| 3:444 2°983 +1°255)+ ‘980 |+1°954 + 327] + 1137 |+ °410/+ °256/+ ‘605 /+ °228) + ‘150 Standard Deviation ...| 15°903 | 11°894 | 24°748 4:140 1°734 4:076| 2°543| 6:021 | 2°266 1°488 + ‘888 }+ °664/+1°381 + °231| + ‘097 |/+ -290/+ -180|/+ °480|+ °161/ + -106 Coefficient of Variation | 73°663 | 75°104 | 66°030 52°016 32°311 | 65°504 | 71°523 | 63:006 | 65°806 | 49°683 +4112 |+4:192 |+3°686 +1°287) +1°804 |+4°657 |45°085 |+4°410 | +4°678 | +3°532 Range of Variation ...| 4—88| 1—61 | 5—149 | 3—21 | 1°5—10°5| 1—15 | O—11 | 2—25 1—7 | 1:0—6°0 In the adult the mean number of right canals is 22, with a range of 4—88, and of left canals 16, with a range of 1—61. In the young the mean number of right canals is 6, with a range of 1—15 and of left canals 4, with a range of O—11. Thus the mean number of right canals is 36 °/, greater than that of the left in the adult and 75°/, greater in the young. This interesting asymmetry is noted for a number of species by Ludwig, 1889-92, p. 132, who gives H. meaicana with 8 left and 3 right canals. I find that 78°/, of both the adult and young have the C. L. Epwarps Zio greater number of canals on the right side, while only 15°/, of the adult and 9 °/, of the young have the number greater on the left side, and 1°/, of the adult and 15 °/, of the young have the same number on both sides. So Ludwig must have made his counts from the less frequent individuals in which the number on the left is greater. In both adult and young the standard deviation and range of variation are greater for the right canals. In the adult the mean total number of stone-canals is 37, with a range of 5—149, and in the young 10, with a range of 2—25, demonstrating the great increase in the number of these organs through continued budding as the Holothurid grows. Specimen 68 with the large number of 149 stone-canals is exceptional, but 37°/, of the adult have more than 40 stone-canals. This should be particularly noted since Ludwig, 1889-92, p. 131, mentions H. mexicana as having a range of from 11—40 stone-canals. Lampert, 1885, p. 85, gives them as very numerous in two specimens of H. meaicana. The mean greatest length is 8 mm. with a range of 3 mm.— 21 mm. in the adult and 3mm. with a range of 1 mm.—7 mm. in the young. To determine the average length of all the canals of an individual the mode was selected by inspection and measured. The mean average length is 5mm. with a range of 1°5 mm.—10°5 mm. in the adult and 3mm. with a range of 1mm.—6mm. in the young. Thus the number of stone-canals and their length together with their standard deviations increase with age. L. Gonads. The gonads are branched and form a tuft to the left side of the dorsal mesentery. The gonaduct opens dorsally just behind the circlet of tentacles. In most individuals, the sex cells mature in July and August (Edwards, 1889, p. 37). Of the 73 adults, 35 are male, 35 female, 1 undifferentiated and 2 with gonads missing. Of the 45 young, 14 are male, 12 female, 12 undifferentiated and 7 with gonads missing. M. Respiratory Trees. Each of the two main stems of the respiratory tree has short branches whose median terminal twigs are intertwined with the blood-vessels of the rete mirabile. N. The Enteric Canal. The enteric canal is in three loops supported by a mesentery attached to the body-wall. It is large, with delicate wall and always crowded full with calcareous sand. At the posterior end is the expanded cloaca, its tough wall being attached to the body-wall by numerous small muscles. Biometrika v1 35 274 Holothuria floridana and Holothuria atra O. Habitat. ATLANTIC OCEAN: FLoripA, Pourtalés, 1851; Selenka, 1867; MExIco, Ludwig, 1874; West Inpiges, Lampert, 1885; CuBa, Havana, Ludwig, 1883; Lampert, 1885; Jamaica, Ludwig, 1883; Porro Rico, Clark, 1901; St THomas, Lampert, 1885; St BarTHOLOMEW, GUADALOUPE, Théel, 1886; VENEZUELA, Puerto Cabello, Ludwig, 1883 ; Lampert, 1885; Azores, Hérouard, 1902; AFRICA, CaPE OF Goop Hore, Simon's Bay, Théel, 1886. The specimens in this paper are from BAHAMAS, ABACO, Green Turtle Cay; New ProvipENcE, Nassaw; Fioripa, Elliott's Key, Key Largo, Caesar’s Creek, Indian Key, Vaca Key, Bahia Honda, between Salt Pond Key and Stock I., Key West, Tortugas; Porto Rico, Boqueron Bay, Fajardo, Mayaquez, San Juan; CuBA, Havana; Haiti; St THoMAS; CARIBBEAN SEA, Swan I., Curacoa I. Semper, 1868, p. 88, says that Holothurids of this species live together in great crowds upon sandy places of the coral reefs, and ordinarily are so completely covered with small sand-grains that they are noticed only by the trained eye. Gardiner, 1901-8, 1908, notes this species as one of the sand-feeders found on the sand-flats and reefs within the lagoons of the coral reefs. Ill. HOLOTHURIA ATRA JAGER. For the characters in which H. atra is like H. floridana I will simply refer to the descriptions given above. Tables of the characters observed are given as XXIV. and XXV. on pp. 275 and 276. A. Body. a. Form. Similar to H. floridana. b. SIZE. TABLE XXVI. 1. Length in cm. | | Adult — Young Number of Cases... 12 8 Mean : aoe 16°367 +1°475 8°200+ -628 | Standard Deviation As 7577 +1:°043 2°634+ °424 Coefficient of Variation ... 46°295 + 6°374 32°121+45°416 Range of Variation 10°0—33°5 2°5—11°0 275 C. L. 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Diameter in cm. | Adult Young | Number of Cases ... a 12 | 8 | | Mean hes ee ste 5383+ 286 | 2°325+'212 | Standard Deviation ~ 1470+ °202 | 600+°101 | | Coefficient of Variation .... | 27°314+3°760 | 95°785+°435 Range of Variation nae 3°2—7'6 | 1:'4—3°2 TABLE XXVIII. alr” 3. Volume in cm? v= 9 Adult Young Number of Cases ... sen | 12 | 8 Mean ju B6¢ . | 170°335+33°450 | 20°200+2°495 Standard Deviation ... | 171°793423°653 | 10°461+1°764 Coefficient of Variation ... | 100°856+13°886 | 51°788+8°733 | Range of Variation ve | 49 °46—538°49 1:93—36°19 | | B. Colour. The colour was determined from alcoholic specimens by the method described on p. 244 for H. floridana. a. COLOURATION. 1. Pedicels and Papillae. The dorsal stalks of the adult are seal-brown in all but one individual in which they are light Prout’s brown, while the ventral stalks are seal-brown except in two cases of light sepia, and one where some are drab with a ring of seal-brown. In the young both the dorsal and ventral stalks are seal- brown except in one individual where they are of the darker clove-brown. The ends of the appendages are generally coloured like the stalks, or of some lighter tint, like sepia, clay-colour, Isabella-colour, or cinnamon. Semper, 1868, p. 88, describes the ends as whitish in life. 2. Distribution of Colour on the Body. As graphically shown in Plate I. 160— 167, the body is almost always of a uniform seal-brown. ‘Two of the adults have blotches of light sepia on the ventral side and one has Prout’s brown mid-dorsally. One of the young has a circumanal ring of dark pearl gray and another is clove- brown. Sluiter, 1895, notes a red (steinrot) colour in life. Pearson, 1903, speaks of some specimens when alive being quite black above but pink below. Sluiter, 278 Holothuria atra 1894, thinks that the variety amboinensis must be given up because of colour intermediates from deep black to clear yellow at the basis from which the ambulacral appendages arise. TABLE XXIX. Cc. Tentacles and Ampullae. a. NUMBER OF TENTACLES. Number of Specimens Mean S 06 Standard Deviation Coefficient of Variation ... Range of Variation | | | Adult Young 12 8 19°583 + *169 19°125+ ‘278 868 + 120 1166+ °196 4°430 + °610 6096 + 1°028 18—21 17—20 The 20 tentacles normally found as the mode in H. atra are distributed according to the scheme of symmetry given for H. floridana (cf. Fig. A, Pl. V.). Variation in the Number of Tentacles and the Relation of those Present to the Normal Symmetry. TABLE XXX. Variations with less than 20 Tentacles. Distribution in accord with the scheme of symmetry given in Fig. A. Absence of tentacle in particular radius indicated by 0. Mid-Ventral Total | ! : Right Dorsal Left Dorsal Right Ventral Left Ventral Nee Serial ©” | Number) pee rg SE , | at | d2| v2 | ot | at | ae | v2 | oF | d1 | d2| v2 | of | di | d2| v2 | v1 | U1 | 12 a es SS St a a eS 2a ln BOS | 0;.—|— -|;—];—]—};—]|]— us 159 |—|]—|o};—| | —— = 0 a | 160 | —|—]—|— ne a Se pS | so | 165 0 ea 5 = 166 | —}—}]—}—}]—f/—}]—f—-}—- — 0 S| 168 | — | 0 | ee a || 0 Sel i rl Number Among the 8 variates there is the same decided tendency to reduction in the number of tentacles as shown in H. floridana, since 7 (87°5 °/,) have less than the normal number of 20. Only 1, an adult, 161, with 21 tentacles has more than The extra tentacle is d3, left dorsal radius, and all 5 tentacles of the dorsal inter-radius are in asymmetry, to the left of the mesentery. In 151, 158 and 160 the mesentery is attached at the junction of the dorsal inter-radiale with the right dorsal radiale ; in 161, far over on the right dorsal radiale. the norm. C. L. Epwarps 279 b. BRANCHES ON TENTACULAR AMPULLAE AND VARIATION IN THEIR NUMBER. Only 1 Holothurid, 151, varies from the norm in having branches to the ampullae. There are in all 25 branches distributed as follows: right dorsal radius d2(1), v2(1), mid-ventral radius r/(1), 72(2), /2(1), 11 (5), left ventral radius v1 (1), v2 (1), d2(1), left dorsal radius v1 (2), v2 (1), d1(8). This case is even more remarkable than 7 of H. floridana (p. 252), and since with a volume of 538 cm. it is the largest individual in the series it shows that the branching of the ampullae, when it appears, is associated with the more advanced age. One specimen, 155, has 1 of its tentacles of small size. D. Pedicels and Papillae. a. DISTRIBUTION PER SQ. CM. (Counted as in H. floridana, p. 253.) TABLE XXXI. Dorsau VENTRAL | — ———— —E — | Adult | Young Adult | Young | = - | erenenere a Number of Specimens | 12 | 8 12 8 Mean BOF on . | 16°58441°612 | 30°572+2°011 | 44°500+2°651 | 72°7144+4°114 Standard Deviation : 8°28141°140 | 7°889+1°422 | 13°617+1°875 | 16°138+2:909 | Coefficient of Variation ... | 49°935+6°875 | 25°807 +4°652 | 30°599+4°213 | 22°194+4:001 | Range of Variation | 8—30 | 18—41_s| 21—74 58—100 Table XX XI. demonstrates that in the adult there are 2°6 as many appendages in the ventral region as in the dorsal, and in the young 2'4 as many. In both the adult and young the standard deviation is much greater in the ventral region *. Compared with H. floridana, the appendages are more numerous and crowded, especially in the trivium. Selenka, 1867, p. 326, notes that the ventral pedicels are more numerous in the older examples. Ostergren, 1907, p. 195, notes the presence among the larger pedicels of numerous very small pedicels which hold fast the protective covering of weeds and other foreign bodies. [* In this as in several other cases cited by the author, the statement as to variability depends upon using the standard-deviation and not the coefficient of variation as the measure of variability——Eb. ] 280 Holothuria atra TABLE XXXII. b. DISTRIBUTION OF PAPILLAE AROUND THE ANUS. | In Groups Age Number of Groups Indefinite | Tctal | 0\ 4 | ealsl4ls | Iagiee' 8 aan ig gars Fee Adult... 0 | 0 | 0 | oO} 1] 4-| 7 12 Young 2 | 0 | 0 | OP) Oy) st, | 3 8 | | L | Table XXXII. shows that all of the adults have anal papillae. In 42°/, the papillae are in groups, and in 58°/, they are indefinitely distributed. Of the 8 young, two have no anal papillae, three have 5 groups and three have the papillae indefinitely distributed. E. The Body-wall. a. THICKNESS IN MM. (Determined as in H. floridana, p. 256.) TABLE XXXIII. Adult Young | ee Number of Specimens... 12 8 Mean vee als ofa 1717+ 173 1575+ °052 Standard Deviation aan “886+ 122 ‘217+ ‘037 | Coefficient of Variation ... 51°599+7°104 13°746 + 2°318 | Range of Variation “eto 6—4:0 1:0—1°5 The mean thickness of the body-wall is only ‘14 mm. greater in the adult than in the young. The range in the adult shows one 4mm. thick, but in most cases it cannot be said to grow much thicker with age, in which it differs decidedly from H. floridana (cf. p. 256). In H. floridana the mean thickness of body-wall is 2:4 greater than in H. atra. Thus the body-wall in H. atra is comparatively thin, soft and flaccid while in H. floridana it is nearly always much thicker, and even when not thicker, it is usually hard and firm, especially in the adult. Lindmann, 1899, claims that in the changes of consistency in the body-wall from hard to soft the albuminous element of the slime-secretion plays the most important part. While this may be true of the physiology of these tissues, yet I should account for the specific difference above noted in the greater thickness and the much larger number of spicules found in the body-wall of H. floridana (cf. p. 256). The standard deviation, especially in the young of H. atra, is very small. C. L. Epwarps 281 b. Pits. Over most of the surface of the body and the ambulacral appendages are found shallow, crater-like depressions which may be called pits (Fig. J). Fie. J. Pit with thick, pigmented wall. A table lies just beyond the outer edge of the pit. x 320. The mean dimensions are about ‘15 mm. x ‘1 mm. and their centres, in general, average about ‘3mm. apart. Each has a thickened pigmented wall (Fig. K) in which epidermal cells are crowded and which is more or less clearly separated from the surrounding tissue by crescentic clefts (). Fic. K. Section of pit; p, pit; a, x, clefts separating wall from surrounding tissues ; 1, lacuna; s, s, spaces from which tables have been dissolved. x 400. The opening of the pit is either approximately circular (Fig. J) or else slightly elongated and about 057mm.x‘03mm. At times when the lip of the pit is Biometrika v1 36 282 Holothuria atra nearly closed the opening is a narrow slit. In sections it is seen that beneath the blind bottom of the funnel-shaped pit (Fig. K) there is a closed lacunar space, sometimes spherical, but more frequently drawn out into an elongated canal- like space (/). The sections show the characteristic loosely woven connective tissue fibres and the spaces (s) from which spicules like the tables in (Fig. J) have been dissolved. Fisher (1907) seems not to have noticed my preliminary paper (1905) in which these pits were first mentioned, and hence has failed to include in his description these and some of the other characters by means of which I have clearly differentiated H. atra from H. floridana. F. Calcareous Spicules of the Body-wall. The spicules are not so numerous as in H. floridana and the warts found in that species do not occur. a. TABLES. For the general description of the development, structure and variation of the tables there is no distinction to be made from H. floridana (ef. p. 256 et seq.). b. TABLES OF BIviIUM AND TRIVIUM IN H. ATRA. For this study data were taken from 16 specimens collected all the way from the Hawanan Islands to Mozambique. Ordinarily 10 tables were taken from each TABLE XXXIV. Tables of Bivium and Trivium. Disc Crown Nao ee | Number Di ee | PY Number| Diameter | Diameter | Diameter ey of jamere! oe of of Hole | not includ- | including Holes Spines bes | ing Teeth ue ling Teeth «| Teeth uw Mean 3°740 713 47°927 | 65°870 |: 11960 9°225 19°710 44°030 + ‘069 |)+ *O97) + °251 + 590 #°055 | + 148 | + ‘156 + °300 Standard 1257) 1°758 4°558 9°780 ‘999 2°637 2°79 5°439 ee Deviation |+ -049 |+ -683| + ‘178 +416 +039) |) + 2105 |) 9 E01 + °212 | OTS" | Coefficient of | 31-008 |245°65 9°511 14-840 §°355 | 28°580 14°100 12°350 Variation |+1°208 |}+ :957 +3°704 | + 624 +°325 | +1°136 + °569 + ‘500 Range of | Variation 0—9 | 0-—10 | 35:2—60°8 | 41:92—92-22) 8—15 | 3:2—19-2 | 12°8—25°6 | 32-0—57°6 ———— | | Mean 3°578 669 44°603 47°629 12°162 9°190 18°780 38°756 + 094/+ 094) + °326 | +449 +063 > + ‘155 + °150 +°337 Standard 1°652 | 1°667 5°763 77355 1117 2°709 2°626 5°953 Vente Deviation {+ ‘066/+ ‘068; + ‘231 +:°318 +045 | + °110 + 106 + °238 “| Coefficient of | 46°100 |249:07 12°920 15°432 9187 29°476 | 14:000 15°350 Variation {+1°845|/+ ‘997} +5:199 | +°068 | +°367 | +1:192 | + ‘577 + 623 Range of Variation 0—9 O—9 | 28-8—60°8 | 31°1—70°0 | 8—15 | 3:2—16:0 12°8—28°8 | 25-6—57°6 C. L. Epwarps 283 of the dorsal and ventral regions. The determinations for the species, recorded in Table XXXIV. were made from a total of 150 dorsal and 142 ventral tables. 1. Disc. In the form of the disc, dorsally there are 119 (79°3°/,) square, 18 (8:7 °/,) irregularly square, 13 (8°7°/.) round, 2 (1°3°/,) irregularly round, and 3 (2°/.) irregular; ventrally, 92 (64°8 °/,) square, 16 (113 °/,) irregularly square, 18 (12°7 “/,) round, 7 (49 °/,) irregularly round, 9 (6°3 °/,) irregular. In general, square may be taken as the prevailing form. The mean number of peripheral holes is 4, which is from 1 to 2 less than in H. floridana. Pearson, 1908, p. 202, notes that “the discs of the tables are smooth and have no peripheral perforations.” The study of my series shows that Pearson’s description cannot be held as typical for the species. The mean number of spines is ‘7 while 82°/, of the tables have discs without spines. In all of the characters of the disc this species agrees closely with H. flort- dana (cf. p. 258). 2. Height. The dorsal tables are 66 w high, 38°/, higher than the ventral, and altogether they are higher in H. atra than in H. floridana. 3. Crown. The mean diameter, both including and not including teeth, the length of the teeth and the mean diameter of the hole, are slightly greater in this species than in H. floridana. The mode for the number of teeth is 12; the mean being slightly less dorsally and slightly more ventrally. As in the case of H. floridana, the dorsal tables have more peripheral holes, more spines, broader crown, larger crown-hole and longer teeth than the ventral tables, albeit in some characters the differences are so small as scarcely deserving of notice, while the number of teeth is slightly greater ventrally. c. ROSETTES AND ROSETTES WITH HOLES. In its simple condition the rosette has a somewhat elongated central bar with forked ends (Pl. IV. Fig. 23). The ends fork (Fig. 24), and the branches thus formed grow toward one another. Later additional branches may appear at the middle of the central bar (Fig. 25). A large majority of the rosettes remain open as in Figs, 24 and 25, although the curved ends of contiguous branches are often in apposition. On some of the rosettes are little knobs, while others present slight irregularities of the surface which might be taken for knobs. When the distal portions of any two of these branches fuse, a hole is formed (Fig. 26) and such a spicule is placed in the class of rosettes with holes (Figs. 26—27f). In the bivium there are 145 (96°7°/,) rosettes and 5 (3°3 °/,) rosettes 36—2 284 Holothuria atra with holes, and in the trivium 130 (86°7 °/,) rosettes and 20 (13°3 °/,) rosettes with holes. TABLE XXXYV. Rosettes and Rosettes with Holes. | RosErres Rosettes wirHh Howes: | 5 | Greater Smaller Number Greater Smaller Diameter | Diameter of Diameter Diameter | 7 a Holes Lb Bb | | | Mean ... An Tes 24°662 17°148 1°400 24-000 19°200 | | +°220 +157 + 121 | +2°569 +1°289 Standard Deviation ... 3°931 2803 400 | 8°518 4:293 | Dorsal +°156 +111 | +. °085 | +1°817 + ‘916 | | | Coefficient of Variation 15°941 167348 28°571 | 35°492 22°351 + ‘631 +°'698 | +6:094 +7°570 +4°767 Range of Variation ... | 9°6—33°6 | 9°6—24:0 1—2 19°2—33°6 | 14°4— 24:0 Mean ... ae ses 24°886 17°022 1°350 26°400 18-240 |} +279 +154 + ‘099 + '886 + 369 Standard Deviation ... 4-717 | 2597 | 654 | 5°873 2°448 | Ventral +°197 | +:°109 + ‘070 + *626 + °26) Coefficient of Variation | 18°954 15°259 48°430 22247 13°418 | +:'793 | +:°638 +-5°165 | 9373 4 ae 1-43il | Range of Variation ... | 14°4—43°2 / 96—24:0 1—3 19°2—38°4 | 14°4—24°0 | i} | | In their general dimensions and the increased size of the rosettes with holes these spicules in H. atra agree with those of H. floridana, Only 3°/, in the dorsal region are rosettes with holes and 13°/, in the ventral region. Of the 25 rosettes with holes found among the 300 rosettes and rosettes with holes of my statistical series, only two have 3 holes, four have 2 holes and 19 have 1 hole. The rosette with holes (perforated plate) of H. atra is often more or less similar to the developmental stages of the perforated plate in H. floridana. The rosettes nearly always show some of the arching of the branches of the bar (Figs. 24, 25), preliminary to the formation of the two central and the one or more distal holes of developmental Types a (Fig. 37) and b (Fig. 38) of H. floridana. Thus Fig. 27a resembles T'ype a. Type b with the 4 additional distal holes, 2 at each end, is often clearly indicated, albeit rarely, if ever, having all the distal holes completed (Fig. 27b). (Cf Selenka, 1867, Pl. VII. Fig. 4.) Occasional somewhat elongated “buttons” occur with two pairs of larger central holes and one distal hole at each end (27c). In one case there is an incomplete button of this type but with three pairs of central holes (Fig. 27 d). This button is formed from Type a by the growth of a bar through each central hole. Fig. 27a shows such a bar projecting into the right central hole. If ina C. L. Epwarps 285 rosette like Fig. 25 with median lateral bars the apposed terminal processes fused, a button like the above would result. In 156, from Samoa, there is a marked tendency toward the formation of these patterns. But even when holes are present the ends of the rosette branches curl out and project freely, only very rarely forming the smooth contour often found in Types a and b of H. floridana. In my statistical series 6 °/, have one hole (Fig. 26); 1°/, two holes and only a fraction of 1°/, more than two holes (Fig. 27). By special searching outside of the statistical series rosettes were found with as many as six holes completely formed (Figs. 27b—d). EVEN THEN THE FULLY DEVELOPED PERFORATED PLATES OF H. FLORIDANA (Figs. 39—41), WITH A MEAN NUMBER OF 13—15 HOLES, ARE DISTINCTLY DIFFERENT FROM ANY FOUND IN H. arra. So also the rosettes differ in the two species. In H. atra they are more elongated, the parts more nearly at right angles to one another and the whole more delicate, while in H. floridana they are stellate, appear heavier, often thicker at the centre and the branches have swollen ends (cf. Figs. 23—27 d with 28—33). Sometimes rosettes like those of H. atra are found in H. floridana, as well as stages inter- mediate to the stellate form typical of the latter species. The possession of peculiar perforated plates and in almost all cases the different kind of rosettes, are among the chief characters which have led me to separate and re-establish H. floridana as a distinct species. Number per sq. cm. One hundred of these spicules were counted in the field ((2sq.mm.) of a 1 in. ocular and a tin. objective, and thus to each sq.cm. of surface there could be 50,000 spicules. The possible error in this calculation may be placed at 50°/.. As a general rule these spicules are much more crowded in H. floridana (cf. p. 263) but there are exceptions like 30 of that species, which has scarcely more spicules than the least number in H. atra. G. Calcareous Spicules of the Ambulacral Appendages and the Differentiation of Pedicels and Papillae. From 13 Holothurids, 204 dorsal ambulacral appendages were taken, and from 3 specimens, 53 ventral appendages. Certain characters were uot determinable, or absent, 1u some cases. a. Form. In form 18 (8°8 °/,) are cylindrical, 26 (12°8 °/,) conical, but chiefly because of much contraction, 160 (78°4°/,) of the dorsal ambulacral appendages were not determinable. From those determined it may be assumed that a considerable majority in the bivium are conical in H. atra, instead of cylindrical as in H. flori- dana. b. SUCKERS. Suckers are present in 31 (15:2°/.), rudimentary in 1 (‘5 °/,), absent in 121 (59°3 °/,) and not determinable in 57 (25 °/.). 286 Holothwria atra The absence of a sucker is characteristic of the papilla, and since 59 °/, of the dorsal appendages lack this organ they may be considered as papillae. c. END-PLATES. In 12 (5:9°/.) of the dorsal appendages there is no trace of an end-plate, a condition which only occurs in 1°/, of the dorsal appendages of H. foridana. In 2 (1 °/,) the end-plate was not determinable. TABLE XXXVI. Diameter of End-plates in p. Dorsau VENTRAL A B Cc D E A B Cc D i Frequency —_|1(-5°/,) | 89 (46-8°/,) | 70 (36°8°/,) | 22 (11°6°/,) | 8 (4°3°/,) |38(71°7°/,) | 10(18-9°/,) | 3 (5°7°/,) | 1(1-9°/,)| 1 (1°9°/,.) Mean | 450°00 | 283°652 169°349 107°727 78°750 | 669°473 339-000 | 175:001 | 105-000 | 60-000 | +3°778 +2°262 +3°367 +#4:°979 | +10°687 | +11°720 | +7°286 Standard 52°812 27°858 23°412 20°879 97°671 54°950 18°710 Deviation — +2°670 +1°600 +2°381 #3°621 | + 7°557 | + 8°288 | +5152 - — Coefficient of | 18°619 16-450 21°733 26°512 14°589 16°209 10°691 Variation — + °941 + 945 +2°210 +4°471 | + 1129 | + 2°445 | +2°944 — — | Range of Variation — 225—420 | 105—210 60—135 | 60—120 | 465—825 | 240—405 | 150—195 — ae In the bivium there is only one end-plate of Type A, with a diameter less than that of the smallest variate of this type in the trivium. Types A, B and C are larger and more variable in the trivium, and each of the vestigeal rosette-like end-plates, D and £, is found but once, while dorsally D occurs in 12°/, and # in 4°/. of the cases. Comparing Table XXXVI. with Table X XI. it is seen that in H. floridana the mean diameters of all the types are larger, while in H. atra only one dorsal end- plate is large enough to be placed in Type A. So, from a consideration of the end- plates, it is obvious that the evolution by degeneration of the papilla from the primitive pedicel is much more marked dorsally in both species, and that all over the body it has proceeded decidedly farther in H. atra than in H. floridana. Selenka, 1867, p. 326, notes that specimens from the South Sea have the end-discs 4 smaller than those from Florida. Dorsal. d. SupportinGc Rops. In the bivium supporting rods are absent in 146 (71°6 °/,) of the appendages, present in 32 (15°7°/,) and not determinable in 26 (12°7 °/.). given on p. 266 covers the dorsal supporting rods of this species. The description GO. L. Epwarps 287 e. SUPPORTING ROSETTES AND SUPPORTING PLATES. Ventral. The supporting rosettes are found in the wall of the sucker near the end-plate. The terminations of the central bar are broadly branched nearly at right angles to the bar and the spreading branches are often fused to form holes (Figs. 15, 16). In some cases terminal twigs from the opposite ends grow together, thus forming perforated plates with two especially large central holes (Fig. 14). These are the fenestrated, often symmetrically bilateral plates described by Théel, 1886, p. 181. f. ASSOCIATION OF ForM oF AMBULACRAL APPENDAGES WITH TYPES OF END-PLATES IN THE BIVIUM. Type A only occurs once and in a cylindrical appendage. Type B was not determinable in 61 (67°8°/.) cases but in the 29 (32:2°/.) determinable is in cylindrical appendages. Type C is in cylindrical appendages in 3 (43°/,), in conical 6 (8:7 °/,) and was not determinable in 60 (87 °/,). Type D was not deter- minable in 17 (77°3 °/,) but in the 5 (227 °/,) determinable is in conical appendages. Type E was not determinable in 4 (50°/,) but like Type D when determinable, 4 cases (50 °/,), is in conical appendages, g. ASSOCIATION OF SUCKERS WITH TYPES OF END-PLATES. The one appendage with Type A end-plate has a sucker. With Type B suckers are present in 25 (27'8°/,), rudimentary in 1 (1:1 °/,), absent in 33 (36°7 °/.) and not determinable in 31 (34-4 °/,). With Type C suckers are present in 4 (5°8°/.), absent in 51 (73°9 °/,), and not determinable in 14 (20°3°/,). With Type D suckers are absent in 20 (90°9°/,) and not determinable in 2 (9'1°/.), and with Type EF present in 1 (12°5°/,), absent in 6 (75°/,), and not determinable in 1 (12°5°/.). In two appendages without end-plates one has a sucker and one has not. When compared with H. floridana the absence of suckers with Type B is especially noticeable, showing, perhaps, that the sucker is lost first and then follows the degeneration of the end-plate. h. ASSOCIATION OF SUPPORTING Robs WITH TYPES OF END-PLATES. In the one appendage having 7'ype A, supporting rods are absent. With Type B they are absent in 64 (71:1°/,) and not determinable in 26 (28:9°/,). With Type C supporting rods are present in 6 (87 °/,), absent in 58 (841°/.) and not determinable in 5 (7:2°/,). With Type D they are present in 40 (40:9 °/.), absent in 54 (545 °/.) and not determinable in 4 (4°5°/,), and with Z'ype E, present in 4 (50 °/,) and absent in 4 (50 °/.). 288 Holothuria atra In the cases determinable supporting rods are absent in appendages having end-plates of Types A and B and in the large majority of those having Type C, while they are about as often absent as present in those having J'ypes D and E. In the two appendages without end-plates supporting rods are present. 1. CONCLUSIONS AND DEFINITIONS. While agreeing in general with the conclusions and definitions for H. floridana (p. 267), H. atra has part of the appendages with Type B end-plates, without suckers, and represents a more specialized stage in evolution, with the addition of Types D and FE of end-plates in the trivium and Type H in the bivium. H. The Calcareous Ring. The calcareous ring, including the variation of the radialia with notches, is similar in form to that of H. floridana but about twice as large. The growth in the pieces of the calcareous ring is shown in the two following specimens, 155, a small adult, and 158, a large adult :— SPECIMEN RapDIALE INTER-RADIALE | Serial Volume Length Width Length Width Number cm.* mm. mm. mm. mm. 158; 58 5:0 ay) 4:0 255 158 497 75 6°7 5°8 6:0 Selenka, 1867, p. 326, notes that specimens from the Sandwich Islands have + larger calcareous ring. Comparing the area of the radiale, 28sq.mm. in the young adult, 755, with that of a specimen of H. floridana of nearly equal volume, 15 sq. mm. in 42 (cf. p. 268), it is seen that the radiale is 87 °/, larger in H. atra. In the same way the inter-radiale is shown to be 67 °/, larger. Comparing older adults 758 and 56 the volume of the former being 12 c.c. greater (cf. p. 268), the radiale is found to be 108 °/,, and the inter-radiale 169 °/, larger in H. atra. I. Polian Vesicles. The Polian Vesicles are club-shaped and in general arise from the water- vascular ring in two principal groups opposite the bases of the right and left ventral radial canals. In one case, /57, the vesicles arise from the entire extent of the ring-canal. C. L. Epwarps 289 TABLE XXXVII. Polian Vesicles. ApuLt; 12 Specimens Youne; 8 SPECIMENS a 7 | Number of Greatest Number of Greatest Vesicles Length mm. Vesicles Length mm. | Mean oe sea | Standard Deviation Range of Variation Coefiicient of Variation ... 20°750 + 3°835 19°698 + 2°712 94°930 + 6°325 1—56 17000 + 1°639 8°41641°159 49°505 + 6°816 9—42 | | 9°500+ 1°460 6°124+ 1:033 64°458 + 10°869 4—24 13°250 + 1°299 | 5449+ 949 41°121+6°934 8—21 Pearson, 1903, p. 208, notes 3 specimens, each with one Polian vesicle. The wean number of Polian vesicles is 21, with a range of 1—46, in the adult and 10, with a range of 4—24, in the young. Ludwig, 1889-92, p. 115, gives the range as 1—10. The smallest Holothurid, 767, has 10 Polian vesicles, and the smallest number any specimen has is 4. Thus H. atra shows a considerable difference from H. floridana, in which 74°/, of the young have only one Polian vesicle. The mean greatest length increased from 13 mm. with a range of 8mm. —21 mm. in the young, to 17 mm. with a range of 9 mm.—42 mm. in the adult. J. Stone-canals and Madreporites. The stone-canals and madreporites agree in location and form with H. floridana (p. 271). In 164 most of the madreporites are fused. TABLE XXXVIII. Stone-canals. | ApuLt; 12 SpecIMENS Youne ; 8 SPECIMENS - == j i | Number | | Number | | | Greatest Average | Greatest oe z | ~~} Length Length | | ~ | Length | Right | Left | Total Leo igabovt, Right Left | Totaly) sate | | ea Paes meen Mean ... Aris wane | 11:°000 | 12°000 | 24°084 9°500 ollie 8°250 6°375 | 13°250 4°750 /+1°433 |+ 1°769 )+2°933 | + ‘744 + 428 /+ °789)+ 394 | +1155 | + °426 Standard Deviation ... | 7°360 9°083 | 15064) = 3°819 | 2°248 3°307 1654 +4°842) = 1°758 /+1°013 + 1°251 42-074 + °526 +4 B10 /+ °558/+ “279 + “816 + “302 Coefficient of Variation | 66°906 75692 | 62°547 40°195 317594 | 40°085 | 25°937 36°540 | 37°644 /+9°212 +10°421 4+8°612) +5°5384 +44°350 /4+6°759 +4°374 +6'162 +6°348 Range of Variation | 427 7—43 | 15—70 | 5—16 4°5—11]} 1—13 2—8 | 8—21 | 2—8 | | | = Biometrika vr | Average Length mm. 290 Holothuria atra In the adult the mean number of right canals is 11, with a range of 4—27 and of left canals, 12, with a range of 7—43. In the young the mean number of right canals is 8, with a range of 1—13 and of left canals 6, with a range of 2—8. With the mean number of right and left canals about the same in the adult, the left being slightly larger, what asymmetry is present is the opposite to that in H. floridana. In the young the asymmetry agrees with that of H. floridana but is less extensive. In the adult the mean total number of stone-canals is 24, with a range of 15—70, and in the young, 13, with a range of 8—21, not so great an age difference as shown in H. floridana. The mean total number in the adult is 54°/, greater in H. floridana. Ludwig, 1889-92, p. 131, gives the range as 10—70 in H. atra. The mean greatest length is 10mm. with a range of 5mm.—16 mm. in the adult, and 5mm. with a range of 2mm.—8 mm. in the young. Thus the number of stone-canals and their length increase with age. The mean average length in the adult is 40°/, greater than in H. floridana. Selenka, 1867, p. 326, observes that the stone-canals in specimens from the South Sea are about $ longer, but not so many as in Florida specimens. . K. Gonads. The gonads and gonaduct agree with those of H. floridana. Of the 12 adults 7 are male, 2 female, and 3 undifferentiated. Of the 8 young, 6 are undifferentiated and 2 have the gonads missing. This undifferentiated state is in harmony with the conclusion of Mitsukuri, 1902, p. 18, for Stichopus japonicus, that the first-year young and many of the second-year young have the gonads in an undeveloped condition. L. Respiratory Trees. Similar to H. floridana. M. The Enteric Canal. Gardiner, 1901-8, pp. 338—40, has studied the important function of H. atra and other forms, in reducing coral fragments to sand. The coarser fragments are retained in the gut, somewhat reduced in size, while the finer particles are swept along the gut, “ presumably along its ciliated fold or groove.” N. Habitat. INDIAN OcEAN, Lampert, 1885; MozampiqueE, Bell, 1884; MapaGascar, Nossibe, Ludwig, 1883; ALpapra Is., Voeltzkow, 1902; ZANZIBAR, Selenka, 1867; Ludwig, 1877, 1887, 1899; Lampert, 1885, 1896; Tumbat L., Baui, Lampert, 1896; AmirANnTE Is., Bell, 1884; Darros I., Lampert, 1885, Bell; Querimba (S.E. Coast, Africa), Lampert, 1885; Rep Sea, Semper, 1869; Ludwig, 1887a; Kossmann, Lampert, 1885 ; Djedda, Lampert, 1885 ; Ludwig; LACCADIVE C. L. Epwarps 291 AND MaLpivE Is., Gardiner, 1901-3; CryLon, Bell, 1887; Ludwig, 1887 ; Thurston, 1890; Gulf of Manaar, Trincomalee, Galle, Pearson, 1903; BAy oF BENGAL, Bell, 1888; MERGuI ARCHIPELAGO, Elphinstone I., Bell, 1886; NIcoBar Is., Semper, 1868; Lampert, 1885 ; Easr Inp1A Is., Koehler, 1895 ; Koningsberger, 1904; Sumatra, Padang, Ludwig; Lampert, 1885; Java, Selenka, 1867; Lam- pert, 1885; Batavia, Sluiter, 1887; Sunda, Lampert, 1885; Saleh-Bai, Sebang- katan, Lombok, Lwmu-Lumu, Seba (Savu), Kabala dua, Lucipara I., Haingsisi, Roma, Kangeang, Timor, Jedan, Sluiter, 1901; Timor J., Ludwig ; Lampert, 1885 ; Ambon, Sluiter, 1894, 1895; CELEBES, Jager, 1833; Mavcassar, Lampert, 1885 ; Motucca or SPICE Is., Semper, 1868; Amboina, Selenka, 1867; Semper, 1868 ; Lampert, 1885; Théel, 1886; Batjan, Semper, 1868; Lampert, 1885; Ternate, Marenzeller, 1900; Pulo Tikul, Lampert, 1885; Pulu Tibul, Ludwig; PHILIPPINE Is., Semper, 1868; Cebu, Lampert, 1885 ; Mermaidstreet, Lucepara I., Lampert, 1889; AusTRALIA, Adelaide, Lampert, 1885; Great Barrier Reef, Kent, 1893; PaciFIc OCEAN, CAROLINE Is., Ualan J., Brandt, 1835 (Ludwig, 1881); RADACK CHAIN, Chamisso and Eysenhardt, 1821; GILBERT Is., Paanopa (Ocean I.), Nauru (Pleasant I.), Whitelegge, 1903 ; ELLICE Is., Funafuti, Whitelegge, 1897 ; Hedley, 1899; Bedford, 1899a; Rotuma, Bedford, 1899a; Fut Is., Théel, 1886; Lovaury Is., Bedford, 1899; Samoan Is. (NAviGaATOR Is.), Semper, 1868; Viti, Graeffe ; Tonaa Is., Penope, Théel, 1886; Society Is., Selenka, 1867; Lampert, 1885 ; Tahiti, Ludwig, 1883 ; Hawaran Is., Selenka, 1867 ; Lampert, 1885 ; Fisher, 1907 ; CLIPPERTON I., Clark, 1902. The specimens in this paper are from MOZAMBIQUE; ZANZIBAR; ARABIAN Sea; Marsa Is.; Samoa, Apia; Society Is., Tahiti; Hawatan Is., and GaLAPaGos Is. (the last in the collection of Dr H. L. Clark). to 31 — 292 Holothuria floridana and Holothuria atra IV. SUMMARY. A. Characters separating H. floridana Pourtalés (= H. mexicana Ludwig, H. africana Théel) from H. atra Jager. H, floridana Pourtalés Colouration H. atra Jager The lighter tints of the browns prevail as the ground-colour. The markings are dots, spots, blotches, streaks or rings of the browns, creains, grays and whites. Only 12°/, of the adult and 40°/, of the young have the entire body uniformly coloured. In all such cases the dark browns, usually seal and clove, are found. 60°/, of the adult and | 13°/, of the young have the mid-dorsal region | uniform in the browns. When the colours of this region are mixed the dark browns (seal, | clove, Vandyke) predominate with some inter- mixture of creams and grays. | The lateral-dorsal regions are not half so uni- form as the mid-dorsal and with a tendency to the lighter browns and creams. | The ventral region shows almost as much uni- | formity as the mid-dorsal in the adult, and almost three times as much in the young. The lighter browns and creams prevail in the adult and these colours together with the grays in the young. In the adult the percentage of creams is doubled from mid- to lateral-dorsal and again from lateral-dorsal to ventral, thus gradually chang- ing the colour from the dark brown back to the lighter belly. Over the entire body the ends of the ambulacral appendages often arise from dark brown, or | black, spots. The young are more variegated but altogether | these partly-coloured holothurians show much variation in the often fantastic combinations of the 25 tints of the browns, the 4 tints of the creams, the 9 tints of the grays, black and white. Mostly uniform seal-brown in | both the adult and young. The ends of the appendages may be of a lighter tint like sepia, Distribution pedicels papillae sq. cm. of and Number per sq. per | Bivium TRIVIUM BIvVIuM | TRIVIUM Adult 25 Adult 13 | Young 21 Young 35 Young Adult 3b | 45 Adult 17 Young 73 16 as many in trivium as in bivium in adult 2°6 as many in trivium as in plates usually surmounted by a papilla. Found in 63°/, of adult, 98°/, of young, and in ali larvae. In remaining 37°/, of adult and 2°/, of young warts probably present but not con- spicuous and hence not seriated as such. In young warts most often in prominent right and left lateral rows. cm. and 1:4 in young. bivium in adult and 2-4 in young. 65°/, more appen- dages in H. atra than in H, floridana. Skin | Warts, each a heap of rosettes and perforated | Pits, shallow, crater-like de- pressions (‘15 mm. x "1 mm.) in the body-wall, whose thickened, pigmented walls are separated from the sur- rounding tissue by crescentic clefts. Beneath each pit is a closed lacunar space. ©. L. Epwarps SUMMARY —(continued). H, floridana Pourtalés Firm; mean thickness, 4 mm. in adult and 15 mm. in young. More variable in the adult but, in general, “thick skinned.” Flaccid; mean thickness 1°6 H. atra Jiiger mm. in both adult and young. In general, “thin skinned.” Rosettes Perforated plates and rosettes with holes Stellate, central rod short, branches swollen at ends. Growth-stages of the perforated plates. | Average number of peripheral holes in discs of tables Central rod somewhat elon- gated, branches more nearly at right angles. Longer and more delicate. (1) Developmental stages; Type a, 4 holes; | Of the statistical series of 300 Type b, 8 holes. (2) Develo es; me 13 in bivium; 15 in trivium. With age, holes fill up with lime. Developed plates; mean number of holes, | rosettes and rosettes with holes, 2 had 3 holes, 4 had | 2 holes and 19 had 1 hole. Rare variates may have more holes (up to 6) but such per- forated plates are not like the developed perforated plates of H. floridana. Occasional elongated ‘“ But- tons” occur with 2 pairs of central holes and 1 distal hole at each end. 5°2 als | Number of ro- settes and per- forated plates per sq. cm. 5,000,000 to 12,000,000 Pedicels and pa- pillae in biv- lum Large majority cylindrical and with suckers are pedicels. 1 out of 16, papillae. Types of end- plates In bivium, A (47°/,), B (41°/,), C (9°/,), and D (1V/,). In trivium, A (92°/.), B(6°/,) and C(2°/.). Mean diameters of all types larger than in H. atra. 50,000. Majority conical and without suckers are papillae. ia bieann A (5°/.), B(44°/,), C (34°/,), D (11°/,) and £ (4 o/* In trivium, A (72°/,), B(19°/,), C(6°/,), D(2°/.) and H(2°/,). Only 1 in bivium large enough to be placed in Type A, Polian vesicles | Simple, or branched ; solitary, or in tufts; mean number, in adult, 13, with range of 1—92. 74°/, of young with 1 vesicle. Branching and formation of tufts due to growth. Stone-canals Mean total num- ber in adult Mean average length in adult 37, with range of 1—149. | 54°/, more than H. atra. 5 mm. Simple; mean number; in adult, 21, with range of 1— 56; in young, 10, with range of 4—24. 24, with range of 15—70, 7mm, 40°/, longer than in H.. floridana. 294 Holothuria floridana and Holothuria atra B. Characters Common to the Two Species. Dimensions.—In both adult and young the standard deviation is least in the diameter, greater in the length and greatest in the volume. The relatively much larger standard deviation in the volume of the adult when compared with that of the young is to be expected because of the limited range of the latter. Distribution of pedicels and papillae.—In both adult and young the standard deviation in the distribution of these appendages is considerably greater in the trivium, Tentacles.—Mode, 20. As shown by the average standard deviation of ‘7 in adult and young of H. floridana and of ‘9 in H. atra the number of tentacles show but little variation when compared with most of the other characters. The greater tendency in variation to less than the normal number, probably comes from the loss of tentacles by accident rather than from inherent congenital variation. It is therefore likely that the majority of the small and medium sized tentacles are stages in regeneration. Variation in the location of the tentacles lying in the dorsal inter-radius with reference to the mesentery attachment is shown in about 20°/, of the specimens. The tentacular ampullae have branches only in the adult and hence the formation of such branches, when it occurs, comes with advancing age. Pedicels and papillae defined—The typical pedicel is cylindrical, with sucker, end-plate of Type A or B, sometimes with supporting rods different from those of the papilla. The typical papilla is conical, without sucker, with end-plate of Type D or HE and with supporting rods of its own kind. The typical pedicels and papillae are connected by a group of appendages not definitely cylindrical or conical, with suckers either present, rudimentary or absent, having end-plates of Type C and with supporting rods either present or absent. End-plates.—Standard deviation much the largest in 7'ype A, decreasing relatively less and less with each succeeding type. Supporting rods :—in papillae and tentacles ; straight or curved rib-like rods with ends spinose, branched, or expanded, and with 1 to several holes. In pedicels—Straight, or slightly curved, rods with a hole in each expanded end. Sometimes with branched ends and several holes. Connecting links to the perforated plates of the body-wall may be found towards the base of the pedicel. — Tables.—The table developes from a short rod with forked ends. These ends divide and the recurved branches from either end grow together and fuse, forming the 4 larger primary holes of the centre of the disc. Then 4 smaller secondary, and often still smaller tertiary, peripheral holes are formed as the dise is com- pleted. At the same time the vertical rods arise and then are bound together GC. L. Epwarps 295 distally by transverse beams to form the spire and crown. At the last, from each corner, 3 teeth are developed, 2 horizontal diverging at right angles and the 3rd perpendicular to the plane of the others. The characters of the table show increasing variability in the following order, arranged according to the average of tbe standard deviations in adult and young, given after each character :— Number of teeth on crown (1°1), number of spines on disc (1°4), diameter of hole in crown (2°1), number of peripheral holes in disc (2°3), diameter of crown, not including teeth (2°4), diameter of crown including teeth (5°5), diameter of disc (56), and height of table (9°4). The tables in the bivium have more peripheral holes, spines, and teeth, broader crown, larger crown-hole and longer teeth than in the trivium, although the difference in some of these characters is very small. The average mean number of spines on the disc of the table in both bivium and trivium is ‘6 in H. floridana and ‘7 in H. atra while 80°/, of the former and 82°/, of the latter are without spines. Thus it is clearly apparent that the possession of spines is not a differential character for either species, and in connec- tion with the much discussed variety amboinensis of Semper is of no importance whatever. Rosettes—Standard deviation slightly larger in the greater than in the smaller diameter. Calcareous ring—tThe pieces of the calcareous ring are more regular and delicate in the young. A variation of the radiale is found with notches toward the sides of the anterior margin. Polian vesicles and stone-canals.—Increase in number and length with the growth of the animal. C. Additional Characters of H. floridana. Growth.—The embryo during the 5th day after fertilization and still within the vitelline membrane is ‘33 mm. in length, ‘28 mm. in diameter and ‘0102 cm. in volume. In the 75th day it is 4mm. in length, ‘95 mm. in diameter and 1'4175 cm.’ in volume. Adopting a volume of 50cm.’ as the limit in size of the fully developed young, this group averages 7 cm. in length, 2.cm. in diameter and 13cm.’ in volume. The adult average 18cm. in length, 5cm. in diameter and 210 cm. in volume. The greatest length is 33cm., the greatest diameter 8 cm., and the greatest volume 885 cm.3 Tentacles.—20 °/, have less, and only 6°/, more, than the mode of 20. Development of tentacles—In relation to their origin from the radial canals, the 4 primitive tentacles of the 4th day embryo are d1, left dorsal; d1 right ventral ; rl, mid-ventral and d1, left ventral (cf. Scheme of Symmetry, Fig. A, Pl. V). 296 Holothuria floridana and Holothuria atra The remaining tentacles, so far as my series from the embryo extends, arise in the following order.—5th, /1, mid-ventral; 6th, d2, right ventral; 7th, d2, left ventral ; 8th, d1, right dorsal; 9th and 10th, either v1 of right or left dorsal; 11th, r2, mid-ventral; 12th, /2, mid-ventral, and 13th, d2, left dorsal. The tentacle ampullae have branches in 15 °/, of the specimens. Development of pedicels and papillae—The Ist pedicel buds from the posterior end of the mid-ventral radial canal in the 4th day. The next 3 arise from and always to the left of the mid-ventral radial canal and not until the 40th day does a pedicel appear to the right from this radial canal. The Ist pair of papillae appears on the 24th day ventrad from the anterior ends of the dorsal radial canals and will become warts. On the 30th day the Ist pair of pedicels appears from the lateral ventral radial canals. Gradually the number increases until the 75th day when there are 30 developed and 68 buds, mostly arranged in bilateral rows. The smallest of the fully-developed young has 77 developed pedicels and papillae in rows but later on the inter-radial regions of the adult show evenly distributed appendages. Anal papillae.—In 5 groups in a majority of the specimens. Spicules.—The rosettes are characteristic of the young and the perforated plates of the adult. The average of the standard deviations in number of holes in the dorsal and ventral rosettes with holes is 1°5. Perforated plates.—Averages of the standard deviations of each character in bivium and trivium have the following order :— a. Developmental stages ;—number of holes (1:0), width (2°8) and length (3:0). b. Developed plates ;—Width (2°6), length (3:1) and number of holes (3°4). Polian vesicles.—The standard deviation of the number of vesicles and branches is greater than that of the greatest length in the adult, and the reverse is true in the young. The variability in the number of vesicles and branches in the adult is 6 times that of the young and in the greatest length, twice that of the young. Stone-canals.—The standard deviations of the various characters increase in the following order :—Adult, average length (1:7); greatest length (41); number, left (11°8), right (15°9), total (24:7): Young, average length (1'4), greatest length (2:2), number, left (2°5), right (4°0), total (6:0). D. Additional Characters of H. atra. Dimensions.—The young average 8cm. in length, 2cm. diameter and 20 cm.3 volume. The adult average 16cm. in length, 5 cm. in diameter and 170 cm.’ in volume. The greatest length is 33cm. The greatest diameter 8cm. and the greatest volume 538 cm.* : C. L. Epwarps 297 Tentacles.—85 °/, have less and only 5°/, more than the mode of 20. In one case, the largest adult, the tentacular ampullae have 25 branches. Anal papillae —Indefinitely distributed in a majority of the specimens. Supporting rosettes or plates——Are found in the wall of the sucker, near the end-plate of the pedicel. Rosettes with holes —Average standard deviation in number of holes °5, Polian vesicles.—In the adult the standard deviation of the number of vesicles and branches (19°6) is over twice that of the greatest length (84). In the young (6:1) it is shghtly greater than that of the greatest length (5:4). Stone-canals.—The standard deviations of the various characters increase in the following order:—Adult, number, right (1:0), average length (22), greatest length (3°8), number, left (9-0), total (15°0):— Young, number, left (1°6), average length (1:7), greatest length (1'7), number, right (3'3), total (4°8). LITERATURE CITED. BEDFORD, F. P., 1899. Holothurians. A. Willey’s Zool. Results, (2), pl. 17, pp. 141—150, Jan. -——. 1899a. Report on the Holothurians collected by Mr J. Stanley Gardiner at Funafuti and Rotuma. P. Zool. Soc, Lond., 1898, pp. 834-—848, pls. 52, 53, Apr. 1. Bett, F. Jerrr., 1884. Echinodermata in: Report on the Zoological Collections made in the Indo-Pacific Ocean, during the voyage of H.M.S. “ Alert,” 1881—82, pp. 117—152, 509—511, pl. 9, Lond. ——. 1886. On the Holothurians of the Mergui Archipelago. J. Linn. Soc. Zool. v. 21, pp. 25—28, pl. 2. ——. 1887. The Echinoderm Fauna of the Island of Ceylon. Scient. Tr. Roy. Dubl. Soc. v. 3, pp. 648—658, pls. 39, 40, Dublin. ——. 1888. Echinoderm Fauna of the Bay of Bengal. Proceed. Zool. Soc. of London. Branpt, Jon. Frip., 1835. Prodromus descriptionis animalium ab H. Mertensio observatorum, Fasc. 1. Petropoli, 4, 1835. CuHamisso, ADALB. DE & Eysenuarpt, C., 1821. De animalibus quibusdam e classe vermium linneana, in circumnavigatione terrae, auspicante Comite N. Romanzoff duce Ottone de Kotzebue, annis 1815—1818 peracta, observatis. Fasc. 2. Nov, Act. Acad. Caes. Leo- poldino Carol. nat. curios, v. 10, pp. 345—374, tab. 24—33, Bonnae. Crark, H. L., 1899. Further notes on the Echinoderms of Bermuda. Ann. N. York Ac. v, 12, pp. 117—138, pl. 4, July 7. —. 1901. Synopses of North-American Invertebrates. 15:—The Holothurioidea, Am. Naturalist, v. 35, pp. 479—496, 27 text figs. June. —. 190la. The Echinoderms of Porto Rico. Bull. U.S. Fish Comm. v. 2, pp. 281—263, pls. 14—17. —. 1902. Papers from the Hopkins Stanford Galapagos Expedition, 1898—99. 12 :— Echinodermata. Proc. Wash. Acad. v. 4, pp. 521—531, Sept. 30. Davenport, C. B., 1904. Statistical Methods with Special Reference to Biological Variation. pp. I—Vvull. 223, 2d. Ed. N. Y. Dien, M. W. von & Koren, J., 1844. Om Holothuriernas Hudskelett. K. Vet. Akad. Handl., pp. 211—228, tab. 4, 5, Stockholm, Biometrika v1 38 298 Holothuria floridana and Holothuria atra Epwarps, CHARLES Lincotn, 1889. Notes on the Embryology of Miilleria Agassizit, Sel., a Holothurian common at Green Turtle Cay, Bahamas. Johns Hopkins Univ. Cire. Balt. v. 8, p. 37. —. 1905. A Quantitative Study of Holothuria atra Jager and the Reéstablishment of Holothuria floridana Pourtalés (= Holothuria mexicana Ludwig). Science, N.S. v. 21 (532), pp. 383, 384, Mar. 10. ——. 1907. The Order of Appearance of the Ambulacral Appendages in Holothuria floridana Pourtalés. Science, N.S. v. 25 (646), pp. 775, 776, May 17. FisHer, Water K., 1907. The Holothurians of the Hawaiian Islands. Proc. U.S. Nat. Mus. v. 32, pp. 687—744, pls. 66—82. Garpiner, J. S., 1901—1903. The Maldive and Laccadive Groups, with notes on other coral formations in the Indian Ocean. Fauna and Geogr. Mald. Laccad. Archip. v. 1, pp. 12—50, 146—183, 314—346, 376—428, 12 pls., 30 text figs. —. 1903. The breaking-up of coral rock by organisms in the Tropics. Rep. Brit. Ass. 1902, pp. 654, 655, June. Heptey, Cuartes, 1899. Summary of the Fauna of Funafuti. Austr. Mus. Sydney Mem. v. 3, pp. 511—535 (Echinoderms, pp. 529, 530), Sydney. Hérovarp, Ed. 1902. Holothuries provenant des campagnes de la Princesse-Alice (1892—97). Résultats des Campagnes...Prince Monaco, Fasc. v. 21, 62 pp., 8 pls. JAcrR, Guin. Frip., 1833. De Holothuriis. Diss. inaug., Nov. 9, 40, Turici. Kent, SAVILLE, 1893, Great Barrier Reef, p. 240. Korn er, R., 1895. Catalogue raisonné des Echinodermes recueilles par M. Korotnev aux iles de la Sonde. Meém. Soc. Zool. France, v. 8, pp. 374—423, pl. 3. Konrnespercer, J. C., 1904. Tripang en Tripangsvisscherij in Nederlandsch-Indié. Med. Plantentuin Java, v. 71, vi.+72 pp., 9 pls. Lampurt, Kert., 1885. Die Seewalzen. Semper, Reisen im Archipel der Philippinen, v. 4 (3), 310 pp., 1 pl., 4°. Wiesbaden. —. 1889. Die wihrend der Expedition S. M. S. “Gazelle” 1874—76, von Prof. Dr Th. Studer gesammelten Holothurien. Zool. Jahrb. Abth. Syst. v. 4, pp. 806—858, pl. 24. —. 1896. Die von Dr Stuhlmann in den Jahren 1888 und 1889 an der Ostkiiste Africas gesammelten Holothurien. Mit. a. d. Naturhist. Mus. in Hamburg. x11. Jahrgang. Beiheft z. Jahrbuch d. Hamburgischen Wis. Anst. x11. 1895. LINDEMANN, W., 1899. Ueber einige Eigenschaften der Holothurienhaut. Ztschr, Biol. v. 39, pp. 18—36. Lupwic, Hupert, 1874. Beitrige zur Kenntniss der Holothurien. Arb. a. d. zool.-zootom. Inst. Wiirzburg, v. 2, pp. 77—118, 2 pls. Wiirzburg. Thyonidium occidentale n. sp. with Nachtrag. ——. 1881. Revision der Mertens-Brandt’schen Holothurien. Ztschr. f. wissensch. Zool. v. 35, pp. 575—599, ——. 1883. Verzeichniss der Holothurien des Kieler Museums. 22 Ber. d. Oberhess. Gesellsch. f. Nat. u. Heilk., pp. 155—176, Giessen. ——. 1887. Drei Mittheilungen iiber alte und neue Holothurienarten. Sitzungsb. Berliner Akad. (54), 1 pl. —~. 1887a. Die von Fr. Orsini auf d....“Vedetta” im Rothen Meer. gesammelten Holothurien, Zool. Jahr., Abth. Syst. 11. pp. 30—34, ——. 1889-92. (1) Buch. Die Seewalzen. In Bronn’s Klassen und Ordnungen des Thier- Reichs, v. 2, 3 Abth., Leipz. ——. 1898. Holothurien in Ergebnisse d. Hamburger Magalhaensischen Sammelreise. Lief. 3, June, 98 pp., 3 pls. —. 1898a. Brutpflege und Entwicklung von Phyllophorus wna Grube. Vorliufige Mit- theilung. Zool. Anz. v. 21, pp. 95—99, Jan. 31. —. 1899. Echinodermen des Sansibargebietes (in Voeltzkow, Wissenschaftliche Ergebnisse C. L. Epwarps 299 der Reisen in Madagaskar und Ost-Afrika in den Jahren 1889—95). Abh. Senckenberg. Ges. v. 21, pp. 537—563. (Feb. 2) MARENZELLER, E. v., 1900. Holothurien. Abh. Senckenb. Ges. Frankfurt, v. 25, p. 86. Mitsuxuri, K., 1897. On changes which are found with advancing age in the Calcareous Deposits of Stichopus japonicus Selenka. Annot. Zool. Japon. Tokyo, v. 1, pp. 31—42, 3 figs. ——. 1903. Notes on the habits and life-history of Stichopus japonicus Selenka. Annot. zool. Japon. v. 5, pp. 1—21, 4 txt. figs., Dec. OsTERGREN, H., 1898. Ueber eine durchgreifende Umwandlung des Hautskelettes bei Holo- thuria impatiens (Forsk). Zool. Anz., v. 21, Apr. 4, pp. 283—237, txt. figs. —. 1907. Zur Phylogenie und Systematik der Seewalzen. Sirtryck ur Zoologiska Studier Tillaignade Professor T, Tullberg, pp. 191—215, Upsala, Oct. 12. Pearson, J., 1903. Report on the Holothurioidea collected by Professor Herdman, at Ceylon, in 1902. Rep. on Ceylon Pearl Oyster Fisheries, Pt. 1, Supplementary Rep., v. 5, pp. 181— 208, pls. 1—3, 4to., London Roy. Soc. Dee. Pourtatts, L. F., 1851. On the Holothuriae of the Atlantic Coast of the United States. Proc. Am. Ass. Adv. Sce., 5 Meet., pp. 8—16, Wash. Ripeway, Roper, 1886. A Nomenclature of Colours for Naturalists and Compendium of Useful Knowledge for Ornithologists. 129 pp., 17 pls., 8vo. Boston. SELENKA, Emin, 1867. Beitriige zur Anatomie und Systematik der Holothurien. Ztschr. f. wissensch. Zool. v. 17, pp. 291—374, 4 pls., 8vo. Leipz. Semper, C., 1868. Reisen im Archipel der Philippinen. Wissenschaftliche Resultate, v. 1 (2), Holothurien, 288 pp., 40 pls., 4to. Leipz. —. 1869. Die Holothurien Ostafrikas, v. d. Decken’s Reisen in Ostafrika, v. 3, pp. 117—122, 1 pl., 8vo. Abth. 1. Stuiter, C. Pu., 1887. Die Evertebraten aus der Sammlung des Klg. naturwissensch. Vereins in Niederliindisch-Indien in Batavia. 1. Holothurioidea. Natuurk. Tijdschr, v. Nederl. Indie, Batav. v. 47, pp. 181—220, 2 pls., 8vo. Batav, —. 1894. Holothurien. Semon, Zool. Forschungsreisen in Australien u. d. malayischen Archipel, v., pp. 101—106, Jena. ——. 1895. Die Holothurien-Sammlung des Museums zu Amsterdam. Bijdr. Dierkunde Amsterdam, pp. 49—64, Apl. 17. —. 1901. Die Holothurien der Siboga-Expedition. Monogr. v. 44, Uitkomst. H. M. Siboga ...uitgegeven Max Weber, 142 pp., 10 pls., 4to. Leiden, Brill., Oct. TuH&eL, HJ., 1886. Report on the Holothurioidea. Part 2. Report on the Scientific Results of the Voyage of H.M.S. “Challenger,” ete. Zoology, v. 14 (39), 290 pp., 16 pls. 4to. Lond. Tuurston, 1890. Notes on the Pearl, etc. and Marine Fauna of the Gulf of Manar. Govern- ment Central Museum, Madras. VorttzKkow, A., 1902. Die vom Aldabra bis jetzt bekannte Flora und Fauna. Abh. Senckenb. Ges. v. 26, pp. 589—565, May. WHITELEGGE, T., 1897. The Echinodermata of Funafuti. Austral. Mus. Sydney, Mem. 3 (2), pp. 153—162. ——. 1903. The Crustacea and Echinodermata (in) Notes on the Zoology of Paanopa or Ocean Island and Nauru or Pleasant Island, Gilbert Group. Ree. Austral. Mus. v. 5, pp. 8—138, Apr. 38—2 300 Holothuria floridana and Holothuria atra EXPLANATION OF PLATES. Puate Tl. Colour variation in the young of H. floridana Pourtalés (112—93) and of the adult (160—156) and young (166—167) of H. atra Jiiger. The ambulacral appendages (pedicels and papillae) and the regions of the body are represented in a diagrammatic form for each individual of the statistical series as numbered in the column to the left. The appendages under D are dorsal and under V, ventral. The stalk and usually expanded terminal end of each appendage and the various regions of the surface of the body show the average colouration and its distribution for the respective parts. The colours, ‘‘ browns,’ ‘‘ creams,” ‘‘grays,” black and white, are given as they occur in dots, spots and blotches upon the general background, or else as uniform for the whole body, or its different regions. The plate does not always give exactly the colour effects of the original water-colours as described in the text. The predominant tint in 160—167 is seal- brown rather than violet-brown. The violet tone also has modified the grays and creams in 112—93. In 112, 92, and the ventral region of 91, the tint should be clove-brown. Prats II. Colour variation in the adult of Holothuria floridana Pourtalés. General explanation as given for Plate I. The original colours resemble those in Plate I as qualified in the above explana- tion. The colour values are not fully reproduced in the half-tone for the dark shades are browns that range from seal, Vandyke, sepia, and other tints, to clove-brown and black instead of having the uniformity represented. Puate III. Papilla, pedicel and their calcareous spicules. Fics. 10, 11, 13, 17—22 from H. jloridana ; 1—9, 12, 14—16 from H. atra. Fics, 1, 3, 5—13 dorsal; 2, 4, 14—22 ventral. Fics. 1—9, x 554; 10—22, x 260. Fic. 1. Papilla with supporting rods and type HE end-plate. Fic. 2. Pedicel with supporting rods, sucker, and type A end-plate in profile. Fic. 3. Type A, end-plate. Fic. 4, Type A end-plate with larger holes toward the centre. Fic. 5. Type B end-plate. Fic. 6. Type C end-plate. Fic. 7. Type C end-plate with larger, irregular holes, Fic. 8. Type D end-plate. Fic. 9. Type E end-plate. Fics. 10—12. Variation types of dorsal supporting rods. Fic, 10. Nearly straight with ends spinous. Fia. 11. Arcuate with spinous ends branched. Fic. 12, Expanded ends spinous, branched and perforated. Fic. 13. Rare dorsal supporting rosette. Fic. 14. Ventral supporting plate. : Fics. 15, 16. Ventral supporting rosettes with broadly branched perforated ends. Fias. 17—22. Series of ventral supporting rods, nearly straight with more or less expanded, branched and perforated ends (Figs. 20—22) leading through connecting links (Figs, 18, 19) to the perforated plate (Fig. 17) characteristic of the body-wall. Puate IV. Calcareous spicules of the body-wall; their form, size, development and variation. Fies, 28—45, 47, 49, 50, 53, 55—60, 62—66, 68—70, 73, from H. floridana; 23—27 f., 46, 48, 51, 52, 54, 61, 67, 71, 72, 74, from H. atra. Fras. 24, 28—36, 38, 4245, 4751, 53—66, 68—70, 73, dorsal; 23, 25—27 f., 37, 39—41, 46, 52, 67, 71, 72, 74, ventral. All figures x 260. Fias. 23—26 rosettes ; 26—27 f. rosettes with holes and perforated plates of H. atra. Fics. 28—33, 35 rosettes and developmental stages of perforated plates ; 34, 36-—41 perforated plates of H. floridana ; 37, developmental Type a; 38, developmental Type b; 38a, Type b, incomplete Biometrika, Vol. VI, Parts Il and III Plate | DV Mid-Dorsal Dorsal Ventral a8 33 5 se S22 ae 5 Ei Lateral- 3 g Lateral- & a Lateral- Ry 2 DV Mid-Dorsal Dorsal Ventral DV Mid-Dorsal Dorsal Ventral '* 09 oi Y abe ets ee TT a oe O° Ve se” 83 aece a) Sata . : - - bi —_=o t = y . Fy : ‘ . Biometrika, Vol. VI, Parts Il and Ill Plate Il erial umber Lateral- 2’ WV Mid-Dorsal Dorsal Ventral Lateral- Dorsal Ventral Seri: z N ae Biometrika, Vol. VI. Part I. 10 PLATE III. 58 UY) o oo Biometrika, Vol. VI. Part ITI. PAG EV, 09 .” we aS © Ue, Ww As 28 29 30 Rego es. LADS OB ai ® 28a@e 1! . a c i ae hn ee - os ; o> St, Ui - j e ot f PEATE V. Biometrika, Vol. VI. Part II. _! < o a ° (a) I U U VENTRAL C. L. Epwarps 301 and in process of growth; 36, 39—41, completely developed plates, the holes filling with lime until in 41 over 2 of the holes have become filled to pits (indicated by shading) ; 34, incomplete plate of large size. In 34, 39, 40 the basic developmental 7'ypes a and b may be noted surrounded with additional peripheral holes, Fics, 42—49 illustrate the development of the table. Fia. 42, Rod with forked end, Anlage of disc. Fic. 43. Appearance of the 4 vertical rods. Fic. 44. Ends of the 4 prongs begin forking. Fic. 45. Variate with 5 prongs and 5 vertical rods. Fic. 46. Formation of primary and peripheral holes of dise and growth of vertical rods. Fic. 47. The 4 primary and 2 of the secondary holes completed ; joining of vertical rods by transverse beams to form crown; appearance of teeth. Fic. 48. Nearly developed table. Fic, 49. Fully developed table. Fics. 50—62. Series of disc variates. To show the feature of the disc each is drawn with the vertical rods bearing the crown removed at their bases. Figs. 50—54 have the 4 primary holes indicated with developing secondary holes as follows: 50, none; 51, 1; 52,2; 53, 3; 54, 4. Fics. 55—62 show variation in the number of peripheral holes (secondary and tertiary) from 4—11. Fics. 63—74. Series of discs (drawn as above) showing variation in the number (1—10), form and size of spines, accompanied by a modal distribution of holes (64—67) or by an abnormal number and distribution of holes (63, 68—74). In 72, with a nearly circular disc, there are 8 vertical rods with a secondary hole for each rod. PuatEe V. Calcareous spicules of the body-wall and the pieces of the calcareous ring. Fics. 77, 78, 80, 83, 85, 87, 90—98 from H. floridana ; 75, 76, 79, 81, 82, 86, 88, 89 from H. atra. Fics. 77, 78, 80, 83—85, 87, 90—92 dorsal ; 75, 76, 79, 82, 86, 88, 89 ventral. Fies. 75—92, x 260; Figs, 93—96, x 21; 97, 98, x91. Fics. 75—86. Series of crown variates. The underlying vertical rods are indicated by dotted outlines. Fig. 75, normal type with 12 teeth; 76, 2 teeth at each of 3 corners, 3 at the 4th and 1 on a transverse bar; 77, extra tooth on a transverse bar; 78, 3 extra teeth on transverse bars; 79, triangular variate with extra tooth on each of 3 transverse bars; 80, incomplete crown, 1 corner lacking; 81, triangular variate without central hole; 82—84, abnormal variates; 85, incomplete crown from the failure to fuse of the two processes which would normally make a trans- verse bar; 86, incomplete crown with some teeth lacking, 2 bifid and 1 extra vertical rod. Fic. 87. Complete disc, 5 vertical rods and no crown. Fic. 88. Disc and 89 crown, of table with 7 vertical rods. Fic. 90. Disc and 91 crown, of abnormal variate. Fic. 92. Reduced table with only central part of disc and the spire present. Fics. 93—96 from caleareous ring of the adult. Fic. 93. Radiale, usual form. Fic. 94. Hadiale, with anterior border notched toward the sides. Fic. 95. Inter-radiale. Fic. 96. Fused ventral and left ventral radialia, the intervening left ventral inter-radiale included in the compound piece. Fias. 97, 98. More regular and delicate pieces of the calcareous ring of the young, Fic. 97. Radiale. Fic. 98. Inter-radiale. Fic. A. See for explanation p. 248. PROBABLE ERROR OF A CORRELATION COEFFICIENT. By STUDENT. Av the discussion of Mr R. H. Hooker’s recent paper “The correlation of the weather and crops” (Journ. Royal Stat. Soc. 1907) Dr Shaw made an enquiry as to the significance of correlation coefficients derived from small numbers of cases. His question was answered by Messrs Yule and Hooker and Professor Edgeworth, all of whom considered that Mr Hooker was probably safe in taking °50 as his limit of significance for a sample of 21. They did not, however, answer Dr Shaw’s question in any more general way. Now Mr Hooker is not the only statistician who is forced to work with very small samples, and until Dr Shaw’s question has been properly answered the results of such investigations lack the criterion which would enable us to make full use of them. The present paper, which is an account of some sampling experiments, has two objects : (1) to throw some light by empirical methods on the problem itself, (2) to endeavour to interest mathematicians who have both time and ability to solve it. Before proceeding further, it may be as well to state the problem which occurs in practice, for it is often confused with other allied questions. A random sample has been obtained from an indefinitely large* population and r+ calculated between two variable characters of the individuals composing the sample. We require the probability that A for the population from which the sample is drawn shall lie between any given limits. It is clear that in order to solve this problem we must know two things: (1) the distribution of values of 7 derived from samples of a population which has a given * Note that the indefinitely large population need not actually exist. In Mr Hooker’s case his sample was 21 years of farming under modern conditions in England, and included all the years about which information was obtainable. Probably it could not actually have been made much larger without loss of homogeneity, due to the mixing with farming under conditions not modern; but one can imagine the population indefinitely increased and the 21 years to be a sample from this. + Throughout the rest of this paper ‘‘r’’ is written for the correlation coeflicient of a sample and R for correlation coefficient of a population. By STUDENT 303 R, and (2) the & priori probability that R for the population les between any given limits. Now (2) can hardly ever be known, so that some arbitrary assumption must in general be made; when we know (1) it will be time enough to discuss what will be the best assumption to make, but meanwhile I may suggest two -more or less obvious distributions. The first is that any value is equally likely between +1 and —1, and the second that the probability that # is the value is proportional to 1—2*: this I think is more in accordance with ordinary experi- ence: the distribution of @ priori distribution would then be expressed by the equation y= 3(1—a”). But whatever assumption be made, it will be necessary to know (1), so that the solution really turns on the distribution of r for samples drawn from the same population. Now this has been determined for large samples with as much accuracy as is required, for Pearson and Filon (Phil. Trans. Vol. 191 A, p. 229 et seq.) showed 2 that the standard deviation is ——and of course for large samples the distribution ve is sure to be practically normal unless r is very close to unity. But their method involves approximations which are not legitimate when the sample is small. Besides this the distribution is not then normal, so that even if we had the standard deviation a great deal would still remain unknown. In order to throw some light on this question I took a correlation table* containing 3000 cases of stature and length of left middle finger of criminals, and proceeded to draw samples of four from this population+. This gave me 750 values of r for a population whose real correlation was ‘66. By taking the statures of one sample with the middle finger lengths of the next sample I was enabled to get 750 values of 7 for a population whose real correlation was zero, Next I combined each of the samples of four with the tenth sample before it and with the tenth sample after it, thus obtaining two sets of 750} values from samples of 8, with real correlation ‘66 and zero. Besides this empirical work it is possible to calculate @ priori the distribution for samples of two as follows. For clearly the only values possible are + 1 and —1, since two points must always lie on the regression line which joins them§. Next consider the correlation between the difference between the values of one character in two successive individuals, and the difference between the values of the other character in the same individuals. It is well known to be the same as that between the values themselves, if the individuals be in random order. * Biometrika, Vol. 1. p. 219. W.R. Macdonnell. + Biometrika, Vol. v1. p. 13. Student. + Not strictly independent, but practically sufficiently nearly so. This method was adopted in order to save arithmetic. § There are of course indeterminate cases when the values are the same for one character, but they become rarer as we decrease the unit of grouping until with an infinitesimal unit of grouping the statement in the text is true. 304 Probable Error of a Correlation Coefficient Also, if an indefinitely large number of such differences be taken, it is clear that the means of the distributions will have the value zero. Hence, if the correlation be determined from a fourfold division through zero we can apply Mr Sheppard’s* result that if A and B be the numbers in the large and the oe : B : ; small divisions of the table respectively cos Aaeps where # is the correlation - of the original system. But if a pair of individuals whose difference falls in either of the small divisions be considered to be a random sample of 2, their 7 will be found to be —1, while that of a pair whose difference falls in one of the large divisions is +1. Hence the distribution of r for samples of 2 is AN at +1,and BN at —1,where A+ B=], cost R and B= —=, 7 When R& = 0, there is of course even division, half the values being + 1, and half —1; when R=‘66, pa Lon, therefore A =°‘729, and the mean is at ‘729 —:271="458. The s.p.=V1—(458) ='889. It is noteworthy that the mean value is considerably less than R. I have dealt with the cases of samples of 2 at some length, because it is possible that this limiting value of the distribution with its mean of — sin # and its second T ake 2s 2 ne hee moment coefficient of 1 — (= sin R) may furnish a clue to the distribution when n is greater than 2. Besides these series, I have another shorter one of 100 values of 7 from samples of 30, when the real value is ‘66. The distributions of the various trials are given in the table. Several peculiarities will be noticed which are due to the effects of grouping, particularly in the samples of 4. Firstly, there is a lump at zero; with such small numbers zero is not an uncommon value of the product moment and then, whatever the values of the standard deviations, 7 = 0. Next there are five indeterminate cases in each of the distributions for samples of 4. These are due to the whole sample falling in the same group for one variable. In such a case, both the Standard Deviation and the product moment vanish and r is indeterminate. Lastly, with such small samples one cannot use Sheppard’s corrections for the Standard Deviations, as r often becomes greater than unity. So I did not use the corrections except in the case of the samples of 30, yet on the whole the values of the Standard Deviations are no doubt too large. This does not much affect the values of 7 in the neighbourhood of zero, but there is a tendency for larger values * Phil. Trans. A. Vol. cxcrt. p. 141. 196 | L294] #89] FE) OG] Ge] Te} ce}os] Fs) 1s] 21) #2] Fstlat] ef}it]/e|saistirl/e|/zizlolalrielzlelzirie lr |9/ S18] r]¢ | to —t | | - etre) ae ecto tect lgtranlectes lect lect: feces at ct etan| Shes at Neat ee te e | eel ele ee oe Melts |W ole oy) otal ta relma | neeyel melee | ae eae . La HltlHL A LELEL El ele altel ele] eel ela e eee ee Tyre ey eee eer reer eer eer a SI] SIS] SPL Sl SPR Sl Sl A PARR] BS] SL Sl spel] sl sf spell] wl el sleale fa] ALA] &] SA] =] BW] of] om] 6] Ss S } Sy SS eS 1 Sy Sj Sul Su (Sy Su! Sen eS Or aa | Sy Su SO Ou Se! 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This introduces an error into the Standard Deviation of all the series to some extent, but of course the mean is unaltered when there is no correlation. The series for samples of 4 are affected more than those from samples of 8, as the mean Standard Deviation of samples of 4 is the smaller, so that the unit of grouping is compara- tively larger. The moment coefficients of the five distributions were determined, and the following values found *:— Mean | S.D. By b3 Ma Bi Bo Samples of 4(7=0 ) — °5512 | °3038 — 1768 — 1:918 | Samples of 8(7=0) | — 3731 | °1392 — 0454 = 2°336 Samples of 4(7=°66) 5609 | *4680 | 2190 | —°1570 2152 2°245 | 4°489 | Samples of 8 (7=-66) .6139 | *2684 | -07202 | — 02634 02714 1°857 5°232 Samples of 30 (7=°66) 661 ‘L001 | °01003 | —-000882 | -000461 ‘7713 | 4°580 Considering first the “no correlation” distributions I attempted to fit a Pearson curve to the first of them. As might be expected, the range proved limited and as symmetry had been assumed in calculating the moments, a Type II curve 2 +272 resulted. The equation was y= % (1 - a) , the range of which is 2074. / Now the real range is clearly 2, and only a very small alteration in ~, is required to make the value of the index zero. Consequently the equation y¥ =y(1—2*) was suggested. This means an even distribution of r between 1 and —1, with s.D. = ‘5774+ °:010 vice °5512 actual, uw. ='3333 4+ '0116 vice ‘3038, = ‘2000 +016 vice 1768 and §,= 1:800 +12 vice 1:918, all values as close as could perhaps be expected considering that the grouping must make both f, and py too low. Working from y=y,(1—.2?) for samples of 4 I guessed the formula n-A y=y(1—«?) 2 and proceeded to calculate the moments. By using the transformation «= sin 6 we get y= y, cos” 6, dx = cos 6dé, 2 yde=2y0f cos” 0dé, Tv cos” 3 Adé@ — 2y[ cos”! dé, 0 wa r 2 ay da = 2y, / “0 /0 and so on. Whence i 3 Stel) a ee = ———_ = SS —_. Se a . ome ale (y= Dey Bs n+1 n+1 * In the cases of no correlation the moments were taken about zero, the known centroid of the distribution. By SruDEnt 307 Putting n=8 we get the equation y= y,(1—.«*) and ff, = 4 ='1429 + 0050 instead of actual +1392, fy = gy = 0476 + 0038 ; ‘ ‘0454, a ='3780 + 0066 ; o ‘3731, 8.=3 — § = 2333 + 012 5 3 62386. 2 -\ 2021 The equation calculated from the actual moments is y = y, (1 - 3503) whence the calculated range is 1:98, whereas it is known to be 2. The following tables compare the actual distributions with those calculated from the equations. Distribution of r from samples of 4 compared with the equation y = 745 (1 — a)’, wD WD LD 19 ls LD Lo WD vey wD LD Vey ] ] | FP p pr pep ep ey te] ot + ns Ca cele s. lee el S42 V8) |e) Sols) See 1D oy S DW | | wm | wo | wow | 06 Toy ra ey & = ye PSN | |S Sa esd Se SS N = = E aE) |) Steal Saat 5 a IE Cave T ie Wa ee ss EO | ] | pia} ulyreti +p +l] + f 4+ + Actual ... | 64 | 45} | 554 | 67 | 59 | 62 | 63 | 58 | GO| 64] 514 | 418 | 54 Calculated | 65 | 56 56 56 6 | 56 | 56 | 56 | 56 | 56 | 56 56 5 Difference | -1]/—105 | —4 |+11 |+3 |+6 /+7 /+2 |+4 48 | —43 |-143 | -11 From this we get x? =13°30, P= "34. It will however be noticed that the grouping has caused all the middle compartments to contain more than the calculated, as pointed out above. Distribution of r from samples of 8 compared with the equation 150 x 15 =—__.— (1 - 2’). 16 ) SP) |S Sa es tea Ae a ee fe an ie © a > x S06] eS 100 l (Pies + - PIP se |e cee Slee Nees es. eco Le 287.2 |e) 2 1) = Bee ere ae ae |e ~ ~ e- |e }/e,e] es a ie) Sa) ro 89 X > > SS) Sa) wD © ae ] | ee | eo l ] + + f|+t{] + ]+ 4] Actual ... | 2 27 | 44] 60/96 | 1144 | 103 | 85 | 98 | 65 | 373 | 144] 38 Calculated | 44 | 203 | 43 | 67 | 87 | 100 | 105 | 1003 | 87 | 67 | 20$ | 4% Difference | —24 | +6$ )4+1 |-7 49 | +14} -2 | —153/411} |-2 |-53 | -6 |-13 whence y?= 13°94, P =°30. 39—2 308 Probable Error of a Correlation Coefficient In this case the grouping has had less influence and the largest contributions to y? (in the second, sixth, eighth, and twelfth compartments) are due to differences of opposite sign on opposite sides, and may therefore be supposed to be entirely due to random sampling. My equation then fits the two series of empirical results about as well as could be expected. I will now show that it is in accordance with the two theoretical 1 2 : é cases n “large” and n=2, for g= pea which approximates sufficiently closely to n— aby Pearson and Filon’s 52 when 7=0 and » is large. Also when n is large 8, n becomes 3 and the distribution is normal. And if n= 2, the equation becomes y = y, (1 — 2”)“!* where N Yo = 1 . 2 | (1 — 2*)da 0 Put «=sin@. Then dx=cos 6dé, w=% /|[° sec ad9 = 5/0 =0, 0 ae. there is no frequency except where (1 —.«*) is infinite, all the frequency is equally divided between #=1 and #2 =—1 which we know to be actually the case. n—4 Consequently I believe that the equation y = y,(1—.*) 2. probably represents the theoretical distribution of * when samples of n are drawn from a normally distri- buted population with no correlation. Even if it does not do so, I am sure that it will give a close approximation to it. Let us consider Mr Hooker’s limit of ‘50 in the light of this equation. For e=sin 0 y =Yy, cos" 0 21 cases the equation becomes and the proportion of the area lying beyond # = + °50 will be =sin—!'50 e @=— | 2 cos!® dé 6 | 3 cos!’ 6d@ 0 I find this to be ‘02099, or we may expect to find one case in 50 occurring outside the limits + ‘50 when there is no correlation and the sample numbers 21. * If a Pearson curve be fitted to the distribution whose moment coefficients are wg=1l=p,y and H3=0 we have B2=1, B,=0, hence the curve must be of Type II. and the equation is given by 582-9 2 (3 — Bs) a2 m 9 Bo Y=Yo ( = a) where a2 = 203 — 1 and m= or y=Yo (L-a?)}, agreeing with the general formula. By StTuDENT 309 When however there is correlation, I cannot suggest an equation which will accord with the facts, but as I have spent a good deal of time over the problem I will point out some of the necessities of the case. (1) With small samples the value certainly lies nearer to zero than the real value of R, e.g. samples of 2: mean at = sin R, samples of 4 (real value 66) ‘561* + °011, samples of 8 (real value 66) “614+ + 065. But with samples of 30 (real value ‘66) mean at ‘6609 + ‘0067 shows that the mean value approaches the real value comparatively rapidly. 7 por Vvn—1 even if we give the mean value of 7 for samples of the size taken, eg. for samples of 2, S05 eal — (= sin“ R). 7 For samples of 4, calculated} 3957 + ‘0069 ; actual *4680, 5 ‘6 8 ‘3 2355 +0041; actual ‘2684. But samples of 30 calculated 1046 + °0018, actual ‘1001, again show that with samples as large as 30 the ordinary formula is justified. (2) The standard deviation is larger than accords with the formula (3) When there was no correlation the range found by fitting a Pearson curve to the distribution was accurately 2 in the theoretical case of samples of two, and well within the probable error for empirical distributions of samples of 4 and 8. But when we have correlation this process does not give the range closely for the empirical distribution (samples of 4 give 2°137, samples of 8 2°699, samples of 30 infinity) and the range calculated from samples of 2, which is 2V4+ 3p + 18pm,” — 9p,’ 3+ py ‘ 22 ee : . (where fy =1— 5 sin R) ) is always less than 2 except in the case where y, is 1, 2.e. when there is no correlation. Hence the distribution probably cannot be represented by any of Prof. Pearson’s types of frequency curve unless R= 0. (4) The distribution is skew with a tail towards zero. * The value must be slightly larger than this (perhaps even by ‘03) as Sheppard’s corrections were not used. + Again higher, but not by more than ‘02. ete Vn-1 value R, the difference would be even greater. where 7 is taken as the mean value for the size of the sample. If we took the real 310 Probable Error of a Correlation Coefficient (5) Tosum up:—If y= ¢ (a, R,n) be the equation, it must satisfy the following requirements. If R=1, 1 is the only value of w which gives the value of y other than zero, If n=2, +1 are the only values of w todo so. If R=0 the equation n—4 probably reduces to y=yo(1 — 2) 2. Conclusions. It has been shown that when there is no correlation between two normally n—4 2 distributed variables y= y,(1—.«”) 2 gives fairly closely the distribution of r found from samples of n. Next, the general problem has been stated and three distributions of r have been given which show the sort of variation which occurs. I hope they may serve as illustrations for the successful solver of the problem. ZUR FRAGE VOM VIERGLIEDERIGEN TARSUS DER BLATTIDAE UND DER REGENERATION DER FUSSE DERSELBEN. Von TH. 8S. SCHTSCHERBAKOW (Laboratorium des Zoolog. Museums der Universitiit Moskau). In den Jahren 1897/98 wurde eine interessante Untersuchung von H. H. Brindley* verdffentlicht zur Frage der Regeneration der Fiisse der Blattidae in Zusammen- hang mit der Erscheinung eines viergliederigen Tarsus bei denselben. Diese Abhandlung beruhte auf einer grossen Menge Materials. Der Autor hat beimahe bewiesen, dass der viergliedrige Tarsus der Schaben ein Regenerationsprodukt ist, und keine “congenital variation” Erscheinung. Ich nahm mir vor, seine Schlussfolgerungen statistisch zu kontrollieren, da ich 4839 Stiick Stylopyga orientalis zur Verfiigung hatte. Darunter waren erwachsen und geschlechtsreif (22—27 mm. lang) 1768 Exemplare, 402 {/f und 1366 ¢ ¢; nicht geschlechtsreif waren 250 Stiick (von 15—20 mm. Linge); deren Geschlecht nicht festgestellt wurde, da ich die hierzu erforderlichen Sektionen nicht vornahm ; ebensolcher Individuen (von 10—15 mm. Linge) gab es 554, und ebenso geschlechts- unreifer, vor kurzem aus dem Kokon gekommener (von 10—5 mm. Linge und kleiner) hatte ich 2267 Stiick. Brindley hatte nur 3611 Exemplare derselben Art zur Verfiigung: 1635 “adult,” d. h. geschlechtsreifer, und 1976 “young” (nicht geschlechtsreifer), Somit hatte ich mehr Material in meinen Handen, als Brindley, und zwar um 133 erwachsene und 1095 nicht geschlechtsreife Stiick. Alle diese Individuen waren von mir im Laufe von etwa 2 Wochen (Ende April 1907 bis Anfang Mai desselben Jahres) in der Stadt Serpuchow (Gouvernement Moskau, Zentralrussland) gefangen worden, in der Kiiche eines Hauses, in dem die Schaben fast gar nicht verfolgt wurden und reichliche Nahrung fanden in Form von rohen und gekochten Kartoffeln und russischen Roggenbrotes, die in ftir die Nacht unverschlossenen Tischen und Schrinken aufbewahrt wurden. Das Sammeln fand in folgender Weise statt: regelmissig jede Nacht bewaffnete ich mich mit einer entomologischen, flachendigen Pinzette und einem grossen Glasgefiiss mit Spiritus und fing die Schaben auf der Diele, an den Wiinden, in den Schranken, indem ich jedes Stiick vorsichtig mit der Pinzette griff und sofort in den Spiritus * Proc. Zoolog. Soc. London, 1897, pp. 903—916, 1898, p. 924 ff. 312 Der vierqhiederige Tarsus der Blattidae warf. Auf diese Art fing ich sehr wenig Schaben, verscheuchte sie vielmehr. Darum wandte ich ferner folgende Methode an: ich umband die Aussenseite niedriger messingener, eiserner Schiisseln und Glasgefasse mit Lappen, um den Schaben den Zutritt zum Innern dieser Gefisse zu erleichtern und legte grosse Stiicke Roggenbrot (frisches) in dieselben hinein, nachdem ich die obere Flache dieser Stiicke mit ungereinigtem Vaselin beschmiert hatte, der gehdrig mit einer schwachen Liésung Arseniksalz vermengt war. Letzteres wurde dem Vaselin zu dem Zwecke beigemengt, damit die Schaben, nachdem sie vom Brot und Vaselin genossen hatten, nicht im Gefiisse herumliefen und ihre Fiisse nicht beschadigten, und wenn sie in den Schiisseln von einem Ende zum andern rannten unter den Dutzenden und Hunderten ihrer Gefahrten, sich nicht gegenseitig driickten und zu Kriippeln machten. In der Tat fand ich am Morgen in den Gefiissen Schaben, die nicht mehr zu schnellem Laufe fihig waren, wohl aber noch lebten und langsam umherkrochen. Der ganze Fang wurde am Morgen in Spiritus geworfen. Diese Fangweise ergab gute Resultate; nur ihr habe ich die grosse Menge behender, junger Schaben zu verdanken. In dem Hause, in dem ich den Fang ausiibte, lebte nur ausschliesslich die eine Art Stylopyga orientalis, davon iiberzeugte ich mich durch eine Reihe von Besichtigungen und Nachsuchen. Daher bestand mein Material nur aus Reprisentanten dieser Art und unter der ganzen Menge ge- schlechtsunreifer Individuen, die mir als Material dienten, gab es nicht ein einziges Exemplar Phyllodromia germanica. So hatte ich ein absolut reines, reiches Material zur Verfiigung. Nach Durchsicht des ganzen Materials an schwarzen Schaben erhielt ich folgende Zahlen : Geschlechtsreife Individuen. Im ganzen 1768 Stiick. 402 /, 1366 $9. Fille mit viergliedrigem Tarsus im ganzen 427. Allerlei Mutilationen 313*. Nichtgeschlechtsreife Individuen. (a) Lange 15—20 mm. 250 Stiick. Falle mit 4-gliedrigem Tarsus im ganzen 47. Allerlei Mutila- tionen 18. (b) Linge 10—15 mm. 554 Stiick. Fille mit 4-gliedrigem Tarsus im ganzen 51. Allerlei Mutila- tionen 19. (c) Lange 10—5 mm. und kleiner. 2267 Stiick. Falle mit 4-gliedrigem Tarsus im ganzen 5. Allerlei Mutila- tionen OF. * Unter ‘‘Mutilation”” verstehe ich allerlei Briiche der Tarsen (Fiisse) an verschiedenen Gelenken, Beschidigungen und allerlei Verkriippelungen an denselben und ihren Teilen. + Es gab wohl Mutilationen unter den Individuen von dieser Griésse, aber in Riicksicht darauf, dass das Material héchst spréde und briichig und in starkem Spiritus gelegen hatte, habe ich dieselben nicht mit in Rechnung gezogen, da ich annehme, dass sie durch das Herausholen des Materials aus dem Gefiss entstanden sind. Tu. S. ScutTscHERBAKOW 313 Im ganzen 4839 Stiick. Gesamtzahl der Falle mit 4-gliedrigem Tarsus 530. Gesamtzahl der Mutilationen 350. In Prozenten ausgedriickt wiirden unsere Zahlen wie folgt erscheinen : Geschlechtsreife Individuen ; °/, der 4-gliedrigen Tarsus im Verhiiltnis zur Gesamtzahl der Individuen: zur Zahl der f/f: zur Zahl der 2 2: 24,15 20,69 25,109. Geschlechtsunreife Individuen ; °/, der 4-gliedrigen Tarsus fiir (a) Individuen von 15—20 mm. Linge 18,8 (0) » » MOIS 9,205 (c) a 3 0b. 4, 3 und kleiner 0,22. Fiir die Gesamtzahl der geschlechtsunreifen Individuen 3,35. Fiir die Gesamtzahl der geschlechtsreifen und geschlechtsunreifen Individuen 10,95. Wenn wir unsere °/,-Zahlen mit denen von H. Brindley vergleichen, sehen wir, dass die °/,-Zahlen der viergliedrigen Tarsus fiir geschlechtsreife {bei uns wie bei Brindley fast gleich sind (bei uns 20,69°/,, bet Brindley 20,6°/.). Der Prozentsatz der 4-gliedrigen Tarsus bei unseren $$ ist hoher als bei Brindley (bei uns 25,109°/,, bei Brindley 21,8°/,). Was aber die geschlechtsunreifen Individuen anbelangt, so hat Brindley nicht den Unterschied nach den Gréssever- haltnissen durchgefiihrt. Wenn wir also die vorletzte Kategorie vergleichen, sehen wir, dass der °/,-Satz der 4-gliedrigen Tarsus bei allen geschlechtsunreifen Individuen bei uns viel niedriger ist, als bei Brindley (bei uns 3,35 °/,, bei Brindley 16,4°/,). Der Gesamtprozentsatz der 4-gliedrigen Tarsus fiir alle geschlechts- reifen und geschlechtsunreifen Individuen ist bei uns ebenfalls bedeutend niedriger (bei uns 10,95 °/., bei Brindley 18,7 °/,). Ein so niedriger Prozentsatz an 4-glied- rigen Tarsus fiir die Gesamtzahl der Individuen iiberhaupt und ebenso fiir die geschlechtsunreifen Formen bei mir, lasst sich dadurch erklaren, wie ich annehme, dass ich ein 14 mal gréssere Anzahl von geschlechtsunreifen Individuen bearbeitete, als von geschlechtsreifen. Ich hatte an geschlechtsunreifen Individuen um 1095 Stiick mehr zur Verfiigung, als Brindley (d. h. 3071, Brindley aber 1976). Man muss beriicksichtigen, wie schnell der °/,-Satz der 4-ghedrigen Tarsus mit dem Sinken der Gréssenverhaltnisse fillt. Besonders in die Augen fallend ist der Sprung des °/,-Satzes beim Ubergang von den 10-15 mm. langen Individuen zu den 10-5 mm. langen und noch kleineren Stiicken. Hatte H. Brindley die doppelte Zahl junger Schaben zur Verfiigung gehabt, so hatte auch er andere °/, Verhaltnisse erhalten. Gehen wir an eine weitere Analyse unserer Daten, um sie mit den Ergebnissen H. Brindleys zu vergleichen. “Tn the great majority of cases only one of the six legs bore a 4-jointed tarsus, though many individuals possessed the abnormality on more than one leg,” schreibt Biometrika v1 40 314 Der viergliederige Tarsus der Blattidae H. Brindley. Er fand, dass in der Gradation bei der schwarzen Schabe sich fol- gendes beobachten lisst : 4-gliedrige Tarsus : an 1 Fuss, an 2 Fiissen, an 3 Fiissen, an 4 Fiissen, an 5 Fiissen, an 6 Fiissen, 588 Falle, 108 Faille, 23 Falle, 10 Falle, 0 Falle, 4 Falle. Ich habe meinerseits nach meinen Berechnungen folgende Resultate erhalten : 4-gliedrige Tarsus: bei der Gesamtzahl aller Individuen (“adult” und “ young”): an 1 Fuss, an 2 Fiissen, an 3 Fiissen, an 4 Fiissen, an 5 Fiissen, an 6 Fiissen. 397 Falle, 67 Faille, 5 Falle, 1 Fall, 0 Falle, 0 Faille. Wenn man aber dieselben Daten nach der Kérperlainge geordnet durchmustert, so kommt man zu folgendem Resultate : Geschlechtsreife Individuen : an 1Fuss, an 2 Fiissen, an 3 Fiissen, an 4 Fiissen, an 5 Fiissen, an 6 Fiissen. 313 Falle, 58 Falle, 5 Falle, 1 Fall, 0 Falle, 0 Falle. Geschlechtsunreife Individuen: (a) Lange 15—20 mm. an 1 Fuss, an 2 Fiissen, an 3 Fiissen, an 4 Fiissen, an 5 Fiissen, an 6 Fiissen. 37 Faille, 5 Falle, 0 Faille, 0—, 0 —, 0 —. (b) Lange 10—15 mm. an 1 Fuss, an 2 Fiissen, an 3 Fiissen, an 4 Fiissen, an 5 Fiissen, an 6 Fiissen. 44 Falle, 3 Fille, 0 —, 0 —, 0 —, 0 —. (c) Lange 10—5 mm. und kleiner. an 1 Fuss, an 2 Fiissen, an 3 Fiissen, an 4 Fiissen, an 5 Fiissen, an 6 Fiissen. 3 Falle, 1 Fall, 0—, 0—, 0 —, 0 —. Brindley’s Zahlen sind viel héher, als unsere (wenn man die Daten seiner Tabelle mit denen der meinigen hinsichtlich der Gesamtzahl aller Individuen vergleicht). Bemerkt muss noch werden, dass mir eine der von mir untersuchten Schaben einen 4-gliedrigen Tarsus an vier Fiissen zugleich hatte. Mehr als 4 anomale Tarsus bei ein und demselben Individuum habe ich kein Mal gefunden, wihrend der englische Verfasser 4 anomale Tarsus in 10 Fallen hatte und 6 anomale in vier Fallen. Man muss bedauern, dass Brindley die Anzahl anomaler Tarsus, die gleichzeitig bei einem Individuum vorkommen, nicht nach Altersgruppen geordnet untersucht hat, indem er letztere durch die Langenmasse des Kérpers bezeichnete. Meine Daten weisen sehr lehrreiche und interessante Spriinge in der Zahl der Falle von anomalen Tarsus bei einem Individuum beim Ubergange zur letzten Altersgruppe auf. Nur bei einem von 2267 Individuen von 10—5 mm. Linge und kleiner Tu. S. ScutscHuERBAKOW 315 wurden anomale Tarsus an zwei Fiissen zugleich beobachtet und nur bei 3 Stiick , die zu derselben Gréssenkategorie gehbrten, wurde ein anomaler Tarsus an einem Fusse beobachtet! Alle iibrigen Individuen hatten also vollkommen normale Fiisse. Wir wollen auch noch hervorheben, dass nicht ein einziges geschlechtsun- reifes Individuum mehr als an zwei Fiissen anomale Tarsus besass. Brindley fand, dass bei den von ihm untersuchten schwarzen Schaben folgende Haufigkeit der anomalen Tarsus in der Reihenfolge jedes der drei Beinpaare (in Prozenten ausgedriickt) statt hatte : 1s Beinpaar : 2's Beinpaar : 3S Beinpaar : “adult”: 26,9°/. 22,9 °/, a0) fe “young Reenlioe |3 Zien fe 56,4 °/. “total: 214°). 25,4 °/, 53,2 °/. Nach meiner Berechnung erhielt ich folgende Resultate : Geschlechtsreife Individuen : 28,33 °/, 24,12 °/, 47,54 °/, Nichtgeschlechtsreife Individuen : 20,38 °/, 27,18 °/, 49,51 °/, “Total”: ZOO 24,71 °/., 48,47 °/, Nichtgeschlechtsreife Individuen (nach Altersgruppen) : (a) Lange 15—20 mm.: Delile |. 7,05 °/, 9,87 °/. (b) Linge 15—10 mm.: 4.08 °/. 6,63 °/, 15,3 °/, (c) Lange 10—5 mm. und kleiner: Os) 3 0°/. 0,15 °/, Bei den von mir untersuchten geschlechtsreifen Formen war der °/,-Satz der anomalen Tarsus am 1%" Paar Fiisse um 1,43°/, hoher, als bei Brindley. Am 2'n Beinpaar bei denselben Individuen ist mein Prozentsatz um 1,22°/, hoher, am dritten Beinpaar um 2,66°/, niedriger, als bei Brindley. Was die jungen Stiicke anbelangt, so ist mein Prozentsatz fiir das 1° Beinpaar um 4,68 °/, hoher, fiir das 2% um 0,52°/, niedriger, fiir das 3" ebenfalls um 6,89 °/, niedriger. Was aber die Rubrik “Total” anbetrifft, so steht die Sache folgendermassen: fiir das erste Beinpaar sind meine Zahlen um 5,39°/, hoher, als die von Brindley, fiir das 2° um 0,69 °/, niedriger und fiir das 3° auch um 4,73 °/, geringer. Die Daten fiir die Nichtgeschlechtsreifen nach Altersgruppen lassen sich nicht vergleichen, da in Brindley’s Tabellen diese Kategorie fehlt. Sehr interessant ist der Umstand, dass sowohl in meiner wie in Brindley’s Tabelle der °/,-Satz der 4-gliedrigen Tarsus fiir das 2" Beinpaar bei den “adult” 40—2 316 Der viergliederige Tarsus der Blattidae niedriger ist als fiir das 18 Beinpaar. Bei den als “young” bezeichneten Individuen (nichtgeschlechtsreif) ist derselbe °/,-Satz héher. In der Kategorie “Total” ist der- selbe bei Brindley hoher, bei mir geringer. Wenn man aber die nichtgeschlechts- reifen Individuen nach Altersstufen untersucht, so wachst derselbe, wihrend er in der Gruppe 10—5 mm. und kleiner =0 ist, in der folgenden Gruppe plotzlich, indem er viel héher sich stellt, als der entsprechende °/,-Satz fiir das 18° Beinpaar. Warum fallt er in der Kategorie “adult”? “The long third pair of legs seem to suffer more from their exposed condition, as compared with the less extended anterior pairs,” sagt Brindley. Warum aber hat das zweite Paar Beine einen geringeren Prozentsatz anomaler Tarsus? Mir scheint deshalb, weil es zwischen dem ersten und dritten Paar befindlich mehr vor Zufillen von hinten geschiitzt ist, als das dritte Paar, und von vorne mehr als das erste. Vor allem leiden durch allerlei Verletzungen die beiden aussersten Paare— das erste und dritte, und dann erst das zweite, das sich zwischen ihnen befindet, wie zwischen zwei Schilden. Diese Erklarung passt aber nur fiir die Kategorie “adult,” die geschlechtsreifen Individuen, und lasst sich durchaus nicht auf die “young” und nichtgeschlechtsreifen Tiere anwenden. Bei letzteren wiichst der Prozentsatz anomaler Tarsus mit dem Ubergange vom ersten Paar zum zweiten und von diesem zum dritten. Gehen wir jetzt zur weiteren Analyse unserer Daten im Vergleich zu denen in Brindley’s Arbeit iiber. “The abnormal tarsi occurred indifferently on the right and left sides—thus, in 1329 cases in S. orientalis 661 were on the right and 668 on the left side,” schreibt Brindley. Meine Zahlen ergeben dasselbe : Geschlechtsreife Individuen : ein viergliederiger Tarsus fand sich auf der linken Seite: auf der rechten Seite: in 212 Fallen in 215 Fallen Geschlechtsunreife Individuen : (a) Lange 15—20 mm.: in 24, in 23 (b) Linge 10—15 mm.: Le ay ea (c) Lange 10—5 mm. und klemer: Pe is, Fo hans Gesamtzahl fiir die Geschlechtsunreifen : » 51, Re ” 52 Gesamtzahl fiir beide Kategorien : » 203, » 267 Tu. S. ScurscHERBAKOW 317 Eine solche Unterschiedslosigkeit fiir das Verhalten der rechten und linken Seite ist ohne jede Erklarung klar begreiflich. H. Brindley stellte auf experimentellem Wege fest, dass nach entsprechenden Verletzungen der Tarsen, die schwarzen Schaben nach den Haiutungen viergliedrige Tarsus erhielten. Er sagt in seiner Arbeit nichts dariiber, ob er irgend welche Verwundungen oder Trauma an dem von ihm untersuchten und konservierten Material vorfand, und wenn er solche vorgefunden hat, weshalb hat er diese Erscheinungen nicht untersucht, weshalb hat er dieselben, so zu sagen, als quantité négligeable angesehen ? Als ich mein konserviertes Material durchmusterte, fand ich am selben nicht wenig verschiedenartige Traumata. In meinen Notizen vermerkte ich bloss die Traumata ante captivationem. Die letzteren besitzen charakteristische Merkmale, die es gestatten, sie unter den Fallen von Traumata post mortem zu erkennen : das ist eine schwarzbraune Narbe an der Stelle der Verwundung, eine gewisse Runzelung des Chitins um dieselbe; aihnliche Merkmale beobachtete ich auch an lebenden Tarakanen (Schaben), die ich in Kiifigen hielt, nachdem ich ihnen vorher die Fiisse an verschiedenen Gelenkstellen beschnitten hatte. H. Brindley selbst sagt, dass bei einer Schabe, die in spirito gelegen habe, eine leichte Briichigkeit der Beine in der Gegend des tarso-tibialen Gelenkes zu bemerken ist, waihrend Femur und Tibia nur gewaltsam getrennt werden kénnen. Die Verwundungen ante captivationem sind scharf unterschiedbar von den Traumata post captiva- tionem et post mortem: eine Narbe mit scharfem Dunkelwerden des Chitins in letzterem Falle habe ich nie beobachtet, waihrend dieses fiir Verwundungen der ersten Kategorie charakteristisch ist. Es ist natiirlich méglich, dass in meinen Zahlen sich Ungenauigkeiten finden: bei dem eiligen Fange von Schaben mit der Pinzette in der Hand konnte ich ihnen Verletzungen zufiigen—und oft entkamen mir solche Schaben und gerieten dann vielleicht nach einigen Tagen unter mein Material, indem sie in die Fanggefiisse krochen. Andererseits konnte ich mit der Pinzette in den Spiritus Schaben werfen, und ihnen hierbei die Fiisse verletzen und diese konnten keine Narbe an der Verwundungsstelle bilden und gerieten auf diese Weise in die Kategorie der Verwundungen post captivationem et mortem, welche ich nicht registrierte. Wenn man aber in Betracht zieht, dass diese beiden Reihen von Verletzungen beim Fange einander entgegengesetzt sind in Hinsicht der Registration der Traumata, und wenn man im Auge behiilt, dass ich mit der entomo- logischen Pinzette, wie oben gesagt, verhiltnismiissig wenig Schaben gefangen habe, so glaube ich, dass in meinen Zahlen nur eine geringe Ungenauigkeit vorwalten kann. Und somit wollen wir an die Betrachtung der Traumata gehen. Vor allem will ich mitteilen, welcher Art Verletzungen ich beobachtete und _ registrierte. Zerreissungen im Gebiet der tarso-tibialen und Femoro-trochanter-Gelenke (sehr selten im Gebiet der tibio-femoralen Einlenkungen), Briiche der einzelnen Tarsen- glieder, Abbrechen der Krallen sowohl am normalen fiinfgliedrigen, wie auch am anomalen viergliedrigen Tarsus—das sind die bei meinem Material hiufigsten 318 Der viergliederige Tarsus der Blattidae Traumafille. Alle diese Traumata wurden an geschlechtsreifen Individuen gefunden ; bei den nichtgeschlechtsreifen wurden dieselben Verletzungen bemerkt, ausgenommen die tibio-femoralen Zerreissungen, die niemals bei ihnen beobachtet wurden. Ausserdem wurden einige andere Verletzungen registriert: Zerreissungen in der Trochantero-coxal-Einlenkung (ein Fall bei einem Imago 7), Abbrechen des ganzen Fusses (1 Fall bei einem Imago ¥*), Abbruch des ganzen Tarsus und Verkriimmung des Tibiaendes (1 Fall bei einem ¥-Imago), Abbruch, der fast initten iiber das erste (von der Tibia aus gerechnet) Tarsusglied ging, so dass die Hiilfte des Gliedes erhalten blieb (1 Fall bei einem Individuum bei der Kategorie 15—20 mm. langer Larven), Abbruch des ganzen Tarsus und Verkriippelung der Tibia (1 Fall bei einem Individuum aus der Kategorie 10—15 mm. langer Larven). Gehen wir an die Durchsicht der ziffernmissigen Daten hinsichtlich der Verwundungen und beginnen wir mit den geschlechtsreifen Individuen. In dieser Kategorie waren alle abmassgefiihrten Verletzungen bei 231 Individuen beobachtet worden, {if 90 und 3? 141, oder in Prozenten ausgedriickt bei 13,06 °/, beider Geschlechter, bei 22,43 °/, aller Mannchen u. bei 10,32 °/, aller Weibchen. Die hierher gehérigen Zahlen sind folgende : Traumata bei Geschlechtsreifen : Tarso-tibiale Traumata : im ganzen 124 Falle von Trauma: am 18" rechten Fuss 8 Falle ie ie linken - 9 ,, Bhan rechten ,, 20 ,, _ linken ee ee ee Orne arechticn emo 8 = " linken a ae far Mallen °/ age 37 Rall. oe 20lgacm ) }70 nn = 56ABY.. Femoro-trochanter-Traumata : im ganzen 109 Falle von Trauma: am 1s" ~~ rechten Fuss 10 Fille rf . linken 5 ALB os ten = 2 ea so OT 53 | 25 ‘ , gp 28,02°,. ns - inken » 14, aoa rechten ,, 27 4, ) , lmken® 34 30 Abbruch der Krallen (fiinfgliedriger Tarsus), im ganzen 22 Falle: | 23 Fille, in °/, °/, =21,1°/,. 61 ” ” ” = 55,96 Wine am 1ste= rechten Fuss 3 Fiille 5 Falle, in °/, °/, = 22,72°/,. ae ae linken os De ORs rechten 5 — ” fe} . ” 9 »” ? »” = 40,90 es - linken = 4 , 4 aes rechten _,, 6, : 8 -, a linken _,, 2 ” » ra 36,36 pe Abbruch Tu. S. ScutrscHERBAKOW der Krallen (viergliedriger Tarsus) : im ganzen 3 Falle: 319 am 1ste= yechten Fuss 1 Fall a oe linken » O Falle Pee rechten sr. 10) o., | das prozentuale Verhaltnis a es linken 2 Ol Ss wurde nicht berechnet. » o yechten , 2 ,, fy linker 4, 0° 3, Abbruch der Tarsusglieder : im ganzen 43 Fille: 4 Glieder abgebrochen : 6 Faille, in °/, °/, = 18,95 °/, 3 ” > i 4 ” » » i 9,3 ae 2 ” ” Ee) ” ” » aaa 20,93 he 1 Ghed = 1:24 Cy, 3 ic De am 1ste>” yechten Fuss 8 Falle von Abbruch . 2 of of ° nar linken £ 4, » x ha, LE ie gten ~—s rechten 4 ” : ” ? > ” e = 20, f fe} » ” linken ” 5 ” ” ”? "2 cs a I. 3" ~—s rechten 11 : : ”? »” ” ” _ 1 1 fe) ” » linken » 11 ” ”? 9%») 22; a ” ° : : lo Tibio-femorale Traumata : im ganzen 4 Falle: am 1se2 yechten Fuss 0 Falle 0 aa linken «, 0 ,, fe hong TeCHtehes 5 O94, 3 | das prozentuale Verhaltnis oa 2 linkent 63,093) 4, 4 | wurde nicht berechnet. 3" rechten , 1 Fall | 1 » » linkn , 0, Sf) Trochantero-coxale Traumata : im ganzen 1 Fall : am 3'" rechten Fuss: Abbruch des ganzen Fusses: im ganzen 1 Fall: am 1%" rechten Fuss. Abbruch des Tarsus und Vorbiegung der Tibia: im ganzen 1 Fall: am 3" linken Fuss. 320 Der viergliederige Tarsus der Blattidae Wenden wir uns den Traumata bei geschlechtsunreifen Individuen zu und sehen wir uns zuerst die Traumata iiberhaupt fiir alle geschlechtsunreifen Formen an. am Traumata ber der Gesamthert der Geschlechtsunreifen : jsten ”» ten ~_ ” Sten ysten ” 9ten ” pten ” Tarso-tibiale Traumata: im ganzen 13 Faille: rechten Fuss 1 Fall iat in °/,°/,= 7,68°/, linken ,, O Falle rechten ,, 1 Fall ) a : linken ,, 8 Fille} 4, ey = SO rechten ,, 5 ,, 2 ; linken 3 3 ‘ 8, ” ” = 61,44 ics Femoro-trochanter-Traumata : im ganzen 11 Falle: rechten Fuss 0 ay 1, an 2/S2f= 9.09 linken , 1 Fall rechten , 1 .,, ; 7 linken - 5 - 2 vate f > 6 op = 22a rechten , 3 ,, Bee linken ,, 4. , Ve pi = C303 ake Abbruch von Krallen (fiinfgliedriger Tarsus) : im ganzen 6 Faille: rechten Fuss 1 Fall lnken , 1 >) ch} 1D oid aoe ae »”» rechten , 2 Faille 7 : linken » 1 Fall Is, » 3 =4oS rechten 1 ” ” = 16.6 FS linken ,, O eae eo ifs Abbruch von Tarsusgliedern : im ganzen 5 Falle: Abgebrochen 4 Glieder, 0 Fiille, in °/, °/,= 0 ” 3 ” » 0 » 9 9 33 ar 0 ” 2 ” ? 1 Fall, ”) ”? = a 1 Glied rechten Fuss 1 Fall linken wlan , * Falle;,; 5 2a i 20) rechten 0 Falle » = 20 9 linken » IL Fall {1, ‘ ‘. I. rechten » 2 Falle ye. e407 linken 3 ON es i > TH. S. ScHTSCHERBAKOW 321 Wenden wir uns nun den Traumata bei denselben geschlechtsunreifen Indi- viduen zu, indem wir sie nach den schon oben angegebenen Altersabstufungen ordnen : Geschlechtsunreife Individuen : (a) Lange 15—20 mm. Tarso-tibial-Traumata : im ganzen 6 Falle: am 1%te2 rechten Fuss 1 Fall a en , linken 0 mie in ie j2— 1616 ils 7 oe rechten, 4, 0 4; ae ” ” linken 4 1 Fall Up ” ” — 16,6 ie ” Sten rechten ” 3 Falle oe A ” ” linken 3 1 Fall 4, ” 99) ea 66,6 Hen Femoro-trochanter-Trau mata : im ganzen 5 Faille: am 1ste" rechten Fuss 0 Falle one f es lnken ,, 1 Fall Li, in °/, “/o = 20°/, me Del rechteie «6 sy 5 nae takers "0 aaa pee 0 Pumice) SP ENECHLEN Wars os 255 , Ee linken ,, 1 Fall Is, Doe or PS 1OU Abbruch der Krallen (fiinfgliedriger Tarsus) : im ganzen 3 Faille: am 1" rechten Fuss 1 Fall in linken ,, O Falle ten ey rechten ,, 1 Fall 1 Lin of 9) = 38,3°/.. ° Pan, oF linken ,, O Falle ,» 3" rechten , 1 Fall {1 he linken , O Falle) } Abbruch von Tarsengliedern : im ganzen 3 Fille: 4 Glieder abgebrochen : 0 Fille, in °/, °/, =9°/, 3 x 5 :0 , ee eas 2 . * ol all) 3504 = 338] 5 1 Glied ‘ -2 Falle , » =66,6°/,. am 1%" rechten Fuss 1 Fall » linken ,, O Faille Pee ieee |e gten ~—s rechten 0 ) é ” ” ” = 0 eee oe ee ten 3s aes rechten ae TOR co: 2, ee aoe ? linken , O., Biometrika v1 41 322 Der viergliederige Tarsus der Blattidae Abbruch des ersten Tarsengliedes in der Mitte seiner Lange: ein Fall: am 3" linken Fuss. (b) Lange 10—15 mm. Tarso-tibial-Traumata : im ganzen 7 Faille: am 1" rechten Fuss 0 Faille Ree ; ” ” linken FF 0) ‘ 0, in be ie = 0 Ip. gten rechten ,, 1 Fall — 49 ° ” ” linken % 9 mate 3, ” » = 42,84 ie ten rechten _,, Diee din ae ” ” linken yy 9 < 4, ” » = 57,12 ths 4 Femoro-trochanter-Traumata : im ganzen 6 Fille: am 1" rechten Fuss 0 Fille oj 0 ° 10 ih Ip = 0 fe » lnken ,,: 0 ;; gten ~—s rechten 0 » ; ” ” = ‘ 2 5 ” ” linken a 2 i p ” ” 3 3, ie , 3 yechten ,, 1 Fall bs : ” ” linken 55 3 Falle | 4, ” ” = 66,4 hss Abbruch der Krallen (5-gliedriger Tarsus) : im ganzen 3 Falle: am 1%" rechten Fuss 0 Falle Lj lnken , 1 Fall ‘ eo rechten, alee = i > linken =, 1, 12» » = 686" gies ~—s rechten 0 Fille ) : ” » 0) = F ee Smee a a °/, = 33,3 °/, Abbruch von Tarsengliedern : im ganzen 2 Faille: 4, Glieder abgebrochen : 0 Fille, in °/, °/, =0°/, 3 7 3 000 rey One 2 . ' es ee Se 1 Glied , »>» » =100°/,. iF in */, °/, = 50°/, il ” FS ie 50 Ye ore linken ,, 1 Fall » 2%" rechten , 0 Falle ee linken ,, 1 Fall » om rechten |; 3 Falle ” ” linken ” 0 a) am 1%" rechten Fuss 0 rail a 0, ” 9 0 sa Tu. S. ScHTSCHERBAKOW 323 Abbruch des ganzen Tarsus und verkriippelte Tibia: im ganzen 1 Fall: am 2" rechten Fuss. (c) Lange 10—5 mm. und kleiner: kein Fall. (Verkriippelungen und Traumata wurden nicht registriert, weil sie in Menge als Erscheinungen post captivationem et mortem auftraten.) Wir sahen schon oben, dass der Prozentsatz der anomalen (viergliedrigen) Tarsus mit dem Ubergange von jedem nach vorne gelegenen Beinpaare zum folgenden steigt und dass besonders dieses Ansteigen am dritten Fusspaar bedeutend erscheint. Wenn wir nun die Traumata nehmen, so sehen wir, dass dieselbe Gesetzmiissigkeit auch bei folgenden Traumata vorherrscht : (1) bei den tarso-tibialen Traumata (bei geschlechtsreifen Individuen, bei den nichtgeschlechtsreifen tiberhaupt, in der Kategorie derselben von 15—20 mm. und von 10—15 mm Lange); (2) bei den Femoro-trochanter-Traumata (bei geschlechtsreifen Individuen, bei den nichtgeschlechtsreifen iiberhaupt, bei denen der Kategorien 15—20 mm., sowie 1O—15 mm. Linge). (3) Abbruch von Tarsengliedern (bei geschlechtsreifen Individuen, nichtge- schlechtsreifen tiberhaupt und denen der Kategorien 15—20 mm, und 10—15 mm. Lange). Was aber den Abbruch von Krallen anbelangt, so ist diese Art Trauma, wahrend sie in Hinsicht auf Gesetzmissigkeit der oben angefiihrten analog ist bei den Individuen die die Geschlechtsreife erlangten, bei den nichtgeschlechtsreifen Tieren keiner greifbaren Gesetzmissigkeit unterworfen (oder eher ohne alle Gesetzmassigkeit). Alle iibrigen Falle von Traumata (tibio-femorale u. s. w.) unterliegen gar keiner Gesetzmissigkeit. Wenden wir nun unsere Aufmerksamkeit den tarso-tibialen und femoro- trochanter-Traumata zu. H. Brindley weist bei Mitteilung iiber seine Versuche iiber die Regeneration des Tarsus bei der schwarzen Schabe in die Tabelle E seiner Arbeit darauf hin, was fiir Verletzungen und an welchen Stellen der Beine er sie den von ihm zu Experimenten benutzten Schaben beibrachte. Unten gebe ich diese Tabelle wieder und fiige derselben rechts ein Rubrik bei, in welcher ich die Prozentsitze der regenerierten 4-gliedrigen Tarsus ausrechnete. Aus dieser Tabelle ersehen wir, dass ausser der oberen Rubrik (“t, torn away from t,’), die tarso-tibialen und Femoro-trochanter-Traumata den gréssten Pro- zentsatz regenerierter viergliedriger 'arsen lieferten. Hierbei wollen wir hervor- heben, dass die Entfernung der bezeichneten Glieder nicht mit Instrumenten (z. B, “scissors”), sondern so geschah, wie es unter natiirlichen Verhiltnissen des Schabenlebens vor sich geht—durch einfaches Abreissen eines Gliedes von dem andern. Aber das ist noch nicht geniigend, die Form der Verletzung selbst, das Abreissen eines Gliedes vom andern an der Stelle der EHinlenkung, entspricht 41—2 324 Der vierglederige Tarsus der Blattidae H. Brindley’s Tabelle E*. Leg Number | Number of i Nature of Mutilation : of Reproductions oleae, Mutilated Mutilations Observed - t, torn away from ¢, one 3k 300 141 47 °/, ae Pin ae eee 2L 21 3 t, divided with scissors {37 109 16 14,61 °/, Totals 130 19 rep naen aps 2k 300 144 Tarsus torn away from tibia... 3R 89 45 48,58 °/, Totals 389 189 ee eth eee 3R 14 2 Tibia divided with scissors ... 31 300 122 39,42 °/, | Totals 314 124 Femur torn away from tro- se ae re hanter : ml : ° e CMe | (3Z 23 11 44,7 °/, Totals 340 152 Totals 1473 625 — der Form von Traumata, die a priori einzig und allein im gewdhnlichen Leben des Insekts vorkommen kann, und die wir schon in unseren oben angefiihrten Tabellen von Traumata beobachteten. Traumata, die sich nicht an den Einlenkungsstellen finden, erscheinen fiir das gewohnliche Leben der Schabe als Ausnahme und dabei, wie wir in den Tabellen sahen, als sehr seltene. Hieraus folgt ganz direkt, dass die von uns in unseren Tabellen aufgefiihrten Traumata von gesetzmiassigem Charakter (der gleich ist mit dem konsequenten Anwachsen des °/, am viergliedrigen Tarsus an jedem folgenden und besonders dem dritten Beinpaar) keine zufalligen sind, sondern notwendigerweise der Regeneration des viergliedrigen Tarsus vorausgehen, wobei das Maximum an Traumata gerade das Paar Beine trifft (das 3"), das auch das Maximum anomaler Tarsus aufzuweisen hat. Der zweite Folgeschluss ist der, dass das Maximum an Verletzungen auf die tarso-tibialen und Femoro-trochanter-Einlenkungen, sowie den Abbruch von Tarsengliedern fallt. Die oben von uns an unserem Material untersuchten drei gesetzmiissigen Arten von Traumata gehoren gerade in die Reihe derjenigen die in Brindley’s Versuchen das Maximum an regenerierten anomalen Tarsus ergaben. Es erscheint also der Schluss sehr walrscheinlich und * In dieser Tabelle sind folgende Bezeichnungen (nach Brindley): R und L=“ right” und “left ” = rechts u. links ; 1, 2 und 3 bezeichnet die Beinpaare der Folge nach ; ¢, und t, u.s. w. die Tarsenglieder, yom proximalen Gliede aus gerechnet. TH. S. ScHTSCHERBAKOW 325 der Wirklichkeit sehr nahekommend, dass der viergliedrige Tarsus, den wir bei der schwarzen Schabe beobachten kénnen, als ein Produkt der Regeneration nach Verletzungen der tibio-tarsalen oder Femoro-trochanter-Einlenkungen erscheint, oder des Abbrechens von Tarsusgliedern. Es ist wahrscheinlich, dass eine jede Verwundung des Schabenfusses (die nicht weiter reicht, als bis zur Femoro-trochanter-Kinlenkung) als Choc erscheint, der eine anomale Regeneration der Tarsus hervorruft, aber nicht jede Art von Ver- wundung kommt im natiirlichen Leben der Schabe vor. Die Neigung einiger weniger Einlenkungsstellen zu Traumabildungen im gewohnlichen Leben der schwarzen Schabe steht, so zu sagen, wahrscheinlich in Abhiingigkeit sowohl vom anatomischen Bau dieser Gelenke, im Vergleich zu anderen, als auch von der Art des Gehens und Laufens bei den Schaben. Brindley bemerkte schon, dass bei der schwarzen Schabe, wenn sie in Spiritus gelegen hatte, sich eine leichte Briichigkeit der Tarso-tibial-Gelenke zeigt, wahrend der Femur von der Tibia sich nur bei einiger Gewaltanwendung trennen liisst. Es wiire sehr interessant den Wieder- stand zu untersuchen, den die verschiedenen Gelenke der Fiisse der schwarzen Schabe dem Abgerissenwerden entgegensetzen. Wenden wir uns wieder unseren Traumatabellen zu. Wenn wir zusehen, wie der Prozentsatz der obenbeschriebenen drei gesetzmissigen Trauma-Arten wachst mit dem Alter der Individuen, so bemerken wir, dass der Prozentsatz dieser Verletzungen bei den nichtgeschlechtsreifen Individuen nicht kleiner ist, als bei den geschlechtsreifen, d. h. dass die Zahl der Traumata mit dem Alter nicht zunimmt (wie man aus dem wenig zahlreichen Material an nichtgeschlechtsreifen Tieren schliessen kinnte). Die Traumata stehen also nach den Altersgruppen in anderem Verhaltnis zum Prinzip des Anwachsens des Prozentsatzes der Anomalien in Abhangigkeit vom Alter, als der anomale viergliedrige Tarsus, Hierin besteht der Grundunterschied der Traumata vom anomalen Tarsus. Wenn wir uns aber wenden dem Unterschiede der Traumata in Abhiingigkeit vom Geschlechte zu, so sehen wir, dass der Prozentsatz an solchen bei den ff hoher ist, als bei den $ ¢, wahrend in Hinsicht des anomalen Tarsus die Sache umgekehrt liegt. Zeigt nicht das eine oder andere Geschlecht, so zu sagen, eine Neigung zu der einen oder andern Traumaform? Fiir diesen Fall habe ich folgende Zahlung zur Verfiigung : Tarso-tibial-Trau mata : wurden beobachtet bei 58 $$ und 48 f/f. Femoro-trochanter-Traumata : wurden gefunden bei 62 $$ und 37 J. Abbruch der Tarsusglieder : fand sich bei 21 2¢ und 17 f¢. Abbruch der Klauen (aim fiinfgliedrigen Tarsus) : fand sich bei 14 $f und7 ¢¢. Die Zahlen schwanken in solchen Grenzen, dass man von dem Zusammenhange eines oder des andern Geschlechts mit einer bestimmten Traumaform nicht sprechen kann, Wahrscheinlich unterliegen beide Geschlechter allen Arten von Verletzungen. 326 Der viergliederige Tarsus der Blattidae Man muss auch noch darauf hinweisen, dass die verschiedenen Arten von Traumata an ein uid demselben Individuum gefunden werden, zuweilen kom- biniert mit der Anwesenheit der anomalen viergliedrigen Tarsus. Es giebt folgende Trauma-Kombinationen : Tibio-tarsales und Femoro-trochanter-Trauma ; bei verschiedenen Geschlechtern an verschiedenen Fusspaaren und auf verschiede- nen Seiten: Tibio-tarsales Trauma mit Abbruch von Tarsus- Ghedern (am normalen Tarsus): bei beiden Geschlechtern an verschiedenen Fusspaaren und auf verschiedenen Seiten; Femoro-trochanter-Trauma mit Abbruch der Tarsenglieder (am normalen Tarsus): ebenso ; Tibio-tarsales Trauma mit viergliedrigen Tarsus: ebenso ; Abbruch der Tarsenglieder (am normalen Tarsus) mit vierghedrigen Tarsus: ebenso, Es kommen Traumata einer Art zu gleicher Zeit an mehreren Fiissen des Individuums vor (z. B. Femoro-trochanter-Traumata auf der rechten Seite am 2%" und 3%" Paar) Derartiger oben angefiihrten Kombinationen von verschiedenen Traumaformen mit viergliedrigen Tarsus an einem Individuum an den Fiissen verschiedener Paare und Seiten (bei beiden Geschlechtern) zihlte ich 39 Falle bei ff und 31 Fille bei f #. Was aber die nicht geschlechtsreifen Individuen angeht, so zihlte ich in der Kategorie 15—20 mm. Lange 2 Falle der oben erwaihnten Kombinationen, in der Kategorie 10—15 mm. Linge—im ganzen nur einen Fall. Wir wollen auch nicht vergessen, dass wir am anomalen viergliedrigen Tarsus ebenfalls Traumata vorfanden: Abbruch von Klauen. Nach der statistischen Aufstellung von H. Brindley und dem vorliegenden Versuche kann man annehmen, wie ich glaube, dass der anomale viergliedrige Tarsus bei Stylopyga orientalis (wie bei allen Schaben) als Produkt der Regeneration des normalen fiinfgliedrigen Tarsus auftritt, nachdem der Fuss eine Verletzung erlitten, hauptsichlich am Tibio-tarsal- oder Femoro-trochanter-Gelenk, oder nach Abbruch der Tarsenglieder. Die Frage von den inneren Ursachen eines solchen Verlaufes der Regeneration, wie er bei den Blattidae vorkommt, kann ich hier natiirlich nicht entscheiden. Das ist schon die Aufgabe des Histologen. Aber ich kann nicht umhin, die Aufmerksamkeit auf die drei oben untersuchten gesetzmassigen Arten von Trauma zu lenken, die am haufigsten im gewéhnlichen Leben der Schabe getroffen werden und als Regenerationsfaktoren dieser vorausgehen; sie verdienen ernste Beachtung auch von Seite des Histologen und um so mehr, als die Frage von den Verletzungen, ihrer Form, Struktur und ihrer Ziffernmissigkeit bis zu dieser Arbeit, soweit mir bekannt, in der Literatur noch nicht angeregt wurde, ausser unbedeutenden Daten, die in Artikeln iiber Regeneration von Newport und Graber zerstreut sind. Serpuchow, Januar 1908. MISCELLANEA. I. Note on Inheritance of Brachydactyly. In an addendum to a memoir on “Split Hand and Split Foot Deformities etc.” published in Biometrika, Vol. vt, Pt. 1, 1908, p. 117, the writer, referring to a statement by Punnett to the effect that no member of a brachydactylous family who is free from the defect can transmit it to his or her offspring, stated that this conclusion is disproved by the family recorded by Hasselwander (Zeitschr. f. Morph. u. Anthrop. Bd. 6, 1903, 8. 510—526), in which such transmission actually occurred, A misprint in the original diagram of the family tree was at the time overlooked, and it appears from a personal communication which the writer has received from Dr Hasselwander, that transmission of the nature stated did not occur. The remaining two families bearing on the matter under consideration, and quoted in a foot- note to the original addendum, may be given in fuller detail. Ammon writes in Die angebor. chir, Krankh. d. Mensch. u.s.w. Berlin, 1842, 8. 96, as follows:—“Merkwiirdig ist in dieser Hinsicht ein von Keltie beobachteter Fall, wo bei den Gliedern einer Familie schon seit zehn Generationen nur der Daumen vollstindig gebildet gewesen war, wihrend an den itbrigen Fingern entweder beide Gelenke, oder wenigstens das Nagelglied fehlte. Eigeuthiimlich war dabei, dass sich diese Missbildung nur in den weiblichen Gliedern der Familie fortpflanzte.” * Joachimsthal in Virchow’s Archiv, Bd. 151, 1898, Folge xv. Bd. 1, 8. 430, writes :-—‘‘ Die 27- jahrige, bis auf die zu schildernden Anomalien an beiden Hinden normale, 160 cm grosse Patientin weiss iiber Verbildungen in der Ascendenz nichts zu berichten. Ein 29- und eine 22- jahrige Schwester haben, wie sie selbst—wenn auch weniger ausgesprochen—verkiirzte Zeige- und Mittelfinger. Der einzige Bruder ist selbst normal gestaltet, besitzt jedoch eine 1-jahrige Tochter mit den gleichen Fingerverbildungen, ebenso wie dies bei einem friihzcitig verstorbenen Knaben der alteren Schwester der Fall war. Unsere Patientin selbst ist Mutter eines jetzt 4-jaéhrigen, normalen Knaben. Von den verbildeten Familienmitgliedern habe ich nur die 22-jahrige Schwester zu untersuchen vermocht, u.s.w.” In the original addendum the Hasselwander family constituted the most conclusive evidence for the transmission of brachydactylia through a normal individual, and this portion of the evidence must be withdrawn without qualification. In conclusion, gratitude must be expressed to Mr Punnett for his courtesy in allowing the writer the opportunity of personally correcting the error which has occurred. July 2, 1908. THOMAS LEWIS. II. Note on Inheritance in Man. The importance of certain considerations being borne in mind with regard to pedigree work is well illustrated by Dr Lewis’ note. On looking at Hasselwander’s pedigree I personally should consider Dr Lewis’ statement correct, not because of the misprint which might attribute some of the children of Fanny to Victoria, a normal individual (for the numbering of the offspring shows that there was a misprint of some sort), but because the writer states directly that the deformed Josepha K. was the child of normal parents. * The original report of the Keltie family has since been found (Hdin. Med. and Surg. Journ. 1808, Vol. 1v. p. 252). The condition was in all probability the same as that in the Farabee family. The women who transmitted the defect were apparently also malformed, though from the text it is somewhat uncertain. 328 Miscellanea Now it is at this point that a very important consideration comes in. The true Mendelian needs the theory of mutations to supplement his position, and other workers, among whom, I think, I may include Dr Lewis, would say that the deformity started in a sport. Now an experience covering many hundreds of human pedigrees leads me to the conclusion, that the appearance of deformity in the offspring of normal parents with nothing further known of the earlier ancestry is too often only another way of stating that we have not been able to trace fully the ancestral and their collateral lines. In very many cases when I can go back through a normal parentage, I find directly or collaterally the supposed mutation or sport recurring, and we have either to assert (i) that there exists a general tendency to sporting in the stock, or (ii) that the deformity is latent and can be carried through normal individuals. It is needless to say that (ii) appears to me a more scientific assumption. To stop short at a normal pair with the statement ‘sport’ or ‘mutation’ is logically incomplete, if we wish to demonstrate that the deformity is handed down only through deformed individuals. We must show for a generation or two in the direct and collateral lines an entire absence of the abnormality. It is a very general experience that these abnormal cases belong to the lower classes of the population, and that in going back in the pedigree we are invariably checked at but a few genera- tions by ignorance as to blood-relationships. Under such circumstances we must either wind up with an abnormal individual of unknown parentage or with normal individuals as in Dr Hassel- wander’s or Dr Lewis’ cases. My first consideration is that we have not the evidence necessary to speak of the latter as determining a ‘sport.’ My second urgent consideration is this: Is not the time ripe for the collection and publi- cation of pedigrees bearing upon normal and abnormal characters in man? There is an immense amount of published material scattered through a wide journalistic area. There is a growing tendency for medical men to record more and more completely family histories*. A collection of published and unpublished material would be of first class value to students of heredity. The primary conditions for such a collection are: (a) that it shall contain the material only; no dis- cussion of hereditary theories shall form part of its plan,—this ought to allow of all schools contributing; (b) that there shall be no selection of special pedigrees for publication, except on the score of their completeness and the peculiar interest of their characteristics; (c) that each contributor should be wholly responsible for the accuracy of his facts and for the genealogies which should be published under his own name. The duty of the Editor should only be to standardise the material received. With a view to providing a collection of this kind, the Galton Laboratory of National Eugenics proposes to issue in parts a Treasury of Human Inheritance, each part will contain 20 to 50 pedigrees arranged on 6 to 10 lithographed plates. The individual plates will be devoted to a special characteristic or abnormality. Each pedigree will be accompanied by a brief account of the family and its members, and when needful by an illustration of the charac- teristic. The Treasury will cover published and unpublished material, and there will be an entire absence of any purely theoretical discussions. Full reference will be given to the source of the pedigree and to treatises where similar cases are discussed. The Laboratory has already received promises of help from members of the medical profession, and from officials in asylums, sanitoria and hospitals for special diseases. Is it asking too much to beg our Mendelian friends to give us cooperation in this matter, or at any rate to decide on the basis of the first number whether they cannot do so? 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Monthly or 10s. per Annum prepaid. \ TO BE OBTAINED FROM THE ROYAL ANTHROPOLOGICAL INSTITUTE, 3, Hanover Square, London, W. AND THROUGH ALL BOOKSELLERS. CONTENTS | (All Rights reserved) PAGE: I. Pigmentation Siac. of ‘School Children in Scotland. } Committee and Grants . 129 Report. By J. F. TocHER, ‘( With Plates I—XXVI, Table: I, and “oe One Diagram in text) . ; 130 Il. Variation, Development and Growth in Holosurta Flovidana, Pouralie ; and in Holothuria atra, Jager. By Cuartes Lincoty Epwarps. : (With Plates I—V, One Folding Table and Six Diagrams in text) 2386 _ _ III. Probable Error of a Correlation Coefficient. By Stupent . , 302 1V. Zur Frage vom viergliederigen Tarsus der Blattedae und der Regenera- tion der Fiisse derselben,. Von TH. 8, ScHTscHERBAKOW wt i atSoey ek Miscellanea. (i) Note on Inheritance of ren. es eee LEwIs . é 327, (ii) Note on Tahentene in Man, By K. PEARSON § . Oat Special Supplement to Vol. VI. Pigmentation Survey of School Children in Scotland. 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The latter had made a special study of the termites of Natal and of the Malay Archipelago, and he published a valuable paper on these insects in the LInnnean Society's Journal, Vol. XXV1. p. 358 et seg., 1897. The notes include some interesting observations on the life-histories of the Natal species of termites, and also a large series of measurements made on one particular species, Z'ermes natalensis Haviland. The general biological observations, which appear to be unrecorded, are being incorporated in a short paper which is about to be published in the Annals of the Natal Government Museum, while in the present paper the measurements will be briefly dealt with. For the elucidation of some doubtful points, Mr Haviland’s observations have been supplemented by some fresh measurements on Termes natalensis and also on other species. As is well known, termites are social insects with an economy bearing some resemblance to that of ants and social bees and wasps. The nature of the in- habitants of a termite-nest varies according to the species and to the season _of the year at which examination is made. If a nest of 7. natalensis be examined in the spring (September) the following different castes may be found: (1) a single queen and a single king, these are the only sexually mature forms that occur; (2) soldiers of two sizes, asexual; (3) workers of two sizes, asexual; (4) winged males and females, not sexually mature; (5) young or immature members of castes (2), (3) and (4). In some species there are several queens and kings in the nest, and the soldiers and workers may be of one size only, or the soldiers may be absent altogether. In ants and bees the workers (and soldiers, when they occur) are sterile females ; while in the termites it appears that both the soldiers and workers are abortive individuals of either sex. There is also evidence for believing that the ultimate Biometrika v1 42 330 Observations on Termites fate of the young on hatching is not predetermined, but depends on the sub- sequent treatment they receive at the hands of the workers. According to this view any given individual on hatching from the eggs may, in the case of T. natalensis for example, develop into any one of five distinct forms or castes, which in no way grade into one another, viz. two forms of soldiers, two forms of workers and the winged sexual form. It is certainly most difficult to form a conception on any theory of heredity as to the means by which hereditary characters could be inherited by such a plastic and modifiable organism as the newly hatched young of a termite. After the first rains the winged sexual forms swarm out of the nest and copulate in the air; they seldom or never appear to return to the parent nest. A pair may succeed in founding a new nest, and will ultimately become the queen and king. , The nest of 7. natalensis is slow in growing, and it remains inhabited for many years. ‘The same queen and king undoubtedly live for a number of years, and in some species (including 7. natalensis) it is not known how they are replaced, should they die or an accident befall them. (2) The Measurements. The measurements were made only on what appeared to be adulé members of the different castes, except in the case of the winged imagos, when on one occasion nymphs with wing-rudiments were measured. An individual was re- garded as adult when the exoskeleton of the head_was firm and had assumed the characteristic yellow or brown colour. This point is, of course, of considerable importance as there is no sharply marked metamorphosis among termites. In any case, whether of soldiers, workers or winged imagos, the same dimension was chosen for measurement, viz. the maximum breadth of the head (ab in figure below). Owing to the varying configuration of the head in the different castes and species, this dimension in certain cases passes through the compound lateral eyes ; Ss D Heads of various castes, viewed from above, showing the line of measurement (a b). A. Imago, Termes natalensis. B. Small Soldier, Termes natalensis. C. Large Soldier, Termes trinervius. D. Worker, Termes trinervius. ERNEST WARREN 331 and when such occurs it was found that the measurement could be more con- veniently and accurately taken if the breadths of the eyes were included in the dimension. It is certain that the inclusion of the eyes in such cases has no appreciable effect on the results, as the correlation of the size of head and eyes is exceedingly close; and the eyes being partially sunk in the exoskeleton complete the contour of the head. It should be noticed that the dimensions taken of the different castes are not perfectly homologous, for some soldiers are blind and others have curiously shaped heads; but they are as nearly homologous as the nature of the case admits, and they may all be regarded as closely comparable measure- ments. The measurement of the selected dimension may be made with sufficient accuracy on account of the comparatively rigid nature of the exoskeleton of the head. Length or breadth measurements of the abdomen would have been quite unreliable. The specimens were in all cases preserved in alcohol. The method of measurement adopted by Mr Haviland is not recorded in his notes; but I have no hesitation in accepting his data as thoroughly trustworthy. The method which I found most satisfactory was to examine the specimen under an ‘aa’ or ‘AA’ Zeiss objective with a camera lucida, and to mark off the dimension on a slip of paper. The termite was flooded with spirit on a slide, and orientated by means of a small piece of glass placed above it. The slip of paper was referred to a scale made with the camera from a stage-micrometer (divided into {5 and mm.) viewed under the same magnification, and the absolute dimension could thus be read off. One or two small series measured by Mr Haviland were re-measured by my method and the results were in close accord. The measurements of Termes natalensis will be first dealt with, and sub- sequently a comparative review of some of the Natal species of termites will be made. (3) Termes natalensis Haviland. As we have already seen a colony of this species consists of one queen and king, numerous soldiers of two sizes and workers of two sizes, also immature young or larvee, and at certain seasons nymphs of males and females, which on becoming winged leave the nest as a swarm. In the accompanying table the means, standard deviations and coetticients Standard Deviation Mean colonies are shown. The measurements refer chiefly to the soldiers and the workers: where the material was available the queen and king were measured, and in nest No. “653” one hundred male and one hundred female nymphs with wing-rudiments were measured (see Table VIII). The nests are arranged in the table according to the season of the year at which the material was collected, beginning with November. of variation ( x 100) of a considerable number of different 422 Observations on Termites 332 76-1 | FO-€ | F-9GT ep | Oe | 1eL | 0-983 | OOL | 98-3 | 88-9 | O-1h3 | OOT | 68-E | G9-FL ) O.68r | 4a] — = 63 ‘SNY | — —= |) creo Ge | Gio |) OGe9 | L-Ore. | COL 16%. | 76-9 || L876 1°86 = = 9.ser | ¢ = — 6¢ Ae OIG eGOrG | OLLOll co | g8-1 | 79-b | 696 | OOT | 923 | ¥6-G | €-€93 | OOT = ae 9-L17 | 2 = — | $249 |} LI “2eIT eel eerie Caco GI SOR-Za er OG:Ghal ASA 7Ge OOlMN Oso atu cOul | Osc0e. 9 OO = = Osi || 4) = == 8I ‘ue 16-6 | 8L-b | 0-191 GO INGE:e | 2e9.6) 10:96 || OOTP 0c) |) OF-L..| 9:67 1-261 = — EDIE | Biedp — = QT “AON NOs@o| ocO-ce |) F-0S1 ES POR || ERO) I AOS CO | SKS || || Pontes |) LO = = 6% ‘SY Git OLS | benel se | £0: | 6.) | @Zrs | OOF | ee:a | €6.9 | ¢-brS | OOT — 06 Avy 16-8 | 69-€ | &-8ST 40° | 16-1 | 49-7 || 9:82 | OOL | G8-e | 80.4 | G.1¢@ | OO = = Oeste) se — | PLO 4 21 -2eW ee ecco py | #66 | 68¢ | 0.086 | OO1 | ¢0-€ | 9&2 | 8-886 | OOT = on Gaara |e = = |su ‘mee ee = 0. 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Gel O-G1R-(5eGuh == = St Ay 62-2 | 29:8 | 6-291 OOT:| 96-1 1 89:F | ¥-68e | O01 |’ 86-6. | 429 | Bare | OOT = — eCity GGT tee = | SLO ie eee | : Clee OleGal tak |NOOL We Las: | G8: |e Gece oon = = Ocly |e | = = if "uve i Oh) = =| 62-7 >| i:Olt) 6:686 | "00. | 6-92 | S221 |) -0re. | O01 = = O01 | rl ie = ZI ‘AON G%-3 | 09-€ | ¥-9GT ep | 71.6 | OF9 | FERS | DOT | Bee G6" | L286 | OOL = = cpasin || © = = (og “Sny = — | 9.191 Pl lesson oO Wi Lekee \sOOW |) [46 | 76:91) Gee 1s00n = = O-Fer | I = = LT Se | = GEG lecha Gisre |) az ze. | 40-9 | &19% | 006 | — = Lr | 2 = — | O19 | 9L we = Ope. 209. | SOpen| COOL Glee |) sk 6-006 | 1006 | 4ES:8 1-06:e) |) tock son he == SI ‘ure GHG |" Teer || 8:09T Gy | Zoe | Fr-L -|-9:186 | OOL | 78-3 | GOL | 6-276 | OOT = = 0.8tr | P ell IL ‘AON — | 90-3 | 99-% | 6-922 | OOT | 9¢-€ | €%8 | 8-18e | OOT aN ae aaa —| — — eZ “SLY Crp | €6-9 | 2.991 rg | ec | 6G-4 | &G2% | OOL | 16-3 | 16-9 | ¥-4ee | OOT = y= 0-Gzr | € — = gt Av 2 lnGiia) Wigher | aGkece. | 68 BE (OreL | O2e6 + | 008 = : = | — | 999 | 9T ‘2eIT -- ae el MOL eee. icone laGean ce Co 9G-¢ |) [9:4 1 S-eso | OOL = — | | $9c7 4 ¢ = = SI ure | 61:3 | 66-9 | BFS | 98 6r-F | OZOL|) €-L2% | OOL = L ONT "A jo "~) ‘d Sg Uvd “ON AN. TOs | ‘d Sg UvdTL “ON “A jo 79) “d 'S UBOTT ‘ON “A jo 46) “ad Sg UvdTT “ON Saryy teen?) 4SON | | hs jo | Woroet[og 7 7 : ‘on | J9 29°C SUAMUOAA TIVING SUMMIOAL TOUV'T SULIGTION TIVIG SUIGION ADUVT AUIVAOYY TU [0.0 =3tU “SISUAIDID NT SaU.la T T WIdVa ‘SoSBO OOT AOf €. Jog SUOTPRIAVp palepuLys Jo pue J. JNoge suvoTU Jo SAO1dd atqeqorg | 333 ‘a s | | | | | = |/—|e | 0g) —'| 2/9 | st] 0c] Ol | 1 | PT] SL| 1 | 60g | eel.) te—ere == | Blvsae Ok (Serie 9 at ene WN ee GT POT Oo Ne GGT Wee eri COL! ove — bee == G6 [262 PP OSa ees e012) See Gh lee ere |e Slay Oe eOb Ike ite Tie ice! NCL EN PROG* eSphil 8eoe— one 11526 eGo"! Sie La Zep tea Res hea Pee a OTe ee Wee) | Oli. iL OU ay, Merle ose —eee Sei) SI EU ROH eG gh POT Gea i Gap ee RE eR Sn aI Pla | SLU ese oe a Oe ihew ace 160 8) 28 es ACCS By cog GGe Ml —aal, idee titer || sc AO OMS = VT aI Oh! 485 oP ateTs Mel 236 666—LEE a ee | MeelcO8 |) =O OTe ite Slemet ale. [esa elem er eee gi aees lL «)\ap oa GiTyl| ace 6 966—TEE Tale Peg gGe lee a] 8s ita eO oR OZ allay = io Cera each Nees AG &66—T6e SF ae a SL oma Oe | ah Geen | Baler VE WO eee Ley 0é6—8Té Se Ok all Sa | 9/00 Geer |Past mC LI6-—S16 Se cc ae ed A ee OO te Ra Cs a are rs re ere: Te fees? es ST aed eee ie ee SN a ea) a Sl bee GUS =| ih ae ee he Ge Al een ee ee ae | | a = o0e=2 908 soa es la. z = {4 een ee G0E— 08 | a Pi = TV "| ¢0e—006. SS es atl car : = To) al G6 er el ara be Fe |e a o EP Parte 2 & “UIT €0-0 = GLI TL9 BLO OLO 899 089 GLO TL9 CLO 049 | 899 089 shes at al 2 | | Ey “OBI SUTMUOM AOUWT SUMIATOG TIVNG ‘oun pu YOUR, “aqMOAONT SUTINP SjSoU XIS WOIF poqoo][0o [eIIezeP “SUSUAIDID AT SOULLAT, TH dlavi 336 Observations on Termites A careful comparison of these frequencies will, I think, lead to the opinion that both of the suggested causes have a share in producing the seasonal variation. The apparent elimination of the small and unfit is best shown in nests “630” and “672” for both the small soldiers and large workers. (5) Ratios and Variation of the different Castes. Having thus noted the presence of a seasonal variability in a single nest, we may pass to the variability exhibited by a series of colonies. It would, of course, have been preferable to have avoided the disturbing element of the seasonal variation by collecting all material at one season of the year; but this was not done as the presence of a seasonal variation was not suspected. In the following table (Table IV.) are given the arithmetical means of the means, standard deviations and coefficients of variation of the four castes in a number of nests (see Table I.). TABLE IV. Means. Gente Number Mean Number | Standard Coefficient of of Nests* of Nests + | Deviation Variation Large Soldiers ... 23 434-015 20 13°64} 3°12 Small Soldiers ... 30 245-00 30 TERMI 3°02 | Large Workers ... | 27 242-21 27 | 5°94 2°46 Small Workers... | 19 156-90 12 4°17 2°65 Male Nymphs ... 1 300°05 1 4:71 ISaiz/ ‘There is no overlapping of the large soldiers and small soldiers or of the large workers and small workers; in other words, there was never any question whether any individual should be classed amongst the “large” or “small” series. With reference to the particular dimension measured there is overlapping between the small soldiers and large workers; but the soldiers and workers are totally distinct in general structure and shape. Ratios. . Mean of Small Soldiers 245°001 a Mean of Large Soldiers ee 434-013 * oe. anal Mean of Small Workers oo 156901 x 100 = 648. Mean of Large Workers 242:206 Thus, in the proportion in size that occurs between the “large” and “small” classes, the soldiers and workers approach each other; the “small” class being more than half the size of the “large” class. Mean of Large Workers 242206 oe Mean of Large Soldiers Ses 434-013 * ED Ske Mean of Small Workers 156°901 1 = -———_— = 04°0U~, ng Mean‘ of Small Soldicich se ee OAS pee * Nests from which less than 10 individuals were available are here excluded. + Only nests from which more than 23 individuals were available are included. + Unit=0:01 mm. ERNEST WARREN 337 Thus it will be seen that the workers are more than double the size of the soldiers of the similarly sized class. The variability of the soldiers, as measured by the coefticient of variation, is greater than that of the workers, the ratios being : Coefficient of Large Workers 2°461 nee Coefficient of Large Soldiers = ag oo & Ie Coefficient of Small Workers 2°647 a Coefficient of Small Soldiers ~1°0— 3.933 * 100 = 87, that is the workers are about 0:8 times as variable as the soldiers. (6) General Variability of the sexual and asexual Castes. The average coefficient of variation for the four castes is 2°8: it is thus seen that the general variability of these termite-castes is distinctly small. The nymphs of the winged sexual forms appear to exhibit extraordinarily little variation. In the case of 100 male and 100 female nymphs (Table VIII. nest “ 653”) the co- efficients were only 1°57 and 1°60 respectively. Unfortunately there is no available material for ascertaining the variability of the adult sexual form before leaving the nest in the species natalensis ; but, as will be seen later, small series of winged imagos have been measured in some of the other species, and there is a general tendency towards a low variability. It has been remarked that there appears to be good evidence for supposing that the young which hatch from the eggs are all alike, and that by special feeding, or by some manipulation by the workers, any one of the five castes may be produced. From this it would be expected that the variability exhibited by all the castes would be about the same; but it has been shown above that the workers are less variable than the soldiers, and that the asexual castes generally are much less variable than the sexual castes. In this connexion, it should be remembered that the individuals in a nest are all produced from one queen and king. The difference in the variability of the castes must therefore be referred to differences in food or other environmental conditions, since they all have a common parentage, and are presumably all alike on hatching. Thus, the tendency to vary is induced or modified by the special food or manipulation received, and the influences necessary for the production of a soldier or worker lead to greater variability than those for the formation of a sexual imago. It appears that either sex may be converted into either soldiers or workers, the potential sex having no effect on the ultimate destiny of the in- dividual. It is clear that the environment has an overwhelming effect on these organisms, it influences the variability and decides on the bodily shape and structure of the developing insect. (7) Comparison of the Constants of a Family with those of the Population. Of small soldiers, random samples from 30 nests were measured. The sizes of the samples were most disproportionate, ranging from 100 to 1600. On adding Biometrika v1 43 TW gO.0=}UQ x Observations on Termites 338 me ball eae | | ges cms (ep [cme | mn en Pe aR mame ceo em NP rl ellen eee ee 0 i oo Reser s ee ee a a ane ; Se ee ee | RS 0s c08. x0) = Baa (ear 0 es | ard a em Ua fmm Dt ee al pend (ual eae deel eo | | La hak pl ee ike el Kaa face a eee ae 2 —}—/1 fo |—|—|—|—|--|—| —| — | 708 668 : i9 — |=] —|—]— Seal cma | smmane: || saul | econo me | emer | Sime (amend ce (OP ea OG a one SL) = = Se en | ee ee Vom | ce [ett eect | 8 () |p fe A Pa er C6665 9¢ 46 = |) Sf - = | | — : OW Ne en a i N eetaeas Beaiay | Se |e ne ae Thee laa (OE OL) = 0° == | = = | |e | 69¢—r9e. Ig S61 | eqn a; Sree | amma leceascma | cre | ecm apne eee PO CHT | cee creel OP cee tet cee (Reco IOS 9S Gime 9 2 a dS Ae 9 | elle rans SN as | ee 0) Gl | &86—I8¢ Ig er oa = a mere ; eee cilie @ Cen Recent (Cs Nel oe || einen On| OSG a SLB ce | — | - = G¢|9 |@ }g |t 16 |—|/—|—|]—/6 | Zeze—es¢ PPL se Wrage — see ae pee er OATS TORN EG ile Go IeLl0 | aaah il eee ae Ole (wine ea 9 | - —|—|—Il1 | | | Oo |}—|]—|1I ]F% | @}]s |g | t }et}|—|—]—]—] Fl} rze—69¢ 9eT Nee Se eS a ee alia a OS Ni OL ESR GG) po lek er ia | See oon —o0e alle il cle eG a te tee RCE Tomi e el GesKiee” Wet el = Phe, all ae Gas eT IG POTS Weerelop. sl Gi) eile (iz sheet eos =enge Cet oe Omni slGr emer liGatle Cale. (Oem hl OR > cao Dell epee eerie Onn Olea. WG SialeTh Wie ieee ln alleaga Dor eee O/Ome Onin Om melee alee eat Poo Hobe (Ce aa o lat | tee (ele ION (eG lee eel carl Oe ale G) - 1c a lmsreae Ghanem teal Get cies 9s 3961 HOPE Teach Ga Sa. lhG™ 1 Se bal Ges T ol eel a a ON sal MOR 8 ea eeesl ome aOl ly Gaels Ge EC "lat | Gr ator GO OM CaniOen ies) | eereOre WL eRON Veter tO) ole) yee ee Qe Oe lie eee peal ea Piel Nie pelec iheiia| == alka nlecgn =a! | ogg SOA MEPIS WTS: (Sl |e se Weal S i | eel eal eal Te WO | Oe! ZN EG Mesa Ol Ea areata eOmrl cus =| oso MGT Cd aCeMIECC NU IGa Os elaGh (cae eh oS et [9 (29 oe) lee) eats 1@ |0 |O | 1L/1T |}—/]7T |G | —] 9L] 02) 91) 9 |—| 2re—ere 20% NCSGR Gone AL ACen ODe ie: | Oe Vi. Lesh \Or |O. (6h | = —— | Tee lie ee eel |e iis be erlerilege || == ere ate. mecalaOUMe! Weil eel wi Cb WS. ede 1S APC | On| snr LG iP ehh SOEs GMCs HSC isa a el eG lee (OT ical leGul ear Ie Ger | gop $802 WL eta GaieeteivGe | 9 |e 8s iL. | OW (ee MOL | te 1S 8 | Se bse Oy |e a) Ge eso Ge etal ocean ZONGEE FOG Sl 2 | SRN Olek 9S | OL Wer | St St | PL.) OF Sh | 8 | Sh | On ba = Set) een -) St b= | ees eee ggg 5808 POLS Myce OC So Pll ORM 6r SE | 16 On leah ORIG OT, Ae SIGs = ha | Oe ta een aa lial We loge — lor PESTS) Ol Mire lela t) TieaO ALS) ly MINE Gauls | Teal eie | te Ge Ole Gi) bine tate a ieie WWee Ge liberal Gee —7ees | | ggg itt OU Se glee Lae een ees bes Ss ated 2. | see ol | ST eG) Be | eT 6G: a8 aa ee ee eel [eon nila" | Sea ee | oe G2 tT Stee ON ee Ga et igo Lease Gr lem Ole I Tp cbiene== st te alae = g |— | see—re | Teen lee ieee Re ate veel Te SG ME tlie) ole OR Bel Deana ste. | seal r | — | 0¢6—8Ié tor |o |—|—le fH Weer | 2G € TP NSS A GS Nee ESTE I hc | a ei en og §8t | 1 ema Gea if TSO, al 6 of ee al eee eel oe ta ly Pio elie Pee eat 1” Wterslee ee a Si alae rr) , 2 | I Bee ines cae eet lec ear (poe ee ee ee lo |e Oar = Ss | ey | Se | Se aa, ¢ | - | 06—806 | it I zai — | €0é—008 | I I = = x66I—L6T | b by b b we wn ™ mM (er Sy a = Sl S S = = b> | g g g g a g g g g Z s|eisl2|/8\3\8 z z z EB E/E,/E;E|E) 2) 8) 2 |S | moon | S[PIO], < ; ea |G |) Gal) : 4 BS Bo alton | Bo ®) @|-o ]'o | © | 5: 649 | 849 | £49] 949 | CLIO | TL9 | ELI | OL9 | 899 | 0&9 | L99 | 999 | £99 | B99 | T99 | 099 | 8G9 | 469 | 7E9 | 069 | £9 | €¢9 | TE9 | 679 | 8t9 | EY9| ITO | 229 | TE9 | LI9 | IseN Jo oa "yon WOLf KOT ‘s7sau OG f Suarppoy DUG ‘punpanzyT sisuanyoNT sawsay, ‘A UTAVL ERNEST WARREN 339 all together there is obtained a population of 8497 individuals derived from 30 different nests. The constants are: Mean 251°8, Standard Deviation 19°86, Coefficient of Variation 7°89. The distribution of the frequencies is irregular, and the polygon shows a well-marked double peak. The cause of this is chiefly attributable to the great disproportion of the size of the samples, and the consequent undue influence of one or two individual nests. To avoid this disturbing effect, random samples of 100 individuals from each of the 30 nests were taken. In this way there results a population of 3000 (Table V.), and the constants are: Mean 2435, Standard Deviation 17:08, Coefficient of Variation 7:02. The distribution of the frequencies is much less irregular than in the former case, and the polygon is consequently much smoother. The coefficient of variation of the population of 3000 is thus 7:02 as compared with the mean value of 3:02 for the families, In other words the variability of the family of small soldiers is about 43°/, of that for the population. The vari- ability of the population compared with the fraternal variability is much higher than was expected, judging from the value obtained from certain breeding experi- ments with a moth, S. clathrata, conducted several years ago at University College, London. The cause would appear to be attributable to the great effect of the environment on the means and variabilities of the different castes of a nest. (8) Correlation of the Means. The correlation between the means of the small soldiers and large workers has been determined in the case of the 27 nests entered in Table I. The correlation- surface is shown in the following table. The calculated constants are: mean of means of small soldiers, 2443 units, standard deviation, 15:29; large workers, 241°4 units and 13:04 respectively. Correlation coefficient =°953, probable error +°012. For the calculation of the correlation between the large soldiers and small soldiers only 20 nests were available. The constants are: Large soldiers, mean of means, 435°5 units, standard deviation, 16°9; small soldiers, 247°3 units and 17:14 respectively. Coefficient of correlation = "831, probable error = + ‘046. Since the probable error is so considerable, there is no reason for supposing that the correlation between the large and small soldiers differs appreciably from that between the small soldiers and the large workers, which we found to be 953 +°012. It may be assumed that the correlation of the means between any two castes is about 9. It is curious that the correlation between similar castes (large and small soldiers) does not appear to be greater than that between dis- similar castes (small soldiers and large workers). 43—2 340 Observations on Termites TABLE VI. Termes Natalensis Haviland. Correlation of the Means of Small Soldiers and Large Workers from 27 nests.* ‘ _ = See RE SEE ie 2 a = ae l | | Se Soe ov Pie | ecw st len Se er Weer etsy |) Shy Unit=0'04mm. } 201 007.) Nell eee ae 1 225.228 2 | eho taasheleee | | 2 229232 10) 2 ela aes | 4 2El2—L56 1 0) 2 | 3 237—2L0 —|— 1 1 ~ 2 Pio | aa | Oana £ 5 2528 |e | 3 249—252 gees | ) 253-256 : | 1 Me i oe ee es) ee 257 — 260 = — 0 261—264 2 ~ : 1 — |— | — 1 265—268 | | 1.<|4— nee 269—272 —}— - 1 —|— 1 2738—276 —|-- | — — |} — | — |] — |] — (0) yew > | 277—280 —|—|— | — | — | é 2 | 2 a G : cline | : ~ a I ae m | 9 2 39 S = 2 | D> Sa) e R 8x SLR Rl/Rlaxel ae sel el sel Sia] s > 1 ES | ae Weed et ee A ee ese bel | @ | Ss | % | xnilisoloeo|slolreis!ial] ss] 50 Vi RX; os i|_o | sis Re ein (See alesene Ih SS) ae Sy) VW | &R oN] X isy) RX iss RX RN NX NR @ Ss | | Ap | (9) Standard Deviation of the Means. The standard deviation of the means of the large soldiers for random samples taken from 20 nests is 16°90, for small soldiers from 27 nests 15:29, and for large workers from 27 nests, 13:04. It is thus seen that the means of different nests vary very considerably, and reference to Table I. will show that this variation is not entirely or even mainly due to the fact that the material was not all collected at the same time of the year. We have here to do with the effect of inheritance, or with that of the slightly different environment of each nest. It will be noticed that the standard deviations of the means for the three castes are all of the same order of magnitude, although that for the large workers is the lowest. (10) Correlation of the Coefficients of Variation. The variability of the members of a nest varies in different nests; thus the standard deviation of the coefficients of variation of random samples of small soldiers taken from 27 nests is 4°42 units, and of large workers 3°40 units. The coefficient of correlation between the coefficients of variation of small soldiers and large workers in 27 nests is 453; but the probable error is + ‘103, which is so great that it is scarcely safe to conclude that we have this correlation very closely. * The smallest number of individuals from a nest was 32. ERNEST WARREN 341 TABLE VII. Termes Natalensis Haviland. Correlation of the Coefficients of Variation of Small Soldiers and Large Workers ; from 27 nests. 2 sire ailalw{[al/alalo;~+]1 Icon eet oo le aval | | | 244—258 —; —];]1}]—;—}]—)—/] 1);— 2 | 259-—278 el 1 1 O70 0) 35) 1) ts) 274—288 |—} 1 1 1 0) ita =a | 4 289—308 |}—)}—] 1 1 0) 2 O 0) 0) 1 5 304—3818 | —|—|—]} 1 | — | — | —| — i Som cocoa ele le |e |e | 2 3B384—B848 | — | — Se |e | 0 3B4I— 363 = —);—]/—}|1};—;—|—-]|— iT 364—378 - 1 : B 1 379—B898 eee | | || es ee SN eee ee 0 394—408 ae ee | O 409—423 -|- | }—}—}—-f;-]aja 564—578 coed ice tactile |e ah — ll 1 };—|]—)— 1 n i: ae 7 Zi ae 60 ~ » RN RN Sy sy} NX N A) s9 A) P) 2) SP) il en ese SO se i lal) la tea ap ™~ ™ XN RN XN XN RN MN N 8 Sr) 9. Sn) 89 4 | | | A correlation table of the coefficients of variation of large soldiers and small soldiers was prepared; but without actual calculation it was obvious that there was practically no correlation present. From this we gather that in any given nest when one caste happens, say, to be particularly variable, it does not follow that every other caste is correspondingly variable. From @ priort reasons one would have expected that the variability of the different castes in a nest would have been closely related, if the variability is to be regarded as an inherited character. If, on the other hand, the variability is to be mainly referred to nurture or to the general environmental conditions, the above results are intelligible. (11) Comparison of various Species. In Table VIII. are given the means, standard deviations and the coefficients of variation of the different castes for all the more commonly occurring Natal termites. Observations on Termites TABLE VIII. Constants of a Series LARGE SOLDIERS SMALL SOLDIERS Name of Species No. of Locality and Date r me l Nest : Coefticient es , |Coefficient No. | Mean | Standard of No. | Mean | Standard Deviation | Variation ; Deviation Variation ~ E ——_ _—— er Mabiareamrrsargcoeuans ED | cere ove) | ey 26, | Hodotermes havi- ro, | Natal, Altitude 3000 ft. | ~ lhe — landi, Sharpe 636 June 27, 1898 None Rona Hlabisa, Zululand, = S Bis ia i June 25, 1903 =e =a oan a aa a =| | Calotermes durba- | 601 &602) Durban, Feb. 15, 1898 80 | 178:3 | 4°45 2°49 None Goons nensis, Haviland 608 Durban, Feb. 15,1898 | — en _ _ Termes natalensis, 653 Natal, Altitude 3500 ft. | | | Haviland 2: July 1898 213} 456°6 15°31 3°36 1100 | 267-7 | 9:50 | 3°55 Termes badius, | 626 | Natal, 1894 124| 288-75| 10-26 | 3:55 | Haviland 625 Natal, 1894 | 7 229-0 | — = | Termes latericius, : Slievrye, Estcourt, Natal, | ~ ar. 2.08 2° | Haviland 647 mane 25, 1898 500 137°4 3°86 81 None occur yy | Natal, Altitude 4000 ft. | -, 56-2 , 2°55 ; ee May 28, 1898 og ee | : Termes Vulgaris, Nonencccnn Haviland ; 628 | Natal, Altitude 4000 ft. | :@ ex, 1s: June 1, 1898 | : ; : : Natal, Altitude 4000 ft. 2, c d : ; 629 June 1, 1898 | 47 76°2 2°25 2°95 | Termes incertus, | Hagen Taken | None occur from one| Natal et a = ae nest | : | Natal, Altitude 3600 ft. y | ope : 633 2 25 83°4 | 2°62 3:14 June, 1898 | | Termes parvus a = None occur en eR, ; Shevrye, Estcourt, Natal, — Hauilsnd Swarm | "March 30, 1899 | e ; ; : 644 make eae {t. 50 82°7 2°12 2°56 _ 7 ca z ea t —— ea | Se) ee — 62L Dee ft. 57 | 1481 | 2°81 1:90 | Ee Yh eh A} »gn | Natal, Altitude 3500 ft. x10 ee, wm 623 May 26, 1898 21 | 151:8 632 } ree ft. 25 147°5 2°60 1:76 - Termes bilobatus, Haviland Swarm = Natal, Oct. 24, 1898... = too Soon: i Natal, Altitude 3500 ft. | , aes =D 639 June 17 20st | 640 | Natal, Se 3500 ft. 27 147°5 2°74 1°86 £0) Natall 16940e ea ogee a ee = — 615 Natal, Altitude 5500 ft. hee ae April 5 | i Badan: eeeumanitz-| ga) 1423 | 6-28 | 4:88 | 70 | 98 | 858, | 3:99 ’ hs} Termes trinervius, | Taken | Rambur from one| Natal, Oct. 19, 1898 _— _— = = = = an = nest Park, Maritzburg, on os cs Seyi im Sept. 15, 1908 —_ — | — a | ae | Rhinotermes Sp. 603 | Durban, Feb. 1898 93 | 187°5 6:06 3°23 91 92°04 3:23 3°51 j ERNEST WARREN ~ 343 of Species. Unit = 0:01 mm. LARGE WORKERS SMALL WORKERS MALES FEMALES ‘oefticl | Coefficient eee. | | | \Coeficient Mean Standard pas neient No. Mean Standard geereee: No. Mean Standard Loemmen’ No.| Mean | Standard aera ‘ | Deviation | Variation Deviation | Variation Deviation | Variation Deviation | Variation . | | | | 360°3 15:45 4:29 | 50 237°3 14°34 | 6:05 = | | oa r= | 380'8 | 13-71 | 3°60 | 84 | 9689 | 12°79] 4-76°/—| — | ee | 3862 | — = 16 | 2785 | — P | | | = 149°8 7-42 4-95 None occur = ce = -- es — | = = | Nymphs with wing-rudiments. 7 Nymphs with wing-radiments 168°5 5°35 3:18 ee 30071 4°71 157 |100! 208-4 | 4:78 1°60 | eG 187°1 8:16 4°36 50 | 132°2 5°74 4°34 — — | — | a 156°8 4°40 2°81 100 1105 | 2-41 2°19 = = \ i} ul | Winged imagos | Winged imagos a= = = Se a ies 20h: 2G1G) = 250° (85) 262.9) 16028 pea cd | | | | H None found Winged imagos | Winged imagos aa aS = 35 | 13842 | 2°71 | 2:02 32 | 1859 | 293 | 215 17:2 3°67 4:76 = | | — 7 None occur Winged imagos Winged imagos a ane a 30 | 113-0 3-09 2:73. | 25 | 119-9 1:94 1-62 105°1 — — == = Winged Imagos Winged imagos = = a None occur 50 | 1129 | 1-71 152 | 43 | 120-4 | 2:40 | 1:99 | | = - = =i = = = 95-1 | 2:28 | 2-40 a, = a ee 94°6 | 2°83 | 2:99 See panes ee _ a | — — —— — |_ _ 160 | 166-4 1142 | 6:86 mad ee = a eee es = _ | | i} | | Winged imagos | Winged imagos = = = _ None occur 26 | 1938 | 418 | 216 | 46| 192-4 | 369 | 1-92 100 | 165°9 7°73 4°66 Sal) ors mE = | | = : : a 36 144°4 779 1:93 Stated to occur, but no specimens | — — = a —_ | fa | a 342 Observations on Termites Ernest WARREN - 343 TABLE VIII. Constants of a Series of Species. Unit = 0:01 mm. LARGE SOLDIERS SMALL SoLprers Lance WorkERS Soact Workers MALes FEMALES Name of Species No. of Locality and Date = ] Sah a ert |B lian rl T = | Nest ‘ Standard Coefficient Standara |Coefiicient * Standara Coefticient 2 Standard Coefficient Epanghan Coefficient | Para A Coefticient ~ — = = ~ — _ — —|— L = = ae Natal, Altitude 3000 fe. ere tlcon : a3 | 960-3 | 1545 | 4:99 | 5 9373 | 14-341 6-05 |—| — ee 635 ane 26, 1898 : 51) 421-4 24-46 580 43 360 5 50 7 505 | Hodotermes havi- ey Natal, Altitude 3000 ft. | as ae = Y 5 280° 13-71 3 268° 7 “76 | = = = | landi, Sharpe 636 Tune 27, 1898 None found 50 380°3 7 60 34 68-9 1279 | 4-76 | | | Hlabisa, Zululand, a ae me o: || saqe meee ee 5 3 | | = June 25, 1903 a 18. | eaee 1G) 20822 | —— : = | | he | Calotermes durba- | 601.&602) Durban, Feb. 15, 1898 | 80) 1783 | 4:45 249 . — = = se 5 _ — ee | — = + = nensis, Haviland | 608 | Durban, Feb. 15,1898 | — | — = — onesocour 50 | 149°8 | 742 | 4-95 Noneyoecns -- - u —— = ‘Termes natalensis, e Natal, Altitude 3500 ft. | | | | Nymphs with wing-rudiments Nymphs with wing-rudiments Haviland | 628 July 1898 213) 456°6 15°31 3°36 1100 | 267-7 | 9°50 | 355 | 1100 | 2627 81 3°20 1100 | 1685 535 318 | 100) 300-1 jh, esa 157 |100! 208-4 4°78 1:60 | Termes badius, 626 Natal, 1894... ... | 124] 288°75 | 10°26 3°55 — — | — — 50 18771 | 8-16 4:36 50 132-2 574 434 _ = -- | Haviland 625 | Natal; e942. J] —]| — — — 7 | 2290 | — — = = ae L - 2 = | = ee | > a | = " | | Termes latericius, 4 Slievrye, Estcourt, Natal. B76, 2.08 9. | ef 6 0 94 a i avila 647 June 25, 1898 >| 500) 137-4 3°86 2°81 None occur 100 1779 5-68 3°20 5] 112-9 4-88 4°32 | = = E _| | wee. | = === | zi == || 5 | | | 62g | Natal, Altitude 4000 ft. | 509! 156-2 | s:97 | 2:55 1563 | 440 | 2-81 | 100 | 1105 | 241 | 219 |—| -— May 28, 1898 Termes vulgaris, | Haviland é | None occur | Winged imagos Winged imagos | my eh, Austria i fis Welle ee i = Ach | tae: a5 |i if Gai 2:35 | 33) 262°3 | 6-92 | 264 | , | | | | = - Le = = A le ——s 2 | 629 Nebel aratnde, 2000 ft. 47 162 | 295 2:95 50 88:2 3-13 3:55 Termes incertus, ; | N Hagen Taken | None occur None found Winged imagos Winged imagos from/ons Natal coed | a | a = — = = = 35! 134-2 2°71 2°02 32 | 135-9 | 2°93 2715 | | ae = E a ee ee Se Z : | 633 |) Natal, Aléitude S600 tt. Vio5)| saad} 2:62) || 8-14 28 | 772 | 367 | 4-76 = | | | , Louk | | | | Termes parvus, Tote 2 | ae S : Winged imagos Winged imagos |) Haviland Swarm | Slieveye, Wetcourl Natal, |_| | es Alano eeart | = = ones oceu: 30] 1130 | 3:09 | 273 | 25) 1199 ) 194 | 1-62 | : Natal, Altitude 3800 ft. | ~ ‘ ¢ : = aa June 23, 1898 Son nezEt | Belo ice = = ai —ibe= ial | CTT eee ae US pp reese || sh if ecI) = || - a = | 19, | Natal, Altitude 3500 ft. | 625 | May 26, 1898 po eet es = i = 5 | 7 i F | 632 | Nataly Alatude? 3600 ft. | 95 | 147-5 2-60 1-76 x 20 10571 = — = = | fags h Termes bilobatus, | Winged Imagos Winged imagos Haviland Swarm | Natal, Oct. 24,1898 ... | — = = = Nonezocenn Pe = = Ts ab ocr Ey mes BES Nelo? alee a rey | Natal, Altitude 3500 ft. | , y _ | | ey June 17 a0 etas/S = i E ay ~ a 2 gag | Natol, Altitude 35001. | 57 | u7-5 | 24-| 106 | = = = eS = — Natal, 1894 .., coe || = — = 615 Natal, Altitude 500 ft. April 5 Town Bush, Pietermaritz-| oe Gi 4 3. burg, April 20,1907 | &4 | 1423 | 623 | 4:38 | 70 | 898 | 358 | 3:99 WO} 166-4 | 149 6:86 —-{| — = | | Winged imagos Winged imagos = = — None occur 26 | 193°8 4°18 2:16 46 | 192-4 369 | 1:92 ‘Termes trinervius, | Taken Rambur from one} Natal, Oct. 19,1898 ... | — — = = = | = = 4 nest | Park, Maritzburg, | Sept. 15, 1908 = eae = = P: am rae cs. Rhinotermes Sp. 603 Durban, Feb. 1898 93 | 1875 6:06 8°23 91 92°04 3-23 | Bol 36) 144-4 779 1:93 | Stated to occur, but no specimens | — = = = = = = — Observations on Termites 344 8-6L G-0€L €-89 P-8¢ 8-68 6-99 g.69 eC a save] ae 6-941 = or | O-LL == 1-6F a "8 SOUULTAZOUTAY 6-48 €-E81 == = 6-911 = [-£9 SUIAIOULIY SOULIOT, 0-F8 Za | = Sa 0-79 =a = a SNIVQO[IG Sola], €.89 — == 9-26 = == aap “snared satay, L-G9 fee | oes ag L-CLT — = a3 SNYAVOUL SOULa J, 0-09 a | ar L-OL | F-O0L | G-OL = a SLIVSTNA SOUL1d J, a aa | = | G8 C.6Z1 | C.E9 — +e SUIOLIOYV] Sota J, = 1-18 | 9.6L | 8-OF 8-F9 L-OL €-6L = snipe saute J, ae 1-86 | 0-€9 O-LE | 9-L¢ | G- FY DG ere SISUATLIVU SOULAA J, aa ae a a | 0-F8 | = = SISUDURGINP SOULIa{O[R,) eas = _ &.9G | G.8 | g.69 ~- ** IPURTIARY SatttazopoFy SOBBUTT ATI | “SIOIP[OY TTBUG | SIOTP[OY TTeUg sa21P 108 AFIV'T — SAPTPTOY [[VUG | SIoyIOA\ OB1VT] | sAOrplog osrery seedy S1IHIO AN SIOYION OIAVTT | SIAYLOA\ [[VUIG SLOYIOAA [[VUIG | StOYLOA\ aBIVT | sAOyIO A, [BUG | SIOIP[og [TeUIg ‘OOL X sunayy fo soyny “XI ATAVL ERNEST WARREN 345 Relative Sizes of the various Castes.—Ratios. Soldiers of two sizes occur in Termes natalensis, Termes badius, Termes trinervius and Rhinotermes sp., and the ratios are given in the 2nd column of Table IX. There is considerable variation in the ratios, and the mean is 62°5. Two sizes of workers occur in five species. It should be noticed that it does not follow that there are two sizes of soldiers when there are two castes of workers and vice versa. The ratios are given in the 3rd column of Table IX. It will be seen that they are fairly constant, the mean (66:9) is somewhat similar to that for the soldiers (62°5). The ratios of large workers to large soldiers are given in the 4th column of the table and they are exceedingly variable, ranging from 57°6 in Termes natalensis to 129°5 in Termes latericius. Various other ratios are given in the remaining columns of the table, and there is no marked tendency for constancy in any of them; although the ratio of workers to winged imagos is less variable than the others. Means of the Coefficients of Variation. The arithmetic mean of the coefficients for large soldiers for the 11 species (see Table VIII.) is 3:26; for small soldiers (3 species) 3°68; for large workers (11 species) 3°74; for small workers (5 species) 3°89; for male imagos (6 species) 2:06 ; and for female imagos 1°98. It is evident from these results that the male and female imagos are con- siderably less variable than any of the asexual castes. The special manipulation, whether of the nature of specialised food or of any other influence, necessary for the production of these castes, appears to increase the variability. With regard to the variability of the asexual castes, it will be noticed that the mean results for the series of species are not in accord with those for the species Termes natalensis. In this species the soldiers were more variable than the workers, but in the mean values for all the species the reverse is the case. (12) Comparison of the termite measurements with those of Wasps. Miss Alexandra Wright, Dr Alice Lee and Professor Karl Pearson have recently completed an investigation on the variability of various parts of the wings of worker, drone and queen wasps (Biometrika, Vol. v. Part Iv. p. 407, 1907). The material employed comprised the individuals from one large nest, and it will be of interest to compare as far as possible the results obtained with those from the termites. In the absolute dimensions the queens, drones and workers of the wasps are in descending order of magnitude with respect to the wing-measurements. In the case of the termites, the means of the head-breadths of the five species (TL. vulgaris, T. incertus, T. parvus, T. bilobatus and T. trinervius) were for male imagos, 163°15 units; workers, 1173 and soldiers, 121°3. Thus, although the Biometrika v1 44 346 Observations on Termites dimensions measured are of a different nature, the wasps and termites agree in the sexual forms being the larger. The absolute variation in the wasps is greater for the workers than for the drones and queens. In the case of the five species of termites, the workers have a mean absolute variation of 467 units against 3°51 for the soldiers and 3°57 for the male imagos; that is, a mean of 4°09 for the asexual castes against 3°57 for the sexual form. The general tendency is consequently for the termites and wasps to resemble each other in this matter. In the relative variabilities (coefficients of variation) the sexual forms (drones and queens) of the wasps are considerably less variable than the workers, the means being: workers, 3°55; drones, 2°60; queens, 1°57. In the termites the means are, as we have already seen, for: large soldiers, 3°26; small soldiers, 3°68; large workers, 3°74; small workers, 3°89; male imagos, 2:06; female imagos, 1:99. There is thus a very striking similarity in these results: the mean of the coefficients for drone and queen wasps is 2°08, and for male and female imagos of the termites 2°02. The asexual wasp caste of workers with a coefficient of 3°55 also compares very closely with the mean of the coefficients of the asexual termite castes, 3°64. The material at the disposal of the authors of the wasp paper did not permit of the examination of the correlation of the different castes in a number of nests, and consequently a comparison on this point with the termites cannot be instituted *. (13) Summary of some of the Results. (1) Although the young appear to hatch all alike and in certain species (7. natalensis, for example) all are the offspring of one queen and king, yet the various asexual and sexual castes of a nest exhibit marked differences in their variabilities. The differences in the variability cannot therefore be regarded as due to inheritance, but must be supposed to arise mainly through post-embryonic - environmental influences. (2) The sexual caste is much less variable than the asexual castes. (3) The relative variability (measured by the coefficient of variation) of the population compared with that of a family (the individuals of a nest) appears to be considerably greater than can be accounted for from the ordinary effects of inheritance‘, and the cause is almost certainly to be found in the moulding influence of a varying environment on an exceedingly plastic organism. [* The relative variability of the species and of the members of a nest is now being investigated and the results will shortly be published. Ep.] {+ The reduction in variability for the case of assortative mating of a large amount has not yet been worked out. For the termites we have in each generation a brother-sister marriage, or an assortative mating, say of ‘5. There is thus only one pair of ancestors in each generation, and the reduction of variability for such a system may quite conceivably be as great as that indicated by the termite measurements, i.e. nest variability 7°37 and general population variability 17:08. Enp.] ERNEST WARREN 347 (4) The correlation of the means of any two castes in a nest of a population of colonies is of very considerable magnitude, being about 9. In other words when, for example, the mean of one caste is above the average, then the mean of any other caste in the nest is correspondingly high. Leaving out the effect of inheritance, this correlation could be accounted for by the fact that similar environmental influences would act on all the members of a nest. (5) The standard deviations of the means of different castes in a population of colonies are considerable ; and there is little doubt that the varying environment of each colony is largely responsible for the great fluctuations in the means. (6) The correlation of the coefficients of variation of any two castes in a population of nests is either moderate or nil, in other words the variability of one caste is in some instances not appreciably correlated with the variability of any other caste in the nest. Owing to the fact that all the castes spring from the same parentage, we might have anticipated that a fairly high correlation would exist. We have therefore evidence that a similar environment can have a varying influence on the variabilities of the different castes. A comparison of these results with those obtained from other social insects would be of much interest, and would throw additional light on the significance, or otherwise, of some of the observations made in this paper. 442 NOTE ON THE SKIN-COLOUR OF THE CROSSES BETWEEN NEGRO AND WHITE. By KARL PEARSON, F.RB.S. THOSE who feel compelled at present to hold their final judgment with regard to Mendelism in suspense, who do not think the statistical proof of its generality by any means yet complete, and who still question on logical grounds many of the statements made with regard to it, have nevertheless been ready to emphasise the paramount service of Mendel in drawing attention to the great factor of segregation in many inheritance problems. This admission can be made without overlooking the facts—too often disregarded—that segregation is not a universal principle, that it is, where it does occur, often incomplete, and that even where it occurs and is more or less complete it does not necessarily follow the simple Mendelian ratios. The theory of the “pure gamete,” the “unit character” and the “allelomorph” may have aided, suggested and controlled much experimental work on inheritance, but this theory has undoubtedly been pushed—chiefly by young and enthusiastic disciples of Mendelism, who thought that at last a formula of heredity requiring no mathematical knowledge had been discovered—far beyond the limits of actual experimental work, or in some cases beyond the inferences allowable from the data actually observed. The public has been dosed by the general Mendelian practitioner with: (DR) x (DR) =(DD) + 2(DR) + (RR) and told that it solved all difficulties. But the higher consultants know that at the very best many complications arise, that even in segregation transitional forms occur occasionally or even frequently, and that “unit characters” are not indepen- dent but often highly correlated. They are also fully conscious that much straining of the theory of probability often is needed to make the ratios fit a simple Men- delian formula. The reason for these prefatory remarks lies in the fact that some time ago it was asserted by an ardent Mendelian that skin colour in crosses between dark and light skinned races would probably be found to obey Mendelian principles. It had been hitherto almost universally accepted that skin colour did KARL PEARSON 349 not segregate, but that in a mixed population all tints according to the degree of mixture were to be found. This view of the matter appeared to be that of men who had long resided among mixed races, and had become axiomatic with the West Indies courts of justice when determining cases of doubtful paternity. The rule of a court of justice is generally one of practical experience in human affairs, but of course we cannot in science take it as conclusive evidence of the absence of segregation. At first sight the question appears to be capable of an easy answer. If Z repre- sents a light skin and D a dark skin, we shall term the pure races (ZZ) and (DD), and the problem turns on whether segregation occurs when we have the mating: (LD) x (LD). Is the result (ZL)+2(LD)+(DD)? Now without any hypothesis as to the nature of the skin of (LD), we ought when mulattos or Eurasians cross among themselves to find 25 p.c. of their offspring at least white skinned, and so readily distinguishable. The problem, however, is not so easily answerable, and for the following reasons : (a) There is a considerable range of variability of pigmentation in the white races, and an equal range of variability in the dark races, which may also be said to have their “blonds” and “brunettes,” although what the negroes term a ‘fair’ negro, would often be called by the European a black. (b) Among the Eurasians in the populous parts of India an inquiry as to parentage is much resented. It is possible to examine the children in the Eurasian schools and often to observe their parents, but the fundamental question as to the parents’ parents, the original (ZZ) and (DD), is generally unanswered. (c) In the West Indies where the race differences are less acute, we are met by the difficulty that 60 p.c. of the children in some islands are born out of wedlock. Many mistakes in paternity are made, and colour as I have indicated is one of the definite factors in deciding this matter in a court of law. Now I do not pretend to have settled the problem for either Eurasian or mulatto strains, but I have endeavoured to set on foot inquiries in the Eurasian schools in India and among medical men in the West Indies which may some day help to answer the problem. This note only proposes to consider some communi- cations I have had with a correspondent in the West Indies. He is a medical man, who, except for his period of training in London, has spent his whole life in the West Indies and knows its people and their ways very intimately. He has most kindly provided me with a series of photographs illustrating some of the mixed types. It is very hard to indicate the various shades of colour unless all the subjects are taken on precisely the same plate, with the same exposure and the same illumination, I am having further observations made with von Luschan’s skin mosaics, but I think the present photographs will suffice to indicate that there is a real gradation in the types. 350 Skin-Colour in Human Crossbreds The questions I put to my medical correspondent were as follows : (1) Is white x negro a blend or not? Is it correct to say that the mulatto is a blend ? Answer. “To this question there is only one answer; it gives a definite well-recognised blend, and a blend which is easily seen and identified by any sensible man who has had any experience. You can infer and state freely, that there is this definite blend. But the colour of the mulatto varies, and practically may be divided into two sections : (a) The brown mulatto, with a colour of light mahogany. (6) The yellow mulatto with the colour of a well cleaned brown boot, which has not been much worn. But I have never seen any reversion to the white or negro type in a genuine mulatto, and I have come in contact with hundreds of them. The yellow mulatto is comparatively un- common here ; roughly speaking I should say under 15 p.c. of all mulattos.” It will be seen from this result that a new problem is opened up—that of accounting for the difference between the brown and the yellow mulatto. The answer excludes the possibility of dominance in the Mendelian sense from the discussion. My Figs. (i)—(iii) give pure negro individuals. Fig. (ii) is described as a perfectly black negress and Fig. (i) as a negro “as black as the ace of spades.”* Fig. (v) is the photograph of a florid Englishman taken with the same camera as control. Fig. (iv) is a representative of the mulatto type. The problem of the difference between the brown and yellow mulatto would be a remarkably interesting one to work out, but the difficulty of the inquiry might be great. Is it, perhaps, due to difference of pigmentation in the European parents? Or, to a difference in negroid race? One point, I think, deserves con- sideration with regard to further inquiry in this field: Does the sex of the white parent make any difference in the colour of the offspring? In searching through literature to find any reference to segregation in the offspring of mixed races, I have come across three cases only, in which the hybrid was directly stated not to be a blend or mulatto. The first case is due to Aristotle+ who describes how a woman in Elis bore a white daughter to an Aethiopian, but this daughter had a black son by a white father. If the case were really authentic, it would be the rule proved by the exceptions, i.e. a Mendelian dominance of the white, followed by a Mendelian segregation, which nullifies this dominance of the white. The second case is cited by Parsons}, who says that a white woman married a negro in York and had by him a perfectly negro child. Here we have dominance of the black. The third case is also due to Parsons; he tells how a white woman had a white child by a negro, but its buttock was black, i.e. it was a piebald. There may well be other cases, but I have not come across them. Now on these three cases no stress whatever can be laid, but they suffice to suggest that, whereas in * Tn all photography of dark races, the high lights reflected from black surfaces must be allowed for. + De generatione Animalium Lib. 1. cap. xv1tt. { Phil. Trans. Vol. tv. 1765, p. 45. Karu PEARSON 351 the bulk of cases the male is a white and the female a black, it would be well to inquire whether a change of sex can produce any differences in the colour of the offspring or in the nature of the dominance. If we accept that (ZD) is a blend, we should expect that mulatto x white would give 50 p.c. of whites and 50 p.c. of blends. My next question was put to test this. (2) Mulatto x white gives a quadroon. Is or is not the quadroon a blend ? Theory says that the quadroon class should consist of half whites and half mulattos. Answer, “With the small exception of the yellow mulattos the quadroon is almost invariably lighter in colour than the brown mulatto, and one is safe in saying that the quadroon is nearly always—say in 90 p.c. of cases—whiter than even the yellow mulatto. Pure white skins do not occur in quadroons. This statement is dogmatic and true.” The next question I asked related to the cross (LD) x (DD). (3) Mulatto x negro. Is this a blend rather darker than the mulatto or not? Theory would say that 50 p.c. of the offspring were mulattos and 50 p.c. negroes in skin colour. Answer. “The mulatto x negro crosses produce what is here termed the ‘Sambo,’ a deep mahogany brown and they produce nothing else. They do not produce mulattos and they do not produce negroes. The Sambo type is very distinct, and there is, as far as my experience goes, no reversion either to the white or black races. 1 have never seen a single case of reversion to either mulatto or negro.” Fig. (vi) shows a Sambo girl of the rather lighter type. The colour is well shown in the hands (not in photograph) which are of a rich chocolate tint, and could not be mistaken for black. Figs. (vii) and (vill) give a Sambo girl darker than the average type, but no one with experience would mistake this girl for a negress. The following pedigree is an example of the range found in a Sambo sibship: 3 (Mulatto) i 2 (Negress) t © i : | | | ¢ o 3 3 ? (Paler (Very dark (Very dark (Dark _ (Pure (Paler mahogany) but plainly but plainly mahogany) Negro) mahogany) not a negress) not a negro) | eee re ee | (Recognisable as not pure negro) The colour range here is from something rather darker than the mulatto to something rather less dark than the negro. In this case the range of colour is fairly wide, and it is open to those whom it pleases to divide this or any other family into two halves, containing the lighter and darker members respectively. The difficulty of such a classification is that the dark mahogany members are quite distinct from negroes and the paler mahogany from mulattos. 352 Skin-Colour in Human Crossbreds Figs. (ix) and (x) give a dark chocolate coloured girl whose mother was the offspring of a mulatto and a slightly higher white strain (? quadroon) and father a negro. We see at once a softening of the Sambo tint. It will be clear that the crosses (ZD) x (ZL) and (LD) x (ZD) are more likely to give us definite answers to our problem than (LD) x (DD) owing to the con- siderable colour range in the Sambo. The next investigation therefore turns on (LD) x (LD) which should give us the segregation in its simplest form. I therefore asked the fourth question, but with some diffidence it must be confessed. (4) Mulatto x mulatto. Does or does not this cross usually give a mulatto in colour? The theorists say that 25 p.c. should be pure white skins, 25 p.c. pure black skins and only 50 p.c. mulattos. Answer. “This statement of those whom you call the theorists is the most ridiculously incorrect of the lot; indeed it would be very comic to make this statement in public before persons who knew. There are now and then slight variations from the usual mulatto brown or mulatto yellow, but you may be quite certain that no pure black skins nor pure white skins come from mulatto x mulatto. You can state this dogmatically.” I may add a few remarks more. Did Mendelism apply to the skin colour of the crosses between dark and light races, we should expect to find only three tints, the light, the dark and the hybrid, whatever the latter may be. The most distant “touch of the tar brush” would be visible, if visible at all, in the presence of the light mahogany of the mulatto. Yet the colour is just visible in the case of the offspring of a quadroon and a pure white I am familiar with, but is hardly dis- coverable in the case where one parent is a pure white and the other a cross between octoroon and quadroon. I think it probable that characters other than skin colour would offer better material for a possible “ mendelising.” The negroid lip, the crimped hair, the characteristic alae nasi, and the peculiar temper are qualities which can sometimes be traced after the disappearance of all colour. It is conceivable that they would fit the Mendelian theory closer than skin colour, and they serve better than colour to predict a distant negroid strain *. Finally, I may say that I do not propose to ask my readers to take the views of my correspondent as conclusive, but they do, I think, deserve great weight. He has mixed all his life with all sorts and conditions of colours, and come into * Another correspondent with 32 years’ experience in a West Indian Island confirms the opinions of my first correspondent, i.e. that blended colour is correct in the cases of mulatto, Sambo and quadroon, If a blackish child occurred in a family which should be mulatto, he would hold that the child was fathered by a black man. In fact he attributes to illicit connexion of mixed races any exceptions to the ordinary rule, and cites as evidence of West India experience the story of the man who said he was so dark in colour because a negro ran after his white mother when she was first married; the reply of the sceptic being: ‘I guess that nigger caught your mother.” The same authority notes that if mulattos intermarry for some time the skin tends to get lighter in colour, but a full blooded negro also gradually inclines to become light in hue (‘‘Pears’ soap colour”) if in a good position and subject to civilising influences. Lastly I may remark that he has noticed that the ‘bouquet d’Afrique” occurs sometimes in a pronounced form in one or two members of cross-blood families, even in Octoroons. Is this a true segregation? Biometrika, Vol. VI, Part IV Plate | Fra. (ii) a Fra. (iii) Fira. (viii) Fig. (ix) Fig. (x) f=) Figs. (ix) and (x)=miulatto-quadroon x negro. Figs. (i)—(ili)=pure negro. Fig. (iv)=negrox white. Fig. (v)=pure white. Figs. (vi), (vii), and (viii) = mulatto x negro. —— A. HEYER 355 I. Picea excelsa Link. A. 15—20 Jahre alter Baum in einem Garten auf der Siidseite meiner Wohnung. Ich wollte zuerst feststellen, ob das Alter der Sprosse oder die Orientierung der Sprosse einen Einfluss auf die Variationskurve ausiibe u. nahm deshalb vier getrennte Messungen vor: an der Ost- u. an der Nordseite des Baumes u. je Nadeln von letztjihrigen u. von alteren Sprossen. (1) 2700 Nadeln von letatjihrigen Sprossen von der Nordseite. (Fig. 1.) Sg LO it 2 18 if 15 16 17 18 19 20 21, 22 238 24 mm. 5 12 20 76 159 263 375 340 343 358 286 202 132 79 33 14 38 2 4 7 29 59 97 139 126 127 133 106 75 49 29 12 5 1%, (2) 2700 Nadeln von dlteren Sprossen von der Nordseite. (Fig. 2.) 9 10 21 12 1 iif 15 16 i 18 19 20 2 22 23 24 25 mm. 14.45 91 197 270 369 355 350 419 303 138 64 38 27 12 7 = 1 (2700) 5 17 34 73 100 187 131 130 155 112 51 24 14 10 4 2 1 ° (3) 2700 Nadeln von letztjihrigen Sprossen von der Ostseite. (Fig. 3.) HORUIMIZ = 1S I 15 16 17 Gs 19° 20 21 22 23 2y 25 26 27 28 mm: 4 21 62 141 261 302 354 442 370 237 175 135 64 36 33 20 19 15 9 (2700) 1 8 23 52 97 112 131 164 137 88 65 50 24 13 12 8 7 63 °., (4) 2700 Nadeln von clteren Sprossen von der Ostseite. (Fig. 4.) GeO 2 G8 1, Wy Wes IK EO BLT 6 48 103 233 366 401 326 282 354 290 125 74 32 15 2 18 38 86 136 148 121 104 131 107 46 27 12 6 7 3 1 Ubersicht Variationsweite Gipfel (1) 8—24 mm. 14 u. 17 mm. (2) 9—25 mm. 14 u. 17 mm. (3) 1O—28 mm. 14 (angedeutet) u. 17 mm. (4) 9—27 mm. 14 u. 17 mm. Diese Ergebnisse zeigen, dass an unserm Baume weder die Stellung der Nadeln an Zweigen verschiedenen Alters, noch die Orientierung der Zweige einen wesent- lichen Einfluss auf die Variationskurve hatten. B. Gleich alter Baum wie A, nur wenige Meter von ihm entfernt stehend. Ich wollte an diesem Baume eine Kontrolle dariiber ausiiben, ob das Alter der Zweige tatsiichlich keinen Einfluss auf den Verlauf der Variationskurve habe. Ich mass deshalb je 1350 Nadeln von letztjahrigen u. von alteren Sprossen von der Nordseite des Baumes. (1) 1350 Nadeln letztjihriger Sprosse. (Fig. 5.) Sao 10 ie te 18 7, 15 16 17 “18° 19 20 21 22 23 2) mm. 2 9 22 35 110 157 189 150 147 200 139 72 52 36 24 5 1 (1850) 1 7 16 26 81 116 140 111 109 148 103 53 39 27 18 4 1 %/,, 356 Uber die Ldngenvariation der Coniferennadeln (2) 1850 Nadeln dlterer Sprosse. (Fig. 6.) 8 9 10 If 225 138 Pi Lo IG Peli 18h 192021 22 oS amis 1 2 12 37 #119 156 176 171 177 #198 150 92 38 15 5 1 (13650) 12 9 27 88 115 130 197% 131 947 iT 68 28) th 4) Sowohl Variationsweite als auch die Lage der Gipfel stimmen miteinander iiberein, aber auch mit den Resultaten von A. C. Gleich alter Baum wie A u. B, in unmittelbarer Nahe derselben. Die Nadeln wurden ohne Wahl von alten u. jungen Zweigen gepfliickt (Fig. 7). 9 10 11 12 13 th 15 6 -17 %@T 19 20 2 22 23 2) (25 526mm 8 67 220 406 699 904 842 700 562 445 299 197 124 84 57 40 12 2 (5668) 1! 12 ' 39 72 123 160!) 148° 123" 99% 9 78. 53 Sb 22) 5) 1 Oe eee | 00 Die Variationsweite erstreckt sich von 9—26 mm., also ungefahr wie bei den vorhergehenden Kurven, hingegen ist diese Kurve unsymmetrisch eingipfelig, mit Gipfel bei 14 mm. D. Nadeln aus dem Gipfel eines etwa 40 Jahre alten Baumes aus dem Walde von Peter u. Paul (Fig. 8). g) 10 11 12 13 Lh 15 16 Aly 18 19 mm. 28 88 214 403 666 579 462 276 76 4 (2803) LOpe 3 76 144 238 207 165 99) 07, "gre i | Variationsweite von 9—19 mm., Gipfel bei 14 mm. E. Hier wurden von unserm Christbaum die Endsprosse des zweitobersten Quirls abgeschnitten u. die Nadeln von zweien derselben gemessen (Fig. 9). 10 JI 12 13 14 15 16 17 mm. 3 41 ‘118 168 225 ~ 173) “49 2 (779) 4.9 (B83 TB “O10. "3289) | 2990) (768) es cine Variationsweite 10—17 mm., Gipfel bei 14 mm. Muster eines eingipfeligen, symmetrischen Variationspolygons. F. Ein 80—100jahriger alleinstehender Baum nérdlich vom Institut Dr. Schmidt. Einer meiner Schiiler, A. Jobin, mass von den ihm erreich- baren Asten 4015 Nadeln (Fig. 10). 2 8 J 5 6 7 8 9102 aL 12 13 Lh 3 6 96 50 66> 88°. 79) EOI 69." " 9157 = +3020 04s oG lie a2 G+ 12> 16 £22 commen? 39 76 101 106 15 16 17 1S 19 20 21 22 23 24 mm. 418 376 310 324 306 210 126 76 62 20 (4015) 104 94 77 81 76 52 31 19 15 5 00 Die Variationsweite erstreckt sich von 2 bis 24mm. Die Gipfel legen bei 7, 14u.18 mm. Diese Messungen wurden im Friihling ausgefiihrt, die iibrigen im Winter, wodurch vielleicht die tiefe untere Variationsgrenze erklart ist. Neu sind die Gipfel bei 7 u. bei 18 mm. A. HEYER Il. Abies alba Mill. 357 A. Ein circa 20jahriger Baum aus dem Stadtpark in St. Gallen (Fig. 11). 4 5 6 7 8 ig) 10 JE 12 15 1 1 6 27 59 104 141 208 293 362 1 1 2 a 17 30 40 59 83 103 17 18 19 20 a1 22 23 24 25 268 240 214 202 137 86 72 46 34 77 68 61 57 39 25 21 13 10 Lh 15 16 377 322 266 108 92 76 26 27 28 mm. 7 14 3 (3500) 5 4 thes Die Lange variiert also zwischen 4 u. 28 mm. u. die Gipfel legen bei 14 u. 17 mm. B. Ein circa 70—S80jabriger Baum aus dem Sitterwald. Nadeln von den vom Boden erreichbaren Asten (Fig. 12). 7 & ) 10 ig 12 13 14 15 16 4 18 26 55 68 87 123 126 113 103 3 13 19 39 49 62 88 90 81 73 21 22 23 24 25 26 27 28 29 30 60 67 47 34 41 35 31 28 25 8 43 48 33 24 29 25 22 20 18 6 Variationsweite von 7 bis 34mm. Gipfel bei 14, 22 u C. Ein 60—7Ojahriger Baum aus dem Sitterwald. erreichbaren Aste (Fig. 13). (One ee LO ES LR 1: Lh Ld 16 17 1S 2 2 9 20 30 61. 7 128 207 244 355 332 2 17 ile | 4 7 13 27 46 52 (s 74 22 23 2h 25 26 a7 28 29 30 ol 2 290 310 283 253 245 217 155 125 94 81 62 64 69 63 56 54 48 34 28 21 Die Liinge der Nadeln variiert zwischen 7 u. 35 mm. 17 u. 24 mm. 17 1s 19 20 90 75 68 56 65 54 48 40 31 82 83 Ssh mm. 5 3 3 1 (1400) 4 2 2 Ile Sine 2 . 25 mm. Nadeln der vom Boden i) 20 21 250 224 253 56 50 56 O2- 3 BL JI MM, 48 18 3 2 (4511) 11 4 1 1 “f, Die Gipfel liegen bei D. Ein ca. 1L5jihriger Baum am Waldrand zwischen Kronbiihl u. Steinach (Fig. 14). 7 8 1K) itil 12 13 14 15 16 iif 1S 19 1 2 4 8 25 55 115 171 227 244 309 286 258 1 1 1 2 16 33 49 65 70 88 82 74 20 21 22 23 24 25 26 a7 28 29 min. 268 324 297 262 233 162 126 71 47 5 (3500) 77 93 85 75 67 46 36 20 13 1 foo Die Linge variert zwischen 7 u. 29 mm. u. die Gipfel legen bei 17 u. 21 mm. 358 Uber die Langenvariation der Coniferennadeln Ill. Larix decidua Mill. A. Etwa 15 Jahre alter Baum im Sitterwald. Es wurden nur die Nadeln der Kurztriebe gemessen (Juli 1908). (Fig. 15.) 6 Uf 8 9 10 Tt 12 13 14 15) 16 Lie 18 3 14 29 35 59 78 98 121 132 158 189 237 202 1 5 10 12 20 26 33 40 44 53 63 79 67 19 20 21 22 23 24 25 26 a7 28 29 mm. 212 227 247 210 186 164 153 130 67 47 2 (8000) 71 76 82 70 61 51 43 22 16 Le Maen Variationsweite von 6 bis 29 mm. Gipfel bei 17 u. 21 mm. B. Etwa 30 Jahre alter Baum im Sitterwald. Nur Nadeln von Kurztrieben (Juli u. Aug. 1908), (Fig. 16). 9 10) 1D) T2RTI3 I 1b a6 ahif 18 19 20 ai 22 ico 24 25 & 2 6 5 7 30 54 62 84 100 149 124 103 105 134 138 142 142 168 11 1 2 7 12 14 19 22 33 28 23 23 30 31 32 32 = 37 26 27 28 29 30 31 82 83 84 85 86 8% 388 89 40 mm. 208 253 327 310 343 356 327 270 192 159 94 69 31 5 1 (4500) 46 56 73 69 76 79 73 60 48 35 91 15 (7 eae Die Lange variiert zwischen 8 u. 40 mm. Die Gipfel liegen bei 17, 28, 31 mm. B*. Es wurden nun noch 500 Nadeln von Langtrieben dieses Baumes gemessen (Fig. 17). ¥ 8 9 0. it 12 ie? Sepeeio ee 16 17 18 19 1 5 4 5 8 28 41 58 39 51 57 75. 45 2 9° 8. 9 15-4538 (785-110) 9745 297 2 1087 asec 20 21 22 28 2 2 26 27 28 29 30 31 mm. 29 19 ll 12 9. I 6S E328 ete 526) 5) 360Ct«Ck (iC si( aT CO SG oe Hier variiert die Linge zwischen 7 u. 31 mm., die Hauptgipfel liegen bei 14 u. 18 mm. IV. Pinus montana Mill, var. pumilio. Von einem in einer Anlage der Stadt St. Gallen stehenden Exemplar wurden 19000 Nadeln gemessen u. zwar von je zwei beisammen stehenden nur eine, weil die beiden meistens gleich lang sind. Weil mir an der Lage des hier auftretenden Gipfels sehr viel liegt, so gebe ich zwei Zahlenreihen: die erste zeigt die Ergebnisse nach 8000 Messungen, die zweite nach 19000 Messungen, u. zwar blieb von 8000 KARL PEARSON 353 contact with them every day in a large but poor practice. He has, I feel sure, no bias to any theory of heredity, and I think my questions first put the modern theory before him. The main point is that the segregation in the second genera- tion to pure white or black skins does not occur. One quotation more from his letters, which had reference to the question of whether the lighter shades of the mixed race might have a dark skin as a latent quality. “Now I think the question you wanted an answer to is this: When the mixed breed approaches the European side, are there reversions to a definitely negroid type? You reserved your opinion when I saw you in the summer, until I had formulated my experience, That experience is that such reversions are comparatively rare, sufficiently rare to be practically disregarded in a court of law in the decision of bastardy paternity cases. I cannot give you definite statistics, the subject, as you may well imagine in a mixed race community like this, bristles with delicate social difficulties. After many years of medical practice here among all classes and colours I feel sure that I am justified in saying that the reversions to the negroid type are distinctly uncommon. Of course in families of the mixed breed you will often see a difference in colowr pure and simple ; this is not at all uncommon, and I would make a marked distinction between this phenomenon and the phenomenon of a throwback to the negro. You will not infrequently see the same thing in European families, and if you are going to consider it in the case of Englishman x Negro, you must also consider how it would apply in the case of Englishmen x Englishwomen.” I take it that my correspondent is here referring to the continuous variability within the family—demonstrably inheritable,—which some disciples of Mendel term “fluctuating” variability and believe to have no importance for the theory of heredity. Sports’ or ‘ throwbacks’ do occur, but are really rare; the milder form, i.e. the form which is barely evident in tint is not uncommon, but only a practised or accurately observing eye would detect it. ‘Sports’ to the pure white or the pure negro are practically unknown ; in all my life I have not heard of a single one.” In view of the opinions I have cited above, I think, the suggestion that skin colour ‘ mendelises’ should not be vaguely made until some very definite evidence in its favour is forthcoming. I should welcome any views on the above four questions from those having life-long experience of mixed races, or having from mission or medical work special opportunities of studying the offspring of mixed races. Actual data as to skin tints taken on Broca’s or von Luschan’s scales would be very valuable, and any photographs of individuals of mixed race, taken when possible alongside individuals of the two pure races, will receive a ready publication in this journal. Biometrika vt 45 UBER DIE LANGENVARIATION DER CONIFERENNADELN. Von A. HEYER (St. Gallen). Im 1. Heft des 1. Jahrganges dieser Zeitschrift (Okt. 1901) veréffentlichte mein Freund Herr Prof. Dr. Ludwig in Greiz in seiner Arbeit Variationsstatistesche Probleme wu. Materialien u. a. auch meine Messungen der Nadeln einer Kiefer (Pinus silvestris). Auf pag. 22 1. ¢. zitiert er eine briefliche Mitteilung, in welcher ich ihm von einer “ Einheitslinge” gesprochen hatte, deren Multipla die Kur- vengipfel zu bestimmen scheinen. Als diese Einheitslange drangte sich mir schon bei den ersten Tausendmessungen die Liinge von 7 mm. auf. Ich liess dann die Sache Jahre lang liegen u. beschiftigte mich mit den Correlationsverhaltnissen zwischen Linge u. Breite der Laubblatter von Prunus spinosa (Referat in den Verhandlungen der Schweiz. Naturforschenden Gesellschaft 1906 in St. Gallen), wobei in der Langenvariation der Blattspreite merkwiirdigerweise auch die Gipfelzahlen 24 u. 28 mm. zum Ausdruck kamen, die ich bei Pinus silvestris gefunden hatte. Besonders diese Tatsachen bestimmten mich, wieder zu den Coniferen zuriickzukehren, um auch an anderen Arten die Langenvariation der Nadeln zu studieren. Ich stellte mir die Aufgabe, die Untersuchung iiber alle in der Schweiz wild wachsenden Coniferen auszudehnen. Das ist nun in den letzten 14 Jahren ge- schehen. Wenn es auch erwiinscht ware, besonders von den langnadeligen Arten noch andere Individuen herbeizuziehen, so scheinen mir doch die bisher gewon- nenen Resultate einer vorlaufigen Publikation wert zu sein. Ich hoffe dadurch auch andere Forscher anzuregen, sich auf diesem etwas verlassenen Felde zu betiatigen, wo die Arbeit zwar miihsam u. zeitraubend ist, wo aber sicher wertvolle Resultate zu gewinnen sind. Gemessen wurde stets frisches Material u. zwar mit emem gewohnlichen in Millimeter eingeteilten Massstab. Die Liingen wurden in ganzen Millimetern niedergeschrieben u. die Resultate in der Regel nach 1000 Messungen geordnet. Um einen bequemeren Vergleich zu erméglichen, habe ich bei den kurz- nadeligen Arten, wo zugleich mehrere Individuen zur Untersuchung gelangten, die Frequenzen auf °/,, reduziert u. die graphische Darstellung nach dieser Reduktion vorgenommen. A. HEYER 359 unverandert auf 49 mm. bis 19000 bei Controlle von 1000 zu 1000 der Gipfel (Fig. 18). 14 15 16 17 18 19 20 21 22 238 24 25 26 27 28 29 80 B81 382 33 215 2 4 5 9 14 15 18 26 30 29 45 42 56 78 68 82 113 3 2 7 #4 #7 +12 20 20 22 30 47 59 61 85 97 109 125 135 161 198 34 35 86 38% 88 89 40 41 42 4B bh 4B YO fv 48 49 50 120 144 168 170 203 223 210 207 266 287 335 419 424 436 429 453 428 225 276 326 381 415 428 440 461 542 561 689 790 803 844 847 871 796 51 52 538 54 55 56 5Y 58 59 60 61 62 63 Gh 65 66 319 293 296 226 211 149 150 146 124 105 63 59 45 54 39 28 736 730 695 634 600 541 493 472 442 372 316 305 268 246 216 176 67 68 69 70 V1 72 78 Yh VE V6 77 78 79 80 “81 mm. 390897 18 13) 8 8 8 6 4 #1 TF — — —) = (8000) 185 146 111 97 72 49 52 40 40 31 15 11 7 2 1 (19000) Die Variationsweite war also nach 8000 Messungen von 14 bis 77 mm.; durch Hinzukommen lingerer Nadeln verschob sie sich nach oben um 4 mm. bis 81 mm. Der Gipfel 49 aber blieb unverindert. V. Pinus Cembra L. A. Ein etwa 15jihriger Baum in einem Garten am Rosenberg, St Gallen (Fig. 19). Es wurde von den 5 an einem Kurztriebe stehenden Nadeln je nur eine gemessen, da die 5 meist gleich lang sind. 10° a 22 18 ds 1 16 @7 18 19 20 21 22 28 2h 2 1 _- 3 3 3 1 5 3 9 8 5 6 5 9 12 26 27 28 29 80 81 82 83 8h 385 36 387 38 8 4O Al 13 16 #18 21 23 18 418 21 31 36 35 40 32 49 55 38 2 48 th 36 46 4Y JB 49 50 S51 52 58 54 55 56 5} 44 67 57 81 83 76 76 102 86 84 94 83 90 98 96 114 58 59 60 G61 62 68 64h 65 G66 67 68 69 70 7 72 73 111 98 93 90 107 122 94 97 92 108 108 113 125 838 86 78 th YS WG wy 78 79 80 81 82 83 84 85 S86 8% 88 89 84 73 46 56 52 41 32 24 23 28 21 9 10 10 5 5 90 91 92 98 94 95 96 97 mm. ae Se ie T4000) Die Variationsweite erstreckt sich hier von 10 mm. bis 90, resp. 97 mm. Die Zahl der Messungen ist noch viel zu klein, um bei einer so grossen Variationsweite festsitzende Gipfel zu liefern, Immerhin erscheinen die Anhiufungen bei 49, 57, 63, 70, 77 u. 83 mm. bemerkenswert. 360 Uber die Léngenvariation der Coniferennadeln B. Ein Baum aus der Umgebung von Pontresina (Engadin). Uber das Alter desselben habe ich keine Anhaltspunkte (Fig. 20). 20 21 22 28 1 3 4 6 PSS) 25, cas) ony a@& ay 28 CBD BOC BL CBR CBB BY 24 y) 15 10 16 22 18 19 19 on oc Ne} iy a a a | a. cc dole (80 EO 35° 39 TO el 2 71 98 109 124 1388 178 194 209 Bl. 27" 43" .Ane sgn 1 70280 51 52 58 54 55 56 57 58 59 60 61 62 63 Gh 234 250 289 304 300 320 365 349 362 368 348 302 300 283 261 65 66 67 68 (69 7O Yi “72 78 "7 075 6 Wome 259 206 216 200 148 124 101 84 79 56 46 43 25 39 26 80 8iy 82 88 8) 85 “86 "87 _ 88) (89) (90) 91 s92mname 31 45 14! 45) (8 97 at, (oR ee eee O00) Die graphische Darstellung zeigt, dass die Zahl der Messungen an diesem Baume noch um einige Tausend vermehrt werden miisste, um ein einwandfreies Polygon zu liefern. Leider war es mir einfach unméglich, das dazu notwendige Material zu bekommen. Die Variationsweite erstreckt sich von 20 bis 87 resp. 92 mm. u. die Gipfel liegen bei 56 u. 59 mm. Beim Vergleich der Variations- polygone der beiden Biiume A u. B, als von letzterem 4000 Nadeln also ebenso viel wie von A gemessen waren, fiel mir auf, wie der Engadiner Baum ein viel einheitlicheres Polygon mit einem einzigen deutlichen Hauptgipfel (bei 59) aufwies als der in St. Gallen gewachsene Baum A. Ich vermutete, dass hier das Klima von Einfluss sein kénnte, weil das Engadin zwar einen kurzen Sommer, aber mit fast stets schénem Wetter aufweist, so dass das Wachstum ungestort vor sich gehen kann, wiihrend St. Gallen mit vielen triiben u. Regentagen ausgezeichnet ist, an denen die Temperatur rasch fallt u. so das Wachstum hemmen muss. Es ware eine Frage fiir sich, durch weitere Messungen diesen Beziehungen nach- zugehen. VI. Taxus baccata L. A. Ziemlich alter Baum im Sitterwald bei St. Gallen. Da derselbe einen iippigen Stockausschlag besitzt, so mass ich die Nadeln dieses Ausschlags (7000) u. die der Krone 5000 besonders. (1) WNadeln des Stockausschlags. (Fig. 21.) 9 10 LE aS ee OO ee eee ate ee) ae 2 1 19. 32 72 107 147 140 163 250 227 217 230 274 291 28 24 85 86 27 28 :- 29 80 81 82 88 84 35 36 313 327 298 299 327 404 332 317 288 295 264 228 182 165 of 88 89) YO AL 2 Be OR i eS) 249 mms 175 148 107 101 76 77 43 26 19 7 7 4 1 (7000) A. HEYER 361 (2) Nadeln aus der Krone. (Fig. 22.) TO Lie 12 18 TLL 1b | IG 17 18 19 20 21 22 7 24 39 #52 79 80 74 110 99 105 112 133 156 238 24 25 26. 2 28 29 80 81 82 838 $84 88 179 207 193 208 242 296 278 248 263 294 274 258 251 89 4O 4L 42 4B A 45 TOM. : 7 208 205 132 79 48 28 22 12 4 1 (5000) Bei (1) variiert die Liinge zwischen 9 u. 49 mm, u. die Gipfel legen bei 14, 17, 24, 28, 32,37, 42 mm. Bei (2) erstreckt sich die Variationsweite von 10 bis 45 mm. u. die Gipfel liegen bei 15, 17, 24, 28, 32 mm. B. Baum neben meiner Wohnung, angebaut. 6 7 8 @) LOM IT P12 IS LE 15 LG Tf 18 19°20 3 17 44 77 +121 199 311 402 473 565 668 1024 1054 995 881 21 22 28 24h 25 26 2% 28 29 80 B81 82 83 384 85 mm. 769 708 499 373 234 181 125 99 65 49 26 20 11 4 3 (10000) Die Kurve ist eingipfelig, Gipfel bei 18 mm., wahrend die Variationsweite zwischen 6 u. 35 mm. liegt. VIL. Juniperus communis L. Ein Strauch von der Hinterkreuzalp bei Trogen (St. Appenzell). 3 4 5 6 7 8 g) 10 11 12 11 39 73 93 130 160 151 165 179 207 15 Lh 15 16 17 18 TD 20 21 22° mm. 224 254 238 204 151 95 63 33 20 10 (2500) Variationsweite von 3 bis 22 mm., Hauptgipfel bei 14 mm., Nebengipfel bei 8 mm. (Fig 24). VIII. Pinus silvestris L. Der Vollstandigkeit wegen wiederhole ich auch noch die Zahlen von Pinus silvestris, die in der eingangserwihnten Arbeit von Ludwig schon publiziert sind. 7 8 9 10 1 12 TS) this Ay thep 9 aS) 0) Fp 8 15 32 27 47 «55 114 136 183 233 317 386 463 5380 603 2: o 2. 25 26 27 98 29 80 81 82 88 34 85 386 701 773 922 820 807 832 921 727 602 469 390 263 189 140 102 3Y 38 389 4O ft J2 4B 4h BS $C 4% 48 49 mm. 69 52 27 18 8 4 5 1 2 oa 2 2 (12000) Biometrika v1 46 ‘die Ldngenvariation der Coniferennadeln Ubei 362 ve ZE O€ 8% 9% vs ZZ OT BI 9} bl Zi ol 8 9 + Ov BE YE FE TE OF BZ 9F HS BS OT BI OI HL ZI Ol 8. 9 O€ 8% 9% #% ZG OT BI 91 HLZL OL 8 9 & @ NS Ve mae * ya Or dk Ov 91 Or ZL ieee a fy oo 001 oor 9%.r% TOT BI Oi wi ZL Ol 8 9 F Zo v GOT BI OI vl GL OL B 9 Pv Of 8% 9% HJ ZZ OZ SI 91 vl ZL O18 9 vi = ae 81 or Ov Of 8% 9% HJ ZZ OT BI It vI Zi Ol 8 9 9 6 ooL ool Bt Ot rl ZLOlLdes 9 Zoos BL Oi vl LOL B 9 | mn Zt 1% du oot]. ; 92% GU OF BI 9 wl ZO! 8.9 »F 9% po 73 OT BL OI bl ZLOL 8 OB Qf bE ZE OF BZ 9S HG GOT Bl 91 vl ZI Ol 8 9 +& a eo _= 8 ool 0% x. or Or oo UE G 6 08 ve aE sot 00t ool 00% 96 ve TE OF BZ 9% HJ TF OU BI II pL viol s 9 ¥ vi vl Au Las 8% 9% bt 2% OF BI OI Hl ZI Ol 8% 9% PS Z% OF BI 91 HL SI Ol S PL oot O€ 8% 9% $% ZG OT Bl OI FI ZI Ol B I H.S O 363 A. Hryrr eX4 vd St ° Ov o€ Yd Ol os ov os 0z ol oot Ov Or A Sh ooL 001 De Zh og oot 00% 00% vz OO OdL Ort oo0e ooe ost cE gz lost 00% oor oor ZS Ove 00h PB 08 OL 09 os Ov oe 0& (00% loo0e (oleh 00s 009 toler 008 6s 9S OS oot Ost 00% OS% OO€ ose 6l 08 OL o9 os Ov o€ iex4 o1 lord Or 09 08 oo 6b Zs OZL ey £9 06 os (oy 09 os or oe 0% Oot 00% oOo€ 8 L 007 6v OOS 009 00d 00s 6% 006 46 —2 364 Uber die Ldngenvariation der Coniferennadeln Die Variationsweite lhegt zwischen 7 u. 49 mm. u. die Gipfel legen bei 24 u. 28 mm. Vergleicht man nun die Gipfel bei den verschiedenen Arten, so fallt vor allem auf, dass die gleichen Gipfelzahlen wiederkehren, ohne Riicksicht auf die Art. Es sind das die Gipfel 14 u. 17 bei den kurznadeligen, dann 24, 28, 32 bei den Pflanzen mit mittellangen Nadeln. Auch 49 kommt zweimal vor. Stellt man von allen untersuchten Pflanzen die Gipfelzahlen zusammen (wobei ich fiir die Baume mit mehreren Zahlenreihen stets nur eine beriicksichtige), so ergibt sich, dass von den 52 deutlich ausgesprochenen Gipfeln 26 auf Multipla der Lange 7 mm. fallen [1:(7) +11:(14)4+3:(21) + 4:(28) +1: (42)+2°(49) + 1:(56)4+1°(63) +1:(70) +1:(77)], 21 fallen in die Mitte zwischen solche Zahlen hinein u. 5 fallen anderwarts. (Zaihlt man jede vorkommende Gipfelzahl nur einmal, so erhalt man 21 Gipfel- zahlen u. davon sind 10 Multipla von 7.) Solche Mittelzahlen waren zwar genau 10,5; 17,5; 24,5; 31,5 ete. mm. Da aber mit der Millimeter-Einheit ge- messen wurde, betrachte ich die auf die benachbarten Ganzen fallenden Gipfel als eigentlich in die Mitte gehdrend, zumal ausser 17 tatstichlich auch 2 Mal der Gipfel 18 auftritt, ausser 24 auch der Gipfel 25, ausser 382 auch der Gipfel 31. Bei der schén gebauten Kurve Fig. 23 tritt deutlich die Tendenz hervor, den Gipfel zwischen 17 u. 18 zu fixieren. Es scheint demnach, dass in der Tat eine “ Hinheitslinge,” wie ich sie schon friiher vermutet hatte, bei der Fixierung der Gipfel eine Rolle spiele. Vielleicht ist diese “ Einheitslange” 7 mm. u. die zwischen den Multiplen gelegenen Gipfel sind Summationsgipfel, entstanden durch die Combination zweier Kurven mit Gipfeln bei den benachbarten Multiplen von 7 mm. Oder aber die “ Hinheitslange” ist 3,5 mm. u. die Multiplen davon waren 7; 10,5; 14; 17,5; 21; 24,5; 28; 31,5 etc. Es sei noch besonders darauf hingewiesen, dass die Variation oft in der Nahe von 7 mm. beginnt u. in der Nahe der oben hervorgehobenen Zahlen aufhért, ohne dass ich einen sehr grossen Wert auf die wirklichen Anfangs- u. Endpunkte der Kurve legen méchte, da ja der Zufall eine sehr grosse Rolle spielt, indem er uns einige wenige Nadeln, welche diese Endpunkte bestimmen, in die Hinde spielt oder aber vorenthiilt. Ks ist nun auffallend, dass die von mir bei den Coniferen gefundenen Gipfel- zahlen auch bei Laubholzern vorkommen. Ich selbst hatte einige derselben bereits bei den Blattern von Prunus spinosa ermittelt. In einer interessanten Arbeit Beitrige zur Physiologie des Flachenwachstums der Pflanzen von G. Ritter (Bot. Centralblatt, Bd. xxu. Abt. 0. 1907) wird versucht, diese Gipfellagen zu inter- pretieren. Es handelt sich dabei um die Langenvariation der Laubblatter von Vacciniwm Vitis Idaea, V. Myrtillus u. Myrtus communis u. es werden die Gipfel bei 10, 14, 17, 20, 22, 24, 26, 28, 32,36 mm. gefunden. Diese Zahlen verhalten sich wie die Quadratwurzeln aus den Fibonaccizahlen der Haupt- u. Nebenreihe. Wenn nun das Langenwachstum pflanzlicher Organe schubweise nach der Fibonac- cireihe erfolgt, so ist es sehr plausibel, dass beim Flachenwachstum der Zuwachs in einer Dimension schubweise nach den Quadratwurzeln aus diesen Zahlen vor A. HEYER 365 sich geht. Nun fragt es sich: handelt es sich bei den Coniferennadeln auch um Flachenwachstum in dem Sinne wie bei den Laubblittern der oben genannten Pflanzen? Doch wohl kaum, Hier sollte man annehmen diirfen, geeignetes Material fiir das Studium des Liingenwachstums vor sich zu haben. In diesem Falle liesse sich schwer erklairen, wie die Gipfel trotzdem kollidieren. Ausserdem bin ich nicht iiberzeugt, dass die Gipfel bei 20 u. 22 mm. in den Ritter’schen Reihen echte Gipfel sind. Zwei Gipfel, die nur durch eine einzige Klasse getrennt sind, kommen mir immer verdichtig vor, besonders wenn sie geraden Zahlen angehéren, weil—ich habe eimige Erfahrung darim—diese Zahlen stets unwillkiirlich bevorzugt werden auf Kosten der ungeraden. Es wire sehr gut méglich, dass 21 der wahre Gipfel ware, u. dann wiirde er in meine Zahlenreihe passen (siehe tibrigens Ritter |. c. Fig. 3). Vorlaufig, nachdem verhaltnismiissig noch wenig Material vorliegt, kann die Theorie jedenfalls keine endgiiltigen Siitze aufstellen. Die niachste Aufgabe auf diesem Gebiete wird sein, durch grosse Zahlen die Gipfel definitiv festzustellen, ganz besonders aber diejenigen der héhern Klassen, durch Untersuchung von Material von recht ausgedehnter Variationsweite. STATISTICAL STUDY OF ANTI-TYPHOID INOCULATION. By G D. MAYNARD, F.R.C.8.E., Pretoria. IN a paper read before the South African Medical Congress of 1908, Major Buist, R.A.M.C., has collected a considerable number of figures relating to anti- typhoid inoculation. The conclusion that he considers these figures lead to is that inoculation is of decided benefit, both in preventing attack and in lowering the case mortality. It seemed that in view of the sparseness of the statistics at present available, it was more than ever desirable to examine such as we have by modern statistical methods. To base deductions on percentages, apart from their probable errors, is likely to lead to wrong conclusions ; and it is only by the help of methods such as those here employed that we can hope to learn all that the data signify. The statistics used in this paper have been obtained from the above-mentioned source, with the exception of the table containing the Transvaal figures, which were kindly supplied to me by Major Buist at a later date. The coefficients of correlation—between inoculated and freedom from attack, and between attacked and recovery (in the inoculated)—have been calculated by the “four-fold table” method of Professor K. Pearson. The probable error of these values has been assumed to be three times the error found by the formula E,,= 67449 (1 —7?)/V(n—1). In two cases the long method was employed to check these results, but in neither case was the difference material. The figures contained in Tables I and II were obtained from a census of the whole army, taken by the military authorities. The data are admittedly in- complete owing to the absence of some of the troops on manceuvres or on board ship, and further it is not certain that all cases of inoculation were correctly returned as such. The period covered is from March 1, 1906, to February 28, 1907. Although Major Buist quoted data for the inoculated in the British Isles, these G. D. Maynarp 367 have not been used in this paper. No case of enteric having occurred among the inoculated, the correlation would have appeared high; but the absence of a case amongst a small number of inoculated men has clearly no significance in view of the comparative rarity of the disease, and the small probability of a man, in- oculated or uninoculated, being attacked. Tables HI and IV refer to local outbreaks in two regiments following their removal abroad. Tables VI and VIII contain statistics obtained from seven large Indian Stations, between January | and June 30, 1907; these returns are stated by Major Buist to be the most complete, and are free from most of the errors that are found in the other figures. TABLE I. Results of Antityphoid Inoculation. Stations Abroad. 1/3/06 to 28/2/07. Inoculation + = i . ; | Not attacked ... | 786 30757 | 31543 | Attacked | 5 193 | 198 | —_— eee rs | | Totals ... | 791 | 30950-81741 | | | h=—1-961324, =2'498566, ‘924375 — 5606774 + 2°487017% — 245024724 7 + 00202 =0, r= — 0020+ 0114. TABLE II. Indian Stations. 1/3/06 to 28/2/07. Inoculation + sy Not attacked ... | 2122 | 37113 39235 Attacked nee 8 | 770 778 Totals ae 2130 37883 40013 h= — 11142560, k=2:065319, — 1869876 + -214177° + 069277! + °873987° — 1:667017? +7 —+16165 =0, 7 = "2556 + 0095. 368 Statistical Study of Anti-Typhoid Inoculation TABLE III. 17th Lancers in India*. Inoculation + = me | | Not attacked ... | 148 | 481 | 629 | Attacked a 2 58 | 60 A | Totals ae 150 539 689 | h=-—-‘780018, k= 1°358832, — 010975 — 1218494 — 05523973 — 5299567? +7 — 34425 =0, r= "4802 + 0593. [* The absence in Pretoria of Mr Maynard does not permit me to ascertain from him the source of the total for uninoculated. In Lieutenant Luxmore’s Report, Journal of Royal Army Medical Corps, Vol. vint. p. 492, the strength of the regiment is given as 593 including 84 women and children. Of the five officers’ wives, three were inoculated ; of the 79 remaining women and children none were inoculated. This would make the unattacked who were uninoculated about 100 less than the number given by Mr Maynard and would increase the correlation. The report, however, in its present form is not one from which it is easy to draw any definite conclusions. The actual proportions of the inoculated and uninoculated in the Delhi squad are not given, although it is possible that the visit contributed to the outbreak. It is not clear how fav the draft of the regiment numbering 96 which reached India two months later is or is not included in the returns of cases. If wholly uninoculated, it would account for the 96 additional persons in Mr Maynard’s table, but some at least appear to have been inoculated (Luxmore, p. 492). If cases of enteric among this draft are included among the last 20 cases reported by Luxmore, then the total 593, given on his p. 492, does not apply to the incidence. Lieutenant-Colonel Leishman writing in the same Jowrnal, p. 465, of the outbreak in the 17th Lancers at Meerut says : “The report of the attached medical officer, Lieutenant Luxmore, furnishes a striking piece of evidence as to the protective effect of the inoculations. .....The uninoculated portion of the regiment served, unintentionally, as ‘controls* and the fact that of 63 cases 61 occurred among these controls, and only two among the inoculated men of the regiment, is one the significance of which it is hard to minimise.” According to Lieutenant Luxmore’s Report, there were only 61 cases (59 uninoculated and two with the first inoculation dose) not 63. Without knowing the totals of inoculated and uninoculated in the regiment it would not be easy to express the significance really borne by Lieutenant-Colonel Leishman’s statement. But several other points of view may be suggested of the 150 inoculated; 13 per cent. were officers and officers’ wives, whose environment and average age probably differ much from those of the non-commissioned officers and men. Of the 150 inoculated two were attacked ; of the 79 uninoculated women and children included on the strength of the regiment only one appears to have been attacked, a rather less percentage than in the case of the inoculated. Further the so-called ‘‘ controls” cannot be considered as true controls, until it is demonstrated that the men who are most anxious and particular about their own health, the men who are most likely to be cautious and run no risk, are not the very men who will volunteer to be inoculated ; thus a spurious correlation may be produced between attack and absence of inoculation. The age frequency of both classes ought to be further given in every report. Clearly what is needed is the inoculation of one half only of the volunteers, equal age incidence being maintained, if we are to have a real control. The subjection of the inoculated and uninoculated to exactly like conditions of service ; the exclusion of officers and their wives, and the women and children from the strength on which percentages are based (and the discovery if possible of why these classes are relatively immune!). Useful points even as statistics are now given would be the addition of the age frequencies and the sickness record (other than that of enteric) of the inoculated and uninoculated groups. Until a far higher standard of statistical observation and statistical reduction is adopted, we cannot possibly call, with Lieutenant-Colonel Leishman, the Report of Lieutenant Luxmore a striking piece of evidence as to the protective effect of the inoculations. What is needed at present in the Army Medical Department is a trained statistician alongside the trained bacteriologist. Eprror.] G. D. MAyNnarpD 369 TABLE IV. 38rd Coldstream Guards. Cairo 1906—1907. Inoculation + ee, Not attacked ... 330 368 698 Attacked a 1 13 14 712 Totals tes | 381 331 h= — ‘088128, ' = 2°060759, — 1094275 + 0282374 — 5369273 — 0908057? + 7 — 40792 = 0, r='4987 + 0577. TABLE V. Transvaal Districts. 1/3/06 to 28/2/07. Inoculation + =. Not attacked ... 219 6690 6909 Attacked Bs 5 65 fi Totals a 224 6755 6979 h=—1'850840, & =2°325187, 0101057 — 183659 + 1°78157 — 2°15177472 +7 + °205165=0, p= — "1504 + 0237. TABLE VI. Seven Large Indian Stations. January 1st to June 30th, 1907. Inoculation + = Not attacked ... 2192 7940 10132 Attacked ae 15 117} 188 Totals 45 2207 8113 10320 h=—°793153, &=2-092043, 0129675 + :22566r4 — -208747% — 829657? +7 — 18746 =0, r= "2395 + 0188, Biometrika v1 47 370 Statistical Study of Anti-Typhoid Inoculation r 1p rE, N Table V. Transvaal .. | —'1504+ 0237 6°345 6979 Table I. Stations Abroad ... | —:0020+°0114 0°175 31714 Table VI. 7 Indian Stations ... +2395 +0188 12°739 | 10320 | Table II. | Indian Stations ... +°2556 + 0095 26°905 40013 Table IIT. | 17th Lancers a + :4802 + °0593 8:098 | 689 | Table IV. Coldstream Guards +:°4987 + °0577 8°643 712 Mean = ‘2203 + ‘0649. Mean weighted with 7/£#,.='2745 + 0048. Mean weighted with V=:1357 + 0003. We see that four of these results give a positive and two a negative correlation ; and the mean calculated with or without weighted ordinates is positive. In Tables I, II and V, it will be noted that the number of the inoculated is very small compared with the total, and therefore the probable error of the class group— inoculated and attacked—is large. A small alteration therefore in this group (which is to be reasonably expected in another sample from the general population of the inoculated) would consequently largely affect the value of 7. | | CV GU GT HOY SH 00 09 69.1 AGT OD I SH fedeaicah st | g 3S sy s 98-TI—$8-01 PUPA, site eemaeles mcrae once rose Ae We batitlacs tee dS = 2 Ss GB. OE =a OP NM Te (Reigseee, SS al GN ES Sa BOIS) eS NN ae Nes ail ale ee : : ° Rees eoe- Oi Soi6me|lalel We lags eee go> enema as la AP led ol ikl enM@el IL 3 aL - = & 48-6 —98-6 {alldal ORS SSS SS Bes eshSS eeet 0 Se Se eal ce al ellis So & : == wd ~ Ss = 68.6 —G8-8 | | achat ac eoriios orev: Meno sec 1: nlc oles ve) Pa GMirt | ras | | B oe | an eS faa) G39 — Ff alee GSH HO St AED ON St IS NIA GN Sos ES OUGNICOIG AC | a Ss a : =e or x ya) a [| AA 1d WYO HID 19 TVG GT 4 GN | | a A) ~ 68-L —G8-L [Pet CD UGN C9 GN. C500) ONO OES ON STN | [a | ! | S — Boe S 68. —88-9 | | ESR ON ACN CO ets SO OI ee SO CN So rt C3 mrt | | s g s = = cS 68.9 —G8.9 4 | OD I DG HOW OOO ADAMO MO A a “= = = = S 8-9 —98-9 RC) Pk ae a eo a 2 3, a 5S 98-4 —GE-G ie i Pe a gc ecg a aR S ~ a SSSRASRSLSSBBLSSSBESSSRESSSaEss IDIDIWINODODOORAARRG 0 SS DS HAAARSSSSSH n ee) ee Ne ee Oe ater eld ea aN Coe lis bee SUsSsegn: SSKRASAGSSKSgssrsgssxr SYSsges a “31515 1GH1HIHSSOSGSKHKKKHHHHHAARAAASSSSS ‘sojosndaog poolg jo yysueT TABLE B. Total Length (with tail) and Length of Corpuscles. R. temporaria, Tadpoles. Body Length (with tail). Kari PEARSON Sopdaen jo Wascen 3 Ee RISO CeO IO ROO OAS Aae S E cia R 68-81 —G8-81 Misia gcse = een rel el ey let ies 98-69 —G8-1T allen ee ores eel aoa eae Th So teat lene Fe ° 98-14 —S8-04 | | | tel Le BOR RTT PH eel) ie Mes | ° $8-09—GE-68 ae FRSA tesa Marea eli Lo Metta evl pl lvehs PTF) | ° gs-es—oe-ee | PII LL IARARE@@ 8 Pett iii R 68-86 —G6-L8 | tatters Hep OOY | | | | | Tals G8-LE—SE-98 PTAA AST ATS Peat RRP Sy se A at ° G8-98—G8-.98 eae em ec pe 1) It" | 2 96.08 —08-48 Lee eee ee en-te—se.se | | Delle lemeeiecctaecy epee ge oe 4), Melitta a gs.ce—ae.0e || 1 | | [AS [ate [aa | lil des 68.68 —GE T¢ | | | aOR CN MCE AOC 02 Sel en : | | 2 ee | | H | COO) Beh Co) OY CAEN SHES lahat || j , | He ae ¥ e | Aiea eee jouer | | ne open | | ANAHA | OCOHRACHEAAOAIAM HA eda a ee-se—oe.e | ||| | [POPPERgneregnegenran jan) || | R CCUG aC Geog Wie ete rt aN TO te tel Loh fs mae 68.6 [1 | | [RAS DOCAMMARANOM AG OA AIOION | | oe oe. —96-6 || | {| [AMAAPCORyoowOmom] | ||| ia] || ps 98-48 —98-86 | | [RAP esha eR Age GEEK gen | ja | | |= G§-8E—4E+B6 Lie WL elena CCRT SO arene es el a bac 98-86 —GE- 16 es [HA OME TO TOM Ua al ieee 66-1e 98-08 lies ea ile es [AKRAM wAUSoOANAoOAA DA | Lll tye 98-08 —98-61 a ree Oe ree banal tess GE. 6I1—GE- 81 1a | | pA | Ht mmMoonntantrotaAtaaae | | “2 96-81—96- AT PL | LL lal [santo mmoomee | [a] |] | | | ddd) dy eeur—se-ar JILL ILI LIS pit eegeeereaa posi] |i dg SSELSSS LS SARLSS SRLS SSSESSSRESE WIDIDMWMW DOO OORRRARRADBDAADAAA DSSS) SS 4 rt Study of Blood Corpuscles of Tadpole 414 AA MID OMAK DMONRAOMNMNMARROMORROOOCn s[eqo, i801 —96-0F G | | | eu: a 8 —98 20 G6 S[RqIOT, GS-51 —GS-6F GE-BY—4E- TF GS-19 —G8-0F GE. 0%—48.-68 GE-6E—GS-8E GE-8E-—GEAAE GE-LG—G4E-9G GE. 98 —GS-4E GE-9E—GE-VE GE-4E—GE-EE GE-E8—GE-6E GE-68—GE-1E GE. TSE —4S-08 98-08 —G8- 68 GE-66—GS-8E G8-86--9E- LE GE LO—GE- 96 GS-96 —GS- GE GE-GE—GE-46 GE-TE—48- GE GE-66—Gb- TE GE-TE—48-06 GE. 06—GE-6T GS-61 —&8- 81 GE-8I—GE-LT GE-LI—GS- 91 "yup} ynoypun pun ‘rey quoyyIMm ypu ypbueT fipog ‘O WTavVi yysueq Apog ‘sapodpny, ‘prvp.oduay ue [rey YQIM yysaery Apog 415 Kart PEARSON NAONR A DONG SALON GZI | OOL seq, GT-6—46-8 G6:8—GL.8 GL 8—GG-8 | §G-8—GE.8 tT l—]t || — | KH | Hf 68-8 —9r.8 YS) = 1 GT-8—G6-L et ee ae ete = || = | = eee ee Te i a) Se at Beet a | ee ee | pel a | Saat ee ee tp MS ap I ee ee) a eee ae? — = ae ar ey Se ete ie or le ae ie ite |) ete) —!i—|]—lPp |—|1]F% |r |9 |9 | OT] etie |9 |G |r | 2k | — | 86-9—S2-9 | ie tS ie ele te a hee oe ee ee ae ie GL 9—4G-9 TS | S59 | ee eS OR Per 8 ree 39 |e le GG.9—G8.9 —!itT |—/|6 1/6 |¥% |6 | 68/1] 9T} Ge] o0e] et1/6 | FT1/6 | 2 [4 GG-9—GT-9 @fi/t |—j/2 1/8 |F | IL] ee]¢ | OL] FT| 2416 | IT} 9t}6 | 24 {1 GT-9—46-G e€fel—lPpr |r ]ses9 |stiz |e8e}] et] 24218 18 |st}/s |e {Tt G6-G—GLG 6 |r |—!1e |S |S | FL] el] BE] Ol} or] a}6 |¢ |erj;2 |4 48 Ghee G—GG.G EOS | 88 1S GL et) CE | 216 a) St 1 6h) LE 1 re) 8] ek. |e GG-G—GEG r 13 |—!/1t!/9 |¢ | 24 | PL] €t | 2401 et |] &t | 6L | PL | 9e@ | OT] 2 1 6 GS-G—4T-G GG Ne Nie 6B lt iO |Oe ese WR eS Oh sie ee GI-G—G6-4 I | == ae GLO eGo WeG ee a tee eee | eSe 8 Ge i= 1G G6-4—GL-4 | ma eel SIG lee eG oe ep GIT ee Qe le. 1 GL T—GG-4 Sy |e | Ee | I |) | ii ee GG.4—GE-4 | Say ee MG a ead a CCE Gr eT: Meyer Gem kOe Wie pO S ae C7, SS te aa a A ee | ee tee) er coe = te = == | it Ne = | |) See eas sage | sila || = | Name | cae ac 2 I |—|—] &2-8—9¢.¢ = | | i a | | eta = S| eee alll a GS Ge Gre, == | Si — Tie ee eee ee [a Ge a0: 6 i a No — i | i mw | ST Si CSS) Basia al IS TSS SSS shat Ie Seek hed) eecaaa Patel e ou i k lh U io I i. | nN | | | i | | | | eed Pie sa esl se fines Pe Se pe |e See) PO cern Pte oa ca fa Ss ‘yyouery Apog ‘saposnduog fo yypnarg puv yybuay hpog ‘da Widvi ‘sqjodpny, “nunsodwag “ay ‘soposudaog poolg Jo yyprorig Study of Blood Corpuscles of Tadpole 416 H | GLLL] 1 | 0 | I | G | GI | FL | | LT | €3 | e¢ | 69 | 66 | 99 | 8L |zor | 191 B81 | PLL PEL | E81 | SEL | OL | 9€ | GE | 9 | OF | HL | | z| € | TL] s[eqoy, I | a a ee | a a eat | Se S| Slee | a Se eee exes I = I Sg abel (acy seer (Ae Oe = G6-8—GL8 j = rs I TE seen | eee mee | cd (eee | ae (cece el eee (|| GO oar. 0 = aa i a a SSS = = G9-8—GE-8 id = I = | eS ad Se SS aS S| SS Sale| ee me SS See LS. id Fe ele ee 1 a ee ee en e—¢6.y, € I = Ue te a i i a a i a SS ae 9 Te ee es Se Se i ar a | SS a = Gh hl GGL 8 SP Se a ee ec a ee a = 99-L—96-L ee = if so el ee Se to te ee es eee it | GE-L—GTL Loe la |S | cel eee ele Colle Sous te bay (eGo Gaal chLe |G xl fn Reena = a ie cell od | Poof Gis ic I Tie Coe aloes (Gi ONG seis dCs Gees Coen rau ee ol Cane aT ; = = = G6-9—GL9 V2 Oe Vice crea a |e ee Cee eee LRG. eC bGo lira Gal Ol lege ls alere (bomen pe lec Sev seed sll eel eel Pe 16 == I SS WS ae ie SS IA it) ee ee ee te ea = -] 99.9—G8-9 COI Nee |Sar | cee Cea leGe boar eSw Co Osco Slel O: tiaclel Touleeoulmese| GlalectalmOarieee lute |) ihe | 98-9--GI-9 oS alae elemleCuueOule Om ih IC) |e Ou lees a ese | pr ctl Oculae lecie lesa lccleOadeco ce | sls |e | liar o=-ae, @ CONSE cary are laters medl ao (nGe Ue eG | 2G Lr Wor cS Tore ico | Gi nee lsels|-094| chalnGe || ole sete alah ce.c-—o7.¢ HA i LN es ip Ree | A ome ya ne iene aT ees |] Presa || coi WEG an [geet esa ea eT GliG—GG-G orf i—|—|t]t | t | t | t -|}—|4 /F | Ot} 9 |e | 1] ot] | et| or] 1) rt\er|9 |¢ |r |e | 1 |—|\—|—|—l[ 9¢-s—ee.¢ SCR ew aaa Se a= | S 191 98h OL | t OR OL | Gli 06 |9Si7| Gir Ze.|.66 [82 1) 2 i OnsleGe OF lees a) | Nene gre CRIM ale ees lmer lea) aie = Gn | ahh 8 bee) Le Ge eeon WOnelS/ Si el sl eoyelefelelelelel/2z/2]/s/slszlelelele]/e}ealalalala ml] SO] se] NH ds bend cS ~ Nn iss) mi ixe) ~e i) ds i Ne} ~ Qr ies) i Ne) ~e N So me Ne} ~]} QM] Gl Ww N_ Sp Sep Gy A N i Nn On an N a oO Nr i nr q OX oO or rn i | tl | 1b} fori 22 |} 42 | 69| 67 | 49} 18| 16) 6| 3| 2) 1|— |] - 336 | c | 62—] 6) 14] 27 | 22] 72 | 135 | 164 | 206 | 1383 | 64) 50] 8] 8] 2} 1}/—] 912] | 66—| 5| 17 | 32] 42 | 135 | 260 | 364 | 462 | 307 | 185 | 107 | 28 | 12| 6/ 5] 1] 1968 S| 7O—] 8 | 25 | 42 | 69 | 164 | 364 | 554 | 794 | 558 | 252 | 166 | 55 | 21] 11] 8] 5] 3096 | S| 74—|]| 5 | 25 | 37 | 67 | 206 | 162 | 794 | 968 | 798 | 386 | 212 | 74/19| 14] 9] 4] 4080 @ | 78—]| 5 | 20 | 35 | 49 | 133 | 307 | 558 | 798 | 678 | 379 | 220/63 | 25| 5/ 9] 4] 3288 | s2—}] 1| 3/| 22/ 18| 64 | 185 | 252 | 386 | 379 | 222/111 | 42) 9] 3] 4] 3] 1704 a | 86—} 2] 6 | 20| 16| 50 | 107 | 166 | 212 | 220/111] 62/19] 9] 1) 4] 3] 1008 Smee es | 93:| 6) 8 | 28 55) 74! 63 | 42| 19/ 29] 3] 1] 2] 2 312 | ae welele2 | 4) 3) 8. |-12| 21) .19| 2) 9) 9| 3|—| 1] 2] 14 ,i20 Sue ae || 2 )+ 2) 6) i} 14) 5} BY 1] 1a) r}—}1a)— 48 Smog || a | | 5| 8 9 9 4 AN OS OL or ey a 48 106 Me S58 Mt A eS eB Bo) Tee | ae 24 | Totals | 48 | 144) 264 | 336) 912 | 1968 | 3096 | 4080 | 3288 | 1704/1008 | 312| 120] 48 | 48 | 24 | 17400 In this table “46—” signifies the group of corpuscles with 46 for index, and any value up to but not including 50, and so on. DATA ON VARIATION IN THE COMB OF THE DOMESTIC FOWL*. By RAYMOND PEARL anp MAUD DEWITT PEARL. 1. Mucu of the evidence adduced in support of Mendel’s law as a general method of inheritance has been derived from breeding experiments with the domestic fowl. The work of Bateson, Hurst, and Davenport has served to make it a classical object of research in this field. One of the most obvious of the “unit characters” of poultry is the form of the comb. All students of inheritance in this group have included the study of the comb in their work. The behaviour of the various comb types in inheritance is frequently cited as a well-nigh perfect example of typical allelomorphism. The different comb types—single, pea, rose, etc.—are commonly said not to blend in cross-breeding, but instead to be inherited in a strictly alternative manner and in accordance with Mendel’s law. In spite of the extensive use of comb form in poultry as a character in the study of inheritance there has been, so far as we are aware, no particular study ever made of the degree and character of variation within each of the several known types of comb. About a year ago an opportunity was afforded one of us to carry on extensive breeding experiments with poultry. The plans made for the prosecution of such experiments included the investigation of the inheritance of comb characteristics. It was felt to be highly desirable in connection with this work to gain some sort of idea of the degree and manner in which there was variation within each of the several comb types. Such questions as the following suggest themselves: How far from the normal in any direction may the single comb, for example, be expected to depart in pure bred birds?) What degree of variation, biometrically considered, do the various comb characters exhibit? The work of Weldon on peast and on Lychnist{ has demonstrated the importance of such studies in relation to the analytical investigation of Mendelian phenomena. All studies of this kind take their point of departure in an attempt to analyze * Papers from the Biological Laboratory of the Maine Agricultural Experiment Station. Orono, Maine, U.S.A., No. 8. + Biometrika, Vol. 1. pp. 228—254. + Ibid. Vol. 11. pp. 44—55. Raymonp PEARL AND Maup Dewitt PEARL 421 a broad Mendelian category. In Mendelian discussion “single comb” is a “ unit character.” All “single” combs are put together in one category, all “pea” combs in another. But nothing is more certain than that all single combs are not alike in respect to any feature whatsoever, even including their “singleness.” How much and in what ways do they vary? Do the variants within the category mendelize? Are all variants exactly equivalent in crossing with other categories ? An answer to these and other easily suggested questions could not fail, it seems to us, to throw light on the problem of the constitution and physiology of the gametic determinants of “ unit characters,” assuming that such determinants exist. In this paper we have endeavoured to give a clear and, so far as possible, quantitative description of the nature and amount of variation normally occurring in a homogeneous pure bred strain of Barred Plymouth Rock hens in respect to the form and size of the comb. The aim of the paper is purely descriptive, and it is regarded by the authors as preliminary to the analytical investigation of comb inheritance. 2. Up to this time we have only been able to collect anything approaching a statistically adequate amount of material regarding comb variation for single combs alone. There is a certain fitness in taking up this comb at the start, because it is the primitive form*. In the course of the routine work of the laboratory, there came an opportunity in connection with certain autopsy work to examine and record the condition of the comb in a series of adult Barred Plymouth Rock hens. The hens from which the combs were taken for this work had been carefully and closely selected in their breeding for more than 25 years. During the last nine years they have been “line-bred.” This means that no new “blood” had been introduced into the stock during that period. Consequently, the material is racially exceedingly homogeneous. Indeed it would be difficult to find anywhere material for the study of variation more homogeneous than that dealt with here. All the birds whose combs are included in this study were females, and adult. In age they varied from eleven months to about five years. The great majority of the birds were two years and over in age. Since the comb attains its full development within the first year of a hen’s life and probably does not thereafter change in form—except as the result of accident or mutilation— this difference in the age of the different birds used is not significant. Mutilated combs were not included in the study. As will presently be made clear to the reader, the comb is an exceedingly variable structure in fowls. It varies both in size and in form. So great and of such a peculiar character is this variation that its biometrical appreciation is a rather perplexing problem. A priori one would be inclined to say that fewer things would be easier than counting the number of points on a single comb or measuring its height. Actually we have found it practically impossible to do * Cf. Davenport, C. B., ‘Inheritance in Poultry.” Carnegie Institute of Washington. Publ. No. 52, p.65, ‘‘The primitive form of the comb is the single comb seen in the wild species of the genus Gallus, and in most domestic races.” 422. Data on Variation in the Comb of the Domestic Fowl either of these things directly in a satisfactory way. At the outstart of the work it was felt to be absolutely essential to get some kind of a picture of each in- dividual comb. Practical considerations ruled photography out as a means of reaching this end. Resort was had to drawing the combs actual size with the aid of a camera lucida arranged not to magnify or distort the image. In this way one can get an accurate outline of the lateral aspect, or, more correctly, of a sagittal section of the comb. It was at first thought that it would be best to make such drawings with the comb still attached to the head. Experience showed however that this was not the case. More uniform and accurate repre- sentation of the base of the comb could be made if it was removed from the head. After this was learned all the combs were removed before they were drawn. They were cut off with a sharp scalpel, great care being taken to ensure that the cut evenly followed the contour of the top of the skull. The severed comb was put on a flat surface after removal, and the basal cut edge was made, as nearly as possible, a straight line. After the outline of each comb had been drawn, the area bounded by the outline of the comb was determined by means of an Amsler polar planimeter to tenths of a square centimetre. Our procedure was as follows: the area of every comb was measured twice; if the results of the two measurements did not agree, a third measurement was then taken. If this measurement agreed with one of the others, it was taken as the final result. If it did not agree with either of the other two, an average was taken of the three measurements and the average recorded as the area. Every effort was made to attain accuracy in the planimeter measurements, and it is believed that the figures given are substantially correct. In addition to the comb area, the length of the comb was measured. This was done by placing a sliding arm-caliper on the outline drawings, and adjusting it so that the arms touched respectively the most anterior and posterior points of the comb outline, with the bar of the caliper parallel to the base of the comb. It was desired to measure the height of the comb, but attempts to do this directly failed. The reason for the failure will be apparent if one examines the figures. The top of the comb is an irregular, serrated line. It is quite a matter of accident which particular point of region of the comb happens to be highest. If one were to measure the height at different points in different combs, it is plain that one would not always be measuring morphologically identical or even comparable things. Thus, in one case (Fig. 27, Plate I.) the highest part of the comb might be at the very posterior end, and in another case well toward the anterior end (Fig. 93, Plate III.). Height measurements made on such a plan would have no particular significance. Yet comb-height is a very significant thing, parti- cularly in cold climates. The tall comb (e.g., the Leghorn type) is much more liable to be frozen than is the low Plymouth Rock comb. It is highly important to get some measure of height in a study of comb variation. After a careful study of the problem we have reached the conclusion that a fairly trustworthy and significant measure of comb-height will be obtained if we take the height of a rectangle having a length and an area equal to that of the comb. We have accordingly determined this value for each of the combs, by dividing the measured area by the measured length. as the “calculated heights.” These measurements are given in Table I. The RayMonpD PEARL AND Maup Dewirr PEARL total number of combs included is 81. The values so obtained are designated 3. The actual outlines of the combs studied are shown, somewhat reduced in size, in Plates I. to III. Combs 35 to 49 inclusive present a different appearance * The values tabled are the figures to the nearest whole number, obtained by dividing the area by the lengths. TABLE I. Data on Comb Variation. 7 ] | Comb Area Length in aeprimnes Comb Area in | Length in> eles : 2 eight in ; A | height in Number | in em. mm. mime Number cm, mm ee | =: 1 3°9 47°4 8 OV 8°3 60°9 | 14 2 76 615 | 12 58 4°7 bord | 9 3 4:3 ape © | 8 59 53 56°0 9 4 Flesh 57°8 13 | 60 4°] 49°1 8 5 5'5 47°6 12 | 61 3°6 43°6 | 8 6 3°4 49°3 7 62 Neo, 54°8 14 df 9°5 61°5 15 ID 4°8 54°8 9 8 41 45:4 9 | 64 4°5 41°8 11 9 3°9 49°2 8 || 65 12°7 62°3 20 10 3°6 46°4 8 | 66 75 54°9 14 11 3°4 3i3 9 || 67 52, 479 | 11 12 Byel! 54°9 9 | 68 Ai, 460 | 10 IkS5 70 56°8 12 69 4°6 43°2 11 14 50 49°0 10 | TO 7:2 51°0 14 15 1°8 B73 5 | 7 70 48°9 14 16 56 576 | 10 | 72 3°7 42°3 9 17 5°7 54°8 10 73 8°7 56°6 15 18 4:7 48 °7 10 TA 6°8 51°4 13 19 74 62°6 | 12 V5 Die 51°4 10 20 4:2 46°0 9 76 75 54°2 14 21 4°3 55°4 8 1S 46 4°8 45°9 11 22 81 61°8 13 7 70 51:4 14 23 56 53°0 11 i) 8 75 51°6 15 24 Dell 55°5 9 || 80 5°6 49-4 11 25 3°9 49-4 8 81 8°5 57°0 15 26 4°6 54°0 9 2 ie. 52°6 14 a7 4:7 46°0 10 || 83 1195} Sone 4 28 4:7 45°5 10 84 1°6 35°0 5 29 4°] 51°0 8 85 1:3 32°4 4 30° ee 56°9 13 86 4:7 45:0 10 31 3°5 45°5 8 | 87 oe 42°8 12 32 4°2 51°3 8 88 6°4 47°2 14 33 4:2 55°4 8 89 2°4 38°6 6 3h AR) 37°4 us 90 DE 47°2 11 50 tSho7f 63°6 14 91 5'8 52°2 11 51 42, 48°7 9 92 8°6 66°7 | 13 52 5°3 48°3 11 93 1163-3} 72°70 18 53 222, 455 | 5 | 94 8°5 61°2 14 54 6°2 563 1l | 95 5:4 42°8 13 55 4:3 52°7 8 | 96 3°8 45'1 8 56 74 60°33) 12 | PLATE III. Raymond PEARL AND Mavup Dewitt PEARL 427 from the others in that the base of the comb is less straight, and the comb is canted at an angle as a whole. This condition results from the fact that these combs were drawn without removal from the bird’s head. It will be noted that measurements from them are not included in Table I. An examination of these plates shows at once the extraordinary degree of variation which exists within a single comb type, even in the most homogeneous material. It is apparent that this variation involves both size and form of comb. We may first turn to a discussion of the variation in size shown in these combs. 4. The distributions of frequency for the 81 birds and the three characters measured are given in Table II. TABLE II. Frequency Distributions for Variation in Area, Length, and Calculated Height of Female Barred Plymouth Rock Combs. AREA LENGTH | CaucuLatED HEIGHT Sree ee kel Eee re Sq. cm. Frequency | Mm. Frequency | Mm. Frequency O5— 1:4 Il 32—34°9 1 | So 44 2 1:5— 2:4 5 35—37°9 5 | 45— 5:4 3 25— 3-4 3 38—40°9 1 5:5— 6°4 1 3'5— 4°4 18 41—43°9 6 65— 7-4 2 45— 5-4 21 44—46'9 11 75— 8-4 14 55— 6:4 8 47—49°9 15 8:5— 94 1l 65— 7:4 9 50—52°9 10 | 95—10°4 9 mo— 84 8 58—55°9 13 10°5—11°4 10 8-5— 94 5 56—58'9 8 11°5—12°4 6 9:5—10°4 1 59—61°9 6 12°5—13°4 6 | 10°5—11°4 0) 62—64'9 3 13°5—14°4 11 11°5—12°4 (0) | 65—67°9 1 14°5—15°4 4 12°5—13°4 2 68—70°9 0 15°5—16°4 O 71—73°9 1 16°5—17°4 10) | 17°5—18°4 1 18°5—19°4 (0) 19°5—20°4 1 The chief variation constants for these distributions are given in Table III. TABLE III. Constants of Variation in Size Characters of Single Combs. | Character Mean Standard Deviation | Coefficient of Variation | nS = —— i. eet ae Area Bas nae 5°59 +°17 cm.? | 2'24+°12 cm.? 39:97 +2°44°/, | Length ... ae 50°80 + 56 mm. 7°45 +°39 mi. 1467+ °79°/, | Calculated Heigh 10°57 + 23 mm. 3:034:16mm. | 28°66 + 1°64 °/, 542 428 Data on Variation in the Comb of the Domestic Fowl From these tables the following facts are to be noted : (1) The average area of the combs of the females of the race of Barred Plymouth Rocks here discussed is in round numbers 54 square centimetres. The average length of comb is a little over 5 cm. This indicates an average calculated height of 104 mm. On account of the way in which the combs were removed (ef. p. 422), this represents the average height above the top of the skull. (2) There is a high degree of variation, both absolute and relative, in regard to each of the size characters studied. The Barred Plymouth Rock female ac- cording to the American Standard of Perfection* has the comb “small, proportional to the size of the specimen, set firmly on the head, straight and upright, evenly serrated, having five well-defined points, those in front and at rear being somewhat smaller and shorter than the other three.” The drawings and figures here pre- sented show that in the absence of special selection in regard to comb size, the character shows a range of variation all the way from the condition shown in large combed types like the Leghorns to the very smallest of single combs (cf. for extremes, Figs. 85 and 93 of Plate III.). (3) The amount or degree of variation, whether measured absolutely or relatively, is not the same for the characters measured. The area shows the highest and the length the lowest coefficient of variation. This relation is to be expected from the form of the comb. The chief factor in determining variation in area is the shape of the serrated portion of the comb. The figures of Plates I. to III. show how variable in shape the combs are. It must be remembered that the comb characters studied are not independent variablest. 5. We may turn next to the consideration of variation in the shape or form of the comb. In the typical single comb such as is shown, for example in Diagram A, there are to be distinguished four regions or parts which are morphologically distinct. Dracram A. Outline of a typical single comb removed from the head. The dotted lines indicate distinct regions of the comb. The comb outline of this figure is a copy of Figure 2, Plate I. These regions may be designated as follows : (1) A basal region (Diagram A, a) forming the attachment of the comb to the top of the skull. From the base springs the vane, or upright portion. In the vane are to be distinguished three portions as follows: * Published by American Poultry Association, 1906. + The value of v 738 directly deducible from that of v 4 ond v L when we know the correlation of area and length. We find for length and area correlation " 4,= 849, from Tare (Cay as vp Iv ,27)- Raymonp PEARL AND MaAup Derwirt PEARL 429 (2) An anterior region (Diagram A, b) having its free border smooth or very slightly and irregularly serrated, typically never deeply and regularly serrated. (3) A middle, serrated region (Diagram A, c). This is the region of the deep and characteristic serrations on the free border of the comb. (4) Try it is negative. (i) may be written fee yr - r oa rem VEEL) VS Vitay— Ve Tay — Val Vy Try — Val Vy vess(iii). I VE4EV 2 —2V Vyray NU+(Ve/ Vy)?— 2 (Val Vy) tay N= Pay? + Cay— Vel Vyy® For practical purposes (iii) is the most convenient formula to use in calculations. V,, and V,, are usually wanted for other purposes and will have been calculated already. The value for 1-7,,2 will have been calculated already in obtaining the probable error of 7,,.. Beyond this the calculation of 7,, can be completed in a few minutes if formula (ili) be adopted. . Vee This formula has already been rather extensively used in series of data which will be published shortly, but I give the following illustrations of the kind of problems to which it may be applied. Illustration I. Correlation between the number of flowers per inflorescence and the number of developing fruits in Staphylea trifolia. Table I. shows the correlation between the number of flowers formed and the number of immature fruits at the time of counting for 270 inflorescences of Staphylea trifolia from the North American Tract of the Missouri Botanical Garden. The countings of the number of flowers and fruits were made incidentally while an investigation of the development of the fruit was being carried on. The series is a short one and represents the inflorescences at Miscellanea | 440 AQAA RS SI HOO H 10 MS n ae NM BQH OR OAS E al iS) a ~~ ‘syinaq Sutdojaaeq ‘gousoselopuyT Jod saaMopq ‘pyofiy vapiydny T ATV Miscellanea 441 a time when no fruits had attained a length of over 20 mm. It is quite probable that many of the fruits which were still developing when the material was examined would have fallen later. Thus while the investigation of the relationship between the number of flowers and the number of fruits developing per inflorescence during the time that the ovaries which fail to develop are being eliminated presents some points of particular interest, conclusions drawn from one series cannot be applied to any other of the same species. The series is here given merely as an illustration of a statistical method. Number of flowers furnishes our x character and number of fruits developing our y character. For constants we get Mean v= 9:193+°243, Mean y= 3396 +°074, 8S. D. w= 5:924+:'172, 8S. D. y= 1:801+:052, Ve =64°444, Vy =53'038, p = ‘369, Val Va = 120d; cat = °457+°033. Tus = — 649+ 024. These figures seem to indicate that while there is a positive correlation of 457 between the number of flowers per inflorescence and the number of fruits developing, the inflorescences are not all affected alike in the large elimination of ovaries which takes place. Only a portion of the flowers formed can develop into fruits, and the negative correlation of —-649 seems to show that the larger inflorescences lose not only actually but relatively more of their ovaries than do the smaller ones. But this conclusion can be applied only to this particular series of data. It may be found later that after the elimination is complete the correlation between the number of flowers and the deviation of the number of fruits per inflorescence from their probable number will rise to sensibly 0, or take a substantial positive value. Illustration II. Correlation between the number of ovules per pod and the number of seeds developing per pod in Robinia Pseudacacia. The relationship between the number of ovules and the number of seeds in a sample of 1427 pods of the black locust collected from 12 trees near Lawrence, Kansas, in the fall of 1905, is shown in Table II. The constants which interest us here are : x , =Ovules, y =Seeds, Mean «= 1271794, Mean y= 7°6874, S. D. r= 2:2763, S. D. y= 3-4938, V, = 18690, Vi = 45°448, V,/Vy = 4112, Ty = 6934009. ze = -365+-015. Here it appears from the substantial positive value of 7,, that the pods with the larger numbers of ovules are relatively more capable of maturing their seeds than those with fewer. But I may add that this is not true in the case of each individual tree, so that more data are necessary before we are justified in extending this conclusion to the species at large. Evidence from another leguminous plant will be of interest in this connection. Illustration III. Correlation between the number of ovules per pod and the number of seeds developing per pod in Cercis Canadensis. Table III. is extracted from a forthcoming memoir on fertility in Cercis Canadensis. The correlations are: v =Ovules, y =Seeds, Try = 6855 + 0046. T x2 = ‘0070 + 0087. Here r,, is so close to 0 that there seems little doubt that there is essentially no relationship between the number of ovules per pod and the capacity of the pod for maturing its seeds. This point will be discussed in detail in the memoir. Biometrika v1 56 Ovules per Pod. 442 Miscellanea TABLE II. Robinia Pseudacacia. Seeds per Pod. 2\3l4 a6 \-6 |) sy | 8 | ol to ar eure eteel te | 17 | 18 i 6 aS, | 1 ha = l | | | bine ag i | | BR Bi | | | —|;—-—|— S POW Aa Sel, Sal aGiliies | =| =| — 9 NW Oui), 294) 28 eal) 7a) 19s Ge enya tee os 10° 4, 6) |, 83.)-97 738) | 38219234) 17 toelees | SS | | 11 5a| 25° 86 | 89. | 845/41 136) 122 MS 7 12 | 3/16/35 | 33 | 39 | 32.| 36 | 19 | 21 | 15 |, 9 | —| — ] — i$} 2:78: \ 14) 17 WS 28) 33a 23" |e 20a On aLOM 2 iB) DL} 2) 4) 41) 81 10] 15.) 12: ) S38) 14 ies 90 68) 15 1} | 2) 3) 1) B45) 8) 6 eTes hey) aan aes One ee ee 16 OT ah HB et Ele SO ea eee 7 |—|—|—) 2) 1/—|—]| 1] 1] 38) 2] —] 4) 4) 5 leone 18 | | 1 35] 2) ae) 1 | a |) Sao aie 19 | — | ees i i || il | par Totals] 29 | 100 | 152] 161 168 | 162] 155) 98 | 97 | 88 | 69 | 44 | 38 | 23 | 22 | 12 | 7 — = ul ————— = : <= — a Sel! \ = TABLE IIL. Cercis Canadensis. Seeds per Pod. Totals = 2 34 | a4 3 510 a 4 2241 i 5 2222 2 6 888 | g| 5 a 2) == Totals 1343 | 409 6000 | Illustration 1V. Correlation between the number of flowers per inflorescence and the number of synanthous flowers in Spiraea Van Houtii. “Excess of nutrition” has been the explanation offered hundreds of times for plant ab- normalities. It seems desirable, therefore, to try to correlate the presence of abnormalities with the magnitude of other organs of the plant in order to see whether they are more frequent in cases in which the organs of the individual have reached an abnormal size. An example of this kind of problem is taken from my notes on abnormalities in the inflorescence of the garden species, Speraea Van Houtiv. The particular abnormality here considered is that frequently designated as synanthy in teratological literature. In the inflorescence of this species the pedicels of two or more flowers are frequently found fused for their entire length. The flowers themselves may have a more or less common receptacle, but the essential floral organs are usually so distinct that they would be counted as belonging to two flowers. The details of the abnormalities do not concern us here, and will be discussed in due time. The essential question which we wish to answer on the Miscellanea 443 basis of data already tabled may be stated: Is an individual flower more (or less) likely to be abnormal if it is borne on a large * inflorescence than if it is produced on a small one ? If the chances of an individual flower being abnormal were in no way influenced by the number of flowers per inflorescence, but the chances of belonging to a synanthy were equal for all flowers, abnormalities would be distributed among the inflorescences in proportion to their number of flowers, and a correlation between the number of flowers and the number of abnormal flowers would result. Therefore this correlation coefficient will not give us the information we desire. What we need to know is the correlation between the number of flowers per in- florescence and the deviation of the number of abnormal flowers from the probable number if abnormalities were distributed among the inflorescences in proportion to the number of flowers they produce. TABLE IV. Spiraea Van Houtir. Number of Flowers per Inflorescence. 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SUILTS O€ 86 =| VE | 9G G 1€ LE 8 6E : sss auoyg 9 €6 =| G | 0 Oi mc! 0G ; cl ae IOORES | Té | 6 | OL T st SG i Gis “" snsaeq 49 ZL | «CGT Il | 92 0 | FI GE r eo ft oc ormdkuy 9L 8F 86 | GI Oy |) 1 ue 5 SG” ea a auARYy IF LL G8 GE L | g¢ 16 LEGO: oo UIT] Il BE Il | 0 O | Iz imc oO | <¢t oc eumorg 6¢ OL LL | 8b G | 9 6GT | GL | 89 2 ae osystd F9 OL 99 | 6€ IL | 248 stl 6 rg | ““(ppuey) sf sce = FOS =| 88k | GVL | GL | 9FE | 999 | 68 | go “* (YsIMg) proyrozog I¢ | GE. | 49 | 28 € | Gl €Il | #6 | Get | *" “* To}N.1940q 8 8T 9T FL O | GL GE g UF TRellteney ; aus¢, ile eels Ge | AT I 9& 97 € GG “ TeyOeW PIO 9 Srl LEL | OF € | Pel GOL | FE | gg "129 PIO SF BL TL | ce v If &P1 Ié | g9 OSS qd MON 67 69 LG |& we V8 99 GL | Ge | IVYOV]Y MON 66 est | OST | €7 0 | 66 6G | «TS: «| GUT | SSN 69 él | OOL | 99 9 | 6L 941° | G@ | FL | “* TeaqT MON 61 | 8 | |r | ¢ | 83 | OF [4 Jee [ut ct Wydg mon | CB SF ee | Sl [| 9¢ ins €L. | 81 | : “+ ysnmduoyy SF 0¢ Oe || <8 @ | 8g 2 LL | Cr | ee JoqyyNbuoyy 91 96 Ie | @ € &G 61 COG t XOIQTINTT ial &Z LZ | 61 0) 1G st ji ETS cee nae IEP VEe sl Meee 9 WGG | 66 57 205 SS Culsalmond 0 1 10 4 10 80 6 3 GB) |) te) -@ 8 é 11 5 29 Q Drumblade 6 1 24 11 il 87 25 3 26 13) 0 31 13 | 10 67 = Drumoak 4 2 16 25 25. 79 18 4 21 Wey) a rai 16 15 61 | = Dyce 5 1 36] 36] 33 80 || 27) 4 35 31| 0 12 g 19 97 — Echt. 3 0) 29 22 26 79 42 4 40 28) 0 26 19 114 s Ellon 6 45) 115} 138 82 91 10 182 | 54] 2 35 68 339 = Fintray 0 2) 30 25 80 eat 27 25) 0 Ss Forgue 1 20 30 51 87 34) 8 35 30) 0 = Foveran 3 9) 62 86 78 8 88 39) 0 mH Fraserburgh x 12 176, 314) 391 8o 5d 396 249) 14 ix} *yvi ch ) 13| 78] 79 82 12 5y | 50] 4 Sh 20 0 16 23 17 87 3 260 ee 3) ie > ES 3 21| 15) 25 87 3 35 15| 3 3 Glenbucket _ 0 ll 3 || 80 4 6 7) 0 xX Glemauick & Tullich 1 2 45 60 79 7 65 38} 2 Huntly Beal 4 67| 134) 137 87 29 193 113) 5 Insch oS 0 23 37 58 sO 5 24 36] 4 Inverurie 3 89} 101 168 80. 22 144 68} 3 \ Keig 6 16 14 13 80 2 9 6} 1 Keithball & Kinkell” | 2 10 16 19 80 16 3 33. 13) 3 Kennethmont ee | 1 19| 31] 10 80 37) 4 23 19| 0 Kincardine O'Neil . | 7 35| 80] 88 79) 63| 8 88 38] 7 = _ sian iat ing Edward 5 5 | Kintnmonth 3| 22 | 23| 0 4 Kinellar 4 ll 10 1 u | Kintore ... 9| 149 | 64] 4 3 Leochel Cushnie 15 64 | 45] 5 $ | Leslie 5 /) Agi |) 18} 0. 0 | Logie Buchan 4) 20 13] 2 1 Logie Coldstone 3 24 20 0 1 Longside 10 98 46) 1 1 Lonmay 6 W4 | 43) 9 o 2 Lumphanan 8 36 0) 9 7 Meldrum 13 96 i) 40 12 7 7 : Methlick 10} 54 2 34 2 65 13 Midmar 7| 38 | 0 14 4) 36 | 36| 6 Millbrex 5 19 | 3 | 16 3 a7 | 91 0 Monquhitter 11 7 2 48 12| 58 | 46) 7 Monymusk ... 13 Bd | 1 | 25 5 40 32 i New Byth i 40 | 5 19 7 60 OF New Deer 221 176 | 6 | 69 ‘ 29, 3 li 10 | 169 81 Newhills.. 31 223 0 99 36} 221 106 2 New Machar 12 66 4 49 6 70 7 0 New Pitsligo 21 143 4 & z Old Deer 8 wall dep 38 8 123 36] 3 33) 84 49 53} 219 | oy Be 2 7 21 148 95 | 14 31 | 121 125 82 359 . Old Machar 3 46 36) 1 14 6 32 93 | 2 5 | 98 c Oyne Pa Pallas aw 5 g Be 2 15} 2 33 | 16 92 |) oy Peterculter ... 24) 113 5| 3 51 24} 193 | 73 6 aR Al its 63 at : 0 =; i | o 7 5 8 Reterhead iy ED) G8 29 136 | 358 73 | 557 | 369] 19 | 167] 367 | 468 | 332 | 1334 3 Pitsligo | 9| 199 | 66 |. s || &# 10/ 11 | 92] 6 | 42] 57) 89 | 80] 977 = Braniay, Be a 0 el oe 5 38 18 10% BB 8 OF Oe oe ae 258 5 tien no | ads ala ape tare | & Bea) Ae | Be as | is 3) oo | as] | =| a] 4 | | on St Fergus 4 an | 18 i a | oF i 17 8 2 16 B) 21 8 54 | Savoch 3 a | al @ 2 22 38 13) 1 25 | 47 26 20} 118 | Skene a) 22 3] 0 | 23 6 0} 27 || 24) 0 By) |) SS |) Te. EB | Stains Sy ee A |) 2) eB) Bhs || 8| 34 | 36| 3 | 15| 45] 33 | 22) 115 | Slains 5 Pi |) WO} B | sy) 7) 25 15 8 14 34 | 1 1s | 22 28 23 1 | Strathdon 12| 42 | 27) 3 | 22! 18 5 : ) tric a et 2 1 49 24 5 31 23.) 5 17} 19 29 21| 86 j sui bew 19) 7 39 | O 67 | 72 31 45 10 79 38 1 48 | 83 31 34) 196 liveness 5) 27 | 27) i) 16) 15) 123, || Is || 68) Bu) O |) an |} me GO |) a) an Tarves & 47 37 | 1 4 17 44 27 12 36 3 " Tough S| wa uN alee es 3 B 40) 7 | 36) 34) 46 | 18] 134 ees Biel ella ll ealnal ees Be at edie 5 | 10) 12 | 13) 40 Turriff all gee aoa ll & | Ball ag : 11] 0 | 14] 24] 10 9| 57 "Tyrie Palmar le 4 oy se es ee) aa 104] 7 | 31/155 | 180 | 110} 476 6 5 8 0 3 8 13 9 33 Wye Wale | A 27 o 0 1 20 15 7 2 19 6 10) 0 20 | 15 10 45 ‘ | 46 25 1 14 37 26 14 6 41 12 1 12 28 | 15 14 69 i — ie | J Waal | Totals -». 6426/1600) 11189 j\6362 283 | 3844),7848| 8682 |5506| 25880 | — | 6890] 1322] 9762 | 5972] 271 | 3677/7293, 7963 | 5284] 24217 20 igmentation Survey of School Children in Scotland DID Yysuwvg pun hyunoy “(panwyuody\— AX ATIVE 0g OL 8I GL | OL I rae él g 61 OOT || Vv € 91 OL |S 0 8 LT T Ss | ate oe ee UIOALOP | 66 «| 6 9 Si Ph i) © 9) Ol al MBe ME oye’) Ee 9 SN LO ee a1, 26456 PMOU|TYy pue peoy[losyoor] IIe lereeee SC mOGwE On| (OF 1/88 us| MOGENN ET | SeG exOvell SITs al Lee Or FA GCaulsiemn Oles EOGae | ae8G ee |aGee|n Gee) ot mate proydprsqpor] 661 8E 97 LG | 8g 6 8g g9 VI | €&¢ TOL || GGG 09 GV 49 | &¢ L 68 69 OL | 7g |" * utddy pur o1ousry 8 I g 0) G SG € qT 0 | 4 TOL || 9T I G v 9 IT qT 6 i av “* PIOJ[OU[LY] PUY IOATIUTTS] EST ec lacs eh yr | Tt | srsleor 6 198) 007 enna) 66 | se OS Oley cr) Te lee |e “ero pur uuu | él v € v I 0 v 9 0 |G TOT || 9 0 G € [ (0) I v 0 | 1 aBe epllq[ly pure s1owy[ Ly 0% 9 j VE On 59 g 0 |6 TOL | 06 6 v Se ay, @ | 9 6 @ | 8 oe pe “ aepouryly — —' —— —_ | — _- — _- _- —- — — ee —_ eee eee eee Ul4LVU LY, z8 ct |’ 61 Ge NW La Gey 19 ss | sor, | 9 Il OS ER BS iro 4 | € | 06 | oueyo[ry pue uealry 106 | €9 89 69 |S | € 6L €9 Il | Sb | G02 | L49¢ | 99 68 G8 | 46 | g 6IL | @9 8 | 9 | uowLYy pue MosrelpLy LOL | #3 Ge | GE 6L | 3 Gr. cz € | 8% | OOF || €h1 | Lz 1€ gg |46 | b | €¢ 88 EG UOOWALYy pure wsTpruypry crl oT €€ 69, | Lz I GV €g L GY GOT || VSl LT €€ F8 | 06 T (ig 69 v te || Bae ae uRvUgyTy SPL TE eV Be | &é € cv €g 9 IV GOT || LOT oF GE 19 | 86 & Lg 89 9 (ge |} oe oe “" UOYPepIEyY 9g 6 IE LT |61T | O OL PG % | 8 TOT. || LP v IG It |It | 0 L GG L | IL | °° ygotaereq pur ueuero[ry 0G eV av F6 | 1G G tw 6L 3. | 69 GOT || L6G ge 84 46 | 41 G G9 88 61 | 6G | °" sie “" UBULOYO [TS] Sp 6| I C| «C9 SL e | OneiOan Ole We seh e | 697) OL MECORs I yGae 0G") OCF ai Ome ele Walk Gam AG es) aere coe cee OU earesy Gee atin ers Pena |e or | OMen|alOm Mieiore| MeO To) Ot VrOr 79m 68 1 |e |4 | O | es |] 6 [IT | Is | weyqeqorry pue uopueagqity €P Lk €L GI. /8 0 €L 06 LAS G0L || 88 9 LT EL |G 0 LI IIL I 4 nag ee ge Deh alfp él € j G 16 Onley & 0 |¢ TOI || 6 € G j é 0 | PF if I | 0 i us UTR [OVYIIEAUT | ¢¢ OL 91 OW it 20° 1-66 91 v | IL | ror || 2 6 ial ZG Ona lneh 1z ee | Or [reystuy pue Lyosousypy | sie G g 0 8 @ é I 0 | 8 LOEW LU le Nees 0 |6 G I 9 OMES (ySang) Aereteauy 2 Aereuspy GL GL &@ Té@ | 61 G GG 81 T 96 TOL || 62 Gl | GI |0€ 0) GE 1é & ee |" a on ALCSSPH) 9€ & 4 06 |9 0 8 8 6 | 8L | OF || IP G g og Pf d 8 €1 I | 61 ig ered pure vySey PE9 GGT 8lé@ | O6T | TL Sie esol €86 | 86 | LPL | FOL | 669 | OST 696 S8L | G6 Il | 861 | 90€ [sep til UNUITTY, pur uooung GE v 6 9I |& 0) él g G él TOL || && 8T € 9% 9 I éL 9T € 1% |" ae “* Weppormng cE 0) IL 06 |T T XL ST 0) 6 TOT || OF | T él 96 | T I 8 CE IT 8 io eae ae YSUUSTRID | OL é I OES 0 |8 9 0 |& cOr || FG I z cI |9 Ona le8 91 0 |0 |7 — festo1g pure esuojop | OF iid 91 CLS OF AOL 8ST € 6 OOT || O& I 9G 8I /¢ 0) OL 1G v GI oe ey a ie LO) | €PL | 1e Ig lie (On aaiiien 0G Gg 9 | Ig | gor || set | ge ag 16 |t3 | ¢ | FE | 6h | | SF | + (prempueT) “ | | S16 861 T8G 866 | GEL| 96 | GIG GE &? | 6ZG | GOT || 8F6 | LET ILé 696 | 841} OL | 696 68 €G | €G6 | °° (ysng) uaoypeqduren 8I T él I T O GL g I 0 OOT || 9 v 8 T & 0) al G I 0) a we UvYOsNUTeUpLy | | IG aL €1 VL IIL T &¢G 9 ; 8L | OOF || Fg CT Il 1% [4 T 61 LT € lal = sag a qnoSpry | | 9¢ eI 61 AeA 0 | GI 91 b | 1% | Zor || 6F Cle.) 20 Ol |F ee ealeCay 8I 6 | 9L | wareyonyy pue Sener | | && 14 Il Gr |9 0) VL ol |& 9 OOL | FP : | ST Bt |g 0) CE OL g L a rite “ gpoereyoy | | | | | ged fammpayy yay onpg UTS | yxeq wmmmpeyy) Pe) eT | eg wumrpayy ase nrg | TT) qawq umypoyy poy | are | syBqo S| speqo | SRIOT, Ba TOL ystae gq SUA UIVAL S| SAA wlvVAL | STULL) SAOE "ITADUV N TocHER J. 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GTO | OUES alike ape = ae “* Tjetowyoy 609 | I€1 | SLL | S61 /GOT| 2 | OST | O€% | 6e | est | oF | ees | 6tt | 10s | gat |s6 | 2 | set | ors jee | ost |° - 4 UV F € 1 0 |0 ON Pail I ieyipa Lo? a z 6 “le 10 0 |% | & 6 | 1 3 te is “ qeg Iz v 9 IL IP 0/3 | 8 I |? Ge || Be 6 Ou ae Oe TD 9 6 | ¢€ = ay “ oeaqaryyeEg IPS | G4S] FOE | Suh | LAT} 9 | eke | TIS | 6G | Gee | Ge || 1éeI | ele | 268 | LPP |691| 8L | s9¢} L0¢ |es8 | Ore | °° a “* (ysang.) ty O6> | ZOT| O81 sgl jog | ¢ | 86 661 | 6€ | GFT | 96 || ech | 16 89. O91 ie erg CTI Oe, ee lace. aie ai peTUrTyoNy 669 | GIL | OFe | oct |FI | F | get | 6cz | ge] 0c] ee || 69g | Ett] set | eso lor | + | gat! Tee loe | att | a “* URSsOIpIY 66 9G 6 OF |F L 4°6r GF tin OSs alias | 86 og | Ih |% I | 8% GF a \Ore lcs Wee ae sug AVMOTLY a ae | | | ‘UAV x | | {| | | = - LEGy | L266 | SIFT | POST|889 98 | PEET| OLOT | 62% | SSST| — || SI6F | G46 | LST | SS9T|60L| 42 |EIST| 998T | 29%] Zosr| °° os “ s[RqoL, eee | BEI | OL 8 Ste OSA pa ise PF b | LE | OOF || SEL | 0 COMM LCe RA Galerim (ace FP CO tS aah a ia “* gaa, GE g 8 SRL ees LOL L O | &I | 00r || IF r Glow ladle 18 eS Bil Ge | ROGee|i eet s Bs Avsoio, | Sees = | pr. . . =< | = ag a. pees oe Ave eee wae see 4qloqae J, 9 € i 1Ge USS eae 69 €1 b | IL | 00r || 9F | 91 Sita MIS Conia rr Gains oe be “* URIZUOIZS &% € fE 6 |? 0 |F OLS sie a8 TOL || 1 I 9 G |% SL q 1 |¢ “* AMYoeazZG puw UrTYOyeRayg Lg i PL él |P @ | OL OL v | Ll | 607 || ge g Ole ech, OL s) 108 yaar Il eae 3s ii * grepdeuyy *g eF IL 91 91 jo POL IL 6 | 6L | &0F || 49 9 6€ a OO O | St 1G PGS Pe ne “* pueyynog ss — = == =| | = = = = = | = | = —_— = | = soe aS “* Sa[Ss] [[TvUg ae pay ae ira bee 5h eae | eal aa et ee eevee ee ite er pw a | ech wal pa see | ee. ae Se ee “= uaTeg €9 6 81 86 |8 O | 61 TG 9 | VL | GOr || GL IL 6I 96 «16 iS 1@ Sy tsi ys ssoudryg pur T[eppes ose | 9 OSL | vel |T 0 | 86 OLT | 91 | 99 ||, F0z | L8 99 SSI | O91 |€ ORCC SCHL eco Oe a (ysang) ueqo 0Z r OL omen) Oe ee 8 et GOL || 91 z 8 9... 1.0 0 |g 8 Ouults ss gpepdeuyy yyt0 NN TABLE XV.—(continued). County and Parish Data. ARGYLL. BOYS GIRLS a | Hain Eyes 2 Ham Byes ~ | Parish Totals|| 3 = -——|Totals} & j Fair | Red |Medium} Dark rer Blue| Light | Medium} Dark | F | Pair | Red |Medium| Dark paar Blue | Light} Medium] Dark = 2 = = |; | Acharacle ... co 5 22 0) 15 6 3 10 | 14 i) 6) 12 11 4 33) $ Ardchattan and Muckairn . 2 10 3 17 21 4 16 15 ie) WAN) yf 19 13 56 | Ardgour 3 19} 1 11 18| 3 (J |} BES ak | soil) see TRS | aie}| a eel Ardnamurchan F 1 13] 0 8 @y} 3 5 12] 0 4 1 12 1 18 Ss Campbeltown (Burgh) 53 269 | 10 311 229 | 43} 352 | 265 | 96 | 135) 208) 284 | 198] 915) Ss (Landward) 4 34 5 55 51 6 55. 30 1 40) 21 51 3l 143 = med n 4 10 1) 26 9 3 18 10 i) 6| 15 16 4 40 0 8 0 2 2 ) 6 8 i) 3) 10 1 2 16 <8 1} 22 8 1 12 9 0 15 7 1 1} 20 11 0 32 | Fe | Cumiodden 3) 16 12 1 3 12] 2 5 13 (0) 3) 16 9 4 32 x | Dunoon and Kilmun 41} 306 | 198} 11 269 | 147 | 38} 283 | 163] 13 | 71/190] 218 | 155] 634) S&S | Gigha and Cara 1 13 8| G 5 18 2 8 8 () 6} 20 7 3 36 = | Glassary 3 21 22 0 22 26 4 18 25 2 19) 21 23 12 75 | Nn | Glenaray & Inveraray (Burgh) 8] 0 6 1 2 3 8| 0 1 2 2 8 0 3 2: 13)| | Glenorchy and Inishail lo| 3 21 1B 0) 14 ll} 4 16 22 7) Th) 16) 16 10 53 g | Inverchaolain 7 o; 1 4 4 ) 2 5| 0 3 4 0) 2 5 2 3 12 S. Jura ... fp 4 1 16 7 i) 17 9 1 20 13 i) 8) 15 3 7 43 = Kilbrandon and Kilchattan 21 1 29 25 0 27 16 i 19 21 i) 6] 23 17 ll 57 BY Kilcalmonell .. ob om 15 2 12 24 1 1 10 3 13 16 0) 6| 18 6 12 42 3 | Kilchoman ... ses) (595/13 88 65 2 78 62 | 13 79 44 5 21) 94 45 43 203 = | Kilchrenan and Dalavich ... is) oy? 22 7 i) 21 18| 4 24 10 0} 19) 17 ll 9 56 Sa Kildalton «| 33 6 68 57 3 32 41 6 53. 45 3 33] 38 43, 34 148 Kilfinan -| 38 4 69 42 il 33. 42 7 53. 42 1 27) 69 33. 16 145 R Kilfinichen and Kilvickeon | 41 | 7 38 53 4 31 28] 3 25 49 2} 19) 39 25 24.) 107 SS Killarrow and Kilmeny ...| 63 | 8 62 | 119 5 89 45 | 11 63, 79 3 | 18) 62 68 53 | 201 > Killean and Kilchenzie sa ||. 20 3 27 10 3 20 33 6 32 9 2 37 ll LOT a5} 82 = | Kilmartin ses bce -- — = Qj Kilmodan —.. aoe 3 0 9 6 2 4 3 4 9 20 || 104 9 0 5 6 0 a 5 2 6 20 Kilmore and Kilbride oH 1] 0 4 1 0 Lies 2 i) 6 | 101 2) 10. 6 4 0) 1 4 3 4 12 Kilninian and Kilmore... 31 | 5 31 42 4 | 10) 36 38 29) 113 || 100) 36} 9 46 47 1} 14} 43 59 23) 139 Kilninver and Kilmelford ... air on 9 1 1 6 4 5 1 16 |) 101 2) 0 1 3 2 2 0) 5 il 8 z Lismore and Appin .. coo 54 | 10 69 82 7 53| 67 42 60. 222 || 101 53) 14 65 58 9 58) 57 46 38 199 i Lochgilphead 20 9 28 56 (i) 1} 39 46 27, 113 || 101 53 4 36 38 0) 6| 36 35 34 111 : | Lochgoilhead and Kilmorichy 9 3 15 6 io) 6) 13 6 8 33 || 101 9 1 10 9 ) 1/ 13 6 9 29 | Moryern con 18 1 We 8 ic) 15| 10 16 3 44 || 700 19 5 12 13 1 10] 12 18 10 50 ———————— SL — North Knapdale oon ros 3 o) te jf ok I) © co) 6 8 2 2 a7} 0 20 | c Oban ‘(uve ...{ 61/24] 173 | 129] 0 3/160) 158 | 66 | 66 16 170 98 ° 1| 134 | 150 350 Saddell and Slapness | --/{ 13] 6] 21 | a4] 1 9} 36/ 19 | 11 | 14] 6| 24 | 19] 0 | 8| 38) 18 63 alen ... _ | i} = | Small Isles on. 1, | b= Southend ... 1. ...] 99] 5] 21 | 12] 0 | | u | 10] 7 | 0] i6| i¢ | | a S. Knapdale .. sel eu oe || sae Paw 10 | io/ 2 | 4| 13] 1 | 7) 37| Stralachlan and Strachur ... Lily al 5 1} 2 10 4] 0 4 9 7 | 3 23 Strontian) )22) Wenge <2.) eg94! 020 o een leg : 9 5| 3 7 : 36 Bicone | 13 | 6/2 | 5] 2 ae Yorosay Bl) 20 el) 8) il a | mo) oS ll Bl Bl Bl & Tyree... ees) Oho ac 43) 10 44 32 4 dd 33 4 30} 38 38 | 16 122 | — —— = : [sama Totals ... ong ++» | 1202] 257] 1866 |1513| 77 1676 |1324) 86 688) 1504) 1418 | 927 | 4537 ! | en | | een ie ie EMPCmaoles lec) 4 | 4 259 133 | 4 14) 156 340 119 629 Auchinleck | 118 5 199 | 98] 5 50| 158 180 102 490 a ‘Ayr (Burgh) | 368 | 18 air_|333| 6 |a77|425| 364 | 275 | io | Ballantrae | 0 Si Clot 7) 6 all or! 1S Barr... jee 0) 1 1] 0 | o| o 1 3 1| oe Beith .., 132| 7 230 | 150] 7 {105/195 178 |1s1| 609) § Colmoniel m1 | 2 62 | 47/1 | | 29| 64 | 36| 10] & ‘oylton 6 4 5 nT eh calle a] ae] [isl x] m |e) ao] =o Daily; ss 31| 2 15 | 96] 0 | 96] 9| 4 | a] Go Dalmellington éo3 36) 0 95 39) oO 7| 97| 63 32 199 [eats is 4 || © 196 | 116} 14 | 65/157 | 163 | 94 479 | Preghor | a1 | 0 el gal @ | walomm|) eo | val aot | | Dundonald 157 | 11 9. 95 5 5 ia ae sib [ase uy | od] sta] pp |e] om Bence 5| 0 23 | 3] 0 | 0] 2] 16 | o| 40 Galston 108 | 20 is2 |122| 4 | 93/161) 139 | 96] 479 | lee Girvan (une wy) a). 100 | 6 97 69 3 51 81 90 61 ang ; ” ( Landwar ze 2, a = ns 7 ithe ae al 2 apr [ate | & fausfaae | sete S| a8) » (Landward) . 18 | 1 a UA i 2 io Kilbirnie : 120] 2 a ie 3 a are ie io tt : Kilmarnock (Burgh) al o77 | 507 | 15 |2ra| 700 | 637 | 4a7 | so38 aie, ess) 2 57 | 48] 1 | 11] 56) 47 | 45] 159] Kilwinning a 2 att GD u Tay) 74 | 189) |))103)) 480 Ranlemiahacl 0 261 91} 3 62| 193 185 101 541 pi 10 9 3 22) 13 16 12 63 Scotland in ren y of School Child v Surve to} gmentati y P DT yrwvg pun hyunoy ‘(panuruoo)—vyI KW Le ‘(panwyuoo\— AX AIAVAL g¢ | F1 1 Ga~ 6 0/6 61 Var OCH Reser Oe ai ep aa Scenne Ones bs Col Gee uae a ormydiayog, COM EIEGG 6Z Te a 1 |) ike ee Ser 08 IEEE Tei 9% ras || ii iE eH rai re eee pee ae maeyog oe: Sid | eerie cael (pitas. te [hae ae AO ues) oa a “ ie, ood Se eke 9 (HG |) Ail it | Ge 0g G | 93 | 48 |) gh 16 & 9¢ | OL 6 || Ge GZ € | G |" pao pue(paempury) “ F6e | 6L GcL | 8 | LL @ | 8 G8I | lg | 2 | ¢8 || o6e | eg Gel | 86 | 64 @ 1.89 SiiZien | kOGie Sia |eaus rs (ysing) yurg is) || (Si 61 le NAL ERI 9 LOS, 19S) con «er Dy Oe || Se 0 | Il re eA Gite |e be 2 “"YRALy 9c@ | 19 Z9 €9 | OL ry | 99 GL 146| ¥8 | 06 || 79% | E24 eT 79 | 78 Pe Le 98 USN) 1h, |) 8° a0 INO[IOGV WANVG | | | | | | EL6EL | P6EE] O9GF | LIGP | SOLZ| TAT | Lege!) 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County and Parish Data. AY R—(continued). BOYS GIRLS tS : = = SN _—— Hair Eyes | | 3 | Ham Eyes Parish | Totals || 3 | _— —— —_ | Totals ~ Fair | Red | Medium) Dark Rice Blue | Light |Medium | Dark I © | Pair | Red |Medium Dark | poy Blue | Light| Medium) Dark 3 SS - | | | 2 Kirkoswald ... 9... «| 12 5| 1 o}.14] 480 ni] ag |) am} @ 3] 14] 15 | a) 4) & Largs ... 503 ono op | 1 8 2 Sp |mle2 29 1 20 11 2 7 13 26 10 56 Se Loudoun aca 200 ves | 132 90 | 16 190 | 96 69. 23 140 105 9 179 | 103 74 94 | 450 — Mauchline_... ace |} AEE 64 1 27 85 135 4 161 62 0 29 | 103 114 60 | 306 S Maybole& Maybole V hureh) 140 243 5 64 | 160 307 27 264 V7 6 60 | 135 261 156 | 612 DR Monkton and Prestiwi -| 74 24 2 19 44 106 12 92 Bb 4 25 | 53 96 38 | 212 | = Mui ox 30. 47 2 10 29 51 5 48 37 3 26 34 39 BB} || HEP. ||| a New Gannocle 104 85 2 89 | 106 85 16 108 90) 0 78 | 110 91 63 | 342 aS Ochiltree 38 sl] 0 | 15] 45| 56 7| 49 | 42) 3 | 12] 35] 48 | 44] 139 = Old Cumnock . 144 128 4 126 | 111 145 23 146 119 3 96 | 129 146 86 | 457 | S& Riccarton —... 117 118 | 10 52 | 134 160 18 134 118 1 70 | 113 162 61 | 406 a St Quivox (Landward) and. 1) ‘ lh wee 9 5 | Newton on avs (Landwar a] 13 12158 te 1 22 o 2 OU 8 2 18, a eb) x | Sorn ... 5 nen se | 109 46 1 54 86 88 19 81 51 1 42 73 77 54 | 246 S Stair ... Big 18 1 13 39 21 8 34 18 3 26 39 29 16} 110 &, Stevenston ... 5cO cary [eeu 212 7 259 | 191 203 33, 349 202 | 20 249 | 192 212 195 | 848 Stewarton ... 9... «| 112 42| 1 |.137) 34] 55 15] 97 | 49] 3 | 146] 36] 45 | 6o| 287 | @ Straiton orc as] eel} UG } 11 1) 14 7 7 0 6 12 i) l4|) 9 1 10 Be S: Symington... x0 | 16 13] 4 16 5 7 wi) 8) 8| 2 21 6) 6 6} 39 ay Tarbolton —... eno so) GY | 39] 2 82 42 | 32 10 90 23 1 95 32) 29 28 | 184 me West Kilbride aco s | 32 34 3 23 58 60 10 90 | 65] 5 29) 73 62 46 | 210 g Totals ... ont --- 4476/8938 6977 | 4116| 203 | 2748/5238) 5125 7|795 6483 | 3837) 171 | 2708 | 4911 | 4960 | 3394 | 15973 | tw | | i | | | | = | i = $ ~ BANFF | 8 = os | | 1h ea | Aberlour 21 86 77 ) 84 64) 43 73 | 264 90 84/97] 75 66 4 70 | 63 62 61 | 256 Alvah.. 5 Ba 11 i) 23 10} | Lz 15 65 | 86 20} 7) 226 is 23 12 19 13 67 | Bantt (Bur gh) 20 218 68 3 79 93. 135 83 | 390 85 92 | 31 185 2 77 83. 155 79 | 394 ob (Landward) and Ord | 2 3 25 26| 2 10| 36} 23 9 78 || 85 | 26) 5 30 1 12] 28 26 22 88 | Bellie . ca oon | — = | Boharm oon con ees) 225, 4 42 18 1 15 | 32 26 15 88 || 90 26 8 33 1 17 2] 29 25 92 Botriphnie ... on6 exe 28 2 24 lf 0 7 | 23 24 7 61 87 26 4 19 2, 29 13 14 58 P : { Sr = q is yndie } 4 35 | 0 | 120: |) 25) || 2 3 67 35 | Cabrach 5 14] 0 | 15 | 19| 0 16 sol id Heated ae ae | x fo! 2 5 2 1 1 le 4 | Enzie ... 17 a 2 85 | 31 0) A a | Fordyce 18 125} 2 170 | 125| 9 174 | 120 ae : a3 a 2 174 102 0 139 147 lenrinnes 2 9 1l| 2 6 Grange 3 8) | 12 10} 1 15 7 Inyerayon 15 74| 9 47 55 | 6 35 46, Inverkeithny 7 21) 1 21 7| 0 11 15 Keith ... 29 86 | 2 157 92) 6 130 99 - Kirkmichael i) 8| 2 5 4/1 8 3 | Marnoch 7 54] 4 76 66) 4 88 60 Mortlach 19 43 3 105 38 3 69 57 Ordiquhill ... e 7 19] 4 34 | 22] 1 16 | 13 Rathven (and Buckie) a) | 193 76 198 | 9 349 | 211 2 294 | 209 Rothiemay ... oons||| 2) 4 49 i) | | 66 37 0 52 28 = Ww | || | hes . eee Totals ... coo ++. | 1250/325) 2047 |1147| 55 | 734 (1335) 1626 |1129] 4824 | —- | 1499/ 336 | 1944 |1103} 46 | 761 | 1898) 1622 | 1147) 4928 ey | | | | 5 = BERWICK. os 5 = 5 Abbey St Bathan’s... 9 ...| 5 | 1 5 | 12] 0 0] 8 7 8] 23 || 4 8) 1 4 | 11,] 0 0} 10 5 9] a4] Ayton : 2202111 10) |e 3) |) on 2) 13} 20 | 13] 48142} 19] 0} 12 alae 5| 14 || mi) gal) Bunkle and Preston 4) 0 7 4| 0 3 2 9 1 15 |} 4 11] 0 6 2| 0 6 5 6 2 19 = ( Channelkirk . 10} 1 23 6] 0 5 6 21 8 40 || 42| 10) 3 11 8] 0 3 4 20 5 32 Chirnside a oo «| 32 2 64 16) 0 4 58 37 15 114 || 42 27) 5 46 27 0 i) 48 45 12 105 Cockburnspath ee AS 3| 0 6 9] 0 4 7 3 4 18 || 42 4/0 4 3/ 0 3 4 1 3 i Coldingham ... nto -- | 89 | 14 71 44 2 61 70 61 298 220 || 42 93 7 69 44) 0 50 72 61 30 213 | Coldstream on nee ve. | 54 2 64 43 2 16 51 55 43 165 || 42 B34) 5 51 28 ) 10 38 45 25 118 Cranshaws aD bes 0| 0 2 9| 0 0 6 4 1 ll | 2 0; 0 6 3 i) 0 4 4 “il 9 Duns ... ob aco 00 9 4 22 9| 0 6| 18 14 6 44 |) 42 5 3 16 7 0 4 9 6 12 31 parteton - «| 2] 0 0) 2] 1 yal 0) 3 5 i 42) 3] 0 2 wy © i} 8 0 3 6 | ae les oe ote to) ie B 15 4) 0 17 6 16 2 41 || 42 14 5 25 10} 0 23 10 9 12 54 7 aa neo ach) coo || LK) 2 19 12) 0 8 9 8 18 43 || 42 10} 0 15 4| 0 3 10 6 10 29 a len ccc 0 vee | 12) 0 13 6] 0 10 7 9 5 B1 || 42 9 0 5 8} 0 4 14 2 2 22 eo on. a ae boo |} Uys 3 29 21 1) 8 | 30 19 13 70 || 42 27 3 18 1 i) 1 17 19 12 59 ae an Stitchell’ 008 ng 3 26 8| 0 7 2 15 6 53 || 42 18 1 17 tt 2 5 22 ) 9 45 aa ae : reo 6 ona) £3) 0) 21 13) 2 15 21 14 18 68 || 42] 31 2 14 12 2 17 20 13 ll 61 Tania Aco 2a) ood 8 J 7 5 0 0 14 5 +2 21 || 42 9 4 8 8} 0 1 16 12 0 29 Tony nD oo coo cna 8 1 15 4/0 7 l4 i) 7 28 || 42 8 3 7 Bi) @ | 12 0 4 21 bo aan ID 00 on ae 3 29 19| O 11 38 24 21 94) 42) 25 6 26 12 1 3 32 20 15 70 ww re a se oon cers 2 6 9] 2 8 15 4 2 29 || 42 11 2 16 10; 0 7 5) 11 6 39 “ ms rmacus oo ban 4/0 6 1| 0 5 2 3 1 11 || 42 7) 0 4 |] (0) 8 i) 3 1 12 | oun a0 m0 om 9 4 15 12] 4 4 13 17 10 44 || 39 7 2 10 12) 0 3 5 ll 12 BL 4 661 | GE 99 91 | eee. | Gy g | GL | 26 || ee | 6r 89 G6 | &% IT | 8¢ 61, IL | 8 ae uoreyye"T &B G i e iil @® We L eras GW 1B €1 or 9 0 |6 GT De Ps ; We “'SSIO LPT | 88 oF 68 | FG cualice eT | & $9 | 86 || GST | ee OF tr | Ge 9 | 98 rg Ganley oh LTP €8 91 its 6m ec OP ME REP AR Mes tN psa OF Go| 61 Oneieur 8h Ge Lcmele ty qouund OST | ge Ly re | OT Zanlnoe eg 8 1 LGe Ion Sel 1s 6¢ 9¢ | 7% fe pas Z9 eileen: |: me Aeqstuey) IIL | 81 8G GeamaGe @ | Gl 0g | v | 68 | 86 || OOL | 12 6E Cie ie NS 67 3 |) Si a JoMog | l. ie | | aS ‘SSSHNHLIVO = La) Ss | & OSII | S| OP | L6G | OFT | GI | O€e | Gor 79 | 90€ | — || 80zt | Gos | GIF | LOV | FSET | GS] sIe} L9G IL | £8 “* sTeqog, ~ = €pL | 9€1 | 69% | BPS | 96 OL | 908 | I8z 97 | 002 |7Or|| IOL | PEL | SEs | EFS | 99 Il ieechelmmecee 9F | 9ST (qsingq) Avsoyqoy S OL LI GB SI | OT I | 8 9G I | I |for|| tot | 1% ra Eee |S ate 6h 6 | Ol “* ogng Y4tON = 19 FI €l COMmIEG Z| 6S 9G g | SL |Voz|| 16 61 9 or 19 Ga re Leia 3: Wresury S €9 FI 8 Gola 1 Mec 91 0 | &@ |g¢or|| 98 SI 91 or | ZT y |2e 6E fe [Or oy ALOWLST = ZPL | Pe 19 Coen rl IT | 07 69 2 |oe |gsorll zat | ez 89 12 || 1 0 | Lr 19 LT °St ah opluq[ry = C6 LG CE re | 6 ON EL LP OL | €3 |FOT|| ZOL | 8z 6Z 9g | 6 G | G 6h LEGG ci aerquing, i) - : S ‘ADAG id = | Sa aa | es | | : 7 SS goel | 993 | 4ge | srr] 112! 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Vol. vi. Biometrika. TABLE XV.—(continued). County and Parish Data. to BERWICK—(continued). rs BOYS . GIRLS Fi | | | Har Eyes \s Ham Eyes ns) 2 = Parish | | Totals|) 3% : Totals) Fair | Red |Medium| Dark een Blue | Light | Medium| Dark | | pair | Red |Medium|Dark| 1°, | Blue | Light |Medium Dark | S 7; Pr, i By | Mordingti 6 3 iG 1 4 5 | 16 || 42 7 4 8 5 i) 10 2 6 6 | 24 = Neuthora: | 3 1 4 10 5 5 24 || 42 i) 2 9 12 0 4 4 9 6 | 23 3 | Polwarth 3/1 | o} 6] 12 7) 925 | 42)|| -3i)) a 9 2| 0 ti} @ 7 1} 15 | Swinton eel) TB led 8]/ 19| 26 | 21) 74] 42] 18] 3 32 | 17| 2 7] 19| 26 | 20] 7. BR | Westruther ... Dod 16 6 | 14 ll 14 13 52 42 18 2 9 8 2 9 15 7 8} 39 S Whitsome O35 s-- | 1d} i | 4 19 9 13 45 || 42 14 2 18 20} 2 8 13 15 20 56 a | | | | = 1 | ES) Totals oe .-» | 462 | 72 554 362 | 22 238 | 500 | 435 299 | 1472 || — | 450 | 66 477 303 | 12 211 | 442 | 387 268 | 1308 5 | ! = ul RH = = ¢ | = BUTE. S) | = NM {| | | 3 Io 49 22 2 9 36 29 28 102 || 104) 25 | 10 47 130 9 Bd 25 27 95 = flbnde. 61 47 0 13 21 68 25 127 || 103) 30 2 69 40 1 14 33 61 34 142 =; Kilmory 39 32 4 12 40 16 18 86 |) 103) 25 ) 16 21 1 6 35 8 14 63 a Kingarth 34 28 5 6 40| 26 19 91 || 104) 12 5 26 22 2 5 35 13 14 67 e North Bute... 49 30 3 18 27 35 21 101 | 104; 14 1 26 28 ny 10 18 25 7 70 = | Rothesay (Burgh) 335 153 | 11 66 | 243 238 154 7O1 || 104 | 200 | 46 281 206 | 10 96 | 242 269 136 | 743 s: | | 3 = | ‘ = | Totals O08 +. | 233 | 71 567 312 | 25 124 | 407 412 265 | 1208 | — | 306 | 64 465 330 | 15 140 | 397 401 242 | 1180 S | | ale at & = = ars ra 8 = CAITHNESS. =o = = 5 we — Bower 2 49 33, 1 27\ 13 39 21 100 || 98 BY 4 | 50. 15 3 39 26 28 18 111 Canisbay 7 62 35 2 24) 36 59 24) 143/97 | 57}; 8 | 53 30 2 16 54 AT 33 150 Dunnet 9 48 11 0 19} 25 40 15 99 || 98 | 27 3 42 11 () 17 19 31 16 83 Halkirk 9 54 36 | 6 35 | 44 40 33 152 || 98 | G4] 4 | 48 33 3 24) 39 46 38 147 Keiss... ‘# 15 9 0) 6 | 10 13 9} 38 || 97 11 3 7 2 ) 11 3 4 5 23 ? Latheron = 11 79 5B | 1 23| 93] 68 | 49) 233 || 971 75 | 8 G5 48 | 3 22!) 76 66 | 35] 199 3 | 6G i 2 a 5 Reay ae neo 8 | 5 30 6} 1 3 3 32 12 9 1 1s | 6! 0 | 19) 14 34 Thurso ten xt 54 27 266 126 2 30 | 175 149 121 59 24 264 | 142 2 37 | 174 147 491 Watten eae ins 29 7 25 20 3 5 36 28 18 40 2 13 29 3 28 22 33 87 Wick (Burgh)... 279 67 394 305 | 46 116 | 244 | 430 301 262 44 330, | 263 | 30 11 } 252 B29 237 929 Wick (Landward) ... 82 12 55 47 4 37 77 44 42 200 || 97 60 8 47 | 43, 3 51 49 26 35 161 iz} if a | = = | | | g Totals ae) «| 711 | 169 | 1141 744 | 68 361 | 805 976 691 | 2833 || — | 744 | 117 996 647 | 50 357 | 775 | 798 624 | 2554 = : a i —- a 2 2 CLACKMANNAN. wn i | 3 Alloa (Town)... 236 44 435 188 1) 56 | 339 331 177 903 || 51 | 243 36 401 182 1 64 | 350 291 158 863 =| 4, (Landward) 59 6 54 31| 0 72) 35 15 28 | 150 || 51 | 56 0 45 19| 1 53] 35 12 21} 121 2 | Alva are 25 6 34 9 1 36 4 27 8 75 || 51 11 2 4 g 1 12 0 5 3 20 = | Clackmannan ... 38 2 117 Mil 2 25 60 87 64 236 | 61 64 6 79 60 1 25 48 77 60 210 : Dollar... ax e 32 | 4 43 26 i 23 47 16 20 106 |) 51 16 6 30 29 0 16 22 28 15 81 Cy Tillicoultry ... orn || 308) | 25 161 138 2 33 | 142 163 91 429 || 51 95 17 147 102 0 25 | 106 142 88 361 . ——— —— | 2) | [5] Totals cop a | 493 87 844 469 6 245 | 627 639 388 | 1899 || — | 485 67 706 394 4 195 | 561 555 345 | 1656 | ae g & & =) DUMBARTON. Arrochar 6 1 17 5 0) 1 8 15 5 29 || 101 | 4 1 18 12 (0) 0 6 20 9 35 Bonhill 344 48 401 320 | 16 188 | 381 273 287 | 1129 || 105) 342 30 363 370 | 16 172 | 389 306 259 | 1126 Cardross . w. | 105 29 198 123, 6 53 | 163 177 68 461 || 105) 87 16 157 89 1 30 | 115 118 87 350 Cumbernauld ... = 42 12 136 61 3 25 99 64 66. 254 10| 38 12 107 62 1 15 85 67 53 220 Dumbarton (Burgh) ... | 288 35 433 226 | 10 86 | 323 379 204 992 || 106) 294 29 388 213 3 68 | 3380 328 201 927 Kilmaronock 18 0 | 13 10 1 18 5 16 3 42 || 105) 20 10) a 21 1 20 7 16 4 47 Kirkintilloch (Town 95 27 141 106 3 66 | 127 109 70 372 || 12) 98 29 128 106 | 11 78 | 124 101 69 372 oH (Land. | 79 il 77 55 6 23 | 109 56 40 228 12) 74 19 86 44} 11 27 | 95 55 57 234 sss. an | 13 iL 17 15 0 2 13 19 12 46 | 105 12 1 15 10 2 iT el) 8 6 40 New or E. Kilpatric 65 21 158 51 0 21 | 116 110 48 295 || 19) 70 19 158 63 0) 41 | 129 97 43, 310 Old or W. Kilpatricl 157 32 311 190 | 17 105 | 204 220 178 707 || 22) 184 32 290 169 9) 87 | 227 202 168 684 = | Roseneath Ae 099 15 0 15 20 2 4 29 16 3 52 | 105) 11 1 7 16 1 6 18 10 1 35 Row... m0 .-- | 181 33. 271 156 | 13 147 | 159 161 187 654 || 105) 188 20 218 152 | 13 128 | 185 142 136 591 iS) = | Totals ie ... | 1408} 250 | 2188 | 1338) 77 739 |1736) 1615 | 1171) 5261 fee 1422| 214 | 1940 | 1326) 69 679 |1729| 1470 | 1093} 4971 lis | Scotland 7 urvey of Schoot Children Ss On «& gmentat . y t di 26 G9 9 1€ Ie | 2 T | OL vE 9 | 7L | 96 G &¢ 46 | 6 O | OL LE Pies e om ae quodueg && I 4 GL | & i | 8 & T | OL | 9% i Lie | 4 v 6 | 6 G IT 6 et eS PIPASNOT G8 GG |. 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(7 16 0 6l |¢€ L-1/9 g esa 1G) AY || 06 {8 0 Ol (& 0 |2 € 0 |OL WOPSULATRS) | 99 Ol GL =|€S =| 1% I L Gla | 8 We ee eon Gior 1@ |9t |8t @ |11 91 G | rE OMY WOT | | “HDUNANIGH | PLES TOIL) OGLT | GOLT| 124 | €9 |2TZ1| eeoe | 1ez |scot| — |) gt9¢ |re1t| tr6t |ozet| cee | eF 9EEL| ZOE | GIS | COST | “ s[Bq0, | | | 36 | OL € vl | 0 |6 6 Ge CL kell ers Or 9 Gl | GI SNS GZ 16 ; TT YIEYLOISO AA Vi = | = — |— — — vt Kerydure A | 6 ip | vail 8 g 0 |G IT O | 91 | 96 || 9% | ¥% OL 9 9 0 |g PL Saale a a woaud T, og Cline 2 og | 0 OM esl 61 WO A aS I Oi ait € 9% | 0 OES SL I (rei “ ygaesaopun y, | 18 | 1G 9€ 0@ | OL 8 |) 8s GT 4 | 66 | 9 || 2 | 8 OF 8% | OL IT | ¢¢ él ve Ges “* ppeatoy4.toT, mer) €1 LT GZ | OL L | 6@ I CEN OD sae §8S) 20) ina 0@ | OMIEGE €1 Da kGG ae = PIVAaLy, €€% OG 18 16 | ¢ y | 6 €1 | 69 | 96 || 9S | HL 68 v6 | 2 Ome, SII OM 89) es oa aequburg | Ig 17 9 ! ¥G Obs iat LI T | 8 146 || @ 16 Z v LG One ail 6 SiG i 7 “ o8unyl 49 4—2 TABLE XV.—(continued). County and Parish Data. & DUMFRIES. BOYS GIRLS Har Eves s | Harr Eyes = 7 SS : Totals || ‘5 Totals} = Parish ] aa) Tat F ; = | Red | Medium} Dark Rice Blue | Light] Medium | Dark A Fair | Red | Medium| Dark} p), ¢4,| Blue | Light Medium] Dark S = | ) oe = \isnensn lira lo3 | 262 [162] 4 | 128] 120] 236 | 149 go | 296 | 118) 7 | 111198] 188 | 139) 566 | = H Applegarth &Sibbaldbie 7| 2 3 1 ° 10 12 17 20 A 18 a Q es FS a8 of ae w kir 20 pees|| aL, 2 5 7 a 3 2 2 2° 23 ls VGesate | 32] 3 16 22] 0 13 - a0 ve 1 13 | 33 18 16 a ies Caerlaverock | 10) 65 8! 0 6 § g Ae) as | Closeburn 2 8 36 | 0 8 2 e 20 9 168 ES | Cummertrees 9 1 fra |0. 0 ‘ tal ~ | Dalton ue 10 2 9) 0 7 1 15 5) 0 36!) 8 | ers 2 21 | 25 4 37 197\0 76 G | Dornock 19} 2 21) 0 4 ae 308 % Dryfesdale col) aes) 44] 1 57 ui 189 epb 4 oe) ~—S Dumfries (Burgh) «| 253 | 54 221\| 9 73 30 B71 | 207 | 7 a S ” (Landward) 101 | 23 98 | 4 63 23 157 97 1 oA SF Dunscore oes sant 124 |) 3 Bd 8 15 2 26 24 10 7f Durrisdeer 22 0 25 2 8 3 29 V7 1 87 g Eskdalemuir 4) al 3 o og a 7 ‘i 2 19 | = Ewes 3] 5 0 * 5 Glencairn 27; 5 29) an 15 2 16) 1 6) > Gretna ... e823 8 32] 0 2 7 25 | 2 eS Hoddam | 5 98 | 0 6) 2 23)\) a 106 | Holywood oO pra tesa 5 23 1 4 5 12 2 fe = Hutton and Corrie |..| 13) 3 8| 0 22 3 9 i) 67 | Johnstone erp | et ba 10| 0 0 9 (A 2 71 | wD Keir 10 2 5 1 12 | 4 4/0 Br | S$ Kirkconnel l 1 OF} a oO} i) 3 1 w ~ Kirkmahoe sos] LOU ERO; 10} 0 2 0 7 i} 21 3 Kirkmichael ... of 2G al 16] 1 7 } 5 19| 2 ie | = Kirkpatrick Fleming... | 38 3 | 40} 0 10 3 33 | 2 13 | * Juxta =... 17 4 11 1 21 5 9 1 68 Langholm an we | 74 15 65 | 2 26 9 69 | 3 272 Lochmaben... ceeiil) 90) 6 45 0 38 6 43 0 237 Middlebie on colt eka) 1G 32 1 7 8 42 i) 141 Moffat ... AT 6 62 1 49 9 50] 2 235 z Morten 99 | 6 15 | 0 4 7 7} 0 82 Mouswald 9 1 9 | 92 4 1 8 1 23 | Penpont 13) 4 10 | 0 9 6 1o| 1 65 | ‘ | St Mungo | Sanqubar | Tinwald Porthorwald | Tundergarth | Tynron Wamphray | | Westerkirk | i ‘es }. | | | | Totals nee ... | 1503 | 262 | 2502 |1336| 43 | 745 |1826] 1941 | 1134] 5646 || — | 1658) 251 | 2085 |1217| 63 | 721 |1702] 1750 | 1101, 5274 | | | | EDINBURGH ] | | Borthwick 2] 16 | di) 2 ) 18) 36) 21 | 10} ‘e5il|47') a1) is) a9 1 eels 12 10 | Carrington 0 3 a) @al) wp 0 8| 20 || 47 9| 3 5 1 3 0 9 | | Cockpen 9|/ 82 | 49] 2 19| 65| 56 | 30] 170] 47] 45) 8) 62 2) 47 56 21 a, Coliuton = 21 184 3 | 75) 124) 106 | 65| 370 || 46 85| 18) 147 | 3 60 116 73 3 | Corstorphine ,.. 12 65 2 | 28 57 76 35) 196 | 4G 43/10 | 59 2 7 62 53. 30 Le3| Cramond 10| 64 4 18] 54] 47 | 35] 154 || 46] 47] 8] 60 2| 14] 65| 26 | 30 ese | Cranston 3 40 DES Fell |i5r32 31 | 12] 106 || 47 46 2 36 | 0 16 38 34 9 s ) | Crichton 1 57 1 Pegi S31 31 13 94 |) 47 23 ) 41 | 3 22 28) 19 18 87 is) ‘ | | Currie .. ll 83. 1 16 53 72 42| 182 || 46 51 9 72 i) 20 45 | 57 46| 168 S [ Dalkeith (own) 18 160 2 27| 139 89 61] 316 || 47 85) 17 140 i 15| 125) 101 58} 299 | ist | Edinburgh ‘ity 529 2 98 | 1484) 2927] 2992 | 2416) 9819 || 44 | 2593} 485 | 4008 9 | 1437 | 2908 | 2996 | 2402) 9743 a « (G Pala and Soutra 1 i) 0; 16 18 1 B4 || 47 14 2 1 0 0 13 17 5 35 5 i) 27 35 22 23| 107 |) 47 45 6 49 WY) 32 36 23 41| 132 ; 3 ) 2 0 18 12 32 || 47 8 1) 15 i) 1) 0 18 16 Bd Inveresk (Landward), 8 2 0 16) 29 26 20 91 |) 46 32] 10 23 0 14] 24 25 15 78 | Kirknewton & E. Calder 95 6 13 Ba 99 68} 264 || 47 o1 12 125 2 Ba 89} 111 57} 291 f | Lasswade 437 6 221) 212) 282 194} 909 || 47 | 270) 66) 395 7 | 183] 243) 283 193} 902 | Leith Burgh 2630 42 611| 1888) 1978 | 1314) 5791 || 45 | 1602} 289 | 2443 |1448| 36 | 642/1913) 2009 | 1254) 5818 | Liberton 168 8 74 93} 120 111} 398 || 46 | 110) 22 150 61 1 66 89] 102 87) 344 ' | Mid-Calder ... 18 0 5 33. 17 7 72 vA 24 3 25 17 0 5 23 23 18 69 | Musselburgh ot 361 3 127] 284) 229 170) 810 || 46 | 2 50 385 219 4 | 142/ 280) 325 186} 933 |3 Newbattle 17 0 13 4 6 8 31 | 47 7 1 11 3 0 7 1 7 7 22, ( Penicuik 109 1 26| 44 94 71| 235 || 47 59) 13 95 48 2 21 62 89 45) 217 : Ratho ... 71 1 26 49 57 25| 156 || 46 41} 11 4d 33. 2 25 50. 32 24] 131 J 7 | Stobhill 144 3 78| 103) 104 66| 351 | 47 | 101) 19 158 57 4 81 85) 101 72| 339 ‘ |, | Temple 19 0 29) 5 7 18| 59 || 47 | 23) 4] 12 8] of] 23] 5] 12 7) 47 \ | Vest Calder 54 1) 41 30. 44 37| 152 || 47 62 8 66 33 0 50) 47 40 32| 169 no q | | a ; | Totals ado + |5387/1169| 9217 5025| 186 | 3044/6416] 6642 | 4882| 20984 | — | 5822/1084! 8656 | 5033| 212 | 2957/6398| 6687 | 4765 | 20807 | = al —. Pigmentation Survey of School Children in Scotland 28 ‘DID YsSisvq puv hyunoy ‘(panuyuoo\— AX ATAVL C—O Peace oe ec | Ol |e Tee ear | rr | eo nes tr | le) er | Cane (a ti le el i | i” ee ent1 | 962 | 629 |. 6er | 6oe| 4 | Sto] 989 | 28 | O8r | Ze || G00% | Oe? | Gs | 969 | HE] GS] Ter] 968 | GOL) 96h | = Myeog een |s0n 9 el | 9 0 | Ot OW 2 It | 9¢ || eo | @t | 91 OPAL OR IMOI | AOS I Aol {OP a. Comusernting oot | #¢ | 8¢ |W |6 © 1epGe le OOF TO KOS 9, 29) || G6 9 PSO. s|nSOne e799 Co Gora Sle ae Geme |e giclee Aa, Arsuyyeg 99 | FI 9% | 93 | 0 0 | & Ie | 9 LI | 89 || %9 IL | 6a 4300 22 OY Wie) Bs Os Ge omen ain 81 z 6 ele €- 20 P Teale Ol a) 2oelast € 9 I € @ | 0 L Ol lpr alee Aqypnui1ezyouy ecp 49 | Sos | 7FL| Oc.| @ |e | S6L | 0G | PPL | 69 || 98h | 79 | 106 -| SLT | vr | © | COL) Ose | 66 | Pel | uvLepiayqouy 9% OL € g 8 Q | 2 8 j 6 Gg || 8G € €1 6 € 0 |F FI j 8 "+ (daqse 4) LoyNASUY GEL | FF 1g Ir | 9F G | eg Lg L SIL. |) 49 i) SSL ||| SE Or OF | 8I 6 | BF Ks OL | SL | °° (eyseq) royynaysuy ZrL | se | th | OF | 06 te ao Oe Gia Ee Oe |e | CA SI 8 echo |) ae eco | eae ae LOD ASG ya oo O«dWB I LI | 0 0 |@ 61 t |0 | 9¢ || & Leia fea OL | 0 0 |F He OO WR PR ee Chis “AHI | 9e93 | e6¢ | 178 | 169 | goo | 1m | Pe9| I66 | PET | 9e8 | — || BeLz | TOO] 9EB | BL) SL4g | GE} 0S9| 890T | O9T | 6I8 |)" ~~" = SIMIOL — =F — —- | H 9g | LI 6 om cia On Vet] | Gr € IZ || 88 || 1S | 91 el 91 | 9 0 |6 LI Ge eeGeclc.) a see gaeun way 8ZL_ | eI Ge E99) OG i) 0 cleo. a aeLG fi Iv | 88 || vel | 91 ep | 9a | 61 IL |€3:|.9¢ | or |r |. <> ugnourdedg OGmaSGanl eS) leeds lil Cur lOGTa lakOGme [neu tl (OG sesso Ol |eee a Od: oHIROG Mlols aimcoun pe ones OI 9 | G epdaqueyyyT saorpuy 4g €IZ | og | 79 | 6% | OG NOR Nese eeObm | Le 06 |) Lis. 3) lt TL TOM. | Eee mC eV ee Shen Glee inG le” | sea eee CIC) GO| G I 91 | 9 0 /¢€ 6 ¢ |ot |06||¢e |8 G fh G anes Ol Go Wh Ol ess Means tiade ec PLOUU HT oe |e 8 ey lat (Ope as Ol Te Oe OSs ecco ticle Golan El plea Daeo Di A290 Sime ck eee CLAS TONG 19. | 08 | 99 Ie |7e | 0 | 9% | GL |6 | *E | 06 || OIT | ST Coun UGS 1re | On LS C9 SIGs Sela t|) este Seopuaoouy 86 | OF «| GS | CG Osea) (6Ge |59: wlace | 86s SOI) (Gr Vegas OGe) ROT es) Ole eCGe saree Olen elie. atten moss SSOTUTY] — =) = | — — — — | (ysing) sor110 77 O6b=|' hr! 89 | ee: | eo | 8 | TP 19 |8 | 22 | se || 98st | oe | 9¢ | Og | os L |s¢ | o¢ |8 [e9 | (paeapaey) urstg Log | PPL | 6ST | OIL | g | 1] I9t | 7 | 086 | 98 || see | Lat | OBI | LOT | 89 ¢ | 9IL| ort | es | Fea fo = 7° (qsang) urstq 9¢ | 6 re «| 9L | 2 T | 61 Sie Whee VAL |106)\ Cle HEE VG eae. eG S \46. | se |9. | SL | “ emnPaIpg re | SL ce | 6% | & 0 |e | ve |b | | 68 | ZB | ST ge | | LT | FI or | 9 lol cess ae eee OTA CT chs | LG 16, | Go “em ere |) COL lee. | Poe lh68 |p 06S, | 29° 1) SLT. |peS) "| 2G) eG OSU Rel ATE O8e9) fe een 2 ee SRE Cl TRE | PO. | 68a OSs | eee | 9 BGZ | “PURIST SPL | SSilleree 1060") “See COOL, 02 S| GA .| SSI | Sl 06-9 oruareay Si ro 7 9 1% 0 |% Te */ se |e) 06 || 61 6 9 g I Tis G poof Se Sa esata Shee eG 1G. veo Her T 1GG eo. aod Ze | 76 || ss | St LI 9% | I Gt sh} GC SPL ee o[epuody) zo | 8 7 a 3 a) €) GPa ler ¢ |e | 06] se |? oo eo tee T | 1% I rs Eo Off 2 oe eruatg €61-| €9°| €9 . | 26 | 09 I |9r | 2 |8t | 9e@ | se |] 02 | Ig | £9 [Go| CO Ge | CGri ot ei rlmiece| Wiese OTC 88 8 7G) 6n 2 ee e9 |%3 |e | 6s ise | 6 cp || 03 «| 0 | ST 6h 7 Til page epee Soh Ly: | greg |ummrpayy susr| ote |" FE | gre ummpayy) per jaa |g | yaeq mamgpayy) seq) ont ATT | yaw | warpoyy pow | wea s[eyoy, | ——- & || spRoL, — ystieg SAAD UIVA = \| SAA | ULV AL STUID SAOE ‘NIOTH or) N J. 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GT FZ rm | 6 || OS GI F pe pees oe So eSo TG) cg SI cl og | 3% 0 | 9 6 € 1g | ¢ || €9 1G Th OS |i at Onna €Z G SI om "* ssoqqyny Site |) GHhe €¢ aS || 6 0 | 61 +9 g 93 | ¢¢ || Gel | 9% SL or | Tt 0 | 8 €8 g Coan aks a [reap Gr |) Sa OL Ley Gl Tealass 99 g Gel Wes || 0s. | Le ZIt | ge | 61 I | 9F 66 Se Waa |p oe = aISseT[OK 8Z P L ol |e ole GI 0 OL | 6¢ || LE 6 OL él | 9 @ 6 LI I 8 ies as yoourey) rg LI GI ZL. | OL Coalecil IZ g Gl | ¢ || v2 tZ LT (ae || Teil Cy yar} is € Git pe" Re saqurey 9L LI GS SL | 61 Omnuaa &% I og 1 S¢ llr oT LG Gt | 91 0 | St G8 cemlieg Giles lah sis Leon cLund@) TABLE XV.—(continued). County and Parish Data. ELGIN. BOYS GIRLS | Hain Eyes 3 Hair Eyes Parish Totals = > — | Potals Fair | Red |Medium| Dark) p1°4,| Blue |Light Medium | Dark 5 | Pair | Red |Medium| Dark | ,7°,| Blue |Light Medium | Dark Alves 3 49 15] 0 4{ 20 45 9 78 || 89 13 2 63. 9 1 7 19 54 8 88 Bellie 14 118 53 2 55 51 63 51 220 |) 88 36 18 92 46 i 50] 27) 63 53. 193 Birnie . 2 1 27 1 5 5 24 4 38 || 90} 23 3 4 19 3 6 13 25 8 52 Cromdale 9 42 19) 1 24) 26 7 18 85 || 91 22 7 23 25 1 18 24) 21 15 78 Dallas ... 4 5 5| 1 ni) 8 6 9) | 219) || 90) eras ea 2| 0 2| 6 4 6| 18 Drainie 16 158 79 2 70 | 100} 84 90 | 344 || 88 74 15 | 114 75 6 52 80 88 64 284 Duffus ... 17 134 60] 5 52) 65 112 67 296 || 89 74 4/ 108 57 2 28 69 91 57 245 Dyke... 6 40 14 1 2 24 38 18 82 || 89 24 4 | 34 22 0 2 29 35 18 84 Edinkillie 6 32 27 2 15 23 27 14 79 || 90 17 3 16 19 1 7 16 24 9 56 Elgin (Burgh) 23 146 116 3 168 | 107 120 127 522 || 88 | 220 24 161 144 8 144 | 110 159 144 557 Elgin (Landward) 8] 50 | 58| 7 | 50] 50| 66 | 30| 186] 88] 72| 8/| G1 | 41| 8 | 53] 35| 5B | 44) 190 Forres are) _ Kinloss 10 34 23 0 16; 36 |» 37 19 108 || 59 33 8 29 28] 0 9 25 24 40 98 Knockando 5 65 27) 0 34 25) 33 18 110 || 90} 34) 9 72 46 0 34 51 56 20 161 New Spynie 6| 17 6] 1 Al i) RO |) ee Rea 6G) Tl 1) 3] 0 it 8 3} 20 Rafford.. 2 10 8 1 5 7 5 8 25 || 90 10} 3 9 3 i) 6 16 1 2 25 Rothes .. 75 12 78 AT 5 44 61 71 41 217 || 90 74) 10 82 40 7 50. 49 64 50 213 St Andr ews Liianbryde 42 6 16 B4 2 1 36 30 33 100 || 88 39 3 26 19 3 1 33 28 28 90. Speymouth 6a 44 10 56 23 1 | 19 | 56 43, 16 134 || 88 41 7 57 23 ) 20 66 29 13 128 rquhart. oe 23 2 VW 9! 0 | 6 16 13 16 51 || 88 21 3 19 13 i) 15 15 9 17 56 | —|— —- * Totals oct «| 819 | 160 | 1068 650 | 35 573 | 722 836 601 | 2732 || — | 836 | 134 991 634 | 41 505 | 691 841 599 | 2636 FIFE. 7 Abdie ... occ 0 i) 18 4/0 0 10 1 19 2 ) ) 17 1 4 22 Aberdow: on a | 55 11 59 18 3 18 55 10 54 31 1 20 46 44 32 142 Anstruther (Easter) ... 15 10 57 42 9 18 40 7 57 53 2 16 41 31 44 132 Anstruther (Wester) ... 8 2 14 4/0 3 9 2 8 7| 0 8 B Auchterderran 124 29 230 102 | 0 44 | 176 20 195 d4 2 36 Auchtermuchty 4 i) 7 @|) 2 3 1 1 4 o|] 3 3 Auchtertool 9 || 15 | (28 ||| 20:)) 0 2} 20 6| 21 22 | 0 ) Ballingry 44| 8 | 78 | 66) 3 6| 64 10/ 66 | 54/| o 9 Balinerino 12 1 30 10| 0 14/ 11 4 10 10/ 0 6 Beath ... 495 | 109 | 895 | 481 | 25 | 324 | 526 s2| 686 | 518| 7 | 309 Paraben Chins) (aa) a) ae) 36 |) 0) eile v4} a | aa] 2 Las, a : a Cameron on 19 5 | Bo 15 | 0 16 15 2 1 | ie) 19 Carnbee 15 3 | 14 | 6 1 | 22 3 2 10 Carnock 8 1} 9 2 6 12 oO; 0 2 Collessie 44 13 46 | 1 19 35 5 1 19 Crail 25 3 28 0 1 40 | 3 10) 2 Culross ... 18 5 17| 0 1} 30 3 0 2 Cults... 14 4 | 36| 3 9 24 | 0 | 2 6 Cupar (Landward) 4 2 at |} (0) 0) 3 2 | ) 0 Dairsie .. 29 3 ll| 4 11 9 | 5 | 3 5 Dalgety 13 1 pat 0 ||) e110) 10) 1| o | 18 Dunbog coo ‘ i 4| 0 0 4 4 1 0 Dunfermline (Burgh) .. Bd 248 6 | 133 | 296 266 34 3 146 4 (handward) 29 182 | 11 117 | 200 392 288 18 8 151 Dunino 0 9] 0 32 |} 55 8 1 2 1 Dysart, (Burgh) 15 51 | 8 262 || 54 92 15 8 54 Elie. 5 17 i) By) 3 0 0 Falkland 15 42] 1 7 | 10 ) 9 Flisk 2 | Ht) @) 0} 0 0 Forgar r 3 33 | 1 4] 7 25 | Inverk ing sco 14 78 4 18 2 13 Kennowa j rT 32 | 0 7 0 | 30] Kettle ... 0 3] 0 1 i) 0 Kilconquhar 9 39 | 0 6 0 5 Kilmany 1 | 1 0 2 Kilrenny 9) 66 | 3 13 ) 90 Kinghorn 18 43, 2 6 2 40 Kinglassie 4 200 end 2 0 21 Kingsbarns 2 14| 0 0 0) 11 Kirkcaldy (Burgh) 43 280 | 19 4 2 | 223] 8.| 90 » &Dysart (Land.) 5 57 1 8 Bd 30 1 6 Largo ~ a0 085 10 22 3 7 41 29 1 21 Largoward 2 5 1 1 13 0 3 3 0) 0 12 ail 5 Leslie 24 48 | 0 D199) 10 | 211 88 | 0 17 | 68} 211 93, Leuchars ll 5D ©) i 83 i 2 9 71 51 9 10 79 wf) 48 Lochgelly 36 239 4 188 | 275 952 || 53 | 244 46 dda 196 | 3 175 | 306 267 185 Markinch 24 92 6 93 | 112 481 |) 54 | 118 18 213 95 il 81 | 116 143, 100 Monimail 4 21 5 2 16 12 2 j 9 7 16 13 1 18 7 10 11 Moonzie il 1 5 2 ll 3 17 0 2 3 1 10 1 0) 12 Newburgh 12 76 42 3 49, 36 39. 11 84 46 2 51 22 58 51 Newburn 1] 1 0 1 4 6 2) 55 | 72 3 1 5 3 8 1 7 3 Pittenweem ... Bl GF 42) 3 12| 56 | 55 | Ae 6 7 67 | 0 14| 70 46 57 St Andrews (Burgh) 12 | 112 74| 8 50 | 81 259 || 55 | 75 |, 21 81 63 | 10 35 | 91 G4 60 on (Landw; san 5 2 9 13 | 0 0 14 29 || 55 8 0 4 15 0 ) 13 a i St Monance 69 16 82 32 5 36 | 62 204 || 55 | 81 20 60 40 | 3 25 61 51 67 Scoonie |) || aie) is} 10 | 10 32 || 54 5 |. 3 24 6] 0 9 6 16 7 Springfield 22 10 28 13 0 5 26 73 | 57 25 2 27 12 2 2 32 21 13 Strathmiglo 58 8 57 30 il 33 Al 149 |) 57 54 7 45, 46) 2 33 44 39 38 Wemyss 17 4 64 19} 0 0} 23 104 || 54 25 5 55 |} 0) 0} 33 39 22 = i Totals 3085 | 618 | 5340 | 2946) 156 17681 4112 |2724| 19145 |) — | 3518] 547 | 4575 |2850} 98 | 1709/3317] 3813 | 2749) 11588 | | 86 pimpjosg rw uaippyg yooyay fo haamgy wuoynuoulrg UAHOOg, We nt Scotland ab 4 f School Children Q Survey 4 ton gmentat A ay? 30 9 \8 i Kes | OB 8T GOG siesca ey Wy Ne eas a 0 -|¢ Ga i's) Se. aseceraon @ «| GL g € @ (Sd I eS Gh || Bek v g I ORS 0 G lL si : va[ Yoo] eg | 0G Ess Wt SAL Pri WR SE ye Meroe Gi 6 i AGI Ae oil €G |G OL | 9 uoujeaqury SIL | 61 CommmlGra el Sl vO" 9c Ig | 4 |ve | 89 || Zr | 8% Ge 2 Ki Oe IL AS ee) Sue rer ea 969 |Get | SFL | OPT | SOL | OL |€cl'| G6l | PE | POT | 4 |) 099 |LeL | PIS | AAT | Zer | 9 |é6rL | Gee | 9¢ |7et |=°.. °° ammouiry eee 8 Gees ie Ol We 9 Tt |9 L49\\ 7B |B Se 8 0 |g g Gore Glee sos ancl UOpAATYT | 8) ler 9 OL |6 0 +9 Conan liven |9 49 || Gh | OL 7s | eee [| O1 LE Tome es “ss sepqgouury GY 0G q OL L 0) 8 61 G €T 64 || 09 CT 91 1é 8 0) 9G 81 G rI ae AS youuty €h | GL eh Wd WO 1) 81 Canin 89 || S| BL 06 |6 \sl | 0 >\or OF 1S 18 Suty}0 3 GEL | 98 IVS Gs | tee (ae qr 7-99") 0sn +e pe =|8% (SE | 0 jE Gy |G |€p |: 9 soplegreauy 9F | 9I Aaa 41k ae Wal LT Ae LO \\ LS NST I =|63 «=|F S| 8z 81 € 19 ; “ AQUIeIOAUT 6g 16 P Ol Olen kOe s aLt €L Oy le Seales: 9 id Wil Oe We LT oe ae ary yng) cg | 4 Die 1 Siew Oma rell 81 Z |26 | 941/68 |PT SG ce eEle 0. rz SH 1G ANS | ; VISTUETH 6I |0 6 i ie Owe g Came az 49 || 6L |0 6 6 l 0 |9 r OG a ‘ "** STUUR] E) | se |8 Tee cee ae 0 |FI z Sem NSIE = Reaeicd 1G Nie a0 Tt AeLSe G 0 |8 ok eae STTMOT |e |8 MN We ONE i aie KG) ial 6 9 49 || Bb | 8B L T let ale Sel SCae iar ail “" (preapueq) — “ | 3G | 89 98 {1g |06 {8 |9¢ ZOl | €L |9r | 49 || 188 |e OTT LOO e iG | OF Oe Velie Wee Open. _ (ysang) aeyt0,q St |G 91 |Ot |0 OS au 8 0 |6 GL || 86 10 ZI =|9L |0 OL ib Lo 6 oh “7 Wey | 49 | 81 OG) Glee | lee Os Gt €l L |83 | 44 |] COL | 9% OG at WAGs 7G 2 | Glen Om LY Seanas > pe) eS eae | 8& 9 I Ou |% 0) L OL I 0G | 89 || 6F | &I €l OL |¥1 0 |FI GG I ral AVAON pur olsseq | SOL | II GS 6 AS SH Ie ie 6F |G {68 | 49 || BOL | zz 6 Cae | Sia bales ali8e CE (16 6G 12 ee eueqoruung | 86 |6z CCMITS) Ol 0. alee 02 |e |r | 99 || Zot |e 16 |98 [SL |0 |9 6&6 | 8 | 6% > aaa) | GIES | SkOS | SEBS | THEE] SOIT | OST | FELIS] OFSE | Teh | HOT] 99 | OS98 060Z) GEES | CLES BEZL | ESI | 9ZIZ) es6E | SOF | GO0z (qsing) eepunq 46 «(9 P Lam Se ee a8 OL 0 |8 GL || 78 19 9 Oly Clam len) 2 éL CeeaeL " xBAOTO puv Ayouy.10 78 AT OSs GSC ae O= 8 PE Vee) epee Geer lee | 085, iS Gl SR Gl oe we og | OL |0¢ “ S1eIg COL | ZI OSs | 1S a |.Ce it: = 0g tg |8 |or | Zo ||. ar 9c PS) WEG (26 EF.) ee Ep |G lip ery Aulaes) op OPT I Po NES. 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County and Parish Data. FORFAR. > BOYS GIRLS | Hair Eyes s Ham Eves Parish Totals iB rere Pair | os Tet : Saal 2 Z Pair | Red Medium) Dark | Black Blue | Light ety Dark| A | Fair | Red | Medium Dark wen Blue Dight|stedium| Dark | = | Aberlemno a 16 4 28 13] 0 26 | 7| 5 5 | Airlie... go], 6) || aig 2| 0 a | Gl as 1510} 8 |S LS asin | rag Arbirlot eal) 23) Oi ae |) al © 7 | 16) 57 all | . Auchterhouse so} E44) i 7 6} 0 9 1| 35 alee Arbroath (Burgh)... | 302] 53 8 | 353| 5 361 | 363) 1241 ae 3 Barry .. -| 95] 20 81] 4 139 | 73] 415 169/17 Brechin (Burgh) 83| 93 5 | 103] 1 150 | 99] 455 lowell 38 oD (Landward) .! 30 6 27 21 i) 14 18 84 | Be fs Broughty Fer ry (By Bh) 191} 49} 393 298] 12 210 206 883 19 0 Careston : 3] 2 i 11 0) 6 | 7| 93 WoT) 1 Carmyllie 47] 5| 47 | 93] 1 34 | 98) 193 al | Craig... 30] 10] 30 8] 2 25 | 18! 80 mall ow | Cor’ tachy and Clovax td 3 13 i 4 6 6] 34 re : Dundee (Burgh) .. |2009| 468 | 3925 | 2126) 122 2929 | 2090! 8650 apeel aet| » (landward)... | 99]. 8 26] 0 aif | esailiroe 2194) 120 Dunnichen 22/ 9 38) 39 32! 109 || 35) 0 | Eassie and Nevay 12] 1} 92 | 14] o 13 | i9| 49 lie |Edzell ... 3a] 5| 47 | a6] 1 26 | 26 103 13/0 Fern... 9 1| 7 1 0 12 i) 28 i ° Forfar (Burgh) 50| 17 | 134 70| 10 115 73| 281 cal og jena (Landward) 1| 4] 93 13 1 7 o5\lleds 56) 8 Fowlis Easter BI) 101/49) ||) stall) =a 1 Blea 9} 1 | Glamis 0 4 6| 0 9 0| 19 eS 14} 0 Glenisla 2} 48 | 21| 0 2s | ia! 89 || 3 B® Guthrie ol a7 71 0 Ee A ey 18 13] 0 | Inverarity 3 | 1 | 98 2 12 Aa 5 uf it 0 | InverReilor 5 9 a 2) noe 17 17| 4 sae 2 30 () BA 23) 120 52 23 | Kettins 3 2 10! 0o 20 12 59 Ge 23 1 Kinnell 2 26 (0) 16 15 2 18 16 0 Kinnettles 1| | iol 4 1 relies 19 8} 0 Kirkden 2 | 5| 0 iil Sl ee 3 ag Kirriemuir 36 | . ES =e G 0) Taeupensie eta | alas a || ee) Ge 195 | 193] 10 Lintrathen 2 10 5 9 19 “Es ie 26 8 Lochlee 2 8] 0 4 “lee V7 | 14) 8 a ogie Pert 3 bl. 0 16 7 45 a iz Z Lunap 8 1/ 138 Gi Os 15 8 1 12 5 0 Lundie... ll} 2 7 EY Oa 3 2) 12 3 4 Ti 10) Mains & Strathmartine | 36 9 57 26] 4 37 | 132] 31 5 58 7} 3 Maryton 8 1 12 12 el 23 10 | 7 2 12 5] O Menmuir 15] e220) 14) fo) on) ers 8 o; 15 | 0 Monifieth 9 102 fos 4 14 43, | 102 | 13 85 40] 1 7 Monikie 9 45 39] 1 | 17| 44] 43 | 8 41 50} 1 g Due | Montrose (Burgli) 30 252 126 3 107 | 162 183 14 211 92 7 68 | 158 144 110 480 55 rnd a | | 3 | | — | Murroes | 66 il 3 14 Oo | 4] 42 30 3 2 15 0 2 33 18 18 71 Navar and Lethnot 1 0 10 3| 0 3 4} 4 0) 4 3/ 0 2 5 6 1 14 Newtyle 10 5 40 18 0 15 18} 21 2 2 14 iL 11 | 22 17 18 | 68 Oatblaw 8 1 23 9 i) 17 2) 16 | 2 LOWS ee) 0 15 1 13 6) 35 Panbride 26 ll 96 22 2 4 89 | 35 4 75 1l 1) 3 | 59 25 31 | 118 Rescobie : Cul 5) 3 5| 0 Tel) CON 0 6 3| 0 yi) Ol wl 1) St Vigeans & Arbroath), 5, Al a Noe : a | 5 Chandwara) {| 22| 7] 81 | 36] 0 | 23 43 1| 54 | -25 | o | 24) 14) 41 | 99 | 108 Tannadice an 16 6 25 15 1 3 18 6 23 21) 4 4) 2d 27 21 76 Tealing 7 6 14 18 i) 19 7 9 5 18 10 0 19 10 13 9 51 | f i IL | \ } Totals 3887, 878 | 7173 | 3966) 194 | 2594/4493) 5177 | 3834) 16098 || — | 3922] 785 | 6313 | 3840) 211 | 2315/4188! 4834 | 3734 { 15071 | HADDINGTON. = = 1 | | | Aberlady Tht | 15} AT 13 0 17 21 10 74 | 43 V7 1 33. 19 0 7 28 17 18 70 Bolton ... 5 3 8 4 0 1 58 4 20 || 43 3 2 8 (0) 0 2 4 4 3 13 Dirleton 11 7 13 13 0 7 17 13 44 |) 45 7 0 i 8 0 5 1 18 8 32 Dunbar (Burgh), 64 14 145 48 7 47 83 64 278 || 4a 72 12 122 51 6 Be 91 82 56 263 + (landward) 10; 2 10 9 2 i) | 13 7 33 || 43 23 1 11 10 0 1 18 18 8 ts Garvald 8 1 6 19 0 3 | 8 6 Be || 43 14 6 7 17 ) 2 32 5 5 Gladsmuir goa 18 5 39 22 2 39 13 15 86 || 43 20 3 31 29 0 30 18 19 16 Haddington (Burgh) - 74 14 143 mt 1 63 120 50 303 || 43 97, | 22 162 81 1 66 | 96 134 67 Inner’ wick 0 o 7 5 24 12 0 19 ll i 48 || 43 29 2 10 18 0 23 17 ll 8 Morham S 7 3 7 7) 0 2 8 3 24 |) 43 8 2 8 11 0 4 10 6 9 North Berwick 82 16 108 55 3 47 69 53 264 | 43 91 16 86 57 1 44 | 102 50 55 Ormiston 28 11 81 17 2 25 | 45 27 139 || 43 27 9 70 16 0 31 41 32 18 Pencaitland 9 3 25 19 4 7 | 19 1bl 60 || 43 24 2 16 16 10) b) 22 18 9 Prestonpans 71) 138) 149 82] 3 73 | 96 84] 318 || 43} 96) 15} 101 75| 1 65 | 68 82 73 Salton ... 15 4 21 8 1 9 19 9 49) 43 16 2 20 13 2 6 9 24 14 Spott 8 6 13 5 0 7 5 6 382 || 43 1 5 7 2 0 1 4 6 4 Stenton 14 2 16 11 0 6 23 4 43 | 43 18 0 19 18 1 5 14 24 13 While ‘Tyning} 38/ 6| 18 | 16| 2 | 1] 42| 24 | 13] soll ys] 97! 3] i | 15] 2 | 1] 28) 20%] 9 Whittinghame | 8 0 9 9 0 i) 12 9 5 26 || 43 11 1 13 4 tH) 4 18 3 4 Yester .., =m) 9 5 30 26 4 7 13 30. 24 74 || 43 | 24 4 18 36 4 13 16 22 35 a | P | Totals 497 | 123 912 466 | 31 | 380 | 589 641 419 2020 | — | 625 | 108 770 496 | 18 | 353 | 637 595 432 i 0g aun Mounjyuaubirg i s ~* iv) ( = ~ i) MN S Ss. = = = g 3 =. = £ S ~y Ss Vy aTHOOL We Pigmentation Survey of School Children in Scotland 3 DD YStLD Pup hqunog ‘(panuyuod)— AX ATAVL (| LLGP | SE0L| OIG | L8ET) 9E6 | GIT | O€EL}] O&9T | STS | €8eL i: Lé6P | SSOL| PSPL | PLPL| 8E6 | 6 | G8EL| 6881 | LES | €6GL | e, STP}. 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CTL €¢ 6€ GG 1G (0) GE 19 6 tS a 14, O9T OF LV GG 8L O 9¢ 19 8 | ¢¢ “* SOTdeAo(T Aroyourg, OG 8 66 IL G if €L 1G lf TL | Th 9¢ FL Gg L (0) @) OG GI a7 LI x cs youqynqry ‘ANIGUVONISM “uyLaOULONg, ‘IA JOA “quamieddug TABLE XV.—(continued). County and Parish Data. INVERNESS. BOYS GIRLS, Harr Eyes Ham Eyes Parish = Totals |) District — Totals Fair | Red |Medium| Dark | p1°%),| Blue |Light|Medium| Dark | Fair | Red |Medium|Dark|,,1°t,| Blue |Light|Medium| Dark | Abernethy and Kincar-) dine Alvie Arisaig and Moidart Barri Boleskine & Abertartt Bracadale Croy and Daleross Daviot and Dunlichty Dores Duirinish Duthil & Rothiemurehus Glenelg Glengarry Harris Insh Inverness (Bur; -gh) a (Landward) | Kilmallie Kilmonivaig Kilmorack Kilmuir Laggan Moy and Dalaros North Uist Petty Portree Sleat ... Small Isles Snizort South Uist Stenscholl Strath ... Urquhart&Glenmoriston, IH OW NIE ROR ao) OwHowas HOORRHOaAHPOHOr 91 01 100, | shire || 24 99 89 o1 of 99 OL 99 100 & 94 108 91 92 92 100 100 ion| 98 99 | a4 91 98 91 91 107 89 99 GE 99 a mieilen = SEHD EH HO DBWWNEWOOHNOUH HE NWUIN ER EASCOAH LN _ wo HH Swe RH OH ONE NN UHAATRDEHOTONONOHPHEHRONWOrON 7 5! 7 7 6 Totals 1389 | 454 119 1387 1038 Gs d fin pupjjoog ue vamppiyg jooyas fo fiaaing uorwjuaul ] ] ] | | | | Arbuthnot... - «..| 17} 4 0 oO} 7) 35°) 14) 56) 7% HN al eee Ta) 4) SE eShN yy) EE) 8| 50 Banchory, Devenick | "65 8 0 18 55 AT 40 160 | Th 43, 9 61 | 0) 21 52 39 33 145 i Ternan 52 | 20 Ol} AGL) 72h |) CTA |p soi || 2571 79 60) 11 58 3 | 36| 55) 51 | 44] 186 Benholm bd | 38 1 16) 50] 37 | 19] 122 72 57| 4| 54 3 | 96) 53) 4% | 32) 158 Bervie ... 48 | 14 o | 21/112} 49 | G4} 246 72 81} 14] 111 5 | 54] 96] 32 | 80] 262 Dunnottar 6 7 |) 278\ 114s) 8a) |) 52h! S77, 7% |100) 16} 83 4 | 41] 97] 109 | 40] 287 Durris ... | a ty) S| ag 5 4} 19]| 7 a8 | 2] 29 0 | 10} 34 8 | 13| 65 Fettercairn ... k 3 3 | 12] 32] 40 | 22] 106 ie) || Bar|) By) 1 19] 52) 17 | 13] 101 Fetteresso & Rickar ton 7 26 4 68 | 112 128 88 396 Th | 131 36 147 6 74 | 154 105 88 421 Fordoun mei 39: |) 8: 0 | 15) 54) 57 | 39] 165) 73 GD] 7 | eB 1 17] 41] 45 | 93] 196 Garvock 9| oO 0) 0/| 10 7 6] 23 72 4/ 0 8 | 0 o| 8 4 4| 16 Glenbervie ey |- al 0 5} 11 27 5| 48 i || Bi Bil 0 5} 92) 27 8| 62 Kinneff & Catterline Alea 2/9) |e 26) | 270 | 72ll a 4 31 2| 24 2 |) Ge] BH) 1a) ye Laurencekirk ... 65 | 17 6 22] 838 63 44] 212 ve 65 13 72 ul 22) 65 60 45 | 192 Maryeulter 19°) 11 1 21 22 19 | 18 80 Ty 28 6 21 ) 24 5 21 13 63 Marykirk 19} |e) o | 14] 12] 26 | 10] 62 i |) Bil 8 8 1 16] 12] 16 9| 53 Nigg 30| 4 o | 26) 41 95 | 97) 119 Th 28} 9] 43 0 | 16] 56] 29 | 292} 193 St Cyrus 20| 7 2 2) 35] 62 | 21] 190 72 18))|) ae7al ee: 1 3| 29) 70 | 23) 125 Strachan -| 17 1 O |) 1G) 3B me Ze) Ge 79 Tey at 17 1 19} 7 10 Byler | | ar 3 . Totals 647 | 141 | 1050 | 739 | 26 | 360) 870 | 822 | 551 | 2603 — | 797) 146| 929 | 640] 36 | 413 | 866 | 752 | 517 | 2548 KINROSS. | | | Cleish . i3| o| 6 8] 0 45 | (ee Sh 8} 27\| sy | 10) 2] 13 || 10] 0 5) 4 Ey |) | 85 Fossoway & Tulliebole | 12 5 36 22) 4 12 | 23 26 18 79 57 23 6 | 21 11] 4 9| 19 24 12 64 Kinross ses 46] 12] 109 | 47; 1 | 22] 64] 86 | 43] 215 57 70| 6] 92 | 50] 1 | 21| 84] 76 | 38) 219 Orwell . 39/ 7] 81.| 25] 0 | 23] 45| 51 33.| 152 5 LN ON WET | Beh Oi ByA|| BDI) Be |) aR! aS) Portmoale 16) |) (2!) 36) |) ent 10) 5} 98} 27 9| 69 5 i | eh | we @ Oy) 2G] ae |) Wa Be | | | | | Totals... ...| 125 | 26 | 268 |118| 5 | 66 | 168! 197 | 111) 542 — 159 | 26 | 223 | 113) 5 65 | 172] 179 | 110 | 526 KIRKCUDBRIGHT. Anworth 18] 5 2m | 21 | 0 | 16) 21] 24 8| 69 3h 1G) Bi BE | SO | By |) ea] ee 6| 65 Balmaclellan Al ah) SP 1 Ti; © 2) 15] 13 |) eM 34 ai @\| ie) wi @ | 4 | 9 6| 29 Balmaghie 19} 4] 20 | 20] 0 1| 28] 931 13| 63 84 C153 28 |e | ae | ee 2) Bargrennan WU ON) OD | RG) | we TG 4) 34 34 14] 0 3 8] 0 | 12 4 9 0} 25 Borgue ... 19} 9] 54 |.32] 0 | 36] 22] 31 | 95] 114|| 3% AS By BG | BO ee em || Shi) Bye || me) iy | Buittle ... ©) i) $2 |) Wa] a 1| 18% 93 | 11] 53 34 TGS) | e223 Oe | ees |e | 2 | waHOOL, “Ee toe Og8 | I61 | 146 | ehS | 931 | 8 v0G | 1SE | [vi |9ce | 22 || 686) | SAT 98e | OLE ern | OL | O2e |= ear "| or || 19cele ne orkqurig | OSL | 6% €9 co | § I rg 9¢ Tale | eSCRe se ORi 3 |38¢ LL g9 | 9 0 GE 16 Pr Ogi), | ec neraetae 7S a5 aoa Tey 676 | 6 98 NP EO 8¢ 66 €1 | 64 | 7. || OoF | #6 G81 | IVL | OF | 8 6 OUT Gene OG) lnceee mavens apepuoay Be0G | €8F | Z8G | 94 | 17S | SI | LOG] 9F8 | 16 | OLE | 6 || 6GIZ| L4HV | OIL | GLA] LIS | OJ | O6F | 126 | GOL | 619 |" ~* **olupity MUVNVI | : | S CELE | 06g | G18 | OF6 | 068 | 9E | BBL | SOOT | IST | E84 | — | 9POE | E89 | E26 | 996 | F8r | OF | G98] 9ST | OAT | SIL | Fag Nammines: E S190 Ts gg PS | | S | | i | | Z erp | GIL | 91 | SOT | g¢ SL SG V6PE SEP i=nem | Ve SIS NPAT tpt eel sg Oe OA se eG ed re > 1g | 8 61 LI GET 0 | aI 1@ r LI | 7& || 99 IL GE 06 | &1 0 | 0Z IZ r % |" % wyoyutay, | AS 79S | LG 88 G6 -| @ | 09 06 | el | 66 | 9¢ || 08% | 19 GOT |) 62° 49s 9 | 8L COS POs MOR eee. ee toonbodJ, = LG |g IL 6 Z 0 1% PL I 8 1§ || vv if ra 91 | 9 ils A tail LT I Gla an Meas pur[suoy, Se 6I |g 9 G € 6 |P L G v 96 || SI ¢ @ G 6 0/6 6 IL 9 He a So]So110 J, > 10L 6 G ce | €&% I | 0€ eF r €@ | 76 || Gel | GG OF | 6 S | 8G L9 i Le taal Cea. ae LMA] ~ 7% | 1 €L ib € OA SE 6 € 8 TE || 66 9 OL 9 L Te ah3 OL I 6p te, Uns eeu ter s 88 6 ce | 6G € | &% LE L 86 | 7 || OIL | OF 81 Claes 0 | 62 LE Ol | re | 7 Soggy son o 6F =| (0% OL 6 OL O | 9% 81 I P && || OL GZ 1z GP = |aE 0 | 6F a 6«I é aa “ gesrauryy ~ 9€ L 8 6 real Geaiele 6 0 vI | 98 || OF i Oem |e9 AT ie) alae él I PL | * WORYNAYOOrT = 6¢ 6 8% 16 | 1 OM ek 8 g It | 78 || 8F 6 IZ 81 | 0 On eet 1z 0 6 | regan youyedsyary = LET | AL 0g 6y | II 0 | OF Ig g Teaslieves|| 19. |e 99 | 8r | ST Te 4 €8 Si aoe ett) © pea sjoetg corsa a se g 8 z &% ear OL é €l | 7e || 8s 8 9 @ GE 6 | OL 61 S | lee dtaeae * MOOZUNSYALY I8@ 08 6 G6 | BI vy | OL 9IL | 0@ L | 76 || G16 | 38 &6 gg | ST & | &8 CGlmel vig roe he qystaqpnoyary | ‘= | 8¢ 91 eal 6Z | I 0 | & 0G g OL | 7é || 18 IZ 8% 8 | F 0 | 2B GE g Eile || tite, = os uveqyaly cre | 19 18 Sel | 8¢ O | Lh 6yL | €1 | 90L | ve || Tee | eL IIL | Igf | 99 Pen eL6 I8l | 8l | 78 ae ope 10995) > 84 G é 93 | FI S| & LG P G & || 98 PG 61 GZ | 8T Dias LG 9 IZ Py ae AICS: | > er ie i G G 0 |F g I € él i j iz Omer L I P cae feaSuody > og OL 81 OL | Gt 0 |¢ 9 P GT 8 él 8 v él 0 | 91 IL I OL Pas uoy try D eh HAE 81 9¢ | & 0 | I Lr j ral |) 84 IL &E 9€ | @ 0 AIST 9g ©) Cale esr crc eras Cec, | 6 € CT rl | 0 0 |¢ GT 0 al || 48 P €L 8I | @ Oh a LT 9 g sts TewYOrUAssody | ~ 61 9 8 G & 0 |9 6 I € || 06 g 8 v € Tt} 01 G é é ae a 3OOSIOD | = | LOT | ST ks Se | € | LG Fé g iste | sol | 91 GE cv | 06 0 | G OF ¢ 9& | POLAYWNOY puv puso — ~ 8G 9 él 4 G 0/8 éL I i || AT G OL I v LT | 0 FL 0 G ‘ae “ taureydsaed L | | | | < eg femrpeyy |aysrT) onre |USTT yee | umypayy| pew | wer) preg jeamrpeyy qs ong “UM yxeq | ampeyy| poy | areg S | | Pal a ‘~ S[TBqJOT, | a = = |\S[eJOL | => Ss Yslueg x SHAY a1vA = | SAX aIVA || eS STulo SAO of ‘(panwyuoo)— LH OTadd NOMI DID Ysuog pun hyunog ‘(panuyuod)— AX ATAVE ten) J. 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Bc ii6 “* ToUz[Rcy oft: oo “+ gaqtng are + uyolpxlopavdy " 33 plopMVI WOJTOYUVY TY UOPSULAO| ss ae UOISJIL[D abe ag: SITVISIV) ae ae YEAR ee + yOOUUNTI,) om “ TeROTUMARD, are aR ayNIVD me uvyqousnq wey one “ SuRpSNquURD Boe “+ pratLtop[eg pec ano “+ TappUy ye 260 TeatQog TABLE XV.—(continued). County and Parish Data. KIRKCU DBRIGHT.—(continued). oe BOYS GIRLS ] Harr Eyes | Har Eyes y Parish ~—! : — | Totals} >. | Tair | Red | Medium} Dark Hee, Blue | Light! Medium Red | Medium) Dark Prag Blue | Light| Medium} Dark = | 7 Carsphairn _... 2 0) 14 ON /a 4 1 10 v 12 8) 0 2 7 13 6 28 BS Colvend and Southwick | 36 5 40 22] 0 | 20] 42 25 5 34. 27 | 3 25 34 1) 107) & | Corsock on!) 2 2 5 10 el 83 4 8 1 9 6] 0 3 8 6| 19 3 | Crossmichael | 5 6 7 9] 0 2) 18 13 0 15 5] 0 0 15 3 32 Dalry 3) Ol) fo | seo i) en bal) es By die || iH @ | 2 18) || W7|| zai) Girthon | 10 1 1l 16 0 13 4) 8 4 26 5) 0 12 18 10, «50 = Trongray 4 1 i 130 4 6 2 1 5 4/0 2) 4 5| 13 & Kells 21 6 27 32 0 18 25 | 19 4 27 23 2 14 13 25) 78 | Kirkpatrick Durhan 9 QO} 21 18 | 0 Oo} 18 21 5 28 15 | 0 1 28 9) 59 8 | Lochrutton 14 aL 13 11 1 17 6 10 0) 9 11 2 12 8 v\ 36 SS | Minnigaff 2 3 22 49 0 11 19 21 1 18 26 0 10 10 20] 49 Q New Abbey 10 37 29 0 33 19 18 7 27 23 3 29 9 25 88 > Parton ,.. 1 10 8 1 7 6 10 3 9 4/ 0 3 13 1} 24 Ss Rerrick 4/ 67 28 2 39 | 46 25 4 43 30} 1 23 24 19 101 I Terregles ib} 9 2) 0 Wy) 2 2 2) 7 4) 2 3 6 oy 19 s Tongland 1 17 139 | mel 6| 16 12 1| 4 4/0 2 fs ll 5 27 = Troqueer 16 | 100 78 6 35 | 79 105 13 90 60 2 24 95 88 57 264 =. Twynholm 4 21 20} 0 13 | 20 22 4 21 15) 0 13) 17 19 8 57 = Urr 32) «186 140/10 | 58 | 185 141 15 149 133) 12 53 | 162 116 112 | 443 wD (lis | z | | | | J Totals ae | 712 | 176 263 | 865 | 30 | 484 | 956 923 131 1063 | 722 | 36 | 390 | 940 | 815 590 | 2735 3 L | = z LANARK. | ] | | | lo ae | i; | Airdrie ... + | 619 | 109 921 490 20 | 217 | 779 716 447 | 2159 | 9 | 570 91 846 507 18 | 241 | 726 582 483 | 2032 | Avondale 130 32 176 94 8 40 | 141 185 94 | 460 1 79 13 99 58 0 37 87 86 39 249 | Biggar ... ve. | 50 4 97 i) 6 65 77 38 186 1 5 14 56 54) 1 3 65 63 49 180 | Blantyre eee +e | 261 61 425 | 16 | 145 | 310 356 178 | 989 || 15 6 41 351 204 | 8 | 126 | 242 271 191 830 [Bae i 24) 258) 611| 781 7 Cadder .. 2 7 : . 28 Calderhead 9 eae | Ho) ses) 191 | 112) 3 | 179 “oa ‘sis Cambuslang 2 243 Be an 45 eeu 156| 13 277 132 | Cambusnethan = ( 22 478 | B Gail aa | a ae ee ae 119} Carluke as P/138/1/ 33 2 3 3 2 ne] 9@; a | ad | OF | 9 381 Gaveaels eae | 38 | 8 2B is 8 oe: 206 age 663 | 3 174] 36] 255 | 180] 3 196 124 Carmunnock ... neo 25 3 8 10 0 0 19| 21 46 | eh a 5 cl 5 OF 8 3} Carnwath ... .../ 123] 93! 196] 88/ 3] 60] 102] 121 eal e)|| seal neal negil oa @ 22 12 Carstairs Bde hs G2) TI 70 33. 1 53| 42 32 50 | 177 o 54 ue Hep 73 1 113 | 68 Clarkston... 146] 18] 142] 149/ 9| 76] 133] 151] 104| 46all 9| vo] at Cea oe Cov ington & Thankerton 7 0) 10 a ) 0} 4) l4 6 1 ay uo 100 8 | Crawford) 9 2i|| 21 al) “aail) se9i|) toll arllieraih esl cc a cera elas! Sie Crawfordjobn... ../ 8/ 2) 4] 92/ of a] 4] 8] a3 6] 1) 13] 12/ of 7! 1. Culter ... 1 21 8 2) 1 7 20 7 i 7 6 1b B p f 5 Dalziel ... 2 547 |. 9 59) 117 90, - = ) 9 Dolphinton al tour a0 50 a 117 H neu Oe 6 | 978) 165] 1384) 794] 30 | 366/1129 Douglas... 1}, 65] 59] 12| 97]. 52| 70] 44 2] Ba SE ey a 4 Water 22/ Go| 44/ 0] 5] 84] 39] 36 74] 10} 58 56/ 6) 42) 42 sae i Bu wll. tl Gl am) Al sal ol sail 8) ella 5 ride ... 16 152 39 ie © ‘ Gusta: 7| 36 | a7| || a1] $e 74a | 3 Bil al ca SR ee By ey Glasgow (Burgh) 1597 ’ 31! lols Bi BY 2 33/30) 3) i) 47 oy Gavan a 490 13, 6125 1387) 12447 S244 370 | 3423 | 8503 . Hamilton (Burgh) ue 79 us 1921 454 4065 2346 99 | 1258) 2752 [eo] fa (Landward) 95 3) 473) 83! 624 | 371) 22 | 239) 452 : Lanark (Burgh) ee 40 5 | 530) 94) 605 | 448) 15 | 192) 577 | a (Randwvard) wa 32 2 sD 35, 207 80 2 92} 101 S Larkhall A 70! 2 127 20 95 77) 12) 71} 122 ro) Tesmalagow Hal 3| 308} 49) 535 | 231| 11 | 932] 324 | Libberton 0) a 246) 44) 336 | 180) 7 | 168] 199 E Maryhill of 140 | Z 5 1 0 6) 0 7 0 Wenn Monklande “0 13 | 602] 111] 1017 | 561) 15 | 301/ 727 Old Monkland 131 10 | 199} 25) 219} 90) 3] 95] 168 . Pettinain 2 | 12 | 666] 152) 1164] 685) 292] 334! 758 i Rutherglen 7 325 68 - 2 5 i) 6 5 7) 4 2 r Shettleston ; a d 213 | 42 ‘ 14| 337] 51] 535 | 403) 2 | 924] 385 ; Shotts ... Pel liecas | eas 20) 35 59) | 11| 231] 44] 351 | 214) 15] 85] 257 j Springburn 34 E Apll Gy. ee 45 6 44 40 tt) 52) 16 3 Stonehouse... 10 ¢ 2) 12) 34) 27) 162) 179) 2) 15) 111 ¢ Wandell & Lamington _ 0 0 o } 3] 49 8 110} 37 1 Bl) 54 Wiston and Roberton i) F 1 10 0 10 3 ) ) G é 1 0 10) 3 7 0 0 1 Total 5455) 37: 2 77 7 7 Is os +++ |16455) 3788 | 31329 17736] 837 | 8686 21498 23751 |16280 70145 |) — |16165|3353| 28447 17729] 729 | 8685 20150) 21888 |15700) 66423 } } oe hool Children in Scotland on Survey of Sc t gmentat a 36 Dv Yysing pun hyunog ‘(panuyquos)\— AX ATAVL CSP CRT eRIZeTL Ie 96 I e esiL in FSb | Onl Sen Wer il vere) LS | OST | TAT eOLeie "7 PAG" cece |e coa SET ie Sie = SIMON: 98 j GG 6E | 0G OA 1G L Ge | 68 || 06 9 PL eg | AT @ |) Bi oP 8 oe |*" (preapuey) “ EINE |. 88 |p GS. | GE Letra OG Ole (SSS Goal TT21 1996 06 | 98 | 61 I | 91 6 lie al gee cre (ySang) ware yy 64 | 8 6E | B | OL Tepice ences sl Gy al Ce |n68)"|| 208 16 | & i 8 OmmRCGun|eGGer "(stam Gim eae neers TOPMLD) 78 | 9L | 81 8% | ie | BBW" Ce Nie NOS ne hts |) Sit G3 108 i B dbus Ie ja2 Ag Lee ie ueaplny LE L a Gg 18 Ox i 9 € i OS ies I IL Cle | @ | Wi rel I Le ge Ee gees yorppiy “NUIVN gosr |6eot) ome. |gert| 122 | ge |eott| gtet | ses |egrt| — || OFog |eeor| FOOT | 9z9T| 8I4| Bg | FEOT| 84zB | IT |66sT]" °* STRIOL, ocr | 96 | got | 161] 69 | 6 | 48 | GSI | ¥e | ISL] 6Y | rer | €6 | GFL | 803| 8h | FP | OTLT| OT | 9% | WI] ~ wmagaM e1g | or} ene | 286/99 | & | SEL | LOM | HF | LS | 87 || LE | SEL | 96 | OVE | 6F | F | FEL | BLP | 49 | O18 ]° : Treqdg Plz | 9¢ 1g 19 | 9F T |0¢ | 84 9 | 64 | 6Y || G36 | or | 28 6¢ |re |o | aor | €6 |8 |6L | “* UeYorydsoy, 693 | 8h | 08 LUA GLY. 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County and Parish Data. LINLITHGOW. BOYS ’ GIRLS Harn Eyes 3 Har Eyes Parish 7 ——— | Totals $ ; Totals Fair | Red |Medium | Dark mee Blue | Light| Medium) Dark | & | Pair | Red |Medium| Dark pie Blue |Light| Medium) Dark Abercorn 23d 23 2 40 20 0} 25; 18 27 15 85 || 48) 26 7 23 17| 0 18] 17 25 | 13 7s Bathgate (Burgh) _... | 226 | 54] 376 | 161 | 12 | 226 | 204) 218 | 181} 829 || 49} 234/ 34] 325 | 174] 4 | 160 | 236] 211 | 164] 77] “9 (Landward) 28 4 22 tO 115) GL Th eG 56 || 49} 22 2 14 || @ 16 5 10 14 45 Bo'ness and Carriden 266 | 90} 618 | 301 | 21 | 169 | 389 | 444 | 294 | 1296 |) 48 | 330} 86 | 526 | 317 | 15 | 209 | 359] 395 | 311 | 1274 Dalmeny . 46 6 40 24 1 2) 52 47° | 16} 117 |) 48) 52 4 39 18 | 0 0} 59 32 | 22] 113 Ecelesmachan . 9; 0 15 2 0) 6 3 6 11 26 || 48 9 0 5 6] 0 11 () ni) 8 20 Kirkliston 93} 19} 147 91] 10} 72} 101} 102 | 85] 360 |) 48 | 115 9} 112 | 100] 2 77 | 84| 102 75 | 338 Linlithgow 83 | 24] 139 84 4} 21/ 140 89 84} 334 | 48 | 90| 24) 144 78 | 3 23 | 127 | 122 67 | 339 Livingstone 92} 11] 106 60 2) 41) 97 92 41] 271 | 48) 94] 12 88 57] 1 Cur || 80 48 | 252 Torphichen 79 8 93 45 0 Be 59 87 | 45 225 || 49 79 6 78 50 1 46 61 51 | 56 214 Uphall ... 210 | 67] 472 | 194 4] 59 | 340] 396 | 152] 947 | 48 | 227} 44] 407 | 192] 3 55 | 282 | 373 | 163) 873 Whitburn 144] 26] 210 | 110 4] 48} 208 | 145 93 | 494 || 49 | 181 | 24] 155 87 | 9 59 | 191 | 108 | 98} 456 Totals... ++ |1299| 311 | 2278 |1094| 58 | 718 | 1625] 1664 | 1033) 5040 || — |1459| 252 | 1916 |1103| 38 | 721 |1498| 1510 | 1039] 4768 NAIRN. = Ardclach 1 12 1l| 0 || ey) sh 1 31 || 90 | 17 3 6 11|/ 0 8 9 13 7 37 Auldearn 5 dd 31] 3 30 | 39 | 18 27 | 114 || 89) 24 7 29 23) 1 22°] 28 18 16 84 Cawdor co 4 39 22] 0 3) 31 33 21 88 || 89 | 22 3 32 21] 1 10 | 22 29. | 18 79 Nairn (Burgh) 7 92 16] 1 19 | 36 90 | 26] 171 || 89} 55] 10 90 41] 1 36 | 39 88 34) 197 » (Landward) 20 8 45 17| 0 17 | 58 | 14 6 90 |) 89) 35 7 27 17 | 0 20} 39 25 2 86 | | Totals 136 | 25 232 97 | 4 76 | 171 | 166 | 81 | 494 || — | 153) 30 184 | 113) 3 | 96 | 1387} 173 | 77 | 483 . ORKNEY. | aes eon | eal ; i Cross and Burness 3 18] 0 | 19! 13] 24 109 2] 19 | 14| 0 | 99] 19) 9s 5 [fEday sien eee 0 | o 2 139] (era | 109 a] || Ay Oy) Ot Ml 8] oll oes | vie and Rendall 1 oO Oy 8) ml) ee | 109 Sl og || ai) © |} ie) 6) ted) Bl) as | Firth and Stennis 4 29| 6 | 16| 35] 47 109 7] 28) || 33] 5 | 7) 24] 40 | 24] 95 | Harray and Birsay 2 93 | 1 9 Al | | 109 £| 43 | 16] o | 6 40| 92 | a7) 95 Holm... ... 6 Te) |) 27, 16. | 109: 6} 36 || ell 2 | 30) a) 49) || 1) (eo Hoy and Graemsay 4 6| 1 | 19] 10 |zo9| 12] 1] 10 | 8/0] 13] 9| 3 | 6| 31 Kirkwall (Burgh) 18 76} 7 | 44 145 109| 81| 12] 146 | 65| 2 | 47/114! 83 | 62| 306 » (Landward) o| o 2} 0] 0 2 }109| 9] 1 0 ni} @ || Ol] 2 31) oO 2 Lady. + | ad] 2 92) 1 1 40 | |z09| 13) 4] 92: 96] 0 || of 191) 31 || 15) 65 Orphirs, S| 38) 1 19/ 0 | 10] 30 \t09| 49| 5] 13 | 16] 0 | 10] 37| 99 | 7| 82 Rousay and Egilshay |.) 9 | 4 27| 0 | 98 | 8 | lee) eC) ei) ns I] ee a |) gee] @)) | al) go St Andrews & Deerness| 25 | 2 a7 | 1 | 16 35 109| 32| 2] 27 | 9] 0 | 17] 18] 27 | 8| 70 Sandwiek | 13] 3 13] 0 || 2 19 | 200] 9} 3/° 8 | a3| 0 | 4| 3| is | a3] 33 Shapinsay —... ox 9 4 13 |. 0 4] 2 25 9 | b. | 5 7 g 4 South: Ronaldshay and)! 4, | 4 Ree > | Veval ceil ceccle caccdlhiecsl” Seles Resealp oe aed te _Bunay tl 33] 21 44] 3 | 39] 85] 57 | 109) 61| 11] “81 | 41| 4 | 47] 69| 57 | 95] 198 Stromness 48] 17] 85 | 47| 3 | 13| 79] G2 109) 46] 14] 74 22 7 Bironsay Fa a1) 3] 42 | 10] 0 | 16] 38] 34 | ros 3 aul) ase |aant raul] all euler crcl mae and Flotta 2] 4] 41 | 19] 3 | a4] 3 34 | 9 P | 26| 35 a ota ge 19 4} 31) 34 | 20] 109 |/709| 30] 3] 2 | 30) 3 | 15] 36] 35 | 18] 94 Teste ;, 56] 2] 64 | G4! o | 61] 42] 46 | 37| 186/109! 47] 2] 59 | 38 o | 3c] 32] 42 | 36) 146 Totals 5 | | | otals s+ ss. | 565] 101 | 819 | 496 | 27 | 353 | 615 | 691 | 349 | 2008 || — | 573] 87 | 672 | 405 | 21 | 321] 536) 577 | 324 | 1758 7 SHETLAND. | i if Bressay 8 2 Be 6| 0 5 | 18 : o f 15 | 12] 60|/t0| 14] 4| 2 Delting vnil| 228 5 37 20] 2 45 | 24 10 11 90 110) 23 3] 33 20 7 38 | 20 o il 76 Dunrossness | 82) 14] 42 | 27) 0 | 99] 92] 46 | 18] 115 //270] 50! 9] 38 | 21/ o | 33] 92] 48 | is] 118 er ‘. 8 1 14 il |} 0) 7 3 4 10 24 || 110) 12 2 | 6 1} 0 6 6 1 8 21 Nari Sonsiating’y| 07 | 88] 197 | 209] 4 | 103] 76] 165 99 | 443 ||110/ 110 18 | 157 | s4| 3 | 82) 6o| 197 | 93] 72 ) 7 5 9 } x Way cernies§| 36/ 5] 29 | 24) 6 | 93) 33) a7 | 27} 100}/10| 44| 2) 30 | 16| 3 | 22| 20] 25 | 28] 95 Northmavine ... _...| 33/ 6{| 35 | 92] 2 | 99] 34/ ia | 93| o7|\220/ 20| 6| = | 5 Sundsting & Aithsting | 31 5 26 Fy 9 8 aa 8 2 ela ut 21 a8 Pa ee ieee BY} 26) 41) 0 | 36] 24} 93 | 20 | s0a|}z70) | 5 | 28) 809) 0 aes a vine A ee eer | eal 6 || aollazl) eo |) ay) wena ov) oll ap | aall al} on! al oh oll ae ie ep con call S|) moll ay Il a : P 5 | 7 Wall \Seorness ate | coll aoe 3] 2 | 31) 22! 21 | 97) 101 |\zz0| 25) 5] 22 | 19| 2 | 29) 16] 1 || 16) 73 vant Foul may | Gh aes] @ I Gall oy 11) 56/720) 20|| 0} 9 | 19) 0 | 9) 24] 7 1) 8) 48 als. 22) 2] 25 | 13! 3°| 16] 9] 2 | 19! es |laz0! 15 | 4} 30) || 14) 9 || 20 | 8] 7 | 30) es Total ; | otals =... ... | 871 | 91 | 540 | 346] 21 | 354 899| 382 | 304 | 1369 | — | 378 | 64 | 408 | 261 | 18 | 284 272) 310 | 263 | 1129 (east 9& punjoay wm vuaippyg pooyay fo liaawng woynpuaulrg WAHOOL, “Wf EE ee—ere™mrmrmrn—n—m—raeeEsES | | gS Alness ... i) 8 6 0} s/s 1 ) 93 | 2) 2 4 0| 0 Oo}; 3 5 0 8 3s Applecross | 36] 11) 51 11] 22] 51] 33°| 23 99 AT ))|/) aL)! 435 |) 129) lle 9) eS SG ELAN D7 Ss PE Avoch Heal) We) 2) | O| 47] 16) 42 | 97 93' | 57)| %3)|| G4 | 22)) 10) | 47 | 23!) 39) || 37) Ide) Barvas ... | 91] 5| 87 7562 |0079))\\ rade ee 108 s0| 7| 87 | 49/ 6 | 37 | 75 | 39 | 58 | 299 | Carnoch Hr Ol 2 o| oO] 4 5 0 93 6} 0 3 5] 0 Shey 4 1] 14] Contin ... OW @ 5 Oi] af a 3 1 93 | O 4 9/0] 1]. 2 2 2 7 Cromarty 1 0 10 ) || 10 1 935 | 5 0 23 Oo} 0 2 18 7 1 28 Dingwall vee 93] 18] 95 6] 60| 101] 73 | 69 93 | 96| 16| 86 | 89/13 | 60] 89| 80 | 71 | 300] Levies wde calf SMll|| “Bell Bhs 2] 2) 50] 50 | 22 95 ei A) FA | Ae) 1| 46] 48 | 33] 198 Fodderty > aol S| Bl) o| 26) 49] 41 | 20 93% })534)/e 7| See GO\e | 30) |) lee |edit 340 | eee | ON nT 3 Gairloch 11 9 A ciecsnlaae 6] exo} tem] ai|(eon| ea eerie BH eco ce tet Om cage oer Meneses lest se Killearnan =... ...| 18/ O| 25 | 18/1 | 8] 20] 22 | 62 93 BN) Bs) a ste) |) By) Tes Nal) Ge Kilmuir Easter «| 35 J 26 11 i) 30 20 84 95 7 | 7 Kincardine 1g) 7 | 13 || 83/0) | “6 an\|! 5 9 | 37) 3] 19 | 20/ 2 | 24] 97) 92 | 8] a1 KinlochiLuchacee, salatotle ns See 8 5 55 96 21} 2] 18 | 16] 2 | 14] 292| 16 7] 59 ol peeaaer eyed ; Oo} 2) 3 9 30 ||93d99| 18] 1 Big | ee 25 | Melon enter 7 WEY Ce) nel (ere e5) | 41/298) ||| geil! is) le 18)|) dell san 78 93 22) 1/ 38 | 27] 2 | 22] 20] a4 | 2 §'| Lochalsh ve | 28} 9! 38 | 31) 4 | 30] 11] 44 110 99 | 99} 2] 17 | 34] 1 | 90] 9] 38 Fe 33 2 eqiisoaam Ses a A = wo 4 zt a oe a9 oe | 82 zs a Go 3 29} 73} 79 | 42) 993 Es ae 1 14 { : 9 5 9 10° 15 7 | 10! 42 5 Hes a) et ees m0 as aes BD Fe Bs We | 115 454 108 cg a a 123] 12 | 86/132] 99 | 101] 418 | 19s ci cmalll bs u 1 5 7 95 9| 4} 20) 3 6 4| 32 é Nigg 2 ip 0 = oa f 13] 9) 26 62 98 TE Oy TES ON MO Tey) aes aa fas | Rosemarkie 44 8 | 62 40} 2 a7 49 2 156 os ee 3 Ba ee ; | a a : $8 B Z : : 52 5: 35 26| 60] 3 wn| Rosskeen BN Gl REE NI vey 9) 7) 55| 49 30 95 45| 13| 68 | a3| 2 1L| 65 30 26 16 zg Son) la.) 47 | 324 | 143) 10 | 104 | 152 | 242 645 || 108 || 131) 46] 275 |156] 9 | 97/115] 267 | 138] 617 hee BE 2 5 5 3 5 | Tarbat | See ieeralce alles) calen epee Rall Seay Bl ee |e] 2 | we 33 | al | at | las e t : 5 | E 3 5 35 54 35] 26| 41 | 38] 139 e ee ee 146 19 | 162 | 67 | 9 | 117] 118) 103 | 65} 403 || 108 |111| 17] 125 | 6o| 9 | 93| 89] 91 | 49| 392 Fl erent js] 38] 10| 65 | 50) 2 | 17} 55) 47 | 46] 165 98 7 | 8! 53 | 45] 0 | Is] 46] 46 | 43) 153 Was on eq ees EDI. II ar | 34] 0 | a7] 47) 41 | 12) 137 93 45| 10} 45 | 28] 0 | 32} 49] 39 8} 128 sa = — | |= ! ! | | | F le5| | Totals ... 25 EI 256 | 1777 | 1241) 97 | 903 |1428| 1421 | 894 | 4646 — | 1363) 221 | 1595 |1179| 92 | 879 |1303/ 1369 | 899 | 4450 =| —<--= = 1 | =! Nie al S | ROXBURGH. g | | | = if 7 TI — = —— Ancrum | 4] 40 | 17) 0 | 22 | 3 | - Bednule 5 ji AM @ a “ 18 a | ey eB a8 2 16 | WW} oO) 19) 5) Ww 17 52 Bowden Gi] | ws] he) nell |) 2 t Oe oa ae | ta Castleton i Ala alo oli al ol al 2 | 2 4) By Bet em) ey wah aw | Cavers and Kirkton 2 43 ( g a 2 Bs ou a 2 tf By 2 8 5 2 18 Crailin oxo all ae a o 7 37 25 24| 93 38 28) 4 30 14) 1 3/ 29, 26 19) 77 Bekfor el aa) al ol a 1B ig Pee ed ao 5 pO | Gl we 1 4] 29 Edgerston 0 6 5| 2 ol 6 5 P 2 ) 9} Oo] Ww 2] 92 y 4} 15] 39 Ay) 8) 8} 1 Oo} 2] 20 Ednam... ort 4 B4 5 3 ae Hawick (Burgh)... Eales ical Worse eee ee eal) ce ol Si 2e | Ge | oll ae] 7 nal 26 i eri (Landsrard) ah ss Se ee 270 | 168 | 826 || 88 | 244] 41] 324 | 169] 8 | 192] 241) 931 | 192] 7a¢ Hobkirk noire 5| 30 6| 0 | 93 ll g ai i 3B rotleaol fires ecalare aco amace| & =| Jedburgh | 30] 110 | 86| 4 | 73! 93] 69 |108| ga | ilece aes eel ey, aT eB. 8 Seed Candvariy all ee all @ Al all & 8 US 58 Bs ay Ho e 3 47| 86| 64 | 80] 2977 | t 5 ] Kelso) =) se 3/ 73 | 44] 0 } 33| 42] 49 | 39] 163]) 39 | 43| a5 5 alee Ieee & Lilliesleaf Bee 4 13 13] 3 WV a Fo i 5 51 52] 1 42] 43 34 43 | 162 ar jit os i al sal 15] 50|| 39 PH) EH Te Way ea a] ay] at | Makerstoun ; i) 16 5] o | 5 @ 18 8 au 38, Bi 2 ibe 7) 0 6 7 2 8 23 | | 7] 8 | 12] 30] 39 | ah || a) 9| 2 0) Bim |e gO) gmentation Survey of School Children in Scotland y ee 42 LL01 | gz.) 78@ | 922 | set | Zt | 60% | Per | e9 | GOe | — || BSL | 193 | I9h | LLB | ESB | FL | 62Z] Tee | 89 | OSE |" --" = sTeIoL 1G 6 4 f iz | © 1G L O) it ee NS 91 OL 8 G 0 | OL GI j Gila eas ae *** MOITE X gy [1 id Ee ele 9 eee ales 8 ¢ |6 | oF || 6I I P 74) Ole he lhe) h IT |@ |[°" (pxempueq) = “ O06 | Lr |e OL = ere Or On alenae|= 86 Lie Lee OM Nacen GOS) fl GOe a Oper. I OnaleOe i, 63 | eilpa| Ogee ine (ysangq) $AALES CG, FOL.) 89 Pe Ine @ | s | - Ee LOR Gr Fe 2 sl | z Gaueien|| =6 Sip | ee elon eBoy ie |e z ali Tie Wek P 6 |e | or || 6 I z b |6 OF ir j 0 |¢ | (prempueqy) “ iz | get | 642 | 921 | 91t | of | o1t| gee | OF | 916 | OF | 98 | EBT | GFE | GAL | GsL | ZI | 48 | Ger | 8h | 006 |" (Ysang) speryseTeH 61. |¢€ 6 Pee ci O18 OL Ss evry Gr | 4s 9 6 I o |¢ 9 Ie lal pa hae PUI ce 6/6 L SP ih le Op IO Celesie OVallalpe 2 6 Oe Coie | ON Ce Gia | tee Clee eater JOOSUODDER) ar.) € DEO Miz L eh ee Pe, 2 6 6 |9 0 |¢ Sir KOn aa el te IPTGSV — | bre eal “MUYIMTHS ecez | 119 | ea | 064 | eer | ge | Le¢ | F986 | LPL | 008 | — || 882z | O99 | ZeL | E98 | eer | Ze | Geo] GeIT | SOL | F642; oo STRIOL, ise | | is =| eh GT 08 ce |g O | GI 0€ GMIESCaMINGS || C9) en 96 ve Ii |) Or a 2 Go| (F329 dc wyoyye A 9¢ |6 p cI | 8 ee) 6 @ | st | ee] re | 2 G 9 |9 tT |9 Gi Te |BOm PGi lee “+ peayqorAa y, Gree Or) | ¢ Hi LA WO aie BP ara! Foor Tau ace OO atm ek Gann tO bal¢CGan 0) aikGie |e salar |e Ceme | eitGamll to eemestnE SUDSSTOId a Cie ES Clee. 6 Levis Pie) aS GPP 6s tetra Nic lenignGion | \Llen|c9 On et) Oks a 18G |5Ge alae aa “Ueopyimod ep || 9 Of 962 20 Ons On I [es | c0G Gea, leu ce j 0@ | 2 0 |% CG eh | 4) WrouTremd yy |Gl | OL | OL | 6 0 |6 Iz Teel | 6s" Spe Or™= | MOT Lb ales Ope |) aca 22) IP Olmelas > aan eee OMBORaS CCeer toe Cl en GOL RO | One |C Clan ace OF eGGaneGeull CO OG neste O) I Slee sl ce acca Ieces later lic 6 smu sINgxoyy 8% 6 L | 4 G ais) 4 EP fOLS | 8é ly | OL iit Ey) az 0 -| $1 Or € hie des a 104.19q OY or |¢ j > lkO oO |F P Ost Genes eae ze etn | il On |G Gale J LOTgR eae ee ae = sure Ux”) i |9 6I | 9 |0 Lowes ra (Diy EGE IR Ske he Glan, ee Teen 1 |6 (|36 |? epzeqero_y ce 8 ene 14 || 0) 0 |G 9G ea eo 6E ce | OL II DES 20 0 /€& CG 0 L ay ; “* O1UIP PCARBEOR L1G uel GL Ope \eeGun Oo anne) CL peeAlty eziHem |eGoull OO ELOn et LGe wikcGuOGmIi ea | ON (CGTS KOGm RCOMa| an amt: asol]oT rn 9 Ol |? 0 |¢ 11 Ste oesl ALG. gle alas Ceci) 80! yi.) 38 Tig a levee se WOKE] | i | = | : is | | | | yang |ommpopy aay) ontg |") 0F | yaw wmrpeny| pee | wed | 5 cere ceappoyy) HT) ong, |OOUA yaeq |ammpoyy) por | are s[eq{oL 7 - S[TRIOL - = ysiieg SAAG YIVA & SUA aIVEAL - | | STUIO SAOD (panwjwoo)\— HOU NAXOW DDT ysung pun hyunoy ‘(panuryuod)— AX ATAVL 43 J. F. Tocuer | | PPE | LOE | BS] OT | OS) Zr | 19 | FOP | — || OzEL | Ize | BIF | Lee | 9ez | zt | SOF | FEF | 16 | Te | aS ON } | | | | it Soe | 0 1) re 8) I | 93 | 96 || LOL | 2% GS Ir | PI z | og eg | 2 ep a “aNsuOT, | 81 ZS | SI 1 et 91 r | 9e | 96 || 19 6 cl Il | 92 0 | gz 8 v Tun ea ae “* 4re50y S66 6 0 |¢ or | T / et | g6 || 92 L @ Zl | 9 0 |9 ial P Pr = ze * YQ07T | 0 y | OO eta. 4 ear 0 |S | 96 || FI I iy bo og O-Ps g O | Yr ee sateT 6g S| LP 0 | SF ig ¢ | gr | 96 || 99L | FF 9¢ eevee 0 | IL ec 9 Gaal pee i ueuoplly 6F ge |e 0 | IF 6g € | 0&8 | g6 || 4eL | ge 09 ed, 0 | 8¢ 0g L rode dhe i “ atdspory | 09 Or | OF T 1 66 IL ct | 9¢ | 96 || eoL | ze 1¢ ie | 19 OV ele 6 ja We RATS ad a3! eo fa OZ 1 oe Tore BE € | ee | 96 || 96 0 IF 8. | 61 imc OF F TG eal “* siyoevappy FL Sve he? eal OL y | el |.96 || 6e Neal heey Sip ie NEI € L Sia bee By ssouIn(] r9 ze | 81 L | OF Wh L |e | 96 || PEL | 0g 19 9 | FI gs | I¢ LL 16 A feiie up oy ypour0(] Gl 93 | ZI € | 91 og 8 | 91 | 96 || sot | Te l¢ L@ | 61 arta ZG Br dep Wee Ne “ Ytedg 8 cy | 8 ie here Ig ’ |¢¢ | 96 || IpL | eF LE or | Iz @ | 98 FG 9 ain Pe oe * audTO Il le | 81 Tee Zale | wOS 9 | 17 | 96 || 82 81 91 og | FI 0 | FL 9¢ 6 Gln or * quissy | i ‘dNVIYAHLAS es : | _ : : Se 6PLG | 199Z| OTEL | GOT | SETS} TOLE | LEE | Tees} — || Goes | ZEos| Leos | L18z| GET] LSI | FIPS] FIO | GF | oezs| “ sTezOT, esl eee | Es _ | | : |__ | 9 81 | 91 Ger L1G z et | @r lea | 1 61 Che lent aaa ees if Ole “ ouelqyzeayg GIG | GY | G9T | SI | Lge | 969 | 09 | PLE | 09 |) LerT | BE | Bos | ear | oG1 | es] OFe | G69 | BL | LOE | (qsing) Surpyg S61 || Tl |-2e O | SIL] €@ | €% | 220 | or || I8¢ | oot | tes | z9t | e9 @ | S81 | €83 | ee | cat jo" “ uedURUTyg IOL | 621 | 96 = 1 C6 | kpl” | G6 | Gh 169) OL | Sh LOL | L8I | 86 % | OOT |) LOl +) yee cer | “* SUBIUIN' 49 GOL | L7I | 88 OL | 9IL | sect | st | sot | 79 || ser | 66 rol | VEL | 16 Be OGT, | S861. 1s06.. |-Ser yi” * SpIsMoABIIN 8 GL | I ©) Weel or I 02 | 6¢ || oc g el b |G [ avOlet =o I 93 |°" er “* QLsorT Gey | Ihe | GAT | 91 | 62) L9G | 9 | GZE | BO || BLE | GBS] Sec | 96e | LOL | st | 22e) o6¢ | 64 | soe | -° ai qtoqaery 91 Goals 0 | OL Lye Poe eo Gala 0% 0G Poe 6 er 6t ¢ OF ecod dns Gg 9r | &¢ vy | Gy Po LE ACO eee lize @9 6G Le | e9 Gouacs Pg 8l | GL |°* (prempueq) “ Of2 | r1e | SF 6 | Sok | SbS | Ly | SST | SE ll-pPL | PCT.|- Teses| 992 |e) GeleOSle| tre: lors: pees (umoy,) qyAs[Ly G0€ | €46 | 006 | €1 |] FG3 | GLE | LE | GoE | 79 || POST | Oa | Ose | Ose | sa! 92] 9ce! cer | on | Loe | °° a yynomesuetp j 2. | 6 0 |7 6 0 | 2. | 6¢ || 6¢ J; Il O31 | 12 0 | FI 91 I SG aaa. "+ yoouunsier) G OlMEIRE 1 |9 € ea be) 6G || BE ral r 6 i) Gaalee z I 6 iP By + £aqULy SE eg | 02 ig ks 09 9 or | 9 || 69L | Ze eP LOmmince r | se 99 Hi FG | °° (pavmpueyq) “ vie | 466 | GOL | 6 | OOf | OSh | &F | Les | ZO |] FIL | 6661 See | Tee | 64L| st| goe| ise | He | zos | °° (qoing) YATE YT i 9 I 0 10 p Ome! 69 || 6% Gg GI v G heir 6 0 Gi 5 me sovdruncy FL G% | LG Pa lacs ar € 91 | 6¢ || ¢8 Ge 81 Tle EO Sule Ze 0 Cleese: ce wou day 696 | OL4T | 9EL | GS} 96L | 92E | HE | LBL | 69 |] 164 | G4T | 99% | 110] IL | Gt | Ie! t9¢ | ve | tot | c pas + Laue, 8% 9r | I @ | veil Ig r St eee | Ole aas GP 9 0 | 08 eP G CCS irs a Baa arsdurey) G ae 9) i \e6 IL 0 OL | 6¢ || 6% GL G G F i in L j L ae “* ueargong €I 91 | 9 Oo ge eel Gg L ie MW S| T 6 Ge || i 0 | 9I 6 P Ong pela “* yoouropreg Gr Lemna 1 |) av 8g ¢ O¢ | 79 || PEL | 9¢ Le ge | & @ | 1¢ +9 9 Tes lee ae “ UQay ‘ONITULLS TABLE XV.—(continued). County and Parish Data. ROXBURGH,—(continued). BOYS GIRLS Hair Eyes 3 Ham Eyes Parish : Totals|| 3 - Totals | Fair) Rea |Afeaiom Dark | peek Blue | Light|Medium| Dark 5 | vair | Red |Medium| Dark |,1°, | Blue | Light | Medium| Dark | | Maxton All al i UN ® fm] a 5 7| 237 Gi] al lL 5| 0 4) 10 6 5} 25 Melrose 63| 20] 158 | G2) 3 | 50] 92] 97 67 | 306 77 | 17 117] 56] 5 | 40| 78} 91 63 | 272 Minto ... Til Wily eB 3] 0 o| u 11 10} 32 6] 1 26 2) 0 0) 9) 18 8) 35 Morebattle 92] 2] 21 Ta a 15'|/ 16) 19 Suis 16| 4 12 8) 1 0| 16) 19 6) 41 Oxnam ... eA Oa) 6 5| 0 Ge 3) 14 2) 0 4 4] 0 Oo} 3 2 5 Roberton 15 3} 10 13} 0 4/ 16 11 10 | 41 1K0)/})) 3 ii 9} 1 5 7 7 9 28 Roxburgh 11 Qg| 95 | 22) 2 | 13) 6) 17 | 26) 62 22| 0 22 | 15/ 0 | 10) 19] 19 | 11) 59 St Boswell’s 10) 3] 15 | 17] 0 8} 11 10 | 16) 45 13} 21 9| 0 9| 10] 10 | 15) 44 Smailholm yf Set ae 4} 0 7)|\ 20) 2 i) Soe Il 20] 1 11 10} 0 0} 26| 10 6) 42 Southdean 9 2) 16 14] 0 6] 11 12 12 | 41 | 14] 5 8 14] 1 9| 13 12 8 @ Sprouston 21 3 7 19/ 0 22) 16 5 17 | 60 Agi) ek 12 12) 0 17) 13 5 10 45 Teviothead 124l 20) 5 6/1 6 6 Ge arp ees 18 | 2 9 6] 1 8 5 4 9 36 Yetholm | 25] 5 | 25 TN On|) ab eu 2G | 11} 62 93 | 5 30 | 15] 0 3 30 | 15 73 | | | | aes a | é z = | | | | | Sa me Totals 794 | 168 | 1155 | 639 | 32 | 493) 863 | 782 | 650 | 2788 || — | 800 | 147 | 984 | 587 | 35 423 | 790 | 723 | 617 | 2553 | | SELKIRK. —s T T = sbkirk (||) ale} 5) 0 6| 9 9 Tl eda |pS8a|etaleel 7 4/0 a 4 3 5} 19 Caidonfoot Di LBS ||) 915} (tO) ||), 251)| 9 7| 47/140] 15] 2 6. | rail! 0 || a1 8 7 9) 35 Ettrick aces i 1 6 5] 0 bil 6 3| 19} 40| 3] 3 10 3/ 0 Olly 9 3) 19 Galashiels (Burgh)... 48 | 439 | 137] 12 | 125 | 179] 349 | 183) 836 || 40} 216 | 40 | 335 | 110/10 | 116/178) 279 | 138) 711 » (Landward) 35 ec) 2 4] 0 g| 4 2 1 9] 40| 3] 2 4 10) (ep lee | | 2 By) aul Kirkhope... ...| 15] 3 9 | 1} 2 2) 18 7 | 13] 40} 40] 8} 1 |p 28) Snes By |) TOs 32) Selkirk (Burgh) | 50] 11] 85 | 36| 0 | 47| 40) 65 | 30} 182 | 40 | 37] 11 98 | 54] 0 | 40 43) 70 | 47] 20 of (Landward) . 5 1 7 Gi) 10} 4 4 1 19 || 40 9) 3 8 28 |e el 3 7 2 1 23 SViarrovy enue ecesmtis food te 2) |e ed |e Ol) 0. 5| 8} 10 | 16] 391] 40] 11] 0 7 Oh Ones | ey OQ} Pi | | | Totals 320 | 68 | 591 | 229 | 14 | 293 | 277 | 461 | 261 | 1222 || — | 309 | 63 | 484 | 209 | 12 | 192 | 276] 384 | 225 | 1077 = SS =; — STIRLING. | Airth ... 6| 64 | 31] 2-| 93] 38] 37 | 86] 184]] 62] 50) 3] 58 | 24] 1 | 27) 31] 45 | 33| 136 Baldernock 4 9 | 16] 0 4} 15 9 | EN EN BG) Bh) ate || DL) @ 6| 16] 13 5 | 40 Buchanan 2 i] TH |) AS a5} 5 | 45:|| (29'159)) 10))| Oo} a |) <9) 1 8} 1 5 Ales Campsie 5| 43 | 30] 0 1) 50] 42 8] 101 || 12) 18) 4] 41 12] 0 1] 46) 28 | 10) 8 Denny ... | 34] 361 | 214/15 | 141/211] 266 | 173] 791 |] 63 | 187} 24] 3296 | 196/25 | 136] 176] 259 | 187] 758 Drymen o| 32 | 31| 2 | 16) 14] 18 | 35] 83]| 59] 16] 3] 42 | 95) 4 7A le 257| eel | 240190 Dunipace eer i) 9 4/1 5 4 15 5 29 || 62 7 0 Wf Oo} 0 1 6 7 0 14 Falkirk (Burgh) 44] 521 | 303|12 | 179 | 331] 333 | 299 | 1142 || 62 | 231] 43] 450 | 300| 9 | 162] 297 | 314 | 260 | 1033 » (Landward) 7| 66 | 38| 4 | 33] 61| 48 | 32] 1691) 63| 40] 6] 60 | 37] 2 | 20] 53] 38 | 34] 145 Fintry .. 0. 1 2) jl VS | 02) 7| 9 4 | 12] 32/69) 8] 5 3 6} 1 1| 10 5 || 2B Gargunnock 1 16 | 14] 0 21 | 20 11 7 59 || 59| 12) Oo 9 4/0 9| 12 2 2 25 Grangemouth ... 70| 475 | 326 | 26 | 242 | 326] 386 | 250 | 1204 |! 61 | 305 | 57 375 | 254] 13 | 200 | 273 | 305 | 226 | 1004 Kilsyth (Town) ... | 184] 34] 344 | 180) 2 | 73) 286] 231 | 154] 744 || 12] 182] 41] 348 | 153] 2 | 42] 314] 230 | 140] 726 » (landward) ...| 75| 18| 54 | 83) 2 | 638) 47) 59 | 63] 232]| 72] 68] 11| 74 | 55] 4 | 53] 46] 55 | 58] 212 ee aan) ccol| Ol) 2h eo |) ie) 7| 24) 20 | 90] 711) 59) 24) 4) 47 10! 0 s| 32] 16 | 99] 85 Larbert .| 308] 79} 590 | 377| 18 | 161 | 396] 533 | 282 | 1372 || 62 | 325 | 62| 567 | 329/16 | 179] 371) 485 | 264 | 1999 Topicbee-tge wee #2) 26) |v 12 } 10] 1 5 | 24] 13 8} 60/169] 20} 1 ey SE @ | |) GS 8 | 10| 46 Muiravonside ... 133 | 20] 198 | 120; 7 | 91] 134] 154 | 99| 478 || 62 | 155) 18) 152 | 116/10 | 88] 147] 105 | 111} 451 St Ninians 185 | 24] 157 | 100) 4 | 98/187] 107 | 78| 470 || 59|172| 95} 147 | 95] 3 | 96/179} 101 | 66 | 442 Slamannan... —... | 125 | 33 | 983 |138| 2 | 63| 167 | 251 | 100| 581 || 10| 127) 93] 293 |115| 0 | 52| 141] 193 | 102] 488 Stirling (Burgh) ... | 307 | 78] 699 | 340 | 23 | 150 | 453 | 502 | 342 | 1447 || Go| 374] GO| 695 | 357) 12 | 165 | 442) 515 | 376 | 1498 Strathblane 2) 67 1237 1) 7s F112) 75 9 | eee) ero y || e72:|| a1 Bh |ear2 | moan act) es Ge are) 6 | 18} 58 | | | Totals : 2285 465 | 4014 | 2414| 127 |1399| 2817] 3057 | 2032} 9305 || — |2351| 397 | 3701 |2135| 105 |1310| 2661} 2749 | 1969] 8689 | | | | i SUTHERLAND. ] Assynt ... 19} 9) 36 | 14] 0 | 14] 30] a6 | 18] 78]] 96) 41] 6 BW |) ie] 2 18'| 37 || 11 | 29)} (95 Clyne 42! 6| 54 | 36/ 3 | 21| 40| 37 | 48] 141]] 96) 55] 4 BL |}) 82741] eee 23) | eon |e 28 en |e | ee 3 Creich ... 14} 12} 52 | 28] 2 | 19] 27) 31 | 31] 108]} 96) 16] 8 BO | 1G} 8 |) 22] 23], 1 |) so) “we Dornoch 47} 11) 77 | 51] 8 | 14] 63] 67 | 50] 194 }) 95] 43] 7 7 46} 7 | 18| 32] 64 | 60] 174 Durness 16| 7 Sy) sell a 5| 16] 12 6| 39 || 96] 13] 4 1@, | W2|) 31 71) 13)} 14 6| 40 Eddrachillis 21 | 4] 40 | 32) 7 19) 18] 41 20] 98/96 | 33] 3 38 | 24] 1 | 32] 26] 23 | 18] 99 RS on ow 65) 14| 49 | 37] 0 | 51! 31] 51 | 32] 165 || 96) 56] 15 71 | 29) 1 | 40) 40] 60 | 32) 172 Golspie ... 22! 7) 50 | 58] 0 7| 37} 60 | 33) 137 || 95) 20) 3 69 | 41/ 0 3 | 38} 49 | 33) 193 Kildonan 26| 6] 53 | 71] © | 35] 21) 56 | 44] 156 || 96] 48] 5 48 | 48|/ 0 | 47] 22) 39 | 41] 149 Lairg | 0) 5 8| 0 5| 4 4 1 14 || 96 | 5] 0 1 1/ 0 PHI et 0 1 7 Loth .., 4{ 4) 14 6| 0 6| 12 3 7| 98]|95) 13] 1 10 5| 0 9| 9 2 9| 29 Rogart ... 24 AN ff |) eH) © |) ea} ai 15 9 61 || 96 | 36] 4 16 iG} al 18 | 22 18 12 70 Tongue... 15) 7) 653 | 30) 2 | 14] 41) 95 | 97] 107 ]]96) 25] 1 47 | 24) 0 | 13) 33) 21 | 30] 97 | Totals... 316 | 91 | 494 | 408] 17 | 236»).351 | 418 | 321 | 1326 || —| 404 | G1 | 482 | 303] 16 | 242 | 347 | 344 | 333 | 1266 GF punpjoay w vaippyy jooyas fo fiaaing uoynjuoubed UtHOOT, “AL FP Pigmentation Survey of School Children in Scotland 44 | 7] | | ogtz | 967 | 909 | 29 | gor | ee | t8¢ | 118 | 901 | 619 | — || cots | cor | seo | 68o | 69E | Te | Isc] Ges | CET | FES “* sTeqo, giz |zo | |09 |¢¢ | o |%¢ | got | 6 | og | se] ost |9r.| so | er | 132 | & | es | g8 |9 | 89 SLCOUELC TY zzq_ | oct! git |ost| 92 | + | 2tt| ves | ee | pet | ae || eo | cet | Ist | zor} #6 | F | 48 | O8@ | VE | LET | (ySimg) rovreng gst |oe | er |r | w | 9 | 8¢ | 1% y er es irr lee eye || ep sles) Ste | 9ee or” lar, | "+" yarkotoyg a6 |b 0. | st | 0 Or 1g 0% 1 | 26 '\\ 8 || 98° Is GOP | OEM O On Rete Camlice aiece soruyedyaog ser | sp | so |o9 jer | € | 9F | £8 PL | Or | ee | 97L | ee | 99 | ve | er | | ue | Fe | it | 62 “* oueysurmueg fet rene con ale rae On + ve 6 |19 | ae || ses | er | 79 | ze | ez | & | 6g | Bor | It | 29 | 7 eonqaetD 10 00n77 pIO éL 0) 9 € € Oo | tT G T 8 AR || tll aXe ¢c G v 0) 1 L te re ; “a8 oN] MON wy | el | 9 02 |¢ Om iGhe | Ror O° or | se || Le. 12 € es | > Leal aot) 08. | 6 “ TMAyDoTY Goue C mime ee el) |ste)|9 || 06 1798 QueliiT "eee. Wega oc s*|asec 2)| Ft | 8) ls eOlean are || 6406 a qeasory Cele Sc ween One ceel) fo) te. 09 9 | ry | 26 \ll'vok |e. | 496-8) Le |. 76 || So eiep | ey Sy ies "+ UepreULpy Ei 0G a OG: ke | 96 | 1 | 22 4\ lor e | 17 | se |leet | se | i |e | es | 0 | eo: | oF | aL] ge TOUUDAAT Sy PILelre Ge -\Go. | or | %-\'re [> se ve ry. lees ZOU | ois |e cee *lege #1 1S” Cee cur Miya nr ele ce ULMOOMTY Giiee eocan Pe Ocoee (GG. Ie Fe 4 areas) TL MeL Gus |e. \ss6o ul cn | Sie (16 “Ice hl, 2 9/09 - | mocaumitgu are pOORATYL oon lees | 26 | 6S7| 2t.| 0 | se | Ze 7 |ce | as |loot jer | og | a |at | t |oe | a | et | ve a youy eee | OW er 62 | 9 OP Vee | ela eee neeneee Oleh cle eGumal| eee Ke eas eae ee a | "* T0zLOSSETH | | | a = = ae x21 | a yavg ummpeyy)sqseq) ome YSIS) yxeq jumrpayy) pow | red S yavg jounrpayy | yyavT| entg Tat | yieq Mpa, pay | 2a spejoy, | re & || srsoy,|——— = = SS ag ystreg SHAQ IVA = SAA, YIVA = STUID SAOT “NMODOIM yg yng pun hyunog (‘panuyuoo)— AX ATAVL J. F. Tocuer 45 TABLE XVI. Observers and Schools contributing to the Data of the Pigmentation Survey of School Children in Scotland*. COUNTY OF ABERDEEN. Burgh of Aberdeen.—Ashley Road, Mr W. Ross (77); Broomhill, Mr R. A. Watson (77); Causewayend, Mr Rose (77); Commerce St., Mr J. Peter (77); Ferryhill, Mr J. D. Anderson (77); Frederick St., ?(77); Hanover St., Mr W. D. M¢Lean (77); King Street, Mr. T. Hynd (77); Kittybrewster, Mr J. MeKenzie (77); Marywell Street, Mr W. Fyfe (77); Middle, Mr J. C. Barnett (77); Mile End, Mr J. F. Cruickshank (77); Old Aberdeen, Mr W. B. Duguid (77); Porthill, Mr W. Stewart (77); St Clements Street, Mr D. B. Lothian (77); St Paul Street, Mrs J. S. Skea (77); Skene Square, Mr A. Green (77); Skene Street, 1 (77); Westfield, Mr W. Robertson (77); Woodside, Mr J. A. M*Hardy (77); York Street, Miss Spalding (77); Deaf and Dumb Institution, Mr Alex Pender (77); Normal, U. F. C., 2(77); St Margaret’s Mission, Sister Katharine Mary (77); St Peter’s, R.C., Mr J. Brady (77); Cathedral, R.C., Mr P. M°Grath (77); Gordon’s College, Mr C. Stewart (77); Rose- mount, Mr J. Findlay (77). Parish of Aberdour—Aberdour, Mr J. Reaich (83); Auchmedden Mr W. Swanney (83); Parish of Aboyne and Glen Tanar—Aboyne, Mr J. Cruickshank (79) ; Glen Tanar, Mr W. Walker (79); Parish of Alford—Alford Village, Mr D. C. Crabbe (80); Gallowhill, Mr A. M°Creadie (80); Parish of Ardallie—Ardallie, ? (82); Ardallie, Female, Miss J. Kemp (82); Parish of Auchterless—Badenscoth, Mr. Geo. Ironside (82); Kirktown, Mr A. Longmore (82); Parish of Belhelvie—Balmedie, Mr C. E. Glennie (78); Craigie, Miss Fraser (78) ; Menie, Miss Jane Watt (78); Wester Hatton, Mr M. 8. Craib (78); Parish of Birse—Birse, Mr G. Innes (78); Finzean, Mr W. Adams (78); Forest, Miss Eva Shaw (78); Parish of Bourtie —Bourtie, Miss Taylor (80); Parish of Cairney—Alehousehillock, Miss G. Gray (87); Cairney, Mr P. Stuart (87); Ruthven, Mr W. Johnstone (87); Windyraw, Mr A. Middleton (87); Parish of Chapel of Garioch—Chapel, Miss E. J. Fordyce (80); Logie Durno, Mr J. B. Robson (80); Parish of Clatt-—Clatt, Mr W. Stewart (80); Parish of Cluny—Cluny, Mr W. Harper (80); Cluny, U. F. C., Miss Deuchars (80); Corennie, Lady Gordon Cathcart’s, Miss J. A. Ironside (80); Parish of Coull—Coull, Mr A. Howie (79); Parish of Crathie and Braemar—Aberarder, Miss M. Catto (79); Braemar, Mr J. Badenoch (79); Crathie, Mr W. Brown (79); Crathieside, Mr W. Strath (79); Inverey District, Miss 8S. MacFarlane (79) ; Inverey, R. C., Miss M. Dallastone (79) ; Parish of Cruden—Auchiries, Miss M. Campbell (78); Bogbrae, Mr J. C. Coutts (78); Hatton, Mr W. Littlejohn (78); Errol, Epis, Mr Miller (78); Parish of Culsalmond—Tillymorgan, Mr A. J. Wallace (80); Parish of Drumblade—Drumblade, Mr J. Taylor (87); Parish of Drumoak—Drumoak Central, Mr J. R. Littlejohn (79); Glashmore, Miss J. A. McBeth (79); Parish of Dyce—Dyce Overtown, Miss L. R. Mitchell (80); Dyce village, Mr G. Murray (80) ; Parish of Echt—Cullerley, Miss M. J. Barron (79); Kirkton, Mr R. C. Burnett (78); Waterton, Miss E. Peace (79); Parish of Ellon—Berefold, Mr R. Thomson (82); Drumwhindle, Mr L. Gavin (82); Ellon, Mr D. Cameron (82); Esslemont, Mr A. Cairns (82); Parish of Fintray— Disblair, Miss J. Meldrum (80); Hatton, Mr C. Smith (80); Parish of Forgue—Forgue, Mr R. Wright (87); Largue, Mr J, Gray (87); Forgue Episc., Miss J. B. Duncan (87); Parish of Foveran—Cultercullen, Mr J. Rose (78); Foveran, Mr J. Watson (78); Newburgh Mathers, Mr Williams (78); Parish of Fraserburgh—Fraserburgh, Mr J. A. Sutor (83); Fraserburgh, * The figures in brackets refer to the Districts, where blanks with a query occur, the names of teachers were not supplied. 46 Pigmentation Survey of School Children in Scotland Infant, Miss Milne (83); Academy, Elementary Dept., Mr R. Lees (83); Broadsea, Mr J. W. Broome (83) ; Female Industrial, Miss N. Brown (83); St Peter’s Episc., Mr J. Gray (83); Parish of Fyvie—Fyvie, Mr A. Bremner (82); Steinmanhill, Miss J. A, Calder (82); Woodhead, Mr D. Davidson (82); All Saints’ Epis, Mr M. Sangster (82); St Katharine’s, Miss A. Forbes (82) ; Parish of Gartly—Braes, Miss J. W. Emslie (87); Central, Mr W. Smith (87); Parish of Glass— Beldorney, Miss M. M. Duguid (87); Glass, Mr D. Wood (87); Parish of Glenbucket—Glen- bucket, Mr J. N. Watt (80); Parish of Glenmuick and Tullich—Ballater, Mr J. Lawson (79) ; Birkhall, Miss A. Begg (79); Inchmarnock—Miss C. Forbes (79); Kinnord, Miss R. Begg (79) ; Parish of Huntly—Gordon, Mr D. M. J. James (87); Kinnoir, Miss A. Allardyce (87) ; Longhill, Mrs H. Kemp (87); Parish of Insch—Insch, ? (80); Parish of Inverurie—Market Place, Mr J. Philip (80); Infant School, Mr J. Rennie (80); St Mary’s Epis., Mr J. Stuart (80); Parish of Keig—Keig, ? (80); Parish of Keithhall and Kinkell—Keithhall, Mr Geo. Kemp (80) ; Parish of Kennethmont—Kennethmont, Mr G. Cheyne (80); Old Town, Mr P. Campbell (80) ; Parish of Kincardine O’Neil—Greenburn, Miss J. A. Ogg (79); Kincardine O’Neil, Mr A. T. Ross (79); Tornaveen, Mr P. Wallace (79); Torphins, Mr J. W. Williams (79); Parish of King Edward—-King Edward, Mr J. Elphinstone (86) ; Parish of Kininmonth—Kininmonth, Mr G. M. Farquharson (84); Parish of Kinellar—Kinellar, Mr A. Forrest (80); Parish of Kintore— Kintore, Mr W. Keys (80); Leylodge, Miss A. Riach (80); Port Elphinstone—Mr J. Ritchie (80) ; Parish of Leochel Cushnie—Cairncoullie, Mr G. Shearer (80); Corse, Mr E. 8S. Mearns (80); Craigievar, Mr A. Grassick (80); Cushnie, ? (80); Parish of Leslie—Leslie, Mr G. Riddell (80); Parish of Logie Buchan—Tipperty, Mr L. Smart (78); Parish of Logie Coldstone— Logie Coldstone, Mr J. B. Anderson (79); Migvie, Miss E. Robertson (79); Parish of Longside— Kinmundy, Mr. A. MeD. Younie (84) ; Longside, Mr A. Center (84) ; Rora, Mr A. F. Annand (84) ; Parish of Lonmay—Blackhills, Mr L. M¢Leod (83) ; Lonmay, Mr J. 8. Ewen (83) ; St Combs, Mr R. Mirrless (83); Parish of Lumphanan—Lumphanan, Mr R. McLean (79); Parish of Meldrum— Commercial Road, Mr C. F. Bearsley (82); Kirk St., Infant, Miss M*Rae (82); Tulloch, Miss M. Cooper (82); Parish of Methlick—Cairnorrie, Mr J. Macdonald (82); Methlick, Mr A. C. Kirton (82); Parish of Midmar—Midmar and Corsindae Memorial, Mr J. Grant (79); Parish of Millbrex—Millbrex, Male, Mr. P. M*Donald (82); Millbrex District, Mr E. Ironside (82); Parish of Monquhitter—Garmond, Miss M. A. Lyall (82); Greeness, Mr J. M. Stephen (82) ; Monquhitter, Mr W. Barclay (82); Parish of Monymusk—Monymusk, Mr A. W. Simpson (80); Sir Arthur Grant’s, Miss E. M. Scott (80) ; Tillyfourie, Miss M. Main (80); Parish of New Byth—-New Byth, Mr M. A. Clark (86); Upper Brae, Miss J. Wilson (86); Parish of New Deer—Cairnbanno, Mr J. Macpherson (84); Knaven, Mr W. Hadden (84); New Deer, Mr H. Cowie (84); do. Infant, Miss Morrison (84); Oldwhat, Mr A. Dunbar (84); Whitehill, Mr G. Greig (84); Bonny- kelly, Miss A. B. Oliphant (84); Parish of Newhills—Blackburn, Mr J. Ligertwood (78) ; Bucksburn, Mr M. G. Gerrard (78); Kepplehills, Miss Jackson (78); Kingswells, Mr D. J. Williamson (78) ; Stoneywood, Mr C. Frazer (78); Parish of New Machar--New Machar, Mr J. G. Moncur (78); Parkhill, Miss A. J. Crane (78); Whiterashes, Mr J. M°Gregor (78); Parish of New Pitsligo—Glasslaw, Miss E. Davidson (84); New Pitsligo, Mr J. Will (84); St John’s Episc., Miss Fowlie (84); Parish of Old Deer—Bulwark, Miss Watters (84); Clochan, Mr R. D. Robertson (84); Fetterangus, Mr. W. Scorgie (84); Maud, Mr J. Law (84); Old Deer, Mr J. B. Gillies (84); Shannas, Mr P. S. Pyper (84) ; Stuartfield, Miss 8S. M. Thomson (84); Parish of Old Machar—Bridge of Don, Miss B. W. Killoh (78) ; Denmore, Miss A. Robertson (78) ; Whitestripes, Miss A. Dey (78); Parish of Oyne—Oyne, Mr Riddell (80); Parish of Peterculter—Countess- wells, Miss A. M. Duncan (78); Craigton, Mr D. A. Farquhar (78); Cults, Mr F. Croll (78) ; Eddieston, Miss J. Rennie (78); Burgh of Peterhead—Academy, Mr J. Don (81); Buchanhaven, Miss J. C. King (81); Central, Mr A. M°D. Reid (81); Infant, Miss A. Forbes (81); North, Mr W. Murray (81); North, Infant, Miss E. Barclay (81); St Peter’s Epis., Miss E. Bruce (81) ; Parish of Peterhead (Landward)—Blackhills, Mr W. Smith (81); Boddam, Mr 8. M°Kim (81); Burnhaven, Mr D. J. Mitchell (81); Parish of Pitsligo—Pitsligo, Miss H. Strachan (83) ; Rosehearty, Mr A. Forbes (83); Sandhaven, Mr W. J. Caird (83); Parish of Premnay— J. FE. Tocuer 4] Premnay, Mr W. L. H. Cruickshank (80) ; Parish of Rathen--Inverallochy, Mr D. C. Dundas (13) ; Rathen, Mr J. Jack (83) ; Cortes, Mr E. Cowie (83); Parish of Rayne—North, Mr W. Black (80) ; Old Rayne, Miss M. U. Morrice (80) ; Parish of Rhynie—Dutfts, Miss A. M°Gillivray (87) ; Lesmore, 2 (87); Parish of St Fergus—Central, Mr J. Cormack (81); Northern, Miss J. Gall (81); Parish of Savoch—Braeside, Mr W. Ferguson (82); Savoch, Girls, Miss EK, Penny (82) ; Parish of Skene—Central, Mr G. Mitchell (79); Garlogie, Miss J. F. Harper (79); Westhill, Miss A. Mackie (79); Parish of Slains—Collieston, Miss H. Leslie (78); Slains, Mr Harper (78); Parish of Strathdon—Corgarff, Mr A. Merriless (80); Forbeston, Miss F. Rennie (80) ; Knocklea, Mr J. Forbes (80); Strathdon, Mr J. B. Innes (80); Tillyduke, Mr C. Farquharson (80); Parish of Strichen—Strichen, Miss J. Aiken (84); Techmuiry 2nd, Mr P. Seath (84); All Saints’ Epis., Miss M. J. Greig (84); Parish of Tarland—Tarland, Mr J. Forbes (79); Parish of Tarves—Auchedly, Miss C. P. Hay (82); Barthol Chapel, Mr. W. Wilson (82); Craigdam, Mr J. Davidson (82); Parish of Tough—Tough, Mr Chas. Stewart (80); Parish of Towie—Ardlair, Miss J. Collie (80) ; Towie, Mr J. M*Lean (80); Parish of Turriff—Ardmiddle, Mr J. Roy (86) ; Birkenhills, Mr J. Dilworth (86); Fintry, Mr J. Clark (86); Turriff, Mr D. L. Phease (86); Parish of Tyrie—Tyrie, Mr A. Coppland (84); Parish of Udny—Udny Green, Mr W. Sim (82) ; Parish of Ythan Wells—Corse, Miss J. Tocher (82); Ythan Wells, Mr J. M*Pherson (82). COUNTY OF ARGYLL. Parish of Acharacle—Eilanshona, Mr J. M°Gregor (100); Glenborrodale, Miss A. F. Cameron (100); Kinlochmoidart, Miss J. J. Macnaughton (100); Mingarry, Miss K. Edmonson (100) ; Parish of Ardchattan and Muckairn—Achaleven, Mr W. W. Ewing (101); Glenetive, Mr K. J. Robson (101); Letterwood, Miss A. Connell (101); Parish of Ardgour—Ardgour, Miss Stuart (100) ; Duisky, Miss A. MeMillan (100) ; Trislaig, Miss A. Campbell (100) ; Kingair- loch, Miss C. MeMillan (100); Parish of Ardnamurchan—Kilchoan, Mr A. C. Storrer (100) ; Burgh of Campbeltown—Dalintober, Mr D. Fisher (103); Grammar, Mr R. Y. Cunningham (103); Millknowe, Mr J. Kirkwood (103); St Kierans, R. C., Miss T. Fisher (103); Parish of Campbeltown (Landward)—Auchencorvie, Mr J. Templeton (103); Drumlemble, Mr D. Cameron, Kilmichael, Mr W. H. Edgar (103); Peninver, Mr D. M. M*Neil (103); Parish of Coll—Acha, Miss M. Tyre (100); Arinagour, Mr R. MacTaggart (100); Cornaig, Mr T. Johnston (100); Parish of Colonsay and Oronsay—Kilchattan, Miss J. Campbell (102) ; Parish of Craignish—Craignish, Mr J. Kay (101); Barbreck, Miss M. Ferguson (101); Parish of Cumlodden—Furnace, Mr W. G. M¢Kinlay (101) ; Parish of Dunoon and Kilmun—Ardentinny, Mrs M. C. Giffen (104); Dunoon Grammar, Mr W. Dock (104); Glenlean, ? (104) ; Innellan, Mr D. Ritchie (104); Kirn, Mr J. Connell (104); Rashfield, Miss J. Bruce (104) ; Sandbank, Mr A. M*Neilage (104); Strone, Mr W. Baird (104); Parish of Gigha and Cara— Gigha, Mr T. Scott (102); Parish of Glassary—Cairnbaan, Miss S. M¢Intyre (101); Glassary, Mr J. Pemmell (101); Minard, Mr G. Nicolson (101); Parish of Glenaray and Inveraray— Bridge of Douglas, Miss Gibson (101); Parish of Glenorchy and Inishail—Bridge of Orchy, Mrs Machaine (101); Cladich, Miss C. Russell (101); Dalmally, Mr J. Macdonald (101); Parish of Inverchaolain—Inverchaolain, Mr T. M*Nab (104); South Hall, Miss J. B. Fraser (104) ; Parish of Jura—Ardlussa, Miss M. B. Spiers (102); Knockrome, Mr G. H. Fisher (102) ; Small Isles, Mr W. Mehintock (102); Parish of Kilbrandon and Kilchattan—-Ardincaple, Miss A. Mackay (101); Luing, Mr C. Clubb (101); North Luing, Miss M. Orr (101); Parish of Kilcalmonell, Clachan, Mr J. Mackie (102) ; Whitehouse, Mr J. Ross (102); Parish of Kilcho- man—Gortan, Mr A. Mackay (102); Kilchoman, Mr A. R. Scott (102); Kilnave, Miss M. R. Hayes (102); Port Charlotte, Mr A. M*Dougall (102) ; Portnahaven, Mr N. Orr (102) ; Rock- side, Miss M. Ferguson (102); Parish of Kilchrenan and Dalavich—Ardchonnell, Mr J. M*Leod (101); Dalavich, Miss M. Smith (101); Kilchrenan, Mr W. L. Bruce (101); Sonachan, Miss J. G. M*Kenzie (101); Parish of Kildalton—Ardbeg, Mr H. Bisset (102); Glenegidale, Miss 48 Pigmentation Survey of School Children in Scotland M. Bell (102); Kintour, Mr J. Marnie (102); Oa, Miss MacDougall (102); Port Ellen, Mr D. McLachlan (102); Parish of Kailfinan—Ardlamont, Miss Simpson (102); Kilfinan, Mr J. MacCallum (102); Millhouse, Mr D. MeDonald (102); Otter Ferry, Mrs W. Stewart (102) ; Tighnabruaich,.Mr A. Barrett (102); Parish of Kilfinichen and Kilvickeon—Ardchevaig, Mr A. R. Campbell (100); Bunessan, Mr J. MeMaster (100); Creich, Mr A. Stewart (100) ; Erraid, Miss G. M¢*Kechnie (100) ; Iona, Mr Jas. Wood (100) ; Pennyghael, Miss C. L. Pagan (100); Parish of Killarrow and Kilmeny—Bowmore, Mr J. Bryce (102); Kiels, Miss M. E. Falconer (102); Kilmeny, Mr W. M°Fadyen (102); Mulindry, Mr D. MacBean (102); Newton of Kilmeny, Mr W. P. Cameron (102); Parish of Killean and Kilchenzie—Ballochintee, Miss J. M°Gibbon (103); Glenbarr, Mr W. Agnew (103); Kilchenzie, Mr W. M¢Culloch (108) ; Killean, Miss C. Livingston (103); Rhunahaorine, Mr W. Bain (103); Parish of Kilmodan— Kilmodan, Mr J. MacInnes (104) ; Stronafian, Mr P. A. Munro (104); Parish of Kilmore and Kilbride—Kerrera, Miss M. Rodger (101); Strontoiller, Miss F. C. Sinclair (101); Parish of Kilninian and Kilmore—Fanmore, Miss G. Warnock (100); Morinish, Miss M. Clark (100) ; Tobermory, Mr J. 8. Levack (100); Parish of Kilninver and Kilmelford—Kilmelford, Miss J. B. Robertson (101); Parish of Lismore and Appin—Balachulish, Mr A. M¢Callum (101) ; Bali- garve, Mr J. Wilson (101); Baligrundle, Mrs Campbell (101) ; Duror, Mr R. Macgregor (101) ; Glencreran, Miss M. M°¢Kenzie (101); Lettermore, ? (101); Port Appin, Miss A. MeGlashan (101); Strath of Appin, Mr D. Macpherson (101); Carnock, Glencoe St Mary’s Episcopal, Miss Janet Stewart (101) ; Parish of Lochgilphead—Ardrishaig, Mr A. Ramsay (101) ; Parish of Lochgoilhead and Kilmorich—Kilmorich, Mr J. B. Logan (101); Lochgoilhead, Mr W. Gilchrist (101); Parish of Morvern—Bunavullin, Miss H. Stewart (100); Claggan, Miss J. Robertson (100); Lochaline, Mr D. B. Fletcher (100); Parish of North Knapdale—Bellanoch, Mr A. Dixon (102); Parish of Oban ; Burgh, High, Mr J. Beattie (101) ; Parish of Saddell and Skipness—Carradale, Mr J. R. M*Innes (102); Saddell, Mr W. Jenkins (102); Skipness, Mr T. Johnston (102); Sperasaig, Mr J. 8. Barwell (102); Parish of Southend—Glenbreckrie, Mr R. Montgomery (103) ; Southend, Mr J. Morton (103); Parish of South Knapdale—Auchoish, Miss J. Campbell (102); Dunmore, Mr D. McArthur (102); Inverneil, Miss L. Mactavish (102) ; Ormsary, Miss K. Blair (102); Parish of Stralachlan and Strachur—Poll, Mr A. N. Sheridan (101) ; Stralachlan, Miss J. E. Munro (101); Parish of Strontian—Strontian, Mr D. Cameron (100) ; Parish of Torosay—Crogan, Miss C. M¢Kinnon (100); Kinlochspelve, Miss Mackinnon (100); Lochdonhead, Mr W. G. MacBean (100); Parish of Tyree—Cornaigmore, Mr D. MeKinnon (100) ; Hillipool, Mr G. M*Donald (100) ; Ruaig, Mr D. Gunn (100). COUNTY OF AYR. Parish of Alloway—Alloway, Mr J. Turnbull (31); Parish of Ardrossan—-Academy, Mr J. Butters (29); Eglinton, Mr W. Comrie (29); Parish of Auchinleck—-Auchinleck, Mr J. Henderson (26); Cronberry, Mr Jas. Hyslop (26); Glenmuir, Miss Mary Stuart (26); Lugar, Mr Wm. Hume (26); Ayr Burgh—Grammar, Mr Hy. Robertson (25) ; Newton on Ayr Academy, ? (25); Russell Street, Mr A. D. Murphy (25); Ayr Episcopal, Mr Jas. Scott (25) ; St Margaret’s, R. C., Mr L. Gemson (25); Parish of Ballantrae—Auchenflower, Mr J. M. Ferguson (32); Ballachdowan, Miss J. 8. Dale (32); Glenapp, Miss J. Leask (32); Parish of Barr—Rowantree, Mr J. Brown (31); Parish of Beith—Academy, ? (30) ; Greenhills, Mr T. Stevenson (30); Gateside, Mr J. J. Bone (30); Parish of Colmonell—Barrhill, Mr D. Millar (32) ; Colmonell, Mr A. Beattie (32); Corwar, Mrs Weir (32); Lendalfoot, Miss H. Gray (32) ; Pinwherry, Miss W. Holms (32) ; Parish of Coylton—Coylton, ? (31); Little- mill, Mr W. Guthrie (31); Parish of Crosshill—Crosshill, Mr Duncan (31); Kilkerran, Hillside, Miss M¢Creath (31); Parish of Dailly—Kilgrammie, Mr D. Taylor (31) ; Wallacetown Works, Mr D. Guthrie (31); Parish of Dalmellington—Benwhat, Mr A. McArthur (31); Lethan Hill, Mr D. Vallance (31); Parish of Dalry—Blairmains, Miss J. M¢R. Deacon (30); West End, J.B; TOCHER 49 Mr D. Campbell (30); Parish of Dalrymple—Dalrymple, Mr A. Lockhead (31); Hollybush, Infant, Miss Johnstone (31); Kerse, Mr A. Lyle (31); Parish of Dreghorn—Dreghorn, Mr Jas. Mair (28); Parish of Dundonald—Dundonald, Mr H. Gibb (28) ; Loans, Miss J. C. Brown (28) ; Troon, Portland, Mr W. Scott (28) ; Troon, St Patrick’s, Miss Murphy (28) ; Parish of Dunlop— Dunlop, Mr A. Brown (30); Parish of Fenwick—-Fenwick, Mr W. Brown (30); Parish of Galston—Allanton, Miss Hunter (28) ; Galston, Mr A. Young (28) ; Town of Girvan—Girvan, Mr M. J. Finlayson.(31); Girvan, H. G., Mr M. J. Finlayson (31); Parish of Girvan (Landward)— Assell, Mr H. Raeburn (31); Doune, Mr J. Eaglesome (31); Girvan, Mr D. Thomson (31) ; Burgh of Irvine—Bank Street, Mr R. Selkirk (28) ; Fullarton, ? (28); Fullarton, Loudon Street, Mr W. Mitchell (28); Parish of Irvine (Landward)—Annick Lodge, Mr J. Dunlop (28); Parish of Kilbirnie—Glengarnock, Mr R. Gray (30); Ladyland, Mr J. Fulton (30); Female Industrial, Miss Turnbull (30) ; St Bridget’s, R. C., Mr H. MeGrath (30) ; Parish of Kilmarnock (Landward) —Crooked Holm, Mr T. Duncanson (28); Grougar, Mr C. 8. Macdonald (28); Rowallan, Mr J. Clelland (28); Burgh of Kilmarnock—Academy, Dr H. Dickie (27); Academy H. G., Dr H. Dickie (27); Bentinck, Mr D. Walker (27); Glencairn, Mr Thos. Amos (27) ; Hamilton, Mr G. H. Innes (27); High Street, Mr G. Smith (27); West Netherton, 7 (27); Parish of Kilmaurs—Crosshouse, Mr J. Wilson (28); Kilmaurs, Mr D. McNaught (28); Parish of Kalwinning—Auchentiber, Mr H. Paterson (30); Eglinton District, Mr R. Brothertone (30); Kilwinning, Mr W. Blair (30); Parish of Kirkmichael—Kirkmichael, Mr J. Kirkland (31) ; Parish of Kirkoswald—Townhead, Mr T. Chapel (31); Parish of Largs—Fairlie, Mr H. Allan (23); Parish of Loudoun—Newmilns, Mr A. Hood (28); Parish of Mauchline—Crosshands, Miss C. Mitchell (26); Mauchline, Mr J. Campbell (26); Parish of Maybole and Maybole West Church—Cairn, Mr A. M. Nisbet (31); Ladyland, Mr J. 8. Porteous (31); Minishant, Mr J. Clark (31); Parish of Monkton and Prestwick—Monkton, Mr Jas. Howat (26); Prestwick, Mr W. Beaton (26); Parish of Muirkirk—Glenbuck, Mr J. Rodger (26) ; Wellwood, Miss Bella Ross (26); Parish of New Cumnock—Beoch Side, Miss MeLennan (36); Dalleagles, Mr A. H. Mackay (36); New Cumnock, Mr J. A. Wales (36); New Cumnock, R. C., Miss M. Connolly (36); Parish of Ochiltree—Ochiltree, Mr A. Andrew (26); Sinclairston, Mr A. Green (26); Parish of Old Cumnock—Garallan, Mr J. B. Wilson (26); Old Cumnock, Mr J. Dick (26); Skares, Miss J. Wilson (26); Old Cumnock, R. C., ? (26); Parish of Riccarton— Hurlford, Mr H. Andrew (28); Riccarton, Mr A. Inglis (28); Barleith, Miss I. Paterson (28) ; Parish of St Quivox—St Quivox, Mr A. Moody (26); Parish of Sorn—Auchencloigh, Miss Forrester (26); Catrine, Mr J. Monie (26); Sorn, Mr Ed. Robertson (26); Parish of Stair— Stair, Mr T. E. Scott (26); Parish of Stevenston—Kyles Hill, Mr Geo. Tait (29); Stevenston, Mr J. Taylor (29); Ardeer, Mr W. Reid (29); Parish of Stewarton—Kingsford, Mr W. Hastings (30) ; Stewarton, Mr A. L. Watt (30); Parish of Straiton—Loch Doon, Mr A. H. Campbell (31) ; Straiton, Mr W. MacMorland (31); Parish of Symington—Symington, Mr Jas. Currie (26) ; Parish of Tarbolton—Annbank, Mr J. M*Arthur (26); Parish of West Kilbride— West Kilbride, Mr J. G. Lyon (23). COUNTY OF BANFF. Parish of Aberlour—Aberlour, Mr W. Philip (90); Edenvillie, Mr D. R. Mackay (90) ; Craigellachie, Miss E. H. MeWilliam (90); Parish of Alvah—Alvah, Mr A. Stuart (86); Dun- lugas, Miss C. Simpson (86); Linhead, Mr J. H. Fraser (86); Burgh of Banff—Academy, Mr M°Pherson (85); St Andrew’s Epis., Miss I. Marr (85); Parish of Banff (Landward)— Headrooms, Miss Adamson (85); Hilton, Mr A. Scott (85); Parish of Boharm—Boharm, Mr R. Grant (90); Forgie, Miss M. Gill (90); Maggyknockater, Mr T. M. Smith (90) ; Parish of Botriphnie—Botriphnie, Mr J. Innes (87); Parish of Boyndie—Blairmaud, Miss A. Adamson (85); Boyndie, Mr W. Ledingham (85); Whitehills, Mr Geo. Wilson (85); Parish of Cabrach—Lower, Mr T. Robertson (87); Upper, Mr J. S. Burns (87); Parish of Cullen —Cullen, Mr W. Cramond (85); Parish of Deskford—-Deskford, Mr W. Smith (86); Parish of Enzie—Enzie, Mr W. F. Nichol (87); Port Gordon, Mr J. Reid (87); Parish of Fordyce Biometrika. Vol. v1. Supplement. 7 50 Pigmentation Survey of School Children in Scotland —Bogmuchals, Miss I. D. Craik (85); Brodiesord, Mr J. A. King (85); Fordyce Academy, Mr A. Emslie (85); Portsoy, 2(85); Sandend, Mr Henry Cumming (85); Portsoy Female Industrial, Miss Liddell (85); Parish of Gamrie—Longmanhill, Mr J. Carine (85); Macduff, Mr D, Renton (85); Macduff Murray’s, Mr J. Panton (85); Parish of Glenrinnes—Glenrinnes, Mr 8. Wilson (90); Parish of Grange—Grange, Mr J. D. Burns (87); Parish of Inveravon—Glenlivet, Mr T. Laing (91); Inveravon, Mr A. Myron (91); Morinish, Mr D. M. MacDonald (91); Tomnavoulin, Miss M. A. Henderson (91); Ballindalloch, Lady McPherson Grant’s, Miss E. 8. Myron (91); Tombae, St Mary’s, R. C., Miss A. Gordon (91); Parish of Inverkeithney—Easterfield, Miss Jessie Galt (87); Kirktown, Mr J. E. Taylor (87); Parish of Keith—Achanachie, Miss J. A. Henderson (87); Fife Keith, Infant, Miss J. L. Ander- son (87); Keith, ? (87); Tarry Croys, Miss M. 8. Robertson (87); The Glen, Miss J. Crane (87); Newmill, Mr A. Johnstone (87); Parish of Kirkmichael—Kirkmichael, Miss M. Gordon (91); Parish of Marnoch—Aberchirder, Mr D. Stewart (86); Culvie, Mr J. M¢lvor (86); Marnoch, Mr W. C. Shand (86); Netherdale, Miss J. Merson (86); Aberchirder Epis., Mr Morgan (86); Parish of Mortlach—Mortlach, 2(90); Parish of Ordiquhill—Ordiquhill, Mr A. Donald (86); Cornhill, Mrs J. M. Kemp (86); Parish of Rathven—Arradoul, Miss E. Johini (85); Buckie, Mr A. Muir (85); Findochty, M. J. Geddes (85); Rathven, Mr J. 8. Paterson (85); Buckie, Lady Cathcart’s Indust., Miss J. Cocker (85); Parish of Rothiemay— Rothiemay, Mr J. Geddes (87); Ternemny, Mr J. Mackie (87). COUNTY OF BERWICK. Parish of Abbey St Bathan’s—Abbey St Bathan’s, Mr E. J. Wilson (42); Parish of Ayton— Burnmouth, Mr C. M. Alexander (42); Parish of Bunkle and Preston—Preston, Miss Robertson (42); Parish of Channelkirk—Channelkirk, Mr H. M. Liddell (42); Parish of Chirnside—Chirn- side, Mr R. Kincaird (42); Parish of Cockburnspath—EKcclaw, Miss Nicholson (42); Parish of Coldingham—