Pot verre Weiner ne Nah an lino 0 tw fall ~ Nea Nea > — nite Hina Bathe ght Na Mh) can WTR HatN ERSTE Pst herhy aER ay MON PN Tas erin Ay Ue Ah ain ay ive PV Vcan han Gens} { an) : is ‘ \ iy ' i rc nN i ‘ ; ’ bn . ‘ . ' " i T . A ‘ vat Y i é 1 ' Baro TREK A A JOURNAL FOR THE STATISTICAL STUDY OF BIOLOGICAL PROBLEMS EDITED IN CONSULTATION WITH FRANCIS GALTON BY W. F. R. WELDON KARL PEARSON AND C. B. DAVENPORT VOLUME Iil JANUARY 1904 TO DECEMBER 1904 CAMBRIDGE AT THE UNIVERSITY PRESS LONDON: C. J. CLAY AND SONS, AVE MARIA LANE anp H. K. LEWIS, GOWER STREET NEW YORK: THE MACMILLAN COMPANY LEIPSIC ; BROCKHAUS BOMBAY AND CALCUTTA: MACMILLAN AND CO,, LIMITED [All Rights reserved] IFO 155 Sac a i @ Cambridge : PRINTED BY J. AND C. F. CLAY, AT THE UNIVERSITY PRESS. III. VIL. VIII. xT CONTE NAS: Memoirs. On the Result of Crossing Japanese Waltzing with Albino Mice. By A. D. DARBISHIRE . : : Graduation of a Sickness Table by Makeham’s Aad By JOHN SPENCER : : : : Preliminary Note on the Protective Value of Colour in Mantis religiosa. By A. P. DI CESNOLA Measurements of One Hundred and Thirty Criminals. By G. B. GRIFFITHS. With Introductory Note by H. B. DonKIn A First Study of the Weight, Variability, and Correlation of the Human Viscera, with Special Reference to the Healthy and Diseased Heart. By M. GREENWoopD, Junior Sui Massimi delle Curve Dimorfiche. Dal Dr FERNANDO DE HELGUERO Experimental and Statistical Studies upon Lepidoptera. I. Varia- tion and Elimination in Philosamia cynthia. By HENry EDwAaRD CRAMPTON On the Laws of Inheritance in Man. II. On the Inheritance of the Mental and Moral Characters in Man, and its comparison with the Inheritance of the Physical Characters. By KARL PEARSON . A Study of the Variation and Correlation of the Human Skull, with Special Reference to English Crania. By W. R. MAcDONELL On Inheritance of Coat-Colour in the Greyhound. By Amy BARRINGTON, ALICE LEE, and KARL PEARSON Note on a Race of Clausilia itala (von Martens). By W. F. R. WELDON : : : ‘ : : : Merism and Sex in Spinaz niger. By R. C. PUNNETT . 58 60 63 84 113 131 299 313 iv Contents XIII. Note on Mr Punnett’s Section on the Inheritance of Meristic Characters. By KARL PEARSON . XIV. On the Measurement of Internal Capacity from Cranial Circum- ferences. By M. A. LEwenz and Kari PEARSON XV. Etude biométrique sur les variations de la fleur et sur Vhétérostylie de Pulmonaria officinalis L. Par EDMOND GAIN . Miscellanea. (1) On some Dangers of Extrapolation. By Emity Perrin (i) On Differentiation and Homotyposis in the Leaves of Fagus sylvatica. By Kart PEARSON, with the assistance of MARION RADFORD (111) Albinism in Sicily and Mendel’s Laws. By W. F. R. WrELpoN (iv) A Mendelian’s View of the Law of Ancestral Inheritance. By KARL PEARSON (v) Onan Elementary Proof of Sheppard’s Formulae for correcting Raw Moments and on other allied Points. [EDrrortrAt.] (vi) On the Correlation between Hair Colour and Eye Colour in Man. By Karu PEARSON (vii) On the Correlation between Age and the Colour of Hair and Eyes in Man. From Notes by Dr Ginzo Ucuipa (vi) On the Contingency between Occupation in the Case of Fathers and Sons. By Emity PERRIN (ix) Ona Convenient Means of Drawing Curves to Various Scales. By G. Upny YULE (x) Albinism in Sicily—A Correction. By W. BAaTEson Plates. Parco (i) “Sun” and “Shade” Branches of the Beech . to follow p. (11) Backs of typical Beech Leaf Sprays . ‘ ; 4 Parr II. and Parr III. Plates (i) to (1). Whitechapel Crania to face p. (i) Normal Male Skull. W. 45. N. facialis. (11) a W. 45. N. lateralis. (i11) ; e W. 45. N. basalis. PAGE 363 366 398 469 471 106 106 216 (iv) Normal Male Skull. W. 45. N. verticalis. (v) 3 ‘ W. 76. N. lateralis. (v1) a - W. 76. N. basalis. (vil) . ‘ W. 76. N. verticalis. (viii) 3 2 W. 7101. N. occipitalis. (ix) és : W. 69. N. lateralis. (x) i : W. 163. N. lateralis. (x1) m 3 W. 163. N. basalis. (xli) o, * W. 163. N. verticalis. (xii) . _ W. 163. N. occipitalis. (xiv) * i W. 147. N. facialis. (xv) ” M W. 147. N. occipitalis. (xvi) Normal Female Skull W. 10. N. facialis. (xvii) - ¥ W. 10. N. lateralis. (xviil) e 55 W. 10. N. basalis. (xix) . ' W. 10. N. verticalis. (xx) e ” W. 18. N. facialis. (xx1) Rs ~ W. 18. N. lateralis. (xxi) E 5 W. 18. N. basalis. (xxill) 2 . W. 18. N. verticalis. (xxiv) = ys W. 18. N. occipitalis. (xxv) * 5 W. 7044. N. facialis. (xxvl) a - W. 7044. N. occipitalis. (xxvil) , . W. 149. N. facialis. (xxvill) ie - W. 149. N. lateralis. (xxix) 55 5 W. 149. N. basalis. (xxx) . . W. 149. N. verticalis. (xxxi) 5 5 W. 149. N. occipitalis. (xxxil) Special Skull. W. 7042. Ossicle of Bregma. (xxxlll) 3 uf W. 223. Ossicle of Lambda. (xxxiv) - is W. 226. Double Ossicle of Lambda. (xxxv) x 5s W. 217. Simple Interparietal. (xxxvl) i " W. 7096. ‘Tripartite Interparietal. Os pentagonale and Ossa triangularia all separate. (xxxvil) Special Skull. W. 218. Tripartite Interparietal. Contents only separate. (xxxvili) Special Skull. W. 219. Tripartite Interparietal. and right Os triangulare separate. Ossa triangularia Os pentagonale vi Contents (xxxix) Special Skull. W. 7052. Tripartite Interparietal. Os pentagonale and left Os triangulare separate. (xl) Special Skull. W. 221. ‘Tripartite Interparietal. Os pentagonale only separate. (xli) Special Skull. W. 231. —Plagiocephaly. (xli) fe Mi W. 7042. Bathrocephaly. (xiii) - re W. 7059. Bathrocephaly with Ossicles of Lambdoid Suture. Left Profile. (xliv) Special Skull) W. 7042. Bathrocephaly with Ossicles of Lambdoid Suture. (xlv) Special Skull. W. 7059. Bathrocephaly with Ossicles of Lambdoid Suture. Right Profile. (xlvi) Special Skull. W. 215. Frontal Process of Temporal. (xlvii) . . W. 214 Unilateral Precondylar Eminence. (xviii) ™ . W. 213. Bilateral Precondylar Eminences. (xlix) . s W. 229. Hamulus mea | Resehinsiehentes (1) a ie 6 W. 229. Hamulus lacrimalis Part IV. Plate (i). Spinax Niger. : : : : . to face p. 313 Plate (11). Auto-icon of Jeremy Bentham, Front Face : 5 393 Plate (i). Auto-icon of Jeremy Bentham, Profile. : , 393 Tables. Part I. Table (i). 100 Ordinary Criminals. : ; . to follow p. 62 Table (i) continued; and Table (11), 30 Lunatic Criminals 53 62 Part II. and Part III. Tables (i) to (viii). Measurements of 17th Century English Crania to follow p. 244 Subject and name indices will be issued every few years embracing several volumes. Votume III JANUARY, 1904 No. 1 BIOMETRIKA. ON THE RESULT OF CROSSING JAPANESE WALTZING WITH ALBINO MICE. By A. D. DARBISHIRE, Balliol College, Oxford. THE object for which the following experiments were undertaken was to test the validity of Mendel’s Principles of Heredity, which have recently acquired considerable importance, by becoming intimately involved in the question of the origin of species. The term Mendelian Principles is used in its widest sense, to include not merely the simple Mendelian phenomena of Dominance or Segre- gation, but the much more fundamental doctrine of gametic purity. MetTuHop oF DESCRIPTION. The method of description employed in this paper is the same as that used in the three reports on these experiments which have already appeared: the mice are classified, according to the relative extent of the coloured patches on a white ground, into six groups. Group 1 (Fig. 1) has more white and less extent of coloured patches than the normal waltzing mouse. The distribution of colour on a waltzer is shown in Fig. 6. I wish to draw special attention to the existence of this group, because Castle*, who quoted my second paper for another purpose, denies that any mice with less colour than a waltzer had occurred in my experiments Group 2 (Fig. 2) has about as much white as a normal waltzing mouse. Group 3 (Fig. 3) has less white (i.e. greater extent of coloured patches) than a waltzer. Group 4 (Fig. 4) has still less white, and leads on to Group 5 (Fig. 5) which has no pure white, but the belly is whitish, not grey. Group 6 contains mice whose bellies are nearly the same colours as their backs. * «Mendel’s Law of Heredity,” Proc. American Academy, Jan. 1903, pp. 583—48, Biometrika 111 1 2 Result of Crossing Japanese Waltzing with Albino Mice The individuals of each group can also be classified according to the colour of the coloured patches. Class a = yellow. Class b = fawn yellow. Class 6 pal oe , Le. that of the house-mouse. Class d = dark wild colour Class e = black. Class f =“ lilac” = pale blue grey ; at present only exhibited by the offspring of hybrids. Class g = chocolate. The letter “p” after a mouse indicates that it has a pink eye, the letter “W” that it waltzes; to take two examples, 2b( pW) is a waltzer, 6d or 6c is a house- mouse. I propose to defer a detailed discussion of the nature of these categories to a later date: but I hope the foregoing remarks will leave no doubt in the reader’s mind as to what is meant by each class; in fact, all the classes except the first two explain themselves. JI am sorry the word fawn was used’ in my second paper, because it is used to denote both a and b by mouse fanciers; @ is simply a yellow colour ; b is yellow, with, in many cases, black in it; at any rate, there are inter- mediate stages linking b with ¢ (ie. pale wild), whereas a is not so linked with ¢ except through b. In cases of intermediate colours the mice are entered 5bc and so forth: a minute discussion of the skins (which are kept) is deferred. METHODS OF REGISTERING. The method of keeping, registering and cataloguing which I now pursue has gradually grown up of itself in the course of a year rather as a result of necessity than by deliberate invention on my part. Lack of a proper method of registering at the beginning of the experiments rendered many of the dealings with mice a matter of great difficulty ; and I suggest that if the reader is taking up work of this kind he will not suffer from a similar inconvenience if he adopts a method similar in principle to that which I am about to describe. During the latter part of the experiment there were some fifteen hundred mice in the room set apart for the purpose ; and it was quite a simple matter to look up in the catalogue book any mouse in the room, and wice versd, to find in the room a mouse of any given ancestry. The method is very simple, and was based on a system of cross-reference, which enabled one to refer (as already stated) from the books to the mice, and from the mice to the books. The following account, then, will be of little if any interest to the reader who does not intend to do similar work. A. D. DARBISHIRE Fig. 2 . 1 Fig. Fig. 4. Fig. 3 5 ‘ | eee Fig, Fig. 5. 4 Result of Crossing Japanese Waltzing with Albino Mice Let us imagine that our object is to make crosses between albino and Japanese waltzing mice, and that we are provided with a stock of waltzing mice which we know to breed true, and of albino mice of authentic pedigree. Two sorts of books are necessary—(i) a book recording the matings, and later on (ii) an illustrated catalogue. The entry of the cross in the mating book is quite simple. The date underneath the description refers to the day on which the mice were put together ; and the occurrences which come to pass on the subsequent dates are also recorded. Cross 1. ? Albino (pure bred) from Mr Steer. Jd Japanese waltzer. Dec. 24, J removed, Jan. 10th. 8 young born, Jan. 16th. ? removed, Feb. 8th. Young sexed, Feb. 25th. The offspring are catalogued in two places for reasons which will shortly be explained: first they are catalogued as soon as the colour of their eyes and coat is discernible ; this might quite well be done in the mating book ; but I find it more convenient to have a separate book (First Catalogue) for the purpose: the coat- colour and eye-colour of each mouse are entered directly they can be plainly seen, so that a minimum number of records is lost through cannibalism or disease: nothing else is recorded; the sex is not (for it cannot be) determined. Such an entry appears as follows :— Cross. 5¢, de.d5ce#3c, 2c12c; lex. 20): The entry in brackets gives the date on which the mice were catalogued ; if this is not done and a note is made in the mating book that a young one of a certain description has escaped or died, doubt would arise in the mind of the observer as to whether that mouse had been catalogued or not. When the young are sexed they are entered in the illustrated catalogue, which, beside the record of matings (already described), is the second kind of book necessary for the observations. In this book each mouse is given a name : thus the first mouse which happens to be described, in the litter of the imaginary cross which we entered in the mating book above, is 1*', the second 1*", and so on. The “a” signifies that the individual belonged to the first litter produced by those parents; individuals of the second litter produced by the same parents would receive the names 1°}, 1%, 1>** ete. Roman numerals are used to indicate the individuals of the family because they are never likely to become too large to be convenient, for litters very rarely exceed, and, in fact, very seldom attain, the number of ten, and 1** is quite convenient to write. In cases of albinos and self- coloured mice, in which the tail is uniformly covered with pigment, I have merely written the description of the mouse, as a picture of such a one would A. D. DARBISHIRE 5 be superfluous: but in all cases of piebald mice I have made a drawing of the animal as seen from the right, left, and dorsal aspects by painting the colour- pattern on outline drawings of mice (printed for me by Messrs Palmer and Howe of Manchester) kept for the purpose; and in cases of completely coloured mice with incompletely coloured tails I have merely drawn one view to show the arrangement of colour on the tail. All mice, which have reached the age at which they are sexed, have been described in this manner. Now suppose that one wants to pair these hybrids (First Crosses) together ; one proceeds in this way. Another mating book has to be used to enter the matings of the hybrids (to avoid hopeless confusion); and the numeral which indicates a cross or pair is preceded by some letter (such as A) to distinguish it from the same number which refers to a cross between a waltzing mouse and albino. I have called these pairs or crosses H, H,, etc. The individuals paired are entered thus in the mating book : A, 2 Taiii fe March 9. Against 7*" in the illustrated catalogue book H, is written, so that one is enabled to refer from the ancestry of a mouse to its place in the room (for of course all pairs of the same kind, i.e. H’s for example, are kept together). When- ever 7°" is mated again to form another pair or cross, the number of each succes- sive pair in which it is concerned is put after it, so that if one wants to find 7° one looks at the last number against its name in the mating book. The value of the illustrated catalogue lies in the fact that in many families the brothers and sisters are so unlike that when they are again looked up reference to the catalogue will convince one that one is dealing with the right mouse: of course they are identified by the number on their cage, so that their picture is not a necessary means of identification, but it is an additional safe- guard against error. Fig. 7 represents a sample page of the illustrated catalogue on a reduced scale. 6 Result of Crossing Japanese Waltzing with Albino Mice DESCRIPTION OF PARENTS. Japanese Waltzing Mice. These animals are distinguished from ordinary (say albino) fancy mice by their smaller size, by their extreme lability to disease, but especially by their curious habit of spinning round, by the ceaseless movement of their heads, and by the retrograde motion of the body when not waltzing. The mice used by me had pink eyes, and bore patches on the body of colour indicated by b: the range of variability in colour was practically nothing; that of the extent of the coloured patch was small: accurate pictures have not been kept of all of them because the simple Mendelian statements, which it was the original object of the experi- ment to test, did not lead to the expectation that minute study of these mice would be necessary; the exact distribution of the colour on the waltzing parent is therefore not known in all cases; in those cases in which pictures of the waltzers were made, a classification of them has been made into (a) waltzers with less colour than Fig. 7, and (8) waltzers with more colour than Fig. 7. All the waltzers used were of pure strain. Albino Mice. In the previous experiments of this kind (conducted by von Guaita) the albinos used were of uniform ancestry, being in-bred for 29 generations ; that is, they were also pure-bred. I obtained my albino stock chiefly from Mr Steer in England, from M. Jeunet in Paris, and from Herr Fockelmann in Hamburg. From the pure-bred mice which I got from Mr Steer I raised in-bred pure-bred albinos, and by mating the foreign mice with English ones I obtained out-bred pure-bred mice. An out-bred pure-bred mouse would have this ancestry for example : $ trom Jeunet x ¢ from Steer ? from Fockelmann x ¢ from Broxup a Baa cs g i > | ~ Albino (out-bred pure-bred) Out-bred cross-bred mice were obtained by crossing black or yellow mice with albinos—in-bred cross-bred were obtained by waiting for a litter, from such a cross, in which there were both albinos and blacks (or yellows), then pairing a black mouse with his white sister, and so on for many generations. A list of all the mice bred during the experiment is given in Appendix L, Tables A to H. THE HYBRIDS. Before describing the results of crossing albinos and Japanese waltzers, I think it is advisable to define clearly the terms which I shall use to describe each generation. The offspring produced by crossing a Japanese waltzer with an albino I propose to call the hybrid, simply ; the offspring of these hybrids paired together, A. D. DARBISHTRE 7 children of hybrids; the offspring of the hybrids crossed with albinos, children of hybrids and albino. These terms are perfectly simple, but it is impossible to be too explicit about terms such as these. The hybrids are invariably dark-eyed; their coat is never completely white, and they never waltz; the two facts about them which strike one immediately are (i) that whereas the parents are all like the other members of their race, the hybrids are by no means all alike ; they exhibit much variability in coat-colour and in the distribution of their colour; (ii) that not only do they differ among themselves, but they are absolutely different from either parent; the character of neither parent can be said to be dominant over the other in the sense that it exists in the hybrid to the exclusion of the other, which is what Mendel meant by dominance. To make up, however, for this deficiency in dominance, the characters of both parents are recessive, in so far that neither of them appear in the hybrid. This is plainly not a case of simple Mendelian dominance, though I am perfectly ready to admit that it may be an instance of the mysterious properties of heterozygotes, confessing at the same time that I do not see how the admission of this fact helps. It seems to me that we have not got any further in this direction than Darwin had when he called phenomena of this kind reversions to ancestral condition. The eye-colour and the amount and nature of coat-colour are not the only new characters which appear in the hybrids: there is a correlation between the size of the patches of colour and the intensity of the colour in such a way that the lighter the colour the more space it occupies. The measure of this correlation is between — 02 and —03. This character of the hybrids is clearly absent in the parents; for, while the waltzers vary slightly in the amount of colour which they possess, the colour itself does not vary: the albinos have no colour at all*. We have up to now merely stated the fact that the hybrids are variable; it remains to try to account for this variability. How Mendelians will account for it I do not know, but I have facts to show that it is due to ancestry of the parent forms. Fraternal correlation. From the Mendelian point of view the families should be all similar; and this would lead to fraternal correlation =0. Fraternal correlations are, however, remarkably like those observed in fraternities which are not cross-bred; taking either the colour of the coat or the extent of the white patches as the character to be examined, we find a fraternal correlation very nearly equal to 0:5. This shows that there is (1) a sensible range of variation within each family, and (2) a con- siderable range in the mean characters of different families. The variation within the family seems to me incompatible with any Mendelian hypothesis which does * The obvious want of “normality” in the distribution of coat-colour and of whiteness in all the generations observed renders the determination of the correlation coefficients very difficult. The process adopted, which is due to Professor Pearson, will be explained and justified in a future paper by him. 8 Result of Crossing Japanese Waltzing with Albino Mice not involve a complexity in the constitution of the waltzing parent, leading to the assumption that its coat-colour depends not on one allelomorph, but on a number. This might be conceivable, but it would involve a reduction in the proportion of albino young among children of hybrids incompatible with that observed in the next generation. We see therefore that characters of hybrids are not compatible with, still less explained by, Mendelian principles ; it still remains to account for them. Parental correlation. If we classify the hybrids into those in which the albino parent was pure- bred, and those in which it was cross-bred, i.e. in which it had some pigmented ancestors, and determine the correlation between the colour of the young and the purity of the albino parent, we find that it is about — 0°15, and the correlation between the amount of whiteness in the hybrids and purity of albino parent about —02. These are quite sensible correlations; they show that there is a distinct relation between the pigmentation of the hybrids and of the ancestors of their albino parent : they show therefore that the albino cannot be said to be gametically pure in respect of its whiteness, but that in order to predict the character of its young a knowledge of its ancestry is necessary. The character of the hybrids is therefore influenced by the ancestry of the albino parent: but it is also affected by the character of the waltzing parent. As has already been stated, pictures of all the waltzing parents of hybrids have not been made, but the waltzing parents of 210 out of the 340 hybrids obtained are represented by accurate diagrams, and these have been divided into (a) those with less extent of coloured fur than the mouse figured in Fig. 1, and (8) those with more; from waltzers of category (a) 113 young have been produced; and from (8) 97. The coat-colour and degree of whiteness in these young is shown in Tables IV. and V. (page 38). It will be seen that there is considerable correlation between the amount of white in the waltzing parent and that in the resultant hybrid. Table V. shows the correlation between coat-colour of hybrids and whiteness in their waltzing parent. In both these characters the coefficient of parental correlation is very nearly }. The amount and nature of the colour of a hybrid are therefore not constant, but exhibit great variability. (a) The hybrid does not show dominance of the character of either parent, and (0) its variability is sensibly correlated, not only with the actual character of the “dominant” parent, but also with the character of the ancestry of the “recessive” albino parent. Whatever theory these facts are to be reconciled with, I maintain that it is not with the theory of gametic purity. How far they are reconcilable with other theories of heredity is a more difficult question. In order to find out whether the results obtained are in accordance with the law of ancestral inheritance, as stated by Pearson (cf. Biometrika, Vol. 1. pp. 211-229), it would be necessary to examine more closely than is here possible the effect produced upon all the coefficients of parental, grandparental, and other ancestral correlation, and upon the paternal correlation by the rigid selection of A. D. DARBISHIRE 9 parents which has taken place in this as in all other hybridising experiments. These results are extremely complex, and cannot be predicted without long and difficult enquiry ; some of them have, however, been examined by Pearson (“ Mathematical Contributions to the Theory of Evolution,” Phil. Trans., Vol. 200 A, 1902), who shows that “sexual and natural selection can sensibly modify the intensity of inheritance as measured by the coefficient of correlation; the former tends to raise, the latter to lower its intensity ” (p. 43). The original statement embodied by Galton and Pearson in the Law of Ancestral Heredity relates to a population in which two conditions hold, namely, (i) all mating is at random; in other words the correlation between the characters of male and female mates in any generation is 0, and (ii) all the individuals in the generation have an equal chance of producing young. Now it is a fact, which is often forgotten, and on which I wish to lay great emphasis, that in the experiments described, and in all cases where two races or breeds are systemati- cally crossed, the first of these conditions is deliberately destroyed, and a process of assortative mating is performed, such that the coefficient of correlation between parents is given the value —1 instead of zero. Thus, in the present case, if we know that the father of the hybrid is an albino, we may certainly infer that the mother is not, and vice versd. The effect of this perfect negative correlation between the parents must be to reduce the coefticient of correlation between parents and offspring to 0 (ie. to destroy the correlation altogether) in every case in which the results of reciprocal crosses are identical. This may be readily seen by a simple illustration: if we call waltzers with more colour 8, and with less a, and the albino parents A, and if we write the female first, the possible unions are : aA, BA, Aa, Alp: And if reciprocal crosses produce the same results, the offspring of aA and Aa will be identical, as will those of 8A and AS. Now suppose that the pairs aA or Aa each produce a offspring of one kind, b of a second kind, while the pairs BA or AB produce ¢ young of the first kind and d of the second: if we make a table of the correlation between (say) maternal character and character of young, it will have the form: ° Young. , Tetley (a+b+c+d) (a+b+e+d) Totals | 2(a+e) | 2(b+d) | 2(a+b+c+d) Biometrika 111 2 10 Result of Crossing Japanese Waltzing with Albino Mice And since every measure of association or correlation becomes zero with the difference of the products of diagonally opposite squares of such a table, we see that whatever measure be adopted must in this case give a value = 0, since the difference of the cross products = (a + c)(b+ d)—(a+c)(b+d)=0. It is of course evident that this important result 1s a necessary arithmetical consequence of the way in which the parents have been mated and of the identity between reciprocal crosses; it does not depend on any theory of the nature of inheritance, and it involves no statement about the mean character of the young produced; the young may be intermediate between their two parents, or exactly like one or the other, or wholly unlike both. A further effect of breeding experiments, which involve sudden (and generally great) changes in the correlations between male and female, is a condition of instability during the first few generations. A race may become stable with any constant amount of assortative mating, but a sudden change results in a condition of instability, making it peculiarly difficult to discuss those first generations which are too often the only experimental data available. These considerations, usually forgotten by those who criticise the law of ancestral inheritance, must be carefully borne in mind by anyone who wishes to realise the questions actually at issue. We have seen that a process of crossing, such as that performed with the mice described, involves a total absence of correlation between parents of either sex and offspring if the individuals of either race are chosen with equal frequency as male and as female parents. It must be pointed out that many of the tables which accompany this paper are not tables showing correlation between all parents of one sex and their offspring; but tables of correlation between all parents of one character, whatever their sex, and their young. An examination of the full list of hybrids given in Table A, Appendix I., will show that the results of reciprocal crosses are so nearly identical as to justify the neglect of sex in the treatment of the data: a table of the correlation between the coloured waltzing mice or the albino mice and their hybrid young such as any of the Tables IV.—VII., may therefore be considered to give approximately the same result as if each referred to half the whole crosses from random unions between waltzing mice and albinos—that half namely in which all the parents are of one sex. € Such a way of regarding the tables is at best only an approximation to the truth ; a fuller discussion of the parental and indeed of all correlations observed during the experiments must be published later: in the meantime the present way of regarding them may be useful as a preliminary test of their compatibility with the law of ancestral inheritance. On the view suggested Tables VI. and VII. may be regarded as showing the result of two operations; it may be considered that first one parent has been — 1s A. D. DARBISHIRE 11 rigidly selected and that secondly the coefficient of assortative mating between this parent and the other has been made equal to —1. By this supposition we are enabled to apply a formula provided by Pearson (Phil. Trans. Vol. 200 A, 1902, pp. 39—40). Fig. 8. If we could make a diagram showing the frequency of any character, coat- colour or other, among mice in general, we may assume that the result would be something like Fig. 8; and the albino mice would be represented in relative frequency and position by one small strip (say A) of such a diagram, the waltzing mice by another small strip (say B). Before the experiment began each set of mice, albinos and waltzers, formed "a separate community, the individuals mating together, either at random or not, and having a standard deviation different from that of mice in general; the assortative mating within these groups we may call 7,,; and let us call the ratio between the standard deviation of albinos and that of mice in general y,, the ratio between that of waltzers and that of mice in general py. Now calling 73, 7; the coefficients of correlation between normal male and female mice and their young, and calling o, the standard deviation of filial mice in general resulting from unselected unions, we have to find the relations between these quantities and &,, &,;,, the standard deviation and parental correlation of the filial mice resulting from a cross, in which assortative mating has been carried so far that the coefficient of correlation between parents, which we will call py, is equal to—1. In the memoir quoted, Pearson has shown* that these quantities are connected by the following relations: Writing for brevity _ Viz — T3Vie if) = 5 ety og — T13 Tie and Bos = eee . — 12 * Pearson’s investigation is not strictly applicable to the present case, because he does not consider the long-continued selection of parents in past generations involved in the statement that the races used are pure. 2—2 12 Result of Crossing Japanese Waltzing with Albino Mice we have >a! =o; {1 am Bas? (1— }”) — Bis (1 = fl) 2 ("12 — Bis bi [) B: Bs}, Dar iis— Os iris a al es Hl) Bis — (Te — Pie fs) Bats Now we are proceeding on the assumption that in the experiments under discussion the two coefficients of parental correlation 7; and r,,; are equal; we may therefore suppress their suffixes and write each =r; further, we may express the purity of the original races used by writing for each of them 7», the coefficient of assortative mating, = 1. We have then Tal nae (Gave ee EG eS ee 91 Bos = Bas ad and our formulae become Si Be aes eae ele i ) 43 = 93 4 fb 4 Pe A ( Piz Pi Ma and Te 1 a. Tr 1 Saar 9 Dy > i (om \r = ( » pa) a ( x Hs) iv f = ie ‘ "Patel é; Now suppose the suffix 1 to denote the parent whose correlations we aré in- vestigating and let us first examine the waltzing parent, so that the suffix 2 denotes an albino; we may fairly say that the ratio of the standard deviation of coat-colour among albinos to that of mice in general = 0, and we have for A, the correlation between waltzing mice and their hybrid offspring, Tha i 2 — 1 -Fa—me) 5 Tha Ree 2 and we see that the value to be expected depends (1) on the correlations between parent and offspring in those simpler cases of random mating first dealt with by Galton and Pearson in the Law of Ancestral Heredity, and (ii) on sy, the ratio between the standard deviation of the selected race of waltzing mice and that of the general population from which they are descended. We have no means of evaluating «4, in the case of coat-colour, but we know that it is small. We may A. D. DARBISHIRE 13 fairly assume for r the value so often found by Pearson and his pupils, and we will therefore write 7 = 4; so that we have which may clearly take a great number of values according to the value of p, ranging from 0 when p,=0 to 1 when y,=%. We have found the correlation between a variable group of selected parents, the mates being invariable. To find the correlation between these invariable mates and their offspring we must write 4, =0; and we have, remembering that p, = — 1, Tee OT 2g Ras = os \" ~39° 9 ae 5 P| , or hn =o; es Hh =-7% ; 2 2 p2 2 and Ss a; {1 mes me ’ ay or Ry = 2 a an Tis 1 eno VA oe and writing r = 4, we have ais 4 Ris —_——. ee Be 4 16 In the attempt to determine correlation between the invariable coat-colour of an albino mouse and the colour of its young, we meet with the difficulty that the correlation coefficient takes the indefinite form - and cannot therefore be directly evaluated. The only character of an albino connected with its colour which can be evaluated is ancestral purity or impurity, that is the absence or presence of pigmented individuals in its ancestry ; and if the albinos be classified into pure and impure it is found that the correlation between the presence of pigment in their ancestry and the amount of whiteness or the depth of colour in their hybrid children is invariably negative (cf. Tables VI. and VII.). On any theory of gametic purity the correlations should of course be zero; they are in fact of quite significant magnitude, and considering the probable error of the method adopted they are not unlike. The values obtained are : Between purity of albino parent and (a) Amount of white coat in hybrid — 0°21 (b) Colour of coat : : . — 016 the differences being well within the probable error of the method. 14 Result of Crossing Japanese Waltzing with Albino Mice It is not suggested that the remarks here offered prove an agreement between the results obtained and those which follow from the law of ancestral heredity. It is contended that the experiment confirms a result, already obtained by Cuénot, that the ancestry of albinos is a factor in determining the characters of the young produced when albino and coloured mice are crossed; it is contended that this result makes it impossible to regard albinism as a character which is transmitted in a state of “gametic purity” by every individual which exhibits it; and therefore since the ancestry of albinos has to be taken into account in predicting their behaviour when crossed, some law of ancestral heredity must be formulated. The present data do not enable us to determine the correlations between parent and offspring with sufficient accuracy to say whether the Galton-Pearson law will fit this case as it fits so many others; but they do enable us to say that the sign of these correlations—the first negative coefficients of direct parental inheritance yet published—is in accordance with that law, and that the results obtained do not demonstrably contradict it m other respects. OFFSPRING OF HYBRIDS, Hybrids have been paired together or crossed with albinos; a third group of unions between hybrids and extracted albinos may perhaps be treated as belonging to this generation. The results of these three kinds of unions will be considered separately. Offspring of hybrids paired together. The unions of hybrids gave altogether 555 young; which were divisible into three groups according to the characters of the eyes and coat: these were Albino : : : : » 13% Coloured or piebald with dark eyes 287 or 284* Coloured or piebald with pink eyes 131 or 134 555 Dividing these mice according to their mode of walking we find that there are Waltzing. j : : : 97 Normal : F ’ : . 458 555 It is clear that the albinos occur in this generation with a frequency indicated by a purely Mendelian theory of albinism regarded as a simple unit character, * There is unfortunately a doubt concerning the eye-colour of three mice; these are all lilac in colour, and I am practically sure that they had pink eyes. I have never observed a lilac mouse which had dark eyes; the omission of the letter p after the lilac mice catalogued in my second paper (Biometrika, Vol. 1. Part 2, pp. 168, 169) is due to inadvertence in proof reading. A. D. DARBISHIRE 15 allelomorphic to a single unit character in the waltzing race; that hypothesis leads us to expect that a quarter of the offspring of hybrids paired together will be albinos; and since 555 = 138°75, the observed result is in excellent accord with it; the difficulty in this, as in all attempts to apply Mendel’s hypothesis, is to discover what are the unit characters concerned. In the preliminary account of the experiment it was evident that the pro- portion of pink-eyed individuals, with colour in the coat, was also nearly }; the number now observed, namely at least 131 and possibly 134, is also a fair approximation to a quarter. So far then the results are not inconsistent with the truth of Mr Bateson’s suggestion (Nature, March 19, 1903) that the character allelomorphic to albinism is pink eye with colour in the coat. Using Mr Bateson’s original notation and denoting albinism by the symbol G, pinkness of eye with some colour in the coat by the symbol G’, the generation is at first sight fairly represented by the formula GG + 24G’ + GG’ where GG’ represents a heterozygous union between the albino and its allelo- morphic element—resulting, for some reason which the Mendelian hypothesis does not provide, in a dark-eyed mouse with a coat-colour variable and generally unlike that of either pure parent. The difficulties of this hypothesis are, however, great, even when we confine our attention to the frequency of the various kinds of individuals in the group, without considering the ancestral and fraternal correlations. In this as in the preceding generation the variability of the dark-eyed mice (heterozygotes of Bateson’s hypothesis) is so great that it is impossible to regard each of them as resulting from the union of similar Mendelian elements; and the relation between pinkness of eye and coat-colour is in the same way inexplicable on the view that there is only one kind of element 6’. The 131 pink-eyed mice are all of colours a, b, or f, that is yellow, fawn-yellow, or lilac; and these must on any Mendelian view represent more than a single kind of gametic element ; but if more than one such element be present, the original waltzing mice must have contained more than a single kind of unit G’, and we have to consider Mr Bateson’s second hypothesis (Nature, May 14), which is that in the formula already given the symbol G’ must be regarded as denoting any one out of a series of different allelomorphic units, each leading, when mated with its like, to the production of a pink-eyed mouse with some colour in its coat. The hypothesis which involves the smallest number of kinds of elements is that one of the colours a, b, or f is a compound character resulting from the union of the other two: we should then have to consider the three kinds of pink-eyed mice with colour in the coat as of different gametic constitution; if we regard yellow and lilac as “pure,” we should have to regard the yellow pink-eyed forms as “ pure dominants,” say of constitution G’G,’, the lilac pink-eyed forms as pure, and of 16 Result of Crossing Japanese Waltzing with Albino Mice constitution G,'G,, the fawn-yellow pink-eyed forms being heterozygotes of composition G,’C,. This hypothesis fails in several ways to meet the facts; and since the objec- tions to this apply with greater force to any Mendelian hypothesis involving a larger number of allelomorphic units, it is worth while to consider them in some detail. The two kinds of elements G,’ and G,’, which are here assumed to be manifested in the pink-eyed young with coloured coats, must be derived from the waltzing grandparents, for the hypothesis of gametic purity at once excludes any attempt to derive them from the albino ancestors: hence either each original waltzer used must have been a heterozygote of composition G,'G,’, or two kinds of pure waltzers G,'G/ and GG,’ must have been employed. I am convinced that neither of these consequences of the hypothesis considered is true. Two mice of constitution G,/G,' paired together should have given young of character and relative frequency indicated by Gy’ Gy! + 2G'Gs! + Gy Gy’, so that all three of the colours observed among the pink-eyed offspring of hybrids must have appeared among the offspring of waltzing mice paired together. Now I am aware that lilac and white waltzing mice are bred by dealers, and I am familiar with their characters ; I am absolutely sure that no one among the many young bred from the waltzing mice used in these experiments was lilac in colour. The second hypothesis that two kinds of waltzing mice were employed involves the belief that one of these was lilac ; and this is also untrue. The known history of the waltzing mice used is therefore incompatible with the view that a and f (yellow and lilac) represent pure gametic elements of which b (fawn colour) is the heterozygote. It is similarly impossible to regard a or f as a character of a heterozygote, b and the remaining character being pure ; for this hypothesis also would involve the appearance of lilac individuals in a quarter (or in the whole) of the young produced by waltzing mice bred together. The behaviour of the waltzing mice when bred together is alone sufficient to destroy the validity of any hypothesis, involving numerous elements G’, which does not depart from Mendel’s doctrines. Mr Bateson has already proposed (Nature, April 23, 1903) to regard the waltzing mice used as heterozygous; if he has once refused to accept the state- ments as to their purity he or others may well do so again. Let us therefore see what happens under these circumstances. The hybrids produced by pairing a heterozygous waltzing form ,'G,’ with a homozygous albino GG will be of two kinds, GG,’ and GG,’ ; it is said that these will be dark-eyed and have some colour in the coat, but at present there is no means of distinguishing between them: all we know on this hypothesis is that the hybrids are of two kinds which are present in equal numbers. These hybrids, being indistinguishable, will be paired at random by any experimenter; so that the offspring of hybrids now considered A. D. DARBISHIRE ike will result from unions of three kinds, of which one will probably be twice as frequent as the other; there will be— GG, x GG giving GG +244) + GG, 2(GG/xGG/) , 2{4464 G4 + GG + G/G,}, GG GG. \; GG + 2GGY + GG, the offspring of hybrids being a series of individuals represented in composition and in relative frequency by AGG + 4GGY! + 4GG.’ + GY'GY + 2G7G.' x GG, where all the zygotes of constitution G’G’ have pink eyes and some colour in the coat. The sum of these is a quarter of the whole population, and we have seen that this is compatible with the observed result; but the three colours in the coat should occur with relative frequency 1: 2:1, or among the 131 (possibly 134) individuals actually found there should be if we call a and f G, and G, Gl Gators oes 32°25 instead of 19 observed. GEG wien: 6450 P 80 observed. GAG ies 32:2 be 32 or 35 observed. Taking either of the possible numbers of pink-eyed lilac mice we find that these results are not impossible on the hypothesis put forward, but the odds against results so divergent as these or more so are about 60 or 70 to 1. The distribution of pink-eyed young might therefore, if not very plausibly, be accounted for by a purely Mendelian hypothesis if that hypothesis did not involve the appearance of lilac individuals in the offspring of pure-bred waltzing mice when paired together. The absence of such individuals might be explained by a departure from the Mendelian statements such as that made by Bateson in several cases, and it might be assumed that the pure waltzing mice have their eye-colour and coat-colour determined by a compound allelomorph (G1 + G,/) not resolved into its components during gametic-formation in a pure-bred individual. This view is consistent with the behaviour of the pure waltzing strain, but it does not lead to the observed frequencies among the offspring of hybrids. The hybrid zygote will on this view be of constitution GG,’ + GG’; and two such hybrids when crossed will give in every 16 young GE -+GE woven once GG +GG@/ ...... twice GG 2 GGe sus: twice GGG siess four times GOGH -2GGs aes twice GGy + GA' Gy fesse: twice GiGi EGa Gs .cieee once GE -4EGYGY oocses once GQ GEGy wines once Biometrika 111 3 18 Result of Crossing Japanese Waltzing with Albino Mice and a zygote of elements G,’ only, or G,’ only can never be produced without assuming that remarkable elimination of some elements from every gamete suggested by Mr Bateson (Proc. Camb. Phil. Soc. xt1.), and so treating the phenomena of colour inheritance in a manner not only foreign to all Mendel’s conceptions, but leading to obvious absurdity if applied to any set of characters other than colours. A further difficulty involved in any of these hypotheses is the correlation between coat-colour and eye-colour. Pink eyes are confined, as has been said, to mice with yellow, fawn-yellow, or lilac coats, and all lilac mice whose eye-colour is certainly known have pink eyes; but dark-eyed mice with yellow or fawn- coloured coats occur in this and in the preceding generation, and their presence is difficult to explain on either of the hypotheses examined. The difficulties we find when we try to describe the various classes of indi- viduals found among the offspring of hybrids are increased when we consider the great variability both in the colour of the coloured patches and in their extent among the individuals of any class, the amount of which may be gathered from Tables I.—VII. The correlations between the various characters exhibited by the offspring of hybrids and the characters of their ancestors are quite inexplicable on any hypothesis involving the purity of the albinos. The correlation between indi- viduals of this generation and the purity or impurity of their albino grandparents— that is the measure of the effect of ancestral pigmentation transmitted through the albino parent—is evident from Tables XX.—XXIII. These correlations are all negative,—the sign, taking the scales in the directions given in the tables, showing that the amount of whiteness is less among the individuals descended from pure-bred albino grandparents, the coat-colour itself being darker ; so that the relation between the albinos used in the original cross and the offspring of hybrids has the same sign as that between the albinos and the hybrids them- selves; the correlation, however, 1s apparently larger, instead of being smaller as might have been expected, the value of r for both colour and whiteness being about —0°3 (Tables XX., XXL). A correlation so large as this is far beyond the probable error of the determination, and it is of course absolutely fatal to any theory which involves the “ gametic purity ” of the albinos, The only character of the pure-bred waltzing grandparents which varies enough to permit of its correlation with the offspring of hybrids being deter- mined, is the extent of the coloured patches. Dividing the waltzing grandparents into a and @ as already explained, the correlations are fairly uniform, the coefficient for colour and for amount of whiteness being about 0°3 (see Tables XXIV. and XXYV.), as in the previous generation; the sign of the correlation between colour in the hybrids and amount of whiteness in their waltzing parent (which of course depends upon the order in which the colours are arranged upon the arbitrary scale) is negative, showing that the waltzing mice with a greater amount of white A. D. DARBISHIRE 19 produce hybrids with darker coat-colour ; between waltzing grandparents and the offspring of hybrids the sign is, however, positive for the same arrangement of colours, so that while the intermediate hybrid offspring of waltzing mice with a large amount of white coat are darker than the average of hybrids, the young produced by such offspring paired together are on the whole lighter than the average. It must be remembered that this relation between the amount of white coat in one generation is a relation of cross inheritance, depending on (though not always simply proportional to*) the product of the coefficients of direct inheritance and of organic correlation. We have seen that the coefficient of organic correlation between amount of whiteness and coat-colour is negative in the hybrids them- selves; in their offspring it has changed its sign and become positive, so that we see the way in which the sign of the coefficient of cross grandparental inheritance has become changed. We see then that both the colour of the coat and the amount of white fur in the offspring of hybrids are correlated about as strongly with characters of one set of grandparents as with those of the other; neither the waltzing grandparents nor the albinos are dominant in the sense that they alone determine the characters of the generation, neither are recessive in the sense that they take no part in such determination. It may be urged that the correlations just determined are without value because the offspring of hybrids are obviously divisible into two groups, albinos and others—and perhaps into three. There is some indication that the correlations between the albinos and their waltzing grandparents is negative, the grandchildren of the whiter waltzers containing a distinctly smaller percentage of albinos than the grandchildren of waltzers with a larger amount of coat-colour: the numbers descended from the various waltzing grandparents are shown in Tables XXIV. and XXV., and it will be seen that the deviation from Mendelian expectation is only great enough to be suggestive among the 112 offspring of hybrids whose waltzing grandparents were both of type a The number of albinos which should be found in this group is 28, and the probable error of the expectation is 0°6745 V + x 2 x 112 = 3:09; the number of albinos actually found is 18, showing a deviation from the most probable result equal to more than three times the probable error, the chance of a deviation so great as this being about 0:0015, or the odds against it about 370 to 1. If, however, we exclude the albinos, and calculate the correlation between the coat-colour or the amount of white fur in the remaining individuals, and the whiteness of their waltzing grandparents, we obtain values very closely similar to those already given, so that in this case at least the apparent dimorphism of the young has no effect upon the grandparental correlations. The parental correlations are considerable, and curiously different for different characters. The correlation between the amount of white coat in hybrids and in their offspring is about 0°7 for both father and mother, showing that the whiter * Cf. Pearson, ‘‘On the Laws of Inheritance in Man,” Biometrika, Vol. 11. Part Iv. pp. 384—5. 3—2 20 Result of Crossing Japanese Waltzing with Albino Mice parents produce a markedly greater proportion of young in which whiteness predominates than are produced by the darker parents; they also produce a larger proportion of pure albinos. In coat-colour the correlation between parents and offspring is much less, being about 0'2 for both parents. The cross-inheritance, as measured by the correlation between coat-colour of father or of mother and whiteness of young, is again positive (in accordance with the positive organic correlation between these two characters in the young), and its value is about 0:2. These various correlations cannot be adequately discussed without attempting a study of the effects due to the selection of parents during the experiment, too difficult for any but a trained mathematician. The hybrids were to a large extent paired together so that the members of a pair were of similar colours, the correlation between male and female members of a pair (weighted with the number of young produced) being about 0°4, so that the coefficient of assortative mating has changed from + 1 in the ancestors of the pure-bred mice, through — 1 in the unions which produced the hybrids, to about 0°4 in unions resulting in the generation now described. The amount of whiteness in the coat of the hybrids was also selected, the correlation between male and female in the unions made being over 0:9; this difference in the degree of assortative mating may possibly account for the difference between the parental correlations in the two cases. We see, however, that both the colour and the amount of whiteness in the coat are variable characters, depending to a sensibly equal extent on characters transmitted by each of the pure-bred parents of the hybrids, so that there is no question of dominance on the part of one or other parent, and no possibility of regarding the characters of the generation examined as depending solely on the individuals paired in the original cross union, apart from their ancestry. In other words, we see that here, as in the hybrid generation, the phenomena observed must be formulated in some way or other in terms of the whole ancestry, and the idea of “gametic purity” is therefore excluded. Waltzing occurs in only 97 out of the 555 individuals resulting from the union of hybrids. When we compare this with the number of pink-eyed individuals (131—134) or of albinos (137) we see that the proportion of waltzing individuals cannot be regarded as a possible quarter. The probable error of the expectation that a quarter of the individuals will waltz is, on the Mendelian hypothesis, 06745 Vv + x 8 x 555 = 6°88 only, and the observed deviation is 1388°75 — 97 = 41°75, the odds against so great a deviation being rather more than 50,000 to 1. As the result here obtained differs from Mendelian expectation in the same direction as that already obtained by von Guaita* and to an extent consistent with the agreement of both, the evidence that the waltzing character does not segregate in Mendelian proportions is very strong. * «Versuche mit Kreuzungen von verschiedenen Rassen der Hausmaus,” Ber. d. naturforsch. Gesellsch. Freiburg, Bd. x. 1898, Bd. xr. 1900. i _ A. D. DARBISHTRE 21 Waltzing is completely recessive to normal walking, disappearing entirely in the hybrids resulting from the cross; its correlations with other characters, parental, grandparental or fraternal, are always small and generally insensible. Except for the fact that the proportion of waltzers among the offspring of hybrids is so widely divergent from that indicated by the theory, waltzing is thus more nearly Mendelian in its behaviour than any of the characters examined. The distribution of waltzing individuals among the various families (see Table A) is, however, less regular than it should be, and in. this way a sensible fraternal correlation is established (Table XIX.) which is not in accord with Mendelian theory. HYBRIDS CROSSED WITH ALBINOS. Unions between hybrids and albinos produced 746 young, of which 368 were albino, the rest being piebald or self-coloured. The gap between albinos and coloured individuals was wider than among the offspring of hybrids paired together, since the Group 1, including individuals in which the pigmented area is smallest, was entirely absent, and only eight individuals fell into the next group 2, the majority of individuals which were not albino being of degree 5 or 6. The coloured individuals had dark eyes, and none showed the waltzing habit. The range of coat-colours was less than among the offspring of hybrids paired together, since lilac did not occur. The relative frequency with which the different colours occurred was strikingly different from that seen among the offspring of hybrids, as will be gathered from the following table : Percentage frequency of the Colours in (a) Coloured Offspring of Hybrids paired together, (b) Coloured Offspring of Hybrids and Albinos. Colour | Hybrid x Hybrid | Hybrid x Albino a 7°66 °/, 6:08 °/, b 22-97 °/. 317°. C 36:36 °/-. 44-18 °° d 455°] 14:55 °° e 18°66 °/. 29°10 °/. f 8:37 °/° 0:00 °° 7 1-44 °/° 2:90 °/. 100°01 99°99 = = | It will be seen that the coloured offspring of hybrids and albinos, which have more white in their ancestry than the offspring of hybrids alone, are characterised first by having considerably less white fur, and secondly by the greater frequency of wild-colour and black, as compared with yellow and fawn-colour—that. is, by the presence of black pigment in larger quantity. with increase in the number of albino ancestors is very remarkable, and no ex- This increase of blackness planation suggests itself at present; it is however in accord with the negative 22. Result of Crossing Japanese Waltzing with Albino Mice correlation already mentioned between purity of ancestry among the albinos employed in making the original cross and the darkness of the hybrids. The albinos of the group seem more obviously distinct from the rest than do the albinos among the offspring of hybrids, and the ancestral correlations are materially affected by their retention or omission. Retaining the albinos the correlation between whiteness of coat and purity of the albino grandparent is about — 0°15 (cf. Table XLV.); between whiteness of coat in coloured individuals alone and purity of albino grandparent the coefficient rises to about — 0°25. We have here a further proof of the extent to which the ancestry of the “recessive” albino affects the coloured descendants of the cross. The correlations with the albino parent are too small to be worth noticing until the probable error of the method employed for their determination can be given; the data are given in Tables XLIX. and L., where it will be seen that nearly all the albinos used as parents were pure-bred, so that the determination of correlations is difficult. The hybrid parent appears to be more closely correlated with the young, both in colour and in amount of whiteness, than the albino, the correlation in both characters being about 0°2, the value found among offspring of hybrids paired together. HYBRIDS CROSSED WITH EXTRACTED ALBINOS. The object of this experiment was to determine if the percentage of albinos produced by such crosses would be different from that produced by crosses between hybrids and pure albinos. The number of albinos obtamed—59 out of 120—is of course an excellent experimental half; but the following considerations should be carefully weighed, (i) the albinos used were not all produced by pairing two hybrids; in many cases (see Table D) they were produced by crossing hybrid and albino, (ii) the hybrids used were in some cases (Gy, Gu, Gis, Gis, Giz, Gio, Gy) the offspring of waltzers and extracted whites, (111) the character the percentage of which one is trying to diminish in the offspring is identical with that of one of the parents: in offspring of extracted hybrids one was able to diminish the number of albinos by diminishing the amount of albino ancestry of the extracted hybrids; but in this experiment, while one does diminish the albino ancestry, one of the parents themselves is always albino; so that the effect of the diminution of albino ancestry is rather swamped. If separate tables are made for, (4) hybrids crossed with albinos produced by the union of hybrids, (ii) hybrids crossed with albinos produced by hybrids paired with albinos, and (111) hybrids from extracted white crossed with extracted albinos, the numbers become so small as to be useless to base arguments upon. The occurrence of pink eyes in seven of the young, or five per cent. of the number produced, distributed among five families (more than one-fifth of the whole number), is clear evidence that these extracted albinos have a power of hereditary A. D. DARBISHIRE 23 transmission, dependent upon their ancestry, different from that of albinos whose ancestry contains no pink-eyed waltzers. GRANDCHILDREN OF HYBRIDS. The children of hybrids consisted roughly of a quarter albinos, a half dark- eyed forms with coloured coats and a quarter pink-eyed mice with colour in the coat. The extracted albinos are unquestionably the recessives: the dark-eyed mice with coloured coats I have termed the extracted hybrids; partly because they occur in the proportion of 50°/, and partly because they are asserted by Bateson and Castle to be what I have called them. The pink-eyed forms with colour in the coat which occur in the Mendelian proportion of a quarter I have called extracted dominants for similar reasons: I feel quite confident that Mendel himself would have sanctioned this classification, since the proportions agree closely with those which he obtained with his peas. The grandchildren of hybrids will be treated of under the following headings: (i) offspring of extracted recessives RR x RR, (11) offspring of extracted hybrids DR x DR, (iii) offspring of extracted dominants DD x DD. (i) Offspring of Eatracted Recessives. As could have been predicted with no fear of contradiction by those who are familiar with fancy mice the extracted albinos when paired together produce only albinos. For some reason I have been unable to breed from waltzing individuals of this category, and therefore the number of young which waltz is small, but it is far below that which would appear on Mendelian expectation, which is 1 in 12. For the albinos may be as regards waltzing either dominant or hybrid, ie. the kinds of pairs of albinos that can be made are three: G) DDx DD. Gi) DDx DR. Gi) DRx DR. Of these pairs, (i) and (ii) should produce no waltzers, and (iti) should produce 1 in 4 The whole number of young obtained was 94, and of these only two waltzed ! (ii) Offspring of Eatracted Hybrids. I think that the most conclusive results which I have obtained are given by the results of pairing extracted hybrids: as the reader is aware, hybrids were paired with hybrids (DR x DR) and also crossed with albinos (DR x RR), the former giving offspring which may plausibly be regarded as consisting of 4 DD+%4 DR+i42#R#, the latter} RR+4 DR. So that, when pairing the children of hybrids to produce the generation which we are now considering, two kinds of extracted hybrids were available, (i) the result of DR x DR (which I will denote H x H=hybrid x hybrid) and (ii) the result of DR x RR (which I will call 24 Result of Crossing Japanese Waltzing with Albino Mice ffx A). With these two kinds of extracted hybrids three kinds of crosses can be made: CE A CHES AE): 2 A xD) CE XA): B.C XA SAG eA: Now in Mendelian language these kinds of pairs are all DR x DR, for the DR produced by DR x RA is not different from the DR produced by DR x DR. And the similarity of these formulae is characteristic of the Mendelian conception of the reproductive organs of the hybrids. a For it is well known that according to this view the hybrid contains equal numbers of germ-cells which produce the dominant character, and of those which produce the recessive ; and this is said to be true of the hybrids however far the individual is removed from the original cross, whether it is the result of the cross (ic. the hybrid) or the great-great-grandchild of this. This is the ground on which the doctrine of the purity of the germ-cells and the law of ancestral heredity flatly contradict one another; the former asserting that DR x DR will produce 25°/, DD, 50°/, DR and 25°/, RR for a very great if not an infinite number of generations ; the latter maintaining that the further the individual hybrid under consideration happens to be removed from the cross the less albinos will it produce: and that two hybrids whose mothers were albinos will produce more albinos than would two hybrids who have no albinos in their pedigree later than their great-great-great-grandmother. This seems to me to afford a case in which experiment could provide a decisive answer. I have made an experiment of this kind: that is, I have tried to see if by pairing together hybrids with different amounts of albino ancestry I could obtain different percentages of albino individuals among the offspring. I have not had time to do this by producing successive generations of hybrids and counting the number of albinos in each: but I have done it by observing the difference between the results of making crosses of form (fx H) x (Hx) (A x A) xa A) and (i x A) xia): The ancestry of these kinds of pairs is perhaps brought more vividly before the reader’s mind by considering the following pedigrees : (i) Wx A Wx A WxA WxA (H x H) x (Hx #) H vou H H = a fl] ) le, dap, Bap, 4e fageee 5e | 5e We) A | Wp B ae A, a sa c, 8e, 5c, 5bp, 6e, 6e H 124a | de | 8c | A | Wal 4 | Wel Be, 4c, 5bp, Sew, 6e H 1248 , | 4e, de, 5bp, Sbp, A H125 | 5c | 3c | 4 |Weldx| Wal 3c, dbpw, 5be, 5e, 5e, 5e, 6c H126a | 2d | 2c | A | WajAx| WB] lew, lew, 2bp, 2bp, 2c, 3c, A H 1268 ” ” ” ” ” ” lap, 2ew, 2e, dap, A H 127a | 5e | 5e WB\|Ax| WB 5e, 5c, 5c, 5e, A HPLZIB ON | 5) | a | 2 | oy | | Sbpw, Sdp, bp, 8c, 6g H128a | 5c | 5c | A | WB\| A | WI 4afp, 4e, 5afp, dew, 6fpw, Aw, Aw H 1288 LB) ” ” ” ” ” 5bp, me H 129a | 5c | 5¢ | A | WB| A | WY 5dp, 5e, 6e, 6fp Jel TERYGE | ee | ec ees Bs ear 2c, 4e, Sbpw, Sew, 5e, 6ew Hf 130 3c | 8c | Wa} A | A | WY lew, 3bpw, 4cew, A, A H 183a | 5c | 5c |Ax| WI\Ax] WI. Qe A H 1338 ” ” ” ” ” ” 5e, 5e, 5e, A, A HT 134 8c | 8c |Ax| WiAx} WI] A, A H 135a | 5e | 5¢ |Ax| W\|Ax] W | 2e, 5bp, 6e, Aw H 1358 ” ” ” ” ” 5dw, A H 136a | 5a| 5¢ | A | WB\|Ax}| W] 2bdp, 2c, 5a, 5a, 5ew H 1368 ” ” ” ” ” ped 4ap, 5bp, 6ap H 187a | 3c | 4c |Ax| Wj)Ax] WY 3q (eyes dark red, not blood-colour) HT 1878 ” ” ” ”? ” 33; 3d, A, A H 188a | 5c | 5¢ |Ax| W) WalAx | 3g, 5c, 5ew, Aw HHT SEB AN ee N55 || 55 i 55. Ik oe 1 gs 5bp, 5bpw, 5e, 6gw, A H 139a | 5e | 8e | A | WB| Wal Ax} Lfp, 3fpw, A H 1398 ” ” ” ” ” ” 6e, 4 Hf 142a | 5c | 5¢ | A | Wa| A | WY Ge, A, A H 1428 ” ” ” ” ” aD de, 5e, 5e, 6e, 6fp H 145a | 2c | 2c |Ax| WB\/Ax}| WY] Qc, A, A, A, Aw Hf 1458 ” ” ” ” ” ” le, fpr, 2c, 2bp H148a | 5d | 5c | A | Wa} A | WI] 5e, 5e, 5c, 6e, A, A HI 1488 ” ” ” ” ” ” 4f, , Se, A, A, Aw HT 150 4c | 5c |Ax| W| A | Wal 4e, 4ew, 5e HT 201 5a | 5a | A | Wa} A | WB] 3a, 5a, 5a, 5a, A, A, Aw H 202 | 5a|5a| A |Wa| A | WB| 4ap, 5ap, A, A H 210 5a | 4c | A | WB, A | WB! 4bp, A, A A 224 3c | 5c |Ax| W| A | Wa! le, 2a, 2e, 3fp*, 3fp*, A Hl 225 3c | 3c |Ax| Wa| A | WB) 2Qap, 3fp, 3c, 3c, 4e, A, dw HT 226 3c | 4c | A | W Ax] Wal 3bp, 3bpw, dew, A, A, A H 227 4c | 2c | A | W| A | WB) 2ew, 20, Bev, 4bpw, 4bpw, 4fp H 228 8c | 4c |Ax| W/Ax| W | Qe, 3c, 3d, A, A, Aw HT 229 2c | 8c |Ax|WB| WB| A | 2fp*, 2c, 2fpw, 3fpw, 3c, 4c H 230 3c | 3c | WB| A | Wa| A 4bp H 231 3c | 3c | A | W\|Ax| Wal 3be, 3c, 3c, 3d, 3e, 4e, A, A HT 232 3d | 4c | Wa| A | A | WB) lbpw, 2bp, 3bp, 3c, 4e, A H 233 8c | le | A | WB| A | WY Qe, Qe, Qe, 2c, 2c, Qe, Yew, A, A H 234 | 2e | 5e | Wa| A | A | WY 2fpw, 30, 5ew, 6fp, 6fp HT 235 Qc | 5c | A | WB| A | WB 2c, 3e, 4dw,-5c, A, A H 262 5d | 2c | A | Wa} A | W | 2bpw, 3bp, 3e, 5bp, 5e, A DAMOWDAD KH ARADAANMNAWSPNWODFWOWNWORWREWONKRNONOADEPNNTAOANNOODERTOANONAD Total 555 * The record of eye-colour in these mice is uncertain. 32 Result of Crossing Japanese Waltzing with Albino Mice TABLE C.—Young Produced by pairing Hybrids and Albinos. Parentage Number era Coloured Young Albinos in 3 2 u 6 5 4 Litter Hi A 3c A A Fils Wa 5e, 5e, 5e, 5e = 4 H2 A 3c A A Ax Wa 4d, 4d, 4e, 5d 5 9 H3 Ae og sls A A | Ax | Wa | 5c, 5e, 5c, 5e, 6c, 6d 4 10 Ht A 5e A A A W 5e, 5d, Ge 2 5 HS A 5e A A A W 6c, 6d, 6d, 6d 1 5 H6 A 5e A A A Wa 6d, 2 4 H 11 A 3c A A A Wa 6e 5 6 H 12 3e A A W A A 3c, 6e, 6e 2 5 H 13 5e A A W A A 5d, 6e 1 3 HT 14 5e A A W A A 2e, 3e 4 6 H 15 A 5e A A A W 3a, 3a, 3e, 6a 4 8 H 16 A 5e A A A Wa 3e, 4g 5 U H 17 A Be A A A W 3d, 3e, 6d 2 5 H2 A 5d A A A Wa 4d, 4d, 4d 3 6 H 26 Ax 8¢ | ADF) AD | A Wa 5d, 5d, 6e 1 4 H 27 3c A A W A A 6e 5 6 H 28a 5¢ A A Wa A A 5e, 5d == 2 H 288 ” ” ” ” ” Y) bd, 6d 3 5 HT 31 A 5e A A A Wa — — — 1 1 H 32 2¢e A A Wa A A 4c, 6c, 6c, 6e 33 7 HI 33 A 5e A A A Ww 6e, 6e, 6e, 6e 4 8 H 34 3c A Ax We A A 5e, 5c, 6d 1 4 HT 35 3c A Ax WB A A 4d, 5d, 5d, 5d, 5d 1 6 H 38 2d A A Wa A A 5d, 5d 2 4 H 39 2d A A Wa A A —- = _ 4 4 HT 40 5a A A Wa A A 6a, 6a 5 7 HT 41 5e A A Wa A A 5c, 6e 3 5 H 43 A Qc | AX Wa A A 5c, 6e, 6e 2 5 H 45S Ax Be | A(T) ADT] A Ww 6e 3 4 H 46 A 2c A A A Wa 3c, 3c, 3¢ 5 8 H 47 Ax 3e | A(t) A(t] A Wa 6e, 6e 4 6 H 48s A 5e y. A A Wa 6e 3 4 H 49a A 5d A A A Wa 6e, 6 3 5 H 498 ” ” ” ” 3c, 5d, 6e 2 5 Hf 51 Ax 5e | A(2)t| A (2)t Wa 4c, 4c, 4e 1 4 H 52 A 3d A A Wa 6e, 6e 3 5 H 55 2Qe A Ax Wa A A 3a, 6 4 6 H 56 Qe A Ax Wa A A 4c, 4e, 6d 1 4 HT 57 Ax Be | A(t) AMt| A Ww 4c, 4c, 4c, 5d 3 a H 58 2e Ax Ax WB | Ax Ax Qa 3 4 H 59 2c A A Wa A A 5e, 6e 5 2 H 60 A 3c A A A Wa 4c, 4c, 6e, 6e 2 6 H 63 3c A Ax Wa A A 2g, 5d, Ge 2 5 H 64 2e Ab PAX Wa | Ax A 2d, 2e 2 4 HT 65 Qe A Wa A A A 6e 3 4 HT 80 A BG A A Ax Wa 5g, 6e 5 7 H 81 5e Ax A Wp A 6e 3e, 4e, 6e, Ge, 6e 4 9 HI 83 5e Ax A WB A 6e 4e, 5e, 5e, 6e 1 5 HT 85 5e A A Wp A A — — — 4 4 HT 86 5c A x A Wp A 6e 5e, 5¢ 2 4 H 87 5e | Ax A WB A 6e 6c, 6e 3 5 HT 88a A 3c Aen eA A Wa 5e, 5c, 6e 3 6 H 858 ” ” ” ” ” ” Ge 5 6 H 92 y, 5e A A 3c, 4e, 6e 3 6 HT 181 A 2Qe A A A Ww Qe, 3c, 3c 1 4 H 140 5e A Ax W A A 3c, 6e 4 6 H 143a A 5e A A W 5e, 6c, 6e 3 6 HT 143; ” ” ” ” ” 4e, de 2 4 H 144a A 4c y. y Ax Ww 2e 1 2 HT 1448 ” ” ” ” ” ” 5¢ 3 4 H 146a 2e Ax Wp A 5e, 6c, 6e 3 6 H 1468 ” ” ” ” ” ” 5e, 5e, 5e 2 5 H 147 3e A Ax W Z y, 3c 4 5 H 149a 5d A A Wa A A 5e, 5e 4 6 H 1498 a3 ” ” ” 99: ” 5d, 5d, 6d 3 6 H 151a 3c A Ax W A A 5e, 5c, 6e, 6e 1 5 H 1518 ” ” ” ” ” » 5¢, 6e 3 5 * Pedigree of these albinos uncertain. + Pedigree unknown. A. D. DARBISHIRE TABLE C.—(continued.) 33 im P t arentage Number pee eve Coloured Young Albinos in 3 Q ” 6 § 4 Litter HT 152 3c A A W A A 6c 5 6 H 158 3c A A W A A 3e, 4be 3 5 isp || 3c | =A A wi} A A | 5bc, 62, 6e 2 5 Hiss | 22 | A | A | Wel A | A | 4e, 4e, Be, Ge 2 6 HT 156 3c A A Wp A A 6e 3 4 H 157 5a A A WB A A 5a, 5a, 5d 3 6 H 158a 5a A A WB A A 5e, 5c, 5e 3 6 H 1588 * bs . - i. Ea 5a, 5a, 5e, 5e, 5e 1 6 eis) ba | A.| 4°) We | 4A | A | be 2 3 H 160 5a A A Wa | Ax A 5e, 5e, 5c, 5e 2 6 HT 161 5a ds A Wa A A 5a, 5e, 5e 2 5 H 162 5a A A Wa | Ax A 5a, 5e 1 3 HT 163 5a A A Wa A A 5a, 5b, 4e, 4c — 4 HT 164a A 4c Ax 6e Ax Wa 5e (pale), 6e 1 3 H 164 ” ” ” ” ” ” 6e, 6e 5 7 HT 16 Ax 3c A x 6e A WB 5e 1 2 H 166 Ax 2¢ A x 6e Ax Wa 5e, 5e, 5d 5 8 H 167 AX 5e Ax 6e A Wa 5d, 6c, 6c, 6d, 6e 3 8 H 168 5a | Ax A WB | Ax 6e da, 5a, 5a, 6e 3 7 H 169 BY Ax | Ax We. | Ax 6e 4c, 5e, 5c, 6e, 6e 3 8 H 170 Ax 5e 6g 6e A WB 5e (pale), 5c, 6g 2 5 H 171 5c Ax | Ax Wa 69 6e 6c, 6e, 6c 2 5 H 172 3c PAgx || Alx Wa | Ax 6e 4c, 4c, 6e 2 5 H 173 5e A A WB A A 5e, 6e, 6e 3 6 H 175 5e A A | We| A A 5b, Bbe, 5e, bd, 4e 2 7 H 178 5e A Ax Ww A A 3c, 5c, 5e 5 8 H 179 5e A A Wa A A 5e, 5c, 52, 5d, 6d 1 6 H 180 5e A A Wa A A 5e, 5c, 5e, 5e, 6e 2 7 H 181 5c A Ax Ww A A 5e, 5e, 6e 3 6 H 182 5e A A Wa A A 5e, 5c, 6e & 6 H 183 5e A A Wp A A 5e, 5e 4 6 His, | 5¢ | A | A | Wel A A | 6e 8 9 H 185 5e A A W A A 4e, 5c, 6e, 6e, 6e, Ge, Be 2 9 H 186 A Se | Ax A A Wp 5e, 5d 6 8 H 188 A 5e | Ax A Wa | Ax 5e, 5g — 2 H 189 A 5¢ Ax A A We 6c, 3e, 2d, Be 3 7 H 191 A Be A A A Wp 3c, Ge, 6e 2 5 H 192 A 5e A A A WB 5e, 5e, 5d, 4e, 6e 2 7 H 193 A 5e A A Ax WB 6e 1 2 H 194 A bad | A A A Wa | 3e¢, 5c, 5d, 6e 5 9 H 195 Ale Se. |. A A A | We | 5e, Se, 5c, 5d, Be 3 8 H 196 A 5e A A A Wa 6d, 6d, 6d, 6d 5 9 H 197 WO 5c |) A A | Ax | Wa | 5e, 5c 4 6 H 198 A 5e A A A ic} 4c, de, 5e, 5c, 6e, Ge, Ge 2 9 Hi99 | A | & | A | A | A | Wel 4e, be 5 7 H 200 A 5e A Ax | Ax W 3be 4 5 HT 203 5a A A Wa A A 5a, 5a, 5e, 5e oy 6 H 204 5a A A Wa Z A 5a, 5a, 5e, 5e 3 i H 205 5a A A Wa A A 5a, 5a, 5e, 5c, 5e, Be — 6 HT 206 A 5e A A Ax W 4c, 4c, 4c, 5c, 5e, Ge 3 9 H 207 A 5e A A A x W de, dd, 5c, 6e, Ge, Ge 3 9 H 208 Be A A We A A 4c, 69 5 7 H209 | 5a | A | A | Wel A | A | 5be i 2 H 212 A 2e Ax A Ax We 3e, Ge, 6e 4 7 HT 218 A 3c Ax A A Wp 3be, 3c, 4c, 4c, 4e 2 7 Hf 214 A 3c Ax Ap Ap Wa 3e, 4e, 6e, 6d 4 8 Mee. || A || 3c | A | A | A | We | 23g, 4e ae 2 H 217 4d A Ax Wa | Ax A 3be, 3c, 4g 3 6 H 218 Qe A rALX We | Ax A 3bc, 3c, 4e, 4e 3 7 H 219 5d A A Wa | Ax A 5e, Ge, 6e 3 6 H 220 Qe A Ax Wa | Ax A 5e, 5c, 5e 2 5 HI 222 4c A Ax W A A 5be, 5be, 3c, 3c, 5e 4 9 H 223 2e A Ax WB A A 4g, 5e 1 3 H 260 ACE AL. | 8 Ax W | 6 | Ax | — — — 1 1 H 261 aos ee! Ax W 6e Ax 4c, 5e 5 i Total 746 5 Biometrika 111 34 Result of Crossing Japanese Waltzing with Albino Mice TABLE D. Results of mating Hybrids with “Extracted Albinos.” (H = Hybrid, FE = Extracted Albino; see teat, p. 25.) Number Catalogue | Parents of | Parents of 5 : . : Offspring in Number Hybrid Albino i Litter G 1 AxW Hx H 3ap, 3bp, 5aw, A, A, Aw 6 G 2 AxW Hx H lbe, 1be, 3c, A 4 G 5 AxW Hx H 5e, 5¢, 5c, 5c, A, A, Aw 7 G 6 AxW Hx H Ye, 3c, 3c, A, A, A 6 G 7 AxW HxH 5bp, A, A, A, Aw 5 G 8 AxW HxH 5c, 5ew, 6e, A, A 5 G 9 Asis Hx H 5bp, 5e, 5c, A, A 5 | G 10 AxW Hx H 3c, 3e, 4e, A, Aw 5 G 11 AxW HxH 5cew, A, A, A, A 5 G 3 AxW HxA A, A, A 3 G 4 AxW HxA 5a, 5a, 5aw, 4c, A, A, Aw 7 G 22 AX, HxA 5e, 5c, 6e, A 4 G 23 AxW Axa 4c, 5c, A, Aw 4 G 24 AxW HxA 5c, 6e, A, A 4 G 25 AxW HxA 6e, 6g, A, A, A, Aw 6 G 26 Ax W HxA Qc, 3c, 5c, Ge, A, A, A 7 G 27 Ax W HxA 3c, 4c, 5cw 3 G 12 Ex W HxA 3bp, 3d, 3gw, A, A 5 G 14 ExW HxA 4c, 5c, 5c, A, A 5 G 15 ExW HxA 5a, A, A, A, A 5 G 16 Ex W HxA 5a, 5a, 5a, 5a, 38e, A, Aw 7 G 17 Ex W HxA 3c 1 G19 Ex W HxA 3e, A, A, A, A 5 G 20 Ex W HxA 3bp, 3bpw, 5c, A, A, A 6 Total 120 eae ee Unions of Type (H x A) x (H x H) Unions of Type (H x H) x (H x H) Unions of Type (H x A) x (H x A) mn A. D. DarsisHirE TABLE E.—Result of pairing “ Extracted Hybrids.” Gatalogue Parentage Number 3 2 y 6 5 2H 36 5b | 3e | 5a | 5a | 6d 2H 39a | 5c | le | 5e | 5e | Qe BLE S9B | yy).|\ 5) 39) 59. | 99 2H 46 4d | 5c | 8¢ | 4e | 5e 2H 48 5a | le | 5a} 5e | 4c 2H 49 6e | 8c | 5e | Be | 5e 2H 50a | 4e | 3c | 4c | 3c | 8c 2H 508 ” ” ” ” ” 2H 51 4c | Ye | 4c | 4c | 3c 2H 52 3c | 5d | 3c | 5e | 5e 2H 58a | 5d | Be | 6d | 5e | 3c 2H 538 ” ” ” ” ” 2H 92 3e | 4c | 4c | 3c | 4e 2H 93 4e | 4c | 4c | 3c | 8c 2H 96 6e | 4c | 5e | 5e | 4e 2H 99 | 4bc| 5c | 4c | 4c | 5e 2H 139 5a | 6e | 5a | 5e | 8e 2H 142 5e | 5c | 8c | 5e | 5d 2H 23 5e | 5c | 5a | A | 5d 2H 28 5d | 4e | 5a | A | 8e 2H 29 6e | 6c | 8c | A | 3e 2H 32 6d |} 5e | A | 2c | 5a 2H 33 5c | 6b | A | Ye | 5a 2H 3h 6d | 38e | A | 2e | 5e 2H 38 6e | 2c | Qe | A | Qe 2H 40 5e | 8c | 5c | 5c | A 2H 41 6e | 6c | Ze | A | Be 2H 43 | 6e | 3e | 5e | Ax] 4e 2H tha | 5c | 2c | 8c | A | 8e 2H 448 ” ” ” ” ” 2H 100 5a | 5d | 5a | Ax] 5e 2H 101 5a | 6e | 5a | Ax} 5e 2H 103 5e | 38e | 5a | A | 5e 2H 106 5d | 4e | Ax| 3c | 5d 2H 107 6e | 2c | Ax] 3c | 3c 2H 118 le | 6e | 3c | 4e | 4e 2H 119 5e | 6e | 5¢e | 5e | Ax 2H 145 6e | 5¢ | 8c | A | 5e 2H 18 6c | 6e | 3c | A | 3e 2H 19 6e | 5c | 8c | A 5a 2H 20 5e | 5a | 3c | A | 5a 2H 22 5c | 3e | 8c | A | 5e 2H 25 5e | 6e | 5a | A] A 2H 26 5a | 4c | 5a | A | A 2H 27 5a | 6e | 5a| A} A 2H 37 6e | 38e |Ax| 3c | A 2H 45 5g | 5¢ | A | 8c | A 2H 110 6e | 5d | 8c | Ax] 5d 2H 111 6c | 5a | 8c | Ax] 5a 2H 112 4c | 5a | A | 5e | 5a 2H 113 6c | 5c | 3c | A | 5a 2H 114 5d | 6c | 3c | A | 8e 2H 115 5e | 6d | 8c | A | Be 2H 116 5d | 5c | 5d] A | 3e 2H 143 6e | 6e | 2e | A | A 2H 144 5a | 4g | 5a | A | 5e 2H 146 5e | 5c | 5a | A | A 2H 147 5a | 6e | 5a | A | 5e 2H 148 5e | 5¢ | 8c | A | 5a Offspring 3a, 5a, 5e le, 2c, 2c, 2c, 5c, 5bp, 5bp 2c, 3c, 4c, 5bp, 5e 6bp 4ap, 5a, 5a, A, A 5d, 5d, 6e, 6e, 6e, 6e 2c, 3c, 3c, 4e, A Qc, 8e, de, 4e, A le, 3c, 3c, 8e, 39 3c, 5e, 5c, 5bp, A 3e, 3e, 4e, 4e, 5d, 6e, Ge, Aw 3bp, 3c, 3c, 5cw, be 3c, 8cw, 4c 2fp, 3c, 3e, 4fp, A 8e, 3g, 5c, 5d, 5d, Ge, A 4be, 4be, 5c, A, A 5a, 5b, 5ew, Ge, 6fpw 5bpw, 5bep, 5be, 5be, 5c, 5e, 5e, 5e2w 5bp, 5c, 5c, A, A 5bp, 5c, 5e, 6e, 6e 5c, 5¢e, 6e, A 4c, 5c, 5c, 5e, 5e Abpw, 5b, 5b, 5e, 5c, 5ew 3bp, 3c, 3c, 4c, 6e, 6e, A 3bc, 3bpw, 5bp, 5bp, 5d, A 5be, 5be, 5e 3c, 6e, 6e, 6e, A 3e, 3c, 3fp, 3fp, 4fp, 4e, 6e, be Bap, 3c, 3c, 4c, 5be, 5c, A 2c, 5bc, 5c, A, A A, A, A 5a, 6c, 6e, 6c, 6ew, A, A 3c, 4e, 4e, 5c, 5e 2e, 4d, A, A 3c, 3c, 3fp, 3fp, 5bp, 5d 3b, 5b, 5e, 5e, 5e de, 5d, 6e, 6e, A, A 3c, 4c, 5c, A, A 6bep, 6d, 6d, 6fp, A, A 3c, 3d, 5c, 5c, A da, 5a, 5a, 5d, 6d, A, A 4c, 4c, 5c, 5c, A 6e, A, A, A 3c, 4a, 4c, 5a, A, A 5be, 5apw, 5a, 6ew, 3e de, 4e, 6e, A, A, A 4e, 5c, 5c, A, A, A 6d, 6d, 6dw 4a, 4a, 4e, 5bp da, 4e, 4e, 4e, 4d, 5a, 5a, 6e SCIOC WEAN An oA. 4d, 4d, 6d, 6¢ 4e, de, 5d, A 5bp, 5bp, 5bp, 5bp, A, A 2fpw, Be, 6e, Ge, Ge, Gew, Bfpw 3e, 4e, 6g, 6g, A, A dbp, 5bp, 3c, 5c, 6e, 6fp, A 3a, 3ap, 5a, 6g, A, A, A, A 3c, 3c, 5c, 5c, 4bep, 4bp, 4ap, 5ap, 5ap 35 Number in Litter ADD BPUAINWAWAANWAUABAUP oan WOON OW OW ON AAD ae Naw OODNANALLUDWDPWAATMIAPLAUNUAD Total 321 5—2 36 Result of Crossing Japanese Waltzing with Albino Mice TABLE F. Result of mating “ Extracted Hybrids” and “ Extracted Albinos.” Catalogue | Parents of | Parents of Offspri Number Number Albino Hybrid eae na itter K 1 Hx H HxA 6e, 5d, 5d 3 K 2 HxA Hx H 4c, 5c, 5c, 5d, A 5 K 6 Hx H Ax H 5e, 5c, 5e 3 K 4 Hx H Hx HH OC An AnaeA 4 K 6 Hx H Hx H 5e, 5c, 5c, A, A, Aw 6 K 6 Hx H Hx H 5e,.5c, A, A, A, A, Aw iG K 10 Hx H Hx H* 3bpw, 4b, 4bpw 3 K il HxaA HxH 6bp, 6e, 6fp, A 4 K 12 Hx H HxA 3bc, 3c, 3c, A, A 5 K 15 Hx Hx H 3bp, 6bp, A, A, A 5 K 16 HxH HxH 2e, Be, 8e, 3c, 4e 5 K 19 Hx A Hx H 3c, 4c, A 3 K 21 HxA Elexate 4e, 4e, 4e, 6d, Ge 5 K 23 Hx H HxAaA AG MOC EDC DC.eAn eARmAleA. 8 K 24 Hx H HxaA le, 2c, 2c, A, A, A 6 K 27 HxA HxH Ge, 6e, A, A, 5 K 28 Hx H HxA 4c, 4c, 5c, 6g, A, A, A 7 K 29 HxA Hx H Qd, 3c, 3e, A, A, A 6 EK 30 HxA HxH A 1 Total 91 * The eyes of the hybrid used (the female) were possibly dark red, not black. TABLE G. Result of mating “Extracted Dominants” and Albinos. (EH =‘ Extracted Albino.”) Parentage Number near Offspring in Pele 3 2 yy 6 5 4 Litter 2H 79 | A |3bp| A | A | 3c | 2c | Be, Be, 4c, 5e, 3e, 8e, Ge, 6e 8 2H 80 | A |3fp| A | A | 3c | 4e 3e, 6e 2 2H 88 |4bp| A | 4c | 8c | A | A Abe, 4bce, 4bc, A 4 2H 90 |5bp| FE | 5a} 5a | 5a] A 5b, 5c, 5c, 5c, 5e, 5e 6 2H 102 | EF |6bp| 5a|Ax|} 5e | 5e | 5a, 5a, 5a, 5e, 5c, 6e, 6e 7 2H 104 | H |2bp| Ax) 3c | 8e | Be | 5e, 5ew 2 2H 105 | H.|2bp| Ax} 3c | 3¢ | 38¢ 3c, 3c, 3c, 4e 4 2H 108 | E |2fp| 5e | Ax! Ge | 3e 3cw, 4e, 4e, 5c, 5c, 6e, Ge, Ge 8 2H 109 | EH |2bp| 5e | Ax] 4e | Be | 4e, 4c, 4c, 4c, 4ew, 4e 6 2H 120 | EF |\6bp| 8c | A | 5e | 5e | 5e, 5e, 5bp 3 2H 123 | EF |\1bp| 3c | Ax] 5e | 5d | Qe, 4c, 4e, 5c, 5c, 6e 6 2H 124 |\4ap| HE | 3c | 4c | 8c | A 4ew, 6e, 6e, A, A 5 2H 125 | EB |\3bp| 5d | A | 5e | 5e 2c, 3bc, 4c, 5c, 5c, 5¢ 6 2H 126 |4ap| E | 5a] 5c | 4c | Ax] 3e, 8c, 3c, 4a, 5d 5 2H 127 |5bp| EH | 5a} 5e | Be | Ax] 5e, 5e, 4e, 6d, 6e 5 cr. 145 | A |3bp| A | A | 5a] 3c | 5b, 5b, 5b, 6b, 6b, 5e 6 er, 146 4c, 5a, 5¢, 5c, A, A, A, A 8 er, 155 - 5a, A, A 3 er. 156 | — 5be, A, A, A 4 Total 98 A. D. DARBISHIRE 37 TABLE H. Result of pairing “ Extracted Dominants.” : Parentage Number Catalogue Offspring in Number 3 2 ” 6 5 j mtier 2H 11 2bp | Bap | 3e 3c 3d 2c 2bp, 2bp 2 2H 12 | 5bp | 4ap | 5e 5e 5a 3¢ 2bp, 4bp, 5bp, 5bp, Sbep 5 2H 13 | Sip | 3fp | Se | Be | Be | do | Of, Of, Bip, Bip 4 2H 15 | 2bp | 4bpw | 5a 5e 5e 5e 3bp, 3bp, 3bp, 4bp, A 5 2H 55 2bp | 6bp 3c 2c 5e 5e lap, 2ap, 2ap, 5ap 4 2H 85 | 3fp | 3ap | Se de 5e 3c 3bp, 3bp, 3bp, 3bp, 3bp, 3bp 6 2H 135 6fp | 6bp 5e 5e 5e 5e 5bp, 5bp, 5bp, 5bp, 5bp, 5bp 6 : Total 32 APPENDIX IL. TABLES OF ORGANIC, FRATERNAL, AND ANCESTRAL CORRELATIONS. TABLE I. Organic Correlation: Whiteness and Coat-Colour in Hybrids. Whiteness. ; 1 2 B 4 5 6 Totals i 2 12 S 292 oi 26 bs 10 fo) @ SS 340 TABLE IL Fraternal Correlation in Whiteness among Hybrids. Second Brother. First Brother. Totals 20 2 3 J 186 6 Totals 20 186 319 221 1104 38 Result of Crossing Japanese Waltzing with Albino Mice TABLE III. Fraternal Correlation in Colour among Hybrids. First Brother. AS a c ad e Totals dy || Z| = 26 | 25 93 co 26 1522 28 12 1588 25 28 66 15 134 iS Ee: 12) U5. 14 41 © S 93 | 1588 | 134 | 41 TABLE IV. Whiteness in Waltzing Parents and in Hybrids. Hybrids. on 48 #93 S Ay | Totals TABLE V. Whiteness in Waltzing Parents and Colour in Hybrids. Hybrids. ne a | c | d e Totals ag Se] a 7 | Gadi 2o qi eco mellls ae 8 5 86 1 5 97 So Te [ie | a6 | 10 — Totals 12 | 162 26 10 210 TABLE VI. Purity of Albino Parent and Whiteness in Hybrids. Hybrids. Pure bred ... Cross bred ... Totals Albino Parent. A. D. DARBISHIRE 39 TABLE VII. Purity of Albino Parent and Colour of Hybrids. Hybrids. E a c | d | e Totals A Pure bred ... 12 174 20 6 212 ° Cross bred ... — 118 6 4 128 | a = Totals 12 | 292 | 26 | 10 | 340 =a I TABLE VIII. Correlation in Coat-Colour between § and % Hybrids mated. Male. . o S S| o oa TABLE IX. Correlation in Amount of Whiteness between § and $ Hybrids mated. Male. Female. Totals 18 82 | 139 70 240 _ 549 TABLE X. Organic Correlation between Whiteness and Coat-Colour in Offspring of Hybrids. Amount of Whiteness. 1 ie 8 4 5 6 Totals = 4 8 6 9 4 32 3 Wy 28 17 25 6 96 = 36 39 15 46 5 152 O 5 8 2 4 = 19 3 15 19 23 3 16 78 eS 9 10 3 1 10 35 © _ 2 os 2 2 6 86 | 114 66 90 43 418 40 Result of Crossing Japanese Waltzing with Albino Mice TABLE XI. Organic Correlation between Coat-Colour and Waltzing in Offspring of Hybrids. Waltzing Not... Totals TABLE XII. Organic Correlation between Amount of Whiteness in Coat and Waltzing in Offspring of Hybrids. A | 1 | 2 3 y | 5 | 6 | Totals Waltzing ... 20 9 18 19 8 17 6 97 Not... ... | 117 | 10 | 68 | 95 | 68 iva | 87 [keane | Totals 137 | 19 | 86 | 114 | 66 | 90 | 43 | 555 TABLE XIII. Organic Correlation between Pinkness of Eye and Whateness of Coat in Offspring of Hybrids. A | 1 2 B | 4 5 | 6 Totals Pink-eyed ... | 137 | 6 | 28 | 37 | 92 | 93 | 18 | av Not... .. | — | 13 | 58 | 77 | 44 | 67 | 25 | 284 More 137 | 19 | 86 | 114 | 66 | 90 | 43 | 555 TABLE XIV. Organic Correlation between Pinkness of Eye and Coat-Colour in Offspring of Hybrids. Pink-eyed ... Not ... seh Totals | 137 A. D. DARBISHIRE 41 TABLE XV. Organic Correlation between Pinkness of Eye and Waltzing in Offspring of Hybrids. A | Pink-eyed | Dark-eyed Totals | | Waltzing ... 20 36 41 Ot | Not... ean WALZ 98 243 458 | Totals 137 | = 134 284 55D TABLE XVI. Fraternal Correlation in Coat-Colour among Offspring of Hybrids. First Brother. | , | Ce | d | e | ff g Totals | | a 297 29 153 | 50 10 987 = 54 4 15 rie 205 2 185 26 1 e382 1] 709 ea 308 Sif 185 70 14 1150 a | Siem eas 14 ae eee 130 =| 185 | 14 92 34 5 609 a 70 jLibea eee! 30 1 235 | N 14 1 5 i 2 45 Totals | 987 | 205 | 709 | 1150 | 130 | 609 | 235 | 45 4070 | TABLE XVII. Fraternal Correlation in Whiteness of Coat among Offspring of Hybrids. First Brother. Totals | 987 | 139 | 638 | 793 | 497 666 | 350 | Second Brother. TABLE XVIII. Fraternal Correlation in Eye-Colour among Offspring of Hybrids. First Brother. A Pink-eyed | Dark-eyed | Totals 5 Ss | Se ed ee ee 987 FA | Pink-eyed ... 972 ae, Dark-eyed ... 2111 5 ee 8 Totals 4070 MN Biometrika 11 —B. a 6 42 Result of Crossing Japanese Waltzing with Albino Mice TABLE XIX. Fraternal Correlation in Waltzing among Offspring of Hybrids. First Brother. Waltzing Not Totals | CO da es ae | = Waltsing ... 124 566 690 Susu) Note a8 566 2814 3380 | AD A SS | Totals 690 3380 4070 | TABLE XX, Correlation between Coat-Colour in the Offspring of Hybrids and Purity of Albino Grandparents. Coat-Colour in Young. () = = - 7 eS g | al } @ | b aN Gi e Ff | g {| Totals “i £ | Both Pure-bred | 80 | 16 | 46 | 89 | 8 | 50 | 14 | 2 | 305 “S ©.) One Cross-bred 30 15 | 29 39 4 19 15 1 152 > | Both Cross-bred] 27 TO Woes A 9 6 lees 98 to eo | | ES | Totals 137 | 32 | 96 | 152 | 19 | \78 | 35 | 6 555 TABLE XXI. Correlation between Whiteness in Coat among Offspring of Hybrids and Purity of Albino Grandparents. Whiteness in Young. ° - = Eg A 1 2 | 3 | J 5 6 | Totals et = @ 0) D 2 | ae | r m = & | Both Pure-bred J 80 6 | 85 54. | 45 58 27 305 SS.) One Cross-bred 30 10 20 37, «dB 22 14 152 >= | Both Cross-bred} 27 3 25 23 | 8 10 2 98 | a= x U SSS Eo Totals 137 | 19 | 86 | 114 | 66 | 96 | 43 | 555 TABLE XXII. Correlation between Pinkness of Eye in Offspring of Hybrids and Purity of Albino Grandparents. Kye-Colour in Young. 2 Cae Se £8 | | Pink-eyed | Dark-eyed | Totals | taxi =| xq z Both Pure-bred... 80 | 65 160 305 “3 8,|} One Cross-bred_... 30 48 74 152 — | Both Cross-bred ... 27 21 50 98 | aa BS [(—————— om | ES | Totals 137 | 184 284 555 Whiteness in A. D. DARBISHTRE TABLE XXITI. 43 Correlation between Waltzing in Offspring of Hybrids and Purity of Albino Grandparents. Waltzing in Young. Correlation between Whiteness in Offspring q 4 n $8 DN ae Ss 4 ‘cs F = Waltzing Grandparents. Grandparents. s | 8 2 at ) fa] Sc (@) in Hybrid Mother. Coat-Colour in Young A a b | c a G0 oh g Totals 13 17 7 i 44 108 12 70 | 129 18 64 24 6 431 14 3 19 14 1 13 6 a= 70 2 a =e | 2 = | 1 5 = 10 137 | 32 96 | 152 19 78 | 35 | 6 55D TABLE XLI. Correlation between Whiteness of Coat in Offspring of Hybrids and Coat-Colour oat-Colour in Y J ( Mother. in Hybrid Mother. Whiteness in Young. 1 2 gs | 4 | 6 6 | Totals — ] } 1 2 5 5 | 16 2 44 12 | 74 | 91 | 55 | 63 | 298 | 431 5 9 | 16 6 | 10 | 10 70 ey) Gt ae es 1 3 10 | i9 | 86 | 114 | 66a 008 ae eons 4 | TABLE XLII. Correlation between Hye-Colour in Offspring of Hybrids and Coat-Colour in Hybrid Mother. Coat-Colour in Mother. Ss os ay SE ee > gq 1 a c | d | e Totals | | | Albino 183 108 14 2, 137 | Pink-eyed ... 11 97 21 5 134 Dark-eyed ... 20 226 35 3 284 | SEE EEE | | Totals 44 | 431 | 70 | 10 | 555 | 48 Result of Crossing Japanese Waltzing with Albino Mice TABLE XLII. Correlation between Waltzing in Offspring of Hybrids and Coat-Colour in Hybrid Mother. Coat-Colour in Mother. z | a | c | d | e Totals oN oh | . arn Sew 8) Waltzing ... 5 74 15 3 97 s 5 | Normal ‘eis 39 357 | 55 i 458 Cia Pa = | Totals 44 | 431 | 70 TABLE XLIV. Organic Correlation between Coat-Colour and Whateness in Offspring of Hybrids and Albinos. Coat-Colour. 2 A | a | b | c | d | e | g Totals ov Ce A 368 | - 368 2/3 a ee ae ee ee een eee yey 8 vl 8 ee ee ae siya 36 S| 4 SS et |) ae Ohh fore es Wena lee bd 2| 5 =| TS yl! U7. (lO S| Pell 8 amor sities S| 6 fi) a ee | eo ag, | ore ed ° | | | Totals | 368 | 23 | 12 | 167 | 55 | 110 | 1 | 746 TABLE XLV. Correlation between Whiteness of Coat in Offspring of Hybrids x Albinos and the Purity of their Albino Grandparents. (A= Pure-bred Albino; A x = Cross- bred Albino. All four Grandparents are indicated, each pair in one bracket.) Coat-Colour in Young. 2 | A i 2 3 4 oD 6 Totals 2S) (4.4) (A.W)... F193 | — 2 19 | 22 | 81 | 68 385 59) (4.A) (Ax... 70 | — | 9 6 | 12 | 39 | 21 150 Aa (d.dx) (A.W). aia A ges 1 5 6 | 13 | 12 68 &) (4.4x) (Ax.W).. Jigy yo ah 9 6 3 5 2 36 poet | (ase. Abe) (AL a, 17 1 8 8 34 28 | (Ax .Ax)(Ax.W) ele 1 es 4 7 9 48 ac | — a | Totals 36 | — | 8 | a6 | 48 | 153 | 120 | 721 ! | A. D. DARBISHIRE 49 TABLE XLVI. Correlation between Coat-Colour in Offspring of Hybrid x Albino and the Purity of their Albino Grandparents. (The Grandparents indicated as in the pre- ceding Table.) A a b c d e Totals | S g ny . | 2B) (4.4) (4.W)... [193 | 17 | 6 | 7 | a2 | 58 | 4 385 53 0/| (A.A) (Ax.W). - 70 1 2 45 13 15 4 150 Ai @| (A4.Ax) (A.W) . 31 aan ee 15 3 17 aS 68 oro. Ax) (Ax. W) 18 = 3 5 1 7 2 36 eal) (Ax:Ax) (A.W) 17 3 = 8 2 3 1 34 es (Ax.dx)(Ax.W) 27 1 = 14 1 5} — 48 oO rT eS Totals fee | 306 23 12. | 162 52 | 105 | 11 721 TABLE XLVIL. Correlation between Whiteness in Offspring of Hybrid x Albino and Whiteness in Waltzing Grandparent. Whiteness in Young. ie = A | 1 2 3 | 4 | 5 | 6 Totals n DO noe SOSce i) a eo ese yp) LOM) SU | 785) von 337 Sire B 108 | — 2 10 | 20 | 55 | 31 226 AS s ———— B & | Totals] 276 | — | 5 | 20 | 41 [133 | 88 | 563 | TABLE XLVIII. Correlation between Coat-Colour in Offspring of Hybrid x Albino and Whiteness im Waltzing Grandparent. Coat-Colour in Young. pe | A a b | C d e g Totals Dm | | y « S N S a 168 12 2 74 3 | 40 | 7 337 ie B 108 8 5 52 12 | 37 | 4 226 aS Gi | : —|-—— = o | Totals 276 20 au | 126 46 77 11 563 TABLE XLIX. Correlation between Coat-Colour in Offspring of Hybrid x Albino and Purity of Albino Parent. Coat-Colour in Young. os 2 Totals Ole ay Pure-bred .., 641 al Cross-bred ... 105 Sq Za =| Totals =< Biometrika 111 7 50 Whateness in Offspring of Hybrid x Albino and Whiteness in Hybrid Parent. Whiteness in Young. Coat-Colour in Offspring of Hybrid x Albino and Whiteness in Hybrid Parent. Whiteness in Offspring of Hybrid x Albino and Coat-Colour in Hybrid Parent. Purity of Albino Parent. Result of Crossing Japanese Waltzing with Albino Mice TABLE L. Whiteness of Coat in Offspring of Hybrid x Albino and Purity of Albino Parent. Whiteness in Young. | | A i | 2 tt) | 4 | 5 | 6 Totals Pure-bred ... | 319 | -- | 5 | 35 | 42-| 138 | 102 | 641 Cross-bred ... 46. | 2 eS 1) | ie is | 22 | 105 Totals 36a | — | 8 | 36 | 54 | 156 | 124 | 746 | Whiteness in Hybrid Parent. Whiteness in Coat-Colour in Mother. TABLE LI Hybrid Parent. TABLE LILI. Coat-Colour in Young. A a | b c a e g Totals 61 a i\ee te a aaa 6 | 15 2 118 ioe os 3 | 30 | 13 | 96 3 152 23 + — 3 Se eae 4 1 39 207 | 21 | 5 | 98 | 36 | 65 5 437 | Totals | 368 | 23 | 12 | 167 | 55 | 110. "| <1 746 TABLE LIILI. Whiteness in Young. QD o = : 3 297 — 8 32 46 100 108 39 — — + 4 14 11 4 = — — ee 2 2 Totals 74 591 72 9 Coat-Colour in A. D. DARBISHIRE TABLE LIV. Coat-Colour in Offspring of Hybrid x Albino and in Hybrid Parent. Coat-Colour in Young. 51 APPENDIX IIL. Note on the Absence of anything like Telegony in the Albino Mice used. It is well known that albino mice, paired together, breed true in coat-colour and in eye-colour. The following table, in which the notation is the same as that used in the previous part of the fo) ? present paper, records a fairly long series of cases in whicb a female albino mouse was mated, first with a coloured mouse of some kind, and afterwards with an albino. The table shows clear] ) y enough that in no single case did an albino doe, which had previously produced coloured young by a coloured buck, fail to produce a truly albino litter when subsequently mated with an albino A a b c d e g Totals = a 28 «18 2 25 i 74 na |) .€ 297 5 Sp 13-2430 | 97 9 591 Fe) pace 39-| 2 — 1 11 11 8 2 72 s |e 4/—]— — = ae aes 9 Totals | 368 | 23 | 12 | 167 | 56 | 110 |-11 746 buck. I. First Non-Albino Mating cranes ! I. First Non-Albino Mating TEES Type of Buck Offspring Offspring Type of Buck Offspring Offspring Japanese Waltzing “Extracted Domin- mouse .., 2c, 2d, 2d, 3d, 5d, 5d 4 alb. ant” 3a (pw) ... | 5a, 5e, 5c, 4e & 4 alb. 8 alb. Waltzer Qc, Ye, Bc, Qe, 2c, Ad 3 alb. Waltzer »» | 5e, 5e, 5e, 5c, 5c, 5c, 5e 6 alb. Waltzer 2e, 2d, 3d, 3d, 4d, 4d (i) Lalb. | “Extracted Domin- | | (ii) 5 alb. ant” 3a (pw) ... | 5be & 3 alb. 7 alb. Waltzer 3c, 3c, 5c, 5c, 5e, 5e | 4alb. | Waltzer ... ta | 26, 20,80, OC, -DC, OG, OC 8 alb. Waltzer 3c, 4c, 4c, 4c, 4c, 4c, 4c 2 alb. Waltzer 2c, 2c, Ye, Yo, 3e 5 alb. Waltzer le, 2c, 2c, 8e, 4¢ 3 alb. Waltzer 60, 5d, 5e, 5e, 5e, 5e, 5e 1 alb. Waltzer ... ... | 4e, 4c, 4e, 5c, 5c, 5c, 5c, 5e | 7 alb. Waltzer Bio, Bia, Bla a, a Xo 8 alb. Normal chocolate Waltzer 5e, 5e, 2c, Ye, Qe, 3c 6 alb. mouse ... 6e, Ge, 6e, 6g, 6g 6alb. || Waltzer ... ... | 3e, 3d (p) 3 alb. Hybrid (5c) 5e, 5d, Ge & 2 alb. 8 alb. Black-eyed Fawn | 6a, 6a, 6a, 6e, 6g 8 alb. Hybrid (5c) 6d, 6d & 2 alb. 2 alb. Hybrid (5c) 5e(very pale), 5c, 6g&2 alb.| 5 alb. Hybrid (5c) 6d, 6d, 6d, 6c & 1 alb. 3alb. |) Hybrid (2c) 5e, 5d, 5c & 5 alb. 8 alb, Waltzer ... All still-born 5 alb. Hybrid (8e) 6c, 6e, 6c, 5d, 6d & 3 alb. 7 alb, Hybrid (3c) ... | 4e, 4d, 4d, 5d & 5 alb. 5 alb. Black mouse 6c & 1 alb. 4 alb. Hybrid (3c) ..- | 6e & 5 alb. 3 alb. | Waltzer 5e, 5c, 5e, 5e, 5e, 5c, 4c 7 alb. Hybrid (3c) ... | 4d, 4d, 4d & 3 alb. 4alb. || Waltzer 5e, 5e, 5e, 5c, 5e 4 alb. Waltzer 5e, 5e, 5e, 5e, 5e, 2c, 3c,3e,3¢| 5 alb. Waltzer 5e, 5e, 5c, 5e, 5e, 5e 7 alb. Waltzer ... 5e, 5c, 5e, 5e, 2e, Be, 4c 5 alb. || Waltzer 5e, 5e, Se, 5e, 5e, 5e 7 alb. Hybrid (2c) 6e, Ge & 3 alb. 1 alb. Waltzer ... 5e, 5c, 5e, 5e, 5e, 5e 7 alb. Black mouse 6e, 3e & 6 alb. 6 alb. Hybrid (3c) 5¢ & 1 alb. 7 alb. Waltzer 3c, 5e, 5e, 5e 2 alb. Waltzer .. 3c, 3c (w), 3c (w), 4c 8 alb. Waltzer ... | 5¢e, 5e, 5e, Qe, 2c, Ye 6 alb. Waltzer 5e, 8¢e, 3c, 8c, 3c 7 alb. “Extracted Domin- Waltzer 5e, 5e, 4c, 3c, 3c 7 alb. ant” 8a (pw) ... | 5a & 2 alb. 8 alb. Waltzer 5e, de, 5e, 5c, be 8 alb. _ ... | 5d, 5d, 5b, 5d, 6,60 & Lalb.| Qalb. | GRADUATION OF A SICKNESS TABLE BY MAKEHAM’S HYPOTHESIS. By JOHN SPENCER, Actuary. SOME time ago an examination of certain sickness tables suggested to me the possibility that for a considerable period of life a law analogous to the well-known law of Mortality of Makeham might be found to apply to Sickness, ie., that the force of sickness at any age w or the proportion of persons sick out of the number living at the precise moment of attaining that age might admit of being expressed in the form A + Bc*, and I made various experiments to test the theory. Since that time Mr W. Palin Elderton, who had also investigated the same point, has referred to the matter in Biometrika*, and in a paper read in September, 1903, before the International Congress of Actuaries in New York, and has given the values of log,,¢ deduced by him from various sickness experiences. The idea of a mathematical law governing Sickness is by no means a novel one. In a paper submitted to the International Statistical Congress in 1860 + Gompertz suggested that for ages between 20 and 60, S,, the rate of sickness at age « or the average number of weeks’ sickness experienced during a year by persons of that age, might be written kg”, from which would follow the relation log S, = A, + B, ¢,”. Again Makeham himself dealt with the subject in 1871 when he read a paper “On the laws of Sickness and Invalidism” before the Institute of Actuariest. He concluded from his investigation of data then available that the quantity h, con- sisting of the number of healthy, as distinct from sick, persons aged « out of l, the number living on the usual form of mortality table, was a function of the form ks*g, this being the shape assumed by the J, column when Makeham’s law of mortality apples. This theory of Makeham’s regarding sickness possesses one or two advantages of some importance and it differs from the other hypotheses * Vol. ur. p. 504. + Reprinted in Journal of Institute of Actuaries, Vol. xv1. p. 329. See also Phil. Trans. Vol. 152, p. 554. t J. I. A. Vol. xvi. p. 408. JOHN SPENCER 53 mentioned above in introducing the element of mortality. It gives (1 — Z) as the force of sickness at age x and leads to the result colog (“) =A,+ B,c.?. The material which formed the subject of my investigation is embodied in Mr A. W. Watson’s important work on the Sickness and Mortality Experience of the Manchester Unity Friendly Society for the five years 1893-1897*. The magni- tude of the data there dealt with—embracing as they do no fewer than 39,000 deaths in the quinquennium and the record of upwards of 7,000,000 weeks of sick- ness—and the care and accuracy with which the observations have been analyzed and tabulated entitle the results disclosed in the volume to a degree of authority to which no previous investigation of the same character can lay claim. Mr Watson’s exhaustive enquiry led him to deal with his voluminous data upon novel lines, and we find tabulated the mortality experience of various sections of the Society grouped according to geographical situation, while as regards Sickness the element of occupation was the factor which determined the classification, the experience of each of the four following groups of trades being published :— (a) Agricultural and General (Normal) occupations ; (b) Building Trades, Railway, Seafaring and Outdoor Labouring Occupations ; (c) Quarry Workers, Iron, Steel and Chemical Workers, &. ; and (d) Mining Occupations. The first of these groups is the one to which the following notes relate. It consists, broadly speaking, of persons engaged in occupations involving no special hazard, and comprises nearly 80 per cent. of the membership of the Society. These lives were during the quinquennium exposed to risk of sickness for 2,352,099 years, while they experienced in the aggregate 5,289,586 weeks of sickness in the period. Throughout the investigation in determining the quantity “Exposed to Risk of Sickness” it was assumed, with a particular object in view, that lives dying in any calendar year during the period of observation were at risk until the middle of the year. In consequence of this assumption the ungraduated rates of sickness which were obtained by dividing the number of weeks’ sickness experienced during the year by persons of a particular age by the quantity “Exposed to Risk” at that age differ from the rates of sickness ordinarily tabulated. They represent rather what might be termed central rates of sickness, or, approximately speaking, values of the force of sickness at the middle of the year. The latter consideration enables us on the hypothesis which I am discussing to write the tabulated rate of sickness in the form A + Bc*t? and suggests a simple method of deducing the values of the constants. Having for reasons which will appear presently come to the * London: C. and E. Layton. 1903. 54 Graduation of a Sickness Table by Makeham’s Hypothesis conclusion that a Makeham curve* would not apply throughout the whole of the table, i.e., from age 16 to 100, I ultimately divided the data for ages 19—78 into three groups consisting respectively of ages 19—38, 39—58, and 59—78. The ungraduated rates in each of these groups were summed, the resulting totals being 20 204 + Ba Sa? c-—1 204 + Bos, — 1 c—-1” 20 and 20A + Bc ~ = - : Differencing these, we have an obvious means of deducing the value of log c”, and hence the values of the other constants. The following are the constants resulting from this grouping t :— A = "747127. B= '00680912. logy) ¢ = ‘0462118. The values of A and B are here given in weeks, and would have to be divided by 524 to furnish the corresponding yearly values. At the outset, in considering to what extent of the table a Makeham curve could be fitted, one or two points presented themselves which made it clear that the hypothesis would not apply for the whole of life. At the beginning of the table the evidence points in my view to a fall for a few years in the rate of sickness, a feature which is not singular to this section of the Society’s experience but is reflected in the observations relating to other occupation groups. Again towards the later years of life, Le., from about age 75, there is an unmistakable decline in the ratio at which the rate of sickness increases and a tendency towards a constant rate of sickness of about 40 weeks per annum as will be seen from the following average unadjusted rates :— Desert Average rate of Se BrOuP | sickness in weeks 68—72 13°78 73—77 21°24 TS—82 29°02 83—87 34°72 88—92 37°25 938—9I7 39°73 Considerable weight may I think be attached to these quinquennial rates since they are based upon a relatively large number of observations, one of the distinctive * In speaking here, and in what follows, ofa Makeham curve or graduation I refer to the hypothesis formulated at the beginning of this paper and not to Makeham’s own theory of sickness. + [Mr W. Palin Elderton has at my suggestion worked out log,,¢ by the method indicated by him in Biometrika, Vol. u. p. 503. To fit Mr Spencer’s range from 19 to 78, he took the origin of his exposed to risk normal curve at 42°5 years, and he found log,,) c= ‘046,0043. Considering the complete difference of method, Mr Elderton’s result closely confirms Mr Spencer’s value. K. P.] JOHN SPENCER 55 features of the new Manchester Unity Experience being the extent of the data at the old ages. It is of course clear that neither the decline in the rate of sickness from age 16 to about age 20 nor the bend in the curve exhibited at the other end of the table could be reproduced by a Makeham graduation without the aid of supplementary curves, and as for the moment I was concerned not so much with a graduation of the whole table as with an attempt to fit an A+ Bc* curve to as great an extent of the table as possible I decided to confine my attention to the facts for ages 19—80. I made various groupings all of which gave a value of log, ¢ approxi- mating to ‘046. Eventually however I chose the data for ages 19—78 for closer investigation and from these deduced the constants given above. The following table shows rates of sickness based on these constants. For purposes of comparison the ungraduated rates are also given, together with the adjusted rates published in Mr Watson’s volume. These latter it may be remarked were obtained from the rough rates by the application. of a 15 term summation formula. Central Rates of Sickness. Rates on porated Official Rates on Taeraduatea: | Official Age Makeham a t Adjusted Age Makeham nan ye Adjusted Hypothesis ace Rates Hypothesis us Rates + - 2 a 20 807 823 *815 50 2°215 2°146 Qe 21 814 “808 810 oi 2°380 2°358 2°347 22 822 810 814 52 2°564 2°550 2°539 23 *830 "824 823 is 2°767 2°764 2°750 2 839 837 834 54 2994 2°958 2°978 25 850 853 845 55 3°247 3°240 3°221 | 26 861 851 856 56 3°527 3496 3481 | a7 874 881 867 57 3°839 3°773 3°759 28 888 876 881 58 4°186 4-096 4°065 29 904 890 898 59 4°573 4°398 4°413 30 922 ‘917 918 60 5002 4°799 4°821 31 942 "952 941 61 5°480 5°320 5°310 32 963 959 ‘966 62 6:013 5°827 5°893 33 “988 1-000 ‘991 63 6602 6°523 6°570 34 1:015 1-009 1:020 C4 7°260 7394 7°335 35 1:045 1:063 1°052 65 7991 8-190 8°183 36 1:078 1-086 1091 66 8804 9°290 9°117 37 1115 1:127 1°136 67 9°709 10-0385 10°153 38 1°157 1:176 1190 || 68 10°715 11°136 11°302 39 1:208 1:257 1:249 =|| +69 11°834 12°472 12°559 40 1°254 1315 1313: || 70 13°079 14°092 | 13°9138 41 1311 1°392 1°378 71 14°463 15°384 | 15°346 42 1°374 1:437 1°443 72 16°003 | —-16°952 | 167846 43 1:444 1°510 1°508 73 17°716 18°202 | 18°409 AL 1°522 1°582 1°574 74 19°621 19°951 20°036 4S 1°610 1°632 1°643 75 21°740 21°619 21°713 4G 1°706 1°726 1:717 76 24°098 | 23°641 23°397 Av 1°814 1°813 1°804 a 26°719 25°055 25-061 48 1°934 1°877 1:907 78 29°635 26°776 26°688 49 2°067 2°037 2°030 79 32°878 28°050 28°265 56 Graduation of a Sickness Table by Makehan’s Hypothesis It will be seen that on the whole my graduated rates run very closely to the unadjusted values until about age 55. Above that age the agreement is not invariably so marked and from age 75, as might have been anticipated, the two series diverge rapidly. Obviously the graduation fails to fit the raw data above age 80 and, apart from this circumstance, the fact that after a certain point the value of the force of sickness would exceed unity, or 521 weeks per annum, forms a theoretical objection to the hypothesis as applied to the final ages in the table. Makeham’s own theory of sickness avoids the latter difficulty, though, after investigation, I conclude that it fails satisfactorily to represent the sickness after age 80 in the table under examination. To show the extent to which the graduated rates of sickness reproduce the actual sickness experienced when multiplied at each age by the number “ Exposed to Risk” I now give the following comparison :— : Excess of | Ratio per cent. Bits onesies weeks | A ae noe Expected over of Excess to roup of Sickness of Sickness Netual NotGal 16—29 659,739 658,029 + 1,710 + 3 380—389 | 645,877 652,620 — 6,743 —1:0 4O—49 700,681 715,141 — 14,460 —2°0 50—59 | 938,759 924,705 | +414,054 +155 60—69 | 1,035,598 1,046,278 | — 10,680 —1°0 70—79 1,609,216 1,005,771 + 3,445 + 3 Totals 4,989,870 5,002,544 — 12,674 — 25 As a final test of the graduation I append the values at 3°/, interest of a benefit of £1 per week during sickness throughout life as compared with those published officially, the mortality assumed in each case being that exhibited by the members of the Society in Non-Manufacturing Districts, designated Area 1 in Mr Watson’s volume. For the purpose of calculating the former values it was necessary to deal with the sickness above age 79 and I made the convenient assumption of a constant rate of sickness from age 80 onwards of 34634 weeks per annum, this being the value of A + Bc given by my constants. The average rate of sickness at these ages according to the observations is only 32°724 weeks per annum, but the adoption of the higher value not only avoids the assumption of a diminishing rate of sickness but introduces a factor which compensates for the deficiency of Expected Sickness up to age 79. Strictly speaking perhaps I should have worked out monetary values from the unadjusted data for comparison with those now calculated, but since the graduation upon which the official values are based is in effect a smoothing-down process which reproduces the prominent characteristics of the rough data, the published values may confidently be employed as a standard of comparison. Values at 3 per cent. of a Benefit of £1 per week during Sickness Biometrika 111 JOHN SPENCER throughout life. A On Makeham og Hypothesis | £ 20 57°44 25 63°26 30 70°25 35 78°35 40 87°74 4S 98°54 50 110°50 55 123 °84 60 137°67 As published £ 57°39 63°22 70°24 78°32 87°58 98°01 109°88 123°21 137°34 57 PRELIMINARY NOTE ON THE PROTECTIVE VALUE OF COLOUR IN MANTIS RELIGIOSA. By A. P. pt CESNOLA, Queen’s College, Oxford. DuRrInG last summer vacation, at Professor Weldon’s suggestion, I undertook a small series of experiments upon protective coloration from a statistical standpoint. The form chosen was Mantis religiosa, which occurs in Italy (where the experiments were made) in two forms, a green and a brown. It is interesting to notice that the green form is always found upon green grass, the brown form upon grass burnt by the sun. The green form is characterised by its more sluggish behaviour; the brown form is more active. For the purpose of this experiment I collected 110 specimens of Mantis religiosa, 45 green and 65 brown. Each individual was tied by a silk thread about six inches long to a plant, the thread being tied round the animal’s thorax, and each Mantis being attached to a separate plant. The individuals were divided into four groups, two green and two brown ; of the green individuals, 20 were tied to green plants in a place covered with green herbage, the remaining 25 being tied to brown plants in a place where the herbage generally was burnt and brown. In the same way, 20 of the brown individuals were tied to brown plants in a burnt-up spot, and 45 were tied to green plants on a green piece of ground. The whole series was tied in this way and exposed on August 15th, and observations were made daily during seventeen days. The death-rate durimg the period of observation may be gathered from the diagrams Figs. 1 and 2, and it will be seen that during the whole period the 20 green individuals exposed among green grass, and the 20 brown individuals exposed among brown grass were untouched by enemies, so that all of them survived. Of the 25 green individuals exposed upon brown grass, the last was killed by August 25th, eleven days after the commencement of the experiment. Of the 45 brown individuals, exposed upon green grass, ten were left on September Ist. On the evening of September Ist a gale occurred, which ultimately swept away the remaining individuals, and brought the experiment to a conclusion. Of the individuals which died, nearly all were killed by birds ; but of the 25 green individuals exposed on brown grass, five were killed by ants. It will of course be necessary to repeat the experiments upon a larger scale ; but they seem to show in a fairly convincing manner the value of protective coloration. BS Number of Survivors Fia. 1. A. P. pi CESNOLA [oo CP a Es es ee ae a ee ee ee : a ee a a a ee ee ee Eh Ee Ee Eee Ee a ee ee ee SS a ee ae ee ee es ee E22 a ee ee ee ee ee ee a7 ee eS ae ae ee ee (ET a a a | Ee Ee ee ee a es ee 4+} as ee ee ee ee a [ogee a ee a ee a ee a E21 RS ES ee ee ee ee ee ee (7 es a es ee ee ee +++ + ++ Ea at a a a a ez aca ae a ee ee ee CS Eel eae Da DD a a 72s Ee ee ae ee a ae ee ee he he be ee ee ee ee Ee a es a a a ee ee ee ee ee Cl ee ee ES Ee a ee ee ee ES Re ee ae Ee ee ee ee ee ee a Ee ee eee ee ee ee 2a a ey ey ee ee ee a ee ee Ee i Ri ee ie he eae Sl ee ee ee eee (3g EE ay | a (Sw a i Ws Lt LEG Ee Ee Ea ee es a ee eee RUBS eS er he Ez Be ee ee ee ee A es a a a ee ee ee RRR iN C7 (Ee Ces SE a DS a a ee ee SS at ee ae SS ee a ee ee Ee FO Ce ae Da Cat a ee 10 ee es a ee ee ee ee" ee i ES SS a es a a a 2S Pe es ae 9 20 21 22 23 24 25 26 29 August September Record of observations of 65 brown individuals of Mantis religiosa, 45 exposed on green and 20 on brown herbage. The circles show the number of individuals on the green herbage alive on each day of the experiment, the crosses the number of individuals alive on brown herbage. Number of Survivors Fig. 2. {=e LES) CE ER a AT ET a eT (Ta No ee Ce Ee ee ee ee ee ee De ee ESC Ee) ae a ee i Ee ES ee ee ee ee ee ee ee ee ee ee) a all A Rs ee a ee De I ae ee ee ee ee ee ee 7 Ee ee a ee ee ee (Eee a RT Se a Fae ee fea ee ee Ee ee ee ee eg (aaa A al es a a 2 ee a ee ee Ee ee a ee ee ee a a as a ee a Ee ee ee es ee Ce ES a (Ea a ae EZ Lae) a a ae a as ee ES ee Ee ee ee ee ae a a ee a ee Fe) ES ES a ee ae ee 2 SE a a ae ee ES ae ae ae RS CR (A (aa EA CC A DS et ee ee ee ES a Ee Ee Es CES EE) Cs CS SS EE TT OS Cae HS 16 16 17 18 19 20 21 22 23 04 25 20 27 28 29 30 31 1 August September Pecord of 45 green individuals of Mantis religiosa, 25 exposed on brown herbage, and 20 on green. The circles show the number of those on brown herbage surviving on each day of the experi- men}, the crosses show the number of survivors on green herbage. 8—2 MEASUREMENTS OF ONE HUNDRED AND THIRTY CRIMINALS. By G. B. GRIFFITHS, M.R.CS., L.R.C.P., Dy. Medical Officer, H.M. Prison Service. WITH INTRODUCTORY NOTE By H. B. DONKIN, M.D., F.R.C.P., One of H.M. Prison Commissioners and Directors of Convict Prisons. THESE Tables are intended only as an indication of the method of certain anthropometrical observations which are now being carried out by the good-will of the Medical Officers of the English Convict Prisons. No conclusion from such a small number of cases is, of course, to be attempted. The whole scheme, of which these notes are but a sample instalment, has for its object the collection of large numbers of observations, anthropometrical and otherwise, on criminals undergoing sentences of three years and upwards, without any selection whatever. It is hoped that in the course of time such results will be attained, as may possibly throw some light on criminological questions which have been raised, and sometimes prematurely solved, by various writers. The present preliminary observations were made by Dr Griffiths at Parkhurst Prison according to forms decided on in consultation with Dr Smalley, the Medical Inspector of Prisons, and myself. It is to be noted that they differ from those which will be made in future in that a certain selection of cases has been made, the larger scheme not having been completely formulated at the time. H. B. DONKIN: Method of Measurement. The person to be measured is seated and looking directly to his front, the head being in the “ Horizontal Position,” Le. so that a pen placed clerkwise over the ear will join the external angle of the eye and the topmost junction of the external ear and head. G. B. GrirFitTus 61 Next, a steel tape, weighted at either end, is placed on the head at the External Occipital Protuberance and carried forward along the Vertex and middle of the forehead to the chin. The weight will keep this tape in position and a similar weighted tape is placed coronally from one External Auditory Meatus to the other over the Vertex. Where these steel tapes cut each other on the Vertex it is agreed for the purposes of these investigations to call the Bregma. The Antero-posterior Curve is the first measurement taken by means of a steel measuring tape joing the Nasion and External Occipital Protuberance. This curve will be cut into an Anterior and a Posterior segment by the tape stretching from one External Auditory Meatus to the other. Next, with the crossed tapes still in position, the Horizontal Curve is taken by passing the measuring tape round the head from the Ophryon along the right side, over the External Occipital Protuberance and forward along the left side to the Ophryon again. The crossed tapes will cut this Circumference into four moieties : (i) Right Anterior. (u) Right Posterior. Gii) Left Posterior. (iv) Left Anterior, In taking this measurement, (1) the whole Circumference is noted, then (2) the distance from the Ophryon to the Right Auricular line, 1e. the tape joining the External Meatus; next, the number on the tape at the External Occipital Protuberance where it cuts the Anterior Posterior one; next, the number on the Left Auricular line. Supposing (1) to be 15 cm., that is the measurement of the Right Anterior Segment, and (2) that the tape marks 380 cm. over the External Occipital Pro- tuberance, 30 — 15 = 15, which is the measurement of the Right Posterior Segment. The two remaining segments are similarly got by subtraction. The Cranial Height is taken :—a vertical standard with a horizontal arm at right angles which will slide up and down is placed by the subject’s side with the horizontal arm pointing coronally across the head and just touching the Bregma. One limb of the callipers is placed in the middle of the External Auditory Meatus, and the other so as just to touch the lower surface of the horizontal arm. The vertical distance is the Vertical Height. Cranial Length is the direct distance from the Glabella to the External Occipital Protuberance. Cranial Breadth is the greatest Bi-parietal Diameter. The Face Length is taken as the distance from just below the middle point of the chin to the Nasion. The Face Breadth is the greatest Bi-Zygomatic Diameter. \ 62 Measurements of One Hundred and Thirty Criminals “Facial Symmetry” is not a measurement but is judged by carrying the steel tape from the External Occipital Protuberance forward to une middle point of the Chin and noticing which side is greater. “ Nasal Deflection ” is judged in a similar manner. The Curve of the Forehead is taken:—the limbs of the callipers are fixed at 10 cm. apart, and one limb placed on the Nasion and the other on the Vertex in the middle line. The curve between these two points is measured with the tape and is the Forehead Curve. The Auricular-Alveolar, Auricular-Nasal, Auricular-Occipital, and Auricular- Mental Diameters are taken with the callipers, and are the distances between the Middle of the External Auditory Meatus and the Alveolar Point, the Nasion, the External Occipital Protuberance, and the Chin respectively. The Chin and Occipital Projections are taken by placing the standard behind the subject with the horizontal arm pointing forward. A weighted tape is hung from the horizontal arm and hangs plumb, just touching the External Occipital Protuberance or Chin; and the distance taken by callipers between the External Auditory Meatus and a steel bar at right angles to this plumb-line is the Projection required. The head measurements are all expressed in millimetres. The Horizontal Circumference is divided into four segments to facilitate the comparison of the Anterior and Posterior and Right and Left Segments. The following terms and abbreviations are used in describing the shape of the Nose :— Rect. = Rectilinear, Concave, Convex, Hump, Und.= Undulating, refer to shape from Nasion to tip; Hor. = Horizontal, Elev. = Elevated, Desc. = Descending, refer to angle from tip to junction with upper lip. The present investigations have been made on 100 “ Ordinary ” and 30 Lunatic Criminals. ‘Cepnalic Index Vertical Index : ) a ae oe ee in je Ae 100 “ORDINARY” CRIMINALS. ‘TABLE I. ReG. anp Cum N 53} ” WGN 964 _—,,, L 623 ” U 327 7 U 88 ” V 356 ” KP 260 ” X53 ” V 357 ” W 433 ” X176 ” Y 428 ” Z134 ” Z 426 ” Z 225 ” a74 ” a 45 ” a 137 ” a 370 ” a 420 ” > 120 ” b 467 > 6 326 ” b 343 ” IX 472 ” b 252 Forgery b 371 Emb b 372 Forgery X 69 Theft 0265 _., b 378 Felony .. b 301 Fraud a 339 Theft Na 48 Theft ... a 474 Burglary b 462 Theft b 349 Felon 6 361 Theft ... Wh 361 Theft TNSb 335 Theft b 357 Shop breaking... b 321 LKTb 242 Burglary _. DMQL 289 Theft b 320 Receiving LISY 1261 Theft P 140 Marder Q91 n Q 433 Cs, R126 Cs, R388, T3897 R475, T7403, M547 (Cs, H826 =, T7295, M145 s, M744, N399 N 63 ” Q430 ,, U 548 Cs, V207 =~, Wi44 Vv 384 =a, W313 ~=C, W504 SC, \ | Antero-posterior ~ Wounding with ZH. nad intent to murder zlemen a 433 Falsifying Accts Facr Poneneay Nose i ke co | # | x . 5 a: 2} = | compra meen eye feed el |e llineiete|| gene ceties a E & a a = Z| 2 5 aS ¢ E S | elealal2) 2) ee.) 6 | ses 5 : | Ey 3 2 CS ay et 435 3 | tS) e ol toss 3 A moa 3°2 133 | 108'1 HB Concave, Elev. 6 138 | 115°0 LR Concave, Elev. 8 133 UR Rect., Hor. $5) 136 HB Hump, Hor. | Bi 143 MB Concave, Hor. | 73°72 135 MR Convex, Blev. i I41 MB Rect., Bley. 132 = MBR Und., Elev. 139 at | HB Coneave, Eley. | 135 a+ | HB Hump, Hor. 136 = | WB Und., Hor. 137 = | MB Rect., Hor. 143 = || HB Und., Hor. 135 =) HSq. Concave, Eley. 142 L+ HB Rect., Hor. | 142 L+ HB Und., Elev. 140 = || HB Und., Rect. 133 = || MB Rect., Wey. | | 143 = LB Coneave, Bley. | 137 UGH. LB Rect., Hor. 135 L+ MB Und., Dese. 145 = AB Convex, Desc. 155 L+ MB Und., Eley. 133 L+ MB Reet., Hor. 130 R+ MB Coneave, Bley. 146 L+ MB Concave, Hor. 136 R+ HB Hump, Dese. | 138 = MB Rect., Bley. | 145 L+ HB | 135 = MB Concave, Hor. | 143 = MB Hump, Rect. 139 L+ | MB Concave, Blev. 136 D+ | LB Hump, Rect. 147 _—— | ME Hump, Rect. 130 | L+ | MB Concave, Eley 143 | = | MB Hump, Rect. 150 || vate | HB Concave, Eley. 135 Ge | MB Coneave, Eley. 140 | L+ LR Und., Bley. 138 L+ LB Concave, Rect, | 135 L+ MB Und., Eley, | 143 = HB Rect., Hley. 137 L+ MB Reet., Hor. 137 Tiree HB Rect., Hor. | 134 L+ LR Concave, Elev. | 137 = LR Rect., Hor. 128 L+ MB Und., Eley. 140 Le+ MB Und., Desc. 148 Li MB Concave, Bley. 132 L+ MB Convex, Hor. 136 = MB Concave, Hor. 139 L+ HB Reet., Hor, 146 R+ MB Rect., Dese. 12 R+ Projecting} Reet., Hor. 133 R+ LB Rect., Elev. 132 = MB Rect., Bley. | 12 Re AB Concave, Eley. 137 n+ MB Rect., Bley, | 41 = HB Rect., Hor. 310) = HN Convex, Elev. 143 b+ MB Convex, Hor. 126 | = AB Rect., Hor. 123 | = HB Convex, Hor. 121 = || HB Reet., Hor. 127 = B Hump, Hor. 136 R+ LB Hump, Elev, 142 R+ HR Convex, Bley. 133 = LB Treet., Mley. 130 L+ M Concave, Eley. 123 = MB Hump, Eley. | 122 = HB Kect., Hor. 133 s MB Convex, Eley. nn 110 110 118 114 117 118 119 117 115 117 115 112 115, 121 110 | 107 115 113 110 114 113 | 118 119 109 108 117 115 116 113 121 117 110 120 124 113 120 120 105 119 115 112 115 It4 112 114 121 | 117 116 110 118 115 112 116 112 122 122 121 122 113 121 123 121 128 115 115 110 117 107 110 Auriculo-Nasal Diameter Gnathic Index Auriculo-Occip. Diameter Occipital Projection Length—Left adherent not adherent Chin Projection Lobule. Length—Right N General Obseryations ee | Auriculo-Alyeol. Diameter Sau ee Auriculo-Mental Diameter 130 133 GEA CaF 130 132 RR) Gl mt Ba Nooo FOWUKUA 130 baw vo DAA (A) An 122 132 135 Locomotor Ataxy W. M. W.M. [tuberance Depression aboye ext. occip. pro- Depression above ext. occip. pro- [tuberance. German Rudiment of Darwin’s Tubercle ‘Rudiment of Darwin’s Tubercle Darwin’s Tubercle Hairs on tips of ears {of External Bars Meati imperforate: Mere vestiges Darwin’s Tubercle L. Depression in sup. oceip. region Malars prominent * Concurrence slight. ran = aoe = ae a a RS A A aE, = (f he | | Xapuy [Bory10 A | xepuy orpeydag 79°8 CO NH Nind Indo AND Rind MOOD MHHODMD AR +O J SS SO 0 8 A | OM DOOD HA OFMANOWDNAHMMNHOO +R Ow Mo Te POW nN MmaNAtTNW + (2) mnmnnanocoO WOUOMUOMOODOONON ~~ 2 ° Po = Orantoat aot Reo | ; : CRIMINALS. | » AN: atl =| “3 ND CRIME iS = | g = 1 Face v ie a Blelelelz|2 =| = | S| : Founneap N 3 T ° 5) ae |e g | ni = OSE AB 7 BE | alis = | & ey | I) Gaya | 8 ra | ' = : : 2/3 h))] == LE I—continued. lege a) eden EB incoales Neate for lmeersre | Ble | |= eee cae i SS en eile Pt he le a/eis 4/¢ ip a Se ealtanaas a) 2|& = i = = al 2 We Slneeii reals a leith st 3 has) et Pe 2 Be = St Er | =} (cea leans cram as W 503 M _|—|— = | iesileealeee lt eatellite Heelies led || eae || 2 ale {| ehh eee ee eee ieee urder allaal ——| : eS al BI a 5 6 | 3 a | 282 iB a 2a en ee S| eae || S pel su lhe re H | 145 | 165 | 565 | 130 — | see esi Pas e I e i 4 epee: || rr s]4|4 a Si) anen iaes ole|s 238 | soil Ser ervchl eas eich | a | g || Slee eens Be |a|e2 G | | | | | 145 | 275 | 290} 135 | 19. le Sil | FS a ict a it Gy (ae 2\4 | 4 qi bo ee 5s yeneral laa 35 | 194 153 | 79°8 | 69'5 a Mes lees 3 eae le|/e|/2)4 | 3 |2s® Observations | | | | | | f | | 69°5 | 120, 128 | 106° | KR 2 5 5 i216 a |o 2 | m@loas |X 228. j | | Ve alhees| | | te | ot uxq | cB | Und. [ea ES styl 3 2 | Be eae | | fee o «+ | 335 | 170 | 165 | 563 | | | | | | Und., Elev. | R | 120 — 4 A a “1X 930 38 SAH es 165 | Bee || seat hneg | weall ea oe | | Se ucarad losses age Wane eel rea tees = a Be ae 4 | 18 2 35 | 15 ieee 293 | 270 j | Fs || efe linexe === Y 95 «| 320 ee 154 | 570 | 130 a 140 | 135 | 270 gH | 32 | 105} 60 63 | N | Defici _ Y ” . | 315 | 4 | 156 | 560 50 | 150 | 140 | 2 ed 126 | | | eficient of last phi ea 2 315 | 170 | 145 | 560 140 | 145 | 135 | 140 | 270) (3300 eS S| MG! = é | efoion tof lect phalanx of Angers lia We sp a 305 | 105 | 140 Bay | 145 | 155 | 130 | 130 iieeor| 280 | rae, 134 | 1033] = x to | LB r | | Index, mid and thumb normal. 46 -- | 335 | 175 | 160 | 65 | 140 | 130 | 15 30 | 275 | 285 | 20 | 129 | 107’5| It c 00 + Coneave, Kley. | 2 | | h ind ring finger Z ” 75 | 160 | 565 | | 130 | 150 | 1 | 38 5 7°5| R+ d 1 LR , ley.) RR | | and are rudi gers of L, See eae | zeal ees etl ee Ie selliceiliess oF ase ieeell ce @_ {fue Hie |) ee nb. ie BUSH | ea | LH | tee) 10a a Gee ee fasten- C a ve | 3 180 3 B5 ler af | 262 | 298 34 128 aos | ra : vs ect., Blev s 2 122 q “ft | 12 a a bag. 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Eden 2 "Rape 2] 310 | 150 | 160 | jo | 140] 145 | 145 | 270 | 300 | 27 | 132 | 103°8 | = c ; Ree seule 116 | 116 | 100 27 | 120 | 140 | 8 3/55] 4 7 “| |MV278 Rape... 300 | 105 69 | 530 | 120 | 1 3 | 145 | 140 | 280 | 200 | pt eral bell L+ a i) ray |leieconttit R | 122 | 122 © 140 | 108 7) 58| 62] 4 | | | 135 | 5s 3 299 2 | 136 | 110° 110 5 onvex, We | 122 | 10070 13 137 | loo ts U 559 Pe ... | 320 || 135 | 555 | 140 eS | 110 | 130 | 250 | 28 116 | 1 35)|| Za || iC LR ; vy. | R pur | i oro 137 | 102 | 143 70 |65| WN Tygso met | San 198 | 70 | $40 | 130 | 10/135 125 abo | 275 6/1 | Hoe) ey | ¢ | ne ue nYiag | 120 | 041 35 Jit; | 137 | ‘08 | 68 | 90 |W 319 --» | 320 | 170 | | 140 | 13 125 | 255 | 28: 125 | 135 OT teal | ee MB | 108 | 107 | 99 125) 97 | 135 8) 70 N I ” as, 2 150 | 5 ‘ 30 | 15 hil ies 285 | 135 | toS4 | L 4 112 oR . ? 7 | 99'0 135 135 | 100 ewe eee ells Rapede: Ce te Sone ome let talelaiet a tetas 3 175 | 165 | 570 | 30 | 150 | 1 5280 279. | 130 | 104" | 110 Tain Hump, Hor. | " 117 | 1017 13 2 | 134 | 10 | 58 | 60] Rudi 2 V 334 Rive . | 325 | 17 5 | 570 | 14c | 150 | 50 | 130 | 260 | 300 he bee 40) D+ | ‘ HB ; , Hor. | R |r 7 136 A 58 | 60 eR OA Earn re 325 | | | 2 ORES OF |e 38 | 115" ne Il Gouvexaclore ING Il | 111 | 100% 30)) 1r5 | 133 < z A rwin’s Tubercli b 331 Theft TY .. | 320 | a | 150 | 540 | 130 | ee 160 | 120 | 260 \ 3 Fe || et 150} + ral o MB , Hor. | Nil} 116 Oo 124) IT 3) 95 | 66 70 N cle se = 70 | 150 | 555 60 | 115 He ee go | 109°5| = ; 110 : Rect., Hor. |N | 122 | 95:0 13 | 122 | 10, TOR as VaeaFraud | 435 | 160 lieaeul peer acyl wzes lees soel seen lage In) 48 elma a ee) ate Rect., Hor. 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By M. GREENWOOD, Junior. 1. Durtine the last few years, thanks to many improvements in our methods of analysis, several of the biometric constants of the human body have been investigated. The coefficients of correlation of almost all the separate bones have been ascertained with some accuracy, and the suspected relationship between intellectual and physical characters has been closely scrutinised. Under these circumstances it is strange that so little work has been done on the weights and correlations of the viscera. Even such a simple measurement as the weight of the heart does not appear to have been calculated from any adequate series of obser- vations. English text-books of anatomy give this weight on the authority of Reid and Peacock or on that of Clendinning. These two sets of observations are based upon very few cases. Peacock and Reid’s results are drawn from 181 males and 110 females, and Clendinning’s from 90 and 71 respectively*. It will be evident, therefore, that no great importance can be attached to them, even if we leave on one side the fact that they afford no materials for the study of correlation. Clearly, the only way to obtain data for the solution of problems concerning the absolute and relative weights of the viscera is to extract as large a series of observations as possible from the post-mortem department records of a large general hospital. The present memoir contains the preliminary analysis of such a series from the pathological data of the London Hospital. It might be supposed that post-mortem records would contain a very large number of available cases, and that the weights of the various organs would be found recorded with considerable accuracy. As a matter of fact, however, simple * Clendinning’s results are quoted in the English text-books, and also in Grisolle’s Traité de Pathologie Interne (9th Ed. p. 200, Vol. 11.). See also, K. Pearson: ‘‘ Variation in Man and Woman” (Chances of Death and other Studies in Evolution, Vol. 1. p. 316); Peacock and Reid: London and Edinburgh Monthly Journal of Medical Science, 1843-6, 1854. 46 Weights of Human Viscera measurements of this kind appear to be rather despised by post-mortem clerks, and the records are, from the quantitative point of view, very disappointing. Weights are frequently omitted altogether; sometimes we read “Spleen about 3 or 4 ozs.”; at others, the ingenious writer appears to have given free play to his imagination, and we read of a man of forty-six years of age having a heart weighing one ounce ! * It is much to be desired that, in future, more accurate methods of recording these simple observations should be adopted, so that large numbers of valuable facts may be rendered available for statistical inquiry. In my own research, after excluding the large majority of the examinations, there yet remained a considerable number of fairly trustworthy data suitable for tabulation, and this paper contains some of the results deduced therefrom, which it is hoped will not be without interest. I propose to divide my subject into four parts: First. I shall discuss the average sizes, variabilities, and correlations of the heart, liver, spleen, and kidneys in the general population, diseased and normal, to be found within a London general hospital. Secondly. 1 shall consider only cases in which the organs were found healthy on post-mortem examination. We shall thus to some extent be able to appreciate the influence of disease in modifying the biometric constants of the organs in question. Thirdly. I propose to deal with the influence of age on the biometric constants for the viscera in man. And, lastly. I shall consider the influence of certain special diseases from the same standpoint. All the data dealt with in this memoir are for males, the number of females in my collection being very much smaller. As far as I am aware, no Investigation of this kind on the viscera has yet been undertaken, and mine does not profess in any respect to be more than a preliminary study. Its object is to draw attention to the need of better post-mortem room records, and to indicate the wide field of valuable research which they open up, not only to the biometrician but to the physiciant. 2. The General Hospital Population. In my first series of tables I have dealt, subject to certain limitations, with a random sample of a general hospital population. To avoid the extreme changes due to youthful growth or senile decay I have tabulated only cases between the * LT. H. Path. Reports, 1899, No. 661. + “Il ne faut jamais négliger de peser les organes, surtout ceux qui sont atteints de lésions patho- logiques; le poids fournit souvent en effet des renseignements précieux sur le degré et sur importance des lésions; on n’oubliera pas cependant qu’il existe sur ce point des variations individuelles con- sidérables....... Le poids total du sujet, la taille, ’age, le sexe sont tout autant de conditions qui font varier le poids des organes eux-mémes.” (Bard: Précis d’Anat. Path. p. 736.) M. GREENWOOD 65 ages of 25 and 55. Such a “random sample” is, of course, also a selection in that it consists solely of those patients who died in hospital, and upon whom a. post- mortem examination was held. Thus it is far from being a random sample of the “general population ” of the country, many classes of which are never found in the wards of a general hospital at all. Evidently the population of a general hospital will chiefly consist of, (1) persons acutely ill, (ii) those suffering from surgical injuries or diseases, (111) sufferers from medical affections requiring special treatment. Chronic maladies of old age, such as bronchitis, indeed, any highly chronic disease, will be under-represented in comparison with the general death-rate. Similarly the number of cases of valvular heart disease and rarer disorders, such as Diabetes Mellitus or Insular Sclerosis and other nervous lesions, will be above the general average. Now, as pneumonia and bronchitis, particularly the latter, form a considerable number of the so-called “terminal affections” responsible for a large majority of all adult deaths, a random thousand necropsies will not give us the information we require as to the quantitative relations of average viscera, post-mortem. The error resulting from too few cases of senile bronchitis will be lessened, if not minimised, by the fact that we have confined our attention to cases of less than 55 years of age. But even thus we have too many cases of valvular cardiac disease, and as this affection tends to produce hypertrophy of the heart, the average weight in the first three tables is probably a good deal higher than that of the ordinary population at death. It is, of course, to be remembered that this “ general hospital population” does not mean the “normal” or healthy one. The above remarks are merely intended to show that a thousand deaths in hospital will not be due to exactly the same causes as a thousand deaths taken at random outside, and that therefore when we proceed to select sub-groups, such as “Normal Hearts,’ “Hearts in Pneumonia,’ etc., the material we have to select from is not what it would have been had we been able to start with 1000 random deaths in the population at large. And so, if we find that the average weight or variability of an organ is diminished when we proceed to special classes, we must bear in mind that possibly the change might not have been so striking if we had had a more representative sample to start from. General Hospital Population. TABLE I. Hearts with Livers. Number 1382. Mean Heart 13°53 ozs. Standard Deviation 4°680 ozs. Mean Liver 63°01 ozs. Standard Deviation 13°314 ozs. Correlation of Heart and Liver °1931+-0175. TABLE II. Hearts with Spleens. Number 1303. Mean Heart 13:07 ozs. Standard Deviation 4-067 ozs. Mean Spleen 6°61 ozs. Standard Deviation 3:345 ozs, Correlation of Heart and Spleen -1827+-0181. Biometrika m1 9 66 Weights of Human Viscera TABLE IIL. Hearts with Kidneys. Number 1293. Mean Heart 13°14 ozs. Standard Deviation 4°134 ozs. Mean Kidneys 12°68 ozs. Standard. Deviation 3°125 ozs. Correlation of Heart with Kidneys :2577+:°0175. In this table the weight is that of the two kidneys taken together. To these results I add a table of the coefficients of variation*, so as to obtain some ap- preciation of the relative variability of the organs in question. TABLE A. Relative Variability in Weights. | | Hearts with Livers | 34:59 Hearts with Spleens | ar mean 32°39 Hearts with Kidneys ... 31:47 Organ Coefficient of Variation Livers... E SoG) | Spo allel) Spleens ... Ar see Bll face eee 50°58 Kidneys ... ee ae gle Wee: .. = - 2463 The substantial difference between the weights of the heart in the cases when livers were measured with hearts and the cases when either spleens or kidneys were measured is due to the fact that the 1382 cases of the former only in part cover the 1292 to 1303 cases of the latter, the additional cases, amounting to three or four hundred, are due to entries in which only two or three weights were given. It seemed desirable to include all possible cases in order to utilise as much material as possible. But there has clearly been some special reason for measuring livers in the case of very large hearts which has not arisen in the case of spleens or kidneys. Thus with livers we have hearts up to 36 ozs., but with either spleens or kidneys only up to 28 ozs. On the whole with respect to both mean and variability, we may consider the hearts with spleens or kidneys to give a more reasonable approach to the biometric constants of the general hospital population than arises in the case of hearts with livers, where there is evidence of much more selection. We notice at once: (a) That the spleen is relatively much more variable than the heart, and the heart than the liver or kidneys. (b) That the heart mean is considerably higher than that usually given in anatomical text-books ft. * The coefficient of variation=100 x Standard Deviation Mean. + Peacock and Reid’s result on 181 male hearts is a mean of 10°699 ozs. The coefficient of variation calculated from their figures by Pearson is 19°825. For the liver, the mean (from 84 cases) is 53°48 and the coefficient of variation 14:32 (Pearson: op. cit. Vol. 1. p. 316). It might, however, be better to compare these numbers with the results given later for the ‘‘ healthy organs.” Pearson says that we may probably conclude from Peacock’s own statements that he ‘“ has cut off a considerable tail of really healthy hearts weighing over 12 ozs.” (op. cit. p. 317). M. GREENWOOD 67 (c) That there are quite sensible correlations between the weight of the heart and that of the other organs. 3. The “Normal” Heart. Let us now consider the “normal” heart. Evidently the ideal normal heart is hardly at present capable of measurement with respect to any character other than those related to its manner of performing its functions. Such an organ ought really to be measured during the life of its owner, and we cannot do this, as we are unacquainted with the exact relation subsisting between body weight and heart weight in the living subject. The following is, perhaps, the best approxi- mation to the truth that we are in a position to make. Correlation tables have been constructed for pairs of organs found to be healthy post-mortem. In any case in which I had the least reason to suspect the existence of disease, the measurements have been excluded. The following results were reached : Healthy Organs. TABLE IV. Hearts with Livers. Number 358. Mean Heart 11-04 ozs. Standard Deviation 1°928 ozs. Mean Liver 60°44 ozs. Standard Deviation 8°948 ozs. Correlation of Heart and Liver -2780+:0329. TABLE V. Hearts with Spleens. Number 517. Mean Heart 11°25 ozs. Standard Deviation 2°073 ozs. Mean Spleen 5:22 ozs. Standard Deviation 1:996 ozs. Correlation of Heart and Spleen -2654 + ‘0276. TABLE VI. Hearts with Kidneys. Number 413. Mean Heart 11°24 ozs. Standard Deviation 1:946 ozs, Mean Kidney* 12:01 ozs. Standard Deviation 2-016 ozs. Correlation of Heart and Kidneys *4004+ 0279. Drawing up a table of coefficients of variation as before we have: TABLE B. Relative Variability of Healthy Organs. | Organ | Coefficient of Variation Hearts with Livers... 17°42 Hearts with Spleens... 18°42> mean 17°71 Hearts with Kidneys ... | 17°30 Livers... oe ee aya eee 14°80 | Spleens ... Eee aes ae ee ool | Kidneys ... ae ee Wes ae 16:80 | * The mean value of the right kidney of 100 males 20 to 55 years of age, as deduced by Pearson from Reid and Peacock’s values, is 5°57 ozs. 9—2 68 Weights of Human Viscera From these results we infer, (a) That the average “healthy” organs are all lighter than those of the average general hospital population, and probably lighter than those of the general population as a whole. The weights are still, however, higher than those given by Peacock and Reid or by Clendinning. (b) In passing from the mixed hospital population to the class of healthy organs, we find in every case the absolute variability is reduced, and by very large amounts indeed, the variability of the heart by over 50 p.c., and the other organs by amounts even 30 to 40 p.c. of their value. (c) Relatively, the healthy spleen is still the most variable organ, and the heart comes second, but the kidneys are now close to the heart and the liver not very far behind. Disease appears to affect the weights of heart and spleen most, of livers and kidneys least. We notice that our value for the coefficient of variation of the healthy heart is now 17:7 as against the result deduced from Peacock and Reid’s measurement of 19°8 and for the liver 148 as against their 143*. We could hardly have antici- pated such good agreement, and it certainly tends to confirm the value of the coefficient of variation as a fairly “steady ” biometric constant. 4. Influence of Age on the Weights of the Viscera. I have first considered the change in the absolute weight of the adult male heart with age, and I have then investigated the influence of age upon one set of correlations and variabilities, i.e. those of heart and spleen. Table VII. gives the correlation between age and weight of heart in the case of health. We deduce the following values of the constants : TABLE VII. Relationship of Weight of Healthy Heart to Age. Number 699. Mean Heart 11°13 ozs. Standard Deviation 2°015 ozs. Mean Age 40°23 years. Standard Deviation 8°500 years. Correlation of Weight of Heart with Age=-1363 + ‘0250. There is thus a distinctly sensible increase of heart weight in health with age, the coefficient of correlation is more than five times its probable error. Still the correlation is smaller than what we might possibly have anticipated. Calculating the regression line we have, if H, be the probable weight of heart in ozs., and A the age in years: HH, = 9°8322 + 0323 A. Thus the average healthy heart gains about 40z. per ten years. For example we have: * Pearson (The Chances of Death, Vol. 1. p. 318) gives 20°49 for the coefficient of variation of the right kidney as deduced from Peacock and Reid’s measurements, as against my values of 16°80 for healthy and 24:63 for general hospital weights of both kidneys. M. GREENWOOD 69 Average weight of Heart at 20 years is 10°48 ozs. 30)» py oan LOSO! y, 40 Gee) eli BO? 55, LEAD u,, i COs Le As far as I am aware, the correlation between age and weight of body in adult males is unknown. We should @ priori expect it to be greater than the above, but it is always dangerous to judge without actual data. The correlation between stature and age is known, and is actually negative; the stature of the adult male diminishing by about 4 inch for ten years after his prime at 28 yearst. We thus conclude that while the stature decreases by 4 unit, the heart increases by $ unit per ten years. When we remember that the healthy heart is on the average much smaller than the heart in disease, and that sickness on the average increases continuously with aget, we shall probably lay less emphasis on the general @ priori idea that the weight of the adult heart increases very sensibly with age alone. For my second inquiry I had unfortunately not sufficient material to divide my healthy hearts into three age groups and thus determine the influence of age on variability and correlation. I should have got less than 180 cases for each table. I was thus reluctantly compelled to deal with hearts in the general hospital population. I divided them into three groups, ages 25—35, 35—45, and 45—55. The following results were reached : Age Influence on Hearts and Spleens of General Hospital Population. TABLE VIII. Hearts and Spleens. Ages 25—35. Number 358. Mean Heart 11:91 ozs. Standard Deviation 3°997 ozs. Mean Spleen 7:45 ozs. Standard Deviation 3°758 ozs. Correlation of Heart and Spleen =‘0785 + :0384. TABLE IX. Hearts and Spleens. Ages 35—45. Number 536. Mean Heart 13°16 ozs. Standard Deviation 4:018 ozs. Mean Spleen 6°60 ozs. Standard Deviation 3°428 ozs. Correlation of Heart and Spleen =°1817 + ‘0282. TABLE X. Hearts and Spleens. Ages 45—55. Number 403. Mean Heart 13°65 ozs. Standard Deviation 4°425 ozs. Mean Spleen 6:21 ozs. Standard Deviation 3°120 ozs, Correlation of Heart and Spleen=:2518+ ‘0315. * Clendinning gives, Ages 15—29, 84 ozs.; 30—50, 94 ozs.; 50—60, 104 ozs. Med. Chirurg. Trans. 1838. See also Peacock and Reid, op. cit. + Biometrika, Vol. 1. pp. 46-9. + Biometrika, Vol. 1. pp. 260 et seq. 70 Weights of Human Viscera Forming as before a table of coefficients of variation, we have: TABLE C. Relative Variabilities of General Hospital Population of Hearts and Spleens at different Ages. | its : Coefficient of Coefficient of Organ Variation Organ Variation Heart, 25—35 | 32°79 Spleen, 25—35 50°42 Heart,35—45 | 30°53 Spleen, 35—45 51-97 | Heart,45—55 | 32°42 | Spleen, 45—55 50°24 We can draw some important results from the above constants. (a) The heart in the general hospital population of adults increases far more rapidly with age than it does in the class of healthy hearts. On the other hand the weight of the spleen sensibly decreases. (b) Theabsolute variability of the heart increases 10 per cent., and the absolute variability of the spleen decreases 17 per cent. during the period considered. These are quite sensible changes. Thus, while the heart tends to grow larger and more variable, the spleen tends to grow smaller and less variable. (c) If we deal with relative variation as judged by the coefficient of variation, we see that the changes referred to under (a) and (b) almost balance each other. Or, the relative variabilities of both heart and spleen remain sensible constants with age and equal to the values found for the general hospital population of adults of all ages in Table A, p. 66. This is further evidence of the real value of the coefficient of variation as a biometric measure of variability. (d) The correlation between heart and spleen steadily increases with age. In the first period it is comparatively small, in the second period it has much the same value as in the general hospital population of adults (see p. 65), and in the third period it approaches the value found for healthy adults. These results are quite reasonable. As death below the age of 35 is generally abnormal*, we should expect to find that the coefficient of correlation was low. Over the age of 45 years there is a slow deterioration of all organs. There is no evidence to show that this degeneration is much more acute in any one of the organs we are considering than in any other. Therefore, although the absolute weights will differ from the normal, the correlation may be the same, and this we see that it actually is. * By “abnormal” is meant here a death due to disease; the result of an accident would be from this point of view a normal death, as probably leaving the viscera ‘‘healthy” under post-mortem record. M. GREENWOOD 71 5. Influence of Special Diseases on the Cardiac Biometric Constants. We are now in a position to consider the effect of some special diseases on the weight and correlations of the heart. Unfortunately, scantiness of material and pressure on my time hindered my developing this most interesting branch of my subject very fully in the present paper. I shall hope to give it further con- sideration in another communication. I have confined my attention here to the heart and spleen weights, variabilities, and correlations in the case of two disease groups. First, Pneumonia (excluding tubercular disease); secondly, Valvular Disease of the Heart and Aortic Aneurism. I regret that the total number of cases available is small. TABLE XI. Hearts and Spleens. Cases of Pneumonia. Number 177. Mean Heart 12°50 ozs. Standard Deviation 2°768 ozs. Mean Spleen 6°59 ozs. Standard Deviation 2°842 ozs. Correlation of Heart and Spleen =:1065 + 0501. TABLE XII. Hearts and Spleens. Cases of Valvular Disease and Aortic Aneurism. Number 166. Mean Heart 19:08 ozs. Standard Deviation 5°950 ozs. Mean Spleen 8°57 ozs. Standard Deviation 5°158 ozs. Correlation = ‘0552 + 0522. Forming as before a table for relative variabilities : TABLE D. Relative Variabilities of Heart and Spleen under Special Diseases. : Coefficient of Disease Organ Variation Pneumonia tas ses oe a Heart 22°15 Valvular Disease and Aortic Aneurism Heart 31:18 Pneumonia ae bos a su Spleen 43°12 Valvular Disease and Aortic Aneurism Spleen 60°16 From these values of the constants we may draw the following conclusions : (a) In cases of pneumonia the mean weight of the heart is above that of the healthy heart (p. 67), but slightly below that of the general hospital population heart (p. 65). The weight of the spleen is somewhat above that of the healthy spleen (p. 67), and only about equal to that of the general hospital population spleen (p. 65). The absolute variabilities of both heart and spleen in pneumonia are far lower than the values in the general hospital population, and only slightly higher than their values in the case of healthy organs. The same remark applies to relative variabilities, which are in the case of this disease somewhat higher than the healthy values, but considerably below those of the general hospital population. We must therefore conclude that pneumonia does not influence in a marked degree the average values or the variabilities of either heart or spleen weights. As it 72 Weights of Human Viscera does raise the variability somewhat, i.e. introduces disturbances in the relationship, we are not surprised to find that it weakens, although again not in a very marked degree, the correlation between weights of heart and spleen. (b) On the other hand, Valvular Disease and Aortic Aneurism send up the weights of both heart and spleen not only vastly above their healthy values, but markedly above the valnes for the general hospital population. Further, their absolute variabilities are increased considerably above the general hospital popu- lation values, and a fortiori above the healthy values. The coefficients of variation of both are also far above the values in health, and that for the spleen above the general hospital values. In the case of the heart, the mean has been sent up so high that although the absolute variability is considerably greater, the relative variability remains much the same. The general effect of these heart diseases is to render the correlation between heart and spleen hardly sensible. If we may judge by these two cases the general effect of disease is to increase the variability of affected organs and reduce their correlation. This is absolutely in keeping with the sensible, but of course less marked, changes we find when we pass from a population with healthy organs to the general hospital population, which of course contains much disease. 6. General Conclusions. The present paper is chiefly intended as an illustration of how effective biometric methods might be from the standpoint of medical science if only there were a systematic collection on a large scale of normal and pathological data. Some definite conclusions, however, may yet be drawn, and some suggestions made on the basis of our numbers. We see sensible, if moderate, correlations between the weights of heart, liver, spleen, and kidneys. It may be somewhat difficult to understand why the heart-kidney correlation is higher than that of the heart with any of the other organs. That the kidney should be more closely associated with the heart than the liver is possibly owing to its more subordinate functions. The liver is the seat of so many important processes that its immediate connection with the heart is not so great as that of the heart with the kidney. The excretion of fluids is so closely bound up with physical changes in the vascular system, and conversely changes in renal structure react so markedly upon the heart and blood vessels that a very close physical relationship appears probable. No doubt the liver is greatly affected in many forms of cardiac disease, but on the other hand serious functional disturbances or even acute inflammation of the liver do not produce heart changes with the same precision as analogous mischief in the kidney does. If this partially and imperfectly accounts for the higher heart-kidney correlation as compared with the heart-liver coefficient, it may perhaps serve as an argument in the case of the spleen. Heart mischief nearly always reacts on the spleen, but splenic trouble does not always affect the heart. M. GREENWOOD "3 If we consider in broad lines the general results of our investigation, we should say that they may be summed up in the statement that both special diseases and the general want of health to be found in a hospital population tend in the same directions, namely, to increase the variability of the organs dealt with and to reduce their correlation. As we pass from the general hospital population to a healthy population we find that variability sinks and correlation rises. To what extent this is an antecedent or concomitant of the diseased state it might not be always possible to assert. In taking any population, low variabilities and high correlations are the two factors which measure closeness to type. As a general rule, under a given environ- ment closeness to type is a condition of stability, we may almost say, of low selective death-rate. Hence we may look upon disease as less stringent approach to type, and high variability and low correlation as a sign of instability *. Of course the capacity to vary absolutely and to alter the relationship of organs must exist, or a race will not be able to effect a change in type with a changing environment. Still, if we trust the theory of correlation by natural selection at all, death before senility as far as it is selective is the destruction of the less fit, Le. of those not approaching within certain limits the type suitable to the environ- ment. Thus it comes about that we shall expect on the Darwinian theory to find the individuals who die of disease in adult life to be more variable and less highly correlated in their organs than the “healthy.” This is precisely what we do find, and the post-mortem room provides direct evidence in favour of the action of natural selection in the case of man. Indeed, in a not very conscious way the medical world has been expressing these very truths of evolution in other words. The figures we have considered showing lowered correlation in the diseased state are a biometric illustration of the truth of Dr Sutton’s aphorism, “ Disease is absence of rhythm+.” In the normal or healthy group we see a population possessing the characteristic marks of stability, small variability, and high corre- lation. In the two special and the general diseased groups we have conditions tending in the opposite sense. In the healthy class we get a closer quantitative relationship between the weights of the viscera, in the diseased there is greater variety of proportions. Indeed, to adopt a well-worn definition, “Among the diseased each organ has a life and growth of its own, irrespective of the needs of the organism as a whole.” Our biometric investigation shows us this independent life and growth leading to increased variability and to lessened correlation, shortly, to those deviations from type which beyond certain limits are incompatible with survival under a given environment ¢. * In the evolution of subspecies it seems probable that the hardiest and most prolific groups have the least coefficients of variation. Thus in an investigation recently made by Mr A. Bacot and the author on the variability of Spilosoma Urticae, it was found that in several series of broods the groups with the largest coefficients of variation had the least net fertility. + Medical Pathology, 1886, p. 95 et seq. + I desire to take this opportunity of expressing my gratitude to Prof. Karl Pearson, to whose staff, among other acts of kindness, I owe the correction of many arithmetical slips in the above results. Anything of interest in this essay is due, either directly or indirectly, to him. Biometrika 11 10 TABLE I. Males. Hearts and Livers. General Hospital Population. Hearts in ozs. G6T-96—G6T-GE GEI-GE—G6L-1E GET-YE—461-8E G6T-€—G6T-6E G6T-GE—GéT-Té G6T-TE—G6T-08 G6T-08—G6T-66 G6T-86—G6T-L6 G6T-LG—G6T-96 G6T.96 —G6T-46 S61-66 —G6T-86 or Oo Ll AANA Loa lilae lila! GBI-96—SEL-16 GEL-YE—G6I-S6 ANOHMNH HN oa (eee ae mee (b) | G6T-Té —G6T-06 | | Tae ies CPO ail malb =a | pamela lee RSP) If rataa at araeCN| ta S6T-06—G6T-6T (re ee eet | G6T-6I—G6T-8T G6T-8I—G6L-AT G6T-LI—G6T-9T oO eS ese ON CCE ST Ce) eNOS [sa [es cl (ics Pease suet echt al beh G6T-91—G6T-GT GEI-GI—S6T-41 GEL-TI—G6I-8T G6T-€1—G6T-6T G6T-6T—S6T- TT G6T-TI—G6T-0T re ON ee as ee dle LD 9 UD 1H 1D 1 1H INH 1 WO L&C re Lg 1g Ss QSKSKSKKKCKKKSKSKSKSSS Taal else Ol ral ed ee Tl ised en sega eee NMWOYFONRMDGONWNRNOOVWAANQSSS REO Rae at ee) SS) SEES SS SOT ES SS Ct ae cl eee MN WN WM W WN VY VN YN NY NY NNVNNNNQ Ea Se DE EN oaletale eel eae ap oneal WMNMGONVWBANHMNINVADANRMOOYSAARSS SURO ObeS resend) Ute SSS) CSSD Soe SCN es S *8ZO UL SIOATT 8 | 22 | 48 76 |151| 162 182] 143 127| 83 93 | 37 | 50 | 36 | 33 13 | 21 | 17 | 24 9|8 |u| 6 4 1f1|4 2] 3 Totals TABLE II. Hearts and Spleens. Males. General Hospital Population. Hearts in ozs. M. GREENWOOD GBT-86—GBT-LE 1° Paige Greet (nly De ela ea ese | = “Gel-9¢ —981-98 We lialesleateest a |aretirtin [ec © GBT-GE—GET-46 | |a | anaae | ee GEI-TE— GET-8E alee se ee ae RN UGEGG —COl-G6 Mase areca (fies antag S GBI-88—G8L-16 ee recycle = GEI-1é—G6T-08 [ee oceaaal| a ay eatoe—ser-er | 1 92 AD OH | conor cerery | | EN NIrOMm~MOA MON SS G6I-8I—G6T-AT j [Owen oNnade G6T-LI—G61-91 os GET-91—G6T-G1 eeu megs Pe G6T-GI—G6L-41 COO Hid Hid | 4 | GET-4I—G6I-E1 SXCE SP EN 90) NO [oars | G6T-61 —G6T-6T ies! esl G6T-61—G6T-TT Ye) yous G6T-II—G6T-01 aoe, G6T-OI—G6ET-6 GéT-6 G6T-8 -—G6T- 83 | 162| 166 | 181 | 127 114 76 | 8s | 33 | 48 | 26 | 35 G6T-4, —G6T-9 Wy tics ics | labe pees G6T-9 —G6T-G 8 19 | 45 aro} | Plt tl | 1d 45 19 1) 1) 1H 1H 1H 1H WH HHH YL pis RRVWVMVVNVWNVBDRNVNVVBBDNRVVWVBARARA Pane Praral opel a ErD EN Oa aL ea RRC RMDMDAOOeWDHDOM ) | baad aL 14 ag Totals ... ji— LS Up Ved sy WOW DHD go—. 2 18°12 Ly 12 Ye kl A 1D 19 19 Qa Q NRWNWN i Ce MRM AO 2D 11:125—12 12°125—18 10°12 ‘szo UL sudetdg 10—2 75 Hearts and Kidneys. Males. Hearts in ozs. TABLE IIL. eneral Huspital Population. ay @ 8 ( Weights of Human Viscera | [ieee Sa GeL-ce—GeT4e Fa | | | |adnaaw| | | [a | GBEYG —OBEGe he Et NN ee a CELE —GOT-08 Mises cel a aa alles eae a a Ic = ceree—eatte | | [AAA | | | | = cette —201-08 | | ame ree iG (ioral |r caroe—eetgt | AAA NMS | | Oo | in 3 GeL-6I 92181 ce ae Sc oa) (to sib | a CELBI—GEL-AT | TER AAND Oe oVe |e | jm | + Get LI—SeL-91 le cia eh Coca Fie || 3 CBT OT SOLE Pie SS ee ele % OFTGT=OGIAE pi SoS RS Se Sy Neal eed | 3 corti —gergy | ANNO OLS AN AAD om mes 4 GOT-GESOGEGL ON ee aes asi ie a ee 3 Geral Sar Gh HOOTSTO Rea [elles aio > G61-1I—S6T-00 | YP SOAR owe ea ee 5 Ce T-01 61-6 BO erased Se | S eBl-6 —Se18 ARE BR SOOSAA | | | x ee Se eee ell eal el 3 es eee J (meas NUNIT el 95 Ile | a La Ld 9 U9 1 1 1H 1H 1H 19 1H 1 HO HW IO 5 5 NNN WN RN NN NNN WYNN NNQ Q Fairs Pamala al \Pall Sale alias ysalmab ies! \ailea) ently ab Laas) RWMDHONNWDMSH OKRADOHARVHS AAA AAS SAAN RNNVNNAN’ Ca id el Ge Tele LD UD 1D 1D 1D 1D Ig WO & DD 19 19 9 VAVAISIVKSKVSHVgggggag alana nviralten hi zalien bln heal im Maa bpea bia lerbienl paharak eal WORWMDAHGHRNMSHNW CK DAGHARH AANA AANA RNVNNVN | nap 12. BE 25 25 DE. 281 5 Totals 6°125—27'1 2 41 25:125—26'1 ard 2 2 a ‘szo ult skouply Spleens in ozs. M. GREENWOOD TABLE IV. Healthy Hearts and Livers. Males. Hearts in ozs. ID wD WD | WwW ww? WD wW Xe) WD 3 NX NX X X RN X X X meh i] eet eh |] als | et ASE et | st || as SIG! OTH |/Ris | Ss] so /] | s ~ al a] 4 s | | | | | | | | [Totals Ney) atoy |ttay key kes rey 1] ey | te ts » RX » isy) » R NX iS] YX al il al il ol i) il ~ ~ ¢ wR | oo Sa |S {|Hn]ae Ss | S&S | a ~ al ial il m IN a SEE op Spall elk oa) 234) bl) Sal si Ik | = | op a *a | 48:125—52°125 9) 12 | 13} 10 Ho leate oo | 2, 2 54 sn 125 2 8 | 15 6 | 10 9 1 1/| — 53 < fe 60°125 6 Sel el WS 7 | 6 4 3 3} 61 a 60°125—64°125 i 3h) 9 | 10 | 2 A BAe il 48 64°125—68'125 1 | 3 Bi) dey |) ey |). 6 5 1| — 45 68:125—/ 2925 1 | 1 4 HE |e 2 i |) 26 UPUAS— Hy ilAsy, || = 1 1 i) 6 7 Ly 2 Dui 76:195—80:125: | —\--1 3 33 3 5) 1); — 22, Totals ... 358 TABLE V. Healthy Hearts and Spleens. Males. Hearts in ozs. Ww WwW en) Lp Ld LD | Ls Ls Ls Ls XR iy sya RN RN SR SY SQ RN RX el [oS Sh) St OS) Se oS Sh poss | Se iro et sees ert Nat Die ebalie, ile | | pale tl fey il J il i ul ey a i! Totals | R RN iss RN isy Sy SN] RN iN] RN mle eat |) st | ee | tt || ek Most i tet || as ~ ~n a Oo dam | SV Sal —- w?W © ~ sl ~ ~ ial s ~ Riga otae A 3.39) 2) 7) 9) 4 |_| — ht apg e125 Sieh pS |) 7 | 12 ).9 | 6) 5) 1)—'| |= 46 F125— 4125 6 | 15 | 21 | 16] 14 | 10 Oot 2} —4101 4:125— 5:125 Ly 2) 25") 18 | dios Ua |) als} 3 5 1 104 OnlZO—— Old) 5 Ol ko! lee Py || WS} |) ales) |) 5 | —f1ll C225 — LO: 1} 5 9 4 | 10 9 2 2 |) ee 44 Wi1Q5—— 8725 | — | 2 7 8 6 | 11 8 4 | 6 1 53. Sib A—— Ray | | 1 2 7 it i) 33 1/ 1) — \ 17 QA IOI As | | = 1 5 | — A || SA i By |) 13 LOO ot — 2, 1 1 | 4 195 — 19725 | — | — — |} — yy) | 1 | 1 1 | — 1 6 Totals 23 | 55 | 96 | 93 | 85 | 64 | 49 | 95 | 23 | 4 | 517 17 78 Kidneys in ozs. Weights of Human Viscera TABLE VI. Healthy Hearts and Kidneys. Males. Hearts in ozs. | | S| |e Pa fee es foe alee ee eat lot el hoe! Wek oar (ase lS ice) fon} | S m isy) Sp) = ww © eh ete Veleah ted) Alcala || al edied treet i I otals | Pf SMe | kee] See ees Pb Poi eee Res CA pee ie all mee ouch ee ~lolalosot|y | ale] slo ~ ™~ ™~ ~ ~ ~ 7126 — B18R 1 | 3) = |) Selon ae ek ea S195 9125 elim Ge) Del ee Se ae ea 9125 —10:1 25 A, |) Feel q@ilin nse Gra mses re hey ll el ld ee) 10125—11:125 | 2) «8 | 93 | 17 It | 24h 28) ol aeeTo 1k196-—19-'195 4 1)| 6 | 10) 99) 19°] 19 1b oF le 8) | et el 19:1265—18:1295 | 1| 4) 17112111 )18) 8|:4 /.14. 68 18:195—1-125 Ve3\ 2 | 8 | TE) 127) Scie atasl Sone TpI25—15:126 | | 7) 4.801 | oe es) aoneah ales (12616125 | 1) Ue) |) 4) Pe esas 16°198-17-125 | — |e, A elidel one 7 TP 1ep = 18 125 ee ll 1 1 Totals 18 | 36 | 75 | 80 | 76 | 52 | 42 | 19 | 15 | 413 TABLE VII. Correlation of Age and Heart Weight. Healthy Males. Hearts in ozs. 16 | 19 | 19. | i |S [rq | 29 | a6 | 1g ne isy) X XN NR RNR | R R isy iss) QR il ~ ~ al al ~ al al al al Sih | OITHITQIlaleloflolar i) ian! n al al a) s al Cee ie Sie Mere fee* Years Ney Ney LD LD wD UD LD Ls LD ‘wD Rl Ri RI RIiL_R ARI Rl RINVQTS el el bal ial il il al al il al 2 Io a > w & 8 + 1 6 © qs N nN n nN al 4s 26th and 26th | 3) 41.7.) 67.3.) 2° By (1 |=) = 38 27th and 28th 3 9 | 10 9 8 3 1 2) —]— 45 29th and 30th 3 6 | 10 9] 12 7 2 1 | 1/|— 51 ; 31st and 32nd 4 lt 9 9 6 4 6] — | — 45 4 33rd and 34th bay She Pesce 7 7 2 33) ool — Ae os on 35th and 36th Wy) 6 4 i) V1) LO 8 1 14 43e he — 46 37th and 38th 33 UE ek) 6 | 10 5 9 1; 4 1 49 39th and 40th | —|] 5} 18] 13/16] 10| 4 1; 3|—¥J 65 Wist and 4200s) — |) 230) Ti AA P71), *Ba| 94) S| Sa — aes JSrde and wjth> |) 25) 13.4) CB ede RBs at Sul ee ae 34 45th and 46th 4 4/13 7 | 10 5 8 3 | 2 |— 57 Aith and 48th Te Pes e ere ba as || ee Ze) cake Te pS | | By) 49th and 50th 1 Te) ale3 5 5 7 5 | — 1 50 51st and 52nd 3) 4 7 il 6 2 6 4 3 42 53rd..and-d54th = [p—=|- 24S aS le 7] eA | — | Sie] 47 54th and 56th 1 1 a 2 1 1 | 1|;—}|— 8 Totals 33 | 77 |140/ 121] 122| 86 | 61 | 28 | 28 | 3 | 699 TABLE VIII. 35 years). Young Adults (25 Males. General Hospital Population. Hearts and Spleens. Hearts in ozs. M. GREENWOOD RQ "i S HOMDODADNOADWOCArLrODMNMONOMA Oo Lal [ee) oO ao HOMAN AR ie) e oD CGESE—GaLLe eet ete] | | a G6T-LE— 961-96 ea | | a GBI-96 —GET-GE te ere te ele tie a G6I-GE—GEI-16 lriririry | | | ~ GBT YE—96T-82 alalla|a! | 2 GBI-8E—9BI-86 ne Pl se Ft a m4 eG 66 ma a | = | | oD Colle Geren! | |aoe | ile] ihe | 2 cer-o¢—oer-6r Fil:| |} | | tale] | | | a GST-6I—96T-8T [era | = | 10 G6T-38I—SeT-s4T 1 | | | le taawtal | lal | ~ GET-LI—S61-9T a et a lice | | © GET-91—S61-ST HOSS sl) SOX [as laa | | © GET-GI—GEL-4T fea STN toy ae A | | | | GBL-TI—GST-8T og ch ameantre | aero EA | z iF a OST-GI—SEL-B1 Ce ack eae enc OC | | 20 Le Sit Ae St RST. | Ma Se ee Se ear a A nal me Le 5 ear-Ft—9et- Or Cosi Cae sei iE ae a DR eae Le) a CET-O1 —GEL-6 | Neko) nD SOS 1d GI CO OD An | | | © Colson eCGL Oh ee is sc cele eles GBL-8 —9GT-L eects re aN le Prltreees wigan re aol: ligule GI-L —GT-9 Parnas | || lala | | [IPEA Me ieee Corn —Gaig hy) (evo | |) |i.) | | | PP IRS Feces LS 4D 49 19.49 1919 19 39 19 19 19 19 19 19 19 89 49 109. 109 19 19 19 MMMM N NW YN YN MN W YN WY NY NNY NNR NNN A ® Pi net St Oa) aa Dial WA SE OS STASIS SSSSSlIss | a Eee es es eae aa [ll ]3 SRLLGGSSSSSRIVGHSHgggys |S Galle eel imal en arpa bea eg ire ee Wee Pes bial mslora marie at rele ARMA ORDHONNHND AHO ORDHAOGWHWANH MANNA AA NHRVAVQWAN ‘szo UL sude[dg 79 80 TABLE IX. 5 years). ~ 4 35— rime of Life ( ie Males. General Hospital Population. Hearts and Spleens. Hearts in ozs. Weights of Human Viscera G6I-66—G6T-86 G6L-86—G6T-LG GET-LEC—G6T-9E GG6I-96—G6T-G6 G6T-Té—G6T-06 G6I-06—G6T-6T G6T-61—G6T-8T ATMA MOAN fee! Sen NMN | eae || een | G6T-91—G6T-GT AWOAMMAHHA [cs eye | | GET-GI—G6L-4T GGT-TI—S6L-ST G6T-€1—G6T-6T Pe SeSe Goey Geli! | | aaa | i ites ROL Oca en | SaseeN |e | AOAC OMm-MIDH | aR | AN | | ss Fil see | 1 | fibeae eee, ONCE RSr ID] ON | st la [cs Lom! Geli —9en Or NO Pr OO O19 H eer jaas lees ae 99190 © 6 O [outa es ae eungOooorrs CN | | | ul OC as} 2OKCX) |) aa | | a paan] pai | | | | 15 | 31 | 59 | 67 76 | 58 50 | 31 39 | 15 | 20| 8 | 18 4| | s Gallon mon leon enaat La 9 69 49 49 49 49 19 1 49 169 49 14 19 1H 19 1H 19 HH I'D RW NN NN NN VN NN VN DY VN W VN VN NY VN VY VN Y Paliral pablus idl eet eel ep! aha) salen i yesh lima nl isal ea psl RHBVWWDOAHDADSARHSVPHOA DASHA Pie a a le Gane ee Meal aber ate AM es Male geal RRRVUVMVMARKRNRRVURVHAUVNCWRWVWRWS bes ae Dvn! Santa! Ba ee ab sh Yel ten) en en lea se ation sh er te HRDMSHOAHDAONRKRHSOHOAWDAOH ANNAN ANANQR ‘szo ut suoatdg M. GREENWOOD GOT -66—GE1-86 GOT-86—G6T LE : COTE GET -9E te s 18: eee 8 G6T-96—G6T-Gé > ee 12 GCT-GE—S6E-46 ad | ws | S6L-4¥E—4ET-86 wy | aie caer en | G6L-80—961-66 Dd as : G6I-66—G6T-T6é D ~~ x ie nT as GET-LE—SET-06 2 = ——__— —_— —_ Sj ; ; me GS6T-06—GET-6T i ~ SAMAR | al = Gé1-61—-GeT-81 | | % x mo ro Oates . | SBE-8E—S6L-LT | | Eo wn ~ ~ al EOS Blo | ase - ‘3 GET LI—96F-91 | | ae ~ ~7 aA m2 OO b= Hid Sos 8g | 961-91 —S6F-ST ool ay ny I~THANR tN ON | cy S is G6T-GI—GEL- 41 | lo | *” os Sm WDOOCONNHMH = GaEYI—SSr-6F age | DH os S = ee GaL-ET-—S61-61 ~— | en coat a 3 | psp ey oa oe GOL-61 —Gel-TT Nv) 3 oO GéT-LI—G6l-0L wa GET-OL-—GET-6 g ———————— sv a Gol-6—-—G6I1-8. wp) aa - - as} | G6I-8 —G6I-L = ie 3 | CPT.) —G7T.9 (OTL, i019 a G G ~ S S | 61-9 —G61-G | LS sy) teat wW iy UES Ley Uy Sy Ley Uy ec SSSSKKKKHHKgsgssgssssgs vl peal nl eal eal BrP al Saal ae sh ast met el al tal “pst tee) Set Gt te NMS OR HAOWNH AHH D-w-DAON Sd Se Tal) teeta 21 Oe 2 eT Ae ele tee es LD OD 2) oO > UD UD US UD LD UD 4H 49 1H ODD RRO RARVRRNVWNWKVWAINRUNWVUNRRRRNR a Spl gral aplapel enh veh ay niin eal aa) el een ental eae Pet HRORHSLHASHARHDSBHSL HAS AAAS ANS NYS NN "szo ul suaeaidg Biometrika 11 SCEra @. ghts of Human V e t We : oe rle|s ot | at | oo | 23 | se |eo}is| 2-| t | 1 | —{er}—}/—|--|—-/—|]—|{1 ]—-—le aa ian To | fe ee | e= | os | Sg Vagaeerc Nc he a a aL |. 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Criterio per giudicare, dati i parametri, se la curva dimorfica ¢ unimodale o bimodale . i : F ; i ; F : ; : c ¢ 9 87 Condizioni sufticienti per la unimodalita : b 5 : : : ‘ : 93 Caso particolare: curve componenti di ugual deviazione normale : : é 96 1. Introduzione. E ben nota la importanza che ha nella Biometrica la curva detta normale avente |’ equazione in coordinate cartesiane ortogonali : (a-b)? y=yoe *. FERNANDO DE HELGUERO 85 Essa ha tre parametri: y, 0, o, pel quali adotteremo le denominazioni di ordinata massima (yo), media (b) e deviazione normale (standard deviation) (a): le y, € @ sono sempre positive. La sua forma é nota (Vedi fig. 1): in un piano cartesiano di assi y= 0, «= 0 essa giace intieramente dalla parte delle y positive, & simmetrica rispetto alla retta a=b che dicesi asse della curva normale. La y & massima per «=b ed ha il valore y), va da ambe le parti decrescendo continuamente fino a rendersi asintotica all’ asse delle w, che dicesi base della curva. Esistono inoltre due flessi corrispen- denti alle ascisse b +o. Si @ trovato che questa curva serve ad esprimere le variazioni di molti caratteri in gruppi omogenei di organismi. Se invece si considera un materiale eterogeneo, risultante dalla mescolanza di due gruppi omogenei, si ottengon delle curve di frequenza dette dimorfiche, osservate per la prima volta dal Livi*. Queste posson graficamente ottenersi tracciando sulla stessa base due curve normali e su ogni Fic. 2. ordinata prendendo la somma delle frequenze corrispondenti alle due curve (Vedi fig. 2). La loro equazione é _@-b,P _(@—b,) y= ye 20,2 fi Yre 20,7 ; _(a-b,) _@—b, se y=yne , y=ye sono le equazion delle curve componenti. Riescono evidenti, per questo modo di generazione, le seguenti proprieta delle curve dimorfiche : * R. Livi “Sulla statura degli Italiani,” Firenze, 1883. Vedi anche Archivio per lV Antropologia ¢U Etnologia, Vol. 13, Firenze, 1883; e Annali di Statistica, Vol. 8, 1883, pp. 119—156. 86 Sui Massimi delle Curve Dimorfiche Come le curve normali giacciono intieramente nel semipiano delle y positive e restan sempre a distanza finita dall’ asse delle «. Inoltre devon rendersi anch’ esse asintotiche a questo asse: percid devono ammettere dei massimi le cui ascisse diremo mode t+. Il modo di formazione ci dice che questi saranno al pit due, come verificheremo rigorosamente in seguito. Possiamo avere, cioe, la unimodalita (un solo massimo), 0 la bimodalita (due massimi separati da un minimo); queste due forme erano gia state osservate dal Livi. Caso limite fra i due e quello osservato dal Weldon{ in cui la curva presenta un solo massimo, ed un flesso (a destra od a sinistra) con tangente parallela all’ asse delle #: allora pud pensarsi che il minimo della curva bimodale sla venuto a coincidere con uno dei massimi. La unimodalita o bimodalita dipende evidentemente dai parametri delle curve componenti: in questo scritto noi ci proponiamo la seguente ricerca : Dati + parametri vedere se la curva dimorfica & unimodale o bimodale. Il numero dei massimi dipende solo da alcune funzioni dei parametri delle componenti; infatti @ questo un carattere invariantivo per spostamenti paralleli dell’ asse delle y e per cambiamento delle scale delle w e delle y. Potremo percid prendere b, = 0, ed allora 6, che indicheremo con 0’ ci rappresentera la distanza fra gli assi. Inoltre prendendo opportunamente la scala delle y potremo fare y,=1 ed yz sara il rapporto delle ordinate massime. Della scala delle « disporremo in seguito. La equazione della curva dimorfica @ allora: a2 _@- bye ye 20,2 ae Yr 20,2 F in cul supponiamo a7 b, (il ché non toglie generalita alla ricerca perche se fosse b, 0, O0. 2. Criterio per giudicare del numero det massimi delle curve dimoryfiche. Noi studieremo adesso le radici della f(a) =0 per risolvere la questione prima enunciata : Dati i parametri delle curve componenti, e percid k, h, b, vedere quanti massimi ha la curva dimorfica. Dovremo percid cercare quando la equazione (a) ammette una sola radice reale e quando ne ammette 3. Nel caso particolare b=0 (ovvero b,=b,), cloe curve componenti con assi coincidenti, la f(w)=0 si spezza nelle due «=0, ed 1+hke"”’=0 che non ammette radici reali perche k& e I’ esponenziale sono sempre positivi; onde in questo caso esiste un solo massimo, per «=0, corrispondente al massimo comune delle curve componenti, e cid era evidente. L’ altro caso particolare h =0, onde o, = o,, lo considereremo a parte. Nel caso generale in cui k>0, O0 ci ricondurremo allo studio delle radici di una equazione algebrica di terzo grado. In generale la (a) puo scriversi: ae 4 en (hat—aba tb) Oe EG) 88 Sut Massimi delle Curve Dimorfiche Ponendo : () a ceca (c) x 2=7 2 kh (b a a) ’ per le radici della (a) avremo 2, = 2. Studiamo le due curve (b) e (c); se le riferiamo agli stessi assi, le ascisse delle loro intersezioni ci daranno le radici della (a). Studio di (b). 2= em (ha? —2ba+b?) Kssa @ una curva normale. Infatti la sua equazione pud scriversi : ean) 1-h 20 nae: Ae hs, oe : oa La moda é h? la deviazione normale RET Yordinata massima e u ‘ ait Le sue proprieta sono ben note, e percid inutile insistervi, Studio di (c). x k(b—2) Pud seriversi kz,v — kbz,+2=0. 22> N K una iperbole equilatera che passa per |’ origine ; asintoti sono le rette c=; =-. Per «<0 0 per #>b, 2, & negativo: onde per studiare le intersezioni colla (b) che ha l ordinata sempre positiva, basta considerare il ramo per 0b). Vedi fig. 3 Per continuare il nostro studio formiamo la derivata della f(«): essa é AO, =l+k {1 = (x a b) (2he — 2b)} en (hat —2be+b%) uguagliandola a zero : 1 ke (Qha? — 2b (1 + h) w + 267-1) =e (ha?—2ba-+b?) FERNANDO DE HELGUERO 89 Ponendo: (b) 2, = en at abt bY) 1 ~ ik {Qha? — 26(1 +h) a + 2b?—1}’ (d) 4% alle radici della 0 corrispondono le ascisse delle intersezioni delle due curve (b) e (d) quando siano inferite agli stessi assi. La (b) @ gia stata veduta. Le(1h) Tr ee ee eae e -X Fig. 3. Studio di (d). 1 “3 fe (Qha® — 20 + hye + 20-1) Per « finito z; non si annulla mai, perd I’ asse delle z @ un asintoto della curva. Perché z; cambi segno deve passare per il valore © e cid avviene in corrispoudenza alle radici della : 2ha® — 2b(h+1)a+ 2b?-1=0, ay ( b(h+1) ¥ Vb? (h? + 2h +1) — 2h (20? — 1) che sono = Do 2h ae b(h+1)F VB (1 —h)? + 2h ovvero: = eo Xa 2h Biometrika 111 12 90 Sui Massimi delle Curve Dimorfiche Ora se 1-26? & negativo, le due radici sono entrambe positive, se 1—2b? e positivo, & positiva solo la #,. Io dico che in ogni caso #, & maggiore di b; infatti si ha: bal) 4+ VA — hy ek O(n 4 1) 6 (leno 7 2h 2 Bp Riguardo ad a, @ positivo solo se 2b?>1, b> 333 in questo caso & minore di b(h+1) 2h In ogni caso 2, e positivo per a w,. Poiché a noi Ja curva interessa solo nel tratto 0 < « 75" E facile vedere che in questo intervallo e sempre crescente, infatti la Vio derivata e positiva. — ue ee Li = ~ ih (2b?-1)° La curva é tracciata in figura. (Vedi fig. 4.) Inoltre per «= 0, 2s Fia. 4, FERNANDO DE HELGUERO 91 A noi interessa solo il ramo indicato colla lettera A, che partendo dal punto (x=0, 23> ) cresce fino a divenire asintotico alla retta #=a,. Conside- 1 k (2b? — 1) riamo ora le intersezioni delle due curve (c) e (d) nell’ intervallo 0 < «0. Percid la R(«)=0 ammette certo una radice reale, positiva, maggiore di b, e nell’ intervallo (0, b) o due o nessuna. Cid posto supponiamo che la f(#)=0 ammetta tre radici reali e distinte 2’, 2”, x”, con a 9, e in tal caso se f(a) >0 curva unimodale, se f(a») <0 curva bimodale. Cosi la ricerca & completamente risoluta nel caso generale. Riguardo al valore delle mode a’, x” nel caso della bimodalité si attengono per approssimazione come radici della /(#)=0: esse sono gid separate poiché O0. Cerchiamo il minimo valore di y per cui questa e soddisfatta qualunque sia h fra 0 ed 1. Prendendo h molto piccolo si ha: 2y+3>0, y>-f. Anche per il valore y=—% la diseguaglianza @ realmente soddisfatta; infatti sostituendo e riducendo si ha he— 13h + $ > 0, 96 Sui Massimi delle Curve Dimorfiche che @ verificata per h = 0, per h =1 ed anche per h = 13 per cui il primo membro aca ay al ni ‘ . as 13)2 assume il minimo valore: 4 {1 — 4 (43)?} > 0. 3 a 1) , la condizione y >— § equivale ab? < 2. Ricordando la posizione y =; ( Percid la curva é certo unimodale se b, os b, < 20, : Come avevamo prima affermato. Potrebbero trovarsi altre condizioni per la unimodalita pensando b non costante, caso completamente trattato, ma funzione di h. Con cid si verrebbero a stabilire delle relazioni fra b,—b,, ¢,e o,. Perd non si ottengono cosi condizioni notevol- mente pitt estese di quelle gia poste. Si potrebbe trovare in modo analogo un numero b, tale che per b>6, il discriminante sia positivo qualunque sia h, perO non st possono stabilire delle condiziont sufficientt per la bimodalita indipendenti da k. Infatti sappiamo che condizione necessaria per la bimodalita @ che f(a) ed f(a) siano il primo positivo, il secondo negativo. Possiamo scrivere : FS (@)=4A,—-hB,, f (%)= A,—kB., dove A,B,, A,B, sono quantita positive. Se esse sono indipendenti da &, 10 posso sempre imaginare /; cosi piccolo o cosi grande che siano f(a) ed f(a») entrambi positivi o negativi. Percid non posson trovarsi valori di b costanti, o funzioni di h indipendenti da k, per 1 quali la curva dimorfica sia necessariamente bimodale. 4. Caso particolare: curve componenti di ugual deviazione normale: h=0. In questo caso uguagliando a zero la derivata si ha: x +k (a —b) e*-% = 0, : se ee das _ 2-8 Poniamo 2ba2 — b?=z da cul & = —o5- al a oy ae L’ equazione diviene : z2+84+k(z-b) & =0= F(z). Dobbiam vedere quando questa ammette uno e quando tre radici reali: a queste corrispondono in generale le ascisse delle intersezioni delle due curve : a So 2y = ke’. i et) 2 ae ee ae dz ha per radici le ascisse delle intersezioni delle curve : = I Peel ed Tg pA FERNANDO DE HELGUERO 97 Una di queste, la z,, & sempre crescente, sempre positiva: Per z crescente da —®a 0, z cresce da 0 a k, per z crescente da 0 a+ o la z varia da k ad o. Le altre due curve sono iperbole equilatere. Per la prima si ha che per z>b, 2<0, —-B0, e<—0%, 24<0; per la seconda per z>b—-1, z24<0, z0. Le intersezioni della z, colla z, sono comprese nella striscia limitata dalle rette z=—-Be z=+)* Quelle delle z; colla z, nell’ intervallo z=— » e z=—(1—D*). Supponiamo che la F'(z)=0 ammetta tre radici reali e distinte: allora fra due intersezioni della z, colla z,, deve esserci una intersezione della z; colla z,. (Vedi fig. 8.) Zz, Ay ' ' ' 1 ! ' ' ' Siccome son tutte curve omali crescenti, le intersezioni delle z, e z, devon comprendere quelle delle z, e z;. Le ascisse di queste siano y, Yo. Esse sono le radici della : (c+ 6°) (2-B)+(24+ B)=2- Bb, ovvero 2—b'+2b°=0 onde y,=—b Vb? — 2, Yoo — ar b Vb ae 2, Inoltre le F(— b*), F'(y), Fyn), #(b*?) devon presentare segni alternati. Ora F(-b)<0 e F(+08?)>0, percid devon essere #’(y) positive ed F' (y,,) negativo. Biometrika 111 13 98 Sut Massimi delle Curve Dimorfiche Evidentemente queste condizioni sono anche sufficienti perche la F (z)=0 ammetta tre radici reali e distinte. Segue che: Condizioni necessarie ed insieme sufficienti perché la curva dimorfica risultante di components normals di ugual deviazione normale sia bimodale sono : (1) y ed Ym reali onde b > 4/2, (2) {b—Vvb— 2} —k (b+ VbP— 2) e PVP => 0 : (b+ NE—9} —k (b— VP 2} PVF <0. Intanto possiamo assertre la unimodalita se b 2c, allora dovremo vedere se sono soddisfatte entrambe le disegua- glanze prima scritte. Nel caso che lo siano si ha la bimodalita; se anche una sola non é verificata la curva @ unimodale. Si ha il caso limite quando é soddisfatta una delle due relazioni : {b — Vb? — 2} —k (b+ Vb? 2} ec? VF = 0, MISCELLANEA. I. On some Dangers of Extrapolation. By EMILY PERRIN, University College, London. (1) Iv is well known that most excellent graduation results both in the case of physical and vital investigations may be obtained by fitting algebraic or trigonometrical curves to a limited range of observation. Such curves are in constant use for interpolation, not only in physics and demography, but also in chemistry, in actuarial science, and in empirical investigations in all branches of technical research. So long as such curves or algebraic formulae are applied for the purposes of interpolation within the range of observation, their use is not only justifiable, but indeed indispensable. This statement of course supposes that a good formula has been selected and has been properly fitted to the observations. When we examine, however, the excellence of fit of even an arbitrarily chosen curve to a given range of data, when we see how it smooths the irregularities, and provides well within the limits of probable error the graduation that the chemist or engineer or actuary is eagerly seeking, we are tempted to continue our empirical representation of the data beyond the range of actual observation and predict the future from the past, or the condition of the unobserved from the observed. This extrapolation is one of the most fascinating fields of enquiry and yet one in which definite conclusions are most difficult to reach and pitfalls frequent and dangerous. How often is this extrapolation indulged in almost unconsciously by the scientific enquirer! We know now that the proportionality of stress and strain is only true within narrow limits, yet the early investigators extrapolated from this linearity all across the mysteries of set, yield-point, and stricture, up to rupture! Within quite recent years we have, we fancy, seen distinguished physicists and chemists running along tangents as if every observation-curve beyond the observed range ended in an indefinitely extended point of inflexion. Yet their want of logic is only com- parable with that of the early physicists who extended Hooke’s Law or Boyle’s Law beyond the limits of observation, or of the later physicists who apply the deductions from Hooke’s Law to the stress and strain of the solid earth, or relations between physical attributes at known tem- peratures and pressures to what may be supposed to happen beyond the range at which it has hitherto been possible to experiment. The present enquiry is, of course, of a much humbler nature, but it may serve possibly as a warning on the dangers of extrapolation. Even if it does not deal with such important pro- blems as the physics of the solid earth, it does deal with things which have been subjected to a like treatment. A parabola of a sufficiently high order—such a curve as has hitherto been often used by physicists and chemists—has been selected to describe the observed range of measurements, and then extrapolation has been attempted at a very small distance outside that range and the results compared with actual observation. When the conclusion to be drawn is merely a note of warning, may we not learn from the lesser as to the greater? It seems to us that such “extrapolation” at least is justifiable. 13—2 100 Miscellanea (2) The data dealt with are drawn from the demographic statistics of the City of Buénos- Ayres and are published in the Annuaire Statistique de la Ville de Buénos- Ayres of which twelve volumes have now appeared. This publication is to some extent a model for municipal statistical work, and we have to cordially thank M. Albert B. Martinez the Directeur de la Statistique municipale of Buénos-Ayres for our copy of this interesting book. Buénos-Ayres is a town which is altering demographically in two very sensible ways; there is a rapidly increasing population, together with improving sanitary and medical conditions, indicated by a falling death- rate and a decrease in the percentage of still-born children. The data in our possession started from the year 1887, but to allow of extrapolation beyond the start of the range we did not use that year. The following thirteen years’ returns were then available for investigation at the time of the inquiry : TABLE I. City of Buénos-Ayres. Vent Population on Deaths per Still-born Dec. 31 1000 per 1000 1888 455,167 27°17 2°45 1889 523,452 28°15 2°49 1890 547,144 30:00 2°36 1891 535,060 24°32 2°46 1892 | 554,713 | 24:05 2°29 1893 580,371 22°40 2°22 1894 603,012 | 22°72 2°06 1895 677,780 | 22°05 1°73 1896 712,095 19°16 1°78 1897 738,484 19°25 1-78 1898 765,744 17°67 1°70 1899 795,323 17-06 1:63 1900 821,293 20:09* 1°68 The problem was then this: Graduate these results by a sufficiently high parabola, and predict by extrapolation the demographic condition of the town before and after the period covered by the above data. The method of solution adopted was as follows: The successive moments of the observations about the middle point of the range were calculated by the processes indicated in Biometrika, Vol. 11. pp. 15 e¢ seg., and the series of best fitting parabolas was determined. We halted when a thoroughly good fit had been found. Thus we stopped at the fifth order parabola in the case of population and at the fourth in the case of the death and still-born rates. Judged by any test of goodness of fit it will be found that within the range dealt with our curves give excellent graduation. For example, the mean error made in fitting the population with a straight line is 16-2 thousands, while the mean error made in using a curve of the fifth order is less than half this, being 6°5 thousands. This connotes a mean error in the population as estimated by interpolation of almost exactly one per cent., which may be considered for all purposes of interpolation in vital statistics as very satisfactory. If we take the death-rate statistics we do not get anything like the same improvement if we pass from a straight line to a parabola of the fourth order. In fact the mean error made in the death-rate by the latter curve is 1:07, while it is only 1:18 if we use the best fitting straight line, or the fourth order parabola makes an error of 4:7 per cent. on an average in the death-rate, the straight line an error of 5-7 per cent. This is a sensible but not a considerable improvement, and it did not seem that a substantially greater gain would be made by continuing the process further. Clearly, when we consider the effect of epidemic sicknesses, we can hardly hope to get a closer result from a graduating curve. *Small-pox epidemic. Miscellanea 101 Lastly, turning to the still-born rate, we have for the parabola of the fourth order a mean error of (051 and for the straight line a mean error of ‘075, corresponding to 2°5 and 3:7 per- centage errors respectively. This is a sensible betterment, but nothing like as good as in the case of the population data. We may say that by using a high parabola instead of a straight line we better the fit two-and-a-half times for the population, one-and-a-half times for the still-born, and one-and-a-quarter times for the death-rate. In the last two cases therefore straight lines would give quite reasonable graduation or interpolation formulae. The actual equations to the curves, the year 1894 being in each ease taken as origin of «, the unit of which is a year, are: Population. Straight line: ¥ =639'1667 + 29'8186.2. Fifth order parabola: ¥y =617°729 +.44:8543x + 3°599, 1100? — 1°555,483.8 — 083,917.7! + 033,424.05. The unit of y is here 1000 individuals. Death-rate per 1000. Straight line: ¥ = 22°5383 — 104282. Fourth order parabola: ¥ = 219981 — 1°345,685x 4+ ‘052,220? + 014,016.23 — 000,330.44. The unit of y is one in the thousand. Still-born per 1000, Straight line: y =2'0471 — 087992. Fourth order parabola : ¥ =2:0173 — 130,8232 + 005,316.27 + 001,983.23 — 000,131.24. The unit of y is one in the thousand. The results obtained by observation and from calculation by the parabolas between the years 1888 and 1900 are given in the accompanying Table II. This table shows at once that the results are quite satisfactory within the range of observation. The same point is brought out graphically from the diagram. Confining our attention to the curves between the verticals Y,V, and Y,V,, we could hardly hope to better the graduation provided. TABLE II. Interpolation Calculations. | Population in 1000’s | Death-Rate per 1000 |, Still-born Rate per 1000 Year = | | Calculated | Difterence Calculated | Difference Calculated | Difference | 1888 | 446 = 9 ! 28°50 +1°33 2°40 | —'05 1889 | 521 =2 | 28:08 - 07 | 247 | —02 1890 540 - 7 27°24 —2°76 2-47 | +1] 1891 543 + 8 26°10 +1°78 2°39 -— 07 | 1892 | 552 - 3 2478 | + °73 2°28 | —Ol | 1893 | 578 —2 || 2338. | +98 | 215 —-07 1894 618 +15 || 22:00 | += ‘72 || 2-02 — 04 1895 | 665 |} 13 || 2072 | -128 | 1:89 +:16 1896 | 709 | -—3 || 19°62 + 46) «1:79 +01 189 | 744 +6 | 1878 | ‘47 «| = «172 — 06 1898 768 +2 | 1896 | a 59 =| «167 —-03 1899 790 —- 5 || 18-12 +106 166 +03 1900 | 831 +10 || 18-40 -169 | 168 00 | | 102 Miscellanea But now let us look at the problem of extrapolation. Can we prophesy what happened in 1887, the year before our range of observation starts, or in the years 1901 and 1902, the data of which have been received since our curves were determined? Table III. gives the actually observed and the predicted results, (i) on the basis of a straight line extrapolation, (ii) on the basis of a high parabolic extrapolation. TABLE III. Extrapolation Calculations. Population in 1000’s Death-Rate per 1000 Still-born Rate per 1000 Year - — ~ aa Parabola | Line Actual Parabola Line Actual|| Parabola Line Actual A A A A A A 1887 || 251 | --187 ; 480] —-08 | 438 || 28°38 |+ -79| 29°84 |42-25 | 27-59 || 2:20 |4+-36| 2°66 |4-82] 1°84 1901 | 985 | + 87 |848} 00 848 | 19°15 |+ °55| 15°24 |—3-36| 18°60 || 1°73 |4-09 | 1:43 |—-21} 1°64 1902 1162 | +284 | 878; +°08 | 870 |! 20°39 |4+4:19 | 14°20 | — 2-00 | 16°20 || 1°79 |4-11 | 1°34 }— 34] 1-68 Mean A | | | Extrapolation | = — 186 |—| 05); — || — 1:84; — 254| — || — | 19] — | -46] — Mean A Interpolation -- 65 — | 16-2 — — 107; — 118; — — 05 | — 08| — Now these results show that for the death-rate and the still-born rate the parabolas give better results for extrapolation than the straight lines, but that both representations have a mean error much in excess of the average mean error of interpolation within the range on which the calculation is based. An examination of the diagram shows that both rate curves are actually inadmissible a little beyond the range, for we see that either calculated rate tends to fall beyond the beginning of the range and rise after the end of it; there can hardly be a doubt that the very reverse of this must represent the actual state of affairs. In the case of the population curves this divergence fromm the facts does not occur; the total population falls before the beginning of the range and rises after the end of it as we should anticipate. But we see that the great closeness of the calculated to the observed population within the range has been gained by immensely emphasising the fall before and the rise after the range, so that the curve becomes worthless for purposes of extrapolation. Indeed while the parabola within the range is two to three times as good as the best representative line, the latter is indefinitely better than the former for extrapolation, giving indeed extremely good results. We are thus forced to the conclusions that: (i) Empirical formulae which fit extremely well within the range of observation may give very bad extrapolation results only just outside that range. (ii) Of two curves that which gives by far the better interpolation results, may give by far the worse extrapolation results. We cannot argue from excellency of fit within a given range to a fitness for prophesying what occurs even just outside that range. Generally we believe that while empirical formulae—including in that term even general laws like Hooke’s or Boyle’s—may be excellent for interpolation within the range of actual observation, they cannot be used in either physics or vital statistics without extreme caution, if indeed they can be used at all, to predict what will occur even just outside that range. While inter- polation and graduation can be satisfactorily carried out by the use of a variety of empirical curves, there is no corresponding method of extrapolation unless we have some solid reasons for assuming that the phenomena can only be represented by a formula or curve of a very definite type. ‘uoTepodeyxgy Jo rasueq Suryeaysnyy! weaseiq % LE a a zO6I 1061 1 6681 8681 3 5! 68st 888) QR oe z06 o 006 6 i L681 9681 s5si reel coat z681 168t osat 68% 81 19a is) | s | { a a8 als eee et {a — elie 1 4 ¢ a oO > ane |! = ‘a = all = ae IE ae le er dk = + + + +— t fs 1 | ° ' 2 oooo0e + 4 vn al L mal c Sea tee i= es Sy o0000% +. 2 z nH 8 > SS ooo00s +> m ~ s y SS ° SS 2 = 000009 a 4 3 [ 3 oy v 5 = rc | eae ey 000002 = Lt z oes 7) 9 000008 Sl eee = > ™ X 7 3 000006 + + — Sze , m 4 > ‘ x ; x | | > 0000001 7 = — sz % nm / ' eg | ; ‘ iu oe 104 Miscellanea II. On Differentiation and Homotyposis in the Leaves of Fagus sylvatica. By KARL PEARSON, F-.R.S., with the assistance of MARION RADFORD. (i) If an examination be made of a beech tree there will be found to be a distinction between the nature of the growth at the free higher parts of the tree and at the lower more accessible portions. Botanists have distinguished these two types as ‘sun’ and ‘shade’ branches. How far these differences of growth are entirely due to differences merely of light or even of air environment may be legitimately doubted. The free south side of a large beech tree does not as a rule abound in sun branches, while the north side exhibits only shade branches. There appears to be not only some factor beyond the light and air environment controlling the develop- ment of the tree, but the age of the tree and the age of the part of the tree considered seem also influential. Sun branches at any rate occur where the growth of the tree is most rapid, and shade branches where it is less rapid. Our experience is that with old and large beech trees, even if they are growing freely on a common, the sun branch is confined to the upper portions of the tree, and a random collection of sprays will result in shade branches only. The accompanying photographic reproductions which I owe to the kindness of Professors F. W. Oliver and A. G. Tansley will illustrate the difference between the two kinds of growth. We have collected a considerable number of sprays from beech trees this autumn and examined a considerable number collected by other persons, and it is safe to assert that a random gathering round the accessible parts of a large beech tree will result in a collection consisting in great bulk or more probably entirely of ‘shade’ branches. (i) Ifa spray representing a year’s growth be cut from a shade branch of a beech tree, there will according to our experience generally be found to be four, occasionally only three, more rarely five leaves upon it. The accompanying Plate II. represents a number of such sprays, the typical forms being I. and II. Looked at from the back we shall call the leaves that fall on the right of the stem of the spray, right-hand leaves, and on the left of it, left-hand leaves. Measuring from the top of the spray down it, the leaves will be called first, second, third, etc., leaves. The leaves are almost invariably—in 99 per cent. of the cases observed—on alternate sides of the stem. 206 such sprays were gathered from the beech trees growing on Highmore Common, not far from Nettlebed on the Chilterns, by Dr Alice Lee and myself—the bulk from very large forest trees. Of these sprays 98, instead of 103 the half, had the first leaf on the right-hand side. In one case the third leaf was the first on the right-hand side; in the remaining 107 cases the second leaf was the first on the right-hand side. On the left-hand side there were 108 cases of first leaf and 98 cases of second leaf. We think we may therefore assert that the first leaf is as likely to be on the right as on the left side of the stem of the spray. The first and second leaves of the spray are both much larger than the third and fourth leaves, and there is a marked differentiation between the first pair and the second pair. This differentiation is so obvious, the second pair being in many cases quite dwarfs, that for the first paper* dealing with beech leaves we did not collect this secondary pair, and such pairs were therefore not included in the countingsof the veins. The object of the present note is to test (i) whether serious error was introduced by disregarding the differentiation of the members of the first pair, and (ii) what eftect the inclusion of the secondary leaves would have upon the homotyposis. (ii) Investigating first the difference between the first leaf on the right and the first on the left without regard to order, and dealing with the same character as in the earlier investi- gation, i.e. the total number of veins on both sides of the main ridge of the leaf, we find : Mean Standard Deviation First Left-hand Leaf... 15432 + ‘075 1:589 + 053 First Right-hand Leaf 15°495 + 074 1°585 + 053 * ««Homotyposis in the Vegetable Kingdom.” Phil. Trans. Vol. 197, A, p. 324. Miscellanea 105 There is clearly then no sensible differentiation between the number of veins or its variability when we pass from the right to the left-hand side of the stem. Next dealing with the leaves taken in order down the stem, and without regard to their right or left-handed position, we have : Number Mean | Standard Deviation First Leaf eee 206 15°684 + ‘071 1°505 + -050 Second Leaf... 206 15'°257 + ‘076 1612 +°054 Third Leaf isis 205 13098 + ‘096 2°034 + 068 Fourth Leaf... 145 | 10559+-°110 1-968 + ‘078 Fifth Leaf aig 23 8348 + 204 1°448 + -144 | The mean of all the first and second leaves together may be compared with the Great Hampden series of 1900, also from the Chilterns : Mean Standard Deviation Highmore Beeches ae 15°471 1574 Great Hampden Beeches 167106 1°735 Considering the difference of localities, of season and class of tree, these results appear to be in reasonably close agreement, and enable us to judge how far any serious error was introduced into the Hampden results by the hypothesis that the large, ie. first or second leaves on the spray, were undifferentiated. The Hampden leaves have clearly more veins, there is a sensible difference of ‘6 in the mean, not very great, but sufficient to show that we had properly excluded the third and fourth leaves, when we collected. In the next place there is a sensible differentiation as we go down the stem, most marked when we pass from the first two leaves to the third, fourth and fifth, but hardly of great importance when we consider only the first and second. If we treat as we did in the Hampden series the first two leaves as homotypes and work out their correlation we find: Homotypic Correlation of first two leaves p= "504 +025, Now let us work this out, allowing for the differentiation between the two leaves. Using the formula given in 7. S. Proc. Vol. 71, p. 302, i.e. : o” Pato? * Gm —TloF 098) we have: p='5042, o?=2°47731, 0) 72='045582 o? — 07° =2'34839. m=2. Whence we find : 7 ="5513. 9 On The actual value given for homotyposis in beech leaves of the Hampden series being ‘5699, it will be seen that only a small change has been made by allowing for differentiation in the present results from the Hampden value. The simple explanation of this undoubtedly being that our leaves were almost entirely, owing to our method of gathering, the first and not the second leaves of the year’s growth. But the present investigation allows us to go a stage further, and to find the homotyposis in beech leaves supposing we take all leaves and not merely the two first leaves of the year’s growth. We have 144 sprays* with four leaves on, five leaves are so rare that we cannot use * Tn the case of the 145 sprays with fourth leaves recorded, there was one in which a third leaf was not available for counting. Biometrika 11 14 106 Miscellanea the fifth leaf. Let us find the homotyposis of the series as a whole, correcting for differen- tiation. We have: p= ‘0300 + ‘0162. In other words, when we do not pay attention to differentiation the homotyposis is almost zero. Clearly the small leaves on the spray could not be disregarded even by a most careless gatherer, without the result being very manifest when the correlation is determined. Now let us allow for this gross case of differentiation by the above formula. We have p= 0300 + 0162, o?=7'28052, o2= 388274, o* — 07 =3'39778. m=A4, Hence : 7 = "0643 + 3809 = 4452. Considering the comparative paucity of the material—only 144 sprays—I think this result may be considered fairly satisfactory. Namely, we find, that judged by the first two leaves the homotyposis is ‘55, agreeing closely with the earlier determination ; judged by the first four leaves of the spray the homotyposis is ‘45. The probable error of either result is certainly not less than ‘04 to ‘05*, and we conclude that the homotyposis in beech leaves cannot diverge much from ‘5. Experience seems to show that the wider range of homotypes taken, if we allow for differentiation, the better the result will be. The present paper is also of interest as showing that a slight differentiation such as that between the first and second leaves, even if it should escape detection, would not radically modify, still less vitiate the results obtained. To get final numbers probably 1000 sprays of four leaves ought at least to be dealt with. The present study, however, will indicate how the student of homotyposis can investigate and allow for differentiation due to position. Other instances are given in the memoir in the &, 8. Proceedings, Vol. 71, pp. 288-313. (iv) A paper has been recently published by Miss Tine Tammest in which two tables are given for the number of veins on beech leaves, having regard to their position on the year’s shoot (Jahrestriebe). The authoress gathered 15 shoots with 9 leaves and 6 shoots with 8 leaves, —all off the same tree. She sought shoots with the same number of leaves as they had inter- nodes : “Diese waren, obgleich die Zahle der Internodien bei dem verschiedenen Trieben ziemlich stark variirt, an dem grossen Baume ohne viel Miihe zu finden” (p. 78). Further the shoots taken were those which had the greatest number of internodes. She found for this single tree : | Position of leaf from base of shoot | 1 2 8 4 5 Mean No. of veins on 15 shoots 9°8 | 11°7 | 13°1 | 13°5 6 shoots 10°0 | 11°7 | 13°3 | 13°8 ” ” | ial ben | Now what is quite clear from this table is that (i) the nature of the shoots dealt with by Miss Tammes is both for number of leaves and number of veins to the leaf entirely different to what would be obtained by a random collection of year’s shoots on the Chiltern beeches. That (ii) had she made such a random collection, her law of periodicity in growth would not have received confirmation from the beech tree at all. * For example, with a deviation of p from 03 equal only to about its probable error, the first term in r will be raised to :10 instead of -06 and thus r would be sensibly °5. + Verhandelingen der Koninklijke Akademie van Wetenschappen te Amsterdam (Tweede Sectie), Deel 1x. Die Periodicitat morphologischer Erscheinungen bei den Pflanzen, pp. 1—148. Maart, 1903. ae 3 Biometrika, Vol. II]. Part I. Plate |. ‘Shade’ Branch. ‘Sun’ Branch. Plate Il. Biometrika, Vol. II. Part 1. * a w Ane \ He - a waive veo P) ya ; — a4 . . . ee bs 1 .” - ow ‘ + ~~ SS : ] i ae i a a i ' + € —~ = .o —~ Miscellanea 107 There seems therefore considerable danger both in drawing conclusions from selected shoots of a single tree in a problem of growth and further in citing such results as an argument as to homotyposis. Probably, but we have no certainty for it, Miss Tammes in selecting shoots with 9 leaves, really made a selection of ‘sun’ branches as distinguished from ‘shade’ branches, but whether her results are universally true for the leaves on all such branches of all beech trees, it is quite impossible to say until a large number have been examined. In the case of the big trees such as we have dealt with from Hampden and Highmore, the task of collecting year’s shoots from ‘sun’ branches will not be an easy one, for in the majority of cases they are very inaccessible. Whether the homotyposis of ‘sun’ branches differs from that of ‘shade’ branches, it is impossible to say ; the larger number of leaves to the shoot on the former, however, would make them better material for homotypic investigation. (v) It may perhaps not be out of place to note here that since the first memoir on homo- typosis was written we have been able to get a short series of 150 woodruff sprays from a lane at Horsham, Sussex. The woodruff was in flower and the whorls were counted from the flower downwards. As compared with the Great Hampden* series we found: Mean number of branches Standard Deviation Great Hampden tes 69 93 Horsham ae sa 6-7 84 The correlation between position and number of branches was ‘26 and the homotyposis allowing for this differentiation was °32. This is a very sensible increase on the ‘17 of the original Hampden investigation, but while the number of whorls to the spray at Hampden was on an average 7 and might reach 10, the mean number at Horsham was 4°5 and never exceeded 5. Hence the material did not provide a good determination of the relationship between number of branches and position’of the whorl. What it does suffice to show is that the Hampden series was justly described as having a value much reduced by neglect of differentiation. We should be very glad if any reader of Biometrika would provide us with 400 to 500 healthy sprays of woodruff after the plant has ceased to grow in the autumn of next year. Description of Plates, Plate I. Illustrations of the so-called ‘sun’ and ‘shade’ branches of the beech. Plate II. Backs of typical beech leaf sprays. I and IJ. Usual forms of spray, with four leaves and indicating the marked differentiation between first and second pairs of leaves. II and III. Seldom forms with five leaves. V and VI. Less seldom forms with three leaves only. The letters Z and / indicate the left and right-hand side of the back of the leaf and the subscript figures the number of the veins. The larger number gives the order of the leaf on the spray stem. III. Albinism in Sicily and Mendel’s Laws. It has been suggested by Castle (1) that albinism in Man behaves in accordance with Mendel’s Laws of Inheritance, and the suggestion is considered probable by Bateson (2). In a recent paper Garrod (3) has endorsed the same view, and has cited the work of Arcoleo in support of it. Arcoleo’s work (4) records 62 cases of albinism observed in Sicily, the greater number in the province of Palermo. Three of the albinos recorded were produced by albino parents, the rest had normal parents. In ten cases it is known that the parents were pigmented, but it is not known whether they produced pigmented children in addition to the albinos. The forty-nine remaining cases were distributed among twenty families, which contained alto- gether 133 children. Now, on the Mendelian hypothesis, that albinism and possession of pigment * The Great Hampden Lane gave no woodruff when examined this autumn, but the hedges had been recently cut down and the banks trimmed. 14—2 108 Miscellanea are allelomorphic characters, albinism being recessive, the marriages which can give rise to albino children are of two kinds only, namely (1) those between albinos of any ancestry, who are by the hypothesis “ gametically pure recessives,” and (2) those in which each individual has some albino ancestry, and is a “ heterozygous” product. Marriages of the first kind should produce albinos only, while a quarter of the children resulting from marriages of the second kind should be albino, the rest being pigmented. Neither of these expectations is justified by Arcoleo’s record. The three albinos produced by albino parents belonged to one family, and it is stated that “Gli antenati furono tutti bianchissimi,” implying a considerable amount of albino ancestry ; yet this family contained two pigmented brothers! Again, the most probable number of albinos among the 133 offspring of pigmented parents, all of whom are known to be capable of producing some albinos, is 33°25, and the Standard Deviation of this expectation is V}x $x 133=4-94. The observed number of albinos, namely 49, shows an excess of 15°75, or about 3:2 times the standard deviation, over that predicted by the Mendelian hypothesis. The odds against any result as large or larger than that observed, if the hypothesis be true, are nearly 2000 to 1; and although this degree of improbability may not be held by some to disprove the hypothesis, it certainly ought not to be adduced as evidence in support of it. The occurrence of segregation in a non-Mendelian proportion is exactly paralleled by the behaviour of the character “waltzing” as opposed to normal walking in mice, recorded by von Guaita and Darbishire. The one fact which is not in apparent contradiction to Mendel’s hypothesis is the behaviour of six albinos who married pigmented persons. One marriage was sterile ; the other five pro- duced altogether 24 children, all pigmented. Taking these records in conjunction with the work of Cuénot (6) and Darbishire (5) on the inheritance of albinism and of other characters in mice, we see that the disappearance of a character such as albinism in the offspring resulting from a cross between an albino and a pigmented individual, and the reappearance of albinism in a portion of the grandchildren, produced when the immediate offspring of the cross are mated, may be associated with very different conditions of the albinos. Cuénot and Darbishire have both shown that the colour of the young produced by a cross-bred albino mouse, paired with a coloured mouse, depends partly on the colours exhibited by the ancestors of the cross-bred albino, thus showing clearly that such an albino, although it should be a “pure recessive” in Mendel’s sense, is not gametically pure. Among mice there is no certain record of cross-bred albinos so impure that when paired together they produced pigmented young; the case of the family recorded by Arcoleo is therefore of great interest, as showing that in Man even this degree of “ gametic impurity ” may exist in albinos. These results show how necessary it is that the phenomena of alternative inheritance should be studied in the light of fuller experimental knowledge concerning the correlations between cross-bred individuals and their ancestors; they show the futility of attempting to express such phenomena in terms of formulae based on the unproved hypothesis of gametic purity. Finally I would urge on'those who have opportunity the great value of a full study of albinism in Sicily. In the province of Palermo, from which many of Arcoleo’s cases are drawn, the percentage of accepted soldiers of pure blonde type (‘con capelli biondi e con occhii celesti ”) is given by Livi (7) as 271; that of men “con capelli biondi o rossi e con occhii celesti o grigi” is 3°8. Albinos are naturally exempt from military service, because of their abnormal eyes, and therefore do not appear in Livi’s table. During a recent visit to Sicily, when I walked over a good deal of country round Palermo with an artist friend, my attention was continually called, not only to albinos, but to the extraordinary fairness of many blonde persons, who were still slightly pigmented. It would be of great interest to know whether these blondes are more often related to albinos than are persons of the darker, more usual type. W. F. R. W. Miscellanea 109 PAPERS REFERRED TO. 1. Castie, W. E., and Farasnr, W. C. Notes on Negro Albinism. Sezence, 1903, XVIL 2. Bareson, W. The Present State of Knowledge of -Colour-heredity in Mice and Rats. Proc. Zoolog. Soc. 1903. Vol. I. 3. Garrop, A. Ueber chemische Individualitét und chemische Missbildungen. Pfliigers Arch. f. d. gesammte Physiologie, xcvm (1903). 4. ArcoLEo, G. Sull Albinismo in Sicilia. Archivio per 0 Antropologia, 1 (1871). 5. Darepisuire, A. D. On the Result of Crossing Japanese Waltzing with Albino Mice. Biometrika, Vol. 11, pp. 1—51. 6. Cutnor. L’Hérédité de la Pigmentation chez les Souris. Arch. Zool. Hup. (Notes et Revue), 1902. Sér. 3, T. x. No. 2. Livi, R. Antropometria militare. 4to. Roma, 1896. -~I IV. A Mendelian’s View of the Law of Ancestral Inheritance. It is a very thankless task to try and correct every mis-statement that untrained minds make when they attempt to deal with a statistical problem. But one can only hope that the persistent exposure of the blunders made by non-statistically trained biologists, when they treat problems of heredity, may ultimately produce some effect. To the statistician nothing is more obvious and intelligible than the independence of the correlations, variations and means of characters. A knowledge of any one of the three involves no knowledge of the other two. Again, equally distinct in his mind are the multiple regression coefficients and the correlations. No practised biometrician could for a moment confuse with the ancestral correlations the multiple regression coefiicients, which appear when we calculate the most probable deviation of an individual from his own type with the known deviations of his ancestors from their types ; still less would he confuse a correlation coefficient with the number of offspring that take after a parent or grand- parent! It is difficult to understand at all the attitude with which a biologist like Professor Castle* approaches a problem in inheritance, but it is summed up in the words that he has not the least idea that there is any distinction between a correlation, a multiple regression coefticient, and the number of individuals who may take after an individual ancestor ! Mr Francis Galton published in his Watural Inheritance (p. 136), “with hesitation” the following statement “consequently the influence of the individual parent would be 4, and of the individual grandparent ;!; and so on.” In his work on Bassett Hounds, Mr Galton subsequently extended this principle by supposing that of the “heritage” as represented by all the offspring together, 4 of the total would on the average have the character of each parent, J; that of each grandparent, 1, that of each great grandparent, and so on. This statement is obviously different from that in Natural Inheritance, where Mr Galton is treating of a blending character. It deals with alternative inheritance. From these numbers Professor Castle deduces “ Galton’s Series.” He calls the parental influence ‘50, the grandparental influence ‘25, the great grandparental -125 and so on. I presume that he understands by this the proportions in the total offspring who will be like each individual ancestor. Against these proportions Professor Castle puts a series which he calls “ Pearson’s * «The Laws of Heredity of Galton and Mendel, and some Laws governing Race Improvement by Selection,” by W. E. Castle. Proceedings of the American Academy of Arts and Sciences, Vol. xxxix, pp. 223—242. 110 Miscellanea Series,” in which he has taken the correlation coefficients with a s¢ngle parent or a single grand- parent etc., as I have deduced them for man and horse as if they were quantities in the least comparable with the number of individual offspring. He remarks: “Comparing Pearson’s series with that of Galton, we see that the parental influence is reckoned as substantially the same by both Galton and Pearson, but that Pearson assigns a much greater influence to the more remote ancestors than does Galton *.” Had Professor Castle merely added up the numbers he gives in this “ Pearson’s Series” he would have realised that they could not possibly represent what he states themn to do; for the four grandparents alone would have had more offspring “like” themselves than the total number of offspring ! Now the Law of Ancestral Heredity as stated by me gives absolutely no means of ascertaining the number of offspring “like any given ancestor”; and if we measure parental influence by intensity of correlation, we should have : Pearson’s Series Galton’s Series Parental Influence ... ae on sis 1/2 1/3 Grandparental Influence... oes = 1/3 1/9 Great grandparental Influence —... ws 2/9 1/27 Great great grandparental Influence ae 4/27 1/81 whence the complete misrepresentation of Professor Castle will be obvious. After calculating a table which he says gives the distribution of the offSpring of a cross between y grey and white mice for 7 generations on Galton’s Law, Professor Castle continues : “The observed numbers, it is evident, agree no better with one of Pearson’s series than with that of Galton. The discrepancies noted between observed and calculated will remain and even be accentuated if we replace Galton’s series with one of thoset suggested by Pearson. For the result will be unchanged in generation II, but the calculated numbers will in most cases diverge still more from the observed ones, in the later generations, because Pearson attaches more weight to the remoter ancestors than does Galton.” Now I suppose Professor Castle had some idea in his mind when he penned these lines, but so far as I can understand the Law of Ancestral Heredity as I have myself enunciated it, the produce of a grey mouse and a fawn mouse might be on the average a green mouse without that Law having anything to say on the point. From it you cannot possibly deduce what number of the offspring of any generation will be like this or that ancestor. It is not a law of types, but of the distribution of deviations from type, and this is a very different thing indeed. The Law of Ancestral Heredity, as I have repeatedly stated ~, makes no assumption as to the mean character of any generation ; it gives no statement whatever as to the number of offspring who are like any individual ancestor. What it does give us is this: the means of determining the probable deviation of any individual from the type of his own generation, when we know the deviations of some or all his ancestry from the types of their respective generations. What then is the simple relation of my Law of Ancestral Heredity to Galton’s series of }, }, 7/5 etc. ? It lies in the following hypotheses: (i) Galton supposes the type of each generation to remain the same, and * p. 224, loc. cit. + Professor Castle quotes the two series I have given in Biometrika, Vol. 11., p. 222, the one as the best geometrical series, and the other as a close series, in which round numbers were taken. + R. S. Proc. Vol. 62, pp. 387 et seq., where all the deviations are expressly said to be measured from the type of each generation, so that any modification of the type may be allowed for. Also in Biometrika, Vol. u., p. 217, where we are again told that the deviation is from the type of its generation, and are expressly warned (p. 226) that no assumption is made that the mean of the fore- casted character is identical or not with any of the means of the foreknown characters. These papers are actually cited by Professor Castle. Miscellanea 111 expressly states that he is dealing with a stuble population. Notwithstanding Galton’s own state- ment as to his series holding for a stable population, Professor Castle does not hesitate to apply it to a cross which produces a totally different population! My types may alter and do alter in any way from one generation to a second. (ii) Galton supposed that we may apply his series not only to the deviation of an individual from type, but to the “whole heritage,” he divides the offspring up into groups of individuals following special ancestors. This is an extension I have expressly and repeatedly disagreed with. I look upon such a distribution as not falling under the Law of Ancestral Heredity at all, but as part of the Theory of Reversion or of Alternative Inheritance. My agreement with Galton consists in the general conceptions (a) that the deviation of an individual from the type of his own generation depends ultimately on the deviations of his particular ancestors from their types, and (6) that the proportions of such deviation from type contributed by each generation of ancestry diminish in a geometrical series. This series is not Galton’s. It may be deduced from the ancestral correlations, and in the case of man, horse and dog the series are within the limits of errors of observation identical. It is these ancestral correlations (which have no relation whatever to type, and are only connected with the regression coefficients which give the proportions of the deviation by complex determi- nantal relations) which Professor Castle cites, and states do not agree with the numbers of coloured mice that von Guaita found descended from albino-grey crosses in successive generations ! Now Professor Castle was perfectly free to ignore my work, or to confess frankly that he could not understand it, but he commits a grave breach of scientific decorum when in a paper, not taking hasty journalistic form but published by the American Academy, he states that “the test of von Guaita’s mice is conclusively in favour of Mendel’s Law and against the law of ancestral heredity,” and yet shows that he has either not read, or not been capable of properly citing, the two papers in which the meaning of this law is discussed. Either Professor Castle is so ignorant that he does not know that a coefficient of correlation cannot be a group frequency ; or, he has directly misquoted my memoirs because any form of argument suffices for the audience he wishes to appeal to. It is a fundamental canon of scientific discussion that, if you wish to contradict a man’s results, you should know what those results are and cite them correctly. It is a breach of scientific decorum to assert that a man’s theory is opposed to certain facts, when you have demonstrably not the faintest notion of what that man’s theory is, or how his results are reached. I stated in my paper of 1903 on the Law of Ancestral Heredity that “as far as the available data at present go, inheritance coefficients for ascending ancestry are within the limits of observational error represented by a geometrical series and by the same series.” Professor Castle remarks : “It should be observed that the ‘available data’ upon which principally Pearson bases his conclusions consist of two cases of pigment inheritance, one in man, the other in the horse. A third well-known series of this sort has not been utilized by Pearson, though our information about it is much more complete and precise than that about either of the other two. I refer to our statistics about colour inheritance in mice recorded by von Guaita*.” Now there are two points to be considered here. Professor Castle states (i) that the information is far more complete and precise, and (ii) that it is available for discussion by aid of the Law of Ancestral Heredity. Any one who has compared the total number of original parents or of offspring in any generation in von Guaita’s statistics will realise that they are absolutely incomparable with the numbers we possess for man, horse or hound. They are also statistically insufficient to give correlation coefficients significant having regard to their probable errors. Further, the data given, as in almost all Mendelian categories, are so wanting in * Castle: loc. cit., p. 224, if) Miscellanea precision that it is impossible to measure the deviations from the mean of any generation and so obtain the correlations. Not until far more precise classifications are made than von Guaita provides would the material be “available.” In the next place, to what material can the ancestral law at present be applied? It was perfectly open to Professor Castle to examine the conditions under which its results so far have been reached. They are stated with perfect precision in my memoir of 1898, and are (i) the absence of assortative mating, (ii) the absence of in-breeding and of selection. Now in von Guaita’s experiments he got mice in which the ancestry had been assortatively mated for generations: he first put like to like or made a perfect coefficient of assortative mating ; and then he crossed like with unlike, or made the coefficient of assortative mating negatively perfect. This coefficient is taken zero throughout my memoir on the law of ancestral heredity, and the reader is told that the author hopes to deal in a later paper with the influence of assortative mating and in- and in-breeding. Notwithstanding this direct warning Professor Castle does not hesitate to speak of the Law of Ancestral Heredity as applicable to von Guaita’s data, and while the pro- pounder of that law has not yet been able to master the difficulties of the analysis which arises when intense assortative mating and generations of in-breeding are taken into account, the biologist remarks that the observed numbers, “it is evident,” disagree with Pearson’s series. Had I been able to master the analysis, von Guaita’s data would not have provided the material upon which the correlations could be based, and so the law itself tested ; they are simply not “complete and precise” enough. Professor Castle, as I have already stated, reaches his result by taking my correlation coefficients for inheritance in man and horse, and asserting that they give the proportions of offspring who will be “like the ancestors.” As I have before indicated, the typical ancestor might be blue and the typical offspring yellow without this having any bearing at all on the correlation coefficients. Personally I have no means of determining whether the law of ancestral heredity holds or does not hold for coat colour in mice. The theory has not yet been worked out in a form covering von Guaita’s cases, and data are only at present being collected complete and precise enough for the purpose. In the face of these facts I directly challenge Professor Castle to confess that he did not when writing his paper know what a coefficient of correlation was, and that he was thus incompetent to discuss the application of the law of ancestral heredity to mice ; or else to show that either the correlation coefficients, or, if he likes better, the multiple regression coefficients, which lie hidden in von Guaita’s data can really be extracted therefrom and are inconsistent with the values which I have found for man, horse and dog, when allowance is made for assortative mating and selection. I do not see that any other course is open to Professor Castle, after his statements that “it is evident” that the numbers do not fit my series and that ‘it is evident” that some fundamental defect exists in the “law of ancestral heredity.” It is time that some check should be administered to this irresponsible and ignorant criticism of biometric methods, a criticism which can confuse a group-frequency—i.e. a number of individuals —with a correlation coefficient, a relation between deviations from type in individuals ; and I therefore directly challenge Professor Castle to justify his statements, or failing that I call upon him to retract them. These statements are as follows : (a) Pearson’s Law of Ancestral Heredity can be applied to test von Guaita’s data for mice, and, (b) When so applied, “it is evident” that it does not fit them. Vouume III MARCH anp JULY, 1904 INOS 2 ccs EXPERIMENTAL AND STATISTICAL STUDIES UPON LEPIDOPTERA. I. VARIATION AND ELIMINATION IN PHILOSAMIA CYNTHIA. By HENRY EDWARD CRAMPTON, Pu.D. Page Prefatory Statement . ¢ 2 : ‘ : ‘ : : ‘ ; : 113 I. Introduction : : : : : : : ; : : : ‘ 114 II. The Material and its Treatment ‘ : . : : : : : : 115 III. Pupal Elimination:—A. Males. : : : : : : : : : 118 B. Females. : : : : Ss : ; 120 TV. Pupal-Imaginal Elimination :—A. Males . : : : : ; : ; 122 B. Females. : : : : : ; 124 V. The Comparative Variability of Males and Females ; : : : : 126 VI. Discussion and Conclusion . ‘ : : : ‘ 3 : ‘ : ; 127 Prefatory Statement. THE present paper consists of an account of a detailed study, by means of statistical methods, of the facts of variation and of the relation between variation and selection in the pupae of the Ailanthus silk-worm moth, P. cynthia. The observations here recorded were made more than four years ago, and they have been continued and extended in subsequent years upon the same and other species of Saturnids. Naturally the scope of the later investigations has materially widened, and in addition to the fundamental problem mentioned above, the existence of sexual selection has been examined, as well as a host of other questions which relate to the process of evolution and its factors. Among these may be mentioned the comparative variability of the two sexes, the variability of individuals at various stages in their life-history, the comparative variability of native and introduced species, and the relation between an introduced species and the same species in its original habitat. The problem of inheritance in pure Biometrika 111 15 114. Hexperimental and Statistical Studies upon Lepidoptera species has likewise been under investigation, and attempts have been made to cross various species in order to ascertain whether heredity in such cases follows the principles of Mendel. The lepidoptera afford extremely favourable material for investigations of the above nature, for they can be obtained in considerable numbers, and they may be bred with not too great difficulty. And a qualification of special importance is to be found in the sharp division of their life-history into three well-demarcated periods, each characterized by peculiar external and internal relations. It is of course clear that the structural relations of the imago must be totally different from those either of the larva or of the pupa, and it is equally evident that these forms have entirely diverse relations to the “environment” at large. Therefore the problem of selection derives an added interest from the comparison of elimination as it appears at one stage with that of another period. Furthermore the imago and the pupa possess attributes which give to each a peculiar value. The former enters upon its final period of life with a rigid and unchangeable organization, incapable for the most part of structural alterations as the result of “functional adaptation.” The pupa excites still greater interest on account of its ability to “use” its various organs in any way. Life and adaptive response are here minimized to their lowest values; and_ helplessly subject to environmental influences and constitutional weakness the pupa awaits the period of renewed activity which culminates in metamorphosis. It is from the very nature of the case impossible to present the results of the several studies carried forward during the past few years in a simple and condensed form. Merely to enumerate the statistical data which have been accumulated would trespass beyond even liberal bounds. Therefore it has been deemed best to offer the statement of problems and results in a series of papers, each dealing with a well-restricted division of the whole field. The present long- deferred account, which initiates this series, indicates as well the point of departure for the later investigations. I. Introduction. The following account is a statement of the results of an examination into the occurrence of “natural selection” in the case of over-wintering pupae of Philo- samia cynthia, as this species occurred in New York City in the year 1899. It is concerned, therefore, with the existence of a definite relation between elimina- tion on the one hand, and the extent and character of variation on the other; and particular attention is directed towards ascertaining the real basis for the selective process. In previous years, when large numbers of the cocoons and pupae of this species had been collected for other purposes, it had been noticed that a great many cocoons contained individuals which had died, although they were apparently perfectly H. E. Crampton 115 normal. And it also appeared that many of the normal living pupae failed to meta- morphose perfectly, whether they were kept in the laboratory or out of doors. The opportunity thus offered was taken for an examination into the phenomena of elimination for two successive developmental periods. The first, or period of pupal elimination, extends from the formation of the cocoon and pupation to the beginning of the formation of the imago. The second period immediately supervenes, and, as the period of pupal-imaginal elimination, is marked by the deeply-seated structural and physiological changes of metamorphosis. The re- duction of the second period, which results in the weeding out of certain of the adult moths, is none the less entirely dependent upon the ability of the pupa to accomplish successfully the production of the imago. On this account, as well as for the reason that the moth is constructed in strict accordance with the lines of the pupa, the examination into selection of this second period may justly be conducted with reference to pupal characters. To the two sections in the following account which treat separately these periods of elimination, a third section is added, which deals briefly with the comparative variability of the pupae of the two sexes. II. The Material and tts Treatment. In December, 1899, all the accessible cocoons were obtained from a small area of less than one acre in the upper part of the City of New York. The cocoons were found principally upon Ailanthus trees, the favourite and original food-plant, where clusters of twenty-eight or thirty were sometimes to be found upon a single branch. Many were taken from vines and fences near these trees, and still others were picked up from the ground whence they had fallen from the trees. It may be noted in passing that these last, far from being unfavourably affected, contained as many living pupae as those which remained attached to the trees. The total number of cocoons was 1090. Upon examination of the contents, 55 (4°8 °/,) were found to contain dead and shrivelled individuals which had failed to pupate. Ninety-three contained pupal cases from which the moths, probably of an interpolated summer brood, had escaped, or where, in nine cases, the fully-formed imago had been unable to emerge from the cocoon. Out of the 942 remaining, 623 had pupated, forming in most cases an entirely normal pupa, but they were dead. Thus only 319 “selected” individuals remained to provide for the continuance of the species. Equal numbers of the dead and surviving pupae were carefully measured, as stated below, and the living ones were kept through the metamorphosis, care being taken to isolate them as this time approached. Only 181 (97 males and 84 females) produced perfect moths, 75 were imperfect to a slight degree, 38 were hopelessly malformed and finally 16 failed to metamorphose at all. The perfect imagines constituted only 16°6°/, of the whole number of individuals which entered the cocoon, from which we may gain an idea of the severity of the con- ditions under which the quiescent pupa exists. 15—2 116 Haperimental and Statistical Studies upon Lepidoptera The comparison of the surviving pupae with an approximately equal number of dead pupae, and the comparison of the perfect survivors with the remainder of the group of survivors, has been based upon the following characters, numbering ten: first, two measures of the pupa as a whole, (1) the total length, the distance Fig. 1. Diagram of the Saturnid Pupa. A—JB in the diagram, and (2) the weight in milligrams; in the second place, a group of characters of the immovable anterior part of the pupa, which may for convenience be termed the “bust,” and which extends back to the posterior ends of the wing-cases, at the level of the line between the fourth and fifth abdominal segments. The characters in question are (3) the length of the bust, the line A—(, (4) the width of the bust, the line D—Z#, (5) the dorso-ventral depth of the bust, the perpendicular line at the point /. From these measures were determined (6) the frontal proportions of the bust, as the ratio between the width and length, and (7) the sagittal proportions, as the ratio between the length and the depth of the bust. In the third place, certain measurements were made of a typical organ, the left antenna, namely (8) the length, the line H—J, and (9) the width, as the line J—K ; from these were determined (10) the proportions of the antenna. All the measurements are in mm. Of these characters two must be omitted in considering elimination of the first period, namely, length and weight, for after death evaporation and the consequent shrinkage of the free abdominal segments render these characters useless. While it is possible that alterations in the characters of the bust may follow death, thus invalidating any comparison between dead and living pupae, these alterations if indeed they occur, must in the nature of the case be very slight. We shall have H. E. Crampton el occasion to recur to this point below. But at any rate elimination of the second period need take no account of this possibility. The antennal characters remain unchanged after death. It will be seen that the “length” of the antenna is only a convenient measure approximating to the real axial length, which dimension it is almost impossible to measure directly. From this it follows that the determination of the antennal proportions is likewise only a convenient approximation, and the value of these characters needs to be further considered below. Following the usual procedure, the determinations of every character in each sex were classified, and the frequency curve or polygon was plotted. It will be seen that each sex will have for every character five groups: all pupae, surviving pupae, dead pupae, perfect survivors, and the survivors which fail to metamorphose perfectly, which last we may term the imperfect survivors. The characters of the whole group need not concern us at this juncture. Now the comparison between the surviving and dead pupae, or between the two sub-groups of survivors, may be based upon the following constants: (1) the range of variation, (2) the mode, or value of greatest frequency, (8) the average value, or mean, (4) the standard deviation, or the index of variability, a constant found by squaring all the deviations from the mean, adding, extracting the square root, and dividing by the number of cases, and (5) the coefficient of variation, a constant of use in some connections, found by dividing the standard deviation by the mean, and multiplying the quotient by 100 to obtain a convenient whole number. Naturally the data at hand permit of much further mathematical analysis, particularly as regards the phenomena of correlation. For the present however attention may be directed only to the fundamental question as to the relation between variation and elimination and the comparison, for the sake of simplicity, may be restricted to the comparable determinations of the mean or average value of any given characters, and of the indices of variation. Before passing to the actual facts, it must be pointed out that statistical treatment of the problem under consideration rests upon the assumption that when differences are found between two corresponding constants, belonging to two different groups, such differences are significant only when they considerably exceed the probable errors of the differences. For example, the bust length of perfect surviving pupae has a certain value for which we may determine the probable error, while the bust length of the comparable imperfect survivors has its mean value with a probable error. If the difference between the two mean values in question should exceed the probable error of such a difference, the chances that the difference signifies selection will be 68 to 32; if the difference exceeds twice the error of the difference the chances of significance are 95 to 5; while if the difference is in excess of three times the probable error the chances of significance are 975 in 1000. ‘Therefore in the following account, a difference between two comparable determinations which lies between the values of le and 2e will be regarded as indicating that selection is here possible, when the difference 118 Experimental and Statistical Studies upon Lepidoptera lies between the values 2e and 3e it will be considered that selection is probable, while if it exceeds the value 3e selection will be regarded as certain. As the same relation obtains between the differences and their probable errors in the case of comparable indices of variation, selection on the basis of variability may be denoted possible, probable, or certain. II. Pupal Elimination. A. Males. The question at issue may be stated in the following form, Are the surviving pupae the same as those which succumb after normal pupation, or are they a selected group? The fact of limitation as regards the number of survivors stands unquestioned. Is elimination selective? Table I. gives the biometric constants for the total or unselected material. TABLE I. All Pupae. Males (264) Females (356) Standard Deviation Character Mean Standard Mean Deviation | Bust, Length , Width 5 Depth es ee Frontal Proportions » sagittal Proportions 1871987 + 0318 11-0466 + 0235 12°0031 + 0222 60°8220 + ‘1041 66:0606 + ‘0868 0°7673 + 0225 0°5675 + ‘0166 0°5857 +0157 2°5072 +0736 2°0916 +0614 19°3460 + 0292 12°7182 + 0223 135117 + 0220 65°8455 + 0850 69°9438 + ‘0716 0°8192 + 0207 | 0-6262 + 0158 0'6178+:0158 | 23776 + 0601 20041 + ‘0506 Left Antenna, Length Width Proportions »”» ” ” ” 0:5549 + 0162 0:2730 + 0099 7+-0890 2°1447 +0629 11°5124 + 0255 4:2921 + 0082 | 36°6629 + 0682 0°5648 + 0180 0°2293 + ‘0057 19054 + 0482 In the following Tables II. and IIT. are given the numerical determinations for answering our first question. The surviving pupae number 134 as against 130 of the dead pupae. Although the facts appear with clearness in the numerical form, a brief verbal statement may not be superfluous. And in such a com- mentary we may examine separately two questions as to the nature of selection, whether namely it takes place if at all with reference to a certain type, or whether it expresses itself in the figures relating to variability. In bust measurements, the survivors are found to be longer and narrower than the dead individuals. In both of these characters selection in type is certain according to the criterion established in earlier treatment. The survivors are also deeper (dorso-ventrally) than the eliminated pupae, and are selectively different H. E. Crampron 119 TABLE II. Pupal Period. Selection in Type. Males. 3 (e) Proportion | Character Mean; Survivors Mean; Dead rh } Error of of Selection | | Hee Ree iitienence d:€ Bust, Length 18231340453 | 18092440440 +0°1889 | 00631 2e | Probable S#!most | | > picts (certain » Width eis aes | 10°9014+ 0322 = 11:19624+°0320 —~0-2948 0:0453 = Ge Certain , Depth ve wee | 120471 £0304 | 11-9577 £0322 40-0894 | 0-0441 > 2 | Probable » Frontal Proportions — 59°6865 + +1339 | 61-9923 +°1294 | —2°3058 | 0°1850 S> le Certain = 5 Sagittal Proportions 65°9029+°'1206 | 66°2230+°1243 | —03201 | 01731 | le Possible Left Antenna, Leneth ....) 11°3514+-0273 | 11:18704°0367 +0°1644 | 0:0457 S> 3k Certain | 1 ea Width ... | 4°6844+-°0140 4°4784+:0156 | +0°2060 0:0209 > Ve Certain | 3 * Proportions | 41°41054°1190 | 40:11544°1211 | +1:2951 | 0°1696 > Te Certain | | | TABLE IIL. Pupal Period. Selection in Variability. Males. Standard | Standard 5 (e) Proportion | Character Deviation ; Deviation; | ar ) Error of of Selection | | Survivors | Dead erence | nifterence | O:€ |- — | | | | | Bust, Length on ... | 0°7780 +0320 | 0°7441+4°0311 | +0°0339 | 0:0446 <¢ None » Width se ... | 0°5535 +0228 | 0°5424+ 0226 | +0°0111 | 0°0321 ZG None » Depth ... | 0°5227+4°0215 | 0°5450+:0227 | —0:0223 | 0:0312 |} < € None » Frontal Proportions | 2°2631+-°0932 2°1882+°0915 | +0-0749 | 0:1306 < ( None » sagittal a | 2°0701+°0852 2:1016+:0879 | —0°0315 | 0:1224 ae None | | | Left Antenna, Length ... | 0°4686+:0193 0°6218+-0260 | —0°1532 | 0:0323 > 4e Certain | 4 55 Width =... | 0°2412+:0099 0:2645+-0110 | —0:0233 | 0:0147 alle Possible | as 3 Proportions | 2:0423+°0841 | 2°0470+-0856 | —0:0047 | 0:1200 | < e None | | | | with a high degree of probability. Naturally it follows from the foregoing that the survivors are much more slender in frontal proportions, and the difference between the two groups in this regard exceeds twelve times the error of the difference. In sagittal proportions, however, the narrower survivors are only probably different from the others. Remarkably clear results follow from the comparison of the antennal characters. These organs are not only much longer in the survivors, and wider, but they are also stouter than those of the incapacitated pupae; and in all three characters the difference indicates selection with certainty. 120 Haperimental and Statistical Studies upon Lepidoptera Thus we see that in six of the eight characters under consideration, the surviving pupae evidence selection of type: that a typical condition, different from that of the dead pupae, characterizes those individuals which are physio- logically “fit” to survive the vicissitudes of pupal existence. When however we enquire if selection brings about the survival of the less variable individuals, the answer, though equally clear, is negative. Although in the depth of the bust, and in sagittal proportions, the dead pupae are more variable, they are less variable in the length, width, and frontal proportions of the bust. In none of these cases, nevertheless, does the difference exceed its probable error. There is in brief, no selection in variability. And when the facts relating to the antennae are examined, it appears that the survivors exhibit selection in length only with certainty, with possibility in width, and not at all in the variability of the proportionate measure. These statements will be found to be confirmed if the reader examines Table I. alongside Tables I. and III, thus comparing the unselected material with the selected. B. Females. After examining the facts relating to the female sex, we reach the remarkable conclusion that selection of a particular type occurs in all eight characters. In only one instance does the difference between the surviving pupae and the dead pupae fall below the error of the difference. Specifically, the survivors are longer, narrower, and deeper in the bust than the others, and they are also more slender in both frontal and sagittal proportions. Moreover their antennae are longer, wider, and stouter than those of the eliminated pupae. The actuality of selection is still further indicated by the fact that in all characters excepting the proportions of the antennae the variability of the former pupae is far less, and the significance is beyond the range of error due to random sampling. The same general con- clusions are reached if we compare the survivors with the unselected material. TABLE IV. Pupal Period. Selection in Type. Females. 3 (e) Proportion Character Mean; Survivors} Mean; Dead oe ) | Error of of Selection ulerence | 1) fference O:€ = = | | Bust, Length 19°5039 + ‘0363 | 19°1917 + °0448 | +0°3122 | 0:0572 = wy Certain » Width 12°5949 + :0278 | 12°8388 + 0338 | — 0°2439 0:0437 > 5e Certain » Depth ee ... | 13°6007 + 0287 | 13-4250 + °0880 | +0°1757 00-0437 > de Certain » Frontal Proportions | 645727 +0954 | 67:0888 +°1079 | —2°5161 | 01440 >17e | Certain » Sagittal —,, 69°7727 £0927 | 70°1111 #1082 —0°3384 | 0-14.24 > 2e | Probable | | : Left Antenna, Length 11°6426 + 0231 | 11°3833 +°0310, +0°2593 00386 > Ge Certain A Width 4°3182+°0102|} 4:1283+°0126 +0°1899 0:0162 >lle | Certain 5 a Proportions | 37°1250 + °1002 | 36°2667 + 0874 | +0°8583 | 0:1329 > 6e | Certain | H. E. Crampton 121 TABLE V. Pupal Period. Selection in Variability. Females. Standard Standard 3 (e) Proportion Character Deviation ; Deviation ; pee ) Error of of Selection Survivors Dead lulerence | 1 ifference One Bust, Length 0°7150 + 0257 | 0°8826+°0313 | —0°1676 | 0:0399 > 4e Certain » Width 05477 +0196 | 0°6731+4°0239 | —0°1254 | 0°0309 > 4e Certain » Depth ... | 0°5643 +:0202 | 0°6567+°0233 | —0°:0924 | 0-0308 = de Certain » Frontal Proportions | 1:8770+:0674 | 2°1468+°:0763 | —0°2698 | 01018 > Ye Probable » Sagittal oh 1°8230 + 0655 | 2°1535+4-0765 | —0°3305 | 0:1007 > de Certain Left Antenna, Length . 0471140169 | 0°6177+:0219 | —0:1466 | 0-0276 > 5e Certain 9 9 Width 0:2009 +0072 | 0°2517+°0089 | —0:0508 0:0114 > de Certain 5 3 Proportions | 1°9703+°0708 | 1°7387+°0618 | +0°2316 | 0:0939 > Qe Reversed One additional fact may be noted, which is that the type selection in the characters of the surviving females is in all cases in the same direction which it This correspondence is of decided significance. takes in the male sex. Fig. 2. Selection in Type. Pupal Elimination, Females. Left Antenna Length (mm.). AS AIS 21 = 8.6 8.9 92 9.5 9.8 10.1 104 10.7 110 113 116 119 122 125 128 Total m. All Pupae 1 0 0 2 0 3 12 23 41 65 86 65 42 14 2 356 11:5124 Survivors 2 7 16 33 47 37 21 12 1 176 11°6426 Biometrika 111 16 122 Experimental and Statistical Studies upon Lepidoptera Figures 2 and 3 illustrate the general nature of the selection in two cases by graphical representation of the original material and the selected survivors. Fig. 3. Selection in Type and Variability. Pupal Elimination, Males. Left Antenna Length (mm.). 9.5 98 101 10.4 10.7 11.0 M3 106 11.9 12.2 12.5 Total m. o All Pupae 4 3 9 10 18 57 51-67 32 11 2 264 11:2705 0°5549 Survivors 3 6 7 27 29 37 19 5) 1 134 11°3514 0:4686 IV. Pupal-Imaginal Elimination. We may now consider the nature of that reduction which takes place at the time of metamorphosis, and which, although dependent upon pupal abilities, is manifested only when the great changes at this time prove too severe a tax upon the strength of a large number of individuals which were able to survive throughout the earlier period of pupal existence. It has been stated previously that only 181 out of the 310 survivors produce perfect moths. The rest were imperfect to a greater or less degree, or failed entirely to metamorphose, as follows: Perfect Slightly Imperfect Very Imperfect Non-metamorphosed Males 97 (72'3°/,) 14 (10°4°/,) 18 (13°4°/,) 5 (3°7°/.) Females 84 (47°7°/,) 61 (34°/,) 20 (11°3°/,) 11 (6:2°/.) It therefore appears that the females are the greater sufferers, although if the slightly imperfect individuals be counted with the perfect ones the males and females occur in about the same percentage*. * In studying the phenomena of sexual selection in Samia cecropia it has been found that a male which is imperfect to any degree will not copulate, while females which are slightly imperfect may sometimes copulate. These facts will be considered at length in a later communication. H. E. Crampton 123 The two characters of total length and weight are available in considering elimination of this period. It will be seen that beside the enquiry into the manifestation of selection of type and variability at metamorphosis, much additional interest arises when the relation between the selective effects of the two different periods of elimination is examined. Treatment of this period must therefore be two-fold. TABLE VI. Pupal-Imaginal Period. Selection in Type. Males. Mean. Mean. 3 (e) Proportion Character Survivors, Survivors, va ) Error of of Selection Perfect Imperfect merence | Hifference O:e Length 26-9329 + 0822 | 27-0137 +1493 | —0-0808 | 0-1704 < oe None Weight 1:9464+4°0154} 1:9190+°0307| +0°0274 | 0°03438 < oe None Bust, Length 183443 + 0482 | 18119041027 | +0:2253 | 01134 > le | Possible eae » Width 10°8856 + ‘0375 | 10°9702 + ‘0639 | —0-0846 | 0:0740 > le Possible » Depth ... | 12°0506 + 0345 | 12°0379 + 0632 | +0°0127 | 0:°0720 Ye Probable » Sagittal 5 65°7257 +°1355 | 66°3648 +2475 | —0°6391 | 0°2821 > 2e Probable Left Antenna, Length 113896 + 0299 | 11:°2514+-0577 | +0°1382 | 0:0649 Se Probable z » Width 4:6908 +0148 | 4-6676 £°0326 |, +0:0232 | 0-0358 < « | None op + Proportions | 41°3351 + °1359 | 41-6089 +2416 | —0:2738 | 0°2771 < None TABLE VII. Pupal-Imaginal Period. Selection of Variability. Males. Standard Deviation. | Standard Deviation. 3 Ora ainuosoin Character Sanvivore? peciost Rievivors: Tmpertact Ditverenee ee oe Selection | Length 1:2006 + 0581 1:3465+:°1056 | —0:1459 | 0°1205 > le Possible Weight 0:2259 + ‘0109 02769 +°0217 | —0:0510 | 0°0242 > e Probable Bust, Length 0°7082 + ‘0347 0°9265+°0726 | —0°2233 | 0°:0804 > 2e Probable » Width 05482 + ‘0265 0°5765+°0452 | —0°0283 | 0°0523 e | Possible Left Antenna, Length 0-4375+-0211 | 0-5289+-0408 | —0-0914 | 0-0459 | >1e | Possible Probeble on a Width 02173 +0105 0°2941 +:0230 | —0:0768 | 0°0252 > Be Certain 5 - Proportions | 1°9828+:0960 | 2°1783+:'1708 | —0°1955 | 0:1959 < e« | None 16—2 124 Haxperimental and Statistical Studies upon Lepidoptera A. Males. The pupae which produce perfect moths are found to be slightly shorter than those which fail to do so, and the former are slightiy heavier also. In neither case, however, is the difference significant: there is no type selection in these characters. The data relating to the bust measures are of some interest. The perfect survivors are longer, narrower, and deeper than the imperfect survivors, and they are at the same time more slender in frontal and sagittal proportions; in only the last two does selection appear with any degree of probability. It is highly important to observe that in all of these characters the perfect survivors bear the same relation to the imperfect survivors that the whole group of survivors does to the dead pupae. In brief, elimination of the second period appears to be a continuation of the earlier process of pupal elimination. Therefore the finally selected individuals are by far the longest, narrowest, and deepest, and at the same time the most slender ones of all that entered upon pupal existence. In the antenna, continued selection appears as regards length, but while broader organs occur in the perfect survivors the difference between these and the others is insignificant. Finally, the antennae of the perfect survivors are slightly more slender, though here, too, the difference is of no account. Although as we have seen there is no selection indicated in the type values of length and weight, when we compare the indices of variability in the two groups under consideration we find that the perfectly metamorphosing pupae are the less variable. Though this selection is but possible as regards the variability of length, a greater significance attaches to the difference between the variabilities in weight. In all the characters of the bust and of the antenna the perfect survivors are the less variable members of the whole group of survivors, but the difference between these and the other pupae is probably significant only in bust length, and certainly so only in antennal width. To summarize briefly, we find that type selection at the time of metamorphosis occurs with probability only in the proportions of the bust and in antennal length, while very little selection of variability is evidenced. B. Females. The pupae which produce perfect moths are slightly shorter, and slightly lighter than the others, selection being probable in the first case, and possible (almost probable) in the second. While in the males it was found that secondary elimination proceeded along the lines of pupal elimination, the pupae of the other sex show just the opposite relation. Specifically, the perfect survivors are shorter in the bust, and, though narrower as in the previous selection, they are less deep. In the proportionate measures especially they show the reversed nature of selection with the greatest clearness, for they are decidedly stouter in both frontal and sagittal planes with H. E. Crampton 125 practical certainty, while as a result of the earlier pupal elimination the survivors were found to be the more slender in both characters. Equally anomalous are the facts relating to the antennal characters. A rigid selection is indicated in that the perfect ones have much shorter antennae, and as these are about the same in width in the two groups, a strong selection is shown in antenna proportions, the stouter organs being characteristic of the perfect pupae. TABLE VIII. Pupal-Imaginal Period. Selection in Type. Females. Mean. Mean. 5 (e) Proportion Character Survivors, Survivors, ee ) Error of of Selection Perfect Imperfect ulerence | Difference O:e€ —— Length 30°0595 + 11087 | 30°4239 + 0727 | —0°3644 | 0°1307 > Qe Probable Weight 2 +0257 | 2:9173+-0223 | —0-0602 | 0:0340 > le | Possible eae Bust, Length 19°3309 + °0563 | 19°6620 + 0440 | —0°3311 | 0:0714 > 4e Certain » Width 12°5750 + 0482 | 12°6131 + 0347 | — 0°0381 0:0576 —e None » Depth . | 13°5691 + 0437 | 13°6294+4 0373 | —0:0603 | 0:0745 2e | Probable eae » Sagittal i 70:0952 +1351 | 69-4783 £1239) +0°6169 | 01833 | >3e | Certain Left Antenna, Length 11°5500 + 0362 | 11°7271+°03805 | —O-1771 | 0:0474 > de Certain a » Width 43143 4-0152| 4:3218+-0151| —0-0075 | 0-0214 < « | None 3 5 Proportions | 37°4631+4°1511 | 36°8152+°1114| +0°6479 | 0°1877 > Be Certain TABLE IX. Pupal-Imaginal Period. Selection in Variability. Females. Sone = oe (e) Proportion Standard Deviation. | Standard D. ition. C) f . Character Survivors, Perfect SGReiTon) Tipartest Dineen Dine ote roe Selection Length 1°4748 + ‘0714 1:0345 +0514 | +0°4403 | 0:0879 > 5e Reversed Weight 0°3499 + 0182 0°3178+°0158 | +0°0321 | 0°0241 llc Reversed Bust, Length 0'7641+:°0397 | 0°6265+°0311 | +0°1376 | 0:0504 Ve Reversed -5, Width 05869 + 0305 0°5086 + 0252 | +0°0783 | 0°0395 > le Reversed » Depth ... | 0°5933 + 0308 05317 40264 | +0°0616 | 0:0407 > le Reversed » Frontal Proportions | 1°8721+:0974 | 1:8429+:0916 | +0:0292 | 0°1337 < None » Sagittal “3 1°8330 + '0953 1°7630 +0876 | +0:0700 | 0:1294 ame None Left Antenna, Length ... | 0°4919+:0256 | 0:4839+-0215 | +0:0580 | 0-0334 > le Reversed a » Width ... | 0:2070#-0107 | 0-2149+-0106 | —0-0079 | 00150 | >1e | Possible 5 s Proportions | 2°0498+°'1066 | 15844+-0788 | +0°4654 | 0°1325 > 8e Reversed | rN Pe a ae | ee ee ie ee I ele Ns SS 126 Experimental and Statistical Studies upon Lepidoptera Furthermore reversal of selection with respect to variability appears in some - cases with astounding clearness. The perfect survivors are certainly more variable in total length, probably so in bust length, possibly in weight, bust width and bust depth. No significance attaches to the differences in bust proportions. While they are possibly more variable in antennal length, and possibly less variable in antennal width, the perfect survivors are certainly more variable in antennal proportions. These results stand in the sharpest contrast to those referring to pupal elimination. As the proportionate characters of the bust are involved no less than the absolute values it must be concluded, I think, that the process of pupal- imaginal elimination involves certain factors which do not operate during pupal existence. Hence individuals which could and did survive the conditions of purely pupal existence find themselves marked for destruction by the very characteristics which formerly proved advantageous. I regard the reversal on the basis of variability as indicating the same conclusion also. Although discussion of these points may properly be deferred, it may be stated here that the enquiry into the actual basis of the selective processes may lead to a clearer understanding of the apparently conflicting facts. V. The Comparative Variability of Males and Females. The question as to which sex is the more variable is of considerable interest in some connections. It is not directly related, however, to the problem which is treated in the present paper, so that the facts may be presented in a brief form without any discussion at this time. It is clear that it is not possible to determine the relative variability of the two sexes by a simple comparison of the indices of variation for any given character, for with a greater absolute value of any measurement a higher degree of variability is usually associated. A more satisfactory basis for comparison is afforded by the Coefficient of Variation, which is found by dividing the index of variability for any character by the mean value of that character. In order to obtain a convenient whole number, this quotient is generally multiplied by 100. By this means a measure of variability is derived which is independent of the absolute values concerned, though certain mathematical defects, which need not be considered here, may attach to this process. In the subjoined table (Table X.) are given the coefficients of variability of the ten characters of both sexes, for the whole group (eight characters), for the surviving pupae, and for those which metamorphose perfectly. It will be seen that when the whole group is considered, the males are on the whole more variable than the females, the latter being more variable only in two of the bust measures. Among surviving pupae the male sex is far more variable, being less so in antennal proportions solely. And finally the same sex is the more variable on the whole as regards the body in the third group of perfectly metamorphosing pupae; for H. KE. Crampton 127 although the females are more variable in the absolute bust measures of length and depth, the other sex is more variable in the significant proportions of the bust. The lower value of the coefficients relating to the antennal characters of the males is extremely suggestive, I think, in view of the function which these organs perform during imaginal existence. It is now well known, owing particularly to TABLE X. The Coefficients of Variability of Male and Female Pupal Characters. All. Survivors. Perfect Survivors. Character Males Females | Males Females | Males Females Length ... Pe .. | — —— 438 4:20 4:45 490 Weight... S06 ane == —-— 12°43 11°59 14:65 12°21 Bust, Length .... sae | ADI 423 4°25 3°66 3°83 BIOS » Width Sets es 51h 4:92 5:07 4:35 5°03 4°66 » Depth oO es yE7 | Bh 412 | 4:16 487 » frontal Proportions | 4°12 361 3°79 2°90 3°69 2°88 » Sagittal . 3-16 2:86 | 314 261 | 3:00 261 Left Antenna, Length ... | 4°91 4:90 412 4:09 3°84 425 i » Width ...| 5:95 543 | 515 4°66 | 4:63 480 59 % Proportions | 5°26 5:20 4°93 5°30 4:80 T4T the recent work of A. G. Mayer, that the male moth is guided by its sensory antennary organs in finding the female. It is decidedly interesting to find these organs are less variable in the sex for which they are the more useful. VI. Discussion and Conclusion. The facts recorded in the foregoing account relate to eight or to ten characters of the pupae of one species of Saturnid moth for one winter season. It 1s obvious that it would be futile to discuss the bearing of these facts upon the wide question of evolution in any extended form, until the figures here given may be supplemented by others relating to the same and other species of moths, obtained by more detailed studies upon the same and related questions in more abundant material. It is nevertheless necessary to deal briefly with certain aspects of the evidence which has been offered, in order to avoid misconception regarding the main conclusion stated, namely, that there is a real relation between the process of elimination in pupae, and the extent and character of their variation. It may be stated here, that the results of later studies have in no essential way altered the point of view which was arrived at from the consideration of the results of the initial investigation, here recorded. 128 EHuperimental and Statistical Studies upon Lepidoptera But before we may examine more closely into the manifestation of selection in the present case, certain possibilities of error demand frank recognition. (1) The number of individuals is smaller than is desirable for the purposes of statistical treatment. It is clear that this error has been allowed for, in so far as each comparison has been based upon the numerical values of the types or of the variabilities together with their probable errors, and these are determined by formulae which take full account of the number of cases under investigation ; and besides, the occurrence of selection has been asserted only when the difference between comparable indices of variation or between two typical values is in excess of thrice the probable error, certainly a generous allowance. (2) In dealing with graduated values like the various dimensions of the pupa there must always be an error due to the “ personal coefficient.” Enough individuals have been used to render this error negligible, for according to the law of probability the errors in excess will be offset by errors in underestimation. (3) A far more important objection may be urged against the comparison of the surviving pupae with those which were dead when found; and of course the value of the comparison which has been drawn in the present study cannot be considered as final until definite data are obtained showing the effect that death exerts upon the pupal characters under examination. But the objection can be urged only in certain cases, for the rigid nature of some of the pupal structures, like the antenna, is such that little or no alteration can follow death* ; and furthermore it does not militate against the treatment of pupal-imaginal elimination, for all the individuals there considered were alive both at the time of measurement and at the time of metamorphosis. (4) Attention has already been directed to the fact that some of the dimensions used are only approximations, as the length and proportions of the antenna; the former is really the chord of the are described by the axis of this organ. But it is legitimate to suppose that all chords of a given length represent arcs of the same value on the whole, as those arcs with greater curvature will be offset by arcs with less curvature, and that therefore a chord of a certain value will correspond to a certain average value of the arc. At any rate the differences between com- parable determinations of antennal characters in the several groups may be regarded as indicating real differences in antennal structure. And now, turning to the fundamental question of selection, we must recognize clearly at the outset the essential fact that elimination does occur during pupal existence and as well at the time of metamorphosis. Those individuals which reach the end of pupal existence form but a portion of the whole number entering it, and those animals which reach perfect maturity form again a subdivision of the previous group. The fact of reduction in numbers stands unquestioned. We have seen that those individuals which successfully survive the severe conditions of pupal existence or of metamorphosis are structurally different in * T have remeasured dead pupae after a two years’ interval and have indeed found certain minor differences between the original measurement and the later one. In no case, however, of 70 recently remeasured has the difference led to a change of class of the individuals. H. E. Crampron 129 some respects from those which do not, and that the former are on the whole less variable. Consequently we are justified in concluding that elimimation proceeds upon a selective basis; for although we must admit that some of the eliminated, killed by “chance,” may have been just as “fit” as the survivors, yet it is not possible that all of them were. Certainly, all of the survivors were “fit.” Wherefore the observed differences between any two comparable measurements of the two groups afford tangible determinations of the instability of organization with which unfitness is associated. Natural selection is thus found to exist in the material under consideration. Two questions, however, immediately arise: How far is the process natural? and: In what respects is it selection ? The conditions for pupal elimination were certainly natural in every respect, and it is equally certain that the circumstances attending pupal-imaginal elimina- tion were not the same as those which the pupa meets in nature at the time of metamorphosis. For the pupae in the second case were kept in a cabinet in the laboratory for some weeks and were subjected to warmer and drier air than usual. And yet elimination and _ selection appear at the second period no less clearly than during pupal existence. As regards the relation which secondary selection bears to primary elimination, we have seen that the two sexes differ in an interesting way. In the male sex the direction taken by selection is the same in both cases. Therefore we may conclude, if the figures relating to the first period be accredited, that the selective agencies were the same during both periods; or to put the matter in another way, we may say that the same physical characteristics of the pupae were tested in the two periods. But in the female sex it was found that, on the whole, secondary selection took place in the reverse direction, and we must conclude either that the conditions which exercise a restrictive effect at the time of metamorphosis are different from those which operate earlier, that in other words the organic test refers to other pupal functions, or else that the unnatural conditions of the laboratory produce a different result from that which would have occurred in nature. The facts are so different in the two sexes, that a direct investigation of this important problem should, and will, be made. Nevertheless, the fact of primary importance is, not that selection is here natural in the sense that it would have occurred in nature, but that the reduction in numbers proceeds hand in hand with a restriction in certain structural characteristics as regards type and variability. The next point to be noted is, that selection, where it occurs, cannot be based directly upon the characters of the pupa which we have described as showing selection. The pupa does not “use” its antennae, and no conceivable advantage can accrue to the pupa from a longer, wider, and stouter organ, and yet the survivors have on the whole longer, wider, and stouter antennae. Again, it is difficult to conceive how particular dimensions of the bust can serve advan- tageously or disadvantageously in the struggle for existence during the pupal period. What, then, is the actual basis for eliminative selection ? Biometrika m1 17 130 Haperimental and Statistical Studies upon Lepidoptera We approach the true solution of the problem, I believe, when we realize that we are justified in stating nothing more than that the surviving pupae or those which metamorphose perfectly are of particular forms, and are more conservative with reference to those particular forms than are the individuals which succumb. In short, we may not say that the longer antennae serve the pupa in escaping elimination, but we are justified only in asserting that the surviving pupae have longer antennae. When this statement is made for all the characters which exhibit selection, we see that the essence of fitness is a morphological conservatism with reference to certain values of the dimensions under consideration. Certain it is that those which depart widely from the “fit” type are numbered among the dead. According to this view, elimination is based upon the general or total efficiency of any individual. And this value is determined by the proper coordination of functional and structural elements. The actual basis for elimination is, in a word, correlation. If this be slight, a condition of less stable equilibrium arises which renders the particular individual less efticient, and which places it among the unfit. In the present case, however, we are dealing with an organism, the pupa, which does not use its structures; so that any lack of proper correlation is attributable to an absence of proper coordination among the formative factors which control the establishment of pupal structures, or by which the imago is constructed upon the pupal basis. I believe, then, that the test of fitness or unfitness has reference to the physiological and morphological coordination or correlation among the constituent elements of the whole organism, and that any relaxation in either series, in a formative sense or otherwise, results in an instability which may culminate in death and which expresses itself in structural deviation as well as in a higher degree of variability. BARNARD COLLEGE, CoLUMBIA UNIVERSITY, November, 1903. ON THE LAWS OF INHERITANCE IN MAN. Il. ON THE INHERITANCE OF THE MENTAL AND MORAL CHARACTERS IN MAN, AND ITS COMPARISON WITH THE INHERITANCE OF THE PHYSICAL CHARACTERS *. By KARL PEARSON, F-.R.S. (i) Introductory—The Material and its Collection. THERE are probably few persons who would now deny the immense importance of ancestry in the case of any domestic animal. The stud-books, which exist for horses, cattle, dogs, cats and even canaries, demonstrate the weight practically given to ancestry when the breeding of animals has developed so far that certain physical characters possess commercial value. A majority of the community would probably also admit to-day that the physical characters of man are inherited with practically the same intensity as the like characters in cattle and horses. But few, however, of the majority who accept this inheritance of physique in man, apply the results which flow from such acceptance to their own conduct in life— still less do they appreciate the all important bearing of these results upon national life and social habits. Nor is the reason for this—or better, one out of several reasons for this—hard to find. The majority of mankind are more or less conscious that man has not gained his pre-eminence by physique alone. They justly attribute much of his dominance in the animal kingdom to those mental and moral characters, which have rendered him capable of combining with his neighbours to form stable societies with highly differentiated tasks and circumscribed duties for their individual members. Within such communities we see the moral characters developing apparently under family influences; the mental characters developing not only under home training, but under the guidance of private and public teachers, the whole contributing to form a complex system of national education. To use technical * Being the Fourth Annual Huxley Lecture before the Anthropological Institute, reprinted with the sanction of the Council. 17—2 132 On the Inheritance of the Mental and Moral Characters in Man terms, we expect correlation between home influence and moral qualities, and between education and mental power, and the bulk of men too rashly, perhaps, conclude that the home and the school are the chief sources of those qualities on which social stability so largely depends. We are too apt to overlook the possibility that the home standard is itself a product of parental stock, and that the relative gain from education depends to a surprising degree on the raw material presented to the educator. We are agreed that good homes and good schools are essential to national prosperity. But does not the good home depend upon the percentage of innately wise parents, and the good school depend quite as much on the children’s capacity, as on its staff and equipment ? It is quite possible to accept these views and yet believe that the moral and mental characters are inherited in either a quantitatively or a qualitatively different manner from the physical characters. Both may be influenced by environment, but the one in a far more marked way than the other. Since the publication of Francis Galton’s epoch-making books, Hereditary Genius and English Men of Science, it is impossible to deny in toto the inheritance of mental characters. But we require to go a stage further and ask for an exact quantitative measure of the inheritance of such characters and a comparison of such measure with its value for the physical characters. Accordingly some six or seven years ago I set myself the following problem: What is the quantitative measure of the inheritance of the moral and mental characters in man, and how is it related to the corresponding measure of the inheritance of the physical characters ? The problem really resolved itself into three separate investigations :— (a) : Brother- Brother. | Sister-Sister. Brother-Sister. 6 Cc Mean. S.D. Cc orre- orre- orre-' Characters. Mean. | S.D. eat Mean. | S.D. letion| raced Bs || Sc. eBe i aese Cephalic Index..] 78°92 |3°314 | °4861 ] 78°29 |3°988 |°5360 | 78°72 | 7896 | 3-237 |3°882 -4265 irs eee 18452 | 6-454 | -5041 |180-22 | 6-346 |-4251 | 183-82 | 179-20 | 6-563 | 6510 | -4575 2 years Head Breadth 145-23 | 5-739 |-5925 [140-21 | 6-547 |-6208 | 144-24 |140°59 | 5-975 | 5-708 | -5419 (12 years) Head Height } 127:19 |6°479 | °5537 112407 | 6868 |°5237 112736 | 124-80 | 7-081 | 6°226 | -4897 (12 years) 8.D. = Standard deviation, the measure of the variability of the observed character, K. PEARSON 141 It is proper before I go further, to explain how the results for resemblance between brothers and sisters of different ages in head measurements have been made. In the first place a growth curve for each sex and for every measurement was drawn; this growth curve simply consists in plotting the average size of head of a child of given age to that age. Diagram V. represents the growth Diagram V. Growth of Auricular Height in Girls Head. 130 4 ee UE eee ee | ele | | 129 | Ar 1 | [ae ie aa AURICULAR HEIGHT of GIRLS HEAD in MM. y | : —— — Opa ees 4ietsege. Fee. WS) Oia 12 sic 1407 15 Wile) 17" ie) Vis 20 AGE of GIRLin YEARS of auricular height of head of the mean girl from 4 to 19 years of age. The observation points are then smoothed and we obtain the mean growth curve. I cannot stay to discuss these mean growth curves now, but it must be clear that they give us a method of ascertaining the mean head growth of a child from any one year of its life to any other. Now all children do not grow in the same manner, but as we are dealing with average results we shall obtain a reasonable measure of growth by using the growth curve of the mean child. By means of six growth curves like that shown, the length, breadth, and height of every child’s head was reduced to the dimensions it would most probably have at the age of 12 years. Thus we were able to compare the likeness in head measurements of brothers at the swme standard age. This is the method by which the inheritance of head length, breadth, and height, given in Table IL, was deduced*, * By a much more elaborate investigation in multiple correlation I found for resemblance between brothers in head length °54 (see R. S. Proc. Vol. 71, p. 294). The growth correlation not being absolutely linear, I am not sure that that value is better than the °5 of the present simpler method. 142 On the Inheritance of the Mental and Moral Characters in Man Now what are we to understand by “believing” or “not believing” in the value for anthropological purposes of any character? Surely the main point for such purposes is the question of whether or no it be inherited and have small variability within the group? I don’t think if we look at Table II. we shall find the cephalic index worse than other head measurements, especially if we stick to one sex. It has an inheritance coefficient of about 5, just what for practical purposes we have found for other physical characters. So far we have seen surprising uniformity in the inheritance of the measurable physical characters. How are we to extend our results to physical characters not capable of accurate measurement, and to psychical characters? Clearly the whole problem turns on this: Can we find the steepness or slope of this regression line without all the paraphernalia of the correlation table and the means of arrays ? The answer is: Yes; providing we assume a certain distribution of frequency for the character in human populations. This distribution of frequency is given by the Gauss-Laplacian normal curve of deviations from the mean. Grant this distribution, and by very simple classifications indeed we can determine the steepness of the regression line. Now the problem before us is the following one:—Is this assumption legitimate? It is certainly not true for organs and characters in all types of life. But it really does describe in a remarkable manner the distribution of most characters in mankind. We have shown that within the limits of random sampling, it is very true for a great variety of characters in the human skull*. Dr Macdonell has demonstrated it also for measurements on criminals, and you can be fairly convinced of its suitability by looking at one or two diagrams. Diagram VI. gives the distribution of nearly 2000 boys in cephalic Diacram VI. Distribution of Cephalic Index in 1982 Boys. pal Beas f+ -+— ie ; 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 97 93 CEPHALIC INDEX * Biometrika, Vol. 1. p. 443. Frequency. | al _ | = = < ~ a= —_} —___}______+__— : l —. 180: 170 160 150 140 130 120 110 100. 90 80 710 60 50 40 30 20 10 K. PEARSON 143 index; Diagram VII. the distribution of stature in 1000 women; Diagram VIII. the distribution of head breadth in 3000 criminals*. I should be the last to assert that no human characters can be found that do not diverge sensibly from this Gaussian distribution. But I believe they are few, and that for practical purposes we may with nearly absolute safety assume it as a first approximation to the Diacram VII. Distribution of Stature in Women, Sa [= J jearw 52 53 54 55 56 57 58 69 60 61 62 63 64 65 66 67 68 69 70 711 72 Stature of Women in inches. actual state of affairs. This being once granted we can obtain the slope of our regression line by an exceedingly simple process. We can make a mere classifica- tion of the following kind, say, into boys with breadth of head below 145 mm., * Diagram VII. is from the paper on the ‘“‘ Inheritance of the Physical Characters in Man,” Biometrika, Vol. 11. p. 364, and Diagram VIII. from Dr Macdonell’s memoir in this journal, Vol. 1. p. 184. 144 On the Inheritance of the Mental and Moral Characters in Man and boys with breadth of head above 145 mm. For example, here is a simple classification of 2022 pairs of brothers by this process :— Breadth of Head. First Brother. 5 Below 145 Above 145 Totals 3 a Below 145 ... 635°5 307 942°5 ra | Above 145 ... 307 772°5 1079°5 & 3 3 Totals 942°5 1079°5 2022 The result is precisely the same as dividing this ring model (exhibited at the lecture) by a pair of rectangular planes and counting up the number of rings in each of the four spaces. Driacram VIII. Distribution of Head Breadths in 3000 Criminals. le | ! | 7 \ ea | fre / Haste / : L T | | ~ 1 i \ aa] \ j oe aa 15 fon Eee | al aS s | S 5 ! ee r \\ + r L ae ike ii] X\ | / SAS 150 : 140 150 160 LO Head Breadth in mms. Normal curve given by continuous line. K. PEARSON 145 Now from such a division the mathematician can deduce* the slope of the regression line on the assumption of normal distribution. Here, to give us confidence, are the results for head breadth and height in boys, which were worked out both ways :— Resemblance of Brothers. Long table Fourfold division Head Breadth Auricular Height For practical purposes these results are identical. Accordingly let us assume this fourfold division will work, and investigate by means of it a non-quantitatively measurable physical character in man. I choose Health as an example. In Table A (1), Appendix III., we have the distribution of health in a population of 1918 school boys, and in Diagram IX., we have the arrangement of the same material, supposing it to follow a normal curve. My five classes were (i) Very Strong; (11) Strong, being here used not in the sense of physically strong, but of Robust; (iii) Normally Healthy; (iv) Rather Delicate; and (v) Very Delicate. You will see that the “modal” boy is somewhat on the normally healthy side of robust, but that the Very Robusts are more numerous than the Very Delicates and the Robusts than the Delicates. I think the scale is not without suggestiveness even as a general health distribution for the population at large, It gives us for the first time an exact measure of the ranges of delicacy and robustness in terms of normal health. Now I applied this scale to the relation between brothers in health character. I plotted up at the mean of robust boys, a length on this scale equal to the mean on the same scale of the array of brothers of these robust boys; there was naturally a regression towards normal health. I did this for all the possible five arrays}, and I thus obtained the five points given in Diagram X. You will see at once that our five points lie quite nicely distributed about the regression line as found by the fourfold division method discussed above. In other words, there can be little doubt that the general health of boys is a character which closely follows the normal law of distribution, and has a true line of regression. The slope of that line is ‘52, or we may safely say that general health in the community is inherited in precisely the same manner as head-measurements or body-lengths. I now come to the fundamental idea of my comparison of the psychical and physical resemblance of brothers. Suppose we assume that moral and mental qualities in man, like the physical, follow a normal law of distribution, and that * Mathematical Contributions to the Theory of Evolution. VII. ‘‘On the Correlation of Characters not Quantitatively Measurable,” Phil. Trans. Vol. 195, A, pp. 1—47. + For the benefit of the mathematical statistician, I may say that I used the modal group of each sub-array to determine its mean and standard deviation in terms of those of the scale for the whole population. Biometrika 111 19 146 On the Inheritance of the Mental and Moral Characters in Man Dracram IX. Distribution of Health in 1918 School Boys. 120 ee al =<1110 ‘ p00 e ql S | r Hi T 96 S ‘eae +— - | so 8 ; f ; | n + e US | NORMAL'HEALTH le a ar 1 wo 60 oO a | h FS ' if [ a gr ry ie 3 rr sO || Ey | #} 3 2 Ft | I a Z ite 3y é 40 8 co Bit ate g++ é: 30 o} @: 1 ox o! >! a =| El > C1 oO §! | . zis —— 20 9} ' el x RO'BUST =! [cel RATHER DeLee srg Bice |r _* DELICATE alee bal int be VERY ROBUST “30 -250 lor -1'5o0 -o =50; ie} So oO so 20 250 30 O STANDARD DEVIATION=% RANCE of NORMAL HEALTH, roughly. Diagram X. |Resemblance in General Health of 1918 Pairs of Brothers. Pore PERE eS cee otter ates nae a a PA VERY ROBUST ROBUST SECOND BROTHER'S MEAN HEALTH | an 5 Group Mean waee|enn=peee= Group Me V.DELICATE|RATHER DELICATE|NCRMALLY HEALTHY “30 =20 -0 20 30 VDELICATE}RATHER DELICATE |INORMALLY HEALTHY ROBUST VERY ROBUST | FIRST BROTHERS HEALTH K. PEARSON 147 the regression is linear. What results shall we obtain by thus assuming perfect continuity between the physical and the psychical? No doubt the drums will begin to beat the tattoo, we shall hear talk of the hopeless materialism of some men of science. But to use Huxley’s appropriate words: “One does not battle with drummers.” I cannot free myself from the conception that underlying every psychical state there is a physical state, and from that conception follows at once the conclusion that there must be a close association between the succession or the recurrence of certain psychical states, which is what we judge mental and moral characteristics by, and an underlying physical confirmation be it of brain or liver. Hence I put to myself the problem as follows:—Assume the fundamental laws of distribution which we know to hold for the physical characters in man, and see whither they lead us when applied to the psychical characteristics. They must: (a) Give us totally discordant results. If so, we shall conclude that these laws have no application to the mental and moral attributes. Or, (b) Give us accordant results. If so, we may go a stage further, and ask how these results compare with those for the inheritance of the physical characters: are they more or less or equally subject to the influence of environment? Here are the questions before us. Let us examine how they are to be answered. As an illustration I take Ability in Girls. I measured intelligence by the following seven classes. (i) Quick Intelligent; (11) Intelligent; (iii) Slow Intelligent; (iv) Slow; (v) Slow Dull; (vi) Very Dull; and a quite distinct category (vil) Znaccurate-Erratic. Some explanation of these terms is given in Appendix Ia., which contains the general instructions for observation, and the terms themselves were practically formulated by a schoolmaster of considerable pedagogic and psychological experience. My next stage was to ask two or three different teachers in several schools to apply the classification to 30 to 50 pupils known to each of them. The classifications were made quite independently, often by teachers of quite different subjects, and a comparison of the results showed that 80 to 85 per cent. of the children were put into the same classes by the different teachers, while about 10 per cent. more only differed by one class. This gave one very great confidence not only in the value of this scale, but of other psychical classifications when used by observant teachers. The next stage was to obtain exactly, as in the case of Health, a general scale of intelligence*. Diagram XI. gives the normal distribution of intelligence in a population of 2014 girls. It is a curious, if a common result of experience, to find that the modal ability is on the borderland between the Jntelligent and Slow Intelligent. We have here for the first time a quantitative scale of intelligence, and we can at once apply it to the problem of the degree of resemblance between sisters as regards ability. Just as in the case of Health, all the girls of a given class are taken, say the Slow Intelligents, and at the average value of this class, is plotted upon this scale of intelligence, the average value of the intelligence of the sisters of these girls on * Tshould say at once that the Inaccurate-Erratics turned out a surprisingly small class, a fractional per cent. of the community, and that they were not further dealt with. . 19—2 148 On the Inheritance of the Mental and Moral Characters in Man Diagram XI. Distribution of Intelligence in 2014 Girls, One Square = 16 Girls in 1000. Mean: Slow Intelligent Mean: Intelligent +20 +30 QUICK INTELLIGENT SCALE of ABILITY * O=STANDARD DEVIATION =:97 RANGE of “INTELLIGENT” Diacram XII. Resemblance of Sisters in Ability. QUICK INTELLIGENT INTELLIGENT SLOW INTELLIGENT Mean Mean Mean SECOND SISTERS MEAN ABILITY HE 9) ~_Group ie SION) G VERY DULL Ay -0 VERY DULL | SoLe leitowie Choe imelceie QUICK INTELLIGENT FIRST SISTER'S ABILITY K, PEARSON 149 the same scale. We thus obtain the six points of Diagram XII, all well within the limits of random sampling, lying on the straight line found from the fourfold division of the data. The slope of this line is ‘47 or 47, close to 50, in the 100. There can, I think, be small doubt that Intelligence or Ability follows precisely the same laws of inheritance as General Health, and both the same laws as Cephalic Index, or any other physical character. In precisely the manner indicated here all the other physical and psychical characters recorded may be dealt with. But before we sum up our results for the slopes of all the lines thus investigated, it is most essential to make, especially to an anthropological audience, some remarks on the manner in which the individual physical and mental characters have been treated. (iu) Remarks on Individual Characters dealt with. Physical Characters. (A) Health—We have already seen how this was recorded. In order to deduce the correlation two fourfold tables were made. In the one the division was made between Delicute and Normally Healthy, in the other between Normally Healthy and Strong. Theoretically the fourfold divisions ought to be made every- where where possible, and the weighted mean taken of the results to smooth out irregularities, but the labour is too great for practical purposes, and we must content ourselves with a few simple divisions. (B) Eye Colour.—Our division was into light, medium, dark. The eyes corresponding to these classes are stated in the general instructions. See Appendix Ia. For practical purposes the scale is one of the intensity of yellow pigmentation*. In this case, remembering that “medium” is rather a vague class, the fourfold division was taken at each of the four corners of the medium-medium category and the mean correlation of the four resulting tables taken to represent the actual correlation in eye colour. (C) Hair Colour.—This is a character concerning which we sadly need a combined investigation on the part of a physiologist, a chemist, and an anthropologist. In saying this, I am not forgetting the pioneer work of Mr H. C. Sorby published in the Journal of this Institute+. I do not feel perfectly convinced that we have really got to the number of pigments involved. Even if we have, and there be just two, it by no means follows that our nomenclature enables us effectually to separate hair possessing these pigments in various degrees, still less to place in their right position in any scale the cases of blended pigments. Assume by way of illustration * Blue is to be considered as an absence of pigmentation. + Jour. Anthr. Inst., Vol. vu. 1878, pp. 1—14. 150 On the Inheritance of the Mental and Moral Characters in Man only, that there existed two pigments, black and red. We might by placing red at one end of the scale and black at the other, obtain a single scale which would really be a double one, 1.e., a scale of diminishing amounts of black pigment from one end, and of red from the other. In the one case the fairs are classed with red as marking an absence of black pigment and in the other case with the darks as marking an absence of red. Fourfold divisions of this table would then give the correlation between brethren either in the amount of red pigment or in the amount of black pigment. Unfortunately the observer comes across—besides a very deep red type of hair which seems to be pure red, and which shades, if enough individuals are taken, continuously away from “fair reds”—another red, a “dark red,’ which I found frequently described as “brown red” or “dark brown red,” and which seems to be a blend of the red and dark pigments. The existence of these brown reds seems to me the difficulty of the single scale arrangement. It is on this account that some hair scale makers have placed the reds alongside the browns, but this appears to misplace the “fair reds” and “pure reds.” I am at present working on the problem of a practical hair scale, and Iam not at all certain that something corresponding to the artist's conception of “value” is not what we want, if we are to use hair colour asa character for investigations about inheritance. I merely refer to this method because I consider these hair colour results somewhat unsatisfactory and subject to revision and reclassification. There is another point also to which I must refer. I have found a distinct growth in children’s hair colour with age. This, of course, has been recognized in a general way, but our data supply, as soon as we have settled our scale, the quantitative measure of it. Hence, exactly asin the case of head measurements, we ought really to allow for the growth change in hair before measuring the resemblance of brothers. Allowance for this growth, to judge from the effect of growth in other cases, might easily change the value of the correlation by 10 to 15 per cent. I hope to return to the problems of scale and growth in hair colour ; meanwhile I would describe what Ihave done. The hair correlation tables have been worked out in four different ways, namely, by forming fourfold tables at each corner of the “brown-brown” category. By doing this I have endeavoured to allow for the position of the red-browns, which were classified under reds, Le., whenever a division comes for the fourfold table between brown and dark, it is immaterial whether the reds are placed beyond the fairs, between fairs and browns, or between browns and darks. The results given for hair are the means of the four correlations found by working out the tables in four different ways. I believe on any system of “value*” my results will be approximately correct, but it would still need correction for growth, Le., a sensible darkening in the fifteen years of life covered by our observations. On the whole, I publish the hair colour results with reser- vations. * T hope shortly to be able to publish photographic measures of ‘ value” in hair colour. + I think since writing the above I have surmounted the difficulty of scale orders by applying the new method of contingency, which completely dispenses with any scale order: see Drapers’ Company Research Memoirs, I. ‘‘On the Theory of Contingency and its Relation to Association and Normal Correlation.” (Dulau and Co., Soho 8q., London.) K. PEARSON 151 (D) Curliness of Hair.—Our three categories were smooth, wavy, curly. The results are the means of two computations, first with the division between smooth and wavy, and then with the division between wavy and curly. (E) Cephalic Index. (F) Head Length. (G) Head Breadth. (H) Auricular Height. The method of investigating the degree of resemblance in these characters has been already referred to. We may note that, in all cases, the order of intensity in resemblance is head breadth, auricular height and head length. I confess to believing that some of this is due to greater difficulty in getting a true head length, than a true breadth or height, but I do not believe that this is the sole source of the divergence. I shall touch on this subject on another occasion when I come to deal with growth of head in children, meanwhile I would say that it appears to me that a pause arises in the growth of head length which is not perceptible, or at least not so perceptible, in the case of the growth of breadth or height. I should not be surprised to find that the on-coming of puberty affects the growth of head length differently from the growth of head breadth or height, and that a comparison for this character of brothers or sisters, one of whom has and the other of whom has not reached the age of puberty, may to some extent affect our results. This influence would not be fully allowed for by growth curves, as the age of puberty, especially in girls, seems to vary largely, even in members of the same family. (1) Athletic Power—While I have worked with only eight physical and eight mental characters, I have an additional character which it is needful to refer to here, and which it is difficult to class as purely physical. I mean athletic capacity. We may define the athletic individual as one who is not only keen on sports and games, but who is capable in them. This denotes a training and a mental control of hand and eye, and approaches psychical efficiency*. It might therefore be a problem to determine in which class of characters the athletic should be placed. The results, however, of dealing with athletics are from the standpoint of inheritance abnormally high. An examination of the schedules led me at once to the conclusion that much of this resemblance was wholly spurious. Certain schools, boys’ public schools and the larger girls’ schools, pride themselves on an athletic reputation ; hence two brothers or two sisters at such schools are usually returned as an athletic pair. On the other hand, schools without an athletic reputation are too lable to return the two members of a pair as non-athletic, the teachers having little or no knowledge of the game capacity of their pupils. Hence arises the high value of resemblance in athletic power between the members of a pair of brothers or a pair of sisters. This resemblance is largely, perhaps 40 to 50 per cent., * This is confirmed by the high correlations I have found to exist between athletic capacity and many psychical characters. 152 On the Inheritance of the Mental and Moral Characters in Man a result of a differentiation between the class of schools in which athleticism is a cult and the class in which it is not—the town or board school with little play- ground and no game training. To complete the demonstration of this conclusion we need only turn to the mixed schools, whence our brother-sister pairs are drawn. These schools do not exhibit the athletic cult on the same scale, and we get quite a fair and reasonable value for the resemblance of brothers and sisters in athletic power. To obtain the correlation the fourfold division was taken between the athletic and non-athletic. Psychical Characters. (J) Vivacity. (K) Assertiveness. (L) Introspection. (M) Popularity. (N) Consctentiousness. In all these five psychical characters, our schedule admitted of only three possibilities, Le., the cross must be placed in the space allotted to either contrasted character, or on the dividing line between, marking a “betwixt and between” state of affairs. Our tables were prepared with a ninefold system of categories including a “betwixt” column and row. The “betwixts” were not, however, very numerous, and they were then halved or quartered as the case might be into the adjacent groups to save the great labour of working with four fourfold tables and averaging the four results. (O) Temper.—Our categories were: Quick-tempered, Good-natured, and Sullen, with the usual system of “ betwixts.” In a very few instances sullen children were recorded who had occasional outbursts of quick temper. In this classification accordingly, some of the like difficulties arise that we have noted in the case of hair colour. To surmount these, first a division was made between quick temper and good temper, and the correlation found from the fourfold table thus reached. Secondly, the sullen were thrown in with the quick, and the whole classed as Bad tempered in contrast to Good tempered. In the first case we are measuring a certain phlegimatic character, in the second rather the extent of self-control. But the two divisions led to very sensibly the same results. Thus for girls we have the correlations :— Division between Quick and Good temper: *49. Division into Good and Bad (Quick and Sullen) tempers : ‘50. The mean of the two results was then taken as a measure of correlation in the matter of temper. (P) Absity.—We have already (p. 147) discussed this character at some length. All that seems necessary to add is that the division for the fourfold table was taken between Intelligent and Slow Intelligent. K. PEARSON 153 (Q) Handwriting—Some persons may be inclined to question whether this character is properly placed in the psychical class. Is it really a largely muscular characteristic? Personally I do not think it desirable to draw very rigid lines between the physical and psychical, and the present inquiry has much strengthened that opinion. But we have gone far further with handwriting than is obvious on the face of this paper, which is confined to inheritance; and, without anticipating results yet to be published, I would say that, quite contrary to my expectation, very sensible correlations exist between the psychical characters and the hand- writing, which on the other hand has only very moderate or zero correlations with the physical characters. In school children at any rate, temper, probity and assertiveness are all correlated with the character of the handwriting, and I have little hesitation myself therefore in including it with the psychical rather than the physical group. These remarks on the individual characters dealt with may enable the reader to understand something of the method adopted in analysing our material. They will at any rate suggest that many points have been considered and investigated which cannot be even touched upon here, but which have aided us in our classifications and general treatment*. (iv) Comparison of the Values found for the Inheritance of the Physical and Psychical Characters in Man. Thus far my whole object has been to describe the sources of my material, and to throw some light, perchance, on the new methods we have adopted in classification and computation. I have spent a considerable time over this latter topic, because to the anthropologist of the older school, the biometrician too often appears as a juggler in figures. It is impossible, perhaps, to help this at present, when the biometrician is introducing a new calculus, which cannot be learnt without hard work, and which cannot be handled without training. We are not endeavouring to discredit anthropology, but to furnish such branches of it as anthropometry and craniology with new tools—a little sharp-edged to the uninitiated who handle them incautiously—but which will raise anthropometry and craniology in the future into the category of the more exact sciences. Such must be my excuse for describing so fully, and yet, I fear, so ineffectually, the processes we have adopted. It is another point to ask you to admit that I came to this inquiry without prejudice. I expected a priori to find the home environment largely affecting the resemblance in moral qualities of brothers and sisters. I expected to find a spurious emphasis of the inheritance of the moral qualities owing to this environment. Putting any thought of prejudice on one side, accept for a moment the methods adopted, and listen—regardless of the drummers—to the broad results * For example upwards of 120 correlations between physical characters, between psychical characters and between physical and psychical characters have been worked out, tending to throw light on the interrelationships of these supposed widely differentiated sides of the human character. Biometrika 111 20 154 On the Inheritance of the Mental and Moral Characters in Man of the inquiry. You have in Table I. (see p. 140) the mean of the resemblance in physical characters of brothers and sisters from my records of family measurements. You have in Table III. the mean of the physical measurements of our school records—16 series in the first, 24 series in the latter. I venture to say that TABLE III. Inheritance of the Physical Characters, School Observations on Children. Correlation. Character. a Brothers. Sisters. | Brother and Sister. Health a ore me 52 “51 57 Eye Colour 54 "52 53 Hair _,, 62 57 593) Hair Curliness 50 52 52 Cephalic Index 49 54 ‘43 Head Length ... 50 ‘43 “46 Head Breadth... 59 62 D4 Head Height .. 55 52 49 Mean ... | 54 53 | 51 Athletic Power no 75 | 49 remembering the possible slips in measurement and in classification, there is not the slightest doubt that those two series absolutely confirm each other, and give a mean degree of resemblance of nearly 5 between children of the same parents for physical characters. How much of that physical resemblance is due to home environment? You might at once assert that size of head and size of body are influenced by nurture, food, and exercise. It is quite true; even curliness may be subject to home influences. But what is the broad effect of such environment on our coefficients of heredity ? Can any possible home influence be brought to bear on cephalic index, on hair colour, or eye colour? I fancy not, and yet these characters are within broad lines inherited exactly like the characters directly capable of being influenced by nurture and exercise. I am compelled to conclude that the environmental influence on physical characters, however great in some cases, is not to the first approximation a great disturbing factor when we consider K. PEARSON 155 coefficients of fraternal resemblance in man. I do not believe it to be at all comparable with the irregularities that arise from random sampling and occasional carelessness in measurement or in appreciation of character. Now turn to Table IV. giving the degree of resemblance in the mental and moral characters. What do we find in it? Perhaps slightly more irregularity in the TABLE IV. Inheritance of the Mental Characteristies. School Observations on Children. Correlation. Character. Brothers. Sisters. Brother and Sister. Vivacity “A9 Assertiveness ... 2 Introspection ... 3 Popularity “49 Conscientiousness 63 Temper oi Ability ‘44 Handwriting ‘48 values than in the case of the physical characters. The judgment required is much finer; and the classification is much rougher. Let me frankly admit the difficulties of the task, both for observers and computers. I will lay no weight whatever, if you like, on the second place of decimals. But what is the obvious conclusion ? Why, that the values of the coefficient again cluster round ‘5. If anything the average degree of resemblance for the psychical is rather less than for the physical, it certainly is not greater. Personally I would lay not a grain’s weight on the difference. I have illustrated the whole result in Diagram XIII. The two lines representing physical and psychical qualities go bobbing up and down, and cutting and re-cutting one another. No wise man, however, would venture to assert that one or other is sensibly uppermost, or that any of those rises or falls have real significance. We are forced absolutely to the conclusion that the degree of 20—2 156 On the Inheritance of the Mental and Moral Characters in Man resemblance of the physical and mental characters in children is one and the same, It has been suggested that this resemblance in the psychical characters is compounded of two factors, inheritance on the one hand and training or environ- ment on the other. If so, you must admit that inheritance and environment make up the resemblance in the physical characters. Now these two sorts of resemblance being of the same intensity, either the environmental influence is the same in both cases, or it is not. If it is the same, we are forced to the conclusion that it is insensible, for it cannot influence eye colour. If it is not the same, then it would be a most marvellous thing, that with varying degrees of inheritance, some mysterious force always modifies the extent of home Diagram XIII. Comparison of Resemblance for Physical and Psychical Characters. PHYSICAL INTENSITY OF RESEMBLANCE mp oO & ann wo © 0 —_—_{—___+ t SISTERS influence, until the resemblance of brothers or sisters is brought sensibly up to the same intensity! Occam’s razor will enable us at once to cut off such a theory. We are forced, I think literally forced, to the general conclusion that the physical and psychical characters in man are inherited within broad lines in the same manner, and with the same intensity. The average home environment, the average parental influence is in itself part of the heritage of the stock and not an extraneous and additional factor emphasising the resemblance between children from the same home. But we are not yet at the end of our conclusions. By assuming our normal distribution for the psychical characters we have found, not only self-consistent results—linear regression, for example, as in the case of the inheritance of intelligence, but we have found the same degree of resemblance between physical and psychical characters. That sameness surely involves something additional. J¢ involves a like heritage from parents. The degree of resemblance between children and parents for the physical characters in man may be applied to the degree of resemblance between children and parents for psychical characters. We inherit our parents’ tempers, our parents’ conscientiousness, shyness and ability, even as we inherit their stature, forearm and span. K. PEARSON 157 At what rate is that? I show you a table (see Table V.), which represents our present knowledge of parental inheritance in man*, and in other species. I venture to say that—within broad lines—the physical characters are inherited at the same rate in man and in the lower forms of life. The resemblance of parent and offspring is again roughly °5. TABLE V. Parental Inheritance in Different Species. Mean No. of Species Character value | pairsused Source Remarks Man ube rs Stature 506 4886 Biometrika, Vol. 11. p. 358 — . Bee aor Span 459 4873 ditto = » ob oie Forearm 418 4866 ditto = % oe wie Eye colour “495 4000 | Phil. Trans., Vol. 195, p. 106 = Horse... aa Coat colour 522 | 4350 | Phil. Trans., Vol. 195, p. 93 = Basset Hound ... Coat colour 524. gaa. | RS. Proc., Vol. 66, p. 154 | Dams only used Greyhound 306 Coat colour ‘507 | 9279 Unpublished data for two | Dams and sires characters both used Aphis (Hyalopterus | Right antenna : evade eee ay i Aid 3¢ MOTE: Ratios onl Trirhodus) ... | Frontal breadth 439 368 Biometrika, Vol. 1. p. 139 Fevewits fie Protopodite from growth Daphnia Magna ... 466 96 L. S. Proc., Vol. 65, 1899 factor Body length What conclusion flows upon us irresistibly from the inspection of such a table ? Why, that the psychical characters are not features which differentiate man from the lower types of life. If they are inherited like man’s physical characters, if they are inherited even as the protopodite of the water flea, what reason is there for demanding a special evolution for man’s mental and moral side? We look upon the universe and wonder. The man of science probes a little deeper into nature than the ordinary mortal, but the deeper he probes, the greater his wonder, for the more complex and mysterious the universe appears. Do you wish to draw the line of mystery at living forms? Look at the sky on a clear night, and realise that while astronomers have described the motions of a tiny corner of the universe, they have not the least explanation of how and why those motions are taking place. Nay, take the least, apparently most inert particle of metal, and remember that if modern physical views are correct, millions, probably billions of small corpuscles are in relative motion within it, with a complexity and yet probably with an underlying order as great as in the starry universe, even if they be on a totally different scale. Remember that we have scarcely touched the fringe of a description of those motions, and that their why is as inexplicable to us as the motions of the celestial bodies themselves. Note all this, and ask yourselves if there be less mystery * Taken from a memoir: ‘‘On the Laws of Inheritance in Man. I. Inheritance of the Physical Characters.” Biometrika, Vol. 11. p. 379. 158 On the Inheritance of the Mental and Moral Characters in Man in the motions of non-living than of living things. You may call a man who would link up the motion of living to non-living things a materialist. But the materialist in no way lessens the endless mystery of the universe. He knows not what matter is, why it moves, or how he comes to be conscious of its motion. He is but fulfilling the task of science, the linking of mystery to mystery, by bringing them under one common wider conception of the ultimately inexplicable. So it is when we pass from the lower living forms to man. If we see that his physical development is closely allied to brute development, we link mystery to mystery in a common description—a law if you like—but it removes no grain of the ultimate mystery of why life is there, and why it develops. Lastly, turning to the psychical character of man, to some the greatest of all mysteries, we link it wp to the physical. We see the man, not only physically, but morally and mentally, the product of a long line of ancestry. We realise that evolution and selection play no greater, and play no less a part in the production of the psychical character than in the production of the physique of man. Once fully realise that the psychic is inherited in the same way as the physical, and there is no room left to differentiate one from the other in the evolution of man. Realise all this, and two mysteries have been linked into one mystery, but the total mystery is no less in magnitude, and no more explicable than it was before. We know not why living forms vary, nor why either physical or psychical characters are inherited, nor wherefore the existence at all of living forms, and their subjection to the great principle of selective evolution. We have learnt only a law common to the physical and the psychical; we have not raised the one or debased the other, because in a world where the ultimate source of change is utterly inexplicable, whether you strive to perceive it through matter like a physicist, through the lower living forms like the biologist, or through man like the anthropologist, all terminology like higher and lower is futile. Where the mystery is absolute in all cases, there can be no question of grade. But I would not leave you with a mere general declaration that all is mystery, that scientific ignorance of the ultimate is profound. Rather I would emphasise what I have endeavoured to show you to-night, that the mission of science is not to explain but to bring all things, as far as we are able, under a common law. Science gives no real explanation, but provides comprehensive description. In the narrower field it has to study how its general conceptions bear on the comfort and happiness of man. Herein, I think, lies especially the coming function of anthropology. Anthropology has in the first place to study man, to discover the sequence of his evolution from his present comparative stages and from his past history. But it cannot halt here; it must suggest how those laws can be applied to render our own human society both more stable and more efficient. In this function it becomes at least the handmaiden of statecraft, if indeed it were not truer to call it the preceptor of statesmen. If the conclusion we have reached to-night be substantially a true one, and for my part I cannot for a moment doubt that it is so, then what is its lesson for us as K. PEARSON 159 a community? Why simply that geniality and probity and ability may be fostered indeed by home environment and by provision of good schools and well equipped institutions for research, but that their origin, like health and muscle, is deeper down than these things. They are bred and not created. That good stock breeds good stock is a commonplace of every farmer; that the strong man and woman have healthy children is widely recognized too. But we have left the moral and mental faculties as qualities for which we can provide amply by home environment and sound education. It is the stock itself which makes its home environment, the education is of small service, unless it be applied to an intelligent race of men. Our traders declare that we are no match for Germans and Americans. Our men of science run about two continents and proclaim the glory of foreign universities and the crying need for technical instruction. Our politicians catch the general apprehension and rush to heroic remedies. Looking round im- passionately from the calm atmosphere of anthropology, I fear there really does exist a lack of leaders of the highest intelligence, in science, in the arts, in trade, even in politics. I do seem to see a want of intelligence in the British merchant, in the British professional man and in the British workman. But I do not think the remedy lies solely in adopting foreign methods of instruction or in the spread of technical education, I believe we have a paucity, just now, of the better intelligences to guide us, and of the moderate intelligences to be successfully guided. The only account we can give of this on the basis of the results we have reached to-night is that we are ceasing as a nation to breed intelligence as we did fifty to a hundred years ago. The mentally better stock in the nation is not reproducing itself at the same rate as it did of old; the less able, and the less energetic, are more fertile than the better stocks. No scheme of wider or more thorough education will bring up in the scale of intelligence hereditary weakness to the level of hereditary strength. The only remedy, if one be possible at all, is to alter the relative fertility of the good and the bad stocks in the community. Let us have a census of the effective size of families among the intellectual classes now and a comparison with the effective size of families in the like classes in the first half of last century. You will, I feel certain, find, as in the case of recent like censuses in America, that the intellectual classes are now scarcely reproducing their own numbers, and are very far from keeping pace with the total growth of the nation. Compare in another such census the fertility of the more intelligent working man with that of the uneducated hand labourer. You will, I again feel certain, find that grave changes have taken place in relative fertility during the last forty years. We stand, I venture to think, at the commencement of an epoch, which will be marked by a great dearth of ability. If the views I have put before you to-night be even approximately correct, the remedy lies beyond the reach of revised educational systems; we have failed to realise that the psychical characters, which are, in the modern struggle of nations, the backbone of a state, are not manufactured by home and school and college; they are bred in the bone; 160 On the Inheritance of the Mental and Moral Characters in Man and for the last forty years the intellectual classes of the nation, enervated by wealth or by love of pleasure, or following an erroneous standard of life, have ceased to give us in due proportion the men we want to carry on the ever-growing work of our empire, to battle in the fore-rank of the ever intensified struggle of nations. Do not let me close with too gloomy a note. I do not merely state our lack. I have striven by a study of the inheritance of the mental and moral characters in man to see how it arises, and to know the real source of an evil is half-way to finding a remedy. That remedy lies first in getting the intellectual section of our nation to realise that intelligence can be aided and be trained, but no training or education can create it. You must breed it, that is the broad result for state- craft which flows from the equality in inheritance of the psychical and the physical characters in man. Addendum, April, 1904. I hardly know whether it is needful to refer here to a recent article by Mr C. Spearman in The American Journal of Psychology (Vol. xv. pp. 72—101), criticising my results for the similarity of inheritance in the physical and psychical characters. Without waiting to read my paper in full he seems to think that I must have disregarded “home influences” and the personal equation of the school teacher. He proceeded to ‘correct’ my results for the error of what he calls dilation on the double basis (i) of a formula invented by himself, but given without proof, and (ii) of his own experience that two observers’ observations or measurements of the same series of two characters were such that the correlation between their determinations was ‘58 in one case and ‘22 in the other. The formula invented by Mr Spearman for his so-called ‘dilation’ is clearly wrong, for applied to perfectly definite cases, it gives values greater than unity for the correlation coefficient. As to his second basis, all I can say is that if the correlation between two observers of the same thing in Mr Spearman’s case can be as low as ‘22, he must have employed most incompetent observers, or given them most imperfect instructions, or chosen a character suitable for random guessing rather than observation in the scientific sense. Mr Spearman says that ‘it is difficult to avoid the conclusion that the remarkable coincidence announced between physical and mental heredity can be more than mere accidental coincidence” (p. 98). I think I may safely leave him to calculate the odds for or against this most remarkable “mere accidental coincidence.” I may take occasion later to return to Mr Spearman’s paper, but at present it may suffice to say that not only are his formulae, especially for probable errors, erroneous, but he quite misunderstands and misuses partial correlation coefficients (p. 95). Further his statements as to the number of cases desirable for an experiment would be extremely dangerous, if they were in the least likely to be generally regarded. In particular one can only pillory such an assertion as that “It was shown in the same part that the size of the probable error also varies according to the method of calculation—and to such an extent that twenty cases treated in one of the ways described [Mr Spearman’s own new method] furnish as much certitude as 180 in another more usual way” (p. 100). Perhaps the best thing at present would be for Mr Spearman to write a paper giving algebraical proofs of all the formulae he has used, and if he did not discover their erroneous character in the process, he would at least provide tangible material for definite criticism, which it is difficult to apply to mere unproven assertions, K. PEARSON 161 APPENDIX IA, [Any Teacher willing to give assistance in these observations—an assistance which will be duly acknowledged in the final publication of results—is requested to communicate with Professor Karu Pearson, F.R.S., University College, London.] GENERAL DIRECTIONS FOR FILLING UP DATA PAPERS OF COLLATERAL HEREDITY*. 1. The object of this investigation is two-fold : (i) To ascertain the degree of resemblance, mental and physical, between children of the same parents. (ii) To discover, if possible, whether there is any relationship between the external shape of the head and a teacher’s estimate of the general grade of ability of the pupil. Co-operators are warned ab initio that no inferences whatever can be drawn from individual instances or from a small series of measurements. The numerical quantities to be determined are small, and it is only when large masses of observations have been collected from many quarters and have been reduced that reliable inferences can be drawn. 2. The measurements and estimates are to be made on : (i) Pairs of brothers (white data paper). (ii) Pairs of sisters (pink data paper). (iii) Pairs of brothers and sisters (blue data paper). Care must be taken that the right coloured data paper is selected. The names of the measured are only required in case there should be need for the verification of any entry, and they will be treated as strictly confidential. Initials, in fact, may be used where it seems desirable, if the observer keeps a key to them for the purpose of reference should reference be required. The observer should have known well both members of the pair measured for at least six months, and, if possible, for a much longer period. The classification is purposely made rather wide and indefinite in order that there may be less hesitation in classifying. What is needed is the general impression of a teacher who has carefully observed his or her pupils. For both physique and ability it is very desirable that the observer should consult, where it is possible, one or more colleagues before filling up the data paper. To give some confidence in the scales adopted, I may remark that in response to my appeal in the Journal of Education, I received details of some 150 boys and girls tested for ability by three observers independently (language, science, and mathematical teachers) and belonging to half-a-dozen different schools. The agreement in classification was complete in more than 80 per cent. of cases, and only differed by as much as two classes in about 5 per cent. of casest. This degree of accordance is sufficient for the present statistical purposes. 3. I. Physique. In making the record, attention should be paid not only to appearance, energy, and athletic qualities, but to irregularity of attendances owing to ill-health, frequency of visits to school-infirmary, etc. * The quantitative laws of heredity, such as we have reached at present, do not apply to individual cases, but only to the averages of large numbers. It is important to insist on this, because more than one of my helpers on hearing the results of a particular research has seemed disappointed, remarking that the law does not hold for the family X or the brothers Y. + Even this amount of divergence would probably have disappeared after a consultation with regard to the individuals classified. Biometrika 111 21 162 On the Inheritance of the Mental and Moral Characters in Man Il. Ability. (a) Some account of this scale will be found in the Jowrnal of Education for September, 1898, which it might be well for the observer to examine. The following may help to show the significance of the terms : Very Dull. Capable of holding in their minds only the simplest facts, and incapable of perceiving or reasoning about the relationship between facts. Slow Dull. Capable of perceiving relationship between facts in some few fields with long and continuous effort; but not generally, or without much external assistance. Slow. Very slow progress generally, but with time and continual care progress will be made. Slow Intelligent. Slow generally, although possibly more rapid in certain fields. Quite sure of knowledge when once acquired. Intelligent. Ready to grasp and capable of perceiving facts in most fields; capable of good progress without much effort. Quick Intelligent. Very bright and quick both in perception and in acquirement, and this not only of customary, but of novel, facts. Ready to reason rightly about things on purely self-initiative. - Inaccurate-Erratic. Capable of perceiving facts, but quick to form erroneous conclusions about them, illogical and erratic in reasoning. (b) Handwriting. If possible, in addition to this classification, get the pair under investi- gation to write the last lines of Lord Macaulay’s Lay of Horatius, with their own signatures on the back of the data paper. (c) Work. If the individual be good at several subjects, put a cross against all these in the first row; as well as the strongest subject in the next row; if the individual be good at | none, make no entry in the first row, but only in the second row, where best at must be interpreted in this case as least bad at. The individual should be asked his favourite subject and favourite game. Mathematics covers Arithmetic and Geometry: Descriptive Science includes Botany, Experimental Physics, Physiography, ete. Ill. Head Measurements, These are to be made with the head-spanner, full directions for the use of which are given in its case. IV. Harr. Comment seems unnecessary. V. yes. Light covers blue of all shades, light grey, very light green; medium covers dark grey, green, light chestnut, orange and grey combined ; dark covers dark chestnut, light and dark brown, black. VI. Relative Characters. This entry is needful for the numerical reduction of the statistics in those cases in which both brothers have been given the same class, otherwise no use should be made of it. If the characteristic be equally strong in both, write equal, instead of putting a cross. VII. Ifthe alternative characteristics are neither possessed in a marked degree, place the cross on the dividing line. VIII. General Remarks. Under this heading it may be useful occastonally to note any marked physical or mental characteristic of the pair. Care should, however, be taken not to lay greater stress on points of resemblance than on points of diversity. 4. It is most desirable that the head-spanners should not be kept longer than four to six weeks, in order that they may be sent on as rapidly as possible to other schools. They should be returned with the stamped and addressed labels. Any school anthropometrical laboratory desiring to procure a head-spanner of the present pattern, can do so at a cost of 19s. 6d., from the Cambridge Scientific Instrument Company, Carlyle Road, Cambridge. The spanners need to be carefully handled. Should any part be broken or lost the box with the spanner should be returned at once, in order that it may be repaired without delay and again. sent out for use. Any special inquiries should be addressed to me, at University College, London. KARL PEARSON. K. PEARSON 163 APPENDIX IB. Data PAPER FOR COLLATERAL HEREDITY INVESTIGATIONS, B. SISTER-SISTER SERIES. No. in whole series. (Whole, not half sisters.) (Not to be filled in.) Please return this Paper to Professor KARL PEARSON, F.R.S., University College, London. School : Observer : No. in School Series Date: Place a cross against the class of each sister under as many headings as possible, except under III and VIII. Please read first the General Directions. ELDER SISTER. YOUNGER SISTER. 7 Name... so eee ove : Age nea) 200 ove on District of Home I. PuHysique: Very Strong. Strong. Normally Healthy. Rather Delicate. | Very Delicate. | Athletic. Non-Athletie. ELDER SISTER... YOUNGER SISTER .. ; | | II. Asiiity: (a) General Scale. Quick Intelligent. Intelligent. Slow Intelligent. Slow. Slow Dull. Very Dull. Inaccurate-Erratic. ELDER SISTER s a = = YOUNGER SISTER ... See | (6) HanpwritTine : Very Good. Good. Moderate. Poor. Bad, Very Bad. (See Back.) ELDER SISTER | YOuNGER SISTER .., | (c) Work: Classics. | Modern Languages. | History. Mathematics. Descriptive Science, Drawing. — Singing, Music. Good at... j ELDER SisTER ...4 Best at ... = Likes best | | Good at... YounGER SISTER < Best at ... Likesbest} | | (|| (d) Games or Pastimzs: Exper Sister. | YounGER SISTER. Likes... | Good at...| | III. Heap Length. Breadth. Height. a. b. c. (a), {b), (¢), MEASUREMENTS : = Indices ELDER SISTER... (not to be YOUNGER SISTER ... filediin)- IV. Harr: V. Eyes: Red. Fair. | Brown.| Dark. | Jet Black. || Smooth. | Wavy. | Curly. Light. | Medium. | Dark. ELDER SISTER ELDER SISTER YounceER SISTER ... i YouNGER SISTER ... | VI. Revative CAPABILITIES: This is only to be filled in in those cases wherein the two sisters fall into the same class. Physique, stronger in | More Athletic. | Ability, greaterin | Handwriting, better in Hair, darker in Eyes, darker in ELDER SISTER... | YounceER SISTER ... | VII. CwHaractEr, ETC. : , Self- Unself- Self- (gp EOE \ Noisy.| Quiet.|| conscious. | conscious. || assertive. | SBY- || Keen. | Du | Popular. | Unpopular. Temper Quick. | Good- peiireds | Sullen, ELDER SISTER... | eee —| | YOUNGER SISTER ... | VIII. Geyrrat Remarks. Add here any striking features of resemblance or dissimilarity in the sisters. ELDER SIsTER _...| e [On the back of the Schedule spaces were arranged for samples of the handwriting.] 21—2 YOUNGER SISTER ~All 164 On the Inheritance of the Mental and Moral Characters in Man APPENDIX II. Observers and Schools contributing to the Data wpon which this Memoir is based. Aberdeen, A. N. Meldrum; Ferry Hill Public School, J. D. Anderson. Aberuthven School, J.M.S. Math. Acocks Green, Wellesbourne House School, O. Sunderland. Aldenham School, F. B. Stead. Alresford, Swanaton School, W. L. W. Eyre. Barnard Castle, County School, F. Hodson. Bakewell, Lady Manners’ School, H. Martin. Berwick, Berwickshire High School, H. 8. Mabbatt. Birmingham, King Edward’s School, F. M. McCarthy; King Edward’s School, C. J. Wood; King Edward’s School for Girls, M. J. Nimmo and A. L. Parmenter. Bradford- on-Avon, Winsley and Turley National School, Alice E. Griffiths. Bridgend, County School, W. A. Whittan. Bridgewater, St John’s School, E. M. Lucas. Brighton, Brighton and Hove High School for Girls, R. Mayhew. Bristol, Two-Mile Hill Board School, A. F. Bateman. Buckhurst Hill, Oakfield School, E. Linder. Burghead Public School, M. Brenner. Burnley, Higher Grade and Science School, F. H. Hibber. Cardenden, Craigderran School, David Rorie. Cardiff, Eleanor Street Boys’ School, A. C. Badcoe; Intermediate School for Boys, A. Abbatt. Carlisle, High School for Girls, A. Beavor and G. Whiting. Caterham, Congregational School, F. W. G. Foat. Cheltenham, Ladies’ College, Catherine E. Berridge. Chesterfield, Hipper Street School, S. Steel. Clacton-on-Sea, Clacton College, H. Picton. Clapham, High School for Girls, M. Cave and Mrs Woodhouse. Congleton, St James’ School, W. F. Warburton. Cork, High School ° for Girls, H. A. Martin. Darlington, Bowes School, D. L. Smith. Dereham, Swanton Morley National School, J. Lewton Brain. Dewsbury Grammar School, G. Rowland. Dulwich, Alleyn’s School, J. V. H. Coates ; Dulwich College, H. Brereton Baker; Dulwich Village Evening Con- tinuation School, C. T. Hunt. Dollar Public School, J. Begg. Dundee, Monikie School, P. Grant. Durham School, J. T. Johnson. Duffus Public School, J. W. Garrigall. Hpsom, The College, S. R. Browne. Ferry Hill, Bishopton School, T. G. Frankton. Ldinburgh, Fettes College, C. J. N. Fleming and W. I. Sargent. ochaber, Speymouth Public School, A. Geddie. Folke- stone, Sidney Street Board School, J. A. Hugill. Glossop, Arundel School, R. H. Dickinson. Grangemouth, Grange Higher Grade Science School, F. W. Maryon. Grantham, North Raunceby Church School, A. W. M. Drew and W. H. Baily. Great Ayton, Friends’ School, F. R. Arundel. Guernsey, Island of (numerous schools), E. W. Adair and 8. Butler. Halifax Higher Board School, W. Dycke. Harrogate, Western Board School, J. W. Hammond. Haslemere, Fernhurst Board School, H. Watts. Hassocks, Clayton School, L. H. Beecher- Shand. Handsworth, Grammar School, 8. R. Hart. Haywards Heath, National Schools, A. J. Mouncher. Hinckley, Elementary School, O. C. Hirst. Hornsey, Board School, J. C. Hudson. Huntley, Corse Public School, A. C. Rathway. Jlkeley, Grammar School, F. T. Cramphorn. Jsle of Wight, Chorley School, G. E. Jeans. Aeighley, Kiedwich School, T. Appleby. eswick, Keswick School, 8. Horton Barnard. Landewednack, Board School, J. Carwardine. Zeek, High School, T. L. Warrington. Leighton Buzzard, Linslade School, G. F. Andrill. Lerwick, Widows’ Asylum, J. Allen. Leyton, Elementary School, F. J. Chittenden; Technical Institute, H. Hills. rsburn, Ulster Provincial School, W. D. Braithwaite. Llandebie School, T. Mathews. Jiverpool, High School for Girls, E. Canning ; Liverpool Institute, W. 8. Saul. Londonderry, Fahan School, W. A. Dickson. Lyme Regis, National School, J. Radford. London, University College School, J. L. Paton and Staff; Whitechapel Road Foundation School, F. Dixon; Priory Grove Board School, W. R. Suddeley ; Fernhead Road School, J. C. Bedwell; Goswell Road, St Thomas’, Charterhouse, W. W. Wood- ward; New Southgate, High School, J. Fairquire; Chelsea, Cook’s Ground Board School, D. H. Hodge; Walworth, Michael Faraday School, T. M. Upfield; Titchborne Street, St John’s K. PEARSON 165 Girls’ School, A. McGillvray; Radnor Street Wesleyan School, J. W. Parkinson; Fernham Street Girls’ Board School, 8. Carter; Dulwich, High School for Girls, M. Barwell; Highbury, High School for Girls, M. Minasi; Notting Hill, High School for Girls, T. F. Griinbaum ; Camden Town, North London Collegiate School for Girls, 8. Bryant; Limehouse, St Anne’s Schools, C. J. Carter; Hampstead, Soldiers’ Daughters’ Home, C. D. Fawcett; Morley College, J. Denton; Notting Hill School, M. M. Adamson; Limehouse, Higher Grade Board Schools, Thomas Street, J. Crabtree; Old Charton Girls’ School, A. Baker; Hampstead, King Alfred’s School, J. Russell; Christ’s Hospital, C. E. Browne. Manchester, Hulme Grammar School, C. H. Crombie; High School for Girls, C. Coignou; Withington, Lady Barn House School, C. Herford. Mansfield, Brunt’s Technical School, C. E. Stacey. J/argate, New Cross Street Board School, E. Parker. MJarkinch, Star Public School, Wm. McLachlan. Marston Green, Cottage Homes, W. J. Rees. Merthyr Tydfil School, M. J. Swift. Jfilford Haven County School, L. Jones. Morpeth, Netherwitton Board School, J. Anderson. Mewark, Beacon Hill School, W. A.Greames. Wewbury School, C. Cecil Fry ; Donnington School, Mrs Bell. Mewcastle-on-Tyne, Central High School for Girls and other schools, E. W. N. Williams. Newton Stewart, Ewart High School, C. 8S. Dougall. Morwich, Angel Road Board School, B. H. Barber. Nottingham, Berridge Road Girls’ Board School, A. N. Stone; Morley House, B. Smith; Waverley School, H. T. Facon. Oxford, High School for Girls, E. Macdonald; Abbey Road School, Miss Sheppard. Pembroke Dock, County School, G. W. West. Pemberton, St John’s Schools, J. T. Milward. Peterborough, Fitzwilliam School, G. E. Holmes. Peterhead Academy, J. Don. Petersfield, Bedales School, T. J. Garstang. Pinner, Woodridings School, Z. Haes. Polperro School, F. H. Perry-Coste. Pontefract, Ackworth School, G. E. Bell. Pontypridd, Wesleyan School, W. H. Rees. Mill Street Higher School, J. Farr. Portsmouth, High School for Girls, M. M. Adamson. Pwlhel’, County School, J. W. Evans. Reigate, Church High School, E, E. Ardington. tchmond (Surrey), County School, A. E. Buckhurst; Richmond Hill School, H. D. Greig. Royston, Littlington School, W. C. Whitehead. Saffron Walden, Friends’ School, E. W. Sawdon. S¢ Leonards-on-Sea, Silverhill Girls’ School, E. H. Woodd. Sheffield, West- bourne School, Miss Sims. Shrewsbury, Criggian School, R. Brack; Murivane High School for Girls, G. M. Wise. South Shields School, R. Sanderson. Southwold, St Felix School, C. M. Sant. Spennymore School, H. Askew. Spilsby, Spendleby School, A. Teare. Stranraer, Ardwell School, D. Thomson. Swansea Grammar School, E. H. Tripp. Sydenham School, R. Lulham. Taunton, King’s College, E. B. Vincent. Tavistock, Kelly College, P. L. Andrews. Tottenham High School, L. F. Ushendoor. Upholland Grammar School, D. L. Rennard, Warrington, Penketh School, W. E. Brown. Wellington College, G. E. Blundell and H. P. Fitzgerald. West Ham, Castor House Board School, R. Symes. Whitehaven, Girls’ School, W. Blackmore. Winchester College, W. B. Croft. Wimbledon, High School for Girls, Miss Knight. Windlesham Board School, J. Simms. Winscombe, Sicot School, B. Lean. Woodford, Wanstead College, J. B. Martin. Wragby School, T. Dixon-Spain. York, High School for Girls, M. Leader. Yeovil, Kington School, E. H. Davison. YViewsley, St Matthew’s Schools, J.J. Wade. YVstalyfera, County School, A. B. Gully; and other schools. 166 On the Inheritance of the Mental and Moral Characters in Man Second Brother. Second Sister Sister. APPENDIX III.—DETAILED TABLES, I. PHysicAL CHARACTERS, HEALTH. A (i). Brother-Brother. First Brother. A Very Normally | Rather Very strong. SL SLE healthy. | delicate. | delicate. Totals Very strong aE 24 31 115 70°5 Strong ss Seas 31 342 163°75 605° Normally healthy .... 115 163°75 588°5 907 Rather delicate __.... 4 65°75 137°25 313 Very delicate ae — 3 6 22 Totals... cone 70°5 605°5 907 313 22 1918 | A (ii). Sister: Sister. First Sister. Very v4. | Normally | Rather Very strong. BiOne, healthy. | delicate. | delicate. Mletoie: a et a Very strong... Aes 44°5 38°5 175 85 — 109 Strong ses ies 38°5 306°5 1545 74 5 578°5 Normally healthy .... 175 154°5 411 201°5 19 803°5 Rather delicate __.... 85 74 201°5 166 28°5 478°5 Very delicate sss a 5 19 28°5 15 67°5 l I Totals... wef 109 578°5 803°5 4785 67°5 2037 A (il). Brother-Sister. Brother. Very Q Normally | Rather Very : . strong. mEnOnS: healthy. | delicate. | delicate. oes | | | Very strong ae 46 15 a 4 -- 72 Strong nore som 35 174°5 64 22°5 1 297 Normally healthy .... 17 85°25 191°75 505 3 3475 Rather delicate... 9 34°25 69°75 48 3 164 Very delicate aes 1 2 1 2°5 6 12°5 Totals... «| 108 311 3383'5 127°5 13 893 rere | See, Second Brother. Second Sister. Sister. K. PEARSON EYE COLOUR. 167 B (i). Brother-Brother. First Brother. | Light. Medium. Dark. | Totals. Light 558 190 815 829°5 Medium .... 190 426°5 122 738°5 Dark 815 122 228°5 432 ee eee Totals.... ar | 829°5 738°5 432 | 2000 B (ii). Sister-Sister. First Sister. | Light. Medium. Dark. Totals. | | \ Light 438°5 196°5 715 706°5 Medium ..., 196°5 598 136 930°5 Dark 715 136 257°5 465 | Totals... ee | 706°5 930°5 | B (iii) Brother-Sister. Brother. | Light. Medium. Dark. Totals. Light 206°5 66°5 33 306 Medium .... 86 208°25 46°25 340°5 Dark 28 53°25 104°25 185°5 Totals... 7 | 320°5 | 328 168 On the Inheritance of the Mental and Moral Characters in Man HAIR COLOUR. Totals 31°5 3135 C (i). Brother-Brother. First Brother. | Red. | Fair. Brown. Dark. Jet black.| Totals. i Red .... 23 16 12 — 81°5 3 | Fair .... 416 158 67°75 25 | 665 a | Brown 158 394 98°25 8°25 6745 © | Dark... 6775 | 9825 | 328% 19 525°5 & | Jet black 25 8°25 19 10 37°5 Totals we | 81°5 | 665 674°5 §25°5 37°5 1984 C (ai). Sister-Sister. First Sister. Red. Fair. Brown. Dark. Jet black.] Totals. Ei Redi 0 (ee ee eo 22 19 14 1 87 o a Fair .... see ates IY 474 195°5 47'5 —_— 739 ~| Brown ef 19 195°5 474 162°5 4°5 855° S] Dark... we wef 14 47°5 162°5 206 65 436°5 | Jet black .. wn 1 = 45 65 4 16 Totals | 87 739 855°5 436°5 16 2134 C (111). Brother-Sister. Brother. | Red Fair. Brown. Dark. | Jet back Totals. Red .... io Fair ..:. 311°5 | Brown 274°5 2 | Dark... 191 | Jet black 829 K. PEARSON CURLINESS OF HAIR. 169 Totals.... 551 68 D (i). Brother-Brother. First Brother. | Smooth. Wavy. Curly. | Totals. H R= + | Smooth 1556°5 1115 345 1702°5 oo fF) Wavy 111°5 134°5 20 266 3 & | Curly 34°5 20 11 65'5 ® M | | Totals.... a 1702°5 266 65°5 | 2034 D (ii). Sister-Sister. First Sister. | Smooth. Wavy. Curly. | Totals. 8 22 | Smooth 937°5 190°5 98 1226 “ Wavy ws 190° 213° 52 456 8 | Curly 98 52 76 226 D Totals.... 1,226 456 226 1908 D (iil). Brother-Sister, Brother. Smooth. Wavy. Curly | Totals. i Smooth 395'5 | 24 12 431°5 3 | Wavy 106°5 33 11 150°5 ” | Curly 49 11 17 dik | | ). , Biometrika 111 22 170 On the Inheritance of the Mental and Moral Characters in Man L es Te eo | OST} 9ST os] G.LGZ| 9-862] 9-98Z| G-L81] ¢-9¢T] 84 or | 82 96/8 |8 |S |e | seo I | Ft | |e] = == || == = = = = = S| | eto T Sa || eae lle = Dee |e) ae a tN — = — = = = 16—06 a7 SSS] |S =] = == = | 1 = I ad = a = I | y S| amo | ee | me | cell I = = | 7 = I = = — = = —|—] 68—s83 L Sal | | ae hel OT = = le = | = T I — = al 8 SC Nae [Sie lk I 17 Cie |e I g b = j —= SS | SS SS SS | | 29 S88 8 Se ate ae am Ike g g gq |% v g j g 2 = ey el eas 8g ie IS I) tebe G.9 GL | 6 P I 9 € G T I SS SS Sh SS 8. &6 Si ap S| .G:9 G.8 cL | 8 cI al 9 OL T j I | | a OSE || l=-lse lt le lie cl cI OL | LT | ¢8 G71 ral OL 9 8 g Ea | aero? 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GG I € v v “== G € 14.3 G|—|—|—] &-S9T See eal |e ae), Clee fo if 1 Mtb sae lamers [Ad ooati ee | A een A rn eae G Se Se | = I aa = = = I = = = = eed Dell (ere [| ell (Up) BY & € Taw eo — = == — = = — = a = G = LS se el a ae 10 6 GE pees a] efalelesalalg/alslalsjealys “‘syTejOT So] HB 1] S|R] A] se Re Ss x QQ 3 re Ss XN NX es or S SI] Al slr} so Al AL aral asl a a A on A H HR Qn HR R H HR H AL AP Aalay an CARES Sane “LOPSUY-.Lajsyy *sunah ZT 0} poonpas ypbuaT poopy Ma "I9JSIQ puoveg 175 K. PEARSON ‘s[eqO], G-806 ed 10 10 10 Seni el ale ll eee G.66T lee) l | Qt 1 29 AOnAA sloser Me leak aliel Ses G-G6T GE alice AN 19.10 Att Ho Hosta one Iles Hien li? 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Gh |GZ€L |9686 | €€ | G6E| OG] Gh |G9E | BIT | 6 € 1 At SA aaa eh el ed tv 2 BAAS i li id j 8 GUA Ge5|) 8.28 | Gy | 808 See ee 8 OL ey = Ss | SCCHieees |e meee || oe I I OT] 33] G46) G9E] Ge | OF | &6 | Il | 4 VOC S| Flee ae | Or LCT eel I I 4 b g 9 SI) 86 | & | FL | AT | 6 Gea lly | ase Ngee aj cas |e eS ees Neco eee 9 Wars Kee I id G 6 Go OL VE Ser ay g ESS) a Pee] i ae (ele Lie Neer ere |< || id I j id @ | + L 6 g 9 Sh ie Neel Peak | Rese iD ag Ne | a Ua I ll aes Se j 6 € VA ral eC) ore met ot) Fs Gr Bl eal eee py oe |e ee | eo I LO tal 9 I ere OUS | ole) allt 087 CET sales) cee ese ol cae | a ee ee ear a! I CF eG | cai atl eee |e Soe I = srg dere eee arp eee) Saeeaiiea (nee fag arte ct seam NLS eee eee NTO Pe oa eaall arora lr cee Lae (Oey (eee lea sag ccs pe ec ea (a Wend 8 mel enn cere ne ee maa ed ets | era ca aed Gd Ti Whee acre ee™ Nace «I paid PO cae ANN Gora lle a fa | come Pama cee | ce | ae are (oe) a Poa asl le Lat Led Lee’ ed Le’ Land lant len La Lan’ La’ Land La Lat Led Lat Leet Lad Lad ym gaor{ S| 8] SF} SF) SF) s} sels; se) s,s) ss] se] SF] F$] Sf Sj spss 6 nr NX Nr Or Nn Xr NX Nr Or nr n NX a N NX NX it NX NX a “IayOI_ JSILT "LOY JONG -LAYJOLT (1) 9 ‘supah ZI 07 paonpas yypnog poory ‘IoyJOIg puwoveg Sister-Sister. G (ii). First Sister. Head Breadth reduced to 12 years. Biometrika 111 K. PEARSON Ww 2 UD pen) le) pe) uw Tes) tte) pen) AMHIOANDOPCArrADDHAATOCAMVANS Ss ANTODR TR MOOMMOOMR ANANNAR SS PT lata Sees alee set aia] PT US PE Pe le seas at tea eT ATG) OI PSE Ps Sci) is EE at leR le) DSi TST il lat aaleeelres eves se] 1] ° ao D eee on ea a oD 9 oD 10.10 Oe Bale al eee scree cree 10.10 (98 19 Ney Ne JAMIE) eis CS eye ae ; Iw iB.o AI 12 0 PIS PMs dale ees eo Sooo ca 4 Ee on ft oe ce 2S ie.e) 10.19 Ne ao | | oe tal PHH AH mMHOmUAQDHOM fei a AANOARA 16 Mie a ba Le ladsmnaranmoancax let = = = = == == = = = = = = = =z |= = || cae ie me le my ie ia’ le RY ie Lae lad lad lore lad ie ie ioe ioe ie my is ioe seon}S) S| 8} 3S) 8} ss] 8] 8) 8s] 87 sy} X]}sx] S$] sels); s] 8s] $s] si) sig nr] A HN n Hn H nr a nr Hr HR or Nn n an oy nH HR Hl apl~asya "LAY JOLT -LaY JOLT ‘IOYIOI 4SILT ‘sumah ZT 02 poonpas yybrazy pwapy OH "IoYJOI_, puoveg 23 180 On the Inheritance of the Mental and Moral Characters in Man allatlantl | Pel tT eal ellen’ ales PS eee eS ers fen | PTET TT LT Leaner loves leo | ovo | LT sl are ge SS eo al Barco ion ey LGG GGT | G&L GIG | G&G 86 | G66 9.66 Ge 6B | GLE €@ | G-0G PL | GT € C81 € 4 T g T T L — na T oat 60¢ GPL SOT ltd l | a DOD OD CI OD GIT 9-6 VE Te oe to | lo | ico oo + 9 1919 Oto oa Ll leo le VG lheres bier canotes cot clmeralememe 1 alp aliealcatleea| [Vee | alent Y coelieeeli cece) oil SIE sige e| « "s[eqoy, my > s nr G-BTT G.OTT G-8ET G.98T I I v I G G OL IT al IL 61 TL | G61 G.8 GEL 4 Il 6 ial I 9 € I G — = T iss) & & 2 nN Qn G.86T G.96T é G.66T “IOYST JSILT “LOPSUG-Lagsyy “s.uvoh ZT 07 poonpas qyhroyy poo (1) H G-9TT G-6IT G-OIT G-S8OT G.90L ‘I0JSIG PUoIeG 181 K. PEARSON OF G.OST G-G6 1D | 10 eee le de 2 OANA eins | a ee 10 aA tH 1d Ad wd A AN G-8ET re “2 HO 0D 6010 09 G.96T wd Sete NOMA G.6ET "LOISYS- LOYIOLT G.0&T ‘sumah GI 02 poonpas aybriayy poopy ¢.c9 i — — — IT — T T T T T T 9 G 9 L| G9| &F GL 6 OT GET} 9-1 él 6L 91 6r g vl OL v | GOL IT GG} GIL 8 g v 9 qT € g — — Gc. pa Nee T G.86T ‘TOYOIG ‘(m) HW 7 =| 16 G.96T wd 1) QL G18 1 oD 1d C S [eres G-TET G-19 T (ee HNAONDOOHHOANAH ? metre wd 1d I~N ~ : vel te THO 10 69 1 HI G.06T le) ad rd Gist oo 1 20D 6 1d 1 r1 G-8TE GOTT Yen) Si cwow (ea | | he) | | 49 GITT GOTT S[eqO, GAYT G-BYT GOTT G-88T G-98T ae | Rae G-68T G-O8T G.86T G-96T G-YOT ol G-06T ¢-STT G-OLT GAIT G-6IT G-OIL L | ¢.80L 9-901 G.90F “10481 182 On the Inheritance of the Mental and Moral Characters in Man Second Brother. Second Sister. Sister. ATHLETIC CAPACITY. LG). Brother-Brother. First Brother. Athletic. Betwixt. Non-athletic. Totals. Athletic 906 20 140 1066 Betwixt 20 76 9 105 Non-athletic .... 140 9 370 519 Totals 1066 105 519 | 1690 Ta); Sister-Sister. First Sister. | Athletic. | Betwixt. | Non-athletic. Totals. Athletic 638 15 153 806 Betwixt 15 16 11 42 Non-athletic .... 153 11 452 616 Totals 806 42 616 1464 I (iil). Brother-Sister. Brother. Athletic. | Betwixt. | Non-athletic. Totals. | Athletic ace 195 5 43 243 Betwixt ase ase 5 2 2 9 Non-athletic .... 91 5 86 182 Totals 291 | 12 | 131 434 Second Brother. Second Sister. Sister. a). K. PEARSON TI. PsycuicAL CHARACTERS. DETAILED TABLES. VIVACITY. Brother- Brother. First Brother. | Quiet. Noisy. | Totals. Totals as | 1209°5 | 642°5 J (ii). Sister-Sister. First Sister. Quiet. | Noisy. Totals, Quiet 1013 349 1362 Noisy 349 393 742 Totals | 1362 | 742 | 2104 J (ili). Brother-Nister. Brother. | Quiet. | Noisy. | Totals. Quiet 36025 164:25 524: Noisy 79°25 148-25 2 Totals 183 184 On the Inheritance of the Mental and Moral Characters in Man ASSERTIVENESS. K (i). Brother-Brother. First Brother. . Shy. Self-assertive. Totals. 8 ee & Shy a 679 247 926 3 | Self-assertive ... ef, 247 399 646 8 2 Totals vee | 926 | 646 | 1572 K (ii). Sister-Sister. First Sister. | Shy. Self-assertive. Totals. | 5 Sallie ean ed ee: 672 296 968 E | Self-assertive ... a 296 436 732 3 ee Peer WM ' Totals Bate _— 968 732 1700 | K (in). Brother-Sister. Brother. | Shy. | Self-assertive. | Totals. 8 | Shy wa | Self-assertive ... Totals er »| Second Sister. Second Brother. Sister. Te), INTROSPECTION. K. PEARSON Brother-Brother. First Brother. Self-conscious. Unself- conscious. 185 Totals. Self-conscious ... 600 245 845 Unself-conscious 245 550 795 Totals | 845 795 1640 L (ii). Sister-Sister. First Sister. Self-conscious. Unself- Totals. conscious. Self-conscious .. 561 302°5 863°5 Unself-conscious 302°5 588 890°5 | Totals 863°5 890°5 (54: L (iii). Brother-Sister. Brother. | — Self-conscious. : ae us Totals. Consceclous. Self-conscious ... 126°25 210°25 336°5 Unself-conscious 253°75 66°75 320°5 Totals 380 Dial 657 | tt 24 Biometrika 111 186 On the Inheritance of the Mental and Moral Characters in Man Second Sister. Second Brother. Sister. M (i). POPULARITY. Brother-Brother. First Brother. Popular. | Unpopular. | Totals. Popular... 11075 185°5 1293 Unpopular 185°5 147°5 333 Totals 1293 | 333 | 1626 M (ii). Sister-Sister, First Sister. Popular. Unpopular. | Totals. Popular... 1133°5 182°5 1316 | Unpopular 182°5 1755 358 Totals 1316 358 | 1674 M (iu). Brother-Sister. Brother. Popular. Unpopular. Totals. | Popular... 432-75 54-25 487 Unpopular 40°75 26°25 67 Totals 473°5 80°5 | 554 Second Sister. Second Brother. Sister. K. PEARSON 187 CoNSCIENTIOUSNESS. N (i). Brother-Brother. First Brother. | Keen. | Dull. | Totals. Keen 970 216°5 1186°5 Dull 2165 287 503°5 Totals 1186°5 | 503°5 | 1690 N (ai). Sister-Sister, First Sister. Keen. Dull. | Totals. Keen 1071°5 201 UPS Dull 201 2785 479°5 Totals W725 4795°5 | 1752 N (iii). Brother-Sister. Brother. Keen. Dull. | Totals. Keen 366°75 122°75 489°5 Dull 59°75 136°75 196°5 Totals 426°5 | 259°5 686 188 On the Inheritance of the Mental and Moral Characters in Man Second Brother Second Sister. Sister. O (i). TEMPER. First Brother. Brother-Brother. Quick. Quick Good-natured 5 Sullen 39°75 Totals ... | 330°5 O (21). Good-natured. | 152°25 1026°5 106°25 1285 | Sister-Sister. First Sister. Quick. Good-natured. Sullen. 230°5 Sullen. Totals. 1846 Totals. (Quick Good-natured 1338 Sullen 362 Totals... are | 452 1338 362 2152 O (iii), Brother-Sister. Brother. | Quick. Good-natured. | Sullen. Totals. Quick ee ee 60 45°5 10 115°5 Good-natured 68°75 388 43°75 500°5 Sullen 13°25 56°5 18°25 88 Totals | 142 | 490 | 72 | 704 Second Sister. Second Brother. Sister. K. Prarson 189 ABILITY. PG): Brother-Brother. First Brother. Quick- -— Slow- a Slow-| Very ee intelligent. Hansen intelligent. Slow. | gull. | dull. ie. | . Quick-intelligent 88 62 25 42°25 kp) 2 207°5 Intelligent 62°25 313°5 183°75 72°55 | 95 1 642°5 Slow-intelligent .... 42°25 183°75 255°5 73 22°5 8 585 Slow ert 11 72°5 ie 97°5 | 39 + 297 Slow-dull.... 2 95 22°5 39 28 7 108 Very dull... 2 1 8 4 7 6 28 Totals ... wes 207°5 642°5 585 297 108 28 1868 | ( ! PGi). Sister-Sister. First Sister. Quick- jiko Slow- Ja Slow-| Very # yi.7, intelligent. | Hagan | intelligent. slow. dull. | dull. ora Quick-intelligent 118 i 49°5 14 7 1 300°5 Intelligent ot 111 326 213 47 10 5 712 Slow-intelligent .... 49°5 213 204 99°5 | 30 9 605 Slow ono cone 14 47 99°5 64 29 7 260°5 Slow-dull... 7 10 30 29 | 22 5 103 Very dull... ar 1 5 9 7 5 6 33 | Totals... ar 300°5 712 605 260°5 |103 33 2014 PGi). Brother-Sister. Brother. Quick- aM: | Slow- Slow- | Very intelligent. Hateale gone | intelligent. Slow. | gull, | dui. | Los. Quick-intelligent 53 39 23 8 5°25 25] 128°5 Intelligent coon 51 1185 90 25 11°75} 5°75] 302 Slow-intelligent .... 17 775 119 39 15 5 272°5 Slow ee wits 7 28 38 29 7 1 110 Slow-dull .... oe 2 5 5 5 9 5 31 Very dull... rest 1 3 5 — 1 6 16 a ne Totals... | 131 | - 271 | 280 106 49 23 860 ee | 190 On the Inheritance of the Mental and Moral Characters in Man HANDWRITING. Q (i Brother-brother. First Brother. a = Very | . ery | good. Good. | Moderate. | Poor. Bad. yeas Totals. a | ) Sj Very god ...) 52 51 27°5 3 1 — 134°5 a Good .... ae 51 335 294°5 32 4 1 647°5 Moderate ste 27°5 22475 406 101°5 155 2 Minh | Poor... oe 3 32, 101°5 96 15 2 249 5 6 Bad 925 ine i 4 15°5 15 7 1 43°5 ® | Very bad... — 1 2 2 1 4 10 ie) ee ee ee Totals yas 134°5 647°5 CTL 249°5 43°5 10 | 1862 Q (ii). Sister-Sister. First Sister. Very Good. Moderate. | Poor. Bad. Very Totals. good. bad. i Tar ER Gomme! ™ | Very good... 50 29 23 5 - — 107 wm | Good... ae 29 334 170 36°5 6 = 5755 = Moderate ae 23 170 300 90°5 17 5 605°5 ei | Roor! 2. cea +) 365 90°5 68 14 — 214 S|. Bad! | 35 me = 6 17 14 10 4 51 gy | Very bad... — -- 5 — 4 4 13 y Totals = 107 | 5755 605°5 | 214 | 51 | 13 1566 i Q (11). Brother and Sister. Brother. Very Good Moderate.| Poor good. : ete 7 . | Very good... 15 13 ia 3 & | Good... bes 27 146°5 106-75 31°75 + | Moderate at 9 74 140°25 42°75 w | Poor... aes — 13 40 Sill Bad _.... ass — 2) 5 2 Very bad iss — — 1 — | Totals Pee | 51 | 248°5 300 1105 15 | 3 728 | A STUDY OF THE VARIATION AND CORRELATION OF THE HUMAN SKULL, WITH SPECIAL REFERENCE TO ENGLISH CRANIA. By W. R. MACDONELL, LL.D. (1) Introductory. THE following paper is a contribution to the investigation which has been going on for several years at University College, London, under the direction of Professor Karl Pearson, with the view of determining the size, variability, and correlation of various organs and characters in man. Professor G. D. Thane, head of the Anatomical Department in the college, is the fortunate possessor of a collection of human skulls which were discovered in 1893 in Whitechapel, and it is this great series which forms the subject of my inquiry. We have most heartily to thank Professor Thane for unreservedly placing his splendid material at the disposal of the biometric workers in the college. Some of the skulls had been examined by previous observers, and measurements made of a few of the chief characters, with important results to craniology, but a systematic exami- nation of the whole series had still to be accomplished. At Professor Pearson’s suggestion I undertook this very attractive piece of work in 1901, and measured all the skulls in accordance, for the most part, with the system of the Frank- furter Verstdndigung, so far as the condition of the material allowed. In the arithmetical reduction of the measurements I have closely followed the scheme adopted by Cicely D. Fawcett in her great paper on Naqada Crania*. a Biometrika. Vol. Ul., Part Il. Plate xxii. Normal Female Skull. W. 18. N. basalis. ¢ Biometrika. Vol. III, Part II. Plate xxiii. Normal Female Skull. W. 18. N. verticalis. Biometrika. Vol. IIl., Part II. Plate xxiv. Normal Female Skull. W. 18. N. occipitalis. ah i i Biometrika. Vol. IIl., Part Il. Plate xxv. Normal Female Skull. W. 7044. N. facialis. Biometrika. Vol. IIl., Part II. Plate xxvi. Normal Female Skull. W. 7044. N. occipitalis. Biometrika. Vol. IIl., Part II. Plate xxvii. Normal Female Skull. W. 149. N. facialis Plate xxv Vol. IIL., Part I. Biometrika. iy ON “spedaye| “| "OyS aewad jews’ Biometrika. Vol. IIl., Part Il. Plate xxix. Normal Female Skull W. 149. N. basalis. Biometrika. Vol. !Il., Part II. Plate xxx. Sey Normal Female Skull. W. 149. N. verticalis, Biometrika. Vol. IIl., Part II. Plate xxxi. Normal Female Skull. W. 149. N. occipitalis. Biometrika. Vol. IIl., Part II. Plate xxxii. Special Skull. W. 7042. Ossicle of Breqgma ie Biometrika. Vol. IIl., Part Il. Plate xxxiii. Special Skull. W. 223. Ossicle of lambda. @ f a { . - et = ' +, + ~ Biometrika. Vol. IIl., Part Il. Plate xxxiv. Special Skull. W. 226. Double Ossicle of lambda. Biometrika. Vol. IIl., Part II. Plate xxxv. Special Skull. W. 217. Simple Interparietal. Biometrika. Vol. IIl., Part II. Plate xxxvi. Special Skull. W. 7096. Tripartite Interparietal. Os pentagonale and ossa friangularia all separate. “ay Biometrika. Vol. IIl., Part II. Plate xxxvii. Special Skull. W. 218. Tripartite Interparietal. Ossa triangularia only separate. Biometrika. Vol. IIl., Part Il. Plate xxxviil. Special Skull. W. 219. Tripartite Interparietal. Os pentagonale and right Os triangulare separate. Biometrika. Vol. IIL, Part Il. Plate xxxix. Special Skull. W. 7052. Tripartite Interparictal Os pentagonale and left os triangulare separate. Biometrika. Vol. IIl., Part II. Plate xl. Special Skull. W. 221. Tripartite Interparietal. Os pentagonale only separate. . Biometrika. Vol. Ul., Part I. Plate xli. Special Skull. W. 231. Plagiocephaly: ae i oo : ‘ ree che fa a : tee : ' ¥ = : : 7 - ‘gl ao - - + ; - Caney ‘ , > “ + 4 aa “ ‘ : Biometrika. Vol. IIl., Part I. Plate xlii. W. 7042. Special Skull. Bathrocephaly. Plate xl Vol. Ul., Part I. Biometrika. ‘a14fO1d, Ye “ainjng plopqueg fo sasissq yim Aleydeoouyjyeg, Wry yewed 502 7 Biometrika. Vol. IIl., Part Il. Plate xliv. Special Skull. W. 7042, Bathrocephaly with Ossicles of Lbambdoid Suture. Biometrika. Vol. Ill., Part Il. Plate xlv. W. 7059. Special Skull. Right Profile. Bathrocephaly with Ossicles of lambdoid Suture. Plate xlvi. Vol. Ill., Part Il. Biometrika. ‘Jesodwie] JO ssadodd, [eUody "AZM YNYS ered Plate xlv Vol. Il., Part I. Biometrika. “QOUSUILUT AL[APUOSedd, [eIaJeIIU]D WZ MM YMyS jeveds Biometrika. Vol. JII., Part II. Plate x\viii. Special Skull. W. 213. Bilateral precondylar Eminences. as Plate xlix. Vol. Ill., Part I. Biometrika. sIpeUoe] snnwuepf “622 “MC YMIAS Jepeds £ Biometrika. Vol. !II., Part II. Plate lI. Special Skull. W. 229. Flamulus lacrimalis. W. R. MacponeEuu . Diy, up for all characters between the individuals we have selected for representation, and that it is nowhere possible to draw a line and say, here one “type” begins and there another ends. Take the material, however, as a whole whether in our tables of means, or in our tables of measurements or in the plates, and compare it with other series, German, or French, or Scandinavian and we see at once that it has a very marked individuality of its own; that the English, or at any rate the London, skull of post-mediaeval times is a type sui generis. Whether this be the result of Blutvermischung, of selection or of environmental influence or of an absolute differ- ence of ancestry it might be hard to determine. But the fact remains perfectly certain, the English modal skull is markedly differentiated from those at any rate of central and southern Europe. (b) Special Crania. Out of the 292 skulls in this collection, 164 were noted as having some, it may be slight, anatomical peculiarities. As a rule such peculiarities were likely to occur in groups. Thus 280 peculiarities were recorded, or an average of ‘96 to each skull in the series, and 1°71 to each skull specially recorded for abnormality. Of these abnormalities 151 were recorded in skulls supposed to be female and 129 in skulls supposed to be male; the total number of skulls adjudged female was 151 and adjudged male 141. In other words the abnormalities were on an average one to each female and ‘91 to each male skull. It will thus be seen that what greater tendency there is to abnormal variation lies in the female rather than in the male skull. Here as in every case where really scientific methods are applied to the problem there seems no reason for asserting that men show a more marked variational tendency than women. If we turn to the individual anomalies recorded, it may be noted that some of them are very slight, but still the general frequency of anomalous characters seems higher than in most long series of skulls. At first it appeared that possibly the fact noticed on p. 196 (iv) might explain this high frequency, but a second series of London skulls shows the same high, if not a higher, proportion. We are therefore forced to the conclusion that the English skull is probably remarkable for anomalous variations ; in this respect no series we have yet examined appears its equal, except possibly the Esquimaux series at Oxford. Our photographs will show how wide a range of anomalous variation can be represented from this one group. We shall now proceed to consider some of the individual cases, classifying them under: G) Peculiarities of Form. A very frequent anomalous form consists in a post coronal constriction. We have spoken of this merely asa post coronal depression, if 1t 1s localised about the bregma. Post coronal constriction occurred in 19 crania, of which 15 were female, and 4 male, one of the latter being of very doubtful sex. Post coronal depression in 2 Biometrika 111 28 218 Variation and Correlation of the Human Skult skulls of which 15 were female and 12 male. Of course depression passes insensibly into constriction, but the constriction is so markedly more a female than a male character, that for some time one was inclined to consider it might be due to some feminine habit of wearing a tight band round the head. Depression of the obelion occurs in 19 skulls, of which 12 were female and 7 male; flattening of the obelion was noted in one male and a groove of the obelion in one male and one female skull. A coronal groove was also recorded in one male skull. There were isolated cases of parietal flattening and depression of the one or other frontal, A very marked inion was noted in eight cases, naturally the male crania having the majority of 5 to 3. Plagiocephaly was recorded in five cases, three male and two female, and one of the latter is reproduced in Plate XLI. The peculiar shape of forehead which may be best described as a “marked infantile type” was found in four crania all female ; one of these otherwise normal skulls is depicted in Plate XVII. The great length of the English skull is not a little due to the frequency of protuberant occiputs*, and these have been especially noted in our second series. It is further emphasised by the frequency of almost every degree of bathrocephaly. Fifteen bathrocephalic skulls, 9 male and 6 female, were recorded, and an equally high percentage was found in our second series. In 7 out of the 15 cases, bathrocephaly was combined with a more or less numerous system of ossicles in the lambdoid suture (Merkel). Plates XLII—XLV give fairly good representations of two female (W. 7042 and W. 7059) markedly bathrocephalic skulls. A torus occipitalis was noted in 13 skulls, 7 males and 6 females. Turning now to the neighbourhood of the foramen magnum a careful exami- nation was made of the condyles, and single or paired precondylar eminences noted in 14 crania, 5 male and 9 female. One female skull showed a third con- dyle with articular facet (W. 170), and one male (W. 111) had the anterior extremities of the condyles united by an osseous bridge. This is illustrated in the sketch below as it was found impossible to obtain a satisfactory photograph. Plates XLVII and XLVIII illustrate cases of single and bilateral precondylar eminences. (Condylus tertius?) Of other peculiarities we may note the rare case of the hamulus lacrimalis reaching the face figured in Plates XLIX and L; two cases of marked projection from hinder margin of external pterygoid plate (W. 85 ¢ and W. 86 2), two of the porus crotaphitico-buccinatorius of Hyrtl (W. 122 ¢ and W. 128 2), 5 cases of single or bilateral pterygospinous bridge, 3 male, 2 female; and isolated cases of imperfectly developed mandibular articulation (W. 57 2), torus palatinus (W. 149 $, see Plate XXIX), of subdivided foramen ovale (W. 173 ~) and of markedly small right jugular foramen (W. 192 ¥ ??). * Marked occipital projection occurred in four Whitechapel skulls, all four being female. Occipital flattening in one female skull. — W. R. Macponeii 219 (ii) Ossicles and Wormian Bones. Ossicles of the bregma were recorded in 4 cases, 2 male and 2 female, and 1 case (associated with bathrocephaly) is depicted in Plate XXXII. Ossicles of the Jambda occurred in 11 cases, 4 male and 7 female; cases of single and double ossicle W.111. Osseous Bridge of Condyles. of the lambda are reproduced in Plates XXXIII and XXXIV. Ossicles of the asterion occurred in 2 female and 1 male case, and of the pterion in 13 cases, 6 male and 7 female. There was one case of a frontosphenoidal ossicle (W. 212 ¢), 1 case of ossicles in the parietal notches of temporals (W. 7061 ¢) and 1 case of ossicles between occipital, parietal and mastoid (W. 31 #1). Ossicles were recorded in the coronal suture in 3 cases, all male ; in the sagittal suture, in 2 male and 2 female cases; in the lambdoid suture in 29 cases, of which 13 were male and 16 female ; the lambdoid suture had a very irregular line* in the male skull W. 76; in the squamous suture there were 2 male and 2 female cases of ossicles and 1 case (W. 7109 ) of ossicles in the parietomastoid suture. On the whole upwards of 75 cases of ossicles were noted, 37 male and 38 female. We may therefore say that slightly more than 25 per cent. of English skulls have one or more anomalous ossicles. (i) Anomalies of the Sutures. Twenty-four skulls were metopic, or a persistent frontal suture was found in 9 male and 15 female skulls. The mean breadth and minimum forehead breadth of * Complicated sutures were also noticed in skulls 2043 and 762. 28—2 220 Variation and Correlation of the Human Skull these 24 skulls were compared with the means for the whole series with the follow- ing results : Marre Sxuiu FremMaue SkuLu Character Ie General | Metopic | General | Metopic Maximum Breadth... 141 142 135 135 Least Forehead Breadth 98 100 | 93 96 It would thus seem that a persistent frontal suture may allow of a two to three millimetres increase in the minimum forehead breadth, but probably does not influence the maximum cranial breadth. We may perhaps note here that a metopic fontanelle occurred in one case, the male skull, W. 141. Traces of a transverse-occipital suture were found in 8 cases and of an infra- orbital suture on the face in 2 cases, all males. In 1 female skull there was a division of the left parietal bone by a sinuous suture (W. 216), and in 3 cases, 1 male and 2 female, the apex of the occipital squama was produced upwards. Frontal process of temporal, single or bilateral, was noticed in 4 cases, 2 male and 2 female (see Plate XLVI) and a par-occipital process in 1 male skull (W. 192). (iv) Interparietals. As in the Esquimaux, the English skulls provide in both series a very con- siderable number of interparietals, in the Whitechapel series we have 5 male and 4 female. We may divide them into the simple interparietal, Plate XX XV, and the tripartite interparietal, Plate XXXVI. Skull W. 7096 is a good example of this although it is not as clearly shown in the plate as one might have wished. The complete tripartite interparietal consists as in skull W. 7096 of three parts. First the pentagonal shaped centre bone and then two triangular wings. These have been termed by Professor Thane the os pentagonale and the ossa triangularia respec- tively. Almost every form of this tripartite interparietal occurs in this English series. Thus we may have; (i) all three parts free as in Plate XXXVI. (ii) The os pentagonale fused and the ossa triangularia separate as in Plate XXXVII. (iil) The os pentagonale separate and the ossa triangularva fused as in Plate XL. (iv) The os pentagonale separate and the left os triangulare only separate, the right fused as in Plate XX XIX, or (v) the os pentagonale separate and the mght os triangulare only separate, the left fused as in Plate XXXVIII. Cases of one os triangulare separate, and the other as well as the os pentagonale fused did not occur in this series. Still the series is so comprehensive and interesting that it seemed worth while to figure these interparietals fully, so that they may serve as standards for reference in other cases. Taken as a whole the series appears to possess very considerable interest from the standpoint of special or “abnormal variations.” The fact that the same high W. R. MaAcponeELu 22 percentages are maintained in a second English series seems to show that we are dealing with something at anyrate characteristic of the Londoner. It would be of interest to enquire whether the proportions of special variations are greater in mixed races like the English, than in races of relatively purer character. (9) On the Variability of the English Skull. The numerical values of the variations are given in Table VII together with their probable errors. Taking first the capacity, I extract various coefficients of variation from Pearson’s The Chances of Death, Vol. 1. pp. 8328—349, for comparison with our series and the Naqadas. 3 g | English* ... ve we 8:28 8°68 | Parisian French ,.. ie 7°36 710 Modern Italians ... ise 8°34 8:99 Modern Germans... oa 774 8:19 Naqadas_... ae asa 772 6°92 Etruscans ... pee Ee 9°58 8°54 Egyptian Mummies noo || feeil33 8:29 Ainos eee ae re 7:07 6°90 The variability of our series is high, but not quite so high as that of the Italians, and the female skull is shghtly more variable than the male, the English in this respect resembling Italians and Germans. Comparing the coefficients of variation of length, breadth, and height of the skull we find: Length Breadth Auricular Height Race - - - - & ? of “ o 2 English wis 3°31 3°45 3°75 3°54 3°73 4:12 Bavarian t ... | 3°37 3°57 3°89 3°39 4:47 3°91 French { ... | 3°97 3°65 4:21 3°67 — = Naqada§ ... 3:17 314 3°29 3°45 3°86 354 Ainot iB 3°20 3°08 2°76 2°68 3°67 3°18 * My own results are given; Pearson’s figures were based on only 58 skulls—all that had been measured when he wrote. t+ Alice Lee, Phil. Trans., Vol. 196, A, p. 230. + Unpublished reductions of measurements in Broca’s MS., by C. D. Fawcett. § Biometrika, Vol. 1. p. 438. 222 Variation and Correlation of the Human Skull TABLE VII. Variability of the English Skull. MALE FEMALE Character = — Mean Standard Coefficient of WeaG Standard Coefficient of Deviation Variation ” Deviation Variation (Cheon 1476°94+9°73 | 122°3746°88 | 8°28+°47 | 1299°87+8°51 | 112°830+6°01 | 868+°47 ET, 187°35+ +35 GT 325:| 3:29 42213 180'14+ °36 6B8+ 25 | 3544-14 Lf’. 187°76+4 °45 564+ °32) 3:004+°17 180°07+ °57 633+ “40 3°52 + 22 L. 189°06+ °36 627+ 25) 3:31+:13 180°36+4 °35 622+ 25 3°45 4°14 133 140°67+ -°31 528+ 22} 3°754°15 134°68+ ‘27 477+ “19 3°544:14 Ban 9802+ +25 4:°20+ “17 | 4°292°17 93°12+ °23 423+ ‘17 4:55+4°'18 A oe. 132°04+ °34 5°56+ 24) 4:°214+°18 124°56+ °30 4:93+ ‘21 3°96 4°17 OH 114°59+ +25 498- -18:|> 33 73ck 5 109'21+ °25 450+ ‘18 4:12+:'16 LB 101°60+ °25 41325 18) |) 4-07 8 95°34+4 +24 391+ ‘17 4:11+°18 (Ore 524°295+ °88/) 15°02+ °638|) 2:°87+°'12 503°84+ °85}| 14°70+ ‘60 2°92 +12 (Sige 3877-114 °81]) 138°69+ °57 3°63 + °15 362‘764 °84] 14164 ‘59 3°90 +°16 Q 307934 °72| 11°40+ °51 3°70+°16 293:97+ “71 |- 11674 50 3974:17 GH 7O'17+ 30 3°86+ ‘21 5°50 + °30 65°93+ °40 471+ :28 714+°43 GB 90°87 + °45 507+ °32|) 558+°36 84°86+4 “41 459+ -29 5°40 + 34 J Gee 130:05+ ‘57 557+ 40] 4:°284°'31 120°27+ °58 497+ ‘41 4134°34 NH 51°22+ -20 2°60+ 14] 5:08+°27 48°68+ °22 270+ ‘16 5°55 + °32 NB 24°29+ 17 216+ °12| 8°89+°51 2319+ 14 164+ ‘10 7:06 +°42 OL 4306+ +15 181+ ‘ll 4°20 + 25 4117+ 113 145+ ‘09 3°58 +92 O.R 4299+ ‘16 2702+ °12|) 4:°69+°27 40°95+ :14 164+ °10 4:00 + °24 OL 33°46+ °15 188+ ‘ll| 5°61+°33 3359+ +12 145+ :09 4°31 +4°26 O,R 33°42+ ‘18 2°22+ 13} 6°65+°38 33°73+ (13 151+ :09 4:A7 +27 Gass 48°27+ +22 2-744 16} 5°68+°33 45°134 °26 2°95+ +19 6°53 +°'41 Gy. 36°78 + 24 2°85 “17 T'75 + °46 35°22+ -24 270+ ‘17 7°68 +°48 Gy 4466+ ‘21 2538+ 14) 5°67+4°33 Al 538i?) 253+ ‘16 6:10 +°38 GL 95°98 + +35 4°49+ -25] 4°68+°26 90°42 + °40 447+ -28 4:95 +31 Pz 86°°09+ 33 392+ 24 SifePisice Oly 285+ 19 Az 73°°38+ °28 3°41+ °20 73°°90+ ‘29 331+ 21 Nz 65°°19+ °29 Sane 40) 64°"70+ °23 253+ ‘16 Bz 41°-43+ °20 2°50+ ‘14 41°'39+ ‘97 2798+ -19 6, 2 Be filicte, 222 2°53+ :16 28°11 + 24 251+ 17 a, 12°°92+ -29 3°34+ -91 13°13+ +34 360+ °24 100B/L’ 7517+ °24 297+ 17) 3:°95+°:23 7462+ :27 301+ ‘19 4:03 4°26 100B/L... 74°34+ +19 3°26+ ‘14] 4°38+°18 (A fose 8 298+ +12 3:99 +:'17 100H/L’ . 70'40+ °22 267+ +15| 3:°80+°22 69°05+ °*26 291+ ‘19 AD) + 217 100H/L 69°97+ °20 3°22+ +14) 4:61+°20 69°138+4 +18 283+ 12 4:10+°18 100H/B 94°31+ ‘29 458+ -20] 4°864+°'21 92°35+ °24 htsbas. OILy/ 4:16+'18 100B/H 106°26+4 °32 514+ +238) 4°83+:21 108°46+ °28 453+ °20 417+°'19 100G'H/GB 76°52+ °50 539+ °35 | 7:°04+°46 77944 ‘57 626+ ‘41 8:04 + °52 100N B/N 47°55+ °37 458+ 26} 9°64+°55 47°79 + °33 390+ 23 8:16+°49 1000,/0,: ZL 7786+ °32 3°78+ °23|) 4°86+°:29 81°70+ 38 ADB se Dail 5°18+°33 1000,/0,: R 7769+ °38 466+ °27) 6:°00+°35 82°46+ °37 4338+ 26 5:25 + 32 100G,,/G, ... 76°26+ ‘55 640+ °389|) 8°39+4°52 7769+ ‘62 662+ 44 852 +°57 W. R. MaAcbdoneELui 223 The English skull closely resembles the Bavarian in variability of length and breadth, but there is a marked difference between the two as regards auricular height. There are few data for comparison of the coefficients of variation of the circumferential measurements : Horizontal Circumference | Vertical Circumference Race s g 3 7 English ae, css sae 2°87 2°92 3°70 3°97 Bavarian * ... por ane 2:86 3°09 _— Modern Badensians* ... 3:02 2:34 = = Row Grave German* ... 2°70 2°40 = = Naqada_... ibe ae 2°54 2°27 3°32 2°72 Here again we observe that English and Bavarian males are equally variable, and that the English female, unlike the Naqada, is more variable than the male in both circumferences. Relatively to the horizontal circumferences the greater variability in the vertical circumference is in our series very marked. Comparing length of palate, we have the following coefficients of variation : Length of Palate Race : i é g English ee 5°65 6538+ 05 ise 5°67 610+ Bavariang ... 6°42 6°85 Naqada_... 6°49 741 The English and Bavarian differ considerably, but in all three races the female "is the more variable. For profile angle, we can compare the Bavarians and Naqadas : Standard deviation of Profile angle Race ee Pe 3 ? English ... 3°°92 2°°85 Bavarians ... 2°79 375s Naqada_... 2°87 3°66 * Pearson: The Chances of Death, Vol. 1. pp. 356—7. + Length includes spina. + Length excludes spina. § Pearson: The Chances of Death, Vol. 1. p. 328. 224 Variation and Correlation of the Human Skull While Bavarian and Naqada are closely alike, and the female in both races is the more variable, in our series the position of the sexes is reversed, the male being the more variable. Next we have to compare indices: the following table of standard deviations contains the chief material available for comparison, which I extract from C. D. Faweett’s paper, p. 440: B/L H/L H|B Race 3 g 3 g 3 2 7 a ~ | | English ... ... «| 326 | 298 | 3:22 | 2:83 | 4:58 | 3:84 Bavarian te ase 3°50 2°97 = = a pas French ... a Pes 4°43 4:19 3°53 3°67 4:74 4:31 Naqada ... ats wet 2°80 3°12 2°73 2°96 £73 4:66 Row Grave Germans ... 2:28 2:35 2 Aino eae Bis vee | D4 2°54 5 = Here again, so far as a comparison is possible, it appears that the variability of the English skulls is nearly the same as that of the Bavarian. It is to be noted, too, that in all three indices, the English female is less variable than the male. For the remaining indices, the comparative data are meagre. We find the following standard deviations : - besa aan Orbital Index Nasal Index Race — é g é g co g | | 3 English... | 5°39 6-26 |Z 3°78 4:23 4:58 390 | thr UR 4°66 4:33 Bavarian*® ... | 3°26 Be 6°66 5:22 4-43 4°61 Naqada wee 452 | 4:15 ML 5°06 4:57 4:18 4 86 | (25:00 4°78 These figures show marked diversity of results. As compared with the Bavarians, the English have much greater variability in upper face index and much less in orbital index; and while in upper face index and nasal index the Bavarian female has nearly the same variability as the male, the English female is more variable in the former, and less so in the latter. In orbital index, too, the comparative variability of the two sexes is remarkable, and is complicated by the marked difference between the standard deviations of the two eyes in the English male. * Pearson: The Chances of Death, Vol. 1. pp. 325—328. W. R. MAcDONELL 225 In the following characters I will compare the variability of our series with that of the Naqadas only, there being practically no material available for other races, and for this purpose I use coefficients of variation. English Naqadas 3 ? é g | B 4:29 4:55 529 4:47 H 4:21 3°96 3°98 3°66 LB 4:07 4-11 4:88 4-68 S 3°63 3°90 3:19 351 GH 5°50 714 6°08 6°87 GB 5°58 540 518 4°77 J 4:28 4:13 4:16 4°77 NH 5:08 isyfays) 6:13 681 NB 8°89 7:06 7°89 7°28 OL ae 4:20 3°53 4:97 5°30 OR Hee 4°69 4-00 5:02 5°38 OL ose 561 4°31 7:06 6°58 OR eee 6°65 4:47 727 6°85 G, sae 775 7°68 9°29 8:55 GL aie 4°68 4:95 4:8 5:09 100G,/G,... 8°39 8°52 10:23 8:20 | In the midst of great diversity, some features emerge that are common to both races ; e.g. the great variability of upper face height in females, of the breadth of the nose and palate in males and females, also of palatal index in both sexes. It is also noticeable that the variability of orbital height is much greater than that of orbital length in the males of both races. I will conclude this part of the subject by dealing with the variability of the mandibles, for which I give a separate table as before : TABLE VIII. Variability of English Mandibles. Male and Female. Ghnraeter Mean Standard Coefficient of Deviation Variation W, 113'21+°41 6°31 4°29 5°57 +26 W, 95°40 + 46 8°31 + °32 OnMlehso4: hy 30°76 +°21 3°61 +°15 11°73 + °49 43°67 £:14 2°72+-10 623 23 Biometrika 1 29 226 Variation and Correlation of the Human Skull Comparing the coefficients of variation with those of the Naqada race, we find: English Naqada Character Male and Male and Female Male Female Female W, 5°57 7°46 Gulia 7°34 W, 8°71 7°62 7:19 8-11 hy iile7s} 9:93 8°47 9°40 f 6:23 Do 5°31 5°72 From these figures we may conclude that the English mandibles are more variable than the Naqadas in all the characters except Wy. Summing up generally for the consideration of the variability, it is clear that our Whitechapel skulls have very much the same general degree of variation as the Bavarian. There is certainly no marked difference which would allow us to assert that this group is less homogeneous than the Altbayern of Professor Ranke. It would indeed be rash to assert that they are more or less variable than the Naqada. Far more data must be reduced for variability before we can see clearly where we stand. But when once tables of variation have been made out for 30 or 40 fairly long series of skulls we shall probably get a fairly good scale of relative homogeneity for many characters and so be able more easily to detect marked heterogeneity in cranial series. (10) On the Nature of the Frequency Distribution. I will now discuss the variability of the series graphically and analytically, using the notation of Pearson’s memoir on Skew Variation*. I have selected, for both sexes, the 12 characters dealt with by C. D. Fawcettt, and have added a thirteenth, viz., Bb’, or least breadth of forehead, but I do not propose to plot the 26 skew curves representing the distributions of these characters, because in most cases the normal curve represents the distribution with sufficient accuracy for all practical purposes, as I shall now proceed to show. The following table gives the chief analytical constants of the skew curves for the 18 selected characters. The second column gives the number of skulls on which the calculation is based; the third shows the unit in terms of which the 2nd, 3rd, and 4th moments (2, w; and pw,) are calculated ; after the moments follow columns giving §,, 8, with its probable error, 6, with its probable error, the difference between 8, and the number 3, and the “ criterion” 64+38,—28, with its probable error; the next three columns give the mean, the “mode,” or value * Phil. Trans. Vol. 186, A, pp. 343—-414. + Loc. cit., p. 442. W. R. MaAcpboneELu : 227 for which the frequency is greatest, and the “skewness,” or ratio of distance between mode and mean to standard deviation, with its probable error*. Dealing first with the skewness, we observe that in 13 cases it is positive, or the mean is greater than the mode, and in 13 cases it is negative, or the mean is less than the mode. Further, in only two of the 13 cases of positive skewness, viz. VB f and H/L $, and in only two of the 13 cases of negative skewness, viz., Hf and GH ¥, can the skewness be considered as certainly significant when compared with the probable error; of the remaining cases two of the negative skewnesses, L $ and U $, and one of the positive, NH ¢, are perhaps significant; the rest are certainly insignificant. We cannot, therefore, conclude, as C. D. Fawcett was able to do with her Naqada skulls+, that if the mean and the mode do not coincide, the mean will be almost invariably greater than the mode. In our series if we were to draw the curves, the mean would be found in half the number of the curves to be less, and in the other half to be greater than the mode. We will next examine the constants 8, and ®,. If 8,=0 and ~,=3, the curve representing the distribution is the normal curve, and, therefore, in order to see how far the skew curves diverge from the normal we must first observe how much 8, and £8, differ from zero and 3 respectively, and then estimate the significance of the difference by comparing it with the respective probable errors. Columns 8, 9 and 10 enable us to make the comparison. Taking the ./8, column first, we note that in only four cases out of the 26 is /8, certainly significant when compared with its probable error, and these four are precisely those which we have had occasion to notice as exceptional in regard to skewness, viz., Hf, G’H ¥, NB Sf and H/L¢. Insix cases y/A, is greater, but not more than 1} times greater than the probable error, and in the remaining 16 cases /, is less, sometimes very much less than the probable error. A comparison of the 3—£, column with the probable error of 8, leads to similar results; in only three cases is the difference certainly significant ; in the most unfavourable of the remaining cases the difference is less than twice the probable error. Similar remarks apply to a comparison of the criterion with its probable error. Our examination of the constants of the curves thus confirms C. D. Fawcett’s conclusion {: With series of skull measurements such as the present, which are long Jor the craniologist, if short for the statistician, we shall reach for most practical purposes adequate graphical representations of the frequency by using the normal curve of deviations, y = ye VP”. This being the case, I do not propose to calculate and plot any of the skew curves, but will content myself with tracing two normal curves, the one repre- * For the formulae for calculating these probable errors, see Pearson, Phil. Trans. Vol. 198, A, p. 278. + C. D. Faweett on p. 443 says only 5 out of 24 cases have negative skewness, her table shows 6, but this does not affect her argument. t+ Loe. cit. p. 443. 29—2 ton of the Human Skull Variation and Correlat 228 ZOLG: HE9F8- FOLO- + 9866- 8Z-89 | €1-69 | SOT9- + SSTE- 9L06- PSOE. + PE6L-G | LEGL- + PSOP- LLOOT- QtPe. +PELO- FLO. + 6E60-—| ¢O-0L 16-69 | GE09- FPEI9-1—| 6718. —) 9LOE- + 6F18-€ | SOT + G940- | T8G00- O91. +ZLET- GELO- + OF FO: 09-74 €L-PL | 96LG- + TE6L- 9068: 8682: + 609-2 | GFFT. + E90. 6600: PGES. + 69F0- GELO- + PFTO- 66. 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The scale of absolute frequency indicated on the vertical to the left of the diagram gives y. Diacram I. HES I} 104 (pa 9 a i} Ps 8 = Li} Ls 7 | | | 6 ! 64 a { : | t 4 i ea ral APS ZI { mH || 2 5 i hy H 24 | _ 14 : ia ~ 7 173 yee} 185 187 189 191 193 195 197 199 201 203 205 207 Length of Head in Male Crania. Dracram II. 14 us} 124 4 1 10] i ’ 94 8 | | ! 7 : H 6 1 ' 5 ; a Y H re is is 1 ! T pS ————r Lee y+ - + t_, L 129 131 133 135 137 139 141 143 145 147 Breadth of Head in Female Crania, 230 Variation and Correlation of the Human Skull Dealing first with the Lg normal curve—the general equation y= ye", 137 where Yo= = and o = 6'26665, becomes y = 8:7216e-", and the origin is at oN 20r 189:06 mm. I will now apply Pearson’s test of goodness of fit to the curve*. The following table shows the observed frequencies (m,’), the frequencies calculated from the curve (m,), and the ratio (m,—m,’)?/m,: mm. Observed | Calculated oa) 3 176 and under 2 Sul 39 177 4 1°4 4°83 178 3 1:8 “80 179 2 2°4 ‘O7 180 2 3°1 39 181 4 Bit} ‘Ol 182 1 4°6 2°82 183 2 5:5 2°23 184 8 6-3 46 185 9 il ‘61 186 9 1a 292, 187 9 8-2 08 188 11 86 ‘67 189 8 8°7 06 190 10 8°6 23 191 8 8°3 ‘O1 192 8 78 ‘005 193 8 (ol sill 194 1 6:4 4°57 195 4 56 “46 196 5 4:7 02 197 4 3°9 ‘003 198 4 31 26 199 4 2°5 “90 200 4 1:9 2°32 201 1 1°4 “151 202 and over 2 3°4 58 Totals 137 137 23°12 Here the number of groups is 27, and y?= 23:12, and turning to Elderton’s Tables+ we find for n’=27 and y? = 23, that P =°632947 ; that is, if our series of English skulls obeyed the “normal” frequency distribution for the character L the frequency polygon would be more “peaked” in about 63 out of 100 trial samples of 137 skulls each. The normal curve, therefore, fits the observations quite satisfactorily. It is unnecessary to discuss the normal curve for Bf in great detail; its equation is y=11°7026e-"", with centre at 13468 mm. In this case x? = 9°89 * Phil. Mag. Vol. L. pp. 157—175 (July, 1900), and Biometrika, Vol. 1. p. 155. + Biometrika, Vol. 1. p. 161. W. R. MAcDdoNELL 231 and n’=25, and therefore from Elderton’s Table P=:99; that is, in 99 out of every 100 trials we should get a more peaked polygon than the one representing the actual observations. The fit may therefore be considered perfect. These two illustrations show that we must be most cautious in using the peaked or multimodal appearance of a polygon representing the distribution of a character in a short series of crania, as an argument in favour of heterogeneity of race, seeing that the peaks may well be due entirely to random sampling *. In view of Pearson’s article in Biometrika, Vol. u. Part m1. on “ Professor Aurel von Torék’s attack on the Arithmetical Mean,’ I have added to Table IX. a column showing the difference between the mean and the mode, and its probable error. Looking at the absolute values of the difference, we observe that in only three cases does it exceed 1mm. In most of the remaining cases it is only a very small fraction of a millimetre or a point, and when compared with its probable error is quite insignificant. (11) On the Correlation of Cranial Characters. In addition to the 27 pairs of characters which C. D. Fawcett exhibited in her Table XIII.+, I have selected seven other pairs of important characters, and in arriving at the 34 coefficients of correlation I have calculated the sum of the products of the pairs of measurements, instead of forming correlation tables; by this method, somewhat greater accuracy is attained, especially in dealing with circumferences and indices. Thus, let a, b be the measurements of two characters in an individual; M, and M, the means, and a, and o, the standard deviations of the characters, V the total number of individuals; then 7, the coefficient of correlation, = S (xy)/No,o,, and e a = S(M,—a)(M, —b)/N = S (MM, — aM, —bM, + ab)/N = {NM,M,— M,S(a)— M,S(b) +8 (ab)}/N _S(ab) W — M,M,. The following table gives the coefficients of correlation, and includes C. D. Fawcett’s Table XIII. for the sake of comparison. * See C. D. Fawcett, loc. cit. p. 454, and Pearson in Biometrika, Vol. 1. pp. 341—343, where he deals with greatest forehead breadth and greatest skull breadth in 2000 Hungarian skulls. + Loc. cit. p. 455. 232 Variation and Correlation of the Human Skull TABLE X. Correlation of Cranial Characters. Whitechapel English Naqadas Pair of Characters No. 3 No. g No. g No. g L&H 120| 2554-058 117) -425+-051| 134| 4894-044] 163] 2834-048 L&B 131| -240£-055 | 130, 3504-052 | 139] °344+-050| 183| +143 + -049 B& H 116 | 2334-059 | 115) 3404-056 | 129| -273£-055 | 163| -119+-052 |C& H 72| 5014059 | 78| 6004-049] 86) -6424-043] 174] -519+ 046 O&B 72| -6314£-048| 80] -6464-044| 89| -434+-058] 123] 5324-044 O&L 72| 5974-051) 78| -6914£-040| 89] -501+-054| 123] -599+-039 C&Q 72) ‘812+-027| 79| 7444-034] 84] -6564-042| 118] 6034-039 C&U 72| -8204-026| 80} -8484-021) 84] 6814040] 115| -723+-030 C&S 72| 7144-039) 77) -811+-026 | — = = = C & (Sx Ux «@) 72| -879+-018| 77} 8864-016 | — Q&S. 108| 6664-036 | 109| -581+-043 | — a = = U&S 124| 8044-021 | 124| -827+-019 | — a — = U&® 110| -720#-031 | 114| 6154-039) 84| 5124-054) 115) -454+-050 0, & O» (L) 63) 585+-061 57) “1614-087| 81| -4344-061| 108| -477+-050 O, & O; (RB) 68) 4624-064 62| -244+-080| 82] 4054-062) 112] -510+-047 NB & NH 70) “1464-079 64] “1824-081| 84] -343+4-065) 116| 1254-061 G&G; G1) -214#-082) 51| 2554-088) 73) -202£-076| 105] +501 +-049 GH & GB | 53| -189+-089 | 54| °2254-087) 77] -3854-065| 101] -479+-050 H/L& NB|NH ...| 65| 2564-078 57 |--1414-088) 71 !—-050+4-080 | 107 |—-132 + -064 H/L & 0,/0, (L) ... | 58|—325+-079 | 53 |—-057+-092) 70 | -175 4-078 | 100 |- 002+ -067 H/L & 0,/0,(R) ...| 63|—-243+-080| 56] -1024-089| 73| -170£-077 | 102 |—-016+-067 HIL & GG, 56 |—"121+-089 | 44 |—"168+-099 | 59| -1484-086| 87 |—-0414-072 B/L& NBJNH ...| 66| -177+-080| 57|—-212+-085| 75 |—-1484-076 | 120 |—-050+-064 B/L & O,/0, (ZL) 59 159+:°086) 52) 008+°093) 72), +106+:079 | 102 | —-085+ ‘066 BIL & O,/O, (BR) 65 |—-079+ 083 | 54|—-001+-092| 74} -165+-076 | 104 |—-036 + 066 BIL & G,/G, 56|--1894-087| 43) 0564-102} 60) -317#-078| 88| -109+-071 NB/NH & 0,/0, (L)| 60|—-301+-079| 55 |—-186+-088| 77 |—-276+-071 | 112 |—-263 + 060 NB|NH & 0,/0,(R)| 60|—-456+-069 | 58 |—-258+-083 | 76 |—-323+-069 | 113 | —-279 + 059 NB/NH & G,/G, 56| -081+-089| 50|—-0144-095 67 |—-194+-079| 97 | -026+-068 G,)G, & 04/0, (LZ)... | 52|—-230+ 089.) 43 |— 052+ 103 — 62| 118+-085| 93| -108+-069 GG, & O, /O, (BR)... 49 |—2214-092 | 44|—1154-100 65) 177#-081| 94) 2164-066 is — = : B&B ‘y2r| 4324-019 137| 3674-050 | 52 Te | = ; & J 43| 4684-080) 32] -4144-099 | 52 044% = | — = B&S 42| 6204-064) 33| -497+-088| 52 ‘569% | — _ This table shows that our series of English skulls agrees with that of the Naqadas in having a low degree of correlation between most of the characters In this respect the skull differs markedly from the long bones of the leg and arm+. For example, it has been found that in 100 French male and female skeletons the coefficients of correlation between the long bones selected for examination. * Biometrika, Vol. 1. p. 350. + Faweett, loc. cit. p. 455, and Lee and Pearson, Phil. Trans. Vol. 196, pp. 228, 229. 233 W. R. Macpdone.ui ‘gcp ‘d ‘710 +00) ‘pyruqaworg :4,00Meq ‘TO |b ‘SST pue Tel ‘dd ‘1 ‘oA ‘wyruamworg +: [jauopory || ‘Tes “d ‘V ‘96T “IOA “sUPLT “22%q 2 90T “VY Pag § *6e% “d ‘ajoujoojy vag + ‘][NYS you puv prey Surary uo sjyuowtainsveyy + * ‘atquaeduioo Ay1edord you os puv pasn yystey [vjo you pu avfnolny ZGO0.- F611. | S9T | ¢G0.FELz. | 6ST | 6F0.-F ETT. | EST] OGO.F FFE: | GET SFO. FEgz. | G9) PhO. FGF GT ee cis , upebeny *(80-+ 8L1-]| ¢9 |el790-Fere.]| Ze | ¢20-F9Le. |e9 | 6c0.Fser | 28 |xlot0-Fo6rE-]] ¢9 lelpoo-F1I0g¢. Jizg fo" oto §oury a a a 3 ee — |4[610. + ¢Fe.]| OOOT = = = — | || (sesselp eTPPH) yssugq = = = Fe = — |4[o10.¥ zor-]) o00¢ = = = — |r [(spearar) ystsug #L890-+922-]| 66 |{190-*ZL0-]| OO | G0. F8RF- | 66 690. 98z- | OOT |xl190-FF1E-]) 66 |x[490-+960-—]| GOT | *** aaa “* § uRULIOy) GEO. + 6G. | OTE | $ZO.F FEE. | 098 | LEO-+EO-—| OFE | FBO. F680. | 098 9€0-FZEL- | OE | GEO. FTES. 098 |" eg “ T youory 960. FOFE- | S72 | 6G0eF ees. | 9IT | Z0.-FOGE. | OFT | ¢G0O.F OFZ. | TET 190: GZP- | LIT | 8¢0. + GGz. Oér | ystpsupy jodeyooyty Ay ‘ON ‘ON ‘ON ‘ON ‘ON ‘ON é ’ rs £ 3} £ Sel1eg H pue g gq puv T H pue 'T TX WIAVL 30 Biometrika 111 234 Variation and Correlation of the Human Skull ranged from ‘74 to 98*. A similarly high correlation has also been shown to exist between the first finger joints, the coefficients ranging from ‘82 to ‘917. I will now examine in detail the results shown in the Table, and compare them with the results obtained for other races, incorporating in my tables the comparable material which C. D. Fawcett collected in her Tables XV., XVI. and XVII. Length, Breadth and Height Correlations. In the English series we observe that the females are much more highly cor- related than the males in all three pairs of characters. In this respect they agree with the German series, but here the comparison is unsatisfactory so far as height is concerned, the German height being auricular, the English basio-bregmatic. English also agree with Naqada in so far as Z and H is the most closely associated pair in both races. On the other hand, it is the males who are the more highly correlated throughout in Ainos and Naqadas, and also in French except for the pair B and H, where the sexes agree; here again, however, it must be noted that in the case of the Ainos we are dealing with the auricular height. In absolute value of the correlation coefficients we observe that our series agrees fairly closely with the French in the pairs Z and Hf and Band H¢ and with the German in Z and BY, but in no others. Correlation of Breadths. Little has hitherto been done in working out the correlation between cephalic (B), frontal (B’) and bizygomatic (J) breadths: the following table gives all the material that I have been able to find: TABLE XII. Correlation of Head Breadths. B and-B’ | B and J B’ and J Race | | | ¢ oo icrad g 3 g , - | | | English "432 | 367 | -468 | -414 | °620 | -497 Naqadas } ) 111) — | 044) — | 569 | — Theban Mummies | ‘298 | — | :250/] — | 342} — Oraon Tribe ¢ | 587 | — | 409) — | 554) — (living head) | | There is fairly close agreement between English skulls and living Oraons in all three correlation coefficients. The correlation between frontal and bizygomatic breadths is very much the same in Naqadas as in English and Oraons, and in all * Lee and Pearson: R. S. Proc. Vol. 61, pp. 349, 350. + Whiteley and Pearson: R. S. Proc. Vol. 65, p. 130, See also Lewenz and Whiteley: Biometrika, Vol. 1. pp. 345—60. { Biometrika, Vol. 1. pp. 349—351, W. R. MAcponeLi 235 four races it is greater than that between cephalic and bizygomatic breadths. The low correlation between B and B’,and B and J in the two Egyptian series, especially in the Naqadas, is to be noted. In the English, the female is less highly correlated than the male. Correlations of Capacity. TABLE XIII. Capacity and Height, Breadth and Length. C and H C and B C and L Race é 2 g @ é z No. No. No. No. No. No. | | English 2) -501+4°059| 78 -6004°049} 72)| -6314°048) SO) 6464-044} 72) °597+°051] 78 | 6914-040 Nagada | 86) 6424-043] 714) 519+ -046|] 89] -434+-058 (123 -5B2+4°044) 89 501+ °054 | 123 | 599 + -039 German | 100 | -243+-064| 99) -451+-054 | 100 | 6724-037) 99 | *706+-034| 100 | 515+:050| 99 | °687 + -037 Aino 76 | 5444 -054| 52) 5214 °068| 76) 5614053, 52) -5024-070| 76) 893+ 016] 52| 663+ -053 Sioux 57 | 4404-070) — | ae 57| +67 4:05 | — = 57| +54 +£:06 | — = | | zi | | — | a Means 48 “52 ‘60 59 61 66 There is no striking difference between the sexes in our series, such as exists between German ¥‘ and § in the pair C and H, and Aino {and @? in Cand ZL, but here again the English female is more highly correlated than the male, in this respect again agreeing with the Germans throughout, and also with the Naqadas except in the pair C and H. In Ainos the position is reversed. the male being the more highly correlated. We have only Naqadas and Theban mummies for comparison in the case of capacity and circumferences, | TABLE XIV. Capacity and Circumferences. C and U C and Q Cand S Race g g s ? g G3 No No No No No No - } English 72 | 820+ °026 | 80 | -848+:021 72 | 812+ 027) 79) 7444-084) 72 | 7144-039] 77 | -811+:026 Naqada 84 | 681 + -040 | 115 | 7234030] 84) 6564-042 | 118 “603 +039 Theban orall « 2 oo cmennoonbonolle : > : enn iniss 202 | *813+°016| 96 | 826+°022 | 202 | -788+-018| 96| -673+-038 30—2 236 Variation and Correlation of the Human Skull The correlation in the English is remarkably close to that in the Thebans, and considerably greater than that in the Naqadas. In the pair C and U, the female is the more highly correlated, in the pair C and Q the male has the advantage in all three series, but there is no marked preponderance in favour of either sex except in Theban C and Q. Unfortunately there is as yet no published material available for further comparison. In the English, the female is con- siderably the more highly correlated in C and S, but in the pair C and the product USQ the correlation of the sexes is practically equal. Correlation of Circumferences. The only material available for comparison is Naqada and Theban @ and JU, which are included in Table XV. TABLE XV. Q and S U and S U and Q - a | Race o 2 é g o g No. No | No. | No. | No. No. lism | English 108 | *666 +°036 | 109 | 581+ :048 124 | 804+ °021 | 124 *827+°019 | 110 | °720+4°081 | 114) 615 +:039 Naqada - | —_— — | — 84 | °512+4°054 | 115 | -454+-050 one 202 | 665+-027| 96) -625+-042 Mummies | We again notice that English and Thebans are very much alike, this time in regard to the correlation of U and Q, both having a considerably higher correlation than the Naqadas; in all three series, the female has the higher correlation for this pair of characters. In English, for the pair S and U, the female correlation preponderates ; for S and Q, the male, just as we found in the pairs C and U and C and Q. Orbital, Facial and Palatal Measurements. Only the Naqada results are available for comparison. In our series the marked difference between the sexes in the correlation of height and breadth of orbit will be noted: in the left orbit, the correlation is more than three times as great, in the right orbit about twice as great, in the males as in the females. The nose, palate and face correlations are small in both sexes, and their probable errors are comparatively large. In these respects the English differ very markedly from the Naqadas. In the latter, the correlation of height and breadth of orbit is much the same for both eyes and for both sexes, and the palatal and facial correlations are considerable in W. R. MaAcponeLi 237 females. The difference may be partly due to the different methods of measuring the English and Naqada orbit and palate, but in nasal and facial correlations also, where the methods adopted were the same, there is a marked contrast between the two races, Index Correlations. The following Table shows how the chief index characters are associated with each other in the two series, English and Naqada. ’ TABLE XVI. English Naqadas Character cs g of g Chamaecephaly Leptorrhiny Platyrrhiny Platyrrhiny Platyrrhiny L. Hypsiconchy Hypsiconchy* Chamaeconchy | Hypsiconchy + | £. Hypsiconchy Chamaeconchy Chamaeconchy | Hypsiconchy t | Brachystaphyly | Brachystaphyly | Leptostaphyly | Brachystaphyly* Brachycephaly Platyrrhiny Leptorrhiny Leptorrhiny Leptorrhiny * LZ. Chamaeconchy | Hypsiconchy+ | Hypsiconchy Chamaeconchy * R. Chamaeconchy — | Chamaeconcby t | Hypsiconchy Chamaeconchy * Leptostaphyly Brachystaphyly* | Brachystaphyly | Brachystaphyly Platyrrhiny £L. Chamaeconchy | Chamaeconchy | Chamaeconchy | Chamaeconchy R. Chamaeconchy — | Chamaeconchy Chamaeconchy | Chamaeconchy Brachystaphyly* | Leptostapl ylyt | Leptostaphyly | Brachystaphyly* Brachystaphyly | Z. Chamaeconchy — | Chamaeconchy* | Hypsiconchy Hypsiconchy R. Chamaeconchy | Chamaeconchy Hypsiconchy Hypsiconchy L and R denote left and right orbit. The comparatively high degree of association of platyrrhiny with chamaeconchy in both sexes is a marked feature in both races; so also is the very low correlation between the orbital indices and chamaecephaly and brachycephaly in the female of both racest. Cephalic Indices and L, B and H. Table XVII below shows the correlation of the cephalic indices, and the correlation of these indices with length, breadth and height, in English, French * Correlation very small, or almost insensible. + Correlation insensible. { In the above Table I have corrected one or two slips in C. D. Fawcett’s memoir; e.g., p. 460, she states that in the male Naqada chamaecephaly is associated with brachystaphyline characters and the little association in the female is with leptostaphyline characters, A glance at her Table on p. 455 shows that brachystaphyline and leptostaphyline have here got interchanged. p. 462 (a), brachy- cephaly as the table shows is associated with chamaecranial and not hypsicranial characters as inadvertently mis-read. Finally in (b) on the same page platycranial in line 2 of the paragraph must be interchanged with stenocranial in line 3. 238 Variation and Correlation of the Human Skult and Naqadas; also the spurious correlation where it exists. The coetticients have been calculated by the formulae given in K. Pearson’s paper on Spurious Correlation*: to test the results obtained by the formulae, I worked out the co- efficients in three cases directly from the actual numerical values of the characters in the same way as I calculated the coefficients shown in Table X, ie. by summing the products of the actual pairs of values. The results compare as follows :— ee : Coefficient by | Coefficient by Correlated pair formulae products B/L and H/L g (114 pairs) | *439+ 051 436 + 051 B/L and H/L @ (108 pairs) 391+ 055 399 + 055 B/L and H ¢€ (114 pairs) 024 + 063 ‘021 + 063 Ie The results obtained by the formulae and from the actual numerical values will be seen to agree very closely, and confirm C. D. Fawcett’s conclusiont that it seems unnecessary 1n future to incur the labour of deducing the coefficients directly from the measurements. Turning now to the Table, we observe that the spurious correlation between any of the pairs of characters is remarkably alike in both sexes and in all three series}. In our series it is greater than the gross correlation in nine cases, practically equal in four, and in only one is it significantly less; we may therefore conclude, as C. D. Fawcett did from the Naqada and French dataf, that “organic correlation between L, B and H often tends to reduce the result considerably below the value it would have if the lengths, breadths and heights had been selected from the records in random triplets, i.e. below the spurious correlation.” Some further conclusions may be drawn: (a) Dealing with the gross correlation, we see that in English, Altbayerisch, French and Naqadas, if an individual tends to brachycephaly, he will also tend to hypsicephaly. (b) In our series, the correlation between the indices and the lengths which they do not involve is very low for both sexes, and this is true, though not quite to the same degree, of French and Naqadas. * R.S. Proc. Vol. 60, p. 493. Pearson’s general formulae are easily adapted to the particular cases met with in the investigation. + Loc. cit. p. 461. C. D. Faweett’s Table is clearly based on the French measurements and not on the Naqada as stated in the text. + The only other calculation known to me, of spurious correlation in the skull, is that given by K. Pearson, R. S. Proc. Vol. 60, p. 495, for B/L and H/L in 100 Altbayerisch ¢ skulls, viz. 4008 ; but this should be -4347, which is more in accordance with the values in our Table. I may note the following further arithmetical corrections required in that paper: p. 495, read 7, =19795 for 7, ="1243 and py='4347 for -4008; p. 496, read py=°4613 for pp="4557; p. 497, read py = °4333 for py ="3904. § Loe. cit. p. 461, W. R. MAcponeELi TABLE XVII. Correlation of English Cranial Characters, and Comparison with other Laces. 239 English Series Pairs of characters o e | | No. Gross | Spurious } No. Gross Spurious | | | : é: Roe B/E and H/L 11h -4389+°051 | °419+°052 108 391 +°055 494 +049 B/H and L/H 114 5804042 °598+°041 108 5814043 559 +044 | A/B and L/B 114 “4A78 + 049 ‘478+ °049 | 108 522 + 047 "444+ °052 | BIL and H 11h ‘024 +063 | = 108 | —144+:063 a | B/H and L 114 | —:048+:063 | — 108 | — "086 + ‘064 — | H/L and B 114 072 + 063 | -= 108 | —:061 +064 — | B/E and L 131 — "547+ 041 658 +033 | 130 | —*541+°042 | —689+4-031 A/E and L 120 | —-477+°047 615+4°088 | 117 | —-4754°048 | — 674+ 034 B/E and B 131 682 +032 “753 + 026 130 599 + 038 "725 + 028 H/L and H 120 "728 +029 | "786 +023 || - 117 596 + ‘040 "739 +028 | = French Series * B/E and H/L 860 489 +°018 | 4644-019 340 | 576+ 024 477 +028 B/H and L/H 860 4194-020 | 5274-017 | 340 | -417+°030 | 541 +026 A/B and L/B 860 5864 °016 | 508+°018 | 340 503 +027 482 + 028 B/L and H 860 | —-040+-024 | —- 340 068 + 036 — B/H and L 860 | —:170+°023 — 340 —"143 4-086 —- A/L and B S60 126 + 023 | — 340 211 +:°035 — | B/E and L 860 | —*652+°014 | 6864013 | 340 | —'720+°018 | —-705+-018 | A/L and L 860 | —'548+°017 | —'677+4°013 | 340 | — 6224-022 | — 6774-020 B/E and B 860 699+'012 | -727+-011 || 340 | ‘729 +°017 714+°018 | HA/L and H S860 6394014 | *736+4-011 340 | 694+ °019 “7364017 | | | | Naqada Series t B/E and H/L 130 "284+ 054 432+ °048 166 371 +046 438 + 043 B/H and L/H Tess 595 + ‘038 603 + 037 163 527 +039 552 + 037 H/B and L/B 131 601 +037 459 + 046 163 5944-035 508 + 040 B/E and 1 130 | —176+°056 — 169 | —*111 £053 — B/H and L Hsyl — 184+ :057 = 163° | —:115+°053 = H/Z and B 131 — 001 +:059 — 166 | — 0084054 — B/E and L 130 | —°551+°041 694+ °031 169 | —°6134°082 | —°673+4:028 A/L and ZL 131 — 333 + 052 623 +036 166 | —*514+4°089 | —°651+°'031 B/L and B 130 594 + ‘038 "720 +028 169 695 +028 "740 +024 | H/Z and H 131 ‘660 + 033 "782+ °023 || 166 677 +029 759 + 023 * Paris Catacomb Crania. whole series of results now is in better accordance. The values were deduced from copies of Broca’s MS. measurements sent by the kindness of M. Manouvrier to K. Pearson (C. D. Fawcett, loc. cit. p. 456). + C. D. Fawcett, loc. cit. p. 456. A few slight slips in the arithmetic have been corrected, and the 240 Variation and Correlation of the Human Skull Finally, looking at the correlation between the indices and the absolute lengths which they involve, we observe that the following statements hold with regard to all three series, English, French and Naqadas. (c) Dolichocephaly and chamaecephaly are associated with macrocranial characters. (d) Brachycephaly is associated with platycranial characters. (e) Hypsicephaly is associated with hypsicranial characters. In (c), (d) and (e), the association is due entirely to the spurious correlation. The technical descriptive terms are used above in an intra-racial sense. As usual, dolichocephalic, chamaecephalic, stenocephalic denote crania having their B/L, H/L and B/H indices below, brachycephalic, hypsicephalic, platycephalic denote crania having these indices above, the racial mean. Brachycranial, steno- cranial and chamaecranial are used to denote individuals whose Z, B and H are below, macrocranial, platycranial and hypsicranial denote individuals in which these measurements are above, the racial mean*, These terms cannot be used in an inter-racial sense until we have determined inter-racial means, that is, means of racial means, and little progress has as yet been made with such determinations. The only instances of which I am aware are to be found in Biometrika, Vol. 11. p. 353, where Dr Alice Lee has found a scientific classification of cephalic index and nasal index in living races, based on the means of 51 races. (12) General Conclusions. I look upon this memoir as in the first place contributing new material in a reduced form to the collection of biometric data for man which is slowly being formed. Only when that collection is far more complete will it be possible to state general conclusions applying to the whole field of craniology. I venture to think that the chief aim of craniologists at present should be to table the means, standard deviations and correlations of further long series of skulls. When such tables have been formed for 40 or 50 long series we shall have far more light not only on intra-racial but on inter-racial problems. Admitting that this is primarily a contribution to such a biometric descrip- tion of mankind, we are still I think justified in drawing one or two general conclusions, partly with reference to the English cranium itself and partly with reference to its relation to other groups or series. In the first place it will be noted that our material comes from a single centre, and it may be said not to be a fair sample of the English skull in general. The only reply that can be made to this is that whether judged by the biometric con- stants or by a careful appreciation of the material as a whole, the series appears to be homogeneous, and very different from German, French or other continental * See Schmidt, Anthropologische Methoden, p. 296. W. R. MaAcdoneLi 241 series with which we are acquainted. Further it is closely in accord with a second series from an entirely different burial spot on the opposite side of the city of London. We can therefore assert that in the 17th century there certainly did exist a remarkable type in the city of London, which is unlike any continental type with which we are familiar, and which is markedly different from what some authorities have supposed the English type to have been or at least now to be. It is quite true that isolated English skulls are to be found in museums which provide measurements not wholly in agreement with those of our two series*, but such skulls have often been selected as “fine” specimens, and the total material available in no way approaches the long series with which we are dealing. Until another long series or two of English skulls are measured, and are shown to differ sensibly from our two series, we may I think fairly assume that our results describe the English skull, or at least that of the typical citizen of London, in the only series that at present have reasonable weight. Indeed a proof that we are not dealing with anything very local and exceptional may be obtained by the comparison of the biometric constants of our Whitechapel series with those for the whole of Sir William Turner’s Scottish series which I have calculated, correcting a few arithmetical slips in his Table XVI, and placed for comparison in Table XVIII below. The most marked differences are here in the length, breadth and resulting cephalic index, as well as in the orbital measurements. The latter, however, differ so from observer to observer that they can hardly be used as a criterion. The general correspondence is apparent and considering the heterogeneity of the Scottish series, remarkable. When we turn to our series we see that it is markedly differentiated not only from existing continental types but from earlier racial types in Britain by its extreme length. This extreme length seems closely associated with protuberance of the occiput or even bathrocephalic abnormality. In the first gathering of the Whitechapel crania, which covered Nos. 7037—7127 of our Tables there was a distinct attempt to collect skulls of anatomical interest+, but afterwards the whole material was brought to University College. Of course if any large number of the crania had been stolen between the two removals, this would have emphasised the proportion of remarkable skulls in the series. But we do not believe that any sensible effect was produced in this way; and we hold this for the simple reason that in the crania from Moorfields, there is at least an equally large proportion of abnormal or remarkable crania; the latter collection was made on one occasion and embraced we believe the complete series of excavated skulls. Indeed bathro- * Modern English skulls essentially of the present type are indeed to be found in museums, for example the skull No. 565 of the Oxford Collection, which the cataloguer finds ‘‘remarkable for its length.” Did he compare it with any collection of English crania, or only with those of the crania of other races in the museum? Professor Pearson is in part responsible for the inferences drawn in this concluding section. + This fact will explain the extension of the “Remarks” peculiar to these numbers in the Tables of measurements. Biometrika 111 31 242 Variation and Correlation of the Human Skull cephaly and protuberance of occiput are, if anything, more marked in the Moorfields than in the Whitechapel crania*. The great average length, the comparative narrowness and the resulting degree of dolichocephaly, are of course not the only distinguishing marks of the Whitechapel crania, but they are those which strike the most casual observer. They lead us at once to ask: Where can we find anything which in the least corresponds to these English characters ? The answer appears to be only in the Long Barrow crania of this and other TABLE XVIII. Comparison of Scottish and Whitechapel Skulls. & g Scottish Whitechapel Scottish Whitechapel Character Mean |$.D.|C.ofV.| Mean | 8.D. |C.of V.| Mean |S.D. C.ofV.| Mean | $.D. |C.ofV. C.. 1496 | = = aa =) 323°"), 2) sae B00 = a De: 186°8 |7-42| 3-97 | 1891) 6-27] 3:31 | 178°9|7-15| 4:00 | 180-4] 6-22] 3-45 Bis 1443 |5-94] 4:11 | 140-7] 5-28] 3°75 | 1378/5711] 3-71 | 1847] 4-77] 3-54 HW... 132-4 6-10] 4:60 | 1320) 5:56] 4-21 | 1262 5-02] 3-98 | 1246/| 4:93] 3-96 LB Oe ies 1016 |, — = 95:3 |'— | — 95:35 fe: ase 631-2 | —- | | beeee |: — = | 5067 | — | 2) 503-64 LY WH aie een ee 70:2 | — = ee gene 659) — Bs sa 3974 ye ae SAT 30.07) mes — .| 191-6 | — | —. eos) es as NH 524/321) 612 | 51-2] 260, 5:08 | 49:9/2-93| 5-86 | 48°7| 2-70] 5:55 NB 23-21-78] 7-69 | 243] 216] 8:89 | 22:0/1:85| 8-41 | 23-2). 1-64| 7-06 (L181 | 4:20 L 1-45 | 3:53 ‘ oa 260+ - 4 “ “11! Owe, a9-1t}186| 4-76 | 43-04! ‘a 02 tag | Sratl 160 | 430 eet ae! ae ea eee L188) 5-61 ea eee Pe Aes | ae Oe 34-1] 2°58| 7°57 | 33-44 129-29 ees | 384t} 258] 771 | 33-7H vata Fer GL. aa rea) 2 Cyd = gre | =|) 2" goa eee ae 100GL/£B | 949| —| — am Ngee = 92:6" = 94:8 | — im TOOB eoll” 277 sa eh ee 73.) = Teh (sy |) == Be 100HB/Z «... “Oech ee = 700 | — — 70°5. | — 60.17) — — 1OONB/NH| 44:5 13-80] 8-548] 47:6 | 4:58! 9:64 | 441 | 4-64] 1053$| 47°8| 3:90] 8-16 oy PE es ere eer Caron enc ile me 14 §£4:23 | 5°18 1000,/0,...| 87:3 |5-49| 6-298| 77°8t ee gop | 894] 685] 766g] 821t eS eee 100G’H/J..| 544] — | — 6 a eee pe 546.0 2 _ i al is \ * Special prominence will be given to these features in the plates to the memoir on the Moorfields crania. + Apparently only one orbit was measured, and which not stated; O, was measured from the dacryon, and hence is not properly comparable with our O,. { Average of our Z and R. § With reference to these indexes, Sir William Turner writes, p. 603: ‘ Orbital Index....My obser- “vations on the orbital index in the skulls of numerous races have satisfied me that it presents a great ‘‘yange of variation in the same race, and that it possesses only a secondary value as a race character. “Nasal Index. The relation between the height of the nose, measured from the nasion to the lower ‘border of the apertura pyriformis, and the greatest width of that aperture, constitutes one of the most “important anthropological characters of the face.” It will be observed, however, that the variability, as measured by the coefficient of variation, of the nasal index is much greater, both in males and females, than that of the orbital index, and this is true of the Whitechapel and Naqada series as well as of the Scottish. countries. acquainted. W. R. Macponenu 243 They agree with nothing else on the continent with which we are Our crania do not accord with Anglo-Saxon, with Romano-British or with Round Barrow British, but are in general appearance and biometric constants remarkably close to the Long Barrow British. indicate this in the accompanying Table : TABLE XIX. Comparison of Means of Modern English and Long Barrow Crania. I have endeavoured to | iver vs tae Long Barrow | ; | Whitechapel | Moorfields Crania, Oxford, ena Reihengraiber pabroas oe Character | Crania Crania measured by measured by Schiidel + | Rawiiee } Q > , 1 A a%® Te, eu “ 4 “ i pores | 43 to 137 3s | 19 to 4638 Sees eviAculietere | 6 tol63s 13 to 25¢8 eae roe 37 to 54 gs | = = _ > | _ C 1477 1473 —- -- 1455 1498 L 189 189 190 196 | 193 1873 B 141 143 140 140 142 | 142 B 98 98 99 98 | 98 | 98 _ | 132 130 135 137 | 1405 | 138 | 524 527 533 538 534 527 S | 377 379 384 -- 385 379 Q 308 305 320 314 ieee 324 sidelh rll 70 68 70 — 69 69°5 J ie 130 129$ 134 — 132 132 100G’H/.7... 54 52]| 52 — sy 5: 100B/Z.. 74 75 74 71 | 74 76 100H#/Z ... | 70 68 ‘al 70 73 74 An examination of these characters seems to warraut the statement, which is amply borne out by the method of ‘appreciation,’ that the crania of Londoners of not more than 200 to 300 years ago indicate that a very large proportion of the inhabitants of London at that time were of a type which can only be described as approaching that of Long Barrow men. If they were so then, the type is certainly not extinct now, and we may even venture to describe the ancestor of the genuine cockney as a Long Barrow man. Whether the Long Barrow Man has remained a denizen of London through all the invasions to which the country has been subject, or whether a process of selection has gone on, the London environment being suited only to the Long Barrow type, we cannot yet say, but when long series of modern English skulls from other places are dealt with, we shall no doubt see our way further. Meanwhile the only general conclusion which we can reach * Unpublished measurements for which we have heartily to thank Mr E. Schuster. + We must cordially thank Professor A. Macalister for sending us copies of his measurements on these crania. They originally belonged to Thurnam (see his paper: On the two Principal Forms of Ancient British and Gaulish Skulls, 1865; Table I), but Thurnam’s measurements are doubtful and his averages are incorrect. + Deduced by K. Pearson from measurements given in the German Anthropological Catalogue, and in G. Retzius, Crania Suecica Antiqua, Tafel 1., respectively. : § Mean of 7 crania only. || Mean of 6 crania only. 31—2 244 Variation and Correlation of the Human Skull is the simple but startling one, that the London City crania—from Whitechapel to Moorfields—are far more closely allied to the Long Barrow type than to any other. We do not see how to avoid this conclusion, it is hardly needful to say that, if verified, its importance from both the craniological and historical stand- point can hardly be exaggerated. It would mean that at any rate a section— probably a large section—of the English population are not Anglo-Saxon, nor Scandinavian, nor even Celtic, but belong to a still earlier race. Regarding our present material in conjunction with the other series dealt with for comparative purposes, we must draw very similar conclusions to those already propounded in C. D. Fawcett’s memoir, Le.: The correlations between cranial characters are generally low and vary con- siderably from race to race. All generalisation from individual series—or, as it often happens, from individual skulls—to wide craniological laws seems to be idle. The present great need of craniology is the accumulation of intra-racial biometric constants with a view to the ultimate calculation of inter-racial means, standard deviations and correlations. These will provide the only possible basis for a correct theory of race in man, as well as for a really scientific craniological terminology. Appendix of Tables of Measurements. The measurements are tabled in nearly the same manner as in the case of the Naqada crania. The notation used is identical: Thus cr.=crantium, i.e. skull+mandible ; cal.=calvariwn=skull—mandible; f. stands for face. Thus cal.—f.=calvarium— face bones; dome=the roof of the skull only (Schédeldach). These terms are in accordance with those used in C. D. Fawcett’s memoir, and are close to the terms adopted in Germany. Probably the English use of cranium for what is above called calvarium, and of calvarium for “dome,” would have been better. But it did not seem desirable to change from the notation already adopted in Biometrika. In calculating the constants involving length of skull, Nos 186, 7042 and 7059 were excluded on account of their extreme bathrocephaly. In the age statements, which are of course only appreciations, child =an individual less than 15 years, adolesc. 15—20, y. ad. 20—30, ad. 30—50, and old above 50. During the past winter Professors Thane and Pearson went through the whole series of skulls again and the former not only again considered questions of sex and probable age, but supplied the anatomical notes which are embodied in the accompanying “Remarks” on the crania. I have thus not only to thank him for allowing me to work on his splendid material, but also for the time he has spent on a lengthy anatomical examination of the whole series. Added to these matters all biometric workers at University College have had experience of his ready aid and advice at many stages of their investigations. Addenda. The following capacities omitted by oversight should be entered in the Tables: W. 7037, C=1320 and W. 7041, C=1650. The Editors have to acknowledge a grant from the Publication Fund of the Royal Society towards the printing of the 50 plates accompanying this paper. The blocks for these were paid for out of a grant from the Drapers’ Company’s Donation to the Department of Applied Mathematics in University College, London, as already stated on p. 215. | | MEASUREMENTS TABLE I. Remarks r. side of face defective cranial wall large defects small defects vault and base 3°5 base very imperfect cas old? defects in wall 45 | vad. left side very defective, os pentagonale Sag) 3k a5 ad. defect in vault . : ; : ee : 2 ze 2 . ad. zygom. arches defective. infantile type o “cd Al a 2 oo alos read. somewhat plagiocephalic. post coronal triction ; r. occipital flattening ete 225 pao shat ye ad. defective ethmoidal region ad. defective base, numerous worm. ossicles mbdoid suture; ossicle 18 x 8mm, in r, coronal =a uae old? [suture ee ste, a wal as _. | f. sen? fracture across base. slight projection asi-occipital [poral region A D 2" : - post mortem depression and defect in 1]. tem- a 2 a i Ste oe right side of face, 1. zygom. arch defective. mian bone on hinder part sagit. suture 12 PKs to) I 3 : Br) 49 lee ‘i 33 '. y.ad. twowormian bones, together 37 x 26mm., inder part of sagit. sut. projecting into r. parie- ene ea 5 _ = a -£ very imperfect 48°5 z ee y. ad. large occipital defect. metopic; slight ; coronal constriction; bilateral frontal process of | amous temporal ; slight depression of obelion f.+r. orbit. ad. ace, vi f. ad. with defects r. side. [depression obelion | : f. ad. slight defect anteriorly. metopic; slight | na, gag | — ae rage _ | L. L. side of face defective. slightly bathrocephalic ce 52°5 ae er iN ate ie: . large defect 1. side f. ad. slight bathrocephaly ; d. faint depression obelion fe) ae 25 39 ba 33 tf. ad. considerable defect in forepart of base i i y. ad. slight torus occipitalis J ad. wormian bones between occipital, parietal old. defective inr. parietal [and mastoid ad. 1. side of face defective a4 48'S 25°5 at old. defects in base and 1. temporal E ad. with fracture E ad. large occipital defect {to rv. temporal a m5 a3 a 3 oe ad. with 1. parietal defect. frontal process 5 43 ort ‘+r. orbit. ad. ad. defective 1. temporal and ethmoidal regions | old. defective base [bathrocephaly | a metopic ; post coronal depression; slight parietal and 1. occipital defects; slight os depression [part sagital suture y- ad. metopic; wormian bones in hinder | ad depression of obelion | | ({dylar eminences on basi-occipital bilateral I 2 2 c . ac 3 ie p ne | - > eee At y.ad. 1. temporal bone wanting; small precon- ve ie eR wR eg tas este ad. defects in base, slight post coronal de- ee es os Ne Ree ea im yerad: [pression — | 46 | 22 Bou pales) gene, ite pee in base and rv. malar region | = 47 lee 422 2a) 35. | defect in r. malar region | 23°5 : ; sm pea leas | 35-5 ad. 1. zygomatic defect | 515 ew Saad a? : 55 . ad. sphenoid and temporal defective 1. side. | ‘ked bathrocephaly ; numerous wormian bones _pmbdoid suture, slight torus occipitalis li EXE, considerable defects + —s ’ ré - MEASUREMENTS OF SEVENTEENTH CENTURY ENGLISH CRANIAL TABLE I. . | _ = == = 4 = Lenorus Cincouarrerences Face PaLate Inpices | AnGLEs Series| sox pb |e |u| on uls cn | x | nH} NB oO, 0. G ial eer i 5 4,/0, | 0./0 Re File nleeal RETIN peal S| ; 2 js Dt medl regen , | G. | BL’ | aL’) BL | A/L | B/H \@'H/GB| NB|NH 1 1 |GiG | GLY Nz | Az | Be | & 6 | Pz = a | qa Sees Si | = F ie <= = ——|-——-]- = vont = jo 146 | 136 | 120 2. SI | 325 2 5 70°2 5 5 . < | q ¢ wat Ce 3 2h 525 oo Fo) oa pare 43 33. St 35 177 72% 77°7 | 72°3 | 107°4 = = 707 ss 68°6 96 = me = cal. ad. r. side of face defective re 3 56°5 | 25°5 | 44 | 45 33°5 | 34 52 45 719 | 70°9 | 101-4 451 | 76:1 | 75°6 | 86-5 J102 [62°5 | 77 0° = = = lad. ; 4 3? mgt] 97 | — | 114 525 | 374 | 311 92 | 127 | 49° | 23° | ars | 40:5 | 305 | 32 | — | 35°95 754] — | 754} — | — | 75 46:9 | 73°5 | 79 | oii Be |lcabenl ES oe Rane ; 139 = a5 cones z aail es i ee = i i (oR = cal. ad. small defects vault and base 5 | : 140 a7 iG mais jaz 370 a Se : e = eae Nee ela #3 a 67°9 | 110°2 oe S| SE oe) cal. ad. base very imperfect 6 2? — | $8} 125] 110k — | 361 | — 89 x 475 | 2 42 42 34°5 | 33°5 | 4scs | 34°5 69"1 a 5 2 8 8 as = = = cal.—f. old? defects in wall | 9 2 8 ale . oO, ex 7 = . a e 7 \¢ 140 | 99 | 140 | 114 22 10'| 30. 8s ae a 4 A i PG ae ae oe 747 44 2A SION WTS: ‘ 5. 73°°5 | 405 cal. y. ad. left side very defective, os pentagonale H a9) les 13621 2 eal eat aie sie oe 50 44 | 45°5 | 33'S | 33'S | 44°5 | 325 | 73'3 | 733 | 733 ge 3 Ae 80°1 42 761 | 73°6 | 73 94°5 15975 | 80°5 | go°” | 85 | 31°°5 | So° | cal. ad. zs | 10 |#s 127 | $4 | 122 | 109 505 | 381 | 287 76 = alia 26 4 z ee | (v4 6: 66: ar, a SW} Sars, : : ar = eal.-f. ad. defect in vault | J 47°5 3 35°5 | 34 33°5 | 43 33°5 | °9 66°3 | 69 6°3 | 104 82:2 42°1 944 | 944 | 77°9 | SO FS 75°°5 | 39°°5 | 14°5 | 25° go° cal. y. ad. zygom. arches defective. infantile type of <4 forehead. somewhat plagiocephalic. post coronal é 102 | 140 | 120 526 | 381 8s 132 8: 22° ‘oO I i 4 5 . q q a a5 A a 5 g ¥ c al F - constriction ; r. occipital flattenin, | 12 | é 103 | 138 | 119 h 537 385 3 z pe, aD ED hes 30'5 9'5 3! 3 175 | 749 3 bee 104i 7a 404 75°3 | 71-9 | 62°7 | 94°5 J 62°'5 | 78 3975 | 11° =| 28°*5 | 89° | eal. ad. s 4 | 13 |¢ to2 | 128 | 12h 528 | 364 = 75°5 | O81 | rir | cal.—f. ad. defective ethmoidal region | ‘ : al | = cal.—f. nad, defective base, numerous worm. ossicles 14 | 2 | 90 | 129 | 109 k 484 356 | 201 = lees . < = | in lambdoid suture; ossicle 18 x 8 mm. in r. coronal | 751 | 74°6 | 100°8 = 15 z 94 | 127 | 16h 485 | 343 | 309 s = | 80-9 75°6 | 107"1 a | cal.—f. old? [suture eels Pallcod | me ae a Meals | | | | | | | athe E sen? pecture across base. ais Projection le 29 Se ee & 2 23 42 42°5 | 355 | 345 14 34 67°9 | 65:2 | 67-9 | 65:2 | 8s | 5 Yee [res | ece 5 o ies | [oes = as1-occlpita poral region 17 | 3 | 89 | 132 | 116 513 == — | 52 23 4o — | 32-5 Cane a 375 69-3 608 69 oe eae lek Ge | eo | we | 2 20 5 pase (OS NG ee se | 86° } cal-ad. post mortem depression and defect in }. tem- lag |"s sey teal rex Iles agi renee Y oe | | Ssh EES 3S | 74 4255) 15 27°5 | 89° | cal. ad. Meht side of face, 1, zygom. arch defective. 39 s 2. e O 352 | 293 9 2 22° 2 oe ; = f : 2 5 2 5 7 19 9 0 | g2 | 2M tinh 496 | 365 | fee 9 49 5 | 4° 41 33 32°5 | 47°5 | 32 799 | 718 | Tas | pe He 2 69:2 45°9 82°5 | 79°3 | 67°4 93 67° 74° 30 me) 8 | ase ae one on hinder part sagit. suture | | 3 | | 4 | } | | cal. ai vad: swoonmian bones, together 37 x 26mm., | 20 | 90 106 ase Ci ¢: in hinder part of sagit. sut. projecting into r. parie- 21 | ¢ 136 | 101 | 125 | 103 h = | 293 et |) Re oh 3 45 S72 C72 aR 78 DZNaNORE i727 Ware er5e liz62 87° ge va very imperfect | ag | eet y- ae: dene ceninttaN detect metopic; slight | 3 I WWou aid eas a coronal constriction; bilateral frontal process of | cae 44 ag b 533 380 | Es Es a 44 34°5 £2 bie Ea = | 75:8 | gx ay 784 Squamous temporal; slight depression of obelion 24 | ¢ 134 ES 487 aha | 295 = = rE = = = | 771 cal. ~f.+r. orbit. ad. : | 125 é 2 109 26 368 | 208 z = _— 79°3 | 73°4 | 1081 =s cal. - f. ad. with defects r. side. [depression obelion 525 | 308 | 29 2 2 : | 126) |g 140 118 327 | 388 | 309 = a 52°5 44°5 34°5 751 | 67-2 | 74-7 | 66'S | 118 Ws 8 les el es a = eal. —f, ad. slight defect anteriorly. metopic; slight | 27 2 138 | 13h 495 | 366 | 304 52558 |i = 45 =" ||k30, = — | 741 | 70°9 | 73°7 | 70°5 | 104°5 =! % 66: 9 5 72 43 13 | 30 85° | cal. ad. 1. side of face defective. slightly bathrocephalic ot 140 | 107 521 372 299 Raalfpran|| ein Were pean leer rae See | ce cell ee Ie 273 | 107-9 i = | | sat ad. pares defect 1. side 5 3 | 115 h z 2 203 po a 25 33°5 | 45°5 | 32 75°3 5 75°3 | 65 115° 272 | 54-3 yd a3 - oy, ay ae eel Pea —, | calf. ad. slight bathrocephaly 30 : is ae i a8 ae a 5 = — | = =a Bo | 4 el 7 543 | 84°6 | 83:7 | 703 | 93 doks 7° 40 13” | 27 83° ot old. int depression aicten | 11g ht 48 300 | 310 aa Za = | 784 | 71 110°4 es | cal.—f. ad. considerable defect in forepart of base aH 3 140 | 19h 318 \ 301 oD es -- _— = = = = 727 | | | = | | = eb =sfe y ad. slight torus oceipitalis B | | 113 seallis6oNloe = a Fegee | ae = | | 761 2°3 | 105-3] — oa | = || dome. ad. wormian bones between occipital, parietal | 3 3 110k 495 362 393 5 = 45°5 25°5 44 aaa || 52 — | 74:2 | 72° 4g | 72°6 102"2 |} — | 526 el 716 | — roe Joss | 73%5 | 38 ioe 75 ae gait -f. Qe wcelestive inr. parietal [and Paste g 109 }) 524 | 376 a | | = _ — | 74:6 | 701 | 1065} — | | = SEs 3 3 3) (24 | 54° J cal. y.ad. 1. side of face defective a] | 105 h 497 | — | 280 = = Es i = | 73-2 | | Eta = = == = = — |eal.-f£ old. defects in base and 1. temporal Be : 110} 503 | 364 291 = = + a a = A 7o'2 | | | =| = | ad. with fracture | 113 509 | 360 | 309 a: 2 si = oe = | : 68°5 | ] eal ad. large occipital defect to r. tem 1 + y | | 13h 505 | 360 308 = a ia 43 ae Wich) -- — | 83:5 | 716 | 83:5 | 71°6 | 116:7 84 | ad. with 1. parietal defect. eta BrOUaes 41 | 2 | 107 h 476 | — | 285 = es = = 75°7 | 72°9 | 1038 = = +r. orbit. ad. | oa eile | eles lle |e lSle ls = eee antes | “ad a ones ee > ee 3. any ara ella 0 3 anc wae 3. eulleeae Z i : SD SEES athrocephaly 43 ‘ fae 5 | 49°5 | 39 34 34°5 J 40 33°5 | 789 | 67°8 | 78:9 | 67°8 | 116-4] 75-9 45°7 83°9 | 885 | 83:7 | 84 [63° | 75° | ni nal ap ap ad. metopic ; post coronal depression; slight | 44 |-¢ gh 393 = = = | + zB 9° fecal. ad. r. parietal and 1, occipital defects; slight as : | 102 7; 281 = F = Ss 768 68 113 post coronal depression [part sagital suture a 2 | 4 307 89 135 | 53 ‘i = = eel = — ; 74 6-7 | 141 A -— |eal.—f. y. ad. metopic; wormian bones in hind 47 | 3 | a = 8 || — | a5 | 2g5 | aoe fae | age | 2° 4o? | 746 | 72 | 74:2 | 71° | 103°7| 764 | 45:3 | 75-3 | 73:6 56 W665 fya> acre | gm laine | qe [oth 9. depression of obelion a | 12h 30° 3 405 4 335 34 46 34 a |e . "2 3 ate 9 5 | 73 4or'5 | 8 2°°5 ) 81° | cal. ad a i ee Sets | 49 | | ail 307 es aj x Zn 74°5 | 71'2 | 104°6| 736 475 827 | 829 | 73:9 | 95 | 67° 73°5 | 30° Sa | eat5a cal, ad. [dylar eminences on basi-occipital bilateral 50 2 ea ay) = | -- | Fz =e. | = 75°8 67°7 | 1118} ee | 3955) = = cal. y.ad. 1. temporal bone wanting; small precon- a % | 1405 115 h ane 83 = ||45 (22 39 — | 32°5 | 32 43. | 36°5 na eae fe | IE) EO) = =F s= | = | | salt f ad. putes in base, slight post coronal de- ! 2 | 1460 2 wre = >= — =: lis = | A9l bes ee | oem 7273 478 §3 — | 84: = Sa | (Cee ae GEG i 53° ¢ | 1315 17 3°7 = cea A7, 5 | 42 lie an 5 a ; 70°8 | 65°6 | 108 | Sey) lee = | 88° | cal. ad, defects in base and r. malar region [pression rake 114 300 = Wee Di It 35 35 48 36 742 | 747 | 73:4 | 73°9 5 = | cal.—f. ad 8 ¢] - | 139 | 117 h a } 515 5} 47 | 47 | 35s | 35:5 | sis | 40 | 70 | 234 |) 73:9 |) 9973 a SO) S375 95 162%5 | 76° | 415 | 10° | a1 vs BET | | i 2 7 a Se >: 55 7505 | 4 ? | 71-1 | 70:2 | 70°7 | 99:2) — 476 | 75:5 | 75°5 | 77-7 [102 | 66°-5 a) ee 86° cal. ud. defect in r. malar region 55 | | | | ~ =a | 75°3 | 74°7 | 100°7 | ap = Se eas = = 74°°5 | 39 TO%5 | 28°5 | 85 gall Ne a 1. Zyeotoatie defect g 95 | 129 | 13h eialte te | | | | | cal.—f. ad. sphenoid and temporal defective 1. side. | | Pear, peea loon ieee = - — = = 2 = = cai 2 Ad =| | | | | marked bathrocephaly ; numerous wormian bones | 73°3 | 71°7 | 1023 | = = = le | = =| =a ene aes ss alent torus occipitalis > = . = ! ae a -—f. ad. considerable defects Nos. 8 and 48 not seen. es eat ; b= Srey ue peed 3 ea f Sie: Can : pat See) ; 5 462 33 sayeee 22 eS reas $52 33 52°28 11 Se =, Aa a a ee eee LP sy oe et : z Caos < ro * ag te : =. ee Ul " —— J a i a : E ae oe 2s AOS OE he SS fe ee a se be. ; ‘ oe an pegns s. aa 7 a re hat ee apt TEL... LF De tay Se BR ey el BE fr? i : = eee z P ju < ig / nA ~ cE = ques = = a a ea at al = = : % 2 i 2 i : 3 Pe : - : = ' 7 = i i ; : E ; = 3 Z 2 = = Zn a ey fs ; s a 2 Fs aa , “ ~ ~ ~ ; E ah +f : ‘ ¥ = > Ae. 4 ie siican enema een ascent ° So ; a noel ee —himenneines ae 4 \ , “ z : cat “4 y MEASUREMENTS OF TABLE II. Facer 39°5 42°5 2°5 i. 1. malar defect. 32° 3815 33i5 25°5 41°5 42°5 31°5 57 26 41 40 30°5 |. 33 | 32°5 |. 34°5 |. 36 32°5 | 34 49°5 24°5 1o>) is) Un = Remarks f. ad. hinder part defective. infantile forehead f. ad. small ry. parietal defect. ossicle of aste- b bilateral. left mandibular articulation imper- y developed y.ad. both zygomatic arches defective. depres- 1x. frontal. slight precondylar eminences on i-occipital, bilateral ad. l. left zygomat. arch and rv. maxilla defective pld. 1. malar detect. [arch metopic ly. ad. defect in yr. parietal and 1. zygom. ad. defect centre of base. small occipital s. traces of ossicles in lambdoid suture. de- sion in obelion +r. malar bone. ad. ossicle to left of X. y.ad. small defect r. occipital. slight de- . ad. fractured base [pression of obelion pld. slight bathrocephaly ' old. defect centre of base '. old. ethmoidal defect. Projection 3 x 3mm. at on into foramen (? rudimentary condylus tertius) enile. both zygom. arches and centre of base ctive. metopic suture nearly closed. bilateral tal process of squamous temporal. small torus pitalis. traces of ossicles in lambdoid suture y.ad. defects in base, ethmoidal and |. tem- 1. metopic. extensive flattening of obelion. small teral precondylar eminences on basi-occipital * y. ad. ossicles in hinder part sagit. suture defective l. zygom., 1. parietal and occipito- poral. negroid appearance ? |. defect frontal and |. side face. irregular line smbdoid suture defect r. frontal and malar Id. defect 1. side face | old. sagit. sut. completely obliterated ad. right temporal defect. wormians in lamb- .ad. 1. zygoma defective {doid suture y. ad. r. ossicle of pterion y. ad. slight ethmoidal defect, r. ossicle of [pterion projection 8 mm. long from hinder margin tternal pterygoid plate on r. side ad. projection 4 mm. long from hinder margin ternal pterygoid plate on r, side. metopic suture sting for 23 mm. at upper end ad. frontal defect | 1. oecipito-temporal defect, face defective on sides. heavy brow ridges. slight bathrocephaly ad. slight ethmoidal defect [fective Id. large occipital defect, both zygomata de- both zygomata defective | ad. small occipital defect | ad. base very defective ad. centre of base defective ad. metopic suture persisting for 35 min. at rend, traces of trans-occipital suture for about m. ossicle i in fore part 1. squamous suture | ad. slight ethmoidal defect. post parietal ning and slight depression of obelion. traces of -occipital suture for 45 mm. on 1. side i. large occipital and 1. temporal defect, three es in lambdoid suture, largest 20 x 10 mm. right temporal defect MEASUREMENTS OF SEVENTEENTH CENTURY ENGLISH CRANIA. TABLE II. Lenotus Cinco MFERENCES Pace PAvaTe Inpices ANGLES | Serics| =| Sea |e | 7 ] A rr See ee = = Tallin =| E Fy Remarks | No, [Sex] ¢ Plu | u| s | Q@|@H| cp) J | NE NB| 7 JR jipate ison (aCe BIL! | H/L' | B/L | H/L | B/H |\G'H/GB| NB|NH a 2 1)GJG,] GL [Nz | 42 | Be | % | Bren eRie . ees =| | | Ses aes £18 fee | eae | le api Peal Meee a 2 | | | = = | | cz | ota fe = == ||| | — I | 109°4 —— |cal.—f. ad. hinder part defective. infantile forehead 7 | ¥ 11375] 180 |) — | 08 | 364] 305) — | — | — | — | | = | 76:7 | 722 | 1061) 9 — — | - calf ad. small r. parietal defect. ossicle of aste- | | | | | | | | | rion, bilateral, left mandibular articulation imper- 58 | 22? 1305 | 18 $6 | 380 | 302 | 65 il ee * eeelaoteell oss F ‘ | : | feetly developed | 305 | 186 | 186 | sii | 380 | 3024765 | S2 119 | 46 23°5 | 40°5 | 40°5 | 30°5 | 30°5 | 48°5 | 37 72 | 69:3 | 72 69°3 | 103'°8 | 79°3 sui 75°3 | 75°3-| 763 | 95 7! 69° | 40° 15° | 25° 84° eal. y.ad, both zygomatic arches defective. depres- | | | | | | | frontal. slight ly] renee | | | | | | sion r. frontal. slight precondylar eminences on 59 | ¢ a Eales 4. | | al | jabael-cectpitals bilateral 60 | 3 189 34 | 373 Z A, (eae open haere = tees e eae | peor 253 = | | | dome. ad. 61 | 3? 180 is | 373 Fi | Biya eeee (4B 212250 eee Zu all Seog SiS aL = NAS) NGTES EN 255 | ETS ALO 469 | — | 774) — = — | — | — Jeal-ad. 1. malar defect. | 62 | 3 750 234 ae il Peale = eal 22°5 | 41 Ak 33°5 | 33, ae ee a ee ae | ee 1038 pe 43°3 80:5 | — 44°°5 | 16' | 28°5 | 93 cal. ad. left zygomat. arch and r. maxilla defective | 63 | ¢ 180 | ae eS a 5 | 36 |S 3 25 : Aon ee 37°5 50 34 742 Gazi 73°8 | 71°7 | 102°9| 88-1 44°60 81-5 63 45° 15 | 30° 85° eal. old. 1. malar defect. [arch metopie | 65 |¢ Sat 6 he s Sen) {48 | 23 ) 42°5 | 41°5 | 33'S | 33°5 J 46 — | 761 | 68:9 75°7 68'5 | 110°5| 75 50 80°7 =s 2 | 66' 74° | 40° | riS- | 29° | 85° cal. y. ad. defect in r. parietul and 1. zygom. | | | | | = = = 719 | |) cal.-f ad. defect centre of base. small occipital | es | ; | | | | | | | | | traces of ossicles in lambdoid suture. de- | | 1290 | 176 174 | Bsalltscoulsaali ale ; Ven lat 3 = | | ion in obelion 67 |) 1425 asi | — | 209 | 38 leat Vee | 2285 | | AUS) || 11138 | 75°9 | 69° | 75'4 eo tog | — = SS | | = +r, malur bone. ad. ossicle to left of 2. 68 | @ | 1170] 167 peueea ees | |e Sa ee | — | 758 | 681 jaz) — — = Sil = = cal.—f. y.ad. small defect r. occipital, slight de- 69 | s | 1470] 185 188 | 481 | 350 | 29: | | — | 81-4 | 7574 | 108 | eal-—f. ‘ad, fractared bi peariontoRebeal 8 88 13 | 381 | 303 | 66 Age |< pare ine a a aa = | lpomess ‘4 8 i a = 2 E xs Saal 5 cal.—f. ad, fractured base ression of obel |) 2} 1s an S804 F305 NGOs | 28 ese (2Sisp | AusSN sziSs | SUSR S85) sie ao aes 78 | 73 | 708 | 993] 725 || Sil fprsi9)| 748 | Bre | 99 | 60? Saleeaolitea (leak ath mitcnresici: car } 71 | @ | u60} 178) — | ‘oo | 349 | 275 | | == Ps en Fl = cal.—f. old, defect centre of base : | =| | | | 75-4 3°7 | 1185) — — | cal, —f. old. ethmoidal defect. Projection 3 x 3mm. at a a sau |.389)/:310]a7 | =") = Wis7 26 |r Irao: | 33%5)|'33) kaon |iaz geal 574 | 373) 4 Baby 1550.) 355 ae SIE, 102 7. S40) 4@2 i: Od 350 Y a Pa | oy ww bo ter is nit 5a , % AS & AFI tas or wet wo . = MEASUREMENTS OF TABLE III. Remarks R | 32°5 ie ad. left mastoid defect. slight post coronal iction [asterion — ad. centre of base defective. left ossicle of — ad. small |. occipital defect d. both malar regions defective ad. ethmoidal and small 1. occipital defect y. ad. ossicle in forepart of squamous suture r. $555 38°5 34°5 2d. metopic “>| y.ad. large occipital, r. temporal and eth- l defects. metopic. small ossicle of \. 1 x rem. 2 ? 1. temporal and r. zygoma defective. paired idylar eminences. slight post coronal con- on __ ad. metopic [precondylar eminences ad. several defects. slight median and paired = Ad. ad. with large defect, forepart of base. or extremities of condyles united by osseous : see reproduction _. old. base very defective y. ad. with r. temporo-sphenoidal defect. ossicle of pterion on 1. 34°5 | defective 1. zygoma _- ad. slight depression of obelion r. temporal defect __|ad. base very defective __ ad. central defect in base. two ossicles in r, ‘lambdoid suture ad. 30° _ infra-orbital suture on face, both sides 34°5| defective r. zygomatic arch. post coronal con- on. paired precondylar eminences, left larger __ \d. rv. temporo-frontal and r. half face missing. us crotaphitico-buccinatorius (Hyrtl) ad. 44°5 37°5 1. side face and frontal defective. slight post al constriction y. ad. __| ad. forepart base defective 3M : [cinatorius 33 | torus occipitalis, incissura crotaphitico-buc- ad. central part base defective Ea eaexel {defects 33 occipital, slight r. temporal and 1. zygomata ad. tace very defective 33°5 occipital and |. temporal defects y. yr. precondylar eminence __ y. ad. two ossicles r. end of lambdoid su- rach 15 x 10 mm. ad, defective base 4's ad. 30°5 defect. 1. maxillary. metopic ad. defective base y. ad, _ad. metopic ; metopic fontanelle. wormian mm. hinder end squamous suture old. fracture of base _y. ad. spheno-ethmoidal defect. r. ossicle rion, faint post coronal constriction ad. slight depression of obelion ad. [lambdoid suture 41'5 & R aa __ad. right malar defect. some wormians in 35 _ ossicle in fore part r. squamous suture. enoid produced upwards ad. slight l. parietal defect. slight bathro- | ‘ A ~ MEASUREMENTS OF SEVENTEENTH CENTURY ENGLISH CRANIA. TABLE III. = = = 58 rE ‘1 ANGLES = Face PALATE Inpices Lenatas CrmcuMFERENCES: a £ Ls —— ——— Remarks u —— =———— ie is T | | 0,/0, | 0./9, | 5 y 2B | y. 0, (2 G, G. B/L'| H/L'| B/L \ A/L | B/H |\G'H/GB| NB/NH| “74 a NZ) Az Bek Ay 4, PL sx| c | r|u|x2|o|oe|a| om |ze)u|s|q)an|ca| s \nx| ne) 7, tp | 1 oR if a | Peet ! Piel d Sole) 2 i ey es ese | ‘| aes =| tk Salls 57 |e || eee | Ss : : 3 = |— SS re = B | = ales ; Allee 4 raill) , ve ll ed — |val. y. ad. left mastoid defect. slight post coronal — | 182 | 182 | 182 | 130 | 95 | 127 | 107 ror | 498 | 356 | 290] — | 90 | 129 | 46 | 25°5 | 43 | 43°5 | 32°S | 33 38 TAA COIS) ZX) | E98 Heats EES |) E619 |) > constriction {asterion _ 6" | cal.—f ad. F s ee 182 | 185 | 184 104 137 | 116 95 | 513 | 385 | 309 | 65 94 | 135 | 50 33 44 445 | 315 | 30°5 | 48 375] 74°6 | 74 75 74°5 | 100°7| 65°9 66 716 | 68°5 67° | 72°"5 | 405, 95 | 31° 82° | cal. ad. infra-orbital suture on face, both sides 1225 | 180 | 182 | 181 go | 121 | 103 } 99 | 405 | 350 | 273 | 68-5 | 85 116 | 49°5 | 24°5 | 42°5 | 42 35 34°5 145 34°57] 70:3 | 66°5 | 70°7 | 66'S | 105°8| 80°6 49°5 | 82°3 | S21 65) 73°°5. | 41°°5 | 975 | 32' 83 cal. old, defective r, zygomatic arch. post coronal con- o | | 5 | | striction. paired precondylar eminences, left larger = 185 | — | 186 | 136 - | 130] 112k 104 | 514 | 362 | — | 615 | — - 495 | — | 41'5 — |31 = — = = 731 | 69°9 | 104°6 — | = 747 | — = — = a — | cal. y.ad. r. temporo-frontal and r. half face missing. A } | | | 1, porus crotaphitico-buccinatorius (Hyrtl) 1570 | 19g | — | 197 | 138 | 100 | 139 | 118 | 105 | 535 | 303 | a4] — Be) | =| — = = = |= || = - | — | 70 706 | 9973 fae = = |= = — - - = — | cal =f. ad. ; : = 194 | 194 | 195 | 134. | — | 126 | 112 107 | — | 377 | 303 ]73 | — — | 51 _ See ey? = — | 6971 | 64°9 | 68:7 | 64°6 | 1064 = — — | $43 60°"5 | 78 41°"5 | 12' 29°5 | 90° | cal. ola 1 sds fee and frontal defective. slight post | | | coronal constriction 1170 | 169 | — | 170 | 128] 94] 124] 109h | 93 | 484 | 352 | 2900] — - = =V 2S = | SS | SS _ - | 75°3 | 72°9 | 1032] — = | =| = -- = = = — — Jeal.-f. y. ad. — | 136 | 16h —}—|—|34] — _— — | — _— -- = = = |= — 1059 | -- cal.—f. ad. forepart base defective | 174 | 174 84 124 | 106 | 98 | 477 | 343 | 279 | 70 | 120 | 49°5 I 4o'5 | 41 33 34 45) 3! 5 | (23 713 | 73 71°73 | 102'4 |- 84°3 424 81'5 | 82:9 63° 74 43° 14° 29° 88° | cal. ad. , [cinatorius 164 | 164 $5 | 116 | 104 | 93 | 461 | 320 | 274 | 55'5 109 | 45 | 21°5 | 40 39 33 33 42?) | 35 7 78 7o'7 | 110'4| 68'5 47°8 82°5 | 84°6 65° 76° 36° 10° 26° 86° | cal. old. torus occipitalis, incissura crotaphitico-buc- — 1177 hy 13h sor | 353 | 393] — - — — | — _ ~s = = SS — = 768 -- — = _— _ — — — — = — = cal.—f. ad. central part base defective | — | 185 | 94 | 122 | 107 h 95 | 512 | 364 | 29 = | lh = — = = — — | 74 65°9 | 112°3 = — = — = = cal.—f. y. ad. , [defects 169 | 169 $4 | 120 | 102 90 | 480 | 343 | 251 | 61°5, 10 18775) nA | 23 405 | 41°5 | 33°5 | 33 al 33° 787 | 71 78:7 | 71 110°9| 70°7 50 80'7 | 79°5 65°°5 | 73°'5 | 41 9°°5 | 315, cal. ad. occipital, slight r. temporal and 1. zygomata a — | — } — | #45 | 100} 142 | 119 — [s525|) — | 317 | = Tan ee 36°5 —|- = — | 102°1 = = = — = cal. y.ad. face very defective = — |} — | — 143 | 100 | | 116k oat Stn 1 99 130 | 49°5 | 22°5 | 43 40-5 | 33°5 | 33°5 | 47°5 | 35 _ - — = _ 137 45'4 779 | 80°7 eal. ad. occipital and 1. temporal defects | 1505 } 192, | — | 192 | 144 | 95 | 127 | 15h | 98] 535 | 383 | 313] — | = - = 1153 661 | 11374 — -- - — - - Cte ad, slight perce defect. slight bathro- | | | | | | cephaly. r. precondylar eminence 1180 [177 | — | 178 | 131 | 93 | 126 | 103k 99 } 495 | 342 | 275] — = = = = = _ — | 73°6 | 70'8 | 103°9 - cal.—f. y.ad. two ossicles r. end of lambdoid su- | | | ture, each 15 x 10 mm. | = | 176) — | 177 | 142 | 94] — | 108 296 = = = — | 80-2 - = — | — |icall=f. Vad: Tea base — | 178 80 | 128 | 89 | — | 105 h — | — =) = = == 701 = Gone, gue | 1305 | 179 | 177 | 177 | 137 | 101 | 132 | 110 3 | 293 | 68 8S | 122 | 50°5 | 25 Sat CES We | cy? 35°5 | 77°4 | 74°6 | 77°4 | 74°6 | 103°8| 77°3 49°5 — | 73'5 64°°5. | 75° | 40°5 | 7° | 33°5 | 82° J cal. ad. defect. 1. maxillary. metopic rash]. 1/184 | 128 be = | 106 t | 274 lis | = = = 69°6 a =|} =] = = |= — |eal.-f. ad. defective base Bee Zonta] 075) | 1250) 89: = O7 pH = = = =a = pz = = = = dome. y, ad. 1445 1179 | — | 179 | 142) 100 | 133 | 114 LOH | || | = 79°3 | 74°3 | 106-7 — | — eal. —f. ad. metopic; metopic fontanelle. wormian i | | P i aah ie | | | a | 26 x § mm. hinder end squamous suture = |e eK SS) Se = 1 eam a ts a ee | Sr ee | - | 79°99} 65 | 108:9) 9 — = =a = = | — | — |eal.-f, old. fracture of base = || 2 es 2 SST |e = = = = = — | 75°3 | 6774 | 111°7 _ _ —|/— — — ]ecal.—f. y. ad. spheno-ethmoidal defect. r. ossicle J: P € Peri | Nereovicall 7 =| = | | a | of pterion. faint post coronal constriction Z 2 | = = = — | 801 = = = = — | dome. ad. slight depression of obelion 1395 [187 | — Aagilt 163971 | aman |e |= |= = — | 749 | 67°9 | 110-2 - = cal.—f. ad, [lambdoid suture | a5 135 | a aA 306 ie Be | fe ed 25'5 | 43 meat 34 | 44° 36 75 | 73°7 | 719 | 74 971] 79°3 49'5 | 79 | — 62°°5 | 77, | 40°°5 | 11° | 29°5 | 88° J cal. y. ad. right malar defect. some wormians in 555 oi 305 | 73 | | 35 | 51'S | 25°5 | 42 | 405 | 34°5 | 35 47°5 | +3! 77°5 | O81 | 77°5 | 681 | 113'°9| 73°7 4975 8: 843 63°°5 | 74° 42°"5 | 18° 24°°5 | 92° | cal. ad. ossicle in fore part r. squamous suture. | | | | alisphenoid produced upwards Ea SRS NET LEE NE 8 CTT ON NIECE POAT TIC ee ot Faccepagtmtrs aie ed foneh SEH SCM pt eg: { i] they Aim re See ee nc ae NV RS = onneeeer awe ~ a > . Se ea MST er aces Oe ne ac ee es i \ Ve SN ete ote a a Te tee ee fre ) 10h i Re fous hi 7 ht M45¥ L20: % 1325) Laas 7 way RO {17 ee MEASUREMENTS OF _ TABLE IV. Remarks |. ; ad. r. temporal defect. aperture in r. frontal ; mm. with sloping smooth cicatrized margin ily result of separation of sequestrum due to | [tinus faint post coronal constriction, torus pala- d. occipital defects; apex of occipital squama ed. wormians in lambdoid suture ad. ethmoidal and temporal defects ad. 1. temporal defect. occipital squama ged upwards ad. small occipital defect [ x 33 longit. mm. large defects on r. side. ossicle of \. 50 trans. y. ad. r. temporal defect and base fractured, post coronal depression. ossicles in 1, lamb- iture. persistent frontal suture, 3 cms. ad. torus occipitalis old? some bathrocephaly ‘ad. slight depression of obelion. faint post 1 constriction d. large temporal defects. faint post coronal sion. ossicle of pterion bilateral. ossicle in ydoid suture and small one in r. face very defective. post coronal depression slight temporal defect. 1. third molar erupt- iedian prominence 7 mm. wide, 4mm. high at margin of foramen magnum (? third condyle) ‘ry. orbit. ad. wormians in outer part of 1. vid suture arge defect in vault. 1. pterygo-spinous bridge ad. very defective base. faint post coronal d. [constriction Id. 1, temporal defect. post coronal depression 1. facial defect. wormians partly united in d. [l. lambdoid suture AW pe ult4o:5pile 3 ALN ZO'S. |/33" 41 36°5 | 37 d. faint post coronal constriction. third oc- condyle somewhat to 1. median ple. low ele- 8mm. trans. 5 mm. from before back. 5 mm. terior margin of foramen magnum, bearing x facet ld r. malar, 1. zygomatic and small r. frontal flattening of obelion ad. fronto-ethmoidal defect. very large left foramen ovale subdivided ad. post coronal constriction. r. ossicle of bilateral pterygo-spinous bridge ile. 1. zygomatic defect. r. pterygo-spinous 435 | 45 3505) Ile3o ad. large l. temporo-parietal defect d. small r. occipital defect. bilateral ossicle ld ? [of pterion large defects d. with r. malar defect large 1. temporo-parietal andr. facial defects. ; depression of obelion. r. ossicle of pterion old. | ad. small r. occipital defect. faint post | old ? [coronal constriction ad. with r. sphenoidal defect | . ad. metopic; post coronal depression. y developed inion 36. temporal and occipital defects 1. facial and temporal defects. ossicle of X. mm. No. MEASUREMENTS OF SEVENTEENTH CENTURY ENGLISH CRANIA. TABLE IV. TENGTEA Face Pavare Typices ANoLES = =| eee — -— T Remarks | — i ; ; ees 04/0, | On/O, fa y | B | A | On | NB} oy Ch 3 rn | G& | Gs | Be] mye’) Bye | njL | Bi \G'H/GB| NBN 1 a 1 GL] Nz | 42 | Be} a | 0, | Pz | =e = = a See a = ee ee = == — | = | a a ee ky we = O 64" 1086 | — | cal.—f. ad. r. temporal defect. aperture in r. frontal Loz} i295) (MUL7i | d AS I | 1515 mm. WAekaloing smooth cicatrized margin | | probably result of separation of sequestrum due to injury ‘ ica Leen 7 = ore I 10° ey Hi 369 6 | 65-4 | 74°6 | 65°4 | 114 819 46'2 | 82'9 | 83:9 66%5 | 72° | 415 | 15° | 265 | 87° J enl. ad. faint post coronal constriction, torus pala- oy 1 nit me i aoe ae ae Hes 33 a Pate 771 ee 106°3| 75°6 478 81-7 | 82-7 67° 74 | 30) 9° | 30° 83° J cal. y.ad. occipital defects; apex of occipital squama | | produced. wormians in lambdoid suture or | 132 | 114 h | = = = 75°3 | 69°5 | 10873 = { — — _— eal.—f. ad. ethmoidal and temporal defects 96 | 126] 14h = 75:7 | O81 | 1r10r | i eal.—f. ad. 1. temporal defect. occipital squama | | prolonged upwards 98 | 12 117 hk } — — 749 | 69 1086 = | = | ecal.—f. ad. small occipital defect [ x 33 longit. mm. 100 | igi | 122k 24 44 | — | 365] — | 54 36 - — | 69°S | 70'8 | 98°6 —~ ||| 45370 S2c0n) 66° | We Wer = == — | cal.ad. large defects on r. side. ossicle of \. 50 trans. S614) == toh | | = 73:2 ~ — | — — = — |= — _- — — |eal.—f. y, ad. r. temporal defect and base fractured. | | | | slight post coronal depression. ossicles in 1. lamb- | | | | doid suture. persistent frontal suture, 3 cms. 93 | 140 | 125 h = | | lh ls sl ersine tas icosia| = | — | — | = | — Jeal.-f ad. torus occipitalis ror | 141 | 124 h | — | — J — | = J 73:8 72:3 | roan} = | =| |= cal.—f. old? some bathrocephaly 93 | 130] 116k = = a me ee Ral eee ces | ; — | — | — | — Jeal.-f. ad. slight depression of obelion. faint post | | | | | | coronal constriction 103 | 127] 110h 2475 | 41 | 41 36°5 | 37 54 35 — — — | 683} — 8371 48 | 89 | go-2 68°5 | 68°°5 | 43 | —— ]eal. y.ad. large temporal defects. faint post coronal | } | depression. ossicle of pterion bilateral. ossicle in | 1. lambdoid suture and small one in r. 95 | 130} 111 — — — — 143 30°57 71°9 | 67°7 | 71°9 | 67°7 | 106-1 =— —- j= — 63° — | cal. ad. face very defective. post coronal depression To4 | 135 | 115 25°5 | 47 47 35 345 [| 47°5 | 36°5 77°| 718 77° | 78 | 108-1} 74°75 49 745 | 73°4 64° 87° | cal. ad. slight temporal defect. 1. third molar erupt- | ing. median prominence 7 mm. wide, 4mm. high at | | | anterior margin of foramen magnum (?third condyle) 93 | 131) 113 = — | 405 |] — | 32 - — | 747 | 68:9 | 74°3 | 68°6 | 108-4 = 79 eal.—f,+r. orbit. ad. wormians in outer part of 1. lambdoid suture COA me (WL 26 44 44°5 | 33 315 | 50°5 | 4175 | 80°5 — | 805 | — = 816 52 75 =| 70°8 685 | 71° | gos | 15° | 25°°5 | 86° | cal. ad. large defect in vault. 1. pterygo-spinous bridge 90] — | 109h = Jor = | cal.—f. ad. very defective base. faint post coronal S44 earn | RtOd i = - = 751 = = dome. ad. (constriction 90 | 124 109 h — — | 38 — | 36°5 — — | 72°9 | 68:5 | 106-5 96 | cal.—f. ad, 1. temporal defect. post coronal depression 96 | 127 | 114 — — | 42 35 33 = — | 73°9 | 69 74°3 | 69°4 | 10771 — = = | 78°6 | cal. ad. 1. facial defect. wormians partly united in ai — |} ugh - - ~ | | | dome. a (1. lambdoid suture = = = = = |I\7F4 = = = — | dome, ad, 95 | 122 | 103 h = _ — | 746 | 68-9 | 108-2 cal.—f. ad. faint post coronal constriction. third oc- | | | | cipital condyle somewhat to 1. median ple. low ele- | | vation. 8mm. trans. 5 mm. from before back. 5 mm. | | | | from anterior margin of foramen magnum, bearing ; 7 | | | articular facet M1 110 ii a = = = = | 103 | 130 | 114 2 5 7 eeu aa = ae am , 7 domeamold loos 25 430 | 43 33 345 J 49? 67°4 | 107°6 ato) 69° | 72° 39° 10° | 29° 82° | cal. ad. r. malar, 1. zygomatic and small r. frontal 99 | 134 | 18h - | defects. flattening of obelion 2 | = = — 754 | 70-7 | 105-3 - - — = _ = — |cal. -f. ad. fronto-ethmoidal defect. very large 106 | 137 | 117 A inion. left foramen ovale subdivided = = = 74. 69°9 | 105°8 -- cal.—f. ad. post coronal constriction. r. ossicle of 130 5 bs x | | | pterion. bilateral pterygo-spinous bridge TOO (EBON) LES 29 | 435 | 45 | 35°5 | 35 Fass | — 77-9 | 684 | 77°9 | 68:4 | 1130] 77-7 | 5ar3. | 8x6 | 778 59°°5 | 78°5 | 42° ee ee I ee oe anil: 1 zygomatic defect. r. plerygo-spinous 100 | 122} rogh Tage 93 | 127 ie h z= : = = — | 751 | 65°9 | 113°9 = | _ cal. ~f. ad. large |. temporo-parietal defect 93 | 127 13 -|—- = a — = = = 765 70°9 | 107'°9 = = = = = = = _ — calealt Fb small r. occipital defect. bilateral ossicle — | 125] 12h aoe P : a a = A = = = = lome. old? of pterion = |iz2| tos 355 | 43 = | 34's 49 | 38 = | = | 723 | 665 | 1088] 77 50 8o2 | — | 66° |74° |4o? | — | — | — Jel. old. large defects wa 04 | 118 | 102k 3) 42 | = | 325 | = 40, | 33. | 73°3 | 69'3 | 72°9 | 68:9 | t05-7) 88:3 | 4q-7 | Srr2 PS 60°°5 | 72°°5 | 47° | 16%5 | 305 | 89° | cal. y.ad. with. malar defect 4 |i ee 103455! =" 1'39)2 = = — | 674 = —_ - 82° — 57° | 83° | 4o° — — | — | eal. ad. large 1. temporo-parietal andr. facial defects. 97 | 107 h ie. = £ | | | metopic ; depression of obelion. r. ossicle of pterion 89 107 ht = = = 75°7 | 05°7 | 11571 = = || | cal.—f. old. 85 107 h es = | 786 | 66% | 108'2) — = — |= | = eal.—f, ad. small r. occipital defect. faint post 103 17h = = 74°6 | 66:1 | 112-9 | | | — | cal.—f. old? [coronal constriction 98 | — | 10h a Se |e 7 2/3 ESsxn |h109731| 5 — - | cal.—f. ad, with r. sphenoidal defect ; | = 74°6 = | — | -— dome. y. fb, pean post coronal depression. 95 | 134) 119 h nets Seal | | strongly developed inion 90 | 135 | 113 755 | 45 B59 1/ 35.9 Hi p3e 505 | 365 J — | — | 741 | 70°9 | 104°5) 83:5 | 49 77°8 | 809 | 608 66%:5%|744e=np |e eh cal Nace otearnperel and occipital defects 0:5) 35 40 35 755 | 734 | 7571 | 73 103 778 = — | 864 $7°5 [59° 78° | 43° — _ — | cal. ad. 1. facial and temporal defects. ossicle of . | | 15x 10mm, Se peme~reytec esti nace enneree ecteme: 2 ARM sdepmaeee eV RO Sete re 2 TABLE V. Remarks 315 | 34 ad. 1. malar and temporal defects. metopic; t depression of obelion old? sphenoidal and 1. temporal defects y.ad. spheno-ethmoidal and r. temporal de- considerable 1. precondylar eminence. faint coronal depression 7 y. ad. marked post coronal constriction. small r. jugular foramen. minute r. par- ital process > ad. faint post coronal depression > defective ad. very imperfect 7 ad. 34nd forepart skull. old? [pression 7 ad. very imperfect. metopic. coronal de- 7 ad. very large. slight depression of obelion 34d. heavy brow ridges - old? faint depression of obelion sad. torus occipitalis 33 large r. temporo-parietal defect [depression -y. ad. sutures complicated. slight post coronal 32 ad. defect in r. superior maxilla. 1. infra al suture on face 33 1. temporal, facial and r. zygomatic defects. 1 occipitalis pentagonal 37d. occipital and r. temporal defects. slight soronal constriction. nearly complete l. pterygo- us bridge ad. r. temporal and 1. sphenoid defects. slight soronal depression. ossicle of \, 13 x 10 mm. 35 large r. occipito-temporal defect. slight post aldepression. bilateral precondylar eminences 32 ad. r. parietal defect. faint post coronal 34 {constriction 3% large r. ossicle of pterion, 41x12 mm. r. fronto-sphenoidal ossicle? ossicles of loid suture on both sides especially r. flatten- ad depression of obelion ~ad. 1. ossicle of pterion. bilateral precondylar ees (double third condyle). faint post coronal ssion sad. r. fronto-sphenoidal defect. 1. precondylar nee. ossicles of Riolan [10 x 10 mm. 34 flattening of obelion. small ossicle of X, “ad. frontal defect. division of 1. parietal bone, ior inferior part cut off by sinuous suture, g |. lambdoid at junction of inner 2ths, with 2ths, and joining middle of left squamous; de- i portion 63mm. from apex to base and 45mm, base, which abuts against temporal bone ad. fractured 1. parietal. faint post coronal sion. well marked interparietal 3dad. transverse fracture of base. slight post l depression. median element (os pentagonale) srparietal fused with supra-occipital, lateral ats (ossa triangularia) distinct ad. yr. malar defect. interparietal, median tagonale and r. os triangulare elements free. triangulare fused. wormian in 1. lambdoid. d occipital projection 33 traces of os pentagonale, ossa triangularia with parietals? slight occipital prominence ad. slight sagittal ridge. interparietal, median 1t (os pentagonale) free; 1. os triangulare r. very small, 20 x 25 mm. Facs O Oz Sea NE Me RS WE Tie | 48 25 P4085 55 ZO™ 1) AUS [42> |.33 52 24°5 | 46°5 | 45°5 | 35°5 48°5 | 24 |42 | 42 | 35 st 24°5 | 42 41°5 | 31'5 Bp. 2.9 b | 4° a 50 26 42 42 35°5 48°5 | 23 41°5 | 42 35°5 50°5 | 24 44°5 | 42 34 48 22°5 | 44 | 44 34°5 | 3 54 24 46 45 37 44°5 | 22 44 uber) Mh 2)5) 50°5 | 20°5 | 43 42°5 | 33 475 | 24 | 43 sm tlo2:5 505 | 20 41°5 | 49°5 | 33 ' MEASUREMENTS OF SEVENTEENTH CENTURY ENGLISH CRANTA. = J TABLE V. Lesotas CrmcUMFERENCES Face “ a as — s Blade Inpices AnoiEs a plow | a ails Soi 0; Or | een | a= — 189 | | - if aa —| | | Tete te ae B/L'| H/L'| BIL | H/L | B/H \G'H/GB navn 0,0, | 93191 | G4, eae Base | aa |e] ae 132 | 95 | 121 504 | 353 | 296 ag | colenallge A Nae Pl Ba aS aes Ske 190 | | — ; | - cs 5 | 3s | 3? 742 | 68 | 74:2 2° | 2 90 lars i Wine aes | gle ws | i) eahee| 3 a oan | 9) ee oe as | ys | — 5 § al. y.ad. |. malar and ti ie; | | 3 | ese a | slight depression ee detete. melons) ae S| = ay | cal.—f. old? sphenoidal and 1. temporal defects | | ae cia | ay ae y- ad. spheno-ethmoidal and r. temporal de- | | Spl ies ects. considerable 1. precondylur eminence, faint allie | post coronal depression |: : i | ; | ‘ avai | enl.~f. y. ad. marked post coronal iti r : ’ i lel ro d : e : : naey eats Mera 8 ‘al constriction. | 12 98 | — = ~ 81 69 TS fa jugular foramen. minute r. par. 196 | -3) — 136 | 94| — (az 320 aa 72'5 | 68-7 56 pee ad tin ol ce : 2 : ie | = = |r 8: 05 cal.—f. ad. faint post coronal depression i 3) B= = |Su8 rt - dome. defective Bl: ae : le ae Pale Er = = = | 70% = = = cal.—f. ad. very imperfect | 31 | 3 | 1440 135 | 97 | 137 Pas 4 ay |e = = ee ae RE ms SSI a8 (Scio) ieee nper an ; ag = =|. : = = : . = upper and forepart skull. old? it 202 | - | — 38 | 93 499 | 357] - 2: 5 | 46°5 | 45°5 | 35°5 | 35°s ; 5 = re ies ! ae 203 |: | — 138 a 2 506 | ial = = | 70°3 | 71°3 7 985) — 471 | 763 | 78 | 80 1° dome ; ai very Tange alight depres of abelion ie 48 : ae a z = - . ad. very . slight depression of obeli | 204 Vege 130 | 95 520 | 369 | — — | 485 |24 | 42 |42 | 35 | 35'5 = ra : = = | ae a der 42 1260 135 | 94 497 | 348 | 204 ray [hank Were = ae RABS: m1 | — | 74:4 | 49°5 | 83:3 | 84:5 | 8: alles lies doe a roca | = 2. 5r 24°5 | 42 45 | 31 2 62°6 | 106°6 =e 5 5) 29"'5 85° ange. temporo-pa mak ae | ae ale rales EG ESE se i oI: 5 | 13 29°5 | 89 cal. ad. large r. temporo-parietal defect (depressi le ape z re aa ae = 5 = dome. y. ad. sutures complicated. sligh' Pal on} 2] - 13] o1| — le 33 = 6: 513° [31%s | 83° | oat. y. ad. defect inv. superior maxilla; Ir infra | | | 489 | 353) = 115 | 50 26 42 42 35°5 | 37°5 3 474 82°5 | 69°6 orbital suture on face a ek ae | | ne by Sie 3 a A 7 = — |eal.ad. 1. tem 1, faci i 208 | ¢ zai — | 94] 127 493 | 347 | 293 52:3 ae 84°5 | $9°3 rege eo tas pentagonal eee oe | | | P os : = cal, old. ipi a - -|3 | | a - occipital and r. temporal defects. sli “ | : sae an . slight | 210 | 3 | | 3 505 | 373 | — = || | 4u'5 | 42 35°5 | 35 73°4 spinous badge mae ina as z = | | ‘ 211 = ee eo 520 | 368 | 2 = ees ply ; ; : fe : 212 |S 1695 13241 298 ) 124 302 | 354 | 276 — | sos | 24 [44s [42 [34 | 32 : 5 47°4 | 85°5 | 84°5 | 85°7 sell post coronal depression. CaaS ae | E 48 | 102) 142 547 | 388 | 317 BazglPASs|, |22'5)\i44” 44 -34i52 135 ay | Eo PBT = | 798 | 47's) | 764 | 7672 | 76:8 eer cee snipe | | Hae | B2sq | 24 (46 | 45 | 37> 138 By 25 Zale Gt 8 200A |e 79att a (Eaci9 Pas || eeeeill ea 1 Fro | AS es ee bilateral preeondylar eminences | 213 | 1650 | | | 9 | 728 | 75°5 | 724 | 104°3] 69°5 | 44-4 | So-4 | 84-4 jot % go? odie ene ee eee . dale , 5 | 65 84° an R , (constriction ney 4 eal. ad. large r. ossicle of i | | | | | i aon of pterion, 41x12 mm | | . fronto-sphenoidal ossicle? — ossi i ies ; ¥ | = \7n 68-5 | 10. lambdoid sut ts sicle? ossicles of | ae. Ali A a 1 suture on both sides es | 215 | 322] 153 6 | 89 | 125 481 | 344 | 272 a = = = ORE eee nt ge | he : : 7 : -—f, ad. 1. ossicle of pterion. bilateral 216 | ¢ _ 96 | 123 530 | 384 | 319 72'4 | 71'8 | 100°8 depression : sn pon cor Ah a 3 |. ' 4 i 4 | c le third condyle). faint post coronal | | | | oles 7 Pye lea |r Pa lea eee i Bh = calf aaa! fronto-sphenoidal defe | | = 84.78 665 | 117"4 -- ie 735 782 | 719 172) |\\23° go” ad ta seaeee aolan a (ov tomm | | 2 cal. ad. flattening of obeli i =a a = Ballet aie frontal aerentta tele oE Serato: . | Awe | | : | | posterior inferior part eto parictal bong EB | € cut of i 4 ele | loavigailcineabaes ‘ t y sinuous suture, on lo | mel. g 1. lambdoid at junction of inner 2ths, with Reale ) 7 . a ; outer }ths, and joini: i Sibi | 35 | 540 | 382 eo 129 | 50°5 | 20°5 | 43. | 42 — | 7771 | 638 | 1208 = aarees fags és om pe touted 5 . Als i" : across base, whi i $5um | le uM L h ; m4 | = Seis, 77, 1 75 | 325 | 37° pa denression: well marked interparietal Esrigorenel pale ‘ , , . y- ad. transverse fracture of base. sli; a = | coronal depressioi i EM Het | ee le P n. median element 220 | ¢ Ja | | 91 | 7073 | 68-7 | 1022) — a - of interparietal fused with oo ene apenas 410 oolltas | 50°5 | 75% | — | 68-4 ole : dria) distinct me Cae reel eee lla cloments (ossa triangularia) distinct ‘ 221} a] - | || a Fant 125 | 50°5 | 20 415 | 40°5 | 33 © [een a sn inal St al Abe a - sea l| ee 03 pentagonale and r. os triangulare elem Tete | z x 7 | 11474] 87-2 30°6 | 79's . , 1. ox triangulare fused. ian i oni A, | eI | : bes wraered lleaxe 205 | ages | og” | catmarted,osapital prise eee al Al el rallteaen ners 24°°5.| 94° Jcal. ad. traces of j '- ces fused with parietala 2” slight onciotat ee ee Ee ‘ate n 3? slight occipital prom: ' .—f. ad. slight sagittal rid, i P aaah element (os pentagonale) Tre soe bare al enedte fused, r. very small, 20 x 25 a secs crianoulars 2 PRI NOS SES : ce ia ; El “ : . | 4 a Cc ¥. co - = ? : pec emetic Sie nl Priel bul es cnc pathy ose emmcaln ees 2 in RE ta ae ayn obser es Soe 3 : | 7 | | : | = th eae) ig) SE £3 ‘ «3 Je : | | | > ~ Neo ise ¥ nes #) : . : | : : ; ous : : ; | | | ~ i E 3 ' | = = ~ x 4 a = TABLE VI. Remarks NH L 52 — ad. heavy brow ridges. interparietal, os gonale distinct, ossa triangularia fused. slight ndylar eminences ad. ethmoidal defect. platybaric. consider- 47 47°5 38 ossicle of X, 26x 20mm. faint post coronal ‘ssion — | ad. ossicle of d, 33x28 mm. and other es in lambdoid suture — ad. very defective base. ossicle of X, ‘5mm. faint post coronal depression —ad. marked post coronal constriction. paired es of A, each about 20x15 mm. some occi- prominence. wormians, chiefly in r. lamb- suture — ad. traces of ossicle of bregma, 20 x 13 mm. — ad. very defective base. ossicle of bregma, 10mm. r. parietal flattening 39~=COL. and yr. parietal defects. hamulus lacry- reaches face — ad. with basal and left temporal defects. yeephalic, wormian, 15 x 15 mm. in 1. coronal e {depression of obelion 22 24 25 315 34°5 31°5 34°5 y. ad. marked plagiocephaly ; r. side smaller. —ad. plagiocephalic, r. occipital and 1. frontal ning. r. post coronal depression — ad. large occipital defect. slight post coronal ssion. interparietal, os pentagonale and 1. os ulare distinct, r. os triangulare missing bed robust and powerful 32°4 (? y-) metopic. forehead peculiarly in- ‘e in character, slight bathrocephaly. ossicle 17x20 mm. and other ossicles in lambdoid », slight coronal depression 33°¢ zygomatic arches defective —ad. r. zygomatic arch and outer wall of orbit jive. upper r. canine coming through behind jl incisor cal 1. orbit imperfect. very pronounced bathro- ly. large ossicles in lambdoid suture. lozenge d ossicle of bregma, 60 x 50 mm. 33"| slight groove of obelion [wards 6 mm. 34 1. zygoma defective, inion projects down- - ad. slight defect occipital bone 36° r. zygoma defective 30'| —? zygomatic arch, outer wall of orbit and a defective on r. side, heavy powerfully built with strong brow ridges and inion 33 (2 y-) left zygoma defective. infantile type. ossicles in lambdoid suture. slight flattening lion _ old. small defects in both temporal regions. 43 44 41 34 sis pedunculated 30 mm. long x 18 mm. broad scipital region 34 1. malar region defective. large defect in jtal. small defect in region of obelion, pro- due to injury ante mortem. os interparietale, tagonale and }. os triangulare distinct. r. os ware apparently absent; place supplied by . of parietal pentagonal and especially supra- al 30 vd. —ad. ethmoidal defect 33 both zygomata defective [lambdoid suture 31 trace of bathrocephaly. small ossicles in seen. MEASUREMENTS OF SEVENTEENTH CENTURY ENGLISH’ CRANTA. TABLE VI. IypIces Series | No. Sex 222) 2 223 | | 224 225 226 297 208 229 230 < 231 932 | ¢ 233| 2 2037 7038) 2 7040) ¢ 7041 | 7042| = 7044| 2 7045 | 2 7046 | = 7047 | = 7048 | < 7049 | 2 7050) 2 7051| ¢ 7052| ¢ 7053 | ¢ 7054 | 7055 | « 7056 | = B/H |G'H/GB| NB|NH Remarks 113° | 826 we wn to7'1 | 88-9 109°6 107°5 = 106'3) 77°6 1038 = X09; 731 993) 742 cal.—f. ad. heayy brow ridges. interparietal, os pentagonale distinct, ossa triangularia fused. slight precondylar eminences d. cal. —f, ethmoidal defect. platybaric. consider- able ossicle of \, 26x20 mm. faint post coronal ossicle of A, 33%28 mm. and other icles in lambdoid suture ad. very defective base. ossicle of X, 17*15 mm. faint post coronal depression . dome. ad. marked post coronal constriction. paired ossicles of A, each about 20x15 mm. some occi- pital prominence. wormians, chiefly in r. lamb- doid suture eal.—f. ad. traces of ossicle of bregma, 20 x 13 mm. cal.—f. ad. very defective base. ossicle of bregma, 20x20 mm. r. parietal flattening cal, ad. 1. and r. parietal defects. hamulus lacry- malis reaches face cal.—f. ad. with basal and left temporal defects. plagiocephalic, wormian, 15 x 15 mm. in 1. coronal suture [depression of obelion cal, —f. y. ad. marked plagiocephaly ; r. side smaller. dome. ad. plagiocephalic, r. occipital and 1. frontal flattening. r. post coronal depression eal.—f. ad. large occipital defect. slight post coronal depression. interparietal, os pentagonale and 1. os triangulare distinct, r. 08 triangulare missing eal. ad. robust and powerful cal. ad. (? y.) metopic. forehead peculiarly in- fantile in character, slight bathrocephaly. ossicle of \, 17x20 mm, and other ossicles in lambdoid suture, slight coronal depression cal. ad. zygomatic arches defective eal. y.ad. r. zygomatic arch and outer wall of orbit defective. upper r. canine coming through behind lateral incisor cal. ad. 1. orbit imperfect. very pronounced bathro- cephaly. Jarge ossicles in lambdoid suture. lozenge shaped ossicle of bregma, 60 x 50 mm. cal. ad. slight groove of obelion [wards 6 mm. cal. ad. 1, zygoma defective, inion projects down- cal.—f. ad. slight defect occipital bone cal. ad. r. zygoma defective eal. ad. cal. old? zygomatic arch, outer wall of orbit and maxilla defective on r, side, heavy powerfully built skull with strong brow ridges and inion cal.ad. (?y.) left zygoma defective. infantile type. small ossicles in lambdoid suture. slight flattening of obelion eal.—f. old. small defects in both temporal regions. exostosis pedunculated 30 mm. long x 18 mm. broad in 1. occipital region eal. ad. 1. malar region defective. large defect in r. frontal. small defect in region of obelion, pro- bably due to injury ante mortem, 0s interparietale, os pentagonale and 1, 08 triangulare distinct. r. os triangulare apparently absent; place supplied by growth of parietal pentagonal and especially supra- occipital eal. y. ad. cal.—f. ad. ethmoidal defect cal. ad. both zygomata defective [lambdoid suture cal. old, trace of bathrocephaly. small ossicles in 7039 not seen. 7043 a Negro skull. MEASUREMENTS (¢ TABLE VII. Remarks side of face defective. metopic. bathro- numerous ossicles in lambdoid suture 2? 1. malar defect. strongly bathroce- erous ossicles in all defect in r. frontal. metopic. slight | projection. bilateral pterygo-spinous uint coronal depression on r. side 49 24 39°5 — | 365 — || malar defect. post coronal depression. rocephaly. wormians in lambdoid suture, , two on r., one in parietal notch of mn each side. infantile forehead 54 23°5 | 44 34 = t malar defect. inion strongly marked 51 23°5 | 45 45'5 | 34 33 rontal, occipital and zygomatic defects 49 2255 43 25a |es0 35 . zygomatic defect l. zygomatic and r. temporal defects. bure absent, coronal and lambdoid sutures erdolichocephalic, slight coronal depres- | | alar defect. ossicles in lambdoid suture ). minute ossicles in lambdoid suture. marked [fees arch broken. ossicle of pterion. | terparietal bone. torus occipitalis dove of obelion, traces of ossicle of i. f pterion. slight torus occipitalis | zygomatic defect. ossicles of asterion, mm., l. 11 xX If mm. inion well de- l). rv. zygomatic defect [veloped te r. temporal and orbital defect ontal and 1. facial defects. slight groove . terus occipitalis. ossicles of lamb- _ x. temporal defect. ossicle 20x 17 mm. loid suture , ad.). slight post coronal depression. pes of squamous on both sides coronal groove. metopic Ie temporal and occipital defects. slight al depression. r. occipital flattening races of ossicle of bregma , zygomatic and occipital defects extensive temporo-sphenoidal defect. uthrocephaly. numerous ossicles of i o-mastoid sutures. ossicle 12x 12 mm. Ps slight torus occipitalis temporal and r. zygomatic defects I I 2 2 22 22° p ze aye a sae 30's 3 od fracture crossing hinder part 1. parietal. ‘occipitalis 49 23 45 46 30°5 | 30 ad.). post coronal depression. bulging 1 portion of coronal suture on either side 48°5 | 25 Spore, la 345 | large basal and 1. malar defects 53 22 40°5 | 40 34%m I) 30 jopic. faint depression of obelion 2 20° ey 3 3 ie 2 5 ve th 5 ise 3 vemporal defect. metopic. post coronal small r, ossicle of pterion and small | lambdoid suture cml 1) |aix | 26: goma defective : 2 ie vu 325 yecipito-parietal defect lefective 1. zygoma. edentulous save for 45°5 | 22°5 | 42°5 | 43 34°5 ‘ iati | canine. post coronal constriction. torus 1 7062—7088 : th MEASUREMENTS OF SEVENTEENTH CENTURY ENGLISH CRANIA. TABLE VIL. 2 0 0, 0, Inpices Lexotas CrncumreReNces = Remarks p |u| on |cp BL | WIL | nn |ernjen| NajwH oo O11 GajG,| GL | Ne | de | Re J | a | Pz | | | = —|—— a = =|——_ |—_|— = | — — | ——_— SS Ei rt | 67°8 | 104°9| 6771 276 | 8375 | 82° — Io 67° 79 8 26° | 87° Jcal. senile i | a a 136 ao Re foe 7 tere ue eae a8 ae = 36 65 72° poi Was $3° cal. ad. left side of face defective. metopic, bathro- r | | cephalic ; numerous ossicles in lambdoid suture 138 | 99 | 128] 112 98 70°4 | 65°3 | 107°9 = 44/2 — | 849 | 71-7 | 92 [63° | 71° | 46 19° | 27° 90° cal. y. ad.? 1. malar defect. strongly bathroce- | | | phalic, numerous ossicles in \ a : 7 | ror | 132] 114 99 757 | 72'9 | 1038 | 70°2 48'5 82°9 | S29 | 83°7 | 9075 6375 | 78°5 | 38 7°°5 | 305 | 86° cal. ad. small defect in r. frontal, metopic. slight ies | | | occipital projection. bilateral pterygo-spinous | | | | | | bridge. faint coronal depression on r. side 134] 96 | 121 | 111 95 736 | 66°5 | 110°7 = 49 92"4 90°? fecal. old. r. malar defect. post coronal depression. | slight bathrocephaly. wormians in lambdoid suture, | one on 1., two on r., one in parietal notch of temporal on each side. infantile forehead 148 2] 133] 118 102 = 773 193° cal. old, r. malar defect. inion strongly marked 140 | 98 | 118 | 105 98 = 75°0 89° J cal. old. frontal, occipital and zygomatic defects 130 | 8g | 121 | 105 94 79°5 83-7 |87° [cal. old. r. zygomatic defect 130 | 90] 121 | 103 93 75 79 85 cal. y. ad. 1. zygomatic and r. temporal defects. sagittal suture absent, coronal and lambdoid sutures | | | | open; hyperdolichocephalic, slight coronal depres- | | { sion | or | 125 | 112 94 | | 76:9 | 68:7 {az | Sis | 47-9 | 80 | Sgr | Sr-q | 855] 61° | 742 | 45° | 17%5 | 2755 | 15 J cal. ad. | 103 | 132 | 117 99 77°8 | 7173 | 109 = qui — | 79:5 | — } 93°75] 63° 70° | 47° | 17° | 30° | 87°" | cal. ad. 1. malar defect. ossicles in lambdoid suture 96] 133) tr 103 73 70°4 | 103'7| 80 45:2 | 78 | 802 | 79° J 97 J 645 | 735 | 42° | 11""5 | 305 | 85° J cal. ad. (? old). minute ossicles in lambdoid suture. al | j inion well marked gt | 119 | 106 95 76-2 | 657 | 116 | 81°3 407 80:7 | $399 | 90°4 | 96 | 68) 665 | 45°°5 | 18°5 | 27° | 85° cal. ad. 1. zygomatic arch broken. ossicle of pterion. | oe \ eee f tripartite interparietal bone. torus occipitalis EDL | TELE eee) 92 79° | 74:3 | 107-1] 81-7 468 | 80 | 78-2 | — | S95] 66° | 70°°5 | 43°°5 | 15° | 285 | S55 J cal. ad. groove of obelion, traces of ossicle of A. 1 vecol|es S 5 3 | | | 1. ossicle of pterion. slight torus occipitalix Pail eee al aes 9 69'9 | 68:3 | 1023] 706 | 53°3 | 77:1 | 76°7 | 74:2 | 95 J69° | 74°"s 28° | 83° cal. y. ad. al Pah 99 742 | 716 | 1037] 852 | 489 | 798 | 854 | 70°6 | 8975] 63° | 80° 29° | cal. ad. 1, zygomatic defect. ossicles of asterion, 97 | 119 | 109 96 a . r. 18 x 15 mm,, |. 11 x 11 mm. inion well de- roel leeall aed ares 743/65 | 143] 744 | 49 786 | 78°8 92 [672 | 73°5 | 25° |88° Jal. ad. (? old). r. zygomatic defect [veloped 100 | 134] 114 ioe 79°4 | 72°5 | 109°5| 75°85 424 | 761 | 78:2 | 69°7 | 102 $70 70° | | 28° | 82° | cal. ad. large v. temporal and orbital defect | 5 77-1 | 698 | 1105 | | — eee — |/75°9 | 792 | 96 SS = — | — | 89°? J cal. old. frontal and |. facial defects. slight groove | | | of obelion. torus occipitalis. ossicles of lamb- ot} 131 | rik | 96 5 23 | | | | doid suture z 75° | 70° | 10671 == |) = a | = = = | — |ecal.-f. ad. r. temporal defect. ossicle 20x17 mm. | 92] 130] a1 | 101 1s |) is | 4 | | in |. lambdoid suture | : 69°6 | 681 | 102-3) 806 p 2 | q cal. ad. (? y. ad,). slight post coronal depression. 7 102 | 123 | 108 102 Rilieets f frontal process of squamous on both sides 88 | 110 | 107 94 7333) | 8518:)/|tnn/3i)/ 84-3 cal. old. r. coronal groove. metopie 74°4 | 66"1 | 1126) 69°5 cal. senile. 1. temporal and occipital defects. slight 120 | 106 : | post coronal depression. r. occipital flattening | 107 97 75 | 739 713 cal. old, traces of ossicle of bregma | 113k | 106 73'5 | 68 | 69°3, | cal. old. x. zygomatic and occipital defects 74 | 67°3 = | cal.—f. old. extensive temporo-sphenoidal defect. marked bathrocephaly. numerous ossicles of | | and parieto-mastoid sutures. ossicle 1212 mm. Te 9 95 | 134) 11g 101 5 ey repil| in r. coronal. slight torus occipitalis 1650) ]/192 | 97) 342)" 12339 || \no2 73°7 | 749 | 98'S | 1 77°3 cal. old. 1. temporal and r. zygomatic defects et We i 15:5) V7Ay )|)LO2s1) 03735) cal, ad. healed fracture crossing hinder part 1. parietal. 1490 lise 5 96 | 126) uit 99 6°8 | 68: 5 faint torus occipitalis | | 7 Ber })112:7,| 70'8 cal. ad. (? y. ad.). post coronal depression. bulging 92 3 107 = | e | : of temporal portion of coronal suture on either side 99 | 126 | 109 100 732 = = 79°3 | cal. y. ad. large basal andl. malar defects BH 181 209 88 hii) 77'S cal. ad. metopic. faint depression of obelion | 94 | 127 110 98 7773 64°5 | cal. ad. 795 787 | eal. ad. 1. temporal defect. metopic. post coronal 97 | 1 re depression. small r, ossicle of pterion and small 2 133 2 100 a ae ossicles in lambdoid suture 7 | 132) 113 104 70.4 831 | cal. ad. 1. zygoma defective heel lhe al m7 S916 cal. old. occipito-parietal defect 96 | 120 | 103 99 75° 808 cal. ad. — si 79°7 65°3 cal. old. defective 1. zygoma. edentulous save for | retained r. canine. post coronal constriction. torus — == Sh ane | | occipitalis | | 7062—7088 : there are no skulls with these numbers in this series, ee a OS ne ee NR a eae aE eee eT MEASUREMENTS OF TABLE VIII. 108 84 28 42 I _ Ke} wn = fe) oo wn aS nm nn = ee) Neo} | - ion an _ ° Oo ~~ Ke) oo . wn iN) Ne} aS n wn ere unfortunately not kept with their particu + foramen mentale double on left. Face me! Remarks O 0. NH | NB a | 2 | L | 2 | weg ie a eae 47°5 | 24 43 | 43-5032 B15 ajtrongly marked inion ee 3975.40 - | 33°5' | 33 4%. parietal defect. slight torus occipitalis — Mises | 235 | — || 44°5 | 33 32°5 | 4irge r. occipital and 1. malar defects. healed | d fracture in 1. parietal. ossicles in lamb- | | | ure Mees hoe |a3 [eeen| 33 a. side of face very defective. plagiocephalic. | tal and 1. frontal flattening. inion prominent EW ges ere! Bice . half of face wanting | 23. «| 42 415 | 31 | 32°5 |. zygomatic defect. ossicles in lambdoid | | rather prominent inion 27 alias wes | 35 | 36 silarge r. temporal defect and transverse | of base. traces of transverse occipital | We Wy hy t 119 96 meen | 42-5 1125 | go 27°5 | 43 120 87°5 | 29 45°5 a Sal 39°5 | 43 126 | 94 34°5?) 42°5 Sorts 205, | 24°5 | 35° 0 os Ly 193 | 193 189 | 193 197 | 197 183 | 183 179 | 177 181 | 183 196 196 i . ~~. nz v . oe —" MEASUREMENTS OF SEVENTEENTH CENTURY ENGLISH CRANIA TABLE VIII Lenorus Crcoatrenences Face Inpices | | = — — es ee = ~ Remarks | ii ; 5 7 \l 6 3 ee | 0, | 0. Allaicall . 0,/0. 0,10 | | D | B | BY) oH | LB] Lt | Ss | Q | GH} GB | | NH | NB| ia. || te R B/L'| BIL’) BL | H/L | BUH josie ae NB|NH | a 1) G./G,} GL i | 193 144 | 97 | 136 116 101 } 534 | 395 315 63 | 86. 28 | 47°5 | 24 | 43° ie | a2 | 3r5 | 44 | 38 70°5 | 10599} 73°3 50°5 4 | Ta 86-4 | 90 cal, ad. strongly marked inion Rp 93 141 | 94 | 131 119 103 533 | 390} 320] 70 | 87 123 | 54 25°5 | 39°5 | 40 33°5 | 33 45 4o 67°9 | 107°6) 8o°5 47-2 82°5 ae go cal. old. r. parietal defect. slight torus occipitalis 198 | 145 | 100 | 138 117 96 545 | — | 316) 71 | 98 123 | 50°5 | 23°5 — || 445 | 33 32°5 | 49 38°5 | 69°7 | 105 | 724 465 _ 73 786 | S89? eal. ad. large r. occipital and |. malar defects. healed | | | | | | peor eseed fracture in 1. parietal. ossicles in lamb- ‘i | | | id sut 189 | 141 | 99 | 12 IN2}y 102) 1515} ) 1369) | Goo} to) |) — 4) — eS ais) | 43 | 33 55 75 68°6 | 7476 | 682 ws] | 76°7 | 99 $6775 | 72°5 | 40° | 11°*5 28%5 | 84" enlgaiie aida of face very defective. plugiocephalic. | 79 138 94 | 129 | 113 98 } 507 | 361 | 303 = = = Ws | | 43°5 | 31°5 = 78 720 «77 721 1069 | | 724 | e! | =3 ESET eaere eee inion prominent 183 | 134 | 92) 124 | 102 102 | 501 | 349 | 281 | 66°5 | 89 127 | 50 | 23 42 405 | 31 32°5 1 47°5 | 36°5 | 73'2 | 67°S | 73°2 | 67°S |} 1081 | 747 | 46 3°8 | 78°73 | 76°8 96 |65°°5 | 75°°5 | 39° 85 30°5 84° J cal. ad. 1. zygomatic defect. ossicles in lambdoid 197 | — | 100] 137] 11 | 388 8 88 | | | | } | | | suture. rather prominent inion 9 | 37 9 | 3 — 6 88 — [49° |: 27 45 — | 35 36 50'5 36 —- 69°9 — |} 6975) — | 173 5571 WES || = 713 - _— — = — 86° | cal. ad. large r. temporal defect and transverse | | | fracture of base. traces of transverse occipital | | | | | | suture { st a = E — at) =| meh ne = Shee | es. | I p= J! MANDIBLES*. ae os) eee Pr eSice See ee] bee ce | TL Ps Well oy ga |e Waele let | Series | W, | TAS eel uv Savalas ll si). IM alteere BO T¢e|h We |) ah | ie - |. a ee fa Fa a pe | ra e 1 11 87 46°5 36 119 96 =| 47°5 72 | 89? : fe 5 | 27'5 | Bi Poa poe | Saale 89%) | | ca2s5: 108118 — | 34:5?| 45 | (peer toe ase | domes | fs |. ats BB fos at dows | 308 aos | 382 | bar HS ae ire race | comultay 39 ay) ER | 2 5 te | eel 89075 9 GBs | 119°5 | 99°3 | 32°5?| 41 5 = fini7 13535: |478. | 40 | 126 | 94 34°5?| 42° 16 re ee eal (Se uy Se eR | 78 |S 6 | 123 | 105 | 46's | ales, ||! 765 | 245 | ase | pitts) 93° 27'S, | 4655 Tia) |) — proats | = |).4675 | 3 5 | 37'S | 465 | # | 85 | 765 | 24°5 | 355 77 | 114 | 91°5 | 20°5 | 45 113 Se PE ERS CNS Guo te BP || 43 |itos lice | 32 |_| |S | riois| 8 [8 [45 Me |isai5 |e a — | 85 | 33°52] 30's | reall eeaerall uses | 5} 8 31? | gis = — | 30 5 | ab dics | $5 | 333"1 8 ‘Stee | Se | as | a3 ab fe | es ls [4 Paes | aed | | i ee or ese oe 34 43 351005 ue ta7a millage 73) — — | —- Toy NE nee 3) 30'S Be ae a } =e SIT 48°5 82 | 105-5, or 305 | 44 | 118 — 85:52) — Wes | 13 SN = ea lla 4 SES 315 | 43 83 | 121 | 995 | 325 | 45 | | 119 | 106-62} 86° | 22-5 | 43:5 | 14 Sea = ee ie | Fi | 92 | Ae |e Fee ee Eb | 27°52) 40 120 = Bo asa eae | 16 11g 97 | 28 41 | | 50 | — | 108-5 3 {42 Boe at Ss ae 1/30) 46 121 se PSS |) 22 48 16 }124 | 98 | 33°5 | 48 | | ai@mitoeitos:: | ose Weer A ese eae hase eg 122 | — |1g” | — | 49'5 17 | 107 95°5 | 27°38 | 40'S BoMaltoeeahes> | = pass 87 | 104°5| 90 | 36 | 4r'5 | 123 | 1195 | 90 S55 18 = it 33% [48 | | 53 1s oe S ieee 88 | 114°5| 90°5 | 32°5 | 46°5 124 ~ — | 325 | 42 | 19 | — | 90 |i29 | ats ae lise” || el ee ese 89 | — "| 965 | — | 465 125 | 116 | rors | 32-8 | 45:5 | 20 | 102°52 87 | 30 | 415 | 55 malbece) 90°5?| 31° eeal| 80) 116 | 97) IIa5) jaz | 126 — | 110 = 25 Q1 | 108” 925] 31 ‘| gas Fo Mel Met ceealicoe Nee BT I oe LEErS) I [den | C48 5H | 127 | 101? | 81-52] 275 | 39°5 | 22 |i or | 28 | gt | 57 | 1082 oo 2 | Hoe | eae BBs 68" | 20 | 34°5 | 128 | 119 8 |26 | 47 | | 23° | 115'5 109 | 255 | 45/t 58, | 118 | 100°5 | 32 | 7 94 | reas Pei bate 129° | 10 | SE |) a= | cee | 5S | gay 59 | 114'5| 8 Spell ee 95/5 | 30° | 3975 180 | 1185 | 1025? 30 | 45°5 24 jazrs | 98 | 31's | 44"s BOlMeresealll Sees) Nae loco 95 | 106°5| 92° 29 | 43 181 | 105°5 | 88° | 272 | 42-5 | i 25 | 103°5 89 | 35°5 | 42 61 13. | pois A551 ACI} 96 se |LLGES 350 | «47 132 | 102°5?} 87? | 33 41 96 | — | 8 | 25-5 | 44 ealeneeell ces |S feo | 97 |119 | 95 |°— | 43:5 133 | — | 05 | 345 | 39 | 07 «| 12 105'5 31 Bs 83 ari “8 pes i kad | | 98 | 1085) 97 | — | 44 184 | 96:5?| 82 24°5 | 30 28 [1115 | 97 | 24°5 | 465 64 Bet SOeg 42550) ) 99 [125 116 | 32 45 135 | 126 117 — | 50 | 29 1/1135 | 94 | 36° | 40°5 65) | ne) ae) alice | | 100 1 83 29 445 136 | 110 Lica |) 2°5 | 30 | 13 89°5 31's | 45-5 68} | 1185] or 35) | 45 , 101 S| NS 2} 187 | 105'5 | 94° | 29 | 43:5 | 31 _ 88-5 | 31? | go 87. 123'5 aa aa) | 41 | 102. | — | 95 — | 46 188 | 1025 | 99:5 | 302 | 41-5 | 82% | 97's | 77°5) 23? | 40's espaliiczmllpi== 26> lacs haces eee Nee ee 199 | 1055 | 92 24's | at | | [Peete eh RES 69} | 112 | 100'5 | 36 | 42-5 | 405 145 | 97°5 | — | 405 | 34 ur 99 35 | at's 70 i SF ise azo) 105 | 11t's| 8975 | 29 | 4g | 141 | 113 905 | — | gre 35 fms | ot | — | 433 ml |nooh| ares | oer | 433 | | 106 | 114°5| 95°5?| 33 | 43°5 142 | — 2 | das 3 62 || | g i 3 101 32? | 44 Pees A Ee | | eae es | 107 | 195] 88:5 | 295 | 48 143) |) oleae deal las 2 ll a é 4 | | | ——- = These mandibles, when the bones were dug 01 vi rl 8 01 x the great bulk of whi nes were dug up, were unfortunately not kept with their particular crania and as it has not been found possible to satisfactorily sex the gi 1 e ulk o + foramen mentale double on left. + Young adult. § Infantile. them, no statement as to sex has been made. ai sre ony 544 995.0 G48 fi hag G45 5 SA eae ca DUG S43) foe : ec yoe Mf = oh REN 112 e 369. | 300 W3 Roy |) SOE gaa 102 San) 34y eae BAN | er ae ¢ ‘ Males Wa, i irt 2 Reg roe i j a be3 % | i] feet Nerud Boia hid yun) feted pet Sart pend Seed th So sacha G2? potot tora >= Eo. hase 5) OD tes Ti es ON INHERITANCE OF COAT-COLOUR IN THE GREYHOUND. By AMY BARRINGTON, ALICE LEE, anp KARL PEARSON. (1) Introductory. There is little doubt that if money and time were no consideration direct experiments on the breeding of dogs would lead to results of the highest importance not only for the theory of inheritance, but also for the practical guidance of dog-fanciers. To be of the most complete service such experiments would have to commence with two or three generations of in-breeding simply to insure the purity of the various stocks to be employed in the final experiments*. Further, in the description of the selected characters, a classi- fication would have to be adopted of a far more comprehensive character than appears to be usual in a number of recent experiments on hybridisation. Lastly, from the standpoint which we believe to be the correct one, that safe conclusions can only be drawn from the average of large numbers of crossings, at least 50 and probably 100 individuals of both sexes would have to be the basis of an effective experimental stud}. Now the difficulty both in time and money of dealing with such a stud may not in the future be insuperable, but at present to propose it as the only means of approaching the problem of inheritance in dogs is to adjourn sine die any consideration of that problem. In certain points also the extensive breeding records which are already available for dogs possess advantages which are not to be wholly disregarded when we compare them with the special merits of a biometric stud-farm. In the first place we have all the gain which arises from dealing with literally immense numbers. For example, in the present memoir we were able to classify over 10,000 cases of parent and * For example when this is wanting, we find as in the case of some recent experiments on rabbits, inconclusive results reached, because the judgment of purity is based on a posteriori examination of the experimental litter, judgment which might be, and actually was in certain cases, reversed on the appearance of a second litter from the same pair. + 10 offspring of each of 50 hybridisations give an incomparably more valuable result than the 100 offspring of one or two hybridisations to which we are frequently treated. 246 On Inheritance of Coat-Colour in the Greyhound offspring, over 7000 cases of grandparent and offspring, and over 24,000 cases of siblings. Nothing approaching such totals could be obtained by experiment ad hoc. Further, the colour pedigrees for a number of generations were directly available. Against these advantages is to be put in the foremost place the primary value of exactitude and uniformity in record such as might be obtained in a well organised scientific experiment. This counts for a great deal, but it does not count for everything with those who realise what are the probable errors of small series, and how inconclusive such series usually are*. On the other hand also, if we admit the want of scientific exactness and the play of individual judgment in the character classifications of breeders, we have still to remember that when the breeding of a particular species has been long established a conventional scale also grows up which, owing to the contact of breeder with breeder at sales and shows, and further to the regulations of societies. and judges, becomes within broad lines universally recognised and appreciated. Hence, while we fully recognise all the disadvantages of stud-book records, we still hold that highly valuable work may be done in the field of inheritance by accepting the classification of professional, if non-scientific breeders. So far as we are aware no series of dogs has been dealt with or at least any results for such a series published since Mr Francis Galton’s work on Basset Houndst. We have long felt that that work needed supplementing, partly because it dealt with a rather small group of much inbred hounds, and partly because, especially in the matter of paternal inheritance, it presented irregularities, which even raised a suspicion of the goodness of the record}. The greyhound naturally occurred to us as a dog of old standing bred for a purpose—speed— which was not closely and obviously associated with its coat-colour. We were, however, warned -that breeders for coursing did fancy certain colours, and we found that the record as presented by the greyhound stud-books was very incomplete, i.e. a very small proportion of the members of any litter were ever recorded in these volumes. Hence, if selection for record took place largely by colour, we might be misled by the greyhound stud-book in a manner impossible in the case of the stud-book for thoroughbred race-horses. An examination of other dog records left on our minds the same doubt as to possible colour-selection in other cases, and thus, although the inheritance of coat-colour in dogs had been proposed for treatment at the same time as the race-horses were dealt with in 1899§, we had felt bound to leave it untouched. Meanwhile Mr Howard Collins of Edgebaston had also been occupied with the same problem, and troubled with the same doubt. He surmounted the difficulty, however, by the issue to grey- hound breeders of a very large number of schedules in which details of colour of sire, dam, and the whole of the resulting litter were to be entered. In * We have here in another form the great advantage, amid many disadvantages, of anthropometry as compared with craniometry. + R. S. Proc. Vol. 61, p. 403. + Pearson: ‘‘On the Law of Reversion.” J&R. S. Proc. Vol. 66, p. 159. § Pearson and Bramley-Moore: Phil. Trans. Vol, 195, A, pp. 79—150. A. Barrinaton, A. LEE anp K. PraArson 247 response to his request a large number of these schedules were duly filled in. All this material he placed unreservedly at the disposal of Professor W. F. R. Weldon, who in his turn handed it over for classification and calculation to the biometric workers in University College, London. This splendid material, for which we cannot too heartily thank Mr Collins and Professor Weldon, was supplemented by additional data extracted from the volumes of the Greyhound Stud-book*. Thus the four fundamental parental tables were drawn from Mr Collins’ data; four other parental tables for purposes of comparison and control were based on the stud-books. All the eight fundamental grandparental tables were based on pedigrees compiled from the stud-books, for Mr Collins’ data extended to one generation only. Of the nine fundamental sibling tables, three for siblings from the same litter are based on Mr Collins’ data, three for siblings from different litters and three for siblings of the same litter on the stud-books. The extraction of pedigrees from the stud-books and the classification of all the data into tables is the work of A. Barrington+. In the calculation of the correlations, the whole of the 50 sets taken by the fourfold table method are due to A. Lee. The whole of the calculation of correlations by the mean square contingency method was undertaken by A. Lee and A. Barrington conjointly. The labour of classification and calculation has been the work of a good many months, and has been more strenuous than is, perhaps, apparent on the surface. Only the work of putting the numerical results into tabular form and drawing conclusions from them is due to the third joint author of this paper. (2) Nature of colour classifications used. In the classification of the grey- hound we find in the first place the following main colours: Red (R.), Fawn (F.), White (W.), Brindle (Bd.), Blue (Be.), Black (Bk.). Besides these main colours we have a series of doubtful intermediates such as Red or Fawn (R. or F.), Fawn or Red (F. or R.), and a wide range of mixtures or particoloured dogs. Such are Red-White and White-Red (R. W. and W.R.), mixtures of Red, Fawn and White, eg. R.F., F.R., W.F., F. W., B.F. W., FR. W., W.R. F., RB. or F. W., W. F. or R., W. R. or F., and the mixed brindles chiefly W. Bd., or Bd. W., but also: F. Bd., Bd. F., R. Bd., Bd. R., R. Bd. W., Be. Bd., Be. Bd. W., W. Bd. Be. Lastly we have the Mired Blues and Mixed Blacks, including the Ticked (Tk.), e.g. Bk. W., W. Bk., Bk. Tk., Bk. W. Tk., W. Bk. Tk., W. Tk., Be. Tk., Be. F., Be. W., W. Be. In all we have found nearly forty different colour classes. Some of these of course are very similar, others perhaps not so definite as might be desirable; but the bulk of the cases fall into fairly well-defined groups, and the isolated units while they are recorded for future use in our fundamental tables have been embraced in wider groupings in the more manageable tables from which our numerical results are drawn. * At present twenty volumes have appeared. The Editor is Mr W. F. Lamonby and it is published at the “ Field”” Newspaper Office. + Actually she prepared 25 out of the 26 fundamental tables; the remaining table was originally prepared by F. EH. Lutz, but it was revised and modified when the other series were extracted. 248 On Inheritance of Coat-Colour in the Greyhound According to some authorities black and red are the original greyhound colours ; white is said not to be found in any “natural breed of dogs.” Black, red and white are often looked upon, however, as the three primitive “colours” by breeders. A mixture of these colours may then lead to a blend as in “ fawn” and “blue,” to particolour in large patches, to ticking in small spots or to stripes. According to Stonehenge we have the following pedigrees : (a) Bk. x W. nae i : Bk. W. W. Bk. Be. (b) Bk. x R. ne ae cae SS \ | Bk. Bd R R. Bk. Bk. Bd. Bk. F ‘ (c) R. x W [et aga | W. R. R. W. F. We are not convinced that such results pay sufficient attention to ancestry beyond the parents. Bd. x Bd. breeds as large a proportion true to parents as R. x R. or Bk. x Bk. Bk. x Bk. can produce R. and also F. The accompanying tables give the distribution of parents in the case of 2384 dogs and 2200 bitches. Here, to keep the tables within manageable limits, white has not been treated as a separate group except in the case of pure whites. Thus, of the red sires between 4+ and 4 are red and white; of the brindle sires between 4 and £ are brindle and white; of the fawn sires more than 4 are fawn and white; of the mixed black sires # are black and white and about + blue; the remaining } being chiefly blue and white, with a sprinkling of ticked and other rather nondescript dogs. Red shades off into fawn so that quite a large class of sires between 3 to 3 of the reds are described as red or fawn. Besides these we find a few isolated units classed as red and fawn, or red, fawn and white. As the tables stand, pure black contains dogs without mixture of red, fawn, brindle or white; fawn contains fawn, white and fawn; red contains red, red-fawn, red or fawn, and these with white. Brindle contains brindle, brindle-white with a few isolated units of brindle-reds and brindle-fawns. The blue-brindle and brindle-blacks are included in the mixed blacks. For more detailed classifications the reader must refer to the complete tables in the Appendix of this memoir. » Now a reference to the above tables will show that melanism may appear in R. x R. crosses as well as in F. x F. crosses ; that Bd. x Bd. may produce pure white or pure black dogs; that Bk. x R. may give white dogs; and that pure black dogs may produce pure white, red or fawn dogs. To use Mendelian language, the whole race of greyhounds appears to be in a heterozygous condition, and such pedigrees as those we have quoted from Stonehenge appear to have little valency when large numbers are studied. (8) White Dogs. One great defect in our data is made manifest by an examination of Tables I and II; although we have there the parents of 4584 dogs A. Barrineton, A. LEE and K. PrARrson TABLE I. Offspring Dogs. Sires. re F Pure | Mixed : Red | Brindle | White} Fawn Black | Black Totals Red ... 37 10 — 52 19 17 1a) Brindle 4 40 — = u 7 58 Red White 1 = 3 — — Z 6 Fawn = 4 6 = 22, 14 12 58 Pure Black... 1 2 — = 31 30 67 Mixed Black 1 3 — — 19 43 66 Totals = 48 61 3 74 | 90 | 114 | 390 Red ... 19 5 =e is 8 45 Brindle 51 81 3 31 15 25 206 Brindle White 2 1 = 1 _— — 4 Fawn oH 16 8 1 20 il 10 56 Pure Black... 28 2B} 51 Mixed Black 1 1 — 2 5 AS} 62 Totals = 89 96 4 67 49 119 424 Red ... 1 — — 1 Brindle —_ — = a 2 5 10 . White 2 — 1 3 White Fawn bP — — = 5 = 2 7 Pure Black... — = = -- = 3 3 Mixed Black 2 5 10 17 | Totals _ 13 mh cot 41 5 Z Q Red ... 16 10 — 14 13 5 58 Brindle — 39 — — 7 10 56 Fawn | White 1 2 1 = Le 5 a Fawn eas 17 26 1 14 20 35 113 Pure Black... — 2 — = 26 29 57 Mixed Black 3 5 = 10 7 88 1133 Totals — 37 84 2 38 74 167 402 Red ... 15 8 = By 9 5 42 Brindle 8 Be — 7 10 12 70 Pure White = == = = — 2 2 Black Fawn a 4 8 = 15 7 33 32 Pure Black... 49 4] — 22 90 54 256 Mixed Black 8 16 — 20 27 48 119 Totals _ 84 101 = 69 143 124 521 Red ... 23 2 — 11 4 13) 45 Brindle 17 30 - 9 1 9 66 Mixed White 3 = — Uf 1 3 14 Black Fawn et 7 18 — 44 9 10 88 Pure Black... 16 14 — 13 25 38 106 Mixed Black 28 58 — 53 33 115 287 Totals — 94 122 — 137 73 180 606 Grand = 352 | 464 9 | 398 | 436 | 725 | 2384 Totals 32 Biometrika 11 249 250 Dams. On Inheritance of Coat-Colour in the Greyhound TABLE II. Offspring Bitches. Sires. : : _ | Pure | Mixed Red | Brindle | White | Fawn Black eblaek Totals Red... 43 10 — [5 32) 18 15 138 Brindle 2 55 — — 9 10 76 : White — a 3 = 1 1 5 Red Fawn oe 9 8 _ 19 Wl 15 62 Pure Black ... — il = — 29 29 59 Mixed Black — 1 — <= 18 39 58 Totals — 54 75 3} 71 86 109 398 Red ... 22 9 = Ae tee 5 40 Brindle 36 76 2) 22, 9 23 168 White 1 2 — 1 — 2 6 Brindle Fawn sam 8 5 1 25 — 9 48 Pure Black... 5 — oe a 26 16 47 Mixed Black 1 — = 2 3} 60 66 Totals — 73 92 3 54 38 115 375 Red... = — _ 2 — — 2 Brindle — — — — 1 4 5 : White — = — 3 — 2 5 7 White Geen a 10 ae ee 10 Pure Black... Mixed Black = 1 — 2 2 12 17 Totals — 1 _- 17 3 18 39 Red ... 7 1 _- 1133 9 4 45 Brindle = 30 — — 6 11 47 Wawa White — il = 1 2 = 4 sa Fawn a aly 21 4 17 14 20 93 Pure Black... — 2) _— — 27 23 52 Mixed Black 1 6 —— 7 13 70 97 Totals = 25 72 AN 38: ul TF 128 ealmases Red ... 22, 4 — 4 4 4 38 Brindle 4 29 — 7 9 10 59 Pure White 1 = = It Black Fawn ‘ 10 a —_— 23 4 5 49 Pure Black... 7. WPI — 26 89 74 243 Mixed Black 8 16 — u 20 43 94 Totals — W2 83 — 67 126 136 484 Red ... 16 6 — 7 3 2 34 Brindle 17 35 = 11 uf 12 82 Mixed White 2 1 = 3 — oy) 8 Black Fawn cs 6 13 = 43 8 3 73 Pure Black... 18 16 = 11 26 2e 94 Mixed Black 27 43 —- 58 29 118 275 Totals a 86 114 = 133 ie 160 566 Grand - 310 | 437 10 | 380 | 397 | 666 | 2200. Totals eee A. Barrineron, A. Lek and K. Prarson 251 aud elsewhere the parents of at least 4000 others, in no case have we the cross W.x W. This is undoubtedly an important cross and we endeavoured to obtain data on this point by seeking out the pedigrees of all the white dogs whose names were known to us. The paucity of material is due to the fact that very rarely one of a litter is pure white, and we have no evidence of any attempt to breed persistently from W. x W.* Upwards of 50 pedigrees of ‘white’ dogs going back to their 16 great-great-grandparents, and in some cases their great-great-great- grandparents were drawn up with the colours added in all cases where we could ascertain them. But not very definite information could be extracted from these pedigrees. There were six cases only of a W. dog with one parent W., three white dams and three white sires. Of these six cases of W. from parent W. we had no case of the parents of the W. parent being recorded as white. Indeed, no case of a W. grandparent at all. One or other of the grandparents was usually particoloured white. There were 16 cases in which a white dog was recorded from parents both of whom were white particolour. In all these cases there was white particolour in the grandparents in one or more cases, but quite frequently neither parent of a particoloured parent had any white; for example, R. x Bd. frequently gave white particolour. In only one recorded case was there a W. grandparent in this series. Where the grandparents of the W. dog through a particoloured white parent were R.x Bd. we found the white particolour reappeared in the parents of one or other or both of the R. and Bd. grandparents. There were 16 cases of one particolour white parent to the W. dog. In all these cases except one, there was more or less particolour white in the grand- parents. In this one case we have: Risen Bk. x Bk. | | R. x Bk. W. | : a | W. But at least three of the great-grandparents, partly on the red and partly on the black side, were white particolour. There were 19 cases of white dogs with no white recorded at all in their parents, but here again the particoloured white appeared almost always in the grandparents. Of the two exceptions the pedigrees are ; Bk. x Bk. Bk. x Bk. Bk. x Bd. 3d. x F. Bk. x Ba. F, x Re | F. eae ae | W. W. But in both cases the particolour white occurs in the great-grandparents. Of the 18 W. dogs with no recorded white in the parentage, four were from Bk. x R. crosses, one from a Bk. x Bk. cross, and six from Bd. x Bk. crosses. * Mr W. F. Lamonby informs us that no breeder has made a speciality of a pure white strain ; and considers that the attempt to create it would fail as the colours of former generations would crop up. This shows at any rate that leading breeders’ opinion does not believe in white breeding true. 32—2 252 On Inheritance of Coat-Colour in the Greyhound Further, four were from R.x F. crosses, and the remaining five introduced Be., Bk., Bd. and F. crosses of a miscellaneous character. It is obvious from these results that the breeding out of white would be at least a difficult task, and that when white has substantially disappeared for a couple of generations, it may suddenly reappear in full force. If it be suggested that Bk. in the nomenclature would not exclude a white toe, nor W. a small black spot, then the reply must necessarily be that no theory of heredity can be of service for the purposes of evolution which would make one class of a white dog with a black toe and a black dog with a few white hairs on the throat, and professes only to predict when such a class as a whole will occur. The protective value of the coat-colour in the two cases would be wholly and entirely different, and we should have to seek further for those features of the pedigree with which the differentiation could be associated. : (4) Colour Scales and Reduction Methods. When we first started work on the greyhounds, the method of contingency had not yet been developed, and accordingly we made tables for the inheritance of melanism and of red pigment and proceeded to find the correlations by the fourfold division process*. In our classification we must admit having been influenced by the statement-of breeders that brindle is the result of the crossing of red with black. A glance at our Tables I and II will show, however, that we cannot look upon red and black as pure forms giving a heterozygous brindle. We have in percentages based on 332 R. x Bk. [ | i i. | | R. Bd. W. ¥. P. Bk. M. Bk. 22,°/, Oe Lf 12°/, 4a?) 16°/, cases: aresult which is capable of interpretation when we pay attention to ancestry (or, again, on the basis of a mixture of alternative inheritance and _ reversion), but is scarcely reducible to any simple Mendelian proportions, still less is it compatible with R. x Bk. = Bd. The fact that R. x R. or R. x F. very rarely gives black of any kind (although F. x F. can give black), while Bd. x Bd. in the rarest cases gives Bk. of any kind, seems to denote more red than black in ordinary brindle and a closer relation of brindle to red than of fawn to red, although F.x F. in the bulk gives equal amounts of red and fawn. Accordingly we grouped our classes for red and black pigments as follows : Red Pigment Black Pigment (a) Red. (a’) Pure Black. (b) Brindle. (b’) Mixed Black. (c) Fawn. (c’) Brindle. (d) No Red. (d’) Fawn. (e’) No Black. * Phil. Trans. Vol. 195, A, pp. 1—47. A. Barrineton, A. Lee anp K. PrARson 253 (d) contained all dogs with white or black, but no red or fawn of any kind. (e’) contained all red or white dogs or the mixture of these colours with fawn. We are now not at all certain that (d’) does not really contain more of black than (c’). We worked out afresh a certain number of tables in which (d’) was placed before (c’) but without real modification of result. The fourfold division of the red pigment inheritance table was made between (b) and (c), and of the black pigment table between (c’) and (d’) for the first set of cases, and after (b’) when (d’) was placed above (c’). We shall cite these methods as Red A, Black B and Black C, respectively. In contingency we took a 36-fold table as our standard, choosing the groupings R., Bd., W., F., P. Bk. and M. Bk. used as in Tables I and II. We shall speak of this method as Contingency D. In order to compare the fourfold method with contingency methods, 16-fold tables and 25-fold tables were worked out to compare with the fourfold tables adopted for the inheritance of red and black pigment respectively. These we shall refer to as Contingency E, and Contingency F. Further, in order to familiarise ourselves thoroughly with the scope and limitations of the new method of contingency, beside the investigations by mean square contingency adopted in D, E, F, we (a) determined a number of results by mean contingency*; and (b) worked out the mean square contingency in a few cases by 144-fold and 400-fold tables. The object of the latter was to test on a large scale the exaggerating effect of isolated units. The amount of arithmetical calculation involved in this investigation is thus not at all represented in the pages of the present memoir, but we believe it has been of advantage in enabling us to form just appreciations of the scope of the new method of contingency. In future it is likely that all our work on colour inheritance will be done by the use of method D, Le. the application of mean squared contingency to groups sufficiently large not to be sensibly influenced by unit difficulties. Even with our 36-fold table the smallness of the white entries is to some extent a difficulty, but the Coutingency F method shows us that the separation of the small unit groups of white has not seriously modified our results. The results deduced by Contingency D method are singularly uniform and steady as compared with those of the fourfold-table methods, and we believe if it be adopted generally for such pigmentation problems, it will not only free us from any question of pigmentation scale, but afford a good result on a not excessive expenditure of calculating energy. At the same time we can hardly over-emphasise the need for caution when isolated units are scattered over a table divided into a very large number of small classest. As illustration of this we cite the following results for the correlation between siblings—dog and bitch—born in different litters of the same parents. It will be seen that while the contingency result only increases from “49 to ‘51 when we pass from 16 to 36 groups, agreeing well with fourfold table results, we spring up to ‘76 as we increase to 400 groups. In fact, the personal * Draper's Research Memoirs I. ‘* Mathematical Contributions to the Theory of Evolution: XIII. On the Mathematical Theory of Contingency,” p. 31 (Dulau and Co., Soho Square, London). + Memoir on contingency, loc. cit. pp. 16 and 35. 254 On Inheritance of Coat-Colour in the Greyhound equation of any breeder who may call his dogs ‘red-fawn’ when the majority of breeders would call them ‘red’ is sufficient to very seriously alter the results when only 2000 dogs are dealt with. Accordingly, our choice of 16 to 36-fold classifications is based on the experience that these give results substantially in agreement with totally different methods, and we take as our standard process the mean square contingency method referred to above as D. TABLE III. Correlation of Brothers and Sisters from Different Litters. Mean of fourfold Tables (A and B) — ... Aug 521 16-fold Contingency Table E he 6 oh "488 25-fold Contingency Table F a as poo UU 36-fold Contingency Table D hee ine ie 509 144-fold Contingency Table he a ae 640 400-fold Contingency Table ite abs ae “760 Lastly, in case the reader should enquire why we dealt with red pigmentation and black pigmentation and have not considered the inheritance of white, we must remark that while many of the breeders filling in Mr Howard Collins’ papers have noted a white ear or small white patches, ete. on black dogs*, we believe possibly the majority, it is not certain that absolutely all have done this; and we are quite sure that insignificant white patches are not noted in the stud-books. Accordingly it seemed best to confine our attention solely to the inheritance of black and red pigment. At the same time we make no statement as to our belief whether or no these pigments are qualitatively different; we consider that the contingency method enables us to fairly escape any such decision. No satis- factory treatment of the nature of pigment in hair has so far come to our notice. (5) On Direct Inheritance. Parental Correlations. We place here our results for the data extracted from Mr Howard Collins’ schedules and from the stud-books in the case of the four parental correlations worked out by method Contingency D. TABLE IV. | UNSELECTED OFFSPRING OFFSPRING SELECTED FOR RECORD Correlation Number Correlation | Number |- Raw Corrected Sire and Dog... 2392 512 963 ~ 474 542 Sire and Bitch ... 2231 ‘579 913 "404 "462 Dam and Dog ... 2419 a10)5) 963 485 554 Dam and Bitch... 2237 +B 913 “499 572 Mean oe = 532 — ‘466 5382 * Such dogs have been classed as ‘ mixed black.’ A. Barrineton, A. Len anp K. PEARSON 2565 The mean of 12 fourfold tables, three for each parental table, by methods of division A, B, C above, was °526. We think we may therefore safely say that the 36-fold contingency table leads to results in quite good agreement with the mean of the older process of dealing with quantities not quantitatively measurable. Nor are the individual results which by the fourfold method are: Sire and Dog, *538 ; Sire and Bitch, 615 ; Dam and Dog, ‘467; Dam and Bitch, ‘482, widely different. Nor do we find any sensible difference if we consider the inheritance of ‘red pigment’ and of ‘black pigment, the mean parental coefficients being 520 and °529 for the two cases respectively. Lastly, the mean parental correlation from four 25-fold and four 16-fold contingency tables was °492, somewhat less than the value as given by the fourfold method or the 36-fold contingency method, which, as we have seen, are in good agreement. We believe that 53 represents extremely well the average parental relation in pigment in the case of greyhounds. We compare this in the following table with previous pigmentation results : TABLE V. Direct Inheritance of Pigmentation. | Dog Dog Man Horse ; Pre iteks ; Eiye-Colour | Coat-Colour Basset Hound| Greyhound Mean Coat-Colour | Coat-Colour Father and Son ae *55O “491 a Gay le2 | +518 Father and Daughter 437 | +649 ? | 579 | -519 Mother and Son __... “482 "486 508 505 | *495 Mother and Daughter 510 567 544. 532 | °538 = = = _| a | Mean... 495 | 522 | 5296 | ‘532 | 518 This table seems to indicate that there is no evidence at present to show that pigmentation imheritance differs in intensity in man, horse or dog, nor is there evidence to indicate any persistent preponderance of one sex. We should notice, however, that in all four cases the daughter is more like the mother than the son is. On the other hand the daughter is more like the father than the son is in horse and dog, the sex similarity being only preserved in the case of eye-colour in man. We may safely say that the mheritance of pigmentation cannot differ widely from ‘50 for all our series. If we turn to parental inheritance in the case of dogs selected for record we see that the correlation has been reduced, a result which is the general rule whenever selection takes place. The reducing factor is 875. Being completely ignorant of the relative standard deviations of the material under consideration, we can hardly reach a more scientific measure of the selection that takes place in record than this reducing factor. But its value is sufficient to show us that our original hesitation to use the greyhound stud-book was justifiable ; the correlation * See R. S. Proc. Vol. 66, p. 159 ftn. Increased information as to inheritance in dogs confirms the view that the sires given in the Basset Stud-book are unreliable. 256 On Inheritance of Coat-Colour in the Greyhound of parent and offspring is sensibly reduced by selection in recording. Mr Howard Collins’ data enable us, however, to roughly allow for this selection; the corrected values are indicated in the last column of Table IV, and we shall proceed to use a like correction in the following paragraph. (6) On Direct Inheritance. Grandparental Correlations. We can here unfortunately only deal with the data from the stud-books. The greyhounds, whose offsprings were recorded for Mr Howard Collins, appear to be in great bulk, if not entirely, well-known hounds whose names are in the stud-books. The selection arises from only one or two individuals in each litter being recorded in the stud-books. This, as we have seen, weakens the correlation; possibly it arises because the offspring of more fashionable colours only are recorded in the case of a litter, the parents of which may be of less fashionable colours. If we consider grandchildren of stud-book parents, then there has clearly been a selection out of the litters of this generation, not only of some members of each litter, but of whole litters, because certain parents have been omitted from record altogether, as the rejected members of the litters of the first generation. Now the problem thus stated becomes undoubtedly a complex one, as the reduction for influence of selection on correlation, if the selection extends over several generations, is by no means easy to determine. But it seems not unreasonable to suppose that the total distribution of colour in the sporting greyhound, although probably subject to secular change, is not changing very rapidly. In other words, the effect of selection for breeding is to maintain a nearly constant colour distribution for a few generations. If this be so, the chief effect of selection in record is due to the weakening of the correlation by selection of offspring and not to the selection of the breeding parents or grandparents. Accordingly it seems to us that all we can do is to divide the grandparental correlations we find from stud-book pedigrees by the factor ‘875, and treat these as the best approximations available to the grandparental correlations. We have then the following results. TABLE VI. Grandparental Correlations. Mean Square Contingency 36-fold tables. l Grandparent and Offspring | Number tens ae Paternal Grandsire and Dog __... 952 275 314 Paternal Grandsire and Bitch ... 893 229 261 Maternal Grandsire and Dog... 939 264 | 301 Maternal Grandsire and Bitch ... 888 3360 384. Paternal Grandam and Dog __ ... 947 322 368 Paternal Grandam and Bitch ... 900 272 Bali Maternal Grandam and Dog... 911 291 "332 Maternal Grandam and Bitch ... | 863 338 386 Mean... ia — 291 332 * The grandparental tables treated by the fourfold method gave—owing to some extent to paucity of number —rather irregular results. The mean of 16 fourfold tables Red A and Black B was -213, and of sixteen 16-fold and 25-fold contingency E and F tables *247, both less than the 36-fold tables. A. Barrineaton, A. LEE AND K. PEARSON AST | It would thus appear that the grandparental correlation cannot be very different from the mean value 3. If we compare the results now obtained with earlier pigmentation series we have the following table: TABLE VII. Grandparental Relationship. Srare Man Horse Greyhound | Coiailfasicaty Cae aes 0ata Eye-Colour | Coat-Colour | Coat-Colour Mean Paternal Grandfather and Son ous 421 "324 "314 353 Paternal Grandfather and Daughter... 380 361 261 334 Maternal Grandfather and Son a 372 | "359 B01 B44 | Maternal Grandfather and Daughter... | — *297 312 384 | 331 Paternal Grandmother and Son teal 272 *309 “368 316 Paternal Grandmother and Daughter 221 | 204 | 311 "245 | Maternal Grandmother and Son a: 252 261 332 282 | Maternal Grandmother and Daughter | 318 "235% | 386 313 | Mean ne ses 317 296 332 315 | We conclude from this that as in the case of parents, so in the case of grandparents, there is no substantial difference in pigmentation inheritance between man, horse and greyhound. We may reasonably hold that a geometrical series : 2, 2 x 3p oy x (3) 3 x Cor sie will express the decreasing correlations between offspring and ancestry as closely for the greyhound as it does for man and horse. The evidence in favour of a change of sex weakening the intensity of here- ditary influence is of a rather doubtful kind. It has been shown to hold for eye-colour in man by Pearson}, both in the case of direct and collateral heredity, and by Lutz§ for further data in the case of direct inheritance. It does not appear to be markedly true for coat-colour in horses. For greyhounds it is not absolutely true, although the differences are of the probable-error order in the case of the unselected parental relations. Here the sire, as in the case of the horse, has a more marked influence on the coat-colour of the daughter than on that of the son, while the dam for man, for horse and for both cases of dogs is more influential in the case of the daughter than in that of the son. In the grandparental series it does however appear to be true; thus we find: * Erroneously given as ‘2392 instead of 2351 owing to a slip in the value used for log k in finding the equation for r in Biometrika, Vol. 11. p. 231. The value for & is correct, the equation for 7 slightly incorrect. t See ‘* The Law of Ancestral Heredity,” Biometrika, Vol. 1. pp. 211 et seq. t Phil. Trans. Vol. 195, A, pp. 114—117. § Biometrika, Vol. 11. pp. 237—240. Biometrika 111 Bo 258 On Inheritance of Coat-Colour in the Greyhound Grandparental correlations with regard to change of sex: Mean value no change of sex: 350. Mean value one change of sex: 336. Mean value two changes of sex: 306. It is further true for the selection in record values of the parental corre- lations *, Thus we are inclined to think that there really exists a weakening of inheritance with change of sex in the case of the greyhound, but that it is so small that it is lable to be screened by the probable errors of the results. On the whole, for direct inheritance of pigmentation, the greyhound falls quite well into the system formerly found for man and horse. (7) Collateral Resemblance in the First Degree. From the material available on Mr Howard Collins’ schedules we could only obtain the degree of resemblazice between siblings of the same litter. There was no possibility of getting siblings from different litters except by appeal to the stud-books with their selection for record. Since selection for record depends on the personal equation of the breeder, and the points he selects may to some extent involve coat-colour, the tendency accordingly ought to be to emphasise rather than reduce the fraternal correlation. We find, however (Table VIII), that when we compare the un- selected record of the schedules for the same litter with the selected record of the stud-books for different litters that the values are much reduced, i.e. from “676 to ‘529 on the average. Our first idea was that this great reduction must be due to the fact that we are in one case considering siblings from the same and in the other case from dzfferent litters, or that there must be a sensible difference in the degree of resemblance in the two cases. This was opposed to our experience in the case of Basset Houndst. To confirm the supposition in the case of the greyhound, we worked out from the stud-books all three sibling relationships for the case of siblings from the same litter. To our great surprise the result was only slightly in excess of the result obtained for siblings from different litters. In other words, for the greyhound if the same material was used in both cases, the conclusion reached for the Basset Hound seemed to apply, i.e. there was no very marked difference in fraternal resemblance when the siblings were and were not from the same litter. We were thus left in considerable doubt as to what interpretation could be put on the fact that fraternal correlation between members of the same litter when found from the schedules and from the stud-books was so markedly different. It seemed difficult to believe that it could be due to selection for record, because it appeared to us that this ought, as far as it influenced colour, to tend to increase the correlation. On examining our totals for the two cases we noted one point which might conceivably throw light on the matter. In the schedules we had 651 pairs of parents, giving rise to 7484 pairs * The means for unselected and corrected selected values of parental correlation give *539 for no change of sex and ‘524 for one change of sex, a slight difference. + Royal Soc. Proc. Vol. 66, p. 158. A. Barrinaton, A. LEE and K. PrARSON 259 of brothers or about 11°5 pairs to each pair of parents; brothers of the same litter from the stud-book were given by 532 pairs of parents and provided 2144 fraternal pairs, or about four pairs to each pai of parents; lastly, brothers of different litters from the stud-book were provided by 258 pairs of parents, and these gave 1044 pairs of brethren, or again about four to cach pair of parents. Could it be that this difference in the number of brethren to cach pair of parents was the source of the large drop in correlation as we passed from schedules to stud-book? This point was then taken up and investigated*. The members of a litter were given numbers, 1, 2, 3, ... and these were put on tickets and pairs of these tickets drawn at random. In this way 2086 pairs of brothers were obtained, no brother being used with more than one other brother. The table thus obtained is given as Table MMMM in the Appendix. The correlation obtained by the 36-fold table is ‘6697, while for 7454 brothers using every brother with every other brother it 1s 6607. The difference is in fact insensible, but the larger correlation is in the series of non-repeated brothers. We conclude therefore that the difference between the fraternal correlation for brethren from the same litter as taken from the schedules and from the stud-book is not due to any purely arithmetical effect of taking many pairs from large litters. The only other explanation we can give, but we see no means at present of testing its truth, les in the view that the colours of the litter were taken at a much earlier stage for Mr Howard Collins’ schedules, than for the stud-book. In the latter cases dogs are often not entered for a year or two. It is possible therefore that the litter as a whole is more alike TABLE VIIL. Collateral Heredity. Resemblance of Siblings. UnsreLecrep Recorp SeLtectep Recorp Nature of Same Litter, Same Litter, Non- Gee tee | Sibling Pair Repeated Brothers | repeated Brothers | Different Litters | No. |Correlation| No. | Correlation | No. | Correlation | No. | Correlation | | | | Dog and Dog... | 7484 ‘661 | 2086 | 670 2144 524 1044 521 Bitch and Bitch | 6542 700). mall =| = 2002 “595 1010 558 Dog and Bitch | 7175 “669 | a 2864 558 1031 509 7 _ \_ | Mean ...]| — *G7Ge |) == | 670 — | +559 | = 529 * The whole problem is a difficult one, there are so many statistical pitfalls surrounding it. Theoretically it would seem that both for fraternal and homotypic correlations the increase in the number of brothers or of homotypes taken from each unit ought to alter the correlation, actually we cannot find much difference when the same material is worked out with many and with few members of each unit. See the ‘‘ Homotyposis” memoir, Phil. Trans. Vol. 197, A, pp. 310—313; the memoir on ‘‘Mendel’s Principles,” Phil. Trans. Vol. 203, A, pp. 74—77 and the paper on ‘“‘ Telegony in Man,” R. S. Proc. Vol. 60, p. 279. 33—2 260 On Inheritance of Coat-Colowr in the Greyhound in the puppy-stage than the siblings are at a later age, and accordingly this may account for the lessened resemblance of stud-book pairs of brethren. It may be possible later to test this, but at present we can only throw it out as a suggestion, we see no other way to account for the anomalous results of the Table. The last column gives a result agreeing remarkably well with that for Basset Hounds from different litters, but the want of agreement between the first and last column is very striking. We can only ask: Is it due to record at too early a stage ? The above results for fraternal correlation were all found by Contingency D method, i.e. that of mean square contingency for a 36-fold table. For comparative purposes three fourfold division tables were worked out by method Red A and another three by method Black B. We obtained the results given below in Table IX. TABLE IX. Mean Sibling Resemblance. | | Bane Litter | Different mee | Method | Schedules | Stud-book | -——- soS eS Se | = =| | | | 36-fold Contingency D on aes 676 | 529 | | Two fourfold Divisions A and B .. a4 “680 | 538 | 16-fold and 25-fold Contingency E and a | 640 | “498 We see from this that a 36-fold contingency table gives results in sensible agreement with those to be found from the old fourfold division method, while in 16-fold and 25-fold tables the result is very slightly less, showing that the grouping is hardly fine enough. We now pass to the comparison with man and horse, the TABLE X. Resemblance in Pigment of Siblings. Man Horse Dog, Coat-Colour | al a zi Nature of Sibling | Greyhound | Basset Hound Pair ae Eye- | Hair- | Coat- | ‘ SF | | Colour | Colour | Colour i gue ___| Different | Same |Different | | -Gehedules tapaeheo Litters | Litter | Litters | Brother and Brother | 517 | °620 | -623 | 661 524. 521 ] | Sister and Sister ... | °446 570 | °693 | ‘700 “595 558 . 508} ‘526 | Brother and Sister... | -462 | +550 | +583 | -669 | 558 | -509 [J Mean , ... | ‘475 | *580 | ‘633 676 | 559 529 | °508| 526 | A. Barrineton, A. LeE AND K. PEARSON 261 data for which are given in the memoirs cited below*. The results are given in Table X. We sce that we have here a very considerable range of values, that the Basset Hounds and the Stud-book Greyhounds agree well with the mean value for man+t, but that the Thoroughbred Horses and Schedule Greyhounds exceed these values. The only common factor that we see to explain this difference lies possibly in the earlier age of record in the last two cases. The hair- colour changes with growth in the case of children}, but there is probably greater uniformity in the hair-colour of siblings in the first year of life than at any later age—our records are for children in the bulk between 10 and 14 years old—and this is a stage hardly comparable with that of yearlings and puppies, as far as definiteness of hair-colour is concerned§. It will be seen from these results that the suggestion made in Biometrika, Vol. 11. p. 391, that the high value of the greyhound fraternal correlation is due to the action of individual prepotency on members of the same litter, is not confirmed. We consider that in the case of the dog we may safely say that there is no marked difference between the degree of resemblance of siblings of the same and of different litters. After considerable labour we found it impossible to collect enough data from the stud-books for horses to test the same point on twin and non-twin foals of the same parents. Both twins rarely survive to be recorded, and twin foals themselves are infrequent. The point can and will be dealt with on the basis of Darbi- shire’s material for mice. So far, however, even if a co-uterine environment does increase the resemblance of brethren from the same litter in some species, 1b certainly does not appear to do so for all, and at any rate the high value of fraternal correlation in the case of the greyhound is not due to this source. It is peculiar to the nature of the record. We believe as in the case of the horse it may possibly be due to a mere temporary influence on the somatic characters of the embryonic co-environment. This disappears when the record of the colour is taken at a later stage. Should this view be the correct one the stud-book records would after all turn out to be of more value than the schedule records. We should then conclude that judged from pigmentation the inheritance in grey- hounds is given by: ‘466 for parental correlation, and ‘529 for fraternal correlation (different litters). These numbers would be in excellent agreement with the corresponding mean values *460 and ‘519 found for physical measurements in man||. * Phil. Trans. Vol. 195, A, pp. 93 and 106. Biometrika, Vol. m1. pp. 154 et seq. The hair-colour returns have been taken from school children; these children give ‘53 for eye-colour—a result close to Greyhound and Basset Hound values for different litters. + The mean value in the case of man for 9 series of physical measurements in the adult is °519 (Biometrika, Vol. 11. p. 519) and for 12 series of head-measurements in children is ‘513 (Biometrika, Vol. 111. p. 140). + The correlation is not nearly so great as some have supposed, but of this more on another occasion. § In cattle the like difficulty arises. Some are recorded as mere calves and the colour changes a good deal after losing the first coat. Thus a bull calf recorded as a ‘fawn’ may be ultimately a ‘ dark fawn’ or ‘red’ bull. || Biometrika, Vol. 11. pp. 378 and 390. 262 On Inheritance of Coat-Colour in the Greyhound It is possible that the difficulty here suggested, a temporary influence of embryonic co-environment, ought to be more fully regarded when records are taken of breeding experiments, especially in all cases of hair-colour where the ‘adult’ colour may not be sufficiently closely approximated to until after the loss of the first coat*. Still we are not prepared to attribute all high fraternal correlations to such a source as too early record. We consider that there is really greater variation in fraternal than in parental resemblances. Some of it may be due to a permanent effect of co-environment, embryonic or not. The problem is one of considerable interest and yet of great difficulty, and we only hope that more light may yet be thrown on it from further reduction of records or direct breeding experiments. > (8) General Conclusions. Our reductions of the greyhound data indicate : (1) That whether there be one or more pigments, no class of greyhound can be looked upon as purely dominant or purely recessive. The colours of the earlier ancestry crop up in the offspring of parents of definite colours. We do not see how Mendelian principles can be in any way applied to the greyhound. We publish, however, the whole of our tabulated data, and are quite ready to receive and work out reasonable suggestions for its statistical reduction on Mendelian lines. (ii) That as far as ancestry is concerned the biometrical statistical method leads to parental and grandparental correlations sensibly identical with those which have already been found for pigmentation inheritance in man and horse. There can be no question therefore whether the knowledge of the ancestry is or is not important. It is equally important in all three cases, and no good prediction can neglect the high correlations of the ancestry beyond the parents. (au) That if we deal only with the stud-book records there is no difference of a marked character between siblings from the same and different litters, and the values of the fraternal correlation reached are in excellent agreement with those found for Basset Hounds and for pigmentation and physical measure- ments in the case of man. But if we deal with a colour-record made with the litters in a very early stage, we find the highest fraternal correlations yet reached. The nearest approach to them are the coat-colour correlations in the case of the horse, followed at some distance by Dr Warren’s values for Aphis and Daphnia. It is probable that these high fraternal values with fairly uniform parental correlations are due to different sources, possibly to too early recording in the horse and dog, almost certainly to differentiated environment in the case of the insects. We submit, however, that while fraternal correlation ‘clusters’ between °5 and ‘6, * The percentage returns given by Virchow, Pfitzner and others for darkening of the hair with age are fallacious because they are not dealing with the same material at different ages. They have neglected (i) the selection of the fitter—health we find to be correlated with hair colour—and (ii) the children in the primary schools (Virchow) are compared with a totally different group and class in the high schools, We are returning to this matter in another paper. A. Barrinaton, A. Lez AnD K. PEARSON 263 the nature of its variation and its relation to parental correlation are still very obscure. (iv) That so far.as work on the inheritance of pigmentation in the Biometric Laboratory at University College has yet gone, we find that for man, horse and dog in long series the results are in good agreement, and can be described by the statement that ancestral correlations diminish in a geometrical series and sensibly the same series. We hope shortly to publish two further long series of pigmen- tation inheritance statistics; should they give results in accordance with those already reached, no further reductions of this kind will be made by us, for we think the generality of the law will have been sufficiently demonstrated. In saying this we do not overlook the vast amount of material now being collected by Darbishire and others on inheritance of pigmentation in mice, but it is unfortunately not in a form to which it is easy to apply the mathematical processes required. The selection is so stringent, when two true breeding strains are crossed, that it is difficult to apply the complex equations for the influence of selection on correlation. What we should especially like to know would be: (a) after hybridisation, do or do not the offspring of the hybrids, if mated at random inter se, give a stable population? (b) If they do give a stable popu- lation, do the ancestral correlations diminish or not in a geometrical series ? and (c) If they do, are their numerical values sensibly or not the same as those we have found for man, horse and dog? If these questions were answered in the affirmative, then it would be more possible to determine the relationship between so-called Mendelian Principles and the Ancestral Law. The latter seems to apply closely to any fairly stable population with random or nearly random mating, even in the matter of pigmentation. According to the Mendelian hypothesis developed by one of us, the offspring of the hybrids should, if mated at random, give a stable population, and this is likely to be true on many other hypotheses. What happens in such a population? According to the view of some Mendelians both factors of the original cross are, as far as some one character at least is concerned, in appearance, elements of such a population; this being so we ought to be able to see, once the stability of such a population of hybrid’s offspring is established, much more clearly than at present the relation of the two views to each other. The differences between our man, horse and dog returns and Darbishire’s mice returns seem to consist essentially in this: that in the three former or intra-racial results the intra-breeding between differently pigmented members has gone on for generations, while in the latter or inter-racial results there has been separation for generations. But if the offspring of hybrids mated at random give a ‘stable’ population, then we ought to be able to predict at least certain phenomena with regard to the result of crossing its constituents. What is now quite clear about the mice is that ancestry can be no more neglected in their case than in the cases of man, dog or horse. 264 On Inheritance of Coat-Colour in the Greyhound APPENDIX I. 36-fold Contingency Tables. Sire and g Offspring. Unselected Record Sire and 2 Offspring. 3 9 Dam and ¢ Offspring. 55 " Dam and 9 Offspring. 5 ¥) Sire and ¢ Offspring. Selected Record Sire and @ Offspring. = Dam and g Offspring. 53 5 Dam and 2 Offspring. 3 a Paternal Grandsire and ¢, Offspring. Selected Record Paternal Grandsire and ? Offspring. ” ” Maternal Grandsire and ¢ Offspring. - AR Maternal Grandsire and 9 Offspring. . 5 Paternal Grandam and g Offspring. 5 < Paternal Grandam and @ Offspring. 33 a5 Maternal Grandam and @ Offspring. 3 ss Maternal Grandam and ? Offspring. Ps * Brother and Brother. Same Litter. Unselected Record Sister and Sister. Same Litter. Unselected Record Brother and Sister. Same Litter. s 3 5 Brother and Brother. Different Litters. Selected Record . Sister and Sister. Different Litters. e . Brother and Sister. Different Litters. + ; Brother and Brother. Same Litter. Selected Record Sister and Sister. Same Litter. , 5 Brother and Sister. Same Litter. 5 Pr Brother and Brother. Same Litter. Unselected Record. repeated No brother TABLE a. Sire. P. Bk. iM. Bk |i Ba. Fr. | w. 39 Offspring ¥. Totals ... 443 712 490 404 5 PAGE 264 265 265 265 265 266 266 266 266 267 267 267 267 268 268 268 268 269 269 269 269 270 270 270 270 271 A. Barrineaton, A. Lee anp K. PEARSON Offspring ¥. TABLE . Sire. P. Bk. |M. Bk.| Bad. F. W. R. Totals o+ | P. Bk. 209 147 50 39 = 48 493 ao | M. Bk. 94 344 69 78 = 42 627 | Bd. 41 69 216 4] 2 63 432 5 | F. 38 53 53 146 5 58 353 a | W. 2 Hy 3 8 3 3 26 | 8 32 29 41 83 ae 115 300 Totals ... | 416 649 432 395 10 329 2231 TABLE y. Dam. P. Bk. |M. Bk.| Ba. F. | w. | R. Totals 525 | 614 | 438 | 410 | 39 | 393 | 2419 TABLE 6. Dam. P. Bk. |M. Bk.| Ba. F. W. R. | Totals Offspring ¢. TABLE aa. Sire. P. Bk. |M. Bk.| Bd. if W. R. Totals S | PBK... 59 | 57 42 17 1 36 212 Sil Ble a3. 23 64 40 27 2 22 178 | Ba. 16 25 143 28 as 39 251 aaa 11 24 24 34 = 44 137 2 | W. =e 3 2 2 = 4 11 oS | R. 18 10 35 36 = 75 174 Totals .. Biometrika 11 34 265 266 On Inheritance of Coat-Colour in the Greyhound TABLE £8. Sire. P. Bk. | M. Bk.| Bad. F. W. RE Totals o+ | P. Bk, 44 54. 48 18 ane, on M. Bk. 113} 41 29 26 1 | Bad. 24 31. | wey Ppl ee S, F. 12 14 Sill 36 — Z W. 1 — 7 3 S 18 14 14 35 30 = Totals 108 154 277 145 1 TABLE yy Dam P. Bk. | M. Bk. Bd. F, W. R. Totals So es Ble 68 ON Se Oe BR sale = 21 212 no | M. Bk. . 44 | 76 | 17 Oy |) 21 | 178 a Bd. 32 53 104 23 — 39 251 a 10 10 29 25 45 — 28 137 nm | W. — 3 4 1 1 2 11 a R 27 24 | 39 25 i 65 174 Totals 181 265 211 128 2 176 963 TABLE 66. Dam. Totals o+ | P. Bk. ... 211 no | M. Bk. ... 136 | Bd. 248 al | tts 136 @ | W. 16 S R. 166 Totals ... 913 TABLE e. Paternal Grandsire. P. Bk. | M. Bk.| Bd. F. W. R. Totals Offspring ¢. Totals ... A. Barrineaton, A. LEE anp K. Prarson 267 } TABLE ¢. Paternal Grandsire. | P.Bk.|M.Bk.| Bd | F | W. | RB | Totals o+ | P. Bk. 64 49 34. = 56 209 oo | M. ‘ a 136 a 242 5. 127 2 | 15 5 164 Totals 893 TABLE y. Maternal Grandsire. P. Bk. |M.Bk.| Ba | F. w. R. | Totals | Geel DIB eee 56 66 | 40 14 = 30 206 Spulahe Ble %6s 35 58 34 14 = 28 169 ied: 74 33 57 15 3 64. 246 m | F. 33 20 30 20 | 31 134 2 | W. 3 il 2 1 = 3 10 oS | B. 36 29 | 37 17 = 5D 174 | Totals ... 939 TABLE @. Maternal Grandsire. P. Bk. | M. Bk.| Bd. F. W. R. Totals OP: Bk. c:. 65 64 29 9 2 36 205 els Bla 43 41 29 7 =e 12 132 a | Ba. 61 33, | * 67 23 1 54 239 a | F. 35 18 32 25 = 24 134 | W. 4 3 3 3 = 2 15 5 | BR. 25 35 26 16 = 61 163 Totals ... 888 TABLE 1 Paternal Grandam. P. Bk. | M. Bk.| Ba. F. W. | RB. [| Totals So P. Bk. 33 57 60 14 = 44 208 oo | M. Bk. 22 47 54 20 3 27 173 2 | Ba. 34 30 117 19 = 49 249 2b ela) 20 25 24 21 7 39 136 | W. : 3 3 3 heat at 2 11 oO |B. 25 27 46 11 = 61 170 Totals ... | 137 189 304 85 10 222 947 34—2 268 On Inheritance of Coat-Colour in the Greyhound TABLE F. Paternal Grandam. P. Bk. OM. Bk | Ba |) Rew. R. | Totals ot | P.Bk ... |) 33 ey} 48 20 3 49 205 no Me Bee | 18 35 36 13 1 29 132 a |Bd ..]) 34 32 | 113 20 ee 48 247 EF. | 33 23 37 18 2 32 135 @|W .. oe 6 4 a 3 16 5 | BR. 1 81 | 96 33 13 2 60 165 ———— — Totals 141 | 169 | 273 88 8 22) 900 TABLE «x. Maternal Grandam. E Bel M. Biel Bae hem Vive tee So 53 25 ae Maks e a 56. yl) sap 28 a | 46° 680) ap | sae 39 Eo 56. |) 16" || sone ee 41 2 1 4 | 2 S 48 | * 98) as 9 50 gaa | tes.) quae | oe lil) toe TABLE 2. Maternal Grandam. P. Bk. | M. Bk.| Bad. F. We R. Totals OF 57 70 17 17 5 32 198 wp | M. Bk. 35 44 10 13 1 26 129 2 | Bd. 54 47 b4 37 1 43 236 erat 19 40 15 20 1 34 129 | W 3 4 4 2 2 l 16 a 45 = 155 | 863 TABLE p. First Brother. M. Bk. R. Totals 3 - | P. Bk. 136 1774 © | M. Bk. 340 | 1276 181 204 29 103 2133 co | Ba. 187 181 758 150 9 100 1385 = CE 154 204 150 | 486 19 91 1104 q | W. 3 29 9 19 18 11 89 S| aR 558 999 - a Totals 1774 | 2183 | 1385 | 1104 89 999 7484 Sister. Second Brother. Second Sister. A. Barrineton, A. Lez anp K. PEARSON 269 Second Sister. TABLE vp. First Sister. P. Bk. |M. Bk.| Bad. | F. W. Re Womotals PaBkae. 1442 | M. Bk. ... 1871 | Bd. 1258 | F. 929 | W. 93 R. 949 | Totals 6542 TABLE a. Brother. P. Bk. |M. Bk.| Bd. F. W. R. | Totals P.Bk. ...] 887 | 340 | 197 | 119 5 131 | 1609 M. Bk.... | 276 | 1288 | 165 | 262 21 | 102 2114 Bd. ... | 170 213 | 745 133 5 | 82 1348 F. ... | 148 176 | 143 | 469 29 115 1080 W. Be 15 22 20 10 16 9 92 Re .. | 116 72 | 100 94 10 540 932 Totals ... 1612 | 2111 | 1300 | 1087 86 979 | 7175 TABLE pu. First Brother. M. Bk.| Ba. Vv. | RB. | Totals P. Bk. ... 2 232 M. Bk. ... 4 200 Bd. 2 280 F. 2 141 W. _ 1 R. 1 180 Totals ... | 238 P 280 1044 TABLE vp. First Sister. P. Bk. |M. Bk. | Bad. F. W. R Totals . Bk. 88 48 48 24 2 28 238 M. Bk. 48 | 50 21 22 2 154 Bd. 48 21 142 19 4 257 FE. 24 22 19 48 9 145 W. pall arene 4 9 fs 20 R. 98) 11 23 23 3 196 Totals 1010 270 On Inheritance of Coat-Colour in the Greyhound Sister. Totals ... Totals TABLE oo. Brother. P Be | MBE) Bde | W. | R. | Totals P. Bk. 93 | 53 41 22 1 15 995 .. | M. Bk, 49 63 31 16 2 17 178 3 | Ba. 38 36. | 143 21 2 29 269 S| F 17 23 29 42 2 33 146 | W. 2 3 3 1 i 6 16 Re 36 19 22 31 1 88 197 Totals . 235 | 197 | 369 | 138 9 188 | 1031 TABLE ppp. First Brother. : P. Bk. |M. Bk.] Ba. F. W. R. | Totals | P.Bk ...| 220 | 119 72 37 1 47 496 S |M.Bk....] 119 | 122 71 47 16 29 504 cq | Bd. 72 71 298 54 10 55 560 Se 37 47 54 78 2 43 261 S| We 16 2 32 3 | R. 1 291 i) —[ ees nn Totals ... 504 261 2144 TABLE vp». First Sister. Totals a 500 2 379 3) 582 S 285 27 jo) 3 229 D 2002 TABLE oaw. Brother. M. Bk. A. Barrineton, A. Lez and K. PEARSON 271 TABLE ppp. First Brother. P. Bk. |M. Bk.| Bd. | ee | R. | Totals onl = |P.Bk ...] 250 | 83 | 358 45 | 42 478 o|MBk...] 83 | 350 | 60 51 8 27 579 | Bd ...] 58 60 222 45 | 3 | 20 408 =) || ie ies 45 51 45 132 6 28 307 eee eee 2B © 23 6 8 4 29 8 | R. eee 27 20 | 28 4 164 285 Totals ... 478 579 408 307 29 285 2086 APPENDIX II. Classified Colour Inheritance Tables. PAGE AY Sire and g Offspring. Unselected Record : 4 : : ; : 273 B. Sire and 2 Offspring. re Fe 274 C Dam and ¢ Offspring. " 3 : : : : : : 275 D. Dam and @? Offspring. 3 3 : : : : : ‘ 276 AA. Sire and g Offspring. Selected Record . ‘ : : , : : 277 BB. Sire and @? Offspring. » ” 278 CC. Dam and ¢ Offspring. 5 . , : : ‘ F : 279 DD. Dam and @ Offspring. ” ; : 3 F : : 280 E Paternal Grandsire and ¢ Onions. Selected Record 281 F Paternal Grandsire and @ Offspring. 33 * 282 G Maternal Grandsire and ¢ Offspring. 3 35 283 H. Maternal Grandsire and @ Offspring. 3 5 284 I Paternal Grandam and ¢ Offspring. * x : : : : 285 J Paternal Grandam and @ Offspring. sn ss : : ; ‘ 286 K Maternal Grandam and ¢ Offspring. ‘; : : ‘ ; 287 L. Maternal Grandam and @ Offspring. ce 5 E : : : 288 M. Brother and Brother. Same Litter. Unselected Record F : ; 289 Ni Sister and Sister. Same Litter. <5 5 : : : : 290 O. Brother and Sister. Same Litter. s : ; : 291 MM. Brother and Brother. Different Litters. Selected Record : i ; 292 NN. Sister and Sister. Different Litters. 5 Pr : ‘ : 293 OO. Brother and Sister. Difterent Litters. - ; ; : 294 MMM. Brother and Brother. Same Litter. Selected Record , : : ; 295 NNN. — Sister and Sister. Same Litter. FF 43 ‘ . : : 296 OOO. Brother and Sister. Same Litter. 5 297 MMMM. Brother and Brother. Same Litter. Unselected eeord: No brother repeated . : : : : : : : : : : 5 : 298 The following is the complete series of colour and colour combinations we have met with. In each case the order of the colour is supposed to indicate their relative predominance. In the tables A—D, M—O, first compiled, particoloured 272 On Inheritance of Coat-Colour in the Greyhound dogs were grouped into single classes and not distinguished by placing the predominant colour first. Some breeders decline to distinguish between red and fawn; hence the category R. or F. Where } occurs between two columns or rows In a table, it means that one or more colours do not occur in that table at the point indicated. 1. R.=Red. 29. W. F.=White and Fawn. 2. R. F.=Red and Fawn. 30. Bd. F. W.=Brindle, Fawn and White. 3. R. or F.=Red or Fawn. 31. F. Bd. W.=Fawn, Brindle and White. 4, F, R.=Fawn and Red. 32. Bd. or F. W.=Brindle or Fawn and White. 5. R. W.=Red and White. 33. W.= White. 6. W. R.= White and Red. 34. Be. W.=Blue and White. 7. BR. F. W.=Red, Fawn and White. 35. W. Be.=White and Blue. 8. F. R. W.=Fawn, Red and White. 36. Be, Bd.=Blue Brindle. 9. W. R. F.=White, Red and Fawn. 37. Be. Bd. Tk.=Blue, Brindle, Ticked. 10. W. F. R.=White, Fawn and Red. 38. Be. Bd. W.=Blue, Brindle and White. 11. R. or F. W.=Red or Fawn and White, 39. W. Be. Bd.=White, Blue and Brindle. 12. W. R. or F.=White and Red or Fawn. 40. Be. Tk.=Blue Ticked. 13. Bd.= Brindle. 41. Be. F.=Blue and Fawn. 14. Bd. Bk.=Brindle and Black. 42. Be.=Blue. 15. Bk. Bd.=Black and Brindle. 43. Be. Bk.=Blue and Black. 16. Bd. W.=Brindle and White. 44, Bk. Be. W.=Black, Blue and White. 17. W. Bd.= White and Brindle. 45. Be. Bk. W.=Blue, Black and White. 18. Bd. F.=Brindle and Fawn. 46. Bk. Bd. W.= Black, Brindle and White. 19. F. Bd.=Fawn and Brindle. 47. Bk. W.=Black and White. 20. R. or Bd.=Red or Brindle. 48, W. Bk.=White and Black. 21. R. Bd.=Red and Brindle. 49. Bk. Tk.=Black Ticked. 22. R. Bd. W.=Red, Brindle and White. 50. Bk. W. Tk.=Black and White Ticked. 23. R. Tk. Bk.=Red, Ticked Black. 51. W. Bk. Tk.=White and Black Ticked. 24, R. Bk. Pts.=Red, Black Points. 52. W. Tk.=White Ticked. 25. R. Bk.=Red and Black. 53. F. Bk.=Fawn and Black. 26. R. Bk. W.=Red, Black and White. 54. F. Bk. W.=Fawn, Black and White. 27, F.=Fawn. 55. Bk.=Black. 28. F. W.=Fawn and White. TABLE A. Sire and Offspring &. A. Barrinaton, A. Lek and K. PEARSON OA A IL GM LM “M A MPAA Pla Pal ‘og eitiecd “M ‘Pd °d PA OL Sire. 232 t 2 7 284 eel 1 C 4 3 ee 37 Ge Baal aa Biometrika 111 "P suudsyo 3 TABLE B. Sire and Offspring ¢. On Inheritance of Coat-Colour in the Greyhound re oD N WN “AC rcp Voces Cucclas (ar Mest coterie cca Baay ey || S As N x Wag Se | | eee | ees |S ee nN tH > saqeg Pld lle ee ait ata Og ; 1D SS | Gras aa |) soe ON Ge) rat [ak a = € le i 5 "MPI OT Loe bs bel alt Tee See as > = PI Om VP Tea SET aT i Teale sl aa aes = pases (i ac se "M Og | | ALL ee See PSS ae ee “MM | | Die ae a Vesta eae mealies veil? || Sy le es ‘Mae [ay 1a | les 1 las 1 sates a ee a ; A d a ee ee cee ipa ae |S |) 28 Jee peek. (ek eee Apa [ASE [aes cet ||) |S eee ts mes > —_—}— - — $$$ —— = — ae pq ee eee a Ne eee =) als re pres Coes (ia Pl ge pen el te ner ba Se | eel : am b Meo OP ee eee aa eet > = ok Accom as (aca eae (cs nam el elf crca | era |Mlfeolbe a |i ce || Se Bales SS aS 8 Be. W. Be. Bd. Be. F. Totals Bd. W. W f *$ sutdsyo TABLE C. Dam and Offspring &. Dam. A. Barrineton, A. Lene anp K. PEARSON 275 apacrade | 1 tlie t it itil det 1 OM 7 = | "P suudsyo = Ciel “M OR "M. “ML a “MA “W PAI “AM PAL [Sasa se 3 safe |/ 8,5 CN ets eID eet pil a iL Petey Pacl far fies “MYL t0“"°Y © “MC UW < Mom |e) PS ee oe eer) 8 Setor un ale | Sota ees We 5 Pee eee eS i ieee LIRISIIS=LI™ (esa lie |B Pig PELEPEiiihss ie > & aaa Miss é oe ee A eae 3 ea ae cee rier Be oufaaaafiacfaafn~af=alaslaol : - aon Le 3 eg ial eels cee aerpe me See o Ase SS pee gee | | Cr ay ais dizctlioy 4 s SDOy ODDO OSM en eafaafnafa-faofa-$aaf nal of aafa-8-t] ag -afach-—aasfas] =a] =a] aE so -29=*] _ Pre FA OA Rh RRA ‘d surdsyo ; TABLE AA. Sire and Offspring &. Sire. SSS ON eile) matva) Cried OeiGeh Hii! O SH sH lon ey | AN ALL M ALL aL dM “MAL Lal | Moana erst I~ cance oe ah | Soe es he | fl Sotto: het | ena ee a (de ooh [alse Se One aS la | mac | [Peete eC | cele a ome Shire saic | ed Pah — an | 2001 | Boe] | Ler joe] | | Ne) HSH OSH Pitre Seep [eas tt coe lea ee Hil So) OD | ol aM ON- lla | a) i) iA ‘Pp suudsyo -~T 8 TABLE BB. Sire and Offspring ¢. On Inheritance of Coat-Colour in the Greyhound Sire. Ae iS TLL OM a WLM AE © AL AL eee Aa A ae nN "MA Lees Stas eee a oO ‘Bic 2 PE Od [eet il ol af Od “AL 0 "Mod = “MA - PO eae ee ee E Wee = lal | [so OU alee ee alta S aT c moat a | oar a10 | | | mio OD | 3 ee a Ao | im] a | aa ON ee in * fi i i | | ioe) 2 “mpa [Pr it) (senteee pane) | po [a en Gol aa |S “Mat Re re ce alae wig hea ee ee ee te eee lyase al 1) i limtlenle mcs feen Gmeleo ale pelvis ye Py joo MQ OAOO OA | soe | ae © wuzege FR pe FA Pee |S idee ee eae PEGE aMEMEEm : , teh F 4 ee ‘s sutadsyo TABLE CC. Dam and Offspring &. Dam. ALM A AL Ad 1d OM MA og ad SH CO rat re [Paha oes | | [hse He r in] Ges | ioe) Pest! f tet ttt "P suridsyo 80 TABLE DD. Dam and Offspring $. On Dam. Inheritance of Coat-Colour in the Greyhound a MAME ARMEDAAMONMRDAHONE ARH Io » lone) ae I~ OM OO I~ ON N10 co onl Ss fol AN fon) Ig om | °° | SE seat | A rs © Pris tae ce 4/5 ee a Ka ce Pe Pega |) SS eR igre Cohn (al an | ae (os fe fae ee fe gf Lael I) | Ge Ad M P= ll | Rabbi meas facet Sh || || oe yee o9 99.00 Ga OD QOHD HAMA ORO | (ar = = - aes ‘og aca Ml et Mec | am Weer ella ese! abes|i (KTS |) Pes ss He none : c=) i a) Oe Oe ee do A as Vl rll cess tall afl oct || moog Pl ll PP Pee ee le ae “M i ss We fe PV et i ce alee) Pele) |) Go ae ee i : ee 5 es E| ere: Po We ene einen ea | || S me st OD pam | SoCal fosters fei la Lis 3 . . Wey tere ae an an | sas Ina) an ae : Pa A le pole Sal secs || 9 a a kf * i “aT Pa We ete a aR Nien | TT EAE Heep eis || a O75 Keer nl (sO ame || a Seo Baie eee}. co SON eee eek ae as | Ena to Re Re ee) |S —> oncom — Ne} A a; Sa _ = og al nk ee ee awa ianame eye |) Si MoT PPS ee eee ae ae a sea ess a ae Fe i Foes See eA ate Mee ell li: |p sme tO eT het A a tS) ATS eee et a1 lie Rss eee Vena Pack Pe Pech AP alle TER al) AE). "AT me 10 ra | Sp Orv iestsy Geli! | hae | | eS SS Boe eg tote t es ee Bebe tater s Hees ta se ay ae eH get Bech nal Oe a ep 7 a LF sri gash it tw s eee FR ee FR PReme | 8 | Bly ates ey Ser Sc ee ON ee MM | teed ede aeeneeaeamemeem TABLE E. Paternal Grandsire and Offspring &. A. Barrineton, A. LEE AND K. PEARSON 281 LM Ad ALL A ao emacs Ad M ad oD TS | tals Hes toes ol “MAE Lo) Bio! ee lire | fae Paternal Grandsire. eS | | | | |imeecoacan | | | = a : or) ol a4 "P sutudsyo Biometrika 11 36 282 On Inheritance of Coat-Colour in the Greyhound AtaaaQqgqon | | + a aN We) a = ree AL MA] a Lela Pas) aa Sistas I a ese Le ee el eS Bess Wa M eS SH PL ee Leese Dat) TIS ONGRECS: Stes eal fee aa De Mag Pee | pee Pe ee ee eee es iS ded |: — eo Se eels Seeeg an = | = = = ‘Od “ML ay Al se alee 2 S ae on — 7 =a ass _— = MM 9 [et ene aS R © CR ORG Ge! SS —_ Ps nN oS Fong : Qa 8S # al « © OM .& | —_= =e | ee re S a =e > Je Sule ys Gaecr eeee ad an al mn Poe dts ico pat Ss meee FR ee FRM FRO mMe So see Me eS eles DTC ee een et 5 Mt MM dda de APO Oe EERE AME REE : i) ee it fe beh TABLE G. Maternal Grandsire and Offspring &. Maternal Grandsire. A. Barrinetron, A. Lez anp K. PrEARSON 283 rd = HH Pel | ILM Na] | WL A IM “MAA > | ML a “Mog “M clu "Moa af a GC Gg SPoriien! | [2 Pai Pd“ M : : ieee ra “M PA port ee ‘Pd ay » Sie ee | ‘TM | co | “MW = | > J 10-°"Y a : | Iu | W ee 0 tae) Mh cecal ace ae = beds a: be a) 2 Be me Ae Wl mtr) Gite Yn aed 3 Bae Mee ORE ae co ie aie mee ent ere Le Siete ee aR ee eee eRe Seam e mem A A a) A A A A 4 - "P sutdsyo 36—2 284 TABLE H. On Inheritance of Coat-Colour in the Greyhound Maternal Grandsire and Offspring ¢. Maternal Grandsire. a OMMI~KY RNR OMCO te 1O1O re MON AAO a | 2 fon sA) il pan ac od each ext Q1d = eo “4 3 1019 WHO Haeie % of) cae AL MALY ¢ s | AL A 2 aM Fe lalle see) a A Eq one 31 99 20.09 a a 2 nN | S See [pea | pao | ~ fr eet bs fa\e aunget feet | ~ "A OE La Te Leos a "M 39 an ees aS = "Ma Vcore beak islam eet = i ed |: ; oe eee pinnae eS | || = : : ‘Pa M [sr | dl ace es M PE [Pe cones a === ale 25 "CM © "MD R i) “AL IO msi ie eee = S ms tS AG ; A gle [SSG : eee ee oe A A Ary ee ope. ROG aoa eeane Sea se ee Aa e wig foi ae 2 ; aa) od Md & oe ES ERG eS ee Dns: ae a4 Crea PERSE AME REE Mm eo TABLE I. Paternal Grandam and Offspring ¢. Paternal Grandam. wR Barrineton, A. LEE and K. PARSON 285 = LM Ad ooo — n 2 DENAMAHOAMMAHARDOKR HORA HAH AMODOHHOD K a ANAAG Ney OAH oa i ots 5 Alo in eka Ad OM “M Ad "ac | 10° MA lei | “A Pa eel 1d AA Ht Cy el e tl ‘Pd “M “M PA Pd “M “We 108 UM “MU "Y 10“ "P suudsyo 286 On Inheritance of Coat-Colour in the Greyhound "M AD ee MT “M. 6 > aN | | LL AA AE BON Gath ioe} | | | | | [ere cameo aes eee Oe ecm ‘wpa Pd “AM “M PA Pad ‘WOM TABLE J. ' Paternal Grandam. “MH 10 °Y “dM “MU Paternal Grandam and Offspring ¢. "Y 10“y ‘W 10 YY vw M = | | . ¢ aAP~ AN np) W Ne se = TABLE K., Maternal Grandam and Offspring 2. Maternal Grandam. > A. Barrineton, A. Lee anp K. PrEarson 28 ~T pike LM Ae “M Ad > = ae Aa} ALN | 2. _ | ant aera | m0 | ANS a | BID g sae id | —— eyes oa eirsatha: es oe Dee ey eee ees ; edd. bw oe RaeSnae FO as be Fanaa Omer le See tees ane ais Ee AE SS SS oe Me | ‘ AA h of i i h A ‘Pp suudsyo 88 TABLE L. Maternal Grandam and Offspring $¢. On Maternal Grandam. Inheritance of Coat-Colour in the Greyhound | MI Ho |x QO MAUNA i= OS ts || [5 © >| — — ~-—— = = — _ —____—_— [ceeeeee! ALM Aap | | I | Se ea Siler aL aa ql | | | ical cca Ce aie ey aaa La ede || | Ee M 1 cal i, ) ON | Be hae! hes 3 MO eo por BYED UGL OD “H99 oem | 1g $ ae | Ree ‘og ee) a A Dh el ahh ieee >| -—— ——— — — — — — a _ oe Mor flat | PPE ot |S esta) SI) itera ics “M Fae) im rs ae ed ea fe ue a ae Acces | | S| oe 4 as a = ‘aM Wal? Tas acer mama esas icy || | | “ES Moe Pe Tt et eee kai rs a Hiss : Es ot a ) ols wot oa ict ee oe NM | ie} = _ ean “pa M. aaah | ame Omtn AN | N 2) MPA OMA aAAN CaS ON ra | | Nn es > — — ~ — — aaa! “pI aol Cee | f fenltced oe foe) fee oll Seal 8 ECON | Be E~ € ~ DowaMpasn | [al [sa] ] | dl Ih co ar e A eS aia S| pied] eee teh Glee Bee | a 7 owe all A ocean sical ely.) < Wa ub st als esc a0 hat Ue a DRL et | }* ee aS b: Be 8 Elirnae aie —f ee eee | “a eva ae oa | ope gf le ae oO | i a : “ay OM |] |Oomoon) anon) pan |e \ = alsa cae: 2 Bas B oe = Ln ee. rise ee wd ed od 3 eabeed -R pe PA PRPAR |e ‘4 . a . Le} . n c . . td ~ . i ss een ie ee RSS Sse SMe Me bos 289 A. Barrineton, A. Lee anp K. Prarson | | : LOOT | [ee LO@ | SI | €1L | Gz TAN eal Kal “M PA “AM ‘PE ed STIL, a Bitcmecl LL AL “AL WLM Ad “MAE Og ‘a a ya) k i “TOOL YSAT HL ayo Pun Layjoug W aTa VL TOYO PuooG 37 Biometrika 11 290 N. TABLE Sister and Sister. On Inheritance of Coat-Colour in the Greyhound First Sister. a NHHMEAADONHRMEAMDMHRABODA ITA » tod I~ OO RS ann on Otre te} 10 I~ sH xs & a) o co +H 1H pa a o +128 : ston oo 2 Ss) rHto,o,t +IS aq JSTSAT ISR] (WSR ITSP SiS 1S /S Ad ‘a elo A ay Pe Pala a Sees a = a. - on “MONT pnt inal MN) OS BH |TWRS | TANS |S fs “MAL ea] | | | Dt | Seal Sites Sa isaiices oD ON c010 10 6 H S) - ag 5 ome erste |S aad fa Pete Per telco inten oe Pasar | | 3 pa oa | | i Fe a ed amend We 0 call Acide ny 2» | |S Moe (O5(? Pee (Sa sei eae ie ieee eae |= |S Mato pay | T | deb eet aa Se yl aac Ma Pa LT Port eae Wt AHF HHAOA, r- = = ee ‘pa om My | | 4 ile (alee a an eae Pe ea MT a el | ile || me seheete? he] Me aT as Lets Sy ries) sili eee 1 M Ae ay Oa a poe ale paral i lane lial ad fo >|. “TM eae aca id ees ied fe (0 meme ie leyiiogs = ||, | > “M | aA Seal 0 rat rt | | | eam pss 2 A W 1d Ee ae oe) | ; aie et le Bes: | £2 apo ee ee : acs ; Ss — | M Paul | | ey | ee ie ae ete 2 | Lae hal = 4 | pau || ected a i Fe ea S > > Se ee Ors eer oa = Se SS a = = eee = = 3S a ‘a Pa | | te eee ast eel eT ie Pasa lr s Pa |= sae el alae | leet ld vlc i, es Wn a | |e gen aml ana ||) nea oD IN| lta i? || Pei cellist | | | ee Cea | wD — — — _ =a pa I~ kt OOO | aa gs ear aes ies (eas lie | ee cet) a _> a = - <= ee = > SSS a7," er i OP ec Fe te eT i 6 HTC T he ee A a A Sy ea Lea teen [=| Pale ala Poe ee ee (iy Lelie en Fan Oi LI APRN PSUS GS tes dc Cel lie aN a) Velez | Wd RAIN acu (came an alk Te lit 0 Peel | MMT ae [ef eee ket a cli | assets] leer SCs A alae Wa Pa ea ST eee esterase a ms sal 4 SS Pi ae a eilesen ines) ice ‘a Pee cea eee at ama er Gime AP | |S |) ae : eS 5 jes [eas ind Misses an, a te SMM cigeeaees POeSHSS ge FRAe Ema e eee eerie oo Sct ee a Ree ee peer ea SMM M4 tdéeige eee Seer eee SEO eaaMemem “IIYJOIG Puovsg TABLE NN. Sister and Sister. A. Barrineron, A. Lee anp K. PEARSON First Sister. | : APSA" SIRRARR RBA E | S Di tae SP ee [Sasa | SR SED Sa OO TNT S060! Ah C0) sil tah Se Fa maa ap ll PEL ie bhi tilt ittadea aaa PITTI PITT t ttt tititltieds mem POLIT 1 eres] | jest jel s | MAE | | | | |~ | ova | [nage a | 2 Poor FeTiP rimeiiiietiiieds re (1 eet ies Ma PIP iieesise (let lial aS a “M ise) ie N oO iN ANTHTHA | pees | N 2 ae aye ATAAAA soe Geet! | \o me =, HOOT | | RAIDS SH OE} te! Ee 3 pI a | | | oe a ace | ov . js a capa [PROT set eer PPT it lists fe eee ial Tae ee ee ce aah eet HALO Ib en Mes Ce ee aie Pe fo am PTPIT TIPLE die ticiic ds wee POTTER Pr Tri iii ds au fPS™1 Ile" Lilli i lies - ‘y Sess | (Oot | Hered sd | earerat | | a a a a “TIYSTS PUOVIIG 293 294 TABLE OO. On Inheritance of Coat-Colour in the Greyhound Brother and Sister. ¢ NAAANAOADOMWNGT | OND | | Pa —_> = = — — on — — =z = >: CF, Wa i et OO et ae Vee Paani betiaellel | sik |i = —e st Sats eS — — oa === sh aes tcc a Pa |e eae eS eralh. fe ||-25) |) GS eA aes Pe: ; a “M AT wmndIN | xl Peri orete) elie Hop) iach ihe) eee) \—) a S — > | —. — a ——— —— — — si = -- + “og | Iiaaad Re os eae sReumelccteac eit || GS — — = = od AM PS | Pl) esveoce yo i see tieiliesten ce A eg P Tepe | ees eee] aaa lee ees “A Oto ccs cect jr el | ca) | tle") | > — ——— — = — Rae. ae (nn oT Ki eB is || aS a owe ele Jes i Pic |e we CST eae |} SSexeXHGey ee) Tne | | | ~aN us a > — = at “aT pa Fe eae | ae Wn) LSPs Myre m = Sen = eI et ee es ee ee ee Sete | 4 J i a oe oe ee ee = Scie ee) (ret blac ieee ener °2 |S “M pa N | footie oe) Ce elien) | | [Veo | les a = DEI 19.28 | GW BECO. Oi UES | alae é rt MOP Pee ea Tea alee esr sit (a eb Pe see a en cost Kael me fae le |] | Ge EMS Be Il) ee le a ete ligt aledlec cleat) aonb MSS] i Sa rier Sa A | lh lies lt eal Wd eee Oe eee te eet ad ae Pre | ce pee |e ies a (omic a lea Becca e easel yc APM IP pa) |) oe ay g3 | Skeets [ESIBORGN eal are jana |S MMM. A. Barrineton, A. Lem aNd K. Prarson 295 MA SURE eee ee eG Metal eR OLS Lesle lestalayh lc! camaa PITTI itil li ti tlel lil iiet fe MEAN | Maal ial coa| od OD OD ODM | GIy ts Bs Re ee Ne | Oo | bs) =r. 1 = ae | 1 mon Hp a ‘Od bs eS | | [e6) ee Ee ANG | mes a les oe pa od | | | i DAES ig ENO 0S ce) Wa SOS) (Sa eae Pein Soult hal 1 a M 2d | | xo pr ck a bs CS Bs | lence | [SN Ss * Pirie jer per py pou [erp parte pe re Tow ‘ Nea See ae Ee rey a First Brother. TABLE Brother and Brother. t i) ae) a ‘1ayyoig puooeg 296 On Inheritance of Coat-Colour in the Greyhound AL ALA LL lL Ta AA [ree a SS st SON aR GN 1 MEAS Ah rele OO OO | ire aoa ine) as | | ot rH Jom | Niciid i aay ees ec) teal “M A 24 | 31 | 29 | Ne Hl Sede | Biraloosy So} tehien “Og Cue Ls) papa] pou pe mc OND aeons “M °° EINE] ah te AONN HAEMON 22 al mw oo tos ete | aN al AANA OON =i Sister. First PA OM TABLE NNN. Sister and Sister “MPT Pd Ad reuters Nw Ow pen) reseed 4 tf a ee it “TOYSTG PUOIOG TABLE OOO. Brothers and Sisters. Brothers Biometrika m1 etal ALAM AMA Ht MOM Aon ML Ad ad M. “M LE (oO oP) N og “Tog Pa Od A Pd PA 99 AN | ae al os | a a a ase | ee eGo Sehe ne) | seer |e baial a | AN i) a || ee | lon ole Om maa mh) ri ao bo oe) | oa Ooi ioe ) ae) 1d AMA 4 Pa Ad es a opus: Fo Fe AQ AO 217|70| 8 4 ta eet f rt 38 MMMM. TABLE 298 Brother and Brother. First Brother. | Pa ea On Inheritance of Coat-Colour in the Greyhound Nd OM LA __|2uL A AL pS ed ‘Od OM OMA A HON 4 92 | 282 | 150 ee 1 16 29 | 28 3 « € ‘1631 80 | 64 1 ee ei: Ss aches mB = a oe 2 Pt Ae od do Ses Sve Me 8 seuetee FRR pig FES Pee eee |S se pt eect og ees ae nesta eee eee Mite dee PARE ee Re eR ERE ROME MEE am : _ Rh ch A Af ee ee “layjoIg puooag NOTE ON A RACE OF CLAUSILIA ITALA (VON MARTENS). By W. F. R. WELDON. In the first number of Biometrika, I described the result of measuring one of the elements on which the character of the shell-spiral depends in a race of Clausilia laminata. A comparison between the variability of the “peripheral radius ” of the shell, in young and in adult individuals, afforded strong evidence that this character was subject to a process of “ periodic selection” in the race studied. In the early spring of 1902. I collected a number of individuals of C. ctala (v. Martens) on the walls of the Citadel at Brescia, and I made a series of measure- ments of these, comparing 100 young and 100 adult individuals, as was done for C. laminata. The result of this comparison has been entirely negative; there is no evidence of such a difference between young and adults, either in mean character or in variability, as to show that the elimination which occurs during growth is selective with regard to the characters measured. Although it is possible that an explanation of this result, not incompatible with the occurrence of a selective process, may yet be found, I think it mght to publish the result at once, because this is, so far as I know, the first case in which young individuals have been shown to resemble the adults of their race, in the degree of development of characters which may perhaps be called specific, so exactly that it is difficult to believe in the occurrence of any selective elimination during growth. The characters measured will be understood from the diagram, Fig. 1. Each shell was ground on a fine hone, until the columella was approximately cut in half along its whole length, the ground surface having the shape indicated in the dia- gram. The length of the columella in an adult shell is roughly from 13 to 16 mm., excluding the bent portion connected with the clausilium, while its breadth is never half a millimetre. The plane of a section which passes sensibly through the middle of this long and narrow tube cannot make an important angle with the plane which contains the axis of the shell. In young individuals, where the 38—-2 300 Note on a Race of Clausilia [tala (Von Martens) columella is much shorter, the exactitude attainable by grinding is less; but it is still sufficient for our purposes. Fic. 1. The upper part of a section through Clausilia itala, showing the characters measured. In any section, points on the peripheral and columellar spirals are exposed, and by passing alternately from one side of the sensibly flat section to the other, we find points on either spiral separated by an angular distance of 180°. It is evident that the relative positions of two points, P, and P, (Fig. 1) on the peripheral spiral, known to be 180° apart, are determined if we measure in the plane of the section the sides of the triangles AP,C, and AP,C,. By proceeding in this way through the whole section, we might determine the law of growth of each side of the funda- mental triangle APC, as it revolves round the columella, and so obtain data from which both peripheral and columellar spirals could be reconstructed. An attempt was made to do this; but the columellar end of the septum between two successive whorls, which determines the length of PC, was found to be so indefinite that the measurement of this side of the triangle was abandoned. The “ peripheral radius,” AP, called P in the tables which follow, and the “columellar radius,” AC, called Cin the tables, were measured; to obtain a measurement depending on the apical angle PAC, the perpendicular PM, from the peripheral spiral to the columella, was measured ; it was found that by means of the perpendicular cross-lines in the eye-piece of a reading microscope it was easy to determine this perpendicular (called in the tables p) with sufficient accuracy. The measurements were in all cases recorded to 0°01 mm., and care was taken to make them as accurate as possible; for purposes of tabulation, the more variable measures P and C were grouped so that the unit of tabulation was 0:05 mm., the less variable p was tabulated in units each equal to 0°02 mm. The individuals measured were 100 adults and 105 young, the whole number of measures made being well over 9000, though only a part are here discussed. W. F. R. WELDON 301 Having made the measurements of all the sections, it was necessary to find some way of making the results, obtained from one section, comparable with those obtained from another. All that is known about the plane of a given section is, that it is one of the infinite number of planes passing approximately through the axis of the shell. There is no way of determining the angle between the plane of a section and that in which the spiral itself begins. In comparing sections of C. laminata, the measures of the peripheral radius (the only character studied) were tabulated by reference to their angular distance from the plane containing a columellar radius 5 mm. long. Such a method, applied to young and old alike, gives results which are strictly comparable, and it therefore gives a reliable measure of the relative variability in young and in adults; it has however the great disadvantage that the absolute variability is so distorted that the standard deviation of peripheral radii, actually obtained, is nearly worthless as an indication of variability. For the purposes of the present enquiry, an attempt was made, within the limits of every successive 180°, to determine first the mean length and standard deviation of each of the three elements measured, considered by itself, and secondly the mean and standard deviation of the array of any one element, associated with a fixed type of one or of both the others. Thus, starting with a columellar radius of 2mm., in adult shells, and taking every length of this radius which occurred in the following half-revolution, it was found that the range of columellar radii in this particular half-revolution was from 2°00 to 2°49 mm. The mean and standard deviation of this group was determined. Taking the values of P and of p, associated with these values of C, the mean and s.D. of each of these was also determined ; then, by making the three correlation-tables between C and P, C and p, P and p, the mean value and the standard deviation of any one of the three sets of measures, associated with fixed type of either or both the others, could also be found. The mean values of the characters measured, as well as their standard devia- tions, are given for young and for adults in Table I: it will be seen that they are roughly identical. The degree of identity of mean character in corresponding regions of the young and adult shells cannot, however, be adequately judged from these results. Each entry in Table I, except those in the first column, records the Mean or the Standard Deviation of a character, as determined for a group of cases in which the columellar radius varied in length between the fixed limits given in the first column ; but within these limits, the mean value of the columellar radius, and its standard deviation, are largely affected by the mean position and standard deviation of position of the planes in which the sections were cut. These quantities cannot be directly determined, and we have no right to assume without evidence that the mean position of the adult sections, with reference to the origin of the shell-spiral, was exactly the same as that of the sections of young individuals. In order to compare the two sets of results in a more useful way, the regression of peripheral radius-length and that of perpendicular on the length of the columellar radius has been determined from the correlation tables for all the measurements r 0900-0 | $400.0 | 98L0-0F | FZZ0-0F | | | F610-0F | 61Z0-0F 6880-0 GIIL-O | 92€8¢-T 16G¢.T 8G16-0 SI€E-0 | GE9F-9 | EO6E-9 6186-0 GFZE-0 | GGL0-L | 1896-9 | £9.L—¢¢.9 _ 4900-0 | 9900-0 + 0060.0 + | 90@0-0+ 90G0-0F , ZOZO-0F | 9860-0 Z860-0 | GLZE-T LPPE-T €966-0 OGOE-0 | OTGF-E | OFLE- 090-0 8666-0 | 61¢0-9 OL66-G | F¢-9—04-4 | 6200-0 | 9600-0 + C610-0F | ¢L10-.0+ | F610-0F | I810-0F | TL80-0 180-0 | GIGI-L | SPELT L88Z-0 G6GE-0 | €OLF-F | 999F-F 6886-0 0696-0 | OF00-¢ 0666-F 6 F-¢ —GG.F | 9F00-0+ | 1900-0 +. 8Z10-0F | GS10-0F | G€10-0F | Go10-.0+ ; 8890-0 €¢10-0 | LOL6-0 | 096-0 9681-0 6FGE-0 | LELO-E | €899-€ G00E-0 89GE-0 | FEEL-F S6FL-F | F9-F—08-€ éP00-0+ | 8€00-0+ | 610-04 | ZEl0-0F ZE10-OF | 6ZL0-0F | 690-0 €990-0 | I618-0 C9T8-0 6981-0 €G61-0 | LEFO-€ 9LLO-€ Fo6L-0 €16L-0 8éCP-€ C69F-& | 6L-E—OL-E 9600-04 | 100-04 €110-0+ | 9600-0 + SLLO-0+ | 9010-0 | 490-0 | @970-0 | 9889-0 | LF69-0_ 6LOTL-O 6GFT-0 | OLFF-S_ | BISh-S_ FGLIL-0 LLET-O | LO8LG_ | G96L-G_ | 60-€—0¢-6 | 1€00-0+ | 8G00-0+ | 1600-0+ | ¢600-0+ ¥600:0+ | TOLO-0+ | 4970-0 | 60F0-0 | GE8S-0 6686-0 SPET-0 OIFL-O | 8éF6-L | 8196-1 S8EL-0 €0°T-0 | LOZS-G G10G-G =| 6F-G—00-E | ree | Pe eee | | | | | yupy sunox | 4ynpy sunox yupy sunoX yyupy sunox yaupy sunox yupy sunox | snipe l= See = = > as | Teens an TIpe SnIpe’ snipe snipe | Jo squirt Sau[norpuadieg Jo "q's | e[norpuedieg wvoyy Tuas ane ‘ag ence een varus a ‘as | PeunOo eon i Note on a Race of Clausilia Itala (Von Martens) 302 (‘soljowt[[iud ur syuatmemnsvoyy) poudg-11a48) au, fO wo1n Ona -f{7D hana 40 OANSDAUL WOUUAULD haana O SUuorznIVe DID PUD] PUY sanzp UD fT Y ynponay -f1? H p wsUaUluy youag punpunry | PA wnayy T ATaVE W. F. R. WELpon 303 ot young shells, and the mean value of each of these dimensions, associated with a columellar length identical with the mean found for adults in every balf- revolution, has been determined. The two sets of values are given in Table II, from which it will be seen that the values in both series are very close together, and although the differences between the corresponding values of the perpen- diculars are considerable in the lower whorls, they are so irregular that it 1s TABLE II: Mean Peripheral Radius and Mean Perpendicular corresponding to identical Values of the Columellar Radius. | Mean Peripheral Radius | Mean Perpendicular | Columellar 2 = —_ Radius Adult Young | Adult Young | 2°2201 | 19428 1:9783 0°5832 05919 | 2°7807 2°4470 274383 0°6886 0°6927 | 34528 30427 30020 = ~—- 08191 08134 | | 4:1334 3°6747 3°6527 0:9707 0°9569 | 50040 4:4703 44711 | 1:1512 | 1:1358 | | 60519 54216 5°4268 | 153272 1°3555 70755 | 6°4632 64951 1°5326 1°5432 | | difficult to regard them as significant. We may therefore say that in young shells, from 7 to 8 mm. in length, the mean length of the peripheral radius, or that of the perpendicular from the peripheral spiral on the columella, corresponding to a given length of columellar radius, is sensibly identical with the mean value of the corresponding character of an adult shell,—or more shortly, the mean spiral is sensibly identical in young and in adults. There is clearly no room here for the suggestion that selection, or any other process, is changing the mean character of the spiral at a rate which produces any sensible effect between one generation and the next. Such an identity between the mean character of young and of adults was demonstrated for the peripheral radii of C. laminata, and the speedy establish- ment of such an identity is to be expected in every local race, if the Law of Ancestral Inheritance be well founded. The only selective process, which remains to be looked for, is what Pearson has called “ periodic selection,” by which the variability of the race is reduced in every generation during growth, the mean character remaining unchanged in this, though not in all such cases. The standard deviations of the groups of measurements included in every half- revolution studied are given in Table I.; but these are obviously affected by the planes of the sections, and cannot be used in comparing variability. The measure of relative variability, which seems most reliable, is that given by a comparison between the standard deviations of arrays of one dimension in young and adult respectively, corresponding to the same fixed type of either or both of the others. 304 Note on a Race of Clausilia [tala (Von Martens) In order to determine this, the first step was to find the correlations between the dimensions measured, taken in pairs: the correlation coefficients obtained are given in Table III. They were determined for each group corresponding to half a TABLE III. Correlations between the Dimensions measured for every Half-Revolution of the Shell-Spiral. Ver Tep Typ Limits of C = ome = = Young Adult Young Adult Young Adult 2°00—2°49 0°9281 0°9412 0°5296 0°6727 0:5950 06624 +0:0094 +0°0077 +0°0485 | +0°0369 +0°0436 +0°0379 2°50—3'09 0:9451 079528 0°5932 0°7048 0°6317 0°7285 +0°0072 +0:0062 +0°0437 +0:0339 +0:0405 +0:0317 3°10—3'°79 0°9351 0°9439 0°6340 0°6589 0°6552 0:6090 +0:0085 +0°0074 +0:0403 +0°0382 +0°0385 +0:0424 3°80—4°54 0°9647 0°9449 0°6575 0°5510 0°6770 0°5874 +0°0047 +0°0072 +0:0383 +0:0470 +0:0365 +0:0442 4°55—5°49 0°9412 09691 0°6591 0°6551 0°6623 0°6678 +0°0077 +0-0041 +0°0381 | + 0:0385 +0:0379 +0:0374 5'°50— 6°54 0°9450 0949] 05980 | 0°6205 0°6448 0°6412 +0:°0074 +0:0067 +0°0483 | +0°0415 +0°0394 +0:0397 6°55—7°64 0°9609 0°9048 05737 | 0°4509 0°6281 0°5362 +0°0052 +0°0122 +0°0452 | +0°0537 +0:0408 +0°0481 | revolution of the shell-spiral, because within these limits the lines of regression were seen to be sensibly straight, and the ordinary measure of the standard devia- tion of an array could therefore be used with confidence. The high values obtained for correlation between the columellar radius and the peripheral radius seem to show that the measurements were fairly trustworthy, but at the same time the differences between values obtained for corresponding sets of measures in young and in adults are so great and so irregular that it is difficult to see how they can be due to any other cause than error of measurement. In series of only about 100 measures, a single small error of measurement could easily change the second decimal of a correlation coefficient so high as 0°95. From the correlation coefficients, and the standard deviations of the various groups, the standard deviations of arrays were calculated in the usual way, the results being given in Table IV. In this table P means peripheral radius, C columellar radius, and p the perpendicular from the peripheral spiral on the columella. The standard deviation of an array of peripheral radii, associated with a fixed length of columellar radius, is given by the value of op V1—rop; and similarly in other cases. It will be seen from Table IV. that there is no case in which the standard deviations of the arrays of measures from young shells are W. F. R. WeELpon 3065 consistently greater than those of the corresponding arrays from adult shells. In all cases the values obtained cross and re-cross each other in such a way that we cannot infer greater variability in either series than in the other, and we have therefore no proof that any selective elimination of young occurs. TABLE IV. Standard Deviations of Arrays of Peripheral Radi, and of Perpendiculars on the Columella, corresponding to fixed type of one other Dimension. The Determinations made within the limits of Columellar Radius-length indi- cating half a Revolution of the Shell-spiral. bat opN1 =? cp opN1-1",p o,N1-71%¢, o,N1—1p, Limits of Columellar Radius-length Young | Adult | Young | Adult | Young | Adult | Young | Adult 2°00—2°49 | 0:0525 | 0:0456 | 0°1125 | 0°1039 | 0:0347 | 0:0338 | 0:0328 | 0:0342 2°50—3°09 | 0:0467 | 0:0509 | 0°1110 | 0:1165 | 0:0372 | 0:0881 | 0:0358 | 0:0367 3°10—3°79 | 0:0692 | 00614 | 0°1453 | 0:1474 | 0:0436 | 0°0468 | 0:0426 | 0:0493 3°80—4°54 | 0:0592 | 0:0621 | 0°1675 | 0°1535 | 0:0567 | 0°0574 | 0:0554 | 0:0557 4°55—5'49 | 0:0876 | 0°0712 | 0°1953 | 0°2151 | 0:0624 | 0:0658 | 0:0622 | 0:0648 5°50—6'54 | 0:0997 | 0:0933 | 0°2312 | 0°2257 | 0:0787 | 0°0773 | 0:0751 | 0:0757 6°55—764 | 0:0918 | 0:1174 | 0°2589 | 02334 | 0:0748 | 00916 | 0:0728 | 0:0750 To test the possibility of selective elimination still further, the standard devia- tion of an array was determined in every group of measures, for fixed type of two dimensions; the s.D. of peripheral radius-lengths, for fixed type of columellar lengths and perpendiculars, being equal to il op aly 1 Py a 2rep' cpl Pp op a 1 2 ’ — ?T'Cp a similar expression giving the standard deviation of perpendiculars, for fixed types of columellar and peripheral radii. The results, given in Table V., show no indica- tion that the variability of adult arrays is less than that of the corresponding arrays of young individuals, so that here again the attempt to demonstrate a selective elimination during growth is unsuccessful. The method employed in determining the variability of the arrays depends of course for its validity on the linear character of the regression in each case. It does not seem worth while to publish the whole series of 21 correlation tables, from which the results were obtained, but the diagram Fig. 2, chosen at random from the series, gives a fair idea of the regression, and in this diagram, at least, there is no doubt of its linear character. Biometrika 11 39 306 Note on a Race of Clausilia Ttala (Von Martens) TABLE V. Standard Deviations of Arrays of P and p, each corresponding to fixed type of both the other Dimensions measured. S. D. of P for fixed C and p | S. D. of p for fixed P and C Limits of C ] Young | Adult Young Adult 2:00—2°49 00496 0:0452 0:0327 0:0334 2°50—3'09 00449 0:0519 0:0359 0:0367 3°10—3°79 00669 | 0-0611 00424 0:0467 3°80—4:'54 0:0484 0:0546 0:0550 0:0556 4°55 —5-49 0:0863 0-0701 0:0621 0:0647 5°50—6'54 0:0949 0-0912 0:0750 0°0756 6°55—7 64 0:0863 0°1106 0:0858 0:0747 Peripheral Radii. 2 J = .@ boon" =o, ey to 0S Sec nN N N N N a is) o a o oo oO o Do eas ji Ee a 3-12 ES - ES a a 3-17 DS vet td BRRRE ee (iia al ea ee ee ae eee. ca a ae = 342 gece yg ER ae ae ess ES] oS ee ea eae Noe Be es i ia Sl SHY IS Bees ee ea 3°62 geared Eas Ee a ie cas Se a Velen Fic. 2. Regression of Peripheral Radii on Columellar Radii for adult individuals of Columellar radius length from 3:10—3-:79 mm. W. F. R. WeELpon 307 The negative result so far obtained may conceivably be due to either of three causes : (1) The characters of the shell-spiral investigated may not be now subject to selective elimination in C. ttala at all; the correlations already established between the various dimensions measured may result in such mutual adjustment of the parts that within the narrow limits of observed variability any combination of magnitudes of these dimensions, which actually occurs, is sensibly as efficient as any other. (2) The construction of a garden and of public walks round the Citadel of Brescia is a recent thing, and has possibly led to a recent introduction of Clausilia: the condition of the walls of the Citadel is certainly not at present that of an im- portant military fortification; the growth of herbage, the falling out of mortar, and other conditions favourable to the multiplication of Clausilia, have certainly been emphasised during the past few years. It is therefore possible that we have here a new colony, multiplying under exceptionally favourable conditions, and so exempt from forms of selection which affect the species in other localities. (3) The individuals measured, both young and old, were gathered in early spring, after their winter sleep. It is possible that selective elimination of the young takes place largely during the winter, and that individuals of the same length, collected in the autumn, at the close of their period of growth, might be more variable than those which survive the winter. The data at present available do not permit us to decide which of these suggested possibilities represents the truth. I hope to collect evidence on the point during the autumn of this year; I have ventured to publish this preliminary note because the failure to demonstrate selective elimination in any such case as this appears to me in itself a result of some importance. 39—2 MISCELLANEA. On an Elementary Proof of Sheppard’s Formulae for correcting Raw Moments and on other allied Points. [EDITORIAL] SEVERAL biometricians having expressed difficulties to the editors concerning the proof and use of Sheppard’s corrections in calculating moments, we venture to publish the following elementary consideration of the subject taken from manuscript notes of the past few years. For the complete treatment of the subject the reader must always refer to the original paper*. Let the equation to the frequency distribution be y= (2); ydux being the frequency between v and «+éx. Let h be the base unit for grouping the raw material. Let WV be the total frequency and x, the frequency on the 7th base unit h, between t»y—thandw,+3h. Let y,’ be any ordinate corresponding to v,+2’. Then +i, [th ate i OO = ph (4, +2') da’, -ln -1h Now if @ (x) be a continuous function which can be expanded by Taylor’s Theorem, i.e. (7) does not become infinite within the range used : +ih Lied ee ; m= [Abd (0) +i 8" Co) th de -ih 6 i, ae =hp ()+55 (ap) + aa i¥i(ar,\ a GbOh. esaersieveus dani ceee ee (i). Now «, is clearly here any abscissa of the frequency curve and this expression gives the frequency on a strip taken anywhere, provided it has a base 2 and mid-abscissa x. It follows that if 5 denote a sum for all values of 7, h - he oe a 3 (hy (ey!) =H (Gp (0) (2) +57 E (P(e) (2r)") + gaa BCH (02) (@)) Heb. coeeeeenlil where s is any positive integer. * W. F. Sheppard: ‘‘On the Calculation of the most Probable Values of Frequency Constants, for Data arranged according to Equidistant Divisions of a Scale.” Proc. Lond. Math. Soc. Vol. xxtx, p. 353 et seq. Miscellanea 309 Now it is a well-known theorem due to Euler and Maclaurin* that if f(a’) be any function of x, p [fF @) ae =31f (a) - E fla)+ e f'@= a f"" (3) + m4 Lees ity where the term in brackets is to be given its values at the limits of the integration on the left. Hence if f(x), f’ (x), f” (x) ete., all vanish at the ends of the range of values under consideration, we have simply Sf (v= fro QO Sirs iSeoiecssaesasnesceates weeesaceewes reel): Now suppose $? (w) «* are functions which for different values of and s are such that they and their differential coefficients vanish at the ends of the range of frequency. Then PE lay ht : ‘ = {np (2p) = | (x) a du + 34 Jo (x) wda+ 1920 |e (@) DAA . ceseeveeeees (v). But by integrating by parts i $P (0) ated =[pP-1 (x) 09 — sh? (0) 08-1 5 (81) pP-9(0) a2] ceeseeee (vi). This clearly vanishes at both limits if p be greater than s. Hence no term of (v) need be retained for which p is greater than s, Put s successively 0, 1, 2, 3, 4, we find = (2) -|o (x) dx=N, SCR) -|o (@) ada = Npy’, 5 (tty.2%,2) = | (0) ade +2 Wy (u!+ 4 12) 2 hn E (2,2,3) -|o (2) Bdx+6 s iE (x) xedu = N (us + a) ‘ z(n as=[¢ (a) wavs [a (x) dapper V=W( ae +591") (vil) tae 2 1920 tw ae OUR oa: bs i Here py’, po’, os’, #4’ Multiplied by V are the true first four moments about the axis of y of the frequency curve. If we take the axis of y through the mean, we find p,'=0, and if we write for the moments about the mean Vy., Mp3, Vu, and My,, Vv,, Nv,, Nv, for the moments of the frequencies 7, about the mean, we find, since 5 (n,«,8)= Vv., Po=M%=1, y=, =0 h? Lota a TMi ilien op Yoo A cease PERSE ee vevee( Vill). h2 Tht In other words the area, the centroid and the third moment are not changed by using group frequencies for ordinates, and from the second and fourth moments we have to subtract : l?vy — zs ht 1 __ 2 ig” and 5 240 respectively, supposing the raw moments already referred to the mean. These are the well- known Sheppard’s corrections. * Boole’s Finite Differences, Chapter V. The expansion of course depends on f(x) satisfying continuity conditions. i> 310 Miscellanea It will be noted at once that the assumptions made are (i) that Taylors Theorem may be applied to the frequency function throughout the range, i.e. @(«v) and its derivatives must be finite and continuous throughout the range; further (ii) that w*$?(x), where s and p are any integers, and its derivatives are finite and continuous throughout the range, and (iii) that ¢ () and its differentials vanish at the limits. Now (ii) practically flows from (i), but (iii) is a weak spot and must be borne carefully in mind when the corrections are applied. It amounts to saying that the contact is of an indefinitely high order at the ends of the range. This is by no means generally true, the curve frequently meeting the character axis at a finite angle, or even being perpendicular to it. In such cases special processes must be adopted to correct the moments*. The real trouble of the analysis often lies in the fact that until the curve has been fully calculated out, we are not in a position to determine the nature of the contact at the terminals, i.e. we want to know the moments before we can determine whether they ought to be corrected by Sheppard or not. In some cases the graphical representation may suffice to indicate the nature of the contact, but it is by no means conclusive, often indeed misleading. This arises to some extent from the fact that we usually deal with areas, not ordinates, in plotting such graphical representations. If we accept an expansion up to h# as giving approxi- mately enough for practice the value of 7, in terms of ¥,, we can deduce a number of quite useful results from equations like (i). For example, let us take the normal curve: yr 1 y= i e 20°, / 20 ” a = o Here p (@) =% a ae ) a vt — 6072? +304 pr (v)=Y as i? 2%, 20” ht xv —6027,2+304 24 gt 1920 a : Now the second and third terms will be largest when x, is biggest, say v,=3o0 in practice, In this case ~ ne 1 1 mabye 145(5) +5a(3)}- But / will hardly be as large as }o, or say about 12 groups. Then we have 1 1 2, = hy, {1 +79 + vont : Thus the term in /# even at maximum is for practical purposes negligible, but the term in h? may amount to as much as 8 per cent. Accordingly we conclude that the frequency may be found from the ordinate in the case of the normal curve by the formula I? x,2-o6? Nyp=hy, {! + a ee . There is another way of looking at this result. Consider the expression Hence N= hy, {1 + and put o,2=02+ph?, we have on expanding and retaining powers of / up to h', N =e ck ph? (a2 — oc”) phi vt — 6o*x,? +304 None ale a 2o4 t's a® ; * See, for example, Biometrika, Vol. 1. pp. 282—88. Up= Miscellanea 311 tel Or, if p be taken = : i? ane Up= (ay) a5 " (a,) + es PH" (2,). Uy $ (%) +54 (1) + FpBa (Cz) hi div (a,) Thus lo - oe ; which is in all practical cases of no importance. Hence 7,=hx u,, or the frequencies are given by the ordinates of a normal curve for which the standard deviation is oti h?, but if Vv, be the ‘raw’ second moment about the mean we 5 I have seen above that o?=y,— ia 12, Thus oo?=y,, very closely. Or, we conclude that : If the ordinates of a normal curve be calculated from the raw second moment value of the standard deviation, these ordinates will more closely represent the actual frequencies than do the ordinates of the true normal curve, which have to be corrected by the factor ging 1 9%) 24 h o Woe to obtain the actual frequencies. If therefore our sole object is to compare observed and calculated frequencies for a definite series of groups, there are advantages in using the raw second moment in the equation to the curve. Such a curve has been termed by Sheppard a ‘spurious curve of frequency.’ Generally if the raw moments be used to calculate such a spurious curve its ordinates will give the frequencies, but the constants of such a curve are not the constants of the true frequency distribution, but functions of 4 the unit of grouping. As we want as a rule both the constants of the true frequency distribution (for comparative purposes), and the theoretical frequencies to compare with the observed frequencies, we are in some difficulty in the case of curves, which unlike the normal curve, have not their areas tabled. We have either to calculate the spurious curve as well as the true curve, or devise some process by which the areas of the true curve may be found from its ordinates for small ranges h. We have used for some time past the following formulae for finding areas in terms of mid-ordinates in the case of skew curves of frequency : (i) Normal Curve: Origin at mode. lng Y=Yoe 2. 1h? 2? =hxy| 1435 53 =|. (ii) Curve of type: Origin at mode and p=ay. ONY = =) env GS-40 ( ae *) Cae: Area of strip on base h Area of strip on base h _ 1 1? (p+1a?— po?) ey) E +34 td (ata)? (p must be > 2, if this is to be of value near the terminal of the curve). (iii) Curve of type: Origin at mode. 312 Miscellanea Area of strip on base h _ h? (my + my) {2 (m, +m, — 1) — a, a5} =hxy[ 1455 dd, p) where d, and d, are the distances of the foot of the ordinate y from the terminals of the range. (iv) Curve of type: Mode at distance x)= — om from origin. 1 Y=907 Gram OF a’ =a LPM Nigra ae 24» 2) =/) xy[1 yl Ces Re a A) —(a + 2% » | »>—- vtan =r Cc ae Area of strip on base h Biometrika. Vol. UM, Part IV. Punnett. To face p. 313. VotumeE III NOVEMBER, 1904 No. 4 MERISM AND SEX IN “SPINAX NIGER.” By R. C. PUNNETT, M.A., Fellow of Gonville and Caius College and Demonstrator of Comparative Anatomy in the University of Cambridge. CONTENTS. PAGE I. Introduction . 2 : : : : : : , 5 : ; 313 Material and Methods ; : : : : : : : : : 314 Sexual Dimorphism. : : : : : ; : 318 The Numerical Proportion of aie Bere : : : : : : 321 II. Variation and Correlation . j é , : . : : ‘ : 321 Meristic Variability. : : ; : : , : : ‘ 321 Variability in Different Regions : g : : 5 : 5 326 Correlated Variability in the Meristic pened : F : : 3 326 Growth Changes. : : : ; : : : : 333 Variability in the Gard Canals : : : : : : : ; 333 The Hypothesis of Excalation : : : ‘ : : : 334 On Intercalation. : ‘ : : : : 337 Random Increase and iectenss of Benen Note by K. Pearson . 338 Ill. Heredity of Meristic Characters . : ‘ ‘ ; ‘ ; : 2 341 Fraternal Correlations. : . : : 341 Absence of Differential Sex Varney in Mothers : ; 3 : 343 Parental Correlations . ; : : : : : . : : 344 IV. Summary : : : ‘ : : : j : 2 : ‘ 345 Appendix of ae : ; : : : : 2 5 : é : 348 I. INTRODUCTION. In spite of the mass of literature steadily accumulating upon the subject, the question of the origin of limbs still remains one of the most vexed problems in vertebrate morphology. The gill-arch theory of Gegenbaur and the side-fold theory with which the name of Balfour is most closely associated each have their supporters. Both theories are so elastic that each without undue stretching may be made to cover all the facts at present known with regard to the comparative Biometrika 111 40 314 Merism and Sex in “ Spinax Niger” anatomy, embryology, and palaeontology of the limbs themselves. There is however one fundamental difference between them. On the gill-arch theory the various positions of the limbs in the meristic series involve the conception of limb-migration or homoeosis. On the side-fold theory these positions may be supposed to be due to processes of excalation or intercalation of segments, though the possibility of homoeosis is not necessarily excluded. Its inclusion however cannot but detract from the simplicity of the theory. Consequently, if on independent grounds the phenomenon of homoeosis is found to be non-existent, the presumption in favour of the side-fold theory is very great. If, on the other hand, this phenomenon can be shown to be a reality, the gill-arch theory must gain considerable support. For with the balance of evidence equally poised, Gegenbaur’s theory has the merit of deducing the limbs from a structure already in existence. In the present paper a considerable number of one of the most primitive of living vertebrates has been examined and the meristic variations studied with the aid of biometric methods. The key to the limb question has been sought in the vertebral column, and the evidence there gained in favour of homoeosis lends support to the gill-arch as opposed to the side-fold theory of the origin of the vertebrate limb. Before passing on to a consideration of the evidence I would here express my sense of obligation to the Government Grant Committee of the Royal Society for opportunities of visiting Norway for material ; to Dr Nordgaard, Director of the Marine Biological Station at Bergen, for his most kind assistance in procuring that material ; and to Professor Karl Pearson for much generous help in connection with the working out of the statistics. Material and Methods. The material brought together consists in all of 567 specimens of Spinax niger, of which 268 are adult (100 ¢’s and 163 $s), whilst the remaining 304 are embryos almost ready to be born (145 #s and 159 fs). In the adults of both sexes the following points were noted in connection with the vertebrae, spines, and pelvic plexus, though, owing to technical difficulties consequent upon the small size of the embryos, the condition of the pelvic plexus in these was not examined. The raw data are given in the Appendix, Tables 11 to 47. 1. Whole vertebrae. As in all Elasmobranchs the vertebral column is composed of whole vertebrae in the trunk region and of half vertebrae in the caudal region. The whole vertebrae are therefore delimited rostrally by the skull and caudally by the half vertebrae. The junction of the whole vertebrae with the skull is rendered fairly simple of determination by the condition of the spino-occipital nerves. When the skull is viewed from the inside a small foramen is seen just below that for the vagus (Plate I, Figs. 4 and 5). This foramen, which is constant in its position, I regard as belonging to the most anterior of the spino- occipital nerves (x). Neither this nerve nor y immediately behind it ever possesses Soo ata ull R. C. Punnett? . 315 a dorsal root in the adult. A dorsal root may be exhibited by the last spino- occipital nerve, though in most cases it is lacking. The arrangement of the cartilages in this region is somewhat irregular. When the dorsal root of z is present the hinder part of the skull is longer than usual, and, whilst z’ always passes through the skull, 24 issues through a separate intercalary cartilage. In other words, where there is least condensation in this region of the skull, the basidorsal cartilage corresponding with nerve z is fused with the cranium, whilst the interdorsal remains separate and transmits z7 if this be present. When 2? is absent the interdorsal may remain as a separate cartilage, or it may fuse with the basidorsal next behind it. An idea of the amount of variation in this region may be obtained from Figs. 4 and 5 on Plate I. The existence of such variations serves to greatly strengthen the theory of vertebral condensation, though the point with which we are here concerned is that they are not of sufficient magni- tude to materially confuse the nomenclature of this region. The anterior limit of the whole vertebrae is capable of rigid demarcation. The junction of the whole and half vertebrae is in most cases easily de- termined, and the two most rostral of the half vertebrae each show a basi- dorsal and an interdorsal cartilage on either side. Over the Ist, 3rd, 5th,... half vertebrae there are no nerve foramina; they occur only over the even- numbered half vertebrae. From this normal condition variations of two sorts occur. There may be only two pairs of cartilages over the first two half vertebral centra taken together (Fig. 6 a, Plate I), a very large basidorsal and a small interdorsal, which latter, as usual, affords a passage for the dorsal root. In fact, we have here a whole vertebra in which the centrum has become divided, without division of the cartilages forming the neural arch. For purposes of this paper, such a condition has to be reckoned as two half vertebrae. The second form of variation is an incomplete division of the centrum of the last whole vertebra. The division may be incipient only, or it may be fairly well marked on one side whilst absent on the other. In such cases, which are comparatively rare, the centrum exhibiting such incomplete division has been reckoned as that of the last whole vertebra. 2. Half vertebrae. The rostral limit of the half vertebrae has already been discussed. The caudal limit in Spinax is quite well defined, and little difficulty was experienced in deciding the number when the cleaned skeleton of the tail-fin was examined with a simple lens, though the higher powers of a dissecting microscope were used in the case of the embryos. It has been assumed that all the vertebrae, from the junction with the whole vertebrae to the tip of the tail, fall into the same category, viz. that of half vertebrae. Ridewood (99, p. 55) has recently disputed this on the ground that towards the caudal end the myotomes are twice as numerous as in the rostral part of the series. As this point is of great importance for the present paper I may here give the reasons which have led me to dissent from the view taken by Ridewood. 40—2 316 Merism and Sex in “Spinax Niger” (a) On the hypothesis that the half vertebrae do not extend to the end of the tail, but that at some point the whole vertebral condition is resumed, one would naturally look for a transitional portion such as occurs more rostrally between the whole and half vertebrae. No such portion is however to be found. The centra of the half vertebrae become gradually and uniformly smaller till they cease. (8) Occasional variations are to be met with in which an unusually long centrum occurs among the half vertebrae (cf. Plate I, Fig. 3). Such a variation is easily explicable on the assumption that it is a whole vertebra which has failed to split into two half vertebrae. Such centra I have reckoned as equivalent to two half vertebrae. (y) Ridewood states that in Acanthias vulgaris the transition from half vertebrae back to whole vertebrae occurs at about the 24th vertebra from the caudal extremity. This statement led me to examine the position of the spinal nerves in three specimens of this species. The last few segments have no spinal nerves issuing out from them but the attenuated myotomes in this region receive their innervation from nerves passing out more rostrally. By opening the neural canal and using osmic acid the minutest caudal roots were evident. Their mode of exit was uniform to their end, i.e. over every even-numbered half vertebral centrum. Counting gave the following results: Total number | Last half vertebra of half over which a nerve vertebrae root passes out . Specimen A... 67 46 5 B ae 63 50 55 C fas 65 48 In these three cases there could not have been more than 21, 13, and 17 whole vertebrae respectively caudal to the half vertebrae, whilst from the arrangement of the myotomes Ridewood claims that there are 24. Taking all the evidence together, and admitting that the myotomes may show some difference of attach- ment at the end of the tail, there can, I think, be very little doubt but that the centra throughout the caudal region belong to the same class, viz. that of half vertebrae. 3. Total segments. The number of these was obtained by adding the number of the whole vertebrae to the number of the half vertebrae divided by two. Odd half vertebrae were counted as a whole segment, e.g. a specimen with 44 whole vertebrae and 41 half vertebrae was reckoned as possessing 44+ 21 = 65 segments, 4. Anterior spine. The position of this was determined by a sagittal section. It articulates most commonly with the basidorsal and interdorsal cartilages of a single vertebra (Plate I, Fig. 1b). In such cases it has been reckoned as belonging R. C. Punnett 317 to that vertebra. Sometimes it articulates with the imterdorsal of vertebra « and the basidorsal of «+1 (Plate I, Fig. 1c). In such cases it has been reckoned as belonging to segment a. Lastly, it may be carried mainly by a. basidorsal, though to a slight extent by the interdorsals in front and behind (Plate I, Fig. 1 a). Here it has been regarded as pertaining to the segment to which the basidorsal belongs. 5. Posterior spine. A uniform system of nomenclature has been adopted throughout, and what applies to the anterior applies also to the posterior spine. 6. 1st girdle-piercing nerve (1st g. p. n.). The pelvic girdle is pierced by one or two foramina transmitting certain of the ventral divisions of the fin-nerves. When only one foramen is present it transmits the ventral division of the nervus collector. When, as is less frequently the case, two foramina are found, the anterior of them transmits the collector. The most caudal of the nerves which go to form the collector therefore passes down almost directly to the foramen, and it is this, the 1st girdle-piercing nerve, that I have used to estimate the position of the pelvic girdle with reference to the axial skeleton. 7. The nervus collector contains in Spinax several branches lying along the lateral vein (cf. Braus, ’98, Fig. 5, Plate XI). By injecting this vessel with osmic acid, in the way that I have previously described for Mustelus (OO, p. 332), the smallest branches can be readily made out. 8. As post-girdle nerves (p. g. n.), I designate all such as run to the fin on the caudal side of the Ist g. p.n. Thus, if there are two foramina in the pelvic girdle, the nerve passing through the hinder one will be the Ist post-girdle nerve. It not infrequently happens that the fin brinch of the most caudal fin nerve joins with the fin branch of the most caudal but one before entering the fin, thus forming a “posterior collector”; more rarely the “posterior collector” may be composed of branches from three nerves. Such a condition is brought about by persistence of the early embryonic state of things m which a posterior collector is normally present, as Braus has already shown (O02, p. 566). 9. The fin rays were counted for the pelvic fins of a number of fs. A slight difficulty was introduced here by the fact that the last ray may be more or less fused with the distal part of the metapterygium. Whether it was more or less fused, or quite free, the last ray was always reckoned independently. 10. The length of the whole and half vertebral series was determined in a number of gs. The measurements were made from centrum to centrum. The observations made upon the various above-mentioned characters were tabulated separately for adults and embryos, and again for each sex apart. For each of the series so obtained the mean and standard deviation were calculated together with the probable error in each instance. The results are given in full in the Appendix, Tables 12—19. 318 Merism and Sex in “ Spinax Niger” Sexual Dimorphism. One of the most striking points brought out by these figures is a well-marked sexual dimorphism permeating all the meristic features investigated. This is well shown in Table 1, below, and equally for the embryos as for the adults. On looking down this table it will be noticed that the $ adults differ from the TABLE 1. Comparison of the mean (M.) and its probable error (Pe. E.M.) between the sexes and between embryos and adults of each sea. g adults | gembryos} ¢ adults | ? embryos (100) (145) (163) (159) | | 4 ee mu. s«- 15-979 «15-965 | 16-159 | 16-056 Anterior spine PEM. + 046 + 031 + 040 + ‘O31 Postaronenine M. 40-540 40-476 41:170 40-686 | osterlor spine ... P. EM. + ‘060 +:051 + 048 +040 Wihole werkebrac { um. | 44-620 44510 45-061 44-723 eae > (Pe | 077" | 074 Gee 0b 9 e058 ee m. | 40370 | 40:034 | 40-288 | 39-956 EE UNE K _ ee. | 4£°128 | +107 | +7101 | +-091 | | 65-040 | 64-724 | 65-472 64-906 learatinccc: é M. Total segments ... ip pM. | +:071 +065 +°055 | +:056 First girdle-piercing nerve 1. aA ae | Taste | = mae a Post-girdle nerves oes a ween = vo) oa PEM. | +:039 + 030 To ae um. | 5:230 5304 Collector nerves ... was ie. BM. | £030 | = + 024 - The question whether any two values of a statistical constant have a significant difference in value is to be settled by comparing that difference with the probable error of that difference, which by a well-known theorem in the theory of errors is the square root of the sum of the squares of the probable errors of the two given values. Professor Pearson to whom I am indebted for this statement considers odds less than those corresponding to twice the probable error as not definitely significant, with odds corresponding to twice up to thrice the probable error we have probable significance, and with more than three times the probable error there is almost certain significance. Of course a difference less than twice the probable error does not prove that the difference is insignificant, it may merely indicate that the statistics are insufficient in number to adequately distinguish significant differences. Again, persistent differences of the same sign, when each difference is even less than the probable error, increase the odds in favour of a general significance. d's in possessing a greater number of whole vertebrae and total segments, as well as in the fact that both the anterior and posterior spines are more caudally situated. In all these cases, except that of the half vertebrae and collector nerves, the difference in the means of the two sexes is more than three times the probable R. C. Punnett 319 error of the difference, and is therefore doubtless significant. A comparison of these figures for the embryos reveals a similar condition of things with this small difference, viz. that the means of the two sexes are not quite so widely separated as in the adults. See Table 1 bis, p. 320. With regard to half vertebrae the embryos tend to show a rather larger number than the ?s. The difference however is not so marked as in the features just considered, and falls within the limit of the probable error. Consequently, whilst it would be hazardous to attach much weight to this difference, yet the fact that it is found equally well marked in both embryos and adults lends some support to the view that it may not be altogether without significance. In the cases of the 1st g. p. nerve and the post-girdle nerves, the differences in the means for the two sexes are so great that there can be no doubt but that we are here dealing with characters exhibiting a marked sexual dimorphism. The difference in the number of collector nerves is also nearly double the probable error of the difference and is therefore possibly significant. The fact that for both cases the mean of the embryos is in all cases less than that of the adults, coupled with the fact that these differences are probably in every case significant, would seem to denote one of two things. Either selection has been at work during post-embryonic existence, and in such a way that the factors concerned have operated in the same direction for both sexes, or else an increase in the number of segments takes place during this period. But these are points to which reference will be made later. The figures given in Table 1 show that a well-marked sexual dimorphism occurs, and that it cannot be due to selection, since it is almost equally apparent among the unborn young. Such sexual differences have been shown to exist also among other Elasmobranchs where considerable numbers have been examined, viz. in Mustelus laevis ‘OO, p. 339), and in Acanthias vulgaris (O1, p. 24). From which it follows that in attempting to trace ontogenetic changes from a numerical standpoint, this factor must be taken into account as well as the variability of these structures; and any attempt that neglects these factors must necessarily be of comparatively little value. It seems a plausible view that the sexual dimorphism which occurs in the Elasmobranchs is due primarily to the presence of the claspers which are found in the ¢. The enlargement of the distal part of the pelvic fin necessitated by the development of these structures has led to a more rostral position of the pelvic girdle, which in its turn involves correlated changes throughout the meristic series. If there be any truth in the view that the claspers are the determining cause of the meristic differences in the sexes, one would be led to expect no such difference among the Teleostei, where such organs are absent. The only member of that group which, so far as I am aware, has been examined in this connection is Clupea harengus. In his elaborate study of that fish, Heincke (98, p. 95) has shown that there are no sexual differences with regard to the vertebrae or to the position of the fins, paired and unpaired. ” Merism and Sex in “Spinax Niger 320 [aD ‘YW “Wosiveg Tossojorg 01 poyqepul we J 9g pur gE seTqVy, IoJ puv o[qvy, sIq} oq] , ‘aeIqoqIOA [VY Jo osvo oy sog ody ut yuosagrp APQUvoyrusis AyTUo 0q 07 avodde (gze “d 998) poldeouo0d SI UOTyeIIVA sv dey se sS ype oy} wos yuereyrp ApQUvogtusIs o[IyM ‘stoyJOUL pozqsiom oyL, qo ‘dOUIIOF oY} UT Se ‘OIV SUIS oY} “IoAOMOY ‘oseO 10748] OY} UT ATpoysvut tour ere s}Npe pue sokaqtme Toamjoq seoueteyIp oy ‘gsvo uo 4ynq [[e ut sodaqute puv sznpe yy40q 10} yuvogtusSts ATYSty ore soouoieyIp & pure P oy} oly zeyy PUNO; oq T[IM FT ‘SOSVO POUIQWOD oY} WOIf OUBOYIUSIS JO INOAR] Ul Sppo ot} SuIsvedoul snyy ‘ay270 ‘sP ueyqy sh Joy queoyrusis — — —.| = ies ae = = = THyAquoq 16-1 —| PLO. — SOATAU L0JD9TTOF) — — -— | —_ —- — | — — — | aqrqoad ATYStET | ¢.66+) OFF. L+ SOAIOU O[PALS-4S0q — _ — | oo — _- = — — | gqrqoad ATYyStH | 9-11 -| L8g. —| PAu Suposerd-e[pals 4ST giqeqoad ATYSIFT | ZL —| 99¢- - | eTquqoad ATYSTFY | F-E—| PEE. — aTqeqorg LZ-| Z8t-—| erqeqoad ApS | 8.7 —| Zep. —| °° "** squetaSes [240], a[qeqoig F-E—| SEE-— aqeqorg | (0). —| 9EE- -- auoN 9. +) 8L0-+ QuON @. +)/%90. +] °° “* 9eBIqepoa J[ePH atqeqoad ATYStH | ZF —| SEs. — ouON 0-1—| OLT-— | aquqoig €-Z—| €1B-—| eqeqoad AyysSTY 19-6 — Thr. —| 7 OVIGO}AOA OTOU AA. giqeqoad ATYSTH | 1-2 —| PSF. — auoN 8. —|F90.—| aTqeqoad A[y8ryy | z-e-| OLZ-—| etqeqoud ATYSIH | 3-8 — 09. —| *" "+ guids 10L1e4sog s[qeqord 0-6 — | €OL-— OISE € —| PLO. — 2 (GEG Orc L-3—| 160-— e1qvqoad ATYSI | O-€ — O8T- —| °* * outds ro1eqUy = a | = = dONBOYIUSIG | a Vv dOUBOYIUSIG + Vv dOUBOYIUSIG a Vv adUTOIUDIS TT | V | | ynpe 6 —ofaquia $ qupe 2 —odrquia £ osaquia & —oaquia P yupe —yupe Ja}OVIBY, °91@ ‘d uo sv aoULOYIUSIS JO 4saJ, ‘suvaut Jo sIoIIe eyqeqosd Jo sarenbs jo wns,/*y = y ‘2 pue S$ sasse[O Jo sUBdUL JO dOMAIOHIP = "VY ‘adh, fo aouasafiug ur aounoyrubry 820 T ATAV Lx R. C. Punnetr 321 yr The Numerical Proportions of the Sexes. In connection with what has gone before a brief digression on the proportional numbers of the sexes may not be out of place. Storm’s ('8O) experience was that the ¢’s of Spina were rarer than the $s, though he gives no numbers. Records of the numbers of each sex caught off Ask have been made at different times by Braus, Nordgaard, and myself, and are given in the subjoined table. . S ¢ *Braus, July, 1897 ve gL 2 98 Punnett, July, 1901 wae he il 83 :; June-July, 1902 we CAT 65 Nordgaard, July, 1903... we lS 23 218 269 The collected figures agree with Storm’s conclusion, the only case where the g's were more numerous being Braus’ experience in 1897. Braus also collected at Drobak, near Christiania, where he found that the §s were very much scarcer than the $s, being in fact only half as numerous. There are good grounds therefore for supposing that in the adult state the ¢‘s are less numerous than the $s. The sexes are, however, produced in practically equal numbers, for out of a total of 308+ embryos were found 149 fs and 159 ¢s. And this conclusion is strengthened by the fact that in the three different years, 1901-3, in which embryos were collected, the proportion of g's to $s was respectively 35 : 39, 48 : 46, and 66: 74. Consequently from a consideration of the proportional numbers of the sexes before birth and during adult life we are led to conclude that post-natal mortality is greater among the ¢’s than among the $s. This conclusion is of considerable importance, for, as will appear below, statistical treatment of the meristic variations points independently in the same direction. II. VARIATION AND CORRELATION. Meristic Variability. The measure of the variability used is the standard deviation (¢) which has been calculated separately for the adults and embryos, and for both sexes. The results are given in Table 2, and allow of a comparison between the sexes, for embryos as well as for adults. As there is some irregularity in this table a rough approximation to the variability has been made by taking the mean for the first * In his paper on Spinax, Professor Braus gave the proportion of ¢s to 9s as 11:5 at Ask, and5:6 at Drobak (’99, p. 421). In reply to a letter of mine Professor Braus explained how an error had crept into the MSS. on this point and very kindly sent me the actual figures which I have here made use of. + Four of these 3s do not figure in the Appendix Tables, as they were crippled and therefore useless from an anatomical point of view. ; Biometrika 111 41 322 Merism and Sex in “Spinax Niger” five characters given (i.e. the characters determined in both embryos and adults) in each instance. This gives the following figures :— Average value of o for five characters d adults ... asg sede ally) J embryos ae so EAA $ adults Se cape DIR ~ embryos her fae AAO TABLE 2*, Comparison of the Standard Deviation (o) and its Probable Error (v. E.c) between the sexes, and between embryos and adults of each sex. | ¢ adults | g¢embryos | ¢ adults | ¢ embryos (100) (145) (163) (159) | —|— ic | Anterior spine . eee o| + oa + ae ees es + ss potion gin ona Ey BB ME | | Whole vertebrae... Ramee | Foe "Half vertebrae aie eee! [om ore i eerae ees ‘rowtegmats fT, 208 | kaa 08 First girdle-piercing nerve . - aah ee oe a a ae oi | Post-girdle nerves... rr i alae Oe a, | z ae a | Collector nerves x rs eal ees oe) | a zx oe a | (1) Comparison between the adults. The {s appear to be somewhat more variable with regard to the position of the spines and also in the number of half vertebrae, though the difference in each case is not significant. For total segments the variability is almost the same in each sex. The ¢’s are more variable for whole vertebrae though here again the difference is not really significant. The average variability is practically identical in each case (17131 for #s and 1132 for $s). For characters, however, which involve the position of the pelvic girdle and plexus the ¢’s are somewhat more variable than the $s. In the case of the Ist g. p. n. the difference is more probably significant ; it may be significant for the post-girdle nerves. The smaller difference in the collector nerves also points to greater § variability. A comparison then of the variability in the adults only of each sex seems to point (a) to equality of variability for characters involving the spines and vertebral column, and (8) to greater variability * Sheppard’s correction has not been used here. 23 3 R. C. Punnett ‘quRoyrUsis you ATUIeAE0 SOTITZ MOF puv quRoyIUSIs ATpaey oot st 4 Ssasvo IyQO oY} UL ‘Sz[Upe Aof oAdoU Sutodatd-s[pAts 4sag ut pur sodaquia Lof avAqowWOA J[ey Ut yUvoytusts ATqvqoad st qt ‘sokaqtao 1OF yUKOgTUSIS ATUTL}IOD YSOTIT ST doULAYIP oy} ‘evAqoy10A opoym ‘osoyy Jo ouo ut {ss ayy ULYZ O[QPUVA BLOT GINS P oY} YOIYM UL Sosvo OUI ole OLOYLT, “JUROYTUSIS ATTRA GoUIAIAQIpP 943 St oseyy Jo aUO OU UT nq ‘S P oY} ULYY o[QRIAIVA OLOUI aIv S J OY} YOTYA UI SAoZOVIVI[D W9d}AITTZ JO JO MO; ore IOI, ‘eyep oY} Woy popyjes oq ATparey ues 9eIqQozI9A FOU UL syyNpe oyy URYyy 9[QeEIeA oLot AT[VoI ore sofiqma P oy} JOYA, ‘Sexes Y}0q Jo oso oY} ur outds so1ezue oy} Jo uorytsod oy} ur sokiqmie oy} Wey e[qRIRA avow ore syfnpe 042 4yVUy UTeZIa0 Wlees P[NOM 4 eouDdFT “ouTds AOMoZUR oY} UL doUIOBIP JUROYIUSIS oLOUL [IIS v% yng ‘ovAqoqIOA JTeY oY} UT SuUdsgo [eNjzoR pUL STOYZOUL PoP SOM USddA\zoq GOUDIEPIP JUROYTUSIS OU PUY UdY4 oA { SIOYJOUT Jo asvo ay UL SIq} 489} ATUO UO aA4 “UoTZeTNdod [et9UES ay} Woy UOTeIas [[wUIS v SuIeq szuered [enqoe oy} 07 oNp oq Avur Sodrquia oy} Jo szuorrd oy} you are syNpR aaoqe aq} aus ‘SoUBTEyIP JUROYTUSIS SIU, “yueoyTUSts ATquqoad st KPPIQviawa UL souorIAaRIpP STYZ YOIYAM UL AnoJ ATUO ore toy, ‘opquitea sset ore LoyA Yor ut InoJ pue syNpe oY} URYy s]qQvIIVA aIoU oe SOAIQUIA 94} YOIYM UL STOJOVIVYD XIS SNY} oe oIOYJ, — — | — auoN | 6. + | $ZO-+ _ — — = — | — |" *** SQALIT 10JZD9T[O/D = — = yyqnog. | 2.1+ | 190.+ — —- —- — — — |r SOAIOU 9[PAIS-4Sog ne Teal tae TqUPQIg | 86+ | OOL- +! ae — | <— = — — | dAdou Sutosetd-o[pai3 ysItyy [Njyqnoqg 8-I+ | 60L-+ auON I- + | 200.+ auON I. £00: QuUON 9-1 |90T. | °°" “** s]UeUIZES [%}0], aTqeqoig GSH | CLZ+ euON | @ — |0Z0-— aqeqoig @3—- 61Z-—- auON ie 910. | 7" “* gRIqo TOA JTeH atqeqoad ATYySIPY | F-E+ 9zze+) ouONT L-T+ | ¢20-+ auON ¥. IZO- aTqeqorg Cie euliclen eee “** 9BIQ9IIOA 9TOUM | ouON LI+ 9fo-+| ouoN @ -— | g810.- ouONT 0-1— | FFO. — ouON Ff: ('6c0: | <5 “* guids 10110}s0g auoN G —/|L10-—| eUON | BI— | 1g0.—| eTqeqoad ATyStH | g.e— | 9ET-—| eTqQeqoIg | 9.%-|BOT--|* *** ouIds soley dOUBOYIUSIG we Vv soUBOUIUSIG a Vv edUBOIUSIC a Vv dOUBOAIUSIGC UU Vv == on JoyovIisyO ofiquie 6 —of1quia P q[npe 5 —y[npe £ qjnpse é—oArquie 4[npe 2 —ofaquie 2 ‘STg ‘d uo se douvoylusis jo 4saq, ‘SUOLRIASpP plepueys Jo s1oi1e afqeqod jo sorenbs jo uns/*Y =y ‘7 pue s SassE[O JO SUOT}eIAOP PrIepULys Jo ddUaIEyIP = "VY ‘saypwag pup sayvyy waangag pun ‘synpp pup sohuquyg uaamjaq saouasvafig, fo aounoriubry 6 ATAVE 41 324 Merism and Sex in “Spinax Niger” on the part of the ¥‘s for characters connected with the position of the pelvic fins. See Table 3, p. 323. (2) Comparison for embryos. It has been seen above that the average variability for the five characters taken is much greater for ¢ than for 2? embryos (1174 to 1057). The ¢ embryos show a greater variability for the anterior spine but for all the four remaining characters the ¥s are more variable, and in the cases of whole and half vertebrae (and possibly total segments) the differences are so great in comparison with the probable errors of the differences as to leave little doubt but that they are significant. See Tables 3 and 8a. (3) Comparison of embryos with adults. It has been seen that the average variability is greater for the embryos than for the adults in the case of the ¢'s (1:174 to 1:131) and less in the case of the 2s (1:057 to 1:132). The variability for the different characters is somewhat irregular, but there is a striking agreement between the way in which on the one hand the ~ embryos differ from the ¥ adults, and the way in which on the other hand the ? embryos differ from the ? adults. This may be expressed by saying that (a) where the ¥ embryos are less variable than the ~ adults, the $ embryos will be less variable than the ? adults and to a greater degree; (8) where the ¢ embryos and adults are equally variable the ¢ embryos will be less variable than the adults; and (y) where the ¥ embryos are more variable than the ¢ adults, the 2 embryos and adults will be equally - variable. This point is exemplified in the subjoined table, which gives roughly the comparative variability of the embryos and adults in each sex. TABLE 38a. + signifies that the embryos are more variable than the adults. - ” ” less ” ” [ ] signifies that the difference in variability is small and lies within the mean of the probable errors for embryos and adults, i.e. that there is in such cases practically equality of variability. $ embryos are more variable than ? embryos Comparative variability of | gembryo to gadult | 9 embryo to ? adult Anterior spine... | —- by 3p.n.* | — by 5$P.E. -2 PE Posterior spine... | [+], RE | —- 5 1$P5 eRe Whole vertebrae ... | + 4 3RE. | [+],, x P. E. ISP.E Half vertebrae... [+] , 425. =i SEP i: 3 °P.#E Total segments... + , 2P.B [+], wo? = 2 Pe Hence the § embryos as compared with the ¥ adults show a relatively higher variability throughout (except for the anterior spine) than do the ¢ embryos as compared with the ? adults. Again, while the § embryos are absolutely more variable than the ¢ adults, the 2 embryos are absolutely less variable than the * p, £, here signifies the mean of the two probable errors, ise. that for embryos and that for adults. R. C. Pounnert 325 ¢ adults.. If we suppose the groups of embryos and adults with which we are dealing to be fair samples of the whole population, and there seems no valid reason for any assumption to the contrary*, then it is to some such process as the following that we must look for an explanation, We must suppose that higher variability is an attribute of the ¥*, but that, owing to some subsequent process of selection in this sex the variability of adult s is brought down to equality with that found among adult ¢s. This, however, will not serve to explain the lessened variability of 2 embryos as compared with ¢ adults. It is possible that these differences are due to unconscious selection of the embryonic material which is the product of not more than 40 mothers. On @ priori grounds it is therefore most unlikely that this relatively small number of mothers is truly representative of mothers as a whole. To test this point the variability of $ offspring of known mothers was calculated and compared with the variability of the weighted mothers, and the results given in the following table :— TABLE 4. o for embryos | o for weighted mothers (N=115) (Actual No. =25) Anterior spine od 6242 6665 Posterior spine Soe "7447 6715 Whole vertebrae... 9921 8192 Half vertebrae ask 1°5920 1°7358 Total segments 505 9903 1:0495 Average Pe 9987 “9885 Hence when there is identical selection of material the average variability of $ embryos and ? adults is also identical. It is therefore exceedingly likely that the comparatively low variability of $ embryos as a whole as compared with $ adults as a whole is due to the fact that the $ parents were here unconsciously selected. There is every reason to suppose that such a diminution of embryonic variability as the result of unconscious selection obtains equally among the ¥ embryos. The average variability of the § embryos should therefore be appreciably greater than the figure (17174) already given, thus accentuating the phenomenon of greater variability among ¢“ embryos as compared with ¢ adults. In summing up briefly what is to be learnt from a comparison of the variability of fs and $s, embryos and adults, it may be tentatively stated that the average variability of 2 embryos and of adults of both sexes is practically identical, whilst the variability of ¢ embryos is considerably greater. From which follows the [* The variability of the weighted mothers is in one case equal to that of the adult. ¢s. In the four other cases it is less, and in three of them—posterior spine, whole vertebrae and half vertebrae— very significantly less than that of adult 9s. .K. P.] ; 326 Merism and Sex in “Spinax Niger” conclusion that some process of selection takes place among the ¢’s during post-natal existence, leading to a reduction of their variability to the amount exhibited by the unselected 2s. And this conclusion is in accordance with the fact that, whilst the two sexes are produced in equal numbers, the adult ¢s are less numerous than the adult $s. (Cf. p. 321.) Variability in different Regions. That considerable differences in variability, as measured by the standard deviation, obtain for various regions of the vertebral series has already become apparent. As, however, the number of meristic units which goes to make up these different regions differs widely, their relative variability must be compared by means of the coefficient of variability (= ae) These values are given in Table 5a, from which it appears that the variability shows wide differences TABLE 5a. Coefficients of Variation. gadults | ¢ embryos 2 adults ? embryos Anterior spine 4:19 3°47 4°46 3°65 Posterior spine 2°19 2°24 2°20 212 | Whole vertebrae ... 2°57 2°96 2°38 2°44 Half vertebrae... | 4°71 4°79 4°77 4°26 Total segments | 1:61 1°78 1°59 1°61 according to the character chosen—differences on the whole equally well marked in the four groups of embryos and adults. The existence of such differences is antagonistic to the conception of the landmarks along the vertebral series being associated with particular vertebrae, and depending for their various positions on any uniform process of augmentation or reduction taking place in that series. To this point however reference will be made later on (pp. 335-6). Correlated Variability in the Meristic Series. With the idea of attempting to throw some light on the processes at work in the vertebral column, the various characters have been correlated with one another. This has been done separately for the two sexes, as well as for embryos and adults apart. The results given in Table 5b show that there is on the whole considerable agreement in the four groups of material. Where the correlation value between two characters is high for one group it usually exhibits a similar high value for R. C. Punnerr 327 the other three groups, and vice versd. Certain marked discrepancies however are to be found, notably (a) between embryos and adults for the correlation of the anterior with the posterior spine ; (8) between the ~ embryos and the other three groups for the correlation between total segments and half vertebrae; and (vy) between $ adults and the rest for the correlation of anterior spine with total segments. Certain of these discrepancies will be referred to later in connection with growth changes (p. 333). Meanwhile some more or less definite conclusions may be drawn from the table of correlation values. TABLE 5)*. Correlation Values. gadults | gembryos | ? adults | ¢ embryos Whole vertebrae and posterior spine... coe] OL “T742 ‘6540 7218 +:°0304 | +:°0218 + 0297 +0248 Total segments and posterior spine... mas 6753 6832 "6754 5882 | °+°0356 | +:°0290 | +°0282 | +:0316 | Total segments and whole vertebrae... | °5534 | = 6707 ‘5660 6492 +:°0454 | +°0299 | +°0348 | +:°0300 | Whole vertebrae and half vertebrae — ‘5226 | —:5580 -—-4859 | — 5028 | +:0476 | +°0374 | +0392 | +0388 5216 | 2102 +~—«-4828:'| ~~ —-2719 Anterior spine and posterior spine +:°0485 | +:°0524 +:°0420 | +:°0485 Total segments and half vertebrae... se 3745 1945 4397 3266 | | +°0563 | +:0523 | +:0414 | +:0464 | Total segments and anterior spine... be 1544 1684 | 3279 ‘2246 +0645 | +:0528 | +0485 | +:0493 Anterior spine and half vertebrae — 1998 0009 0031 | — -068 +°0635 | +:°0543 +°0542 | +°0517 | First girdle-piercing nerve and post-girdlenerves | — ‘6227 = | — 5758 — | + 0283 + °0254 | First girdle-piercing nerve and posterior spine 5768 — 5398 — +0309 | + 0270 First girdle-piercing nerve and whole vertebrae | “6181 — | +4548 — | + 0286 | £0302 | First girdle-piercing nerve and collector nerves 5590 ~- | 3821 = | £°0318 | £0325 | First girdle-piercing nerve and total segments . 5051 — | 4253 — + 0345 + °0312 Total segments and collector nerves .., | (2056 -- 102 — | | + °0443 + °0376 No. of fin rays and pelvic nerves re es = = | 058 —- + ‘0680 | No. and proportional length of whole vertebrae 5838 - = _ | +0582 | (1) The correlation of each of the various characters chosen with the total number of segments differs very considerably. Thus, for the posterior spine and for the whole vertebrae it is on the average 66 and ‘61 respectively—for the anterior spine and for the half vertebrae only ‘23 and ‘33. To take the case of * Sheppard’s correction has not been used here. ” n “Spinax Niger Merism and Sex 7 328 SOXOS Y}O( OF SoousIeyIp yuvoytusis ATpoxreut oq 03 avedde oso, ‘SOSVd WYSTO oy} JO MMO XIS UL OSe YATA OSVaLOUL SUOI]LIeIL00 OY XOS 10}}R] OZ UL YSnoyyye “opeues oy} Ut Ajuo euo pure ‘epeur oy} ur aouvogtUSis afquqoad Jo sesvo ToYy}O doLY} OAV oLOYT, “ae YYW SurAzisuaqUr uoyRpert09 oy} ‘soutds JoleyUe pur AoTIo}sod useMzoq TOTZe[at109 oy} UT sokIqce pue szNpe WoEAzoeq ‘sokiqutea oY} oJ vyVp you savy AM TOTTM TOF sasvo ‘SaATOU IOZOT[OO OY} YYLA PUY oRAGOJZOA OTOUA OY} YIIM oArou Suroserd-sppus ysxy ayy IO} BOY} Iv SINPv oly} Jo sasvo yueyzoduat ysoun oy} pur ‘sexes omg at]} Jo SokaqUIe VY} UdEAzoq UOTze[e1109 UI soUeIEyIP ou ATQISUOS ST OLOyT, “OA UT ,e_qeqord ATYSIY, pure eeIq} UT s[qeqoad , st 4 “eay osayy JO “TJIM Jeep soseo oa4-4}0IN4 aT] JO WO 9AG UT JuULOYTUSIS ATMO st sOUDTAYTP [LUXS 4VYZ SMOYS Ofek} SILT, | | | es } — | ——a | — — oe ouoN he =] Or! aqeqorg P-64| L0G. +} OO NT | @-1—| €0OT-— OuoO NT G +|. F0.+1 yqnog = |8-1-) &IL-- aqeqorg €Z—) O8T-— arqeqoad {Ty STH cic 11Z- — atqeqord ATYStP] FF TLE. — | 9oulo NT Coe = POs ou0 NT Oh) > ery | TnFzqnog 1g.L+) ¢80-+ aqeqorg GGEt| LIL +| aqeqoig | L-6—| L80.— 9uo0N @ +| 800-+ | Thyqno(y | LT 1| 890. + oulo N L-L+| €F0- + | | eee | somBvoyLUsIg AY A Vv aOUBOYIUSIG U Vv oArquia 6 —ynpe é ofkrquie 2 —4[npe P = oe ts | [HFAqQnog 1 + FOL-+/ "SATAN IOZOT[OD PUL SPOUSES [e40], | aulo N LL+/080-+, syUeurses [v}04 puv ‘u Suloretd-o[pats 4ST | atqeqoad ATYSTF g-E+)| LLT.-+) SeAtou LopaT[09 pu “a Sutoaoid-o[ pals 4ST = \etqeqoad ATUSTH | BE e91- mel svVIGOPIOA sfOYa pure ‘U Surotetd-s[paLs 4ST - | ouON 6 +. 1¢0-+ curds aortezsod pur ‘u Sutortotd-o[ pats 4ST _ edn | ouON | Z-L—| SPO. — | sero oT palS-ysod pu u Stitozord-o[ pats 4ST ouON | 6 +/690-+). aTqrqetg | Pe- |goe-—| °°" avIqoWoa J[ey pue ourds rolloyUW euoN |g. —|9¢0--|- eTqeqoig | %6—-|'PLI--| 7" outds IoloyUY pu s}yUOTASes [VIO], INAqnog | 61+) ZeL— auON |6. —|¢90--|°"" AvAQOPIOA JTVY PUL SJUOUISOS [VO], ouON 3. —1690-— ouoON 19. +) 680-4) °° eulds aorteysod pue outds 1011eyUy ouoN |0.1—-|¢¢0.-| auON 9. — LEO. — "1 — SBAQOPAOA JTVY PUL VR.AGQOZIOA OTOU MA euoN | c. +|ZZ0.+) QuUON Z — @10.— * eBaAqaqdaA O[OYA PUY SzLOUISes [v0], aqeqoig | z.3+|¢60.+. auoON (0. —. 000.-—-| 7 eutds azorreysod pu szusUIses [eyOy, 9aulo N 9-1+ 620-4 mypqnoq =| 81+] g10-+) °°" eulds ao11eysod pue ovaqe}tea 9[OT AA. == = —— | = | = — = adUBOYIUSIG) YW Vv dUVOYIUSIG oD Vv | odaquia $ —oArquia 2 ynupe 6 —ynpe P | pezvpedioo saajovreyo Jo UueVg ‘oTE ‘d uo sv oouvoylusis Jo 4soy, ‘SUOTJV[AIIOD JO sdot1a ajqeqord jo servubs jo wnsA\/*y =Y ‘7 PUB S SASSR]O IOJ SUOT}LIAIIOD UDAAJeq sOUdIAHIG = * Iw (oer : : ‘sangn 4A uoynpatloyn ur saoualafiuy fo aounoYrubry oo HITEVil R. C. Punnett 329 the two spines—-the fact that the average correlation with the total number of segments is nearly three times as great for the posterior as for the anterior would seem to point conclusively to dissimilarity in the factors determining their position*. Certainly they cannot owe their various positions to some uniform process of shortening or lengthening of the vertebral column alonet. Probably one must regard the spines as structures showing oscillations from a mean position backwards and forwards along the vertebral column. These oscillations are relatively greater in the anterior spine (where the c.v. is about 4), and are more independent of the total number of segments because there are no specialized structures in close proximity tending to fix its position. Consequently the correlation with the total number of segments is small, The posterior spine on the other hand occurs in the region of the pelvic fins and of the junction of the whole with the half vertebrae. With the number of the whole vertebrae, and with the position of the pelvics as estimated by the 1st g. p. nerve, it is highly correlated (the average values of these correlations being about ‘72 and °55 respectively). The coefficient of variability for the posterior spine is smaller than that for the anterior, which is probably to be explained by the fact that the high correlations alluded to tend to limit the oscillations of the former structure- These high correlation values force us to conclude that the three structures concerned vary very much in sympathy with one another. The fact that the position of the posterior spine is largely dependent on the number of whole vertebrae and on the position of the pelvic fins must lead us to suppose that its independent oscillations are to a great extent checked, a view that is borne out by the relatively low variability (average C.v.=2:19) of this spine as compared with that of the anterior. Moreover, the intimate relation of the posterior spine with the whole vertebrae serves to explain its high correlation with the total number of segments. For the number of the whole vertebrae is largely dependent on the total number of segments, as the average correlation value ‘61 shows. To sum up, the position of the spines was probably in the first place largely inde- pendent of the total number of segments, and, where no further complications are introduced, remains so, as in the case of the anterior spine. When, however, the spine enters into close relation with other structures whose position is largely dependent on the total number of segments, its variability becomes checked and the value of its correlation with the last-named feature increased. (2) As the vertebral column is composed partly of whole and partly of half vertebrae, one would expect any change in the total number of meristic units to affect both of these regions. This is the case, though not to an equal extent in each. A high correlation exists between total segments and whole vertebrae— a considerably lower one between total segments and half vertebrae. Whilst the * On the hypothesis of random interpolation the ratio of these correlations should be the ratio of the standard deviation of the posterior spine to anterior spine, or on the average ‘892 to ‘636, i.e. rather as 3 to 2, than the observed 3 to 1. + Nor to random interpolation. Biometrika 111 42 330 Merism and Sex in “ Spinax Niger” number of whole vertebrae, the meristic units characteristic of the trunk region, is largely governed by the total number of segments (average correlation =°61), the number of the more variable half vertebrae constituting the caudal region is far less dependent upon this factor (average correlation ='33). From this difference* it must be inferred that the influence of any factor leading to an increase or decrease in the total meristic series will not be equally exhibited in the change in number of the whole and of the half vertebrae. Thus, reduction _ of the total segments will be accompanied by a marked reduction in the number of whole vertebrae, and by a much smaller one in the number of half vertebrae. Hence, the result of increasing reduction of the total number of segments, and consequently of the whole vertebrae, must be to increase the ratio number of half vertebrae number of whole vertebrae’ out on correlating the numbers of the half and whole vertebrae. ‘The correlation value (Table 5b) is fairly high (average =*52) and is negative. In other words, the greater the number of whole vertebrae the relatively smaller is the number of half vertebrae associated with them. Elsewhere (p. 334) reasons are given for supposing that a gradual reduction in the number of segments is in process phylogenetically. The above facts would lead one to suppose that this is being brought about by reduction of the whole vertebrae, owing to their transformation into half vertebrae, and the variations already observed (p. 315) at the point of junction lend colour to this view. At the same time the number of half vertebrae is being reduced caudally but recruited, though to a somewhat less extent, rostrally from the whole vertebrae. Were the reduction in the number of whole vertebrae to keep pace with the reduction in the total number of segments, the correlation between these two characters would be unity. The number of half vertebrae would however be recruited by an increased amount, and its correlation with the total number of segments correspondingly reduced. © Hence, on this view we should be led to expect that the higher is the correlation between the whole vertebrae and total segments, the lower will it be between the total segments and half vertebrae. If we consider the sexes separately this expectation is borne out by the actual numbers. Table 5 6 shows that the correlation between whole vertebrae and total segments is slightly higher in the embryos of each sex than in the corresponding adults, whilst at the same time the corre- That such is actually the case is strikingly brought * The extent to which the whole and half vertebrae respectively would be affected by a change in the total number of segments is more correctly given by the coefficient of regression of either of these two characters on the total number of segments. Thus the value of the regression of whole vertebrae, on o for whole vertebrae the total segments is given by the expression Garortietalnccomients x correlation between whole vertebrae and total segments. In the case of adult 3s this is ax *553='602. Similarly the value of the regression of half vertebrae on total segments is Logs x B75= "353. These two values show clearly that any change in the number of the total segments affects the whole vertebrae much more than the half vertebrae. (The value of o for half vertebrae is 1:901 (Table 2) but this must be first translated into terms of total segments (cf. App. Table 27) which gives the above value 1:002.) R. C. Punnett 331 lation between total segments and half vertebrae is considerably lower in the embryos (cf. p. 327)*. (3) The position of the pelvic fin (as determined by the Ist g. p. nerve) is in either sex fairly highly correlated with the posterior spine, the number of whole vertebrae, and the total number of segments. The value of the last correlation (average ="46) is however sufficiently low to show that the position of this fin cannot be entirely due to any uniform process of reduction or increase in the meristic series. It has already been seen that, of the total fin innervation, part— the collector—is rostral to the pelvic girdle, and part—the post-girdle nerves— is caudal to that structure. On the supposition that the girdle is, so to speak, in a state of oscillation (exhibiting either backward or forward homoeosis, but especially the former), we should be led to look for evidence of such oscillation in the values of the correlations between these two sets of nerves and the position of the 1st g. p. nerve. We should expect an oscillation resulting in a more rostral position of the girdle to be accompanied by a diminution in the number of the collector branches and an increase in the number of the post-girdle nerves. This expectation is fully borne out by the correlations. That between the Ist g. p. nerve and the post-girdle nerves is high (— 62 for gs and —‘57 for $s) and is negative. The smaller the number denoting the Ist g. p. nerve (.e. the more rostral. the [* It may be of slight interest to consider the topic of this paragraph from a rather more mathe- matical aspect. The average correlation between whole vertebrae and total segments is °610 and between half ver- tebrae (in whole vertebrae as units) is ‘334. The mean standard deviation of total segments is 1-072, of whole vertebrae 1:158, and of half vertebrae (in whole vertebrae as units) is 1:096. Hence forming the regression coefficients : 8. D. for whole vertebrae correlation, 610 and S. D. for half vertebrae 8. D. for total segments ; 8. D. for total segments x correlation °334, we see that on the average an increase of one in the total segments will be accompanied by an increase of 66 in the whole vertebrae and an increase of ‘34 in the half vertebrae (measured in whole vertebrae as units). In other words one new whole vertebra is as likely to appear as one new half vertebra (measured as a half vertebra). But the total number of whole vertebrae is about double (44°6 to 20-4) the number of half vertebrae (in whole vertebra units); in other words the effect of increasing or decreasing the total segments is relatively to the whole and half vertebrae sensibly the same as adding or subtracting a vertebra anywhere at random, because the total number of whole vertebrae is roughly twice as great as the half vertebral series measured in the same unit, the whole vertebra. Let w=whole vertebrae, h=half vertebrae (measured in whole as units), t=total segments, 7 = corre- lation coefficient. Then if the total number of segments were constant, since the standard deviations of whole and half vertebrae are approximately equal, we should expect that the expression for partial correlation, i.e. Tor — Tot at Va i wt) (1 ~ 712) should be closely equal to minus unity, for when the whole vertebrae lose one the half vertebrae must gain one. Equating the above expression to —1, and noting that r,,,=°610 and r,,=°334 nearly, we find r,,,= —*54, the average observed value of r,,, is —*52—a very close result. In other words the correlation of whole and half vertebrae is what we might reasonably expect its value to be, the correla- tions for the two parts with the total being as above. In general terms the result is the same as if 50 per cent. of gain or loss of either whole or half vertebral series came from increase of total segments and 50 per cent. from a transfer from one series to the other. K. P.] 42—2 332 Merism and Sex in “Spinax Niger” position of the girdle), the larger the number of post-girdle nerves associated with that position. A considerable discrepancy will be noticed in the two sexes for the value of the correlation between the Ist g. p.n. and the collector nerves. The explanation is probably somewhat as follows. It has been shown by Braus (’O1, p. 620) that the number of collector nerves in Spinax is greater during earlier than in subsequent stages of development. Even in early stages this rostral extension of the collector area has its limits. It is natural to suppose that with forward shifting of the girdle the more rostral of these branches will persist as the rostral part of the nervus collector. As however no nerve whose serial number is less than 21 seems to take part in the formation of the collector during early stages, any marked backward homoeosis in the pelvic area will be associated with a correspondingly marked reduction of the collector nerves. As the girdle shifts forwards the reduction in the number of collector branches will become disproportionately greater. Consequently, where the rostral pelvic shifting is less, we should expect to find a smaller correlation between the 1st g. p. nerve and the collector nerves. And this is actually what takes place. The $s, with their more caudally situated pelvics and greater average number of collector nerves, show a correlation value of only 38, whilst that for the ¥'s, where the girdle is more rostrally placed and the number of collector nerves somewhat fewer, amounts to °55. (4) It will be noticed in Table 5b that certain correlation values are very low. This is the case for those between the anterior spine and half vertebrae, between the total number of segments and the collector nerves, and between the fin rays and the pelvic nerves. On the hypothesis that some uniform process of excalation is going on the mean correlations for the above characters ought not to differ greatly from the mean of the rest, which is somewhere between ‘5 and ‘6. Kspecially should there be a high correlation between the number of fin rays and the fin nerves. On the side-fold theory of limb origin the morphological connection between these structures is so intimate that a high correlation between the two would naturally be looked for, and the fact that there is practically no correlation whatever tells strongly against this theory. Moreover the little that is known on this head for Acanthias, the only other Elasmobranch similarly investigated (Ol, p. 13), is in accordance with the foregoing facts. (5) A well-marked correlation exists between the number of the whole vertebrae and their total length relative to the whole vertebral column. As will be seen (in Appendix, Table 86) the length of the series of whole vertebrae varies between ‘605 and °695 of the whole vertebral column. The range is consequently ‘09, i.e. about 1/7°5 of the length of the series, whilst the range for the number of whole vertebrae is 6 in a series of 48, ie. $. The range of variation in respect of length therefore bears approximately the same relation to the relative length as the range for number does to the total number of whole vertebrae. The value of the correlation is fairly high but should be very much closer to unity if the number is entirely dependent upon the length. R. C. Punnett 333 Growth Changes. Note was made above (p. 327) of certain marked discrepancies in the correlation values. (1) The correlation between anterior and posterior spines is much lower in embryos than in adults. Both anterior and posterior spines are rather more rostrally situated in the embryos than in the adults. The differences, however, in the g's are small and will not serve to explain the very low correlation values of the embryos. Again the variability of the posterior spine is very close in all the groups. When, however, the variability of the anterior spine is examined it 1s at once evident that its value is much less for the embryos than for the adults. It would appear not unlikely that changes in the position of this spine occur during post-natal growth. As these changes are in the direction of higher correlation with a more variable structure, the posterior spine (as estimated by o), they must lead to greater variability in the anterior spine. Such is actually the case. Consequently we must suppose that the anterior spine is subject to a certain amount of change in position during growth. And in this connection it 1s interesting to notice that greater variability is associated with higher correlation also in the case of the characters involving the pelvic nerves of the ¢’s as compared with the $s (cf. Tables 2 and 30—35). (2) The correlation between the total segments and the half vertebrae for Jd embryos is very low. The correlation between the total segments and whole vertebrae in this same group is however markedly higher than in the rest. Here again it is probable that growth changes come in. If during post-embryonic life we suppose that there is a certain amount of transformation of whole vertebrae into half vertebrae, such a process would lead to a reduction in the value of the correlation between whole vertebrae and total segments and an increase in the value of the correlation between total segments and half vertebrae. This is actually what has come about in the adult ¢‘s. Moreover the correlation values bear out the supposition that the same process occurs, though to a less extent, among the $s. The correlation between the half vertebrae and total segments is less in the embryos than in the adults, whilst that between the whole vertebrae and the total segments is greater. It is therefore exceedingly probable that a certain amount of conversion of whole into half vertebrae occurs in either sex during post-natal existence. Variability in the Girdle Canals. That there may be either one or two canals in the pelvic girdle for the transmission of nerves has already been noted. The figures below seem to show without doubt that the number of the canals is connected with the position of the girdle. 334 Merism and Sex in “Spinax Niger” No. of Mean position cases * of girdle {° canal 110 28°69 2 canals 86 28°17 Difference BQ 9 {1 canal 184 29°17 12 canals 112 28:86 Difference 31 The possession of two canals is associated with a markedly more rostral position of the girdle, the difference being half a metamere for the (‘s and a third of one in the case of the ¥s. Now it has already appeared that the pelvic girdle is more rostrally situated in the ~ than in the 2. Consequently we should be led to expect a larger proportion of fish with two canals among the 6s, and this condition - ; no. of fs with 2 canals . 86 - 78-2 is what actually obtains. The no rol fs withaacaeal 8 447 100° no. of 2s with2canals . 112 60°9 no. of 2s with 1 canal * 184 100’ numerous among the Js. Reasons have already been given (p. 331-2) for supposing that the different positions of the pelvic girdle are, at any rate in the main, due to a process of homoeosis, and that such homoeosis is for the most part backward homoeosis (cf. Bateson, ’94, pp. 111 et seq.). Now the preponderance of two canals among the more rostrally situated girdles is explicable on the supposition that this homoeosis is in some measure ontogenetic. The “ Anlage” of the girdle is relatively larger than its ultimate condition. Its width is somewhat greater than the interval between two successive limb nerves, some one of which it must necessarily enclose. Supposing then that rostral migration of the girdle occurs, that structure will at first abut against and ultimately enclose the nerve immediately anterior to it, whilst at the same time retaining as it were its grasp of the nerve which orginally perforated it. That some such process does actually occur is rendered probable by the observations of Braus (O1, p. 590 and Taf. XXIII, Fig. 8) on the arrangement of the cartilage cells. Hence the variations in the number of the girdle canals support the view that the different positions of the girdle are largely due to homoeosis, and that such homoeosis is to some extent ontogenetic, though this is probably confined to the earlier stages of development. whilst the cases of two canals being distinctly more The Hypothesis of Eacalation. In most linear meristic series certain members become specialized in a definite manner and acquire thereby an individuality that serves to distinguish them from the rest of the series. In Spina such specialization occurs in the case of those vertebrae which enter into a definite relation with the fins, paired and unpaired. On the hypothesis under consideration it 1s supposed that such specialized * As the number of canals may differ on the two sides of the same animal each side has been con- sidered separately as a ‘‘case.” R. C. Punnett 335 structural peculiarities become as it were the fixed attribute of certain particular segments. Thus in Spinaw the vertebra that carries the anterior spine is to be regarded as strictly homologous in different specimens. The serial position of such a segment may vary in different individuals—in one it may be the nth, in another the (n+ 1)th, &c. On the hypothesis of éxcalation it is supposed that creatures such as Spinax have been derived from forms with a larger number of segments and that the various positions of the segments with a marked individuality are due to a uniform process of shortening up owing to the vertebral column splitting into a lessened number of parts. The amount of change in position in the specialized segment depends partly on the amount of reduction or excalation in the meristic series of which it is a member, and partly on its original position in that series. As a simple illustration we may take the case of a series consisting of 40 segments, the 10th and 20th of which are specialized, let us say by bearing spines. If we suppose the series to be reduced to 386 segments by a uniform process it is obvious that the spine-bearing segments will now be the 9th and 18th. Reduction of the whole series to the extent of four segments implies a change in position of the anterior spine to the extent of one segment, and in the posterior spine of two segments. In other words, the nearer to the middle of the series the specialized segment lies the greater is the change in its position involved by reduction in the number of the whole series. On the excalation hypothesis we are led to expect (1) a positive correlation between each specialized segment and the total number of the meristic series, and (2) approximate equality in the value of these correlations. Reference to Table 5b, p. 327, shows that the former of these expectations is fulfilled. The value of the correlation between posterior spine and total segments is however very much greater than that between total segments and anterior spine, whilst the value of the correlation between another specialized segment, that of the 1st g. p. nerve, and the total number of segments is intermediate. Such facts throw considerable doubt on the possibility of symbolizing the facts by the excalation theory and the following considerations serve to emphasize that doubt. TABLE 6a. . A. Posterior Spine. Number of segments as 6: 63 64 65 66 67 68 2 Number of specimens is 2 26 91 158 81 33 5 Calculated values for oneal 38-9 396 402 408 41:4 421 49-8. of posterior spine The mean calculated position of posterior spine is 40°8 and is associated with 65 segments, which is the mean of the total number of segments. The standard deviation for the posterior spine (calculated position) works out to + ‘678. Observed values for position of posterior spine : 38 39 40 41 42 43 44 Number of specimens nee 1 21 124 156 81 11 2 Mean position=40°8, o= + :942. 336 Merism and Sex in “Spinax Niger” TABLE 6b). B. Anterior Spine. Number of segments Ns 63 64 65 66 67 68 Number of specimens is 8 58 140 113 52 9 Calculated values for position : ; } 155 = 15°75 16 16°25 16°5 16°75 of anterior spine Then o= + ‘284. Observed values for position of anterior spine: 14 15 16 17 18 Number of specimens nae 2 56 256 60 6 Whence o= +624. TABLE 6c. C. First girdle-piercing Nerve. Number of segments nee 63 64 65 66 67 68 [ume of specimens... 4 44 120 80 42 8 _ {Calculated values for position) 57.54 ° “93.34 988 2999 29-66 uNtanan Qs of first girdle-piercing nerve 5) Mean number of segments=65°5 ; mean of first girdle-piercing nerve=29:0, Whence o= +461. Whilst observed value of o= +°760. Number of segments 560 63 64 65 66 67 68 Number of specimens... 10 38 74 30 14 2 BE y it] Calculated values for fea 27-62 98:06 28°50 2894 99:38 29-89 3s of first girdle-piercing nerve ae) Mean number of segments=65'0 ; mean of first girdle-piercing nerve= 28:5. Whence o= + ‘458. Whilst observed value of o= +°879. If a number of specimens of Spinax are taken, in each of which the number of total segments is known, we may, knowing also the mean number of total segments and the mean position of the posterior spine, calculate the theoretical value of the variability (c) of the posterior spine on this hypothesis. This has been done for the characters anterior and posterior spine and Ist g. p. nerve in ¢‘s as well as fs, and the results are given in Table 6*. For the posterior spine this theoretical value works out to +678, which is considerably less than the observed value +942. The variability of the posterior spine is actually much greater than it should be on the excalation hypothesis. This is also true for the anterior spine where the observed value, + °624, is very much greater than the calculated value + ‘284. The same is also true for the lst g. p. nerve where the calculated values * These correlations were worked out in 1902 on the material collected in 1901 and 1902. It has been thought unnecessary to recalculate these figures by incorporating the material collected in 1903. The differences that would be introduced into the above values would probably be very slight. Rk. C. Punnert 337 +458 and +'461 for ¥s and $s respectively fall much below the observed values +°879 and +760. It is therefore evident that the hypothesis of excalation will not serve to account for the magnitude of the observed variability. On Intercalation. By some morphologists (cf. Baur, ’9'7, p. 52) it has been held that intercalation of segments as well as excalation may go on in a linear meristic series. To take the case of a portion of a vertebral column between two specialized and homologous segments, there are often to be found individuals exhibiting either a less or a greater number of segments than the normal. The former condition we are called upon to regard as the result of excalation, the latter as being due to intercalation ; and to account for variations any such demarcated region of the segmented series must be held capable of undergoing intercalation in one specimen and excalation in another. In order to test this possibility we may consider the case of that portion of the vertebral column which lies between two highly specialized segments, TABLE 7. Correlation of Segments lying between First Girdle-piercing Nerve and Posterior Spine with Segments giving off Post-girdle Nerves to Fin. Hee HE b. $s. 6 — 12-— — 3 7 — 8 14 1 — 23 8 Lats [nee 63 ) — 2 3 8 4 17 10 —- — 1-— tl 2 11 7 = "343 + (063 r= '370 + ‘056 4} viz. the segment whose nerve is the most rostral of those piercing the girdle, and the segment which carries the posterior spine. This division of the vertebral column consists of some 10—14 segments, of which the greater number (nearly three-quarters) are characterized by the fact that their spinal nerves send off branches to the pelvic fin. Now if the variations in the number of these 10—14 segments are due to intercalation and excalation we should expect the variations of those of them which supply the fin muscles to be in sympathy. In other words we should look for a high correlation between the segments bounded by the Ist g. p. nerve and the posterior spine and those which give off the post-girdle fin nerves. These correlations (Tables 7 a@ and b) have been worked out for the Jf and adults and the values obtained are ‘343 and -370 respectively. On the hypothesis under consideration we should expect these correlations to approximate to unity and the lowness of the values actually obtained tells strongly against the Biometrika m1 43 338 Merism and Sex in “Spinax Niger” hypothesis of intercalation. Lastly there is to be considered the possibility that the variations in the number of the meristic series and of its various portions are due to random addition to or subtraction of segments from a normal number. This is a point which, though of the greatest interest to students of variation, is yet extremely difficult for the biologist to test. In the followimg paragraphs Prof. Pearson has very kindly undertaken this task. It is sufficient here to emphasize his conclusion that the observed correlations are not in agreement with the correlations calculated upon the hypothesis under consideration. In other words random interpolation or excision of segments will not explain the variations observed, and we are consequently forced to adopt the principle of homoeosis as the only conception hitherto offered which affords an explanation of all the facts. [On the Random Increase and Decrease of Segments and on the Correlations between the three Vertebral Regions of Spinax niger. By Karu PEARSON. I must first state that I do not fully grasp either the hypothesis of excalation or homoeosis, or the manner in which biometric analysis can be used as a criterion between them. But we can, I think, ask how far the existing correlations are in keeping with: (i) the proportional insertion of segments into a series of three mean groups ; (11) the random insertion of segments into the same groups. Let «=number of segments up to anterior spine, which we will call the anterior series. y = number between anterior and posterior spines, which we will call the median series. z= number beyond posterior spine, which we will call the posterior series. t = total segments = #+y+4z. Let us suppose all these quantities measured in whole vertebrae as units. Let the mean numbers be @, ¥, Z,# Suppose variations &, 7, & 7 to occur in these numbers, so that Gate aS Then if 7 were always distributed in any definite proportions whatever between the three groups, say : E=pPit, 7= pit, O= pst, where p, + p.+p3=1, we should have Cx =PiF7r, Sy= P27, Fz=P3Fr, or: O,=Oz,+o,+0;, Vy2 = Vee = Vay = Vat = Tyt = Ta = 1. R. C. Punnerr 339 These are manifestly inconsistent with the observed values. For adult s I find: %=15:979, o,= ‘670, C. of V. for 2=4°194, y=24561, o,= 785, , 4 Yy=d198, 2=24500, o,= ‘794, 4 4, 2=38'240, t=65:040, o,=1048, ,, 4, t=1611, which are far from satisfying the above relations. Clearly : (i) judged either by the standard deviations or by the coefficients of variation the median and posterior series are equally variable, (11) the anterior series is absolutely less variable than the median or posterior series, but relatively more variable, and (iii) absolutely the whole series is more variable than any subseries only in the ratio 4 to 3, and relatively it is far less variable. The existing correlation and variation values are not given by any distribution of insertions and withdrawals in which the ratio of the changes in the subgroups to the total change remains constant. Next suppose the segments inserted at random, there being no relation whatever between the numbers inserted in any of the subseries. We should then have Loy = Vaz = Cyz = 0, Tai = Cz Ot, Tut = On| Ot, C/O, Ve ye — Orne) a) Yn, oy = Cx/Tn+y- But oz4,=°888. Hence we should expect, with the observed values of the variabilities : tn = 0393, T= i494, Ta= 1513, Teiyt— S47, and %_,24,— 1550. Actually we have : rye= +0671, rye= "1544, Troy, e =+ 6753, Yee — 3197, THr= 6818, Pz, 544 — + 5216, Tay= — 2638, ry = °5648, which differ very sensibly from the above values. Clearly additional segments are inserted in the three subseries in a correlated manner, and the existing series could not result from a mere random insertion of segments, or a proportioned insertion (nor of course by like withdrawals). Whether the original variation was of one of these kinds and the result was then modified by selection, it does not seem possible to assert on the basis of a statistical examination of one race at one epoch. 43—2 340 Merism and Sex in “ Spinax Niger” We can of course analyse the existing relationships; we have the following tables : Regression Coeffictents. Change of a unit in Gives in v y z t z 1 —*225 — 321 099 y — 309 1 ‘066 473 z — 450 068 1 428 The following are the percentage changes in 2, y, 2: Change of a unit in Gives percentage change in x y z t un — —1°41 —2°01 62 y — 1:26 — + 27 1:93 Zz —1°84 + °28 —_— 1°75 These results appear of considerable interest. We see (i) that a gain of one in the total segments makes on the average five times as much absolute effect, and three times as much percentage effect on the median and posterior as on the anterior series: (ii) that a gain in either median or posterior series is accompanied by a very small gain in either posterior or median series respectively, but in both cases by a sensible loss in the anterior series. (iii) Conversely a gain in the anterior series is associated with sensible losses in median and posterior series ; and (iv) gains and losses in anterior and posterior series have the highest relation, ie. the loss of a segment in the anterior series is accompanied by a considerably greater gain in the posterior series than in the median series, and the gain of a segment by a greater loss in the posterior than in the median series. This more intimate relation of the extreme series than of either with the median series seems of considerable suggestiveness. Lastly I have worked out the partial correlation coefficients of the three subgroups on the hypothesis that the total number of segments remains constant, Le. expressions like: Ray = (Try — TxtTyt)/ nl Gar AO aia): Ray =—'4712, Ry =— ‘5727, Ry, = —°*45380. I find Or we find a sensible negative correlation nearly equal to —°5 between all three series. That is to say that if individuals of the same number of total segments be Binartee R. C. Punnett 341 taken, we do not find all the subgroups either constant or again independent, but since the variabilities of the three are not widely different, the loss of a segment by one is roughly on the average an equally divided gain to the other two. For example if the anterior series lose a segment, this is not added wholly to the median series, but rather more than the half goes on the average to the posterior series. In other words for fish of the same total number of segments a forward movement of the anterior spine will on the average be associated with a forward movement of the posterior spine through somewhat more than half the number of segments through which the anterior spine moves. It would thus appear that the existing system of variations and correlations is not consistent with any definite position of the two spines for fish of a constant number of segments; it is not consistent with any system of independent shifting of the spines about their mean positions in the same fish. It is only consistent with an associated motion of the two spines in the same direction, their average motions having a simple ratio. Thus, while the division between whole and half vertebrae (see ftn. p. 331) appears to vary in a manner not inconsistent with random interpolation into the total series, the relation between the three groups determined by the two spines appears to be of a wholly different character.] Il]. HEREDITY oF MERISTIC CHARACTERS. Shortly after the collection of the present data was begun the idea suggested itself that, owing to the viviparous nature of Spina, such data might be used for the determination of fraternal and parental correlations. For purposes of fraternal correlation, 230 embryos belonging to 27 families (110 ¥’s and 120 fs, cf. Appendix, Table 13, Nos. 75—304) are available. As the $ parent was not determined in Nos. 163—168 the number of embryos of which use can be made for calculating parental correlations is 224, belonging to 25 families, The actual calculation of the correlation coefficients, involving correction for the selection of both parents, was very kindly undertaken by Dr A. Lee in Prof. Karl Pearson’s Laboratory, and the results are given in Table 8. The ¥ parents are of course unknown, but their influence has been deduced from the data given for § adults on the assumption that the selection of ¥ parents from the adult § population is equal to that of 2 parents from adult fs. Fraternal Correlations. A glance at Table 8 at once brings out two points of interest, viz. (i) the diversity of the correlation values for the five characters treated, and (ii) the lowness of the average value even after parental selection has been corrected for. (a) The diversity of the correlation values is very considerable, being as high as ‘447 for the whole vertebrae, and as low as ‘254 for the half vertebrae. Moreover 342 Merism and Sex in “Spinax Niger” when the sexes are considered separately these differences still obtain (ef. Appendix, Tables 38 to 42). Thus, in the case of total segments, the uncorrected value for J's is 395, for $s'410, and for siblings 429, values which are all very close together. In one case however, that of the whole vertebrae, the value for the s, ie. 541, is considerably higher than that for the $s, i.e. 371. An examination of Table 40 TABLE 8%. Fraternal Correlations. Raw value Corrected (a) | Corrected (b) | Anterior spine < *309 + 014 320 331 | Posterior spine... 3734-013 394 414 Whole vertebrae ... 495 +012 “436 ‘447 | Half vertebrae... *228+°014 241 254 Total segments... *429 +012 “425 "422 Mean _.... ats 353 363 374 (a) Corrected for selection of mothers out of adult 2 population. (b) Corrected for selection of fathers also, on the assumption that they although unknown were equally selected with mothers. shows that this is largely due to the exceptionally close correlation between the six f° offspring of 2 159 (Table 18, Nos. 261, 263—5, 267, 268), in all of which the number of whole vertebrae is unusually low. In the ¢s of the same family the number of whole vertebrae approximates more closely to the normal. There can be no doubt but that this small group of (’s is largely responsible for the relatively high value of the fraternal correlation for whole vertebrae. (b) The average value of the five correlated characters works out after correction to 375. This value is very much lower than the ‘5 that the Law of Ancestral Heredity would have led us to expect}, and is markedly lower than the ‘475 for eye-colour in man—the lowest value hitherto recorded (cf. Pearson, ’O8, p. 390). In this connection, however, there is a contingency which must not be overlooked, viz. the possibility that a ripe ~ may be fertilized by more than one ¥*. If this be so it would obviously lower the value of the fraternal correlation. We are entirely ignorant of the breeding habits of Spinaz, but the following circumstantial evidence, slender though it is, seems to tell against the above conjecture. In the virgin $ the openings of the oviducts are occluded by the so-called hymen which must be ruptured before fertilization can be achieved. * Sheppard’s correction has been made use of in the three following Tables 8—10. + [The Law of Ancestral Heredity in no way fixes the value of the fraternal correlation, but only the ratios of parental correlation to that of higher ancestors. A fraternal value *5 to ‘6 is found by observation on long series in man, horse, dog, etc. Galton’s data gave °375 for stature in brother and sister. K.P.] R. C. Punnert 343 This is doubtless effected by the claspers of the ¥, powerful intromittent organs deeply grooved for the conveyance of the seminal fluid, and armed with strong spines. Their structure, taken in conjunction with the absence of an ejaculatory apparatus, points to copulation being no momentary action. Now, in several specimens of Spinaz, I was able to examine the embryos in a very early condition shortly after the appearance of the medullary folds. Such early embryos were all at approximately the same stage, a fact which, considered in relation with what precedes, points to fertilization by a single # only. Further reference to the low values of the fraternal correlations will be made later. Absence of Differential Sex Variability in Mothers. Whether $s of a given type tend to produce an excess of either sex is a question which the present data allow of an attempt at answering. The parents were weighted for each character with reference to ~ and ¢ offspring separately, and the means and standard deviations of these two sets of weighted mothers were calculated. The results are given in Table 9. TABLE 9. Showing Variability of Mothers weighted for § and ¢ Offspring respectively. {Number of g Offspring=109; number of ? Offspring=115.} M. P. E. M. o P. E. o Anterior spine 8 se are i: tee S00 Posterior spine {§ | 41082 | $048 | 71 | tom Whole vertebrae 3 | rere cae 3 a eee Half vertebrae {g | 29853 | £105 | £1619 | 2-074 Total segments 6 cele aa ore = OMe The values both of the means and of the standard deviations are exceedingly close in every case. Only for the standard deviation of total segments is the difference between the $ parents, weighted for ¥* and @ offspring respectively, greater than twice the P.E.o. The average value of o for the five characters in the case of the ¢s is ‘994 and for the $s ‘989. From this it may be fairly concluded that the production of an excess either of ¥ or of ? offspring is not associated with any difference of type in the ¢ parent. 344 Merism and Sex in “Spinax Niger” Parental Correlations. The parental correlations, like the fraternal, exhibit great diversity in value for the five characters chosen, varying after correction from ‘215 for the half vertebrae up to 411 for total segments. This last value, which is the highest of the series, is low in comparison with the value of parental heredity in other forms in which Pearson and Lee find that “its values lie between 42 and ‘52 and cluster round -48” (O8, p. 379). The lowness of the average value for the five characters is yet more marked, being when corrected only °307 (cf. Table 10), an exceedingly low value for parental heredity. Allusion has already been made (p. 333) to the possibility of some changes in the meristic series occurring during growth from the natal to the adult condition. Even if we suppose that such changes occur it is probable that they are fairly uniform, and as all the embryos examined were at approximately the same stage it is unlikely that the low values of the parental correlations are in any measure due to growth factors. TABLE 10. Parental Correlations. Raw value Corrected value (a) Anterior spine... "359 + (039 378 Posterior spine... 196 +°043 264 Whole vertebrae ... 168 + 044 215 Half vertebrae ... 238 + 042 ‘270 Total segments... 416 + 037 ‘411 Mean ... ne ‘275 307 (a) The values given in the second column are corrected for selection of mothers out of adult 2 population. The low values of both the fraternal and parental correlations in Spinax are of great interest in connection with a recent contribution of Pearson, “On a Generalized Theory of Alternative Inheritance” (04). Basing his calculations on the conception of gametic purity Pearson finds that the value of the parental correlation should be about ‘3, that of the fraternal between ‘3 and ‘4. These theoretical values are considerably below the values hitherto deduced from actual observations (O08, pp. 379 and 387), and for this reason Pearson is inclined to pronounce against a theory of inheritance involving the conception of gametic purity. “The present investigation,” he writes, “shows that in the theory of the pure gamete there is nothing in essential opposition to the broad features of linear regression, skew distribution, the geometric law of ancestral correlation, etc., of the biometric description of inheritance in populations. But it does show R. C. Punnert 345 that the generalized theory here dealt with is not elastic enough to account for the numerical values of the constants of heredity hitherto observed” (O4, p. 86). These theoretical values do however agree closely with the average values found for Spinax, and it must not be forgotten that we are here dealing with obviously discontinuous characters capable of simple numerical appreciation, and differing in nature, as far as we can at present judge, from any yet investigated. It may well be that the heredity of such characters is governed by Mendelian principles, though at present these principles are impossible of demonstration, owing to the existence of more than one pair of simple, or perhaps also of compound allelo- morphs. To account for such families as that comprismg embryos Nos. 260—270 is difficult except on an hypothesis of dominance, or on Pearson’s hypothesis of “unit prepotency” (O08, p. 389). Here a family of 11 embryos of both sexes exhibits without exception extreme backward homoeosis, whilst the ? parent is characterized by marked forward homoeosis. It seems most natural to account for such a case by supposing that the unknown § parent showed extreme backward homoeosis, and that this condition was dominant over that of marked forward homoeosis. The data are however too scanty and the possibilities too numerous to admit of profitable discussion on these points at present. More is doubtless to be learnt by selecting some simpler case in which the breeding can be easily controlled. This much new knowledge has at any rate been gained by the application of biometric methods, for the magnitude of the parental and fraternal correlations cannot but mean that the varying number of units in a primary linear meristic series does not depend alone on the individual environment, but that it is a character transmissible from one generation to another. IV. SuMMARY. The chief results obtained from an examination of certain meristic characters in 567 specimens of Spinax niger may be briefly summarized as follows :— (1) A well-marked sexual dimorphism permeates the meristic series, the ‘s showing a greater tendency to backward homoeosis than the $s. (2) Equal numbers of fs and $s are born but the evidence derived from the numbers caught points to a preponderance of $s in the adult state. (3) The variability of the ¢ embryos (as measured by the standard deviation) is markedly higher than that of the § adults. In the case of the $s the variability is not very different in embryos and adults. This points to more stringent selection among the ¢’s and accords well with the circumstance of their relative scarcity when adult. (4) A comparison of the variability in different parts of the meristic series tells strongly against the hypotheses of vertebral intercalation or excalation ; and this holds good either on the view that such processes occur uniformly, or that they Biometrika 11 44 346 Merism and Sex in “Spinax Niger” are brought about by random excision or interpolation of segments. The various positions of the different characters studied (e.g. spines &c.) are probably due to homoeosis, and the reality of this factor is brought out by a study of the correlations with one another of the various characters chosen. (5) The study of the variations of the girdle canals supports the view that the different positions of the pelvic girdle are brought about by a process of homoeosis as opposed to one of excalation or intercalation. (6) Certain discrepancies in the correlation values are most readily explicable on the supposition that some homoeotic changes take place between birth and the adult state. Probably only a few characters are affected, and notably the anterior spine. (7) Although the ¢’s exhibit backward homoeosis as compared with the 2s there is no tendency for ? parents exhibiting marked backward homoeosis to produce more ¥' offspring, or for $s showing forward homoeosis to give rise to families having a larger proportion of fs. (8) The values of the fraternal and parental correlations are much below what would be expected on the Law of Ancestral Heredity* and accord better with the theory of gametic purity for the characters studied. Nevertheless the values of these correlations are sufficiently large to prove that the number of units in a primary linear meristic series is not solely due to the individual environment but is a character transmitted from generation to generation. REFERENCES. 1894. Batrson, W. Materials for the study of Variation. London. 1897. Baur, G. Remarks on the question of Intercalation of Vertebrae. Zool. Bull. Vol. 1. p. 41. 1898. Braus, H. Ueber die Innervation der paarigen Extremitiiten bei Selachiern, u. s. w. Jen. Zeit. Bd. 31, p. 239. 1899. ——. Beitriige zur Entwicklung der Muskulatur und des peripheren Nervensystems der Selachier. Morph. Jahr. Bd. 27, p. 415. 1898. Hetncxe, F. Naturgeschichte des Herings. Abhandl. d. deut. Seefish. Vereins. Bd. 11. 1903. Pearson, K. On the Laws of Inheritance in Man. I. Inheritance of Physical Characters. Biometrika, Vol. 11. p. 357. 1904. Mathematical Contributions to the Theory of Evolution. XII. On a Generalized Theory of Alternative Inheritance, with special reference to Mendel’s Laws. Phil. Trans. A, Vol. 208, p. 53. 1900. Punnerr, R. C. On the Formation of the Pelvic Plexus, etc. Phil. Trans. B, Vol. 192, p. 331. 1901. ——. On the Composition and Variations of the Pelvic Plexus in Acanthias vulgaris. Proc. Roy. Soc. Vol. 69, p. 2. 1899. RipEwoop, W. G. Some Observations on the Caudal Diplospondyly of Sharks. Jour. Linn. Soc. Vol. 27, p. 46. 1880. Storm, V. Bidrag til Kundskab om Throndhjemsfjordens Fauna. III. Kongelige Norske Videnskabers Selskabs Skrifter, 1880, pp. 73—96. Throndhjem, 1881. * [See footnote, p, 342, K. P.] R. C. Punyerr 347 EXPLANATION OF PLATE. Fig. 1, a—c. Showing the different positions of the anterior spine with regard to the vertebral cartilages. The numbers refer to the whole vertebra to which the spine is regarded as belonging. bd=basidorsal cartilage, id=interdorsal cartilage. la is taken from No. 146, 1b from 147 and le from 148 of the ¢ adults. Fig. 2. Caudal end of embryo No. 139 x8. The no. 30 indicates the 30th half vertebra. Fig. 3. Caudal end of embryo No. 85x 8. The 33rd and 34th half vertebrae are not separated as regards their centra, Fig. 4, Longitudinal section through occipital region of skull and first few vertebrae. From ¢ adult No. 53. The spinal cord and brain have been removed. Fig. 5. Preparation similar to Fig. 4. From ? adult No. 45. There is less condensation at the base of the skull than in the preceding figure. Fig. 6, a—c. Longitudinal sections through the junction of half and whole vertebrae. The last whole vertebra is in each case numbered. la is taken from ? adult No. 64,1b from ? adult No. 26, and le from ¢ adult No. 34. Fig. 7. View of vertebral column of a single specimen after cleaning. In this specimen there are 42 whole vertebrae and 43 half vertebrae. The anterior spine is carried by vertebra 16, the posterior by vertebra 40. The dorsal spines in the caudal region have been omitted. Note to Appendix, Tables 11—12. These two tables present the raw data for adults of both sexes. Of the abbreviations used g. p. n. signifies the lst girdle-piercing nerve, p. g. n. the post-girdle nerves, and coll. n. the number of nerves which take part in the formation of the nervus collector. Length w. v. and length h. vy. denote the length of the series of whole and half vertebrae respectively and the values given are expressed in centimetres. When two numbers are given for the g. p.n. in a bracket as in individuals 9—11 of Table 11 it signifies that there are 2 g. p. n. and that both right and left sides are similar. 348 Merism and Sex in “Spinax Niger” APPENDIX. TABLE ll. ¢ adults. Individual 2 g 4 #& 6 7 8 9 10 Ll i? -J3 If 15 16) 17m s16mIOmD Om IEE —$ $< — $$$ G.v.n, {i | 29 30 (28 29 28 29 29 23 (29/28/27 28 29 (28 ange 28 29 29 (27 28 3 PEGS Si 89 30 1000, en 3) gn KOO U29N128, 28°29 5 129) |. lovee. » 99 (28 4, (29 Peper a! 9 9 10 9 9 9 9 10 11 10 9 10 9 11 10 10 9 11 9 10 ‘ i . as ” 8 ” ” ” ” ” ” ” ” ” ae ” ” ” »”» ” ” ” ” ” ” conn. {F| & 8 5 6 5 5 5 5 5) 6 4 5 Re i Goa fF 6 5 5 6 : : iF ” ” ” ” ” ” 6 ” ” ” 5 ” ” ” 399 ” 6 ” ” ” ” ” Ant. sp. ———— 16 16 16-1717 16 16 16 16 16 16 18 16 16 16 16 16 16 16 15 15 Post. sp. 39 39 40 40 40-41 42 41 40 41 40 40 40 41 41 41 39 40-41 41 41 40 41 40 W. vert. 45 45 44 45 45 44 45 44 45 44 42 44 45 45 45 48 44 45 45 44 46 45 H. vert. 37 39 42 38 388 44 86 40 40 43 43 41 40 38 40 40 42 40 38 37 37 40 Total segs. | 64 65 65 64 64 66 63 64 65 66 64 65 65 64 65 63 65 65 64 63 65 65 Individual | 23 24 25 26 27 28 29 80 381 82 83 84 85 86 87 88 39 40 41 42 43 G. von, {i |(28 (28 27-28 (29 (29/29 29 80-31 (28 28-29 (27/30 28 29 28 29 28 (28 28 30 28 ~P- Ds 11. (29 [29 28-29 (30 [30(80 98-29 80 189 29 [28 (81%, 28-29 |, sic slCdMe memes Pen (| 9.10: a 9 9 9 9 9% 10-10) 1) 10 29) 39.089 9° 8 LOgdit. 9) 10) 89 as 8: i i ” ” 10 ” ” a 10 22: ” 9 ” ” ” 10 29) ” ” ” ” ” ” Cee Ce eee a Be 566 6) (0) Ce eam Ant. sp. 15 15 15-16 16 17 16-17 16 16 15 16 16 18 16 16 Is Ge toelytbesloieto Post. sp. 39 39 41 42 41 42 40 42 40 40 40 42 40 41 40 41 40 40 39 41 39 | W. vert. 43 43 45 47 45 46 43 46 45 45 44 47 44 45 43 46 44 45 44 45 44 | H. vert. 40 41 39 40 38 38 43 42 41 40 40 38 38 40 42 39 4%.41 41 42 39 | Total segs. | 63 64 65 67 64 65 65 67 - 66 65 “ 64 66 63 65 64 66 65 66 65 66 64 Individual | 44 45 46 47 48 49 50 51 52 538 54 55 56 57 58 59 60 61 62 68 | care fF 29 27 (30 28 (29 (28 29 30 29 28-2928 29 29 (28 (29 29 (27 29-30 30-31 29 pe scares bey ee et py Lima ord) ere ary: 28-2929 29 ,, 30° 5, | (289 29) oes, ae Fi 910 .8 10°10 9 8 9 9° 8 9-9 9 9 9 —=8)) 10 Oo mmon i. 1. 99 ” ” ” ” ” ” 10 ” ” ” ” ” ” ” ” ” 8 6 iA 4 r.| 5 5 6 5 4 5 6 6 5 5 5 5 5 5 6 6 4 4 5 \ 4 none re {I a 4 ” ” ” ” ” 5 4 ” ” ” 6 ” ” ” ” ” 6 ” \ 6 Ant. sp. 1616 16 16 17 15 16 15-1616-1716 16 16 16 16 16 16 15 16 17 ~«18 a Post. sp. 41 39-4041 40 41 40 40 41 40-4140 41 41-4241 42 41 41 40 41 42-43 40 : W. vert. 4543 45 44 45 44 44 46 46 43 44 46 45 46 46 45 44 45 48 45 . H. vert. 4043 42 41 388 41 40 88 37 43 44 42 40 41 41 41 #389 #42 387 = 41 | Total segs. |65 65 66 65 64 65 64 65 65 65 66 67 65 67 67 66 64 66 67 ~~ 66 } Length w.v.|— — 18°6 18°3 19°7 19'819°9 16-2 19°6 21°2 195 19°9 16:2 205 18°8 16:5 17-4 16°7 19:1 15-2 i Length h.v.| — — 10°71 10-4 1011170102 9:2 9-1 1211 11:710%35 9:211:010°0 8:8 96 99 95 83 j Totallength |— — = 287 28-7 29°8 30°8 3071 25°4 28-7 23°3 31:2 80-4 25:4 31-5 28°8 25°3 27:0 26°6 28°6 23°5 | Individual | 64 65 66 67 68 69 7O 7Ll 72 73 74 75 hoya CUA Shei WK) 80 8&1 2 | G a (rx. | 29 29 30 31 (28 29 28 28 29 (28 (27 28-29 28 29 29 (28 28 29 29-30 | gre (i. 29-30 28-29 31 ” (29 ” ” ” ” [39 {38 28 ” ” ” {29 ” ” 29 Dee in {r 9 9 9 8 9 9 10 9 10 9 10 9 9 10 10 10 9 9 9 g- i: 1. 8 10 8 ” ” ” ” ” ” ” ” ” ” 9 ” ” ” ” ” Gala. i 6 6 B 6 5 6 5, 5. 16: (25) ae ba 6 . 5: 5f Ae é Ant. sp. 15 15-16 16 17 15 17 #16 16 16 #16 15 415-1615 15 16 16-1716 15 16 Post. sp. 40 41 43 43 40 41 40 41 39 40 40 40 40 41 41 40-41 40 39 40-41 W. vert. 44 45 47 48 45 44 43 43 44 45 44 43 44 46 46 45 43 43 44 H. vert. 41 40 40 39 40 41 45 44 39 40 41 43 39 39 40 40 42 41 41 Total segs. | 65 65 67 68 65 65 66 65 64 65 65 65 64 66 66 65 64 64 65 Lengthw.yv. | 17:0 20°2 20:2 19°7 20:9 20:0 19:2 14:0 15:1 20:4 19°5 19°0 19°5 20:2 18°3 18:2 17:4 16:2 19°3 Lengthh.v.} 89 10°33 10°33 96 9:1 10°38 11°3 9:1 8°5 10°3 10:4 10°9 10°3 10°4 10'1 9:8 10°6 9:3 10-2 Total length | 25-9 30°5 30°5 30°3 30:0 30°8 30°5 23:1 23°6 30°7 29°9 29°9 29°8 30°6 28°4 28°0 28°0 25°5 29°5 Individual | 83 684 6&5 6&6 6% 88 $89 90 OTe 93 94 95 96 97 98 99 100 G. pen ti 28 29 29-30 Seas {39 {38 28-29 28 29 27 (28 28 28-29 29 29 28 27 1. 29 ” ” ” 29 29 28 28 ” ” ” (29 ” 29 ” 30 ” ” Peon {r|l0 1 9 .9 10 9 10 10 9 9 14 10 10 10. 9 “ _ Ve a SCE, eS ay Ne aN eee e EGON a ACR el Individual | 247 248 249 250 251 252 2538 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 2 Sex $ 9 S 8 @ GF F GF FS BS GS VG KF BK 9 SG Ch come OCC EEL. Ant.sp. |17 17 17 15 16 15 15 17 16 16 16 16 16 16 17 15 16 16 16 16 16 16 16 16 16 1! Post. sp. |41 41 41 39 40 40 40 41 40 40 40 42 40 40 39 39 39 39 40 39 39 39 40 40 42 4 W.vert. |46 45 46 44 45 44 44 45 44 44 44 46 44 43 42 43 42 42 42 43 42 41 44 44 «47 «4 H. vert. |41 40 39 41 39 40 42 41 43 40 40 40 40 39 42 42 44 41 44 42 41 46 40 40 42 «© Totalsegs.| 67 65 66 65 65 64 65 66 66 64 64 66 64 63 63 64 64 63 64 64 63 64 64 64 68 € ; ary 4 ? oa ae oe aN ea Ao ro ~ = (EE Individual] 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 29 Sex oS SS Ss 9 8s 3 ? € 2 F< GS VB BB GF BW ge go A CeCe Smee Ant.sp. {16 16 15 16 16 16 15 15-16 16 16 18 16 16 16 17 16 15 15 15 16 16 16 15 16 15 J Post. sp. |40 41 42 42 42 41 42 39 40 40 41 40 41 40 41 41 40 41 40 40 39 41 41 40 40 4 W. vert. [45 45 46 47 46 45 46 43 45 44 46 46 46 45 46 45 45 45 44 43 44 44 45 44 44 4 H. vert. |39 44 44 40 40 42 40 40 37 39 40 38 40 33 39 41 38 40 41 41 40 41 39 40 40 4 Totalsegs.|65 67 68 67 66 66 66 63 64 64 66 65 66 64 66 66 64 65 65 64 64 65 65 64 64 | oy Individual | 299 300 801 802 38038 304 75-82 from ¢? 84 149-162 from ? 86 211-222 from 2? 155 83-92 ” ” 85 163-164 ” ” (?) 2238-234 ” ” 156 ao ras ae 98-105 ,, ,, 87 165-168 ,, 4, (2) 285-246 ,, 4, 157 Sex Ce 106-107 ,, ~,, 88 169-174 ,, ,, 149 247-259 ,, 4, 158 Ant.sp. |16 15 16 16 16 16 108-118 ,, ,, 89 175-180 ,, ,, 160 260-270 ,, 4, 159 Post. sp. | 41 40 41 40 41 41 114-123 ,, ,, 90 181-187 ,, ,, 161 271-279 ,, 4, 160 W. vert. |45 44 45 44 45 45 124-182)... 92 DE) ke rn bY) 280-258 ,, ,, 161 H. vert. |43 42 40 41 41 42 138-139 ,, ,, 93 194-201 ,, ,, 158 289-296 ,, ,, 162 Total segs.| 67 65 65 65 66 66 140-148 ,, ,, 92 202-210 ,, 4, 154 297-804 ,, 4, 168 R. C. Punnerr 353 0 TABLE 14. if | Anterior spine a 15 16 17 18 No. é adults — 21 60 15 2 98 ¢ embryos — 24 104 15 2 145 ? adults 2 19 81 40 3 145 | @ embryos = 22 107 29 1 159 g adults ¢g¢ embryos @? adults ¢ embryos M. 15:979 15-965 16-159 16-056 | PEM. + 046 031 040 031 lo 6697 “5544 7208 5854 P.E.o 4 0323 0219 0286 0221 C. Vv. 4:19 3°47 4:46 3°65 TABLE 15. Posterior spine 38 39 40 41 42 43 44 No. ¢ adults — 10 41 37 9 3 — 100 ¢ embryos — 18 62 45 18 2 — L145 ? adults — 5 29 67 52 4 2 159 ? embryos 1 8 60 63 25 2 — 159 g adults ¢ embryos ? adults ? embryos M. 40-540 40-476 41-170 40:686 P.E.M. + -060 ‘051 “048 040 o “8879 9103 9057 8625 Pp BE 0423 0361 0343 0281 C. Vv. 2°19 2:24 2-20 2-12 | TABLE 16. WHOLE VERTEBRAE | 41 42 43 44 45 46 47 48 49 50 51 No. $ adults i ees. petal eseeeso dh. “Bh 8. ee Se CK 100 ¢ embryos | 1 7 19 48 42 20 7 — — — 1 145 ? adults - — 7 46 59 #385 183 3 —- — — 163 ? embryos — i 19 50 51 320 7 1 — — — 159 é adults ¢ embryos ? adults ? embryos M. 44-620 44:510 45-061 44-723 P.E.M 2b 077 “O74 “056 058 o 1:1470 13189 1:0722 1:0926 P.E.o 2b 0547 0522 ‘0401 0413 C. Vv. 2°57 2°96 2°38 2°44 Biometrika 111 45 354 Merism and Sex in “Spinax Niger” TABLE 17. Hair Vertesrar | 382 33 384 85 86 387 88 89 40 41 42 43 44 45 46 47 48! No. $ adults —- — — — il 6 11 12 25 18 13 9 3 2 — — — | 700 ¢ embryos 1 — — — 38 #5 18 26 43 18 18 7 4 1 1 — — || £45 ? adults — — — — 2g 12 16 26-297 34 27 13h oases eric) ? embryos — — — 1 8 6 24 22 46 30 17 6 4 — — — ~— | 159 3 adults $ embryos ? adults ? embryos M. 40°370 40-034 40-288 39-956 P.E.M ab *128 ‘107 ‘101 -091 o 1:9008 1:9169 1:9209 1:7022 P.E.o ae “0907 ‘0759 ‘0718 0644 C. Vv. 4-71 4:79 4:77 4:26 TABLE 18. TABLE 19. Toran CoLLECTOR dagarents 62 63 64 65 66 67 68 No. Nees 4 6 Q 4 No. $ adults — 6 23 48 18 9 1 100 é adults 21 113) bom 200 ¢ embryos 1 21 40 49 25 7 2 145 ? adults 16 176 102 2 296 ? adults 2455655 44 23> 1638 gembryos | 1 11 44 61 30 12 — | 159 ae ane M. 5:230 5:304 gadults gembryos ¢?adults ¢ embryos nee 030 024 M. 65:040 64-724 65-472 64-906 o 6301 “6059 P.E.M. £ ‘0707 065 055 056 PEG + -0212 -0168 c 1:0480 1:1536 1:0410 1:0449 C. v. 12-05 11-42 P.E.g + +0499 +0457 0389 0395 C.. Vie 1:612 1:782 1:590 1-610 TABLE 20. TABLE 21. P opt Cir pus| iG, 7a ono Tu) Noe Ist G.-P. | 96 97 28 29 80 31] No. NERVES NERVE 3 adults — 1 18 102 66 13) 200 $ adults 2 19 84 77 14 4 200 ? adults 7 71163 49 6 —| 296 ? adults 6 58 149 79 4 | 296 és Soa os 9S M. 9-360 7:920 M. 28-470 29-057 PE.M. + ‘039 ‘030 P.E.M. + 041 030 o *8188 +7580 o °8713 *7712 PEG + 0276 0215 PoE Oo *0294 *0213 C.v. 8°748 9°570 Cleve 3-060 2-654 355 R. C. PUNNET?® 00€0- * G6F9- = + 0€ tT (eas) | aA 49 99 G9 #9 £9 69 J 910. = Za8g. = # 6ST} Gl OS 19 FF IT ‘auidy 6660: + LOLO- = + So 6F OF Té | | Mss | 44 [) iicaitic= ice aa 469 1910 | rx] soar | | | | ‘ul aj0ym ~pupn squaubay 7702 UWaamMjaqd SU0r}zD]ALL0/) 0660: + GE89- = + GFT] @ L G& 6F OF TS) T G a Oe ee ee a ee aie SEG Neve WO ect ee Gee oe HA |e IDE UG ae ae CAG) || IG SG tS) Ee SHE || SS te T CO oD OO CO meGe ‘sokiquia $ =J pur ‘sokiquia 2 =u ‘ss 4npe=¥q ‘sf y[Npe sajouep a[qvy B AA0gB JY “770N Lovajsod pun sqzuaubhay 7040) uaamjaq swornjatvog ‘6¢ ATAVAL 9 Lb OF OF FR Sh oF J = 8F60- # 61GL- = 6ST} T L O€ TS OG 6 T G G Se | hae Cutis GL 2 AI eee IS Cae) |) eR ESIC SI ee | (GZ CO) | |= Sees OES ES ab see | HOTZ 8 eprom Es Oa I |) as I ee a a eg Pl ee WOR 8160- + GFLL- = + L6Z0- ¥ OFS9- = 4 [i oe oe COG me Cramoraol GL PE 8S SPF FOFO- = FEGE. = 4 8GE0- + 099G. = Oot} T 6 8L &F €@ 9 &@ FF Se Noe ee eng G Te, GR Sie ee eal | 01) G6 ss Seg hei, Le i (ee ge og GEN ee Bole 8 ML eee zej— 1 F ST OL & | CP = ee ie ee fie lor 89 £9 99 G9 #9 8&9 “WW GE HTEAVL G8G0- # FELY- = | 9¢60- = $919. = 4 OOL} T 6 8T S&F €@ 9 45 F060: + LIEL- = + G €& ST G& GE ST 9 8 i 8h Le OF Gh be S&P oP ” Merism and Sex in “Spinax Niger 356 G8t0-. + 6TLG- = # FCG0- F COIS: = # 6 @% 69 09 8 TF GFT} G 8 GF 69 ST ES || === hae ele ee > =e OD 6 G Lee OM AG TEE ie. ee Se RL ST i iw) & B 6 |e T Sf GF OF GF TI FOT} T OL SE 9F FIT IL =e SIE tS eae | ed 6, |l\ae HEHE || AE | &F oh Ih OF 68 8&& SF GF IF OF 68& OGF0- + 868P- = # ctl] F Fr 79 6 FP C8F0-. F 916g: = 4 7 Th ‘samdy L01402UD Puvd Lorwaysod waanjaq SU01QD ALLO) 8860- F 860S- — = # 6cI] F 9 LI OF OF G FE 9 EE T ‘9¢ ATAVL PLEO. F O8GG. — = 4 TI T F %&kL BI 8I &F 96 G6E0- F OI8F- — = + eorj} T — T 1 T &f L F8 66 96 OT GI & SF LF OF SF FP SF GF IF OF 68 8& k& DF 9LF0- F 966G- — = 4 OOT, © € 6 &T 8T G ‘apiqazla ajoyn pup fypy wuaanjaq suoynat0og “So ATAVL 357 R. C. Punnett LTS0- * 890- — = 4 SFS0- + 6000- = + $690- + 66T- — = 4 cPo0- + TE00- = | SvI] © IT 98 69 €& € — T 86 | c Gl T& 96 9T T ST £0 OE ST ‘auidy LOIWAZUD PUD ADAG} MA A L]PY weanjaq SUOUYD]ALLO/) ‘6G HTAVL are ae an S8F0- + 8GE- = 4 E670. 9FGG: = # 8690. + FSYT- = 4 CE90- + FFEL- = | at i SFI} G 1G OF SS G & 6ST] GL. O€ 19 FF IT T cP 36 OF OF TG T nN ~ Ve nN 86] T 6 8ST GB G 9 nl hla het ae 62 |¢ or ¢ 9 & |LO1] 9 8l OF ce b T | OF }6o JT T OL 9 F | £49 99 99 #9 89 & a ‘A ‘amy Lorwajun pun sjuaubay p07 waanjag suorynjatwoy) ‘St ATATVL SG 6F OF 6 F9IV0-. F 99GE- = & aaa ed a FIFO ¥ LOGF- = « : io £900. # SFLE. = 4 € — @ ¢ ¢ 4 (tt oot] T 6 st eF eg 9 i ¢ zg =e L LI — % 2]/— tT 1 — — —|e ¢ ¢ — % arj—- — > 2 t —|] ee e 01 teJ]— ¢ b St > —]z i z te] t 3 ¢ Of OL & Joe? I Caliente, 8) citer I — T | 87 89 49 99 99 #9 89 "W ‘aDLgajla4 JIvy pun sjuaubagy 70,07 waamyaqg suorynpailoy 16 ATAVL r™ Merism and Sex in “Spinax Niger” 358 GGe0- + T3686. = 4 8TE0- ¥ O6S¢: = 4 6L 671 8S 9 006 FIT Lb I g9 | §IT 1G T& 0&8 66 86 k£é 96 9860: + I819- = 4 ie Al W ‘saada xy 109007109 pun arsarny burouard-app.uy 4st waamgaqg suoynjas.op ‘6& ATAVL OLZO- F 86g. = # ‘AD1QA44A A a2oym pup aawany burdosard-aypury) JST waamjag suo1ynjat.og C&S ATAVL b OL FHT 8S 9 = 6060: + 89L¢. = # F9G0- ¥ 8GL¢- - = 4 £820: = L2Z9. — = 004 $8 96a| % 6 GFT 8g 9 ‘ramdgy worsajsod pup aasayy burdsard-aypuig) ys waamjaqg suoynjas1og TS ATAVE 9 Co a => me a Se 9 = Or |§ 8T bE Gl G — ~~ | GF 67 6 §T PLE — 9 FF & T —I|TF S9T 8 cOT, _ OT 7S 8& — — 68} — TL Lr TS 9L — | OF TL Z OT 06 T 8 68 L 2) ra T& 0& 66 8@ TE 0& 66 86 ké T&8 08 66 86 ké ‘TW ‘a W ‘SaadaNT ApLib-9sogq pup aavayy burduard-appury ys, waanjag suoynjasog ‘0 HTAVIL 6890: F 8E8¢- = + 359 0890: 8&0. = 4 NA for) nN 8 6 GE 06 oO T T 6 v T G69. G89. GLO. G99- GG9. GEO. GE9. G69. GT9- G09. W ‘Salida NT I)Aq pun ‘ODAQa}4A 4 aj7oym = shina Uy fo daquinu uaanjag W01n7ALL0/) fo yybuay qouoyodoud pup Lwaqunu waanjag U014Qnj]ALL0) S ‘L6 ATIVE ‘96 HIAVL a = BIE0- ¥ EGEF- = | Gye0- + 1908: = 4 = al 9L&0- = GOT. = 4 SFF0> F 9G0G- = 6FT 8¢ LL GF O08 OGL FF G 8T = | "SO0U8 AT ‘squaubagy 1040} 109997]0) pun sjuaubay 70407 uaamgag suoynjat.og pup away burouad-appury ys~ waangag suornjaL1og SE ATAVL we ATIVE 360 Merism and Sex in “Spinax Niger” FRATERNAL CORRELATIONS. TABLE 388, Anterior Spine. Siblings. 16 79 283 119 5 4486 273 1330 19 r = °3646 + °0257 r = *8085 + °0133 TABLE 39. Posterior Spine. Siblings. 39 40 41 66 112 112 352 294 78 29 294 220 106 3. 78 106 78 — 3 5 4 31 190 184 210 839 654 269 54 202 147 63 8 4474 ae r = '3330 + -0264 r = ‘3863 + 0256 r = 3732 + 0126 TABLE 40. Whole Vertebrae. Siblings. 41 42 43 44 45 46 5 38 2 — — 42 5 20 15 11 — — 3 15 30 75 38 26 47 431 3 1 44] 2 11 75 2298183 94 5 45 | — — 38 183 264 160 23 46 | — “— 26 94 16084! 20 46 145 163 123 9 | 486 W|I a 2B BD Wonca | 10 51 188 598 668 414 55 r = 5407 + -0213 7 - r = -4049 © -0123 These tables are to be read thus: There were 51 pairs of brothers with anterior spine at the 15th vertebra in the case of one of the pair, the other brother had the anterior spine at 15 in 12 cases, at 16 in 34 cases and at 17 in 5 cases; and so on. R. C. PuNNET?T TABLE 41. Half Vertebrae. 361 42 a lwwhosomwn re) a 1—- 1— — 37 5 38 ( 11 3 — 39 i — i — i=) | DW Dw o1D w vo | wimroe | | ! bo Co o> bo rR or g E = 23 16 #138 11 3 ~=éO21 57 20 24 10 5 8 87 oA 24 37 21 7% 135 10 37 24 14 #7 105 5 3 50 3 — 21 — 8 87 135 105 8 | 486 7 = ‘2771 + 0268 18 74 210 351 576 350 251 97 47 r = 12313 + -0139 3 TABLE 42. Total Segments. # Siblings. 63 64 95 189 103 63 64 65 66 67 68 63 64 65 66 67 24 113 200 100 49 J 486 r = 13950 + -0254 r = ‘4101 + *0247 Biometrika 111 144 164 7: 41 164 364 175 43 2 789 15 73175 80 46 67 395 154 1 10 43 46 48 6 ae ae ° > 166 464 789 395 r = °4285 + -0120 46 362 Offspring. Merism and Sex in “Spinax Niger” PARENTAL CORRELATIONS. TABLE 48. Anterior Spine. Mother TABLE 44. Whole Vertebrae. Mother. Offspring. 45 46 So es eee pon Se. Geers 711 7 — Wy Ces i 20 26 26 38 8 11 22 38 1— 2 8 53 72 80 9 r = '168 + -044 TABLE 46. Half Vertebrae. Mother. TABLE 45. Posterior Spine. Mother. 39 40 41 1 1 12 40] 5 12 65 12] 94 41} 1 9 51 177 78 42)— 4 10 30 Offspring. 26 138 7 r = ‘196 + 043 TABLE 47, Total Segments. Mother. 66 33 20 42 49 37 39 40 41 S67 Ml eee ee nee Br edad) Qe ee eS Ey 38] 5 5 6 2 2 38 1424 a 39] 8 6 2 7 9 6 1439 a | 40] 6 7 10 13 14 12 3 165 Z Gi|4az] 2 2 10 7 10 5 8 | 39 ro) &)42]—- — 5 9 7 6 —]27 @|\48) 8 2= 2 1 9% 2 222 SOA i ee ee i 45 == TON co ele 34 r = ‘416 + ‘037 r = ‘238 + :042 K. PEARSON 363 Note on Mr Punnett’s Section on the Inheritance of Meristiec Characters. By Karu PEARSON, I should like to add a few words (as he himself has suggested) as to the results of this portion of Mr Punnett’s investigation. I feel the more anxious to do so because he has broken entirely new ground, which we can only hope will attract the attention it deserves, and so bring new workers to this field. If so, it is desirable to state the conditions under which it is possible to obtain final results. The father in the case chosen by Mr Punnett is quite unknown, hence it is absolutely needful, in order to reach accurate values of the correlation, that we should have enough mothers of each class to insure that the average father of that class is practically the average father of the population. When Mr Punnett first sent me material for reduction it consisted of 88 individuals forming 10 families for maternal correlation, and 93 individuals in 12 families for fraternal correlation. Allowing for four to five classes in the tables, it was obvious that the extreme arrays of offspring would be due to one, or at most two mothers. It was not likely, therefore, that the mean father of these groups would be the mean father of the general population. However, we ventured to reduce the data with the following results :— Correlations. Series I. 88 Individuals in 10 Families 93 Individuals in 12 Families Parental Correlations Fraternal Correlations Character Raw Value | Corrected Value (a) | Raw Value | Corrected (a) | Corrected (b) Posterior spine .. | °440+°'058 534 150 + 023 246 342 Anterior spine ... | 404+ -060 “444 488 +°018 509 530 Whole vertebrae... | °369+:°062 “467 ‘297 + 022 364 ‘431 Half vertebrae .. | 225 +068 281 152 + 023 Miia 203 Total segments ... | 004+ 051 “706 294 + 022 *5O4 ‘714 Mean ae 396 ‘486 | 276 ‘360 444 (a) Corrected for selection of mothers out of adult 2 population. (b) Corrected for selection of fathers also, on assumption that they were equally selected with mothers, although unknown. Corrections made in the manner indicated Phil. Trans. Vol. 200, A, pp. 89—45. Now it will be seen at once that the average corrected parental correlation, i.e. ‘49, is in essential agreement—not-with the ancestral law which fixes no value for the correlation—but with the values we have found for man, horse, and dog. On the other hand the fraternal correlation is very low, 44 or even “36, a value lower than we have yet found for any physical character in 46—2 364 Note on R. C. Punnetts Memoir a long series of mammals. I told Mr Punnett that this value alone seemed sufficient to show that the material was inadequate. He then added 136 individuals in 15 families. They gave: Series II, 136 Individuals in 15 Families 136 Individuals in 15 Families Parental Correlations Fraternal Correlations Character == = = Raw Value | Corrected Value (a) || Raw Value | Corrected (a) | Corrected (b) Posterior spine ... | 096 £°057 142 “473 +°015 ‘479 "484 Anterior spine Aon || el ae 10%) 396 269 +018 "294 318 Whole vertebrae... | °139+°057 iby 7) | *469 + ‘015 “475 “482 Half vertebrae ... | °232+4°055 252 "238+ °019 "246 253 Total segments ... | 3879+ 050 332 |°477+°015 "457 ‘437 Mean 241 260 B85 *390 395 The results were now much lower for the parental correlations, and slightly lower for the fraternal correlations. The differences between the two sets are in a number of cases significant compared with the probable error of the differences, and the only safe conclusion to be drawn is that the two samples from two different years are not random samples of the same population. Mr Punnett tells me that he cannot fix on any difference in the method of collecting or observing the two series. Judging by p. 321 one appears to have been procured at a rather earlier date than the other. Clubbing the two sets together we had the values for fraternal and parental correla- tion given in Mr Punnett’s Tables 8 and 9. These arise from 224 individuals in 25 families for the parental, and 229 individuals in 27 families for fraternal values. The general result is, as we might expect, midway between the two. Can we venture to draw any definite conclusions from these divergent values, and, if so, what? Now, I think we may safely say that Mr Punnett has demonstrated the existence of inherit- ance in these meristic characters ; but that the paucity of material does not allow us to definitely fix its intensity. The values found are very similar in intensity to those first found for stature in man from Mr Galton’s material, mothers and sons ‘302, mothers and daughters -284*. These were based on 200 families. Again from the same data: Brother and brother = ‘391, sister and sister °444, sister and brother °375. On Mr Galton’s hypothesis the ancestral law gives for parental corre- lation *300, and for fraternal ‘400+. Or, we might even say that Mr Punnett’s fish results agree on the average fairly well with those of Mr Galton for stature, and confirm his view of the ancestral law f. But this is, I take it, to miss the real point at issue. Such low values as Mr Punnett finds have been found before in man, in lepidoptera, and in molluscs, but in all these cases in short and doubtful series. They tell neither for nor against the ancestral law, but they are opposed to any hypothesis as to sensibly equal parental correlation in different species and for a variety of characters. That is a very vital point which no one can at present consider finally settled. * Phil. Trans. A, Vol. 187, p. 270 and p. 281. + R. S. Proc. Vol. 62, pp. 397 and 410. + Similarly we have for a short series of 100 families, the inheritance of cephalic index, mothers and daughters ‘300 and brothers and sisters -340, for example. R. S. Proc. Vol. 62, p. 415. K. PEARSON 365 Still in long series for a variety of characters in man, horse, and dog the parental correlation certainly approaches a value about °5. If Mr Punnett’s values were for a long series I think we should have to conclude that the intensity of heredity could vary very much from species to species, and perhaps admit even considerable variation in the same species for the same character at different periods. Hitherto, however, we have found that when we replace our short and doubtful series by longer and more carefully measured or observed data—as we have done in several of the cases referred to above—we approach closer to the value ‘5 for parental heredity. Further, the confirmation of Mr Punnett’s statements on p. 333, as to growth changes in post- embryonic life (and perhaps during embryonic life itself?) would certainly lead us to expect a weakened parental correlation (and in the latter case a weakened fraternal correlation). Anyhow values like ‘3 for parental and *4 for fraternal correlation cannot discriminate between the ancestral law and any form of Mendelian theory, for the former with Mr Galton’s value of the constants actually leads to these values. A value like 5 would be opposed to one fairly compre- hensive Mendelian theory, but possibly not to every such theory. A possible test between the ancestral law and my generalized Mendelian theory is given in my paper: On a Criterion which may serve to test various Theories of Inheritance*. It is there indicated that we should expect the variability of the several arrays in the latter case to be given by a parabola, while with anything like a normal distribution of variations it would in the former case be a straight line. Dr Lee and I applied this test to Mr Punnett’s five parental correlation tables, we calculated the s.p.’s of each array and plotted them to the magnitude of the parental character. But the numbers in the arrays were so small, and therefore their probable errors so large, and there were so few points (especially if we omitted those which belonged to arrays of 6 to 10 members only, and therefore were absolutely untrustworthy), that we got nothing but wild zigzags of three to four lines; these differed between the wide limits of random sampling from neither straight line nor parabola, and were quite insufficient to serve as any criterion. In fact they only again emphasized the lesson we had already learnt from short series that 25, 50, or even 100 families are insufficient to adequately determine the bio- metric constants of a correlation surface for heredity. In saying this I do not for a moment undervalue the importance of Mr Punnett’s work ; he has shown for the first time how heredity in one species of fish can be dealt with, and this is a great step onwards. I quite realize the difficulty of dealing with 1000 mothers, but this is, I believe, the sort of ideal we must bio- metrically propose if we are to reach data sufficiently smooth to give final values to the heredity coefficients, and so available for testing between current theories. * R. S. Proc. Vol. 73, pp. 262—80. ON THE MEASUREMENT OF INTERNAL CAPACITY FROM CRANIAL CIRCUMFERENCES. By M. A. LEWENZ, M.A., and KARL PEARSON, F.RB.S. (1) IN a memoir by Dr Alice Lee* on the reconstruction of the capacity of the skull from external measurements the following results were obtained : (a) Equations giving the probable capacity of the skull from a knowledge of the length, breadth and height for a number of races. (b) Equations giving the probable capacity from a knowledge of the product of length, breadth and height. (c) A demonstration of the small relationship between capacity and cephalic index. (d) Ademonstration that the relationship between capacity and both horizontal and vertical circumferences varied much from race to race, even between allied races. The conclusions drawn from these results were : (i) That on the data dealt with there was no means of getting a small probable error in predicting the capacity of an individual skull from external measurements, but good results might be found from the average of series. (ii) That (b) gave a formula which changed less from race to race than (a), and the mean formula from (b) gave reasonably close results when we paid attention to sex difference. (iii) That the formula for the nearest allied race should, where possible, be selected, and failing any knowledge of evolutionary history then the mean formula based on (0), It will be clear that the above results emphasise the need for judicious caution in using the’ cranial capacity formulae, and also offer hints from experience to those anxious to discover new formulae. * Phil. Trans. Vol. 196, A, pp. 225—264. M. A. Lewenz AND K. PEARSON 367 (2) Dr J. Beddoe has recently taken up the relation of skull capacity to cranial circumferences and published* new formulae connecting the capacity with the product of three such circumferences. Dr Beddoe is a veteran who has done such good service in creating interest in anthropometric matters, that we should hardly have noticed his paper hostilely here, had he not (a) shown in it a complete ignorance of the nature of modern statistical theory, and (b) misinterpreted partly through misunderstanding and partly through faulty arithmetic Dr Lee’s results. There is absolutely no reason why the product of three cranial circumferences should not be taken as a basis for estimating the capacity of the skull, but there is only one scientific way of reaching a suitable formula and that Dr Beddoe has not adopted. We will point out what considerations must guide us in the matter. Let us take first the following three circumferences of the Frankfurter Verstdndigung, U=horizontal circumference, S = sagittal circumference from nasion to opisthion, Q=transverse circumference from the top of one auricular passage to the top of the other in the vertical plane, i.e. the plane which is perpendicular to the “horizontal plane,” and does not generally pass through the bregma. Let C be the capacity, and P=Ux 8 x Q, then we require to find a relation between C and P. In order to do this we must measure C and P for as many skulls of one sex and race as possible and then for as many races as possible to see how our formula changes with race. The process may be illustrated as follows. We take 164 Theban mummy skulls and pick out all those with C lying between 1380 and 1390 cubic centimetres. This is a group well within the probable error of capacity determination. We have 10 such skulls with the values for P in cubic centimetres given below. Now 10 cubic centimetres is about 1/11 of the standard deviation in capacity and we may take 500 cubic centimetres to be very roughly the same proportion of the variability of P. Picking out all the P’s from 58,600 to 59,100 we have the following system : Capacities from P from 1380—1390 58,600 to 59,100 53,407 1310 » 54,482 o, 1853 a 54,568 g 1355 = 57,652 =~ 1360 x 58,892 3S 1365 s+ 59,669 s 1380 2 60,194 R 1426 = 60,277 = 1430 > 60,596 > 1437 62,390 1470 Mean 58,208 Mean 1389 * “De PEivaluation et de la Signification de la Capacité cranienne,” L’ Anthropologie, Vol. x1v. pp. 267—294, 1903. 368 Measurement of Internal Capacity of Skull Now it will be seen at once from these results that to say a skull has a certain capacity does not fix the product of the circumferences, and to say that it has a -certain product of circumferences by no means fixes its capacity. The only thing that is possible for us to assert is that Theban skulls with a capacity of 1380—90 will cluster round the value 58,208 of the circumference product, and skulls with a circumference product between 58,600 and 59,100 will cluster round the capacity value 1389. If these clusters follow—and they do follow—the usual distribution of characters in man, then these mean values are the “most probable values” for product or capacity when deduced from a knowledge of capacity or product re- spectively. Tables can now be dressed giving these “most probable values” for each small range of capacity or product. Such tables are only another form of the corre- lation table and the regression curve, which Dr Beddoe seems to find so mysterious ; they are the only scientific way in 1904 of approaching these questions. Such “most probable values” in the case of most characters in man are found—allowing for the errors of random sampling—to increase uniformly with the uniform increase of the known character, in other words the regression curve is usually a straight line. The equation to this straight line is found by perfectly easy mathematical work and is what Dr Lee gave in her paper for the product of the three diameters, and what we give in this paper for the product of the three circumferences. If such a linear formula is to be used at all this is the only scientific way of approaching the problem. Dr Beddoe himself uses such a linear relation, B,; yet how does he write of the only method of scientifically dealing with a perfectly elementary statistical problem ? “Je me reconnais incompétent pour décider si lidée de corrélation peut tromper quand il s’agit de la forme cranienne et de sa capacité, et si lidée de compensation, moins distinctement appréciable, il est vrai, mérite d’étre étudiée*.” We assert, with a distinct appreciation of the seriousness of the statement, that a writer who cannot realise what correlation is and how it is used in a simple problem of this kind has no right nowadays to deal with craniometric problems at all. It is only by frankly asserting on every occasion this truth that we can hope to render anthropometry in all its branches a real science. The day for the old methods is once and for ever gone. Correlation is simply the mathematical process of finding the best linear relation between the known value of one character and the most probable value of a second. It determines in the special case A and B in the relation: Probable C= 4 +.B x Known Pca, sceteaste sce acecacit (1). Dr Beddoe also wants to find a linear relation between Probable C and a Known P. How does he proceed? In no case does he go through the laborious and necessary work of tabling the mean C for a given small range of P. He simply puts: Probable:C =.6 x Known? fio o..cscenseseecesa ee (i1), * Loc. cit. p. 278. M. A. Lewenz AND K. Pearson 369 and guesses what he considers a suitable value for B! He therefore (1) assumes that his line holds far beyond the range of any actual observation*, for his only ground for putting 4 =0 must be, although he does not state it, that C vanishes with P; (2) neglects the result of all observations hitherto made on human characters, for in no case, that we are aware of—and certainly more than 100 must now have been worked out—is A=0. When Dr Beddoe does not guess B he obtains its value by giving C and P their mean values. Even here as he does not know the mean value of C, he guesses it ! “Je suis bien certain que la moyenne des pesées de cerveaux d’Anglais est un peu au dessous de 1400 grammes et que la moyenne de la capacité de cranes masculins anglais est voisine de 1500 c.c.+” The only reasonably long series of English skulls with which we are acquainted neither give a mean of 1500. This is the type of guesswork which has hitherto passed for science in anthropometry. Even if Dr Beddoe had found by actually examining data that a formula Probable C= Bx Known P held for the skulls of one race, he ought before adopting it generally to have noted Dr Lee’s warning about the changing degree of correlation between circumferences and capacity when we pass from one race to a closely allied race, and accordingly have tested it on other races. He has not attempted this, but finding it did not agree very well with observations on individuals attempted to modify it by introducing corrections depending on the cephalic index. This he has done notwithstanding Dr Lee’s result that there is generally little correlation between cephalic index and capacity, and that what there is varies largely from race to racet. (3) We now turn to our own contribution to the subject. Dealing with the three circumferences U, S, Q defined above, which differ somewhat from Dr Beddoe’s three, we have sought a linear relationship between their product P and the mean value of the corresponding C for four ditferent races. We have used the following male crania: (a) Fawcett’s measurements on 98 Naqada crania. (b) E. Schmidt’s measurements on 164 Theban mummies. (c) Ranke’s measurements on 78 Altbaierisch crania, (d) Macdonell’s measurements§ on 72 English crania, and we have one series for female crania, (e) Macdonell’s measurements on 76 English crania. * While the relation of the characters in man is closely linear for the range found in normal individuals of one race, it certainly ceases to be linear when we pass to ‘dwarfs’ and ‘giants.’ See Pearson: Phil. Trans. Vol. 192, A, pp. 169—214. There is no reason whatever for extending the linear relation like (i) to extreme ‘dwarfs’ and putting 4=0. t Loc. cit. 285. $ See loc. cit. p. 233. § We have heartily to thank Dr Macdonell for providing us not only with the data, but the actual reductions in cases (d) and (e). His own memoir on the English skull appeared in Biometrika, Vol, m1. pp. 191—244. Biometrika 11 47 370 Measurement of Internal Capacity of Skull The following results were obtained : TABLE L Race Mean C | Mean P oc op iiay (a) Naqadag... 1375 57,414 10852 | 4412 "7492 (6) Thebang... 1388 58,285 118-01 4863 8576 (c) Germang ... 1506 64,604 111°54 4997 8587 (dq) Englishg... 1477 60,860 122°37 5206 *8790 (e) EnglishQ... 1300 53,656 112°80 5157 8860 From these results the following equations flow: (a) Naqada § Probable C=317'2 + :01843P (b) Theban § Probable C=1747 +-02081P (c) German ¢ Probable C= 267-44 -01917P \ (d) English §~ Probable C= 219-2 + :02067P (e) English $ Probable C= 263-9 +-01913P Now from these equations certain results at once flow. It is clear: (i) That it is absolutely illegitimate to assume like Dr Beddoe that A =0. Gi) That A varies widely with race and sex, while B varies much less markedly, but possibly significantly. This is precisely what we might expect had racial differentiation arisen by selection from a common stock. Cand P being measured in cm.’ Thus Dr Lee’s statement that the capacity and circumferences correlations varied so much between closely allied races that we could hardly expect to deduce a formula true for all races is fully borne out, when we investigate the relation between capacity and the circumference product. Dr Lee, after showing that the capacity and horizontal and vertical circumference correlations and regression equations varied from race to race, remarked: “ We conclude therefore that it appears unlikely that a reconstruction formula, based on the circumferential measurements of the skull, can be found which will give good results, if extended from one local race to another*.” Dr Beddoe has apparently quite misunderstood the nature of the argument and simply dismisses the difficulty without meeting it with the words: “Le Dr Lee a fait des experiences sur l’arc transverse, mais elle a négligé Vare sagittal, et ses résultats ne sont guere satisfaisantsT.” Dr Lee’s series seem sufficient for her purpose ; it is the fact that they are sufficient but not satisfactory, which Dr Beddoe has no right to shirk. If the reader will compare the above male formulae with those obtained for three races between the capacity and the diameters’ product by Dr Leef, he will * See loc. cit. p. 263, + Loc, cit. p. 269. Dr Lee used two arcs, not merely one as is suggested. $ See loc. cit. p. 243. M. A. Lewenz Anp K. PEARSON 371 at once realise why Dr Lee considered a diametral product formula could be better extended from one local race to another than a multiple regression circumference formula. She did not attempt a product circumference formula. In view of the fact that our formulae vary so with race, it is venturesome to form a mean equation and treat it as an “inter-racial formula,” but for com- parison with Dr Beddoe’s results it is perhaps desirable to do so*. We have as mean formula for males: Brobablet@— 7244-62 SOLO 7 22 a neceeanaadteavnessssers Gas We would only warn our readers to use such a formula with caution. For example, never to use it for females, and only in preference to one of the above four formulae when no evolutionary race relationship can be predicted between the above races and the race to be investigated. We now turn. to the probable error of these results. We have: Probable Error of Individual Prediction. | Formula (a) (Dd) (c) (d) | Probable Error ... 48 41 39 39 To test the value of these results, 15 ¢ skulls (as nearly as possible every thirtieth skull) were taken at random from the Naqada measurements; 15 ¥ skulls from the Theban records (as nearly as possible each tenth skull), and similarly 15 from the Altbaierisch series. In the case of the Naqada crania 8 had an error greater and 7 less than the probable error; in the case of the Theban the numbers were 6 greater and 9 less, and for the Altbaierisch 9 greater and 6 less ; or total 23 greater and 22 less than the probable error, which may be considered very satisfactory. The mean error of the 45 skulls as found from the mean formula is 47:5, corresponding to a probable error of 47:5 x ‘8454=40°2. The theoretical value of this probable error is 40°4. There can therefore be, we think, small doubt that our mean formula will predict the capacity of a single individual skull from circumferential measurements with a probable error of about 40 cubic centimetres. Dr Lee’s diametral product formulat+ showed a probable error of 43 for Aino 's, 55 for German ’s and 52 for Naqada 4's, say a mean value of 50. Actual application to 80 crania gave only a mean error of 49, or a probable error of about 42. Thus we should expect the present formulae to give slightly better results than the diameter product formulae, but for reasons to be given later we hold them quite inferior to those formulae for the living head. * A more correctly inter-racial result is given on p. 386 below. The above is really a mean intra- racial result. + See loc. cit. pp. 234-7. 47-—2 372 Measurement of Internal Capacity of Skull (4) We now turn to Dr Beddoe’s rule B;, which up to the date of writing this he considers his best formula *. If we put Dr Beddoe’s rule into a formula it is, if C be the capacity in cubic centimetres : a 1 Ux S <0" O=(1+ 359 (I-80)) 36000” where J is the cephalic index, U is the horizontal circumference, Q’ is the auricular circumference from the centre of one auricular passage to that of the other, and S’ the sagittal arc from nasion to inion, all in millimetres. It may be written in the form: C=:0000926 I x Ux S’ x Q' + 020874 U x S’ x Q’, where the product U x S’ x Q' is to be read in cubic centimetres and not cubic millimetres. Now let p, stand for U x 8’x Q and p, for Tx U x 8’ x Q’, and let o, be the standard deviation of the character or quantity v and r,, the correlation of * Dr Beddoe gives three formula in his paper B,, By, B,, and calculates some of the results by one and some by another of these rules. He tells us that he has another rule B, in preparation, and that he has been gradually feeling his way. It is against any such process as this that we wish emphatically to protest. Every one of Dr Beddoe’s formulae is a mere guess. In no case does he adopt a certain type of formula and determine by recognised statistical methods the best values to be given to the constants of that formula. If he finds it gives him somewhat too high a series of values he merely reduces it by cutting off a series of percentages from the result. As he tells us Bg is his best formula at present we have used B,. This is designed to give what Dr Beddoe terms Flower’s values, or what we should simply term the capacities properly measured, e.g. not the recognised erroneous values of Barnard Davis. It is obtained in the following manner: he measured his sagittal arc, S’, from the nasion to the inion instead of to the opisthion—of this later more—and since the sagittal are, S', is usually measured to the opisthion, he subtracts 50 mm. from it to find S$’. Next he takes the vertical circumference, Q’, which he measures from the centre of one auricular passage to that of the other. This is really not our Q. Our transverse circumference is measured from top of one auricular passage to the top of the other and ‘‘ vertical,” i.e. perpendicular to the Frankfurt ‘‘ horizontal plane.” He ought not accordingly to have interchanged as he has done our Q with his own Q’. Probably 9 or 10 mm. ought to be subtracted to get Q from Q’, even if we could possibly accept his “ passant par le bregma ou pas loin en arriére”’ as giving even an approximation to the ‘‘ vertical plane.” But as Dr Beddoe appears content to use our Q for his Q’, we have made no attempt to modify it in order to reach an are so vaguely described as ‘‘ passing through the bregma or not far behind it.” As a matter of fact the ‘‘vertical plane” may easily fall 10, 20, or even 30mm. behind it. Lastly, to get the capacity Dr Beddoe multiplies 4 of the horizontal cireumference (U) by 3 of the nasio-iniac are S’ by 4 of his auricular are. He then divides this product by sJ57, and deducts 3 per cent. of the result for each unit of the cephalic index below 80, and adds a third per cent. for each unit above 80. This is the rule which we have represented by the formula in the text. It will be observed that it is by no means so simple as the product formulae we have used, besides being obtained by a theoretically unjustifiable process, B, takes 45mm., not 50mm., off S to get S’ and neglects the cephalic index correction. B, takes 50 mm, off like B,, but takes 4 instead of 3 per cent. for cephalic index correction. It will be seen that the constants are pure guesswork changeable at will. M. A. LEwenz AND K. PEARSON BY} the two quantities or characters v and w; then the proper formula for Dr Beddoe to have taken would have been: Ton. — Tap. Tavs Te Top, —Tep, Tn.0, C= = =. a — (h —m,,) + i = aes (Ds 21 ia (9). ’ Nore Pr LF PiPe Pe Dr Beddoe has assumed that : 7 — Ter foal’ Veps TpPe Tc nr + Yop, — Yep, Vp, p2 ice m . Be = aN et Gye l—-r Gen Yl pip2 Pi Y py, Do Pr Such a result is contrary to all anthropometric experience *. There is of course no reason why a formula like (g) should not be tried for skull capacity, but there is only one scientific method of determining it, namely the discovery of the actual means, standard deviations and correlations of the quantities involved for a long series of skulls. We cannot, in the light of modern statistical science, assume : C=A+D,p,+ Dp, tacitly put A =0, and take a series of guesses at D, and D,, “feeling our way.” But the labour of investigating a formula like (g) is considerable, and no wise person would undertake it without first considering its chances of giving a remunerative result. Let us first enquire into this. Formula (gy) may be written if subscript 2 stands for J: Cant (ntl) Ps whence : 80 = (9. + Yo Mi) SP + Y2 Mp, OL, and ultimately : To Vet = (1+ Yo M:) Tp, Trt + Ya My, i Fi, To= (V1 + Yo Mi) Tp, Top, + Yo Mp, i Ti Tei: Eliminating y, + ym; we have: 1 og, Tpi — Vet Yep, Ter i, Of Tey — Talon Now we know that r,; 1s usually very small, and therefore the terms 7r,; We and 77, will be small; further, r,,, is always positive. Hence y, will be of opposite sign to r,;. Now, so far as we know, nobody has worked out the correlation of p, and J, but since the correlation of p, and C is positive and large there can be no reasonable doubt that that of p, and J will have the same sign as that of Cand J. But the correlation of capacity and cephalic mdex is negative for dolichocephalic races and positive for brachycephalic races. This conclusion * See, for example, the multiple regression formulae given for the long bones by K. Pearson, Phil. Trans. Vol. 192, A, pp. 186-7, for cranial measurements by A. Lee, Phil. Trans. Vol. 196, A, pp. 235-6, and for the like measurements by 8. Jacobs, A. Lee, and K. Pearson, Biometrika, Vol. 1. pp. 349—355, The list might be indefinitely extended. 374 Measurement of Internal Capacity of Skull had already been published in a memoir which has been read by Dr Beddoe. We have in fact the following results: TABLE II. Correlation of Capacity and Cephalic Index. Race eaeaee Number Correlation 3 Thebans 74°8 187 —'15 6 Naqadas 73°2 100 — 13 d¢ English 74:3 77 — 02* }— +15 ¢ Aino ... 76°5 76 - 31 3 Copts ... 77°3 56 —'14 6 Etruscans 78°5 78 | +°22 3d French w. | 79°8 56 +:14 ‘1D ¢ Malays we tL i On 3 Germans 83°3 100 +20 We see from this table (i) tnat the relationship between cephalic index and capacity is slight and irregular, and (ii) that any formula like Dr Beddoe’s which not only puts y zero but gives a value to y, persistently constant in magnitude and sign must be erroneous. (5) Having shewn that Dr Beddoe’s correction for cephalic index must be wrong for individual crania, when we pass from dolichocephalic to brachycephalic races, because in the former on the average the more dolichocephalic, in the latter the more brachycephalic individuals have the greater capacity, we turn to the main part of his expression (as it appears purely and simply in his first result B,, in which he takes the capacity solely proportional to the product p,) and ask whether this is reasonable. A little consideration will show how impossible it is that a formula of the type C=D,p, can at all agree with a formula of the type C= A+ D,p, to which the true theory of correlation leads us. In the accompanying figure the two lines are indicated. It will be seen at once that except near the actual mean values of p and C Dr Beddoe’s formula cannot possibly give the mean or most probable value of any array. If, however, a small skull be taken with thick walls, or a large skull with thin walls, then Dr Beddoe’s formula naturally gives a better result in extreme cases. This is the source of any advantage which may appear in its favour when he proceeds to select large crania, “décrits comme minces ou transparents,’ or small skulls, “décrits comme épais ou lourds,” and points out that for certain such cases his rule gives a better result than Dr Lee’s correlation formula. This he has actually done in Tables II and III of his paper f. The answer to such criticism is that he has obtained his advantage by causing his line to give bad results for the capacity of the average skull of a given product, ie. he has swung it round till it makes an angle with the line of “ probable values.” Thus his guess-work formula is really only a line diverging very considerably from * Deduced from data provided by Dr Macdonell. The result shows that there is sensibly no correla- tion between cephalic index and capacity in the skulls here dealt with. + Loc. cit. pp. 275 and 276. M. A. Lewenz Aanp K. PEARSON 375 the line of most probable values. If he must take a line at all then the only thing open to him is to use the scientific process of correlation and find the best fitting line. i Seale of Capacity. Small ) Small Mean - Large x Seale of Product of Ares. (6) We now pass to the arcs which Dr Beddoe has chosen for the basis of his formula. We take first his sagittal arc from nasion to inion. Dr Beddoe makes no reference whatever to the difficulty of determining the inion even on the skull. The inion is defined in the Frankfurter Verstdndigung as the point where the linea superior nuchae meets the median plane. But since the date of that concordat the further investigation of the matter has shown that this definition is extremely vague. Broca originally defined the inion as the median intersection point of the two lineae nuchae superiores. Merkel pointed out that the protuberantia occipitalis externa corresponded to the meeting point of two lineae nuchae supremae, and termed the meeting point of the lineae nuchae superiores the tuberculum linearum. Further the inion is often prolonged with a V-shaped projection, and in this case we are told that the median point of the base of this projection is to be considered as the inion, or that the lineae nuchae are to be continued on the same niveau until a median point is reached, which is to be the inion*. Now we shall term the median point fixed by the lineae supremae the superior inion, and the point fixed by the lineae superiores the inferior inion. If these two points coincide, as they may do, then this is the inion proper. Now Schwalbe defines the inion as the common inion of the four Jineae when they are concurrent, and as the superior inion when they are not. This will work fairly well on many skulls, but our experience shows that on certain skulls, (i) only the inferior inion can be fixed, * See especially G. Schwalbe: ‘‘Studien tiber Pithecanthropus erectus,” Zeitschrift fiir Morphologie und Anthropologie, Vol. 1. p. 24, 1899. 376 Measurement of Internal Capacity of Skull (i) the two inions can both be fixed, but the inferior may be so far more marked than the superior that without question it would be treated as the inion on the living head, (111) no inion at all can be determined with any certainty. Testing the living head one may say that if an inion can be fixed, one is not definitely certain whether it is the superior or inferior unless both can be determined. That more often than on the skull itself a cautious observer would decline to make any dogmatic statement as to the position of the inion at all. In fact on the skull there is often grave doubt, on the living head there is usually doubt and often gravest doubt as to where the inion should be located; and an occipital torus or a bathrocephalic network of ossicles, both not uncommon in English skulls, may completely put out any seeker for the inion on the living head. In short while it is highly undesirable to use the inion instead of the opisthion in any cranial investigation, the introduction of the inion into measurements on the living head is even more to be deprecated. To illustrate these points we have investigated the inion on an important series (L.S.) of 116 English skulls. There were 50 ~ and 66 $. Among these, owing to defects of one kind or another, 7 / and 6 ¢ had no inion-opisthion distance measurable. The remaining crania we placed before Professor G. Thane and asked him to determine the position of the superior and inferior inions. He most kindly consented to give us all the advantages of his anatomical experience, and we have the following results : Of the remaining 43 § and 60 ¢ skulls the inion was “ unrecognisable” or “undefinable” in 10 ¢ skulls, it was “very doubtful” in 1 ¥ and 2 ? skulls, and “vague” in 2 ¢ and 10 ¢ skulls; thus the ¥ skull gives usually a more marked inion than the ¢ skull. The superior inion was determinable more or less accurately in 41 § and 43 §, the inferior in 28 § and 23 ¢. In 6 f and2 cases the inferior inion only was distinguishable ; only in 5 § and3 ¢ the two inions sensibly coincided. On the living head we very much doubt whether any precise inion could have been determined at all in about 4 of the $ and + to of the cases. A prominent point would have been taken, but whether it would be the inion at all, and if so whether it was the inferior or superior would not be determinable. The difference between the position of the two inions amounted at a maximum to 11 mm. in the ~ and 18 mm. in the §; the average differences between them being 5 mm. in the §“ and 8 mm. in the §. The following are the results of measuring the inion-opisthion distance in mms. : Mae FEMALE Inion Mean | Standard Deviation Mean | Standard Deviation Superior Inion ... | 47:0 4:7 47°2 5°6 Inferior Inion ... 42°3 — || 39:2 — M. A. Lewenz anp K. PrArson 377 Thus taking the probable error for the inion-opisthion distance in the case of the superior inion we see that half the ~ population will have inions less than 45 or more than 50 mm., while half the female population will have inions less than 43 or more than 51 mm. from the opisthion. In the face of such a variability what can be said of Dr Beddoe’s round 50 mm. for both sexes in his formula B, for the inion-opisthion arc? So far as English skulls are concerned he has not got even to the mean value of this are. We can only protest strongly against a formula which involves such a rough approximation as this being used at all—as Dr Beddoe uses it—when dealing with the skull; it could only be used on the living head supposing there were a complete want of anything better; and this is certainly not the case. We now turn to Dr Beddoe’s transverse circumference, Q’ in our notation; we have already seen that it is not the @ of the German or of our measurements, which are taken from the top of one auricular passage to the top of the other. This measurement is made at University College with the skull “horizontal” on the craniophor from the top of one ear-plug to the top of the other. The same point is vital in the consideration of the auricular height. Dr Beddoe without in the least troubling about this point remarks: “ Le rayon pariétal de Barnard Davis était je pense identique a la hauteur auriculaire du Dr Lee*.” The parietal radius of Barnard Davis differs sensibly from the auricular height of the Verstdéndigung, and this error affects all Dr Beddoe’s applications of Dr Lee’s formulae to Barnard Davis’ measurements. We consider that we should be scarcely wrong in allowing even as much as a quarter inch for the difference between the auricular height as measured on a craniophor and Barnard Davis’ parietal radius from the centre line of the auricular passages to the most prominent point of the parietal. This is probably the best that can be done, but it only shows how idle it is to attempt to use non-identical systems of measurements in any enquiry of this kind. We may take this opportunity of strongly protesting against the use of Barnard Davis’ measurements at all for really scientific work. To begin with his capacities are certainly incorrect. Dr Beddoe reduces them to what he terms Flower’s values by subtracting 54, but we have strong reasons for believing that his errors in capacity measurement are not proportional, but to a considerable extent irregular. Further Barnard Davis tabulates his results only to 4, of an inch and this is by no means sufficient for exactitude in craniological investigation. He appears also to have had curious views as to which tenth should be recorded}. In his tables of results for different races he gives in his first column the number of skulls used, but this number does not represent the number used in finding the mean of each character. Hence when the total number is small, as it usually is, no use ought to be made of Barnard Davis’ mean results for calculating the mean capacity of * Loc. cit. p. 271. + For example, in finding means, where he also stops at the first decimal, he frequently (possibly invariably) records 4:29 as 4:2, and there is no evidence that his individual measurements are not treated in the same way. Biometrika m1 48 378 Measurement of Internal Capacity of Skull the race by a formula. The presence or absence of one or two crania in one or other measurement entirely modifies the values. With our modern results for the continuous variation of skull characters within the race the manner in which Barnard Davis—and he appears to be followed by Dr Beddoe—picks the material upon which the average is to be struck is peculiarly annoying. A brachycephalic skull among a dolichocephalic series of three or four cannot be discarded in striking an average simply because it is brachycephalic! Yet this is the sort of line Barnard Davis adopts, and in very few cases is it possible to determine which skulls he has retained and which he has rejected in striking his average for any given character. (7) From such material as this Dr Beddoe has largely drawn when testing his own formulae against Dr Lee’s. He does not give us the information needful to determine whether he has struck fresh averages for himself or used Barnard Davis’ averages. If he has used the latter, he seems unaware that he is frequently using means which do not correspond to the skulls used for the mean capacity, and that this is fatal to the validity of his inquiry in short series. In the next place Dr Beddoe has used no consistent or scientific measure of the goodness of the predic- tion. Generally he has taken the total range of error, which is of course absolutely fallacious. He ought to have used either the mean or mean square error, and to have fixed beforehand what was the standard capacity he proposed to reach. In the next place in using Dr Lee’s formulae he has entirely disregarded her instructions as to the manner in which they were to be used. He has applied male formulae to find the capacity of female skulls, although Dr Lee has insisted on the sexual difference. He has used measurements which are not the measurements of her formulae to substitute in them. And lastly, and perhaps of most importance, is the fact that where we can test his arithmetic it is frequently quite incorrect. Surely the time has arrived when we must put aside all personal regard for a veteran and appeal in the interests of science for a totally different treatment and a totally different sense of responsibility when anthropometric problems are discussed. (8) It is not our purpose in this paper to follow Dr Beddoe page by page and show the fallacy of his conclusions, but it is necessary to illustrate the general character of his methods. The following passage will almost in itself be sufficient: “Les comparaisons suivantes ont trait a trois cranes de Naqada spécialement cités par Miss Fawcett (p. 20 op. cit.*). Manouvrier B, Fawcett Be B, Pet Z Thompson Thane 1408 1371 1843 18382 1322 1294 1289 1270 Ici mes procédés nous conduisent & des résultats plus corrects qu’aucun des autres. Je crois que ma méthode est digne d’étre placée a cOté des autres pour déterminer la capacité cranienne. Je vais maintenant l’appliquer, avec les modi- fications nécessaires, & la capacité des tétes vivantesf.” * The citation is incorrect. It should be Biometrika, Vol. 1. p. 420. + Loc. cit. p. 283. M. A. Lewenz anp K. PEARSON 379 Now as B, and B, are formulae destined to give Barnard Davis’ capacity and not the true capacity they need not be considered here. What we have to compare are Fawcett’s actually measured capacity, Dr Beddoe’s B; and “ P et L.” Now looking up C. D. Fawcett’s paper it will be found that the three skulls referred to have capacities of 1217, 1497 and 1222, which have a mean value of 1812 and not 1343 as Dr Beddoe calculates! Further two out of the three skulls are $ and Dr Beddoe applies the ¥ formula to them to get his “P et L” prediction! Lastly Dr Beddoe entirely disregards Dr Lee’s instruction to apply the formulae for the most closely allied race, if it be known*. As Dr Lee has provided a formula for Nagada crania, Dr Beddoe ought to have used this; he would then have found for the predicted value of the three crania 1218, 1522 and 1197, giving a mean of 1312, differing by no single point and not by 19 as B, does from the observed result. Let us however compare the results for the three crania as found by B;, not with the special Naqada formulae, but with Dr Lee’s general formulae, paying, of course, the proper attention to sex. TABLE III. P and L Predicted Naqada Skull | Capacity Measured B, Predicted Nagada General 1308 1217 1218 (— 1) | 1195 (—22) | 1154(—- 683) B 24> g 1497 1522 (—25) | 1507 (+10) | 1602 (+105) B219 1222 1197 (+25) | 1175 (—47) | 1182 (-— 40) Mean 1312 1312 (0) 1292 (—21) | 1313 (+1) Mean Error — ily 26 69 Now supposing we have followed Dr Beddoe correctly his results were not only 30 cubic centimetres wrong in taking the average of Miss Fawcett’s three skulls, but 19 cubic centimetres wrong in using his own formula! This brings his predicted mean into close accord with Miss Fawcett’s observed mean result. But we see at once on examining the three individual predictions that his success is only achieved by the balancing of large individual errors. His mean error is four times as bad as the P and LZ Naqada prediction and nearly three times as bad as the P and L general formula prediction. Allowing for faults of arithmetic, results similar to these must have been actually before Dr Beddoe when he wrote: “Mes procédés nous conduisent a des résultats plus corrects qu’aucun des autres,” etc. * The University College anthropometric workers have again and again insisted that regression formulae vary from race to race. See Phil. Trans. Vol. 196, A, pp. 243 et seq.; Biometrika, Vol. 1. pp. 460-1; Vol. 1. pp. 347 et seq. 48—2 380 Measurement of Internal Capacity of Skull Hence as he certainly would not have screened them behind a mean value, we are forced to the conclusion that he really did not grasp their significance, or in other words that he is quite unfitted to deal with such statistical enquiries. But Dr Beddoe’s agreement in the matter of the mean of the three skulls when his arithmetic is corrected is not only fallacious because it depends upon large individual errors of opposite sign but because he has used the wrong values of the auricular circumferences. To obtain his Q he ought to have added at least 10 mm. to Miss Fawcett’s Q. If this be done, his values for the three capacities are 1195, 1613 and 1232 respectively, giving a mean of 1847 and a mean error of 49,—results markedly worse than P and £. We do not know whether Dr Beddoe would prefer to somewhat reduce his mean error at the expense of his mean, or to get a good mean with an excessive mean error. As he uses our @ for his own transverse circumference, we must suppose the latter to be the case and shall not attempt to modify this are for the remainder of this paper when applying his 5;. In concluding this section we may note the results obtained by using our new circumferential formulae. We have applied the English ¢ formula* to the female skulls and the mean ¢ formula and the Naqada # formula to the male skull. The following are the results: TABLE IV. Nagada Skull | Capacity Measured | Mean ¢ and English ¢ Naqada ¢, English ¢ Mean Error 1325 (+13) 22 1308 1217 1203 (—14) 1203 (—14) B24» 1497 1542 (+45) 1527 (+30) B21¢9 1222 1230 (+ 8) 1230 (+ 8) Mean 1312 1320 (+ 8) 17 Thus the method of correlation, whether we use diameters or circumferences, gives for these three skulls immeasurably better results than Dr Beddoe’s B,; yet it is as a corollary to his results for these three crania that he writes: A “Je crois que ma méthode est digne d’étre placée a cdté des autres pour déterminer la capacité cranienne.” (9) We have already given our reasons for dissenting from Dr Beddoe’s methods of applying his own and the University College workers’ formulae to his material, and also our objections to the use of Barnard Davis’ material at allt. Still this material, allowing for the rough approximations which have to be made * The only series for which the female data has so far been reduced. + It is greatly to be desired that a complete system of modern measurements should be taken and published, not only on the Barnard Davis collection, but on the remainder of the splendid material in the possession of the Royal College of Surgeons. M. A. Lewenz and K. PEARSON 381 to apply the formulae to it, shows in a sufficiently marked manner the superiority of the correlation formulae over Dr Beddoe’s purely empirical guess-work. We propose to test this on two of Barnard Davis’ series. We will first take a series of nine groups of skulls and predict their means by B,, P and L, and G. F., where G.F. stands for the general male formula (/) for circumferences given on p. 371 of this paper. In order to apply our results we have not taken Barnard Davis’ mean values, which we have seen are unreliable, but have worked out afresh the means for all the § crania in each series for which the entire system of characters needed are given. These characters are (i) the capacity C, (11) the maximum length JZ, (iii) the maximum breadth B, (iv) the auricular height H, (v) the cephalic index J, (vi) the horizontal circumference U, (vii) the sagittal circumference S, (viii) the transverse circumference @ We have obtained Dr Beddoe’s 8’ from S by deducting, as he asserts, 1:97 inches for the imion- opisthion arc, and his Q’ from the intermastoid are of Barnard Davis by sub- tracting 2°3 inches, as he does. We reach our auricular height from Barnard Davis’ parietal radius by subtracting ‘25 inches, and our Q from his intermastoid arc by subtracting 2°5 inches. Only in the case of the Thais which number only four crania have we calculated the capacity of each individual skull and taken the mean result; in all the other cases the formulae had been used on the mean values of the characters. The measurements are in inches except C and J. TABLE V. Mean Values of Characters in 9 Races. Crana. Race No. | Cin ozs. L B H I U S Q Romans of Britain | 8 | 73°3 73 | BT 4:4 i 21:0 14:8 12-1 Australians ... | 16] 67°6 (3) |) 8 4:3 72 20°3 14°7 11°6 New Hebridians... 9 72°1 VEAL Bel 4:5 Ve 20°0 14°8 11°8 Kanakas son ad | 7-0 56 4:8 79 20°3 14:9 12°8 Marquesans en borg vi 56 47 78 20°5 14°8 12°5 Netherlanders ... | 16 79°5 72 ay 4:5 79 20°7 14:7 12°5 Finns... soe || ea 7:0 5°8 4-6 82 20°6 14:8 12°7 Russians ... | et SO Ounn nie 5°8 4°5 78 21-2 15-0 12°4 Thais 1 ... sue [eed |) 76:0) |) 6°6; “|, (5:6 4:85 | 84 19°8 14°6 1853 5 2 1} 81:0 TA | 5:4 4-75 | 73 20°5 15°3 12°6 ees 1 | 79:0 66 | 5:9 4°75 | 89 20°2 14:3 18374 be td 1} 78-0 68 | 55 4-75 | 80 19°7 14:9 12°5 Dr Beddoe’s S’ and Q’ are to be found from the above tabled values by subtracting 2 inches* from S and adding ‘2 inches to Q respectively. The reader may well ask what is the value of such an attempt to reach indirectly quantities directly measurable on the skull? We should reply: Probably no value at all! We have seen that the inion-opisthion are is extremely variable and the same * 50mm. = 1-97, but as Davis’ values are given to 4, inch only the ;3,5 cannot be considered. 382 Measurement of Internal Capacity of Skull statement must be made with regard to the size of the mastoid processes. To assert that the mean value of the difference between the intermastoid arc and the bi-auricular are is 2°3 inches is in our opinion wild guesswork, and even if it were true it neglects entirely the immense variability of this difference. We cannot expect any formula to give good results under such treatment, but as Dr Beddoe has chosen such a test we consent to accept it, especially as it enables us to indicate to the craniological reader the sort of statistico-metrical treatment which seems to have passed hitherto as science. In the following table we give first the supposed measured value of the capacity, 1.e. Barnard Davis’ values less 1/20 and reduced to cm.?; then we give the predicted values and differences of B;, P and L, and G. F., and finally the mean errors of the three formulae. TABLE VI. Comparison of Cranial Formulae on Barnard Davis’ Measurement of Mean Racial Capacity. Race Capacity iB: A P and L A Gee A Romans of Britain... 1385 1490 +105 | 1431 +46 1463 +78 Australians oe 1277 1347 + 70 | 1330 +53 1366 +89 New Hebridians ... 1362 1366 + £=#é64 1309 -—53 1376 +14 Kanakas... AE 1459 1544 + 85 1462 +3 1499 +40 Marquesans tt 1491 1507 + 16 | 1454 — 37 1473 -18 Netherlanders ae 1502 1515 + 13 || 1441 —61 1477 —25 Finns i36 nee 1497 1559 + 62 | 1454 — 43 1499 + 2 Russians... ine 1529 1570 + 41 || 1492 —37 1522 -— 7 Thais nae hats 1483 1539 + 56 | 1430 —53 1487 + 4 | Mean ... ies 1443 1493 + 50 1416 —27 1462 +19 Mean Error ... — -- 50 | — 43 — 31 | In deducing the results P and Z we have, owing to the mixture of races involved, used Dr Lee’s most appropriate formula (10) bis, that in the footnote on p. 247 of her memoir*, based on the best results for the means of 10 races. It will be seen at once that P and Z and G.F. present much better results than B, which is far worse than either in determining the mean value of the whole series, and is worse than our formula by at least 50 per cent. in the mean error. If Dr Beddoe considers that his formula has given all plus errors and therefore can be approximately bettered by reduction in his multiplier, we must call his * Phil. Trans. Vol. 196, A, p. 247. We have used this formula throughout for race means because it is based on racial means and not on individual skulls. Experience has shown that in the long run it works better than (10). The latter is much better for this series, giving a mean value 1446, only three in excess, and a mean error of only 35! We have not, however, taken advantage of this superiority to use it. M. A. Lewenz and K. PEARSON 383 attention to the following table, which is a reconstruction* of his Table III for the eight skulls out of his ten, for which we could find the requisite data : TABLE VII. Race Capacity Bs A || G.F, A d Mountain Chinese . 1473 1423 — 50 | 1407 — 66 @ Cossack... .» | 1530 1406 —124 1371 — 159 @ Hindu i so || BB} 1050 - 83 | 1115 — 18 6 Fatuhivan... sat 1720 1700 — 20 1538 — 182 @ Bodo are .» | 1644 1443 —201 1394 — 250 3 Australian pee eile 1243 — 70 1292 — 21 Q Papuan... . | 1313 || 1228 — 8 | 1263 — 50 dg Dutchman... w. | 1644 1613 — 31 1543 —101 Mean Error... — | — — 83 | _ — 106 Now 8B, is certainly better here than G. F. and the answer is perfectly simple if the reader will turn to the diagram on p. 375. For small skulls with more than the average capacity our result must be too small, but better than Dr Beddoe’s; for large skulls with more than the average capacity Dr Beddoe’s will give a better result than the line of mean values. In the above table Dr Beddoe has only taken three small skulls with more than the average capacity and we are naturally in all those cases better than he is. In the other cases of big skulls he is better than we are, and roughly better as the skulls are bigger. If he had only had a majority of small skulls with big capacities the tables would have been turned upon him. The fact is that nothing can be determined at all by Dr Beddoe’s Tables II and III for ‘thick’ and ‘thin’ crania; by judicious selection of small thin skulls and big thick skulls we can make B, give execrable results as compared to G.F. or P and L, the selection being made before the predictions have been calculated. It all depends upon looking at the diagram on p. 375 and choosing skulls which fall on the other side of the Beddoe line to the regression line. What is quite clear from 5; in Table VII is that Dr Beddoe cannot improve the results given in Table VI without making his position in Table VII much worse; i.e. he must sacrifice his claim to be better than us on selected individual crania. For whereas B, gives far too big values on Table VI, it gives far too small values on Table VII. To really test the corre- lation formulae against the guesswork formula of Dr Beddoe, the individual skulls must be sampled at random and not selected. To do this we started at p. 20 of Barnard Davis’ Thesawrus and extracted the first male undeformed skull with the necessary data on this page, or if there happened to be none on this page, the nearest male skull on the preceding page or pages. We then passed * Dr Beddoe’s Table exhibits a number of misprints or arithmetical slips, and is invalid as far as P and L is concerned, because he has used male formula for female crania, and an erroneous value for the auricular height. 384 Measurement of Internal Capacity of Skull to pp. 35, 40, 55, etc. in order, repeating the process until 20 skulls had been extracted and the following table resulted. To this we applied P and L*, G. F. and B,, with the results in Table IX. TABLE VIII. Individual Crania Sampled at Random from Barnard Davis. sy) | Race pared ee Cyl BENGE | H|I}/ u/s |e@)s | a | (1) Ancient Roman ...| 171 (p. 18) | 70:0 | 7-2 | 5°6 | 4°25 | 76 | 20°7 | 14°5 | 11°7 | 12°5 | 11-9 (2) Anglo-Saxon ... | 674 (p. 84) | 75°0|] 7°4) 5°5 | 4°75 | 74 | 20°8 | 14°5 | 12-4 | 12°5 | 12°6 (3) English... | 1029 (p. 48) | 94:0] 8°0 | 6:3 | 5°25 | 78 | 22°8 | 16°6 | 14:4 | 14°6 | 14°6 (4 Scottish Highlander | 176* (p. 64) | 71-0 | 6°8 | 5°5 | 4°25 | 80 | 19°7 | 13°7 | 11°8 | 11°7 | 12-0 (5) French re apeye (p. 80) | 74:5 | 6°9 | 5:4 | 4:25 | 78 | 20°0 | 14°1 ] 11°6 | 12°1 | 11°8 (6) Italian... ... | 1178 (p. 95) | 73-0 | 771 | 5-2 | 4:35 | 73 | 20-2 | 14-6 | 11-7 | 12-6 | 11-9 (7) Dutch Jew ... | 1828 (p. 110) | 79°5 | 7°5 | 5-5 | 4-35 | 73 | 21-2 | 15-0 | 12-0 | 13°0 | 12-2 (8) Russian Tartar...) 941 (p. 125) | 76°5 | 7°0 | 5°7 | 4°45 | 81 | 20°6 | 14°6 | 12-0 | 12°6 | 12-2 (9) Hindoo BaF ... | 487 (p. 140) | 69:0 | 6°8 | 5°5 | 4°55 | 80 | 19°5 | 14°38 | 12°3 | 12°3 | 12°5 (10) Gond wee vee | 808 (p. 155) | 65-5 | 68 | 4-9 | 4-45 | 72} 18°8 | 14:1 | 11-7 | 12-1] 11-9 | (11) Bodo ... | 735 (p. 169) | 68-0 | 6°8 | 5:5 | 4°55 | 80 | 19°6 | 14-2 | 12-5 | 12-2 | 12°7 (12) Egyptian Arab ... | LOLS (p. 185) | 67-0 |] 7°1 | 5°4 | 4°55 | 76 | 20-1 | 14:4 | 12-0 | 12°4 | 12-9 (13) Fantu ae ... | 262 (p. 200) | 67-0 | 6°9 | 5-2 | 4°55 | 75 | 19°3 | 14°4 | 12°1 | 12-4 | 12°3 (14) Kafir : 586 (p. 215) | 64-0 | 7-4 | 4-9 | 4-35 | 66 | 20-2 | 14°6 | 11-4 | 12°6 | 11°6 (15) Vancouver Islander | 1211 (p. 229) | 85-0 | 7°5 | 5:7 | 4°65 | 76 | 21-0 | 15-4 | 12-7 | 18-4 | 12-9 (16) Aymara... ... | 1198 (p. 244) | 82°0 | 7°1 | 5°6 | 4°75 | 79 | 20°5 | 14°8 | 12°6 | 12°8 | 12°8 (17) Australian ne 99 (p. 260) | 69:0 | 7°0 | 5°6 | 4°35 80 | 20:0 | 14°3 | 12°0 | 12°3 | 122 (18) Sumatran ... ... | 1367 (p. 275) | 67:0 | 7:0 | 5-1 | 4°35 72 | 19°8 | 14:0 | 11-4] 12:0} 11°6 (19) Dyak ase | 280 (p. 290) | 60-0 | 6°6 | 4-9 | 4°65 | 74 | 18-7 | 13-7 | 10-7 | 11-7 | 10-9 (20) Papuan... ... | 1401 (p. 305) | 73-0 | 6°5 | 5-4 4-45. 82] 19-4 | 13-5 | 12-0 | 11°5 | 12-2 Here again we reach the same general conclusions, namely the correlation formulae give not only better means for the whole series, but less mean errors, and this, although a whole series of assumptions has to be made to get any results from them at all, if Barnard Davis’ material be used. The further point has to be borne in mind that B, was ‘guessed’ to fit Barnard Davis’ material, whereas the correlation formulae were calculated from data measured in an entirely different, and we consider, in a far more correct manner? Any mathematician using a formula of Dr Beddoe’s type could get immeasurably better results by least squares or by correlation from Barnard Davis’ data, but the labour would be wasted, for the formula would only apply to the very doubtful measurements of the Thesaurus Craniorum and not to the more reliable measurements now made in both Germany and England. * If L, B, H be measured in inches the formula to give C in cubic centimetres is nearly for males: C=406-01+5°52214 Lx Bx H. This is the mean formula of Dr Lee for finding the capacity of individual crania. + Ozs. of Calais sand. To be multiplied by Topinard’s factor 19-89 to reduce to cubic centimetres and then by 19/20 to reduce to cranial capacities as now measured. The other measurements are in English inches. ‘ + We believe the rise in the mean error from 47 to 64 when we pass from suitably measured crania (p. 371) to Barnard Davis’ material is almost entirely due to the vagueness of the allowances to be made and the crudeness of Barnard Davis’ measurements. M. A. LEwrEnz Anp K. PEARSON 385 TABLE IX. Table of Capacities of 20 Individual Crania Sampled at Random from Barnard Davis. Individual Capacity | B, A | P&L A G. F. A (1) Ancient Roman ...| 1323 1383 + 60 1352 + 29 1383 + 60 (2) Anglo-Saxon aes 1417 1461 + 44 1474 + 57 1457 + 40 (3) English hele 1776 2197 +421 1867 + 91 2011 +235 (4) Scottish Highlander 1342 1259 — 83 1284 — 58 1276 | — 66 (5) French ee SE 1408 1291 —117 1280 — 128 1305 — 1038 (6) Italian ap coo || 137AS) 1347 — 32 1293 — 86 1362 - 17 (7) Dutch Jew os. | 1502 1494 - 8 1397 — 105 1481 — 21 (8) Russian Tartar ...| 1446 1446 0 1386 — 60 1414 | — 32 (9) Hindoo aa .. | 1304 1365 + 61 1346 + 42 1356 + 52 (10) Gond bea don 1238 1199 — 39 1225 — 13 1249 + 11 11) Bodo SB ti 1285 1382 ap tl 1346 + 61 1372 + 87 (13) Egyptian Arab... | 1266 1366 | +100 1369 | +103 || 1370 | +104 13) Fantu Aue we 1266 1318 + 52 1308 + 42 1325 + 59 a4) Kafir S 1209 1281 | + 72 277 | + 68 || 1334 | +125 15) Vancouver Islander 1606 16380 + 24 504 — 102 1575 31 re Aymara... ... | 1549 1524 — 25 1449 — 100 1483 — 66 17) Australian ... | 1308 1366 + 638 1348 + 46 1356 + 53 18) Sumatran ... fe 1266 1222 — 44 1264 - 2 1268 + 2 (19) Dyak eee aoe 1133 1063 -— 70 1236 +103 1133 0) (20) Papuan... seo || LB} 1251 — 128 1269 —110 1263 —116 Mean ee i370 1392 | + 22 1364, | 76: |) 1389.) 79 Mean Error ss — — Ue — 70 — 64 (10) We next turn to measurements made on crania on the basis of the Frankfurt Verstdndigung, for which our formulae have been calculated. Here our difficulty les with deducing Dr Beddoe’s values, but as he expresses satisfaction with the fit of his formula for the Naqada skulls, using our Q, we will continue to use that quantity for his auricular arc Q’. We do not suppose any correction TABLE X. Races Measured according to Frankfurt Versténdigung. Race (4s) Cc L B H I U S Q S’ | Altbaierisch (78) | 1503 | 180°6 | 150°5 | 120°7 | 83°3 | 524°3 | 365-1 | 329-7 | 315°1 English (72) ...| 1477 | 189°1 | 140°7 | 114°6 | 74:4 | 524°3 | 377-1 | 307-9 | 327-1 French (56) ... | 1473 | 180°0 | 143-4 | 112°9 | 79°8 | 518-2 | 366-0 | 312°2 | 316-0 Aino (76) ... | 1462 | 185°8 | 141:2 | 119°3 | 76°5 | 522°5 | 372°8 | 328°5 | 322°8 Etruscan (78) ... | 1454 | 182°9 | 143°5 | 115-9 | 78°5 | 522-8 | 376-0 | 317°0 | 326-0 Malay (39) _... | 1424 | 174°3 | 142-4 | 116-9 | 81-9 | 505-2 | 365-3 | 320°8 | 315°3 Theban (164) ... | 1888 | 181°9 | 136°6 114°3 | 74°8 | 510°8 | 372°4 | 306-1 | 322-4 Naqada (98) ...| 1381 | 185-1 | 134-9 115-6 | 73-0 | 511-0 | 373-0 | 304-2 | 323-0 Copt (59) —... | 1856 | 179:1 | 136°5 | 115-4 | 77-3 | 501-8 | 365-9 | 311-8 | 315-9 Negro (39) ...| 1348 | 182°8 | 133-2 | 115-0 | 72:9 | 508°5 | 367-7 | 306°8 | 317°7 Biometrika m1 49 386 Measurement of Internal Capacity of Skull would be really satisfactory, and least of all to him. We use, as before, Dr Lee’s inter-racial formula from the footnote, p. 247 of her memoir, Le. - C= 321:16 + :000,370L x Bx H. The following results were obtained by using the three prediction formulae. TABLE XI. Predicted Capacities of 10 Races. ] Race C B, A P and L A G. F. A Altbaierisch ... 15038 1530 +27 1535 +32 1493 —10 English ais WT 1439 — 38 1449 — 28 1448 — 29 French ae 1473 1419 — 54 1399 —74 1415 —58 Aino ... aes 1462 1521 +59 1479 +17 1509 +47 Etruscan aa 1454 1494 +40 1444 —10 1477 +23 Malay ... te 1424 1428 + 4 1395 — 29 1415 — 9 Theban see 1388 1376 —12 1372 —16 1397 +9 Naqada ae 1381 1362 -—19 1389 + 8 1396 +15 Copt ... re 1356 1361 + 5 1366 +10 1377 +21 Negro ... iets 1348 1344 - 4 1357 + 9 1379 +31 Mean ae 1427 1427 0) 1419 —8 1431 +4 Mean Error ... — — i[S2) = 23°3 = 252 Again both the correlation formulae come out with a less mean error than Dr Beddoe’s B;, the diametral formula being sensibly the best. For the means Dr Beddoe is slightly better. _We may stay here to note that G. F. is really a mean individual and not an inter-racial formula. The inter-racial formula for these ten races gives us: C=3162 + 01852 Ux Sx Q. This formula should be used in preference to G. F. for race means. It does not however give any very substantial advantage in the present case. We have for the inter-racial arc formula (J. A. F.) TABLE XII. Race Observed | I. A. F. A Race Observed| I. A. F. , A Altbaierisch . 1503 1485 —18 Theban ute 1388 1394 + 6 English ... | 1477 1444 — 33 Naqada ... | 1381 1390 + 9 French ee 1473 1413 —60 Copt ie 1356 1377 +21 Aino .. | 1462 1501 +39 Negro .. | 1348 1379 +31 Etruscan ... 1454 1476 +22 Malay see 1424 1413 —-11 Mean one 1427 1427 0) b Mean Error = — 25°0 M. A. Lewenz anp K. PEARSON 387 We have in this formula the mean value equal to that of the observed races, but the mean error is only reduced °2, in other words our G. F. is not substantially bettered, it is as good a fit as can be got for this series from a linear formula. But this best fitting line is interesting from another point of view, which is exhibited in the accompanying diagram. We have plotted here the observed capacities of 19 races, the above 10 races and the 9 doubtfully measured races from Barnard Davis; the horizontal abscissa is the product in cubic centimetres of the three ares U,S and Q. We have added the cephalic indices. The straight line A.A is the inter-racial regression line based on the 10 races. We see that with the alte eaeiel Sl res. zI550 Wertentetger Dareh (79) Wir baigr74 e2a3ac Aq Bef N Q S ) 8 ‘ Frets (60) Engpsrire | ao SF para | ee trugea: DD 1450 er 6a ba oe gi Mal A Z400 > at 4 « Frotet Cc» oars of Britain (7 F Magedas 3) © Nba H. bridians (y3) 23350 ote Y7) a / Y L500 / -/ 0 Ab stra/i anre|(72) / zRoo ! | tRoo I6000 s7a0o0 38000 53000 60000 61,000 62,000 63000 64900 65000 66,000 67000 Prodiucl Efe eHOxes yx crs? exceptions of the Malays and the Marquesans*, both fairly close to the inter-racial line AA, all the other races above the line are modern Europeans. In other words it would appear that the modern European races gain their advantage in skull capacity over the lower or more primitive races largely by thinner bone. Of the races * «© Without exception the finest race of people in this sea, For fine shape and regular features they perhaps surpass all other nations.” Cook, Voyage towards the South Pole, 1777, Vol. 1. p. 308. 49—2 388 Measurement of Internal Capacity of Skull above the best fitting line Dutch, English, Russians, Marquesans, will have their values as calculated altered for the worse by Dr Beddoe’s correction for cephalic index, the French will remain unaltered (although they want most correction!) and the Altbaierisch and Malay will be slightly improved (although they stand least in need of correction! ). Of the races below the line all but Finns would be improved by correction although in several cases they would be over corrected. But a very slight inspection shows that the corrections needed are in no way proportional to the defect of their cephalic indices from 80. Thus omitting Australians, the Ainos, Kanakas, Etruscans and Romans of Britain* (all over 75) want most correction ; while Thebans, Naqadas, New Hebridians (all under 75) want far less correction. In fact we consider that if Dr Beddoe had formed a similar diagram he would not have laid any stress on his cephalic index correction. What does seem to us to follow from this diagram is the non-linearity of the inter-racial regression line. It is very markedly curved. We have therefore endeavoured to correct by aid of a curved line. Until more data are available, measured and reduced in a uniform manner, it is not worth spending much labour in calculating the constants of possible formulae, but we may roughly point out how we get far better results by correcting for non-linearity of the regression curve for inter-racial results than by attempting to “compensate” by cephalic index. Two hypotheses occurred to us, (i) the regression line instead of being C=a,+ A,P, where P is the product UxSxQ, may be taken C=a,+A,P+a;P? or as parabolic, (ii) the regression line may be taken as logarithmic P + ag = ase”?, The only reason, and it is very slight, for the latter form is that it makes the increment of C not only directly proportional to the increment of P, but inversely proportional to the absolute magnitude of P measured from a certain value. A very similar curve has been found to suit the change in human physical measurements with age. The curve is here used merely as a form judged likely from the observations, and without at present any statement of a theoretical basis being suggested. We have found roughly the constants from the 10 races available. There result the two formulae, P being in cubic centimetres : C=—15319-6 +°531,942P —42075P2/10° C=70404 + 203-05 logy (P — 55682). The disadvantage of the first formula is that with the constants selected, one reaches a value of P after which the capacity begins to decrease, but a very little change of the constants would suffice to throw this value up to, say 1550 cms.5, a value exceeding any racial meant hitherto observed. The logarithmic formula * We are inclined to doubt entirely the data for the Romans in Britain. It differs so widely from Romans elsewhere. We hope that these skulls may be remeasured shortly. + We ask the reader to particularly note the words “racial mean,” for our formulae are not to be transferred without further consideration to the calculation of individual capacities (or indeed to the female sex). M. A. Lewenz AnD K. PEARSON 389 we consider preferable as it suffers from no such defect. Table XIII gives the results, compared with Dr Beddoe’s compensation formula. We see at once that either of our formulae based on the obvious fact of non-linearity is far superior to TABLE XIII. Race Ux Sx Q| Capacity | B, A Eee A hoes: ee A Altbaierisch Aan ||) Copiililts} 1503 1530 | + 27 1493 —10 1490 -13 English ... ... | 60878 1477 1439 | — 38 1470 -— 7 1459 —18 French ... ae 59206 1473 1419 | — 54 1428 —45 1424 — 49 Aino wee aie 63988 1462 1521 | + 59 1491 +29 1500 +38 Etruscan mean | 628277 1454 1494 | + 40 1490 +36 1480 +26 Malay BEG ... | 59197 1424 1428 |+ 4 1425 +1 1424 0 Theban ... san || ayehA283 1388 13876 ; — 12 1389 + 1 1895 + 7 Naqada ... ... | O7991 1381 1362 | — 19 1379 — 2 1387 + 6 Copt ae | 57254 1356 1361 | + 5 1344 —12 13538 -— 3 Negro sie oes 57373 1348 1344 | - 4 1350 + 2 1359 +13 Mean wee eee | O99 DOD 1427 1427 0) 1426 -— 1 1427 10) Mean Error ee _— — — 27-2 = 14°5 — 17°3 Romans in Britain | 61609 1385 1490 | +105 1482 +97 1470 +85 Australians son || aloe) DOT, 1347 | + 70 1316 +39 ily +40 New Hebridians 57234 1362 1366 | + 4 1343 —19 1352 —10 Kanakas ... se 63441 1459 1544 | + 85 1493 +34 1494. +35 Marquesans ... | 62145 1491 1507 | + 16 1489 - 2 1478 —138 Dutch... ae || eB aye 1502 1515 | + 18 1490 —12 1480 —22 Finns AGE ... | 63447 1497 1559 | + 62 1493 — 4 1494 - 3 Russians ine 64614 1529 1570 | + 41 1485 —44 1506 — 23 Thais sits ... | 62827 1483 1539 | + 56 1493 +10 1487 + 4 Mean fas ... | 61596 1443 1493 | + 50 1454 +11 1453 +10 Mean Error one — — — 50 = 29 — 26 Mean of 19 Races 60733 1434 1458 | + 24 1439 + 5 1439 + 5 Mean Error a = — — 38 = Al = 21 his B;, not only in the mean of each series, but in the mean error. In fact in only two cases out of the 19 races is he better than the parabolic and in only three cases better than the logarithmic formula. Thus in his Barnard Davis results he is nearly 100 per cent. worse than the logarithmic formula. Nor can he better himself by changing his multiplier because he has already got a zero deviation from the mean of his series in the Verstcindigung measurements, i.e. the far better series. So soon as material is reduced on a uniform basis for inter-racial data, we believe it will be possible to adjust the constants of a non-linear inter- racial regression formula to read with a mean error of under 14 cms... We do not attempt this at present, because the bulk of sound material is insufficient. (11) We now turn to our last test, that on individual crania measured on the basis of the Frankfurt Concordat. We have taken 45 ¥ skulls by sampling at 390 Measurement of Internal Capacity of Skull random* C. Faweett’s Naqada, T. Ranke’s ‘ Altbaierisch’ and E. Schmidt's Theban mummy measurements. We have applied Dr Lee’s mean formula for individual craniat. B; and the general formula were used as in the series of Table XI. It is impossible to print all the measurements and results for these 45 skulls but the general conclusions are given in the table below: TABLE XIV. Results of the Three Formulae for 45 § Crania. Series Quantity B, PandL G. F. | Naqada Series es Mean Error 64 50 51 Altbaierisch Series ... Mean Error 50 62 49 Theban Series aoe Mean Error 49 46 42 Whole Series... wen Mean Error 54 53 47 Range of Error | +245 to — 169 | +141 to — 164 | +148 to — 165 For a brachycephalic race as we see from the table Dr Beddoe gains by his cephalic index correction and this is the source of his advantage over P and L for the Altbaierisch. But for a dolichocephalic race like the Naqada or Theban he loses; thus his biggest negative error arises in the case of the largest Naqada skull where his correction for cephalic index still further reduces his underestimate. On the whole again we see that the advantage lies with the correlation formulae. Summing up our results we should say that for the skull: (i) Intra-racial and inter-racial formulae can be found for circumferential measurements which are superior, or at any rate equal to Dr Lee’s diametral formulae. (ii) Such formulae give better results when their constants are found by statistical theory than by mere guesswork. (iii) The vagueness of the inion as a point of measurement renders it of the greatest importance that the sagittal arc should be measured from the opisthion and not from the inion. (iv) It is conceivable that a double regression formula would work better than a single regression formula like P and Z or our present G. F. But it will hardly be obtained by taking as the second variable the product J x Ux QxS. (v) Probably the best inter-racial results will be obtained by non-linear regression formulae based on a single product. * For the mummies every tenth skull starting with No. 489 of the Catalogue was taken; for the Naqada every tenth skull so far as possible, allowing for the mixture of ¢ and ¢? on the list; for the Altbaierisch,’ every fifth as far as the requisite data were provided. + C=:000337 L x Bx H+406:01. M. A. Lewenz AND K. PEARSON 391 We hope later to publish double regression formulae for skull capacity, but if it is to be done by the use of an index, we do not believe that the cephalic index is the right character to use, because it has been shown to have small correlation with the capacity, and what correlation does exist changes sign from race to race. On the whole we believe that increased accuracy is to be sought as we have indicated on p. 388* by using non-linear regression rather than multiple regression formulae, unless indeed one variable of the latter be the thickness or the weight of the skull. (12) Having dealt with the application of Dr Beddoe’s formula to skulls, we now turn to its ratson @eétre, i.e. its applicability to the living head. We have already considered one grave objection, namely, that the inion is on the skull itself by no means a definite and easily located point. On the living head we find it even more difficult to determine it with certainty. By throwing the head forward in certain cases the boundary of the area to which the muscles are attached can be appreciated, but “well-marked inions,” 1e. large bony growths in the neighbourhood of the inion, occipital ridges and toruses, especially frequent in English heads, render the exact localisation extremely problematical. Let us suppose, however, that the inion could be ascertained on the living head, then the measurement of the three arcs seems to us entirely valueless on account of the varying amount of hair. Dr Beddoe really makes no attempt to meet Topinard’s objection to the use of these arcs on the living head, except by the remark that abundance and stiffness of hair is not usually met with in combination with intellectual eminence! He gives no statistics, however, of the relative baldness of the average middle-aged agriculturist, tradesman, or man of science. Without such statistics his remark is worthless. Having a bad case himself he simply drops it in order to point out the difficulties of rival formulae! Thus he writes*+: Cette objection en ce qui concerne les cheveux s’applique aussi A la hauteur auriculaire et au maximum de longueur et largeur, lorsqwils sont pris au céphalométre et non avec le compas d’épaisseur. We do not know to what form of cephalometer Dr Beddoe is referring, but any anthropologist would be perfectly incompetent for his task who could not devise an instrument for reading the auricular height by a sufficiently blunt point so that the determination of the height would not be affected sensibly by the existence of the hair. You can clear the hair to one side when measuring the diameters, you cannot possibly get it out of the way when using the measuring tape. This is not mere theoretical reasoning, but the actual result of experience in practice. Next Dr Beddoe endeavours to discredit the allowance Dr Lee has made for the thick- ness of the flesh on the living head. It seems to have escaped him that if the varying thickness of the flesh is a real difficulty in determining the diameters, its effect on his own arcs (in addition to the effect of the hair!) can hardly be described as less than insuperable. But we are not inclined to give much weight * Phil. Trans. Vol. 192, A, pp. 222 et seq. + Loc, cit. p. 285. 392 Measurement of Internal Capacity of Skull to his objection. Comparing the mean diameters found from more than 100 English ~ skulls with the means found on more than the same number of living of heads we have differences of 9, 12, and 11 mm. in the case of maximum length, breadth and auricular height respectively. Dr Lee’s allowance of 11 cms. seems therefore a very reasonable one, and is closer than it appears, for the heads were certainly—allowing for the difference of skull and head—more brachycephalic than the earlier skulls. We do not say that Dr Lee’s method is beyond criticism; on the contrary we recognise all the inherent difficulties of the problem. But we believe these difficulties to be enormously exaggerated by Dr Beddoe, and that he screens behind this exaggeration the far greater difficulties associated with his own method of arc measurement. (13) As to his application of that method to demonstrate the correlation of intelligence and skull capacity, we hold it to be quite fallacious. To begin with he selects a formula—by guesswork—which is theoretically incorrect. He drops his formula for the skull and takes the product of 4 of each of his arcs, and divides this product by 2000. He then increases it by + per cent. for every unit of the cephalic index above 50. In his cranial formula he made no correction for cephalic index when it was 80. He now drops the neutral index to 50 without any justifi- cation or explanation. As we have already seen that the correlation between cephalic index and the capacity of the English skull is negative, his formula will tend to exaggerate the capacity of the brachycephalic and lower the capacity of the dolichocephalic individual heads. Now we believe it to be a fact—whatever may be the explanation, lie it in environment, nurture or difference of race—that the well-to-do classes in this country are now more round-headed than the working classes*, but such are the classes which produce the bulk of the people who work intellectually, and therefore Dr Beddoe’s erroneous allowance for brachycephaly directly tends to emphasise the cranial capacity of the intellectual classes. Dr Beddoe says that according to Dr Lee there is no correlation between the development of the intelligence and the cranial capacity, and remarkst: Les matériaux sur lesquels cette derniére opinion est basée sont rares et peu concluants. Dr Lee makes no such statement at all. What she asserts ist: “That there is no marked correlation between skull capacity and intellectual power.” Dr Beddoe forgets to draw attention to the fact that Dr Lee, in conjunction with ourselves, has actually measured the relation between size of head and intelli- gence, and on far more ample material than Dr Beddoe uses. We find the corre- lation sensible, but so small that it is impossible to base any prediction from the size of head as to general intelligence§. As to Dr Beddoe’s own data bearing * See inter alia Macdonell, Biometrika, Vol. 1. p. 190. + Loe. cit. p. 267. + Phil. Trans. Vol. 196, A, p. 259. § R. S. Proc. Vol. 69, pp. 333—42 and Vol. 71, p. 106 et seq. M. A. Lewenz anp K. PEARSON 393 on intelligence and capacity, we can only repeat Dr Lee’s words, which he would have done well to take to heart, namely that to solve a problem of this kind it is absolutely needful to keep within one “fairly equally nourished class,” and if possible within one local race. We do not minimise the difficulty of doing this, but until it is done no final answer can be given to the problem. Much of the discussion at present might be summed up in such an absurd argument as: The Bavarians have as a race a larger skull capacity than the French; they are a less keen-witted race ; ergo: smaller skull capacity goes with intelligence. We take it such an argument would be quite as valid as Dr Beddoe’s comparison of High- landers and East Anglians, or of Cornishmen of the upper and lower classes. (14) As to whether Dr Beddoe’s reconstructed capacities have any relation absolutely or relatively to the true capacities of the individuals he has measured it is of course impossible to say. But we are in the unique position of being able to test his formula on the head of one of the most distinguished Englishmen not only of his own time, but of all time. For width of view, logical clearness, and intellectual grasp, there were but few Englishmen in his own day, and there have been few since, whom we can consider as surpassing Jeremy Bentham. Bentham died in June, 1832, and a few months before his death he prepared a monograph which was printed in a few copies only, one of which is preserved in the British Museum. It is entitled “Auto-Icon or the uses of the Dead to the Living; a fragment from the MSS. of Jeremy Bentham.” The object of this work was to show “how, if embalmed, every man might be his own statue*.” Bentham left not only his manuscripts but his body to University College, then the University of London, and his Auto-ccon is now preserved there. ‘The head is in a mummified condition, but as the accompanying plates from our photographs will show, gives one a fair appreciation of Bentham in his old age. We still see the “ venerable locks which floated over his collar and down his back”—in the manner of the great German historian—locks which convince one of the difficulty attending any measurements of the ares on the living head. The flesh, if dried, is still there in considerable thickness, and this and the hair render the determination of the inion as difficult, if not more difficult than in the case of the head of the living. The opisthion and basion are exposed, and except for a couple of wires crossing the brain cavity, there is little or no matter left inside the skull; in fact its capacity can be determined as accurately as that of the majority of skulls with which one is called upon to deal. Measurements of this head were taken by one of us. There was a marked projection at 65 mm. from the opisthion, which was selected as the inion. But to be quite sure of the matter Professor Thane was consulted, and he fixed on practically the same point. There was, however, a lower point at 51 mm. from the opisthion, and between these two points a groove could be distin- guished. Whether these two points correspond to a superior and inferior inion it would not, perhaps, be possible to determine, even if the flesh were removed. Anatomical authority spoke strongly for the upper point as inion. We will refer * Dict. Nat. Biography, sub Jeremy Bentham. Biometrika 11 394 to them as measurements agreed within a millimetre with ours. ‘superior ’ and ‘inferior’ inions. TABLE XV. Measurements on the Head of Jeremy Bentham. Auricular Height Measurement of Internal Capacity of Skull We place here the values of the measurements taken on the Bentham head. Professor Thane with his usual kind- ness consented to take the critical arcs and diameters independently, and his 121, Less flesh 116, Average English ¢ 115 Maximum Length 192 Maximum Breadth 153 Minimum Forehead Breadth 105 Bizygomatic Breadth 133? Horizontal Circumference 560 Biauricular Arc 335 Sagittal Are to Gnisihien 380 % 9 ‘Superior Inion’ 315 rs 5 ‘Inferior Inion’ 330 Opisthion to ‘Superior Inion’ 65 3 » ‘Inferior Inion’ 51 Face Height ‘ 144? Upper Face Height ... : 73? Total Height, Basion to Beene 135 Skull Base, Nasion to Basion 105 Profile Length (Alveolar Point to Basion) 89? Palate Length 47? Palate Breadth 35 ? Nasal Height 552 Nasal Breadth . = 1 22 Capacity . 1475 Profile Angle 93° ? Basal Angle 44°°5 Nasal Angle 58° Alveolar Angle 77°5 Cephalic Index 79°7 Height/Length 70°3 Auricular Height/Length 63-0 Face Height/Bizygomatic Breadth 108 Upper Face Height/Bizygomatic Breadth 55 Nasal Index bas Sah 56 2? Palate Index 745 ” ” 186 147 99 127 540 ? U 2 325 ? 365 ? 300 % 315 2 2 2 189 141 98 130 524 308 377 We place these measurements here because they may be of interest for other than our immediate purpose, merely remarking that difficulty of access or other reasons render some very doubtful. We notice at once that Jeremy Bentham’s head is closely identical with that of the mediocre or average Englishman. Apparent exceptions are the very arcs which Dr Beddoe measures, but the difference here is, we believe, solely due to the difficulty of allowing for the flesh, The only real exception we believe to be the and to a less extent for the hair. M. A. LEwenz AND K. PARSON 395 profile angle, the face apparently receding from nasion to alveolar point. This receding character is undoubtedly exaggerated in the photograph, although great care was taken in the endeavour to get the ‘horizontal plane’ perpendicular to the vertical sides of the plate. Still, difficult as the determination of the lower rim of the orbit is in the present condition of the head, we believe the profile angle is truly greater than 90°, and that this is the case receives confirmation from the remarkable smallness of the nasal angle. With the exception of this receding character the head of this man of first-class intellect shows no single measurement—least of all its capacity—which would serve to differentiate it from that of the average Englishman of his time. Statistically, it is idle of course to argue from a single instance; but it is certainly worthy of note that Jeremy Bentham if judged by head-capacity would have been simply mediocre. We have now to see what results the various reconstruction formulae as applied to Jeremy Bentham’s measurements provide. We must note that all the measurements were taken and controlled by Professor Thane’s independent measurements before any formulae were applied. To use Dr Lee’s formula, the thickness of the flesh in its present condition at various points was tested by aid of a fine sharp needle. At the glabella it was 4 mm.; at the bregma 2 to 3 mm., and about the same over the back of the head. We accordingly took the cranial diameters to be L=186, B=147 and H=116 respectively. Applying Dr Lee’s formula C=:000337 x Lx Bx H+ 40601, we find: C=1475 cm.*. To apply the General Formula of the present paper we roughly allowed for the flesh on the basis of a whole circumference for the horizontal circumference, and a half circumference for the sagittal and auricular arcs, taking as our values 540, 325 and 365 mm. This must give a value slightly too big, as we have not allowed for the hair. There results 1511 em.*. Now the actual capacity is certainly slightly over the measured value 1475 and almost certainly under 1495 cm.*. The exact agreement of P and Z with the measured capacity is of course only pure chance. But either P and L or G. F. would suffice to show that Bentham had skull capacity close to the average English value. P and L is of course the more satisfactory because we have made no allowance that was not capable of measurement. We now turn to Dr Beddoe’s formula. We are to take 4 of each of the ares, divide the product by 2000, and add ‘3 per cent. for each point of the cephalic index, about 50. In applying this rule we will give Dr Beddoe. every advantage, which he in his turn has not always given to those whom he criticises. Our auricular are is measured with the head on the craniophor from the top of one auricular passage to the other. From the centre of one auricular passage to the other appears to be 348 mm. The horizontal circumference is 560 mm. and the nasion to the 50—2 396 Measurement of Internal Capacity of Shull ‘superior’ inion 815 mm. The cephalic index is 79°7 points, say 30 above 50. The answer is: C=1221.cm.. To give Dr Beddoe more grace, suppose, which is extremely improbable, that the ‘inferior’ inion is to be taken as the true inion. The sagittal are is now 330 instead of 315 and the answer is: C=1280 cm.’. But we will go even further. Dr Beddoe makes light of the hair when measuring his ares and therefore he cannot consider of much importance the variation in the flesh. We will, however, endeavour to improve his position by allowing for the effect of shrinkage of the flesh on his circumferences, although we beheve that this shrinkage is not comparable with the effect of different states of the hair. It can only be the roughest approximation. A circle of radius r+55mm. has for circumference 27 (7 +5'5) mm. Hence, if 5°5 mm. shrink to 3mm. there would be a drop of 27 x 2°5 mm. in the circumference, say 16 mm. Hence, at the outside we cannot allow more than 16 mm. for change in the horizontal circumference due to shrinkage, and possibly 10 mm. in the auricular are, and say 13 in the sagittal. This gives us as measurements in life: 576, 353 and 328 for ‘superior’ inion, 576, 353 and 343 for ‘inferior’ inion. The first and more probable inion gives us now: C=1346, and the second and improbable inion: C= 1408. Dr Beddoe’s estimate would then be at least 70 cm.’, but most probably 150 to 200 in defect, in the case of Jeremy Bentham! This would not only place Bentham, undoubtedly as able as, if not abler than anybody on Dr Beddoe’s list, at the very bottom of it, but a long way below the mediocre Englishmen with whom he is really identical. Thus, it seems to us, that in the only case wherein we have been able to test Dr Beddoe’s formula and his hypothesis of marked correlation between skull capacity and ability both fail completely. This may be only the exception which proves the rule, but we must confess that it makes us entirely distrust not only his guesswork formula, but the deductions as to ability and skull capacity which he has based upon it. (15) Conclusion. In concluding this paper we want particularly to emphasize one or two points. We are not defending a particular formula; we believe, owing to the results obtained, that a circumferential formula as good as a diametral formula can be reached. We are not fighting a particular group of workers; in particular we believe that Dr Beddoe has done good service in widening the field of anthropometric interest in this country. What we want to emphasize are the following principles : Biometrika. Vol. Ill. Part IV. NN Auto-icon of Jeremy Bentham. Front View. Biometrika. Vol. III. Part IV. Plate iii. Auto-icon of Jeremy Bentham. Profile. vf M. A. Lewenz ano K. PEARSON 397 (a) Statistical enquiry 1s not a field for guesswork and elementary arithmetic ; there is a mathematical science of statistics which must be learnt, and papers dealing numerically with anthropometric and craniometric data which do not now apply this theory are simply outside the field of science. (b) Method in statistical reduction is not the only thing we demand however. In the light of modern scientific enquiry we demand that the craniologist shall distinguish between what holds for a local race of man, and what may be applied to mankind as a whole. We have elsewhere shown* by actual measurements that inter-racial and intra-racial correlations are not the same, and consequently the reconstruction formula for the individual within a given race is not the same as the formula for reconstructing the mean of a given race. Dr Beddoe draws no distinction here, just as he draws no distinction between the sexes, although Dr Lee gives every warning on this point. It is only when we find local race formulae closely in agreement among themselves that we can extend our results and form from them an inter-racial formula. Dr Beddoe makes no attempt to deduce intra-racial formulae from fairly homogeneous racial series by recognised statistical methods; he does not then compare these among them- selves and see whether an inter-racial one can be deduced from them. He simply makes a guess, tries it on a most heterogeneous series, and if it does not fit makes another guess. He applies Dr Lee’s results regardlessly to individuals and to race-means, he uses the same formula for male and female skulls, and where he has no data to offer, although by time and patience he could have collected some, he simply makes the roughest appreciation. This is not science; it is the dilettantism which in the past has made anthropometry and craniometry impossible subjects for academic study. We believe that the time has come to change this, and uphill as the battle will be we shall not hesitate to criticise in the strongest manner papers like Dr Beddoe’s, which sensibly lower the already low standard of cranio- metric science. * Biometrika, Vol. 11. pp. 347—56. ETUDE BIOMETRIQUE SUR LES VARIATIONS DE LA FLEUR ET SUR L7HETEROSTYLIE DE PULMONARIA OFFICINALIS Par EDMOND GAIN, Professeur adjoint a la Faculté des Sciences de VPUniversité de Nancy. TABLE DES MATIERES. Page Introduction 399 Historique . : : : : 400 Généralités, Sone mution aolienoe: anterprétation es praphidues : : é : 402 Prélévement des fleurs et des échantillons : : : : : 5 : ; : 407 Plan du travail . : : : : : . c - : : ; i : : 408 CHAPITRE LI. Influence de la taille de la plante sur la variation dela fleur. ' . F A . 408 Mensurations des fleurs récoltées sur des grandes et sur des petites plantes (Tables I., II. et III.) ees od 5 af a eG Variations comparées des deus “aléporiee miecedentes (Table IV.) : ; : : 411 Table des fréquences des diverses longueurs des organes floraux (Table V.) . : ‘ 412 Valeurs moyennes des caractéres étudiés (Table VI.) : : : : : : : 413 Schémas de quelques types extrémes : 415 Conclusions relatives aux chiffres précédents . : . 7 : : : : : 414 CHAPITRE II. Comparaison entre les plantes brévistylées et les plantes brévistémonées dune localite . 416 Mensurations de fleurs brévistylées et de fleurs eras de Maxéville 1903 (Table VIL.) ‘ : é 417 Table VIII. des fréquences de dimeHnone aed organes floret tes ae es prcedentse 418 Graphiques obtenus avec les chiffres de la Table VIII. . ‘ 454 Table IX. des fréquences de dimensions des organes. (Plantes Recolices A Masaet 1903) 419 Graphiques relatifs 4 la Table IX. . F 3 455 Variations comparées des plantes brévistylées et peer monces de Maxcaile a ae Messein (Tables X. et XI.) : , : : : : 3 : : : : 420 Epmonp GAIN 399 PAGE Fréquence comparée des deux types de fleurs : : : : : 422 Floraison comparée des deux types de plantes (nombre des flee) A ; 5 é 423 Graphiques relatifs au nombre des fleurs : ‘ ‘ 3 : ‘ ; : ‘ 423 Conclusions relatives & la floraison comparée . : : ; : c : “ : 423 CHAPITRE III. Etude comparee des plantes récoltées pendant deux années differentes . : : : 424 Table XII. résumant les fréquences de chacun des 4 lots de plantes recoltées a Maxéville (1903) . : : 3 : : : : F 425 Graphiques obtenus avec les javinen de ip Table XI. : : : ‘ F . 455-6 Table XIII. des mensurations de plantes récoltées & Maxéville 1902 : : 428 Comparaison et conclusions relatives aux plantes de 1902 et 1903, Tables XIV a. et XIV, 429 CHAPITRE IV. Etude comparée des plantes de quatre stations différentes des environs de Nancy (Laxou, Malzéville, Maxéville, Messein) . : ‘ : : : : : ; , : 431 Tables des mensurations des plantes de quatre localités différentes. Tables XV., XVL., XVIL, XVIIL . : : : : : : 432 Tables de la fréquence relative aes vets foneanues drudices “Tables XIX., XX., XXL, XXII. : : ; : : : ; C ; 436 Variabilité comparée dans unite Soro diferentes . : : 441 Schemas représentant les types extrémes ou caractéristiques pour te 4 a one beaded 451 Graphiques relatifs aux Tables XV. a XVIII. : : : : ; . i . 457-8 Caractéres généraux des races géographiques observées . : : 5 s : ; 440 Types moyens théoriques calculés . ‘ : : ; : : : : 445 Variabilité et fixité de Vhétérostylie de la Palinonaine : : : : : : F 447 Schémas des types moyens théoriques . : : : : : . ; : : 451 CHAPITRE V. Conclusions générales . 3 : : : c : A : é : : : ; 449 Graphiques relatives au style, 4 V’étamine, au calice, & la distance du stigmate ad Yanthére . ; : : : : : : : : : : : : . 454-8 INTRODUCTION. Ce travail est relatif 4 la Pulmonaire officinale. Nous avons l’intention de létendre a d'autres plantes @ fleurs hétérostylées en vue de contribuer a la connaissance du phénomene intéressant de |’hétérostylie. Plusieurs herborisations nous avaient montré, chez Pulmonaria officinalis, de grandes variations dans la longueur des styles de chacun des deux types brachy- stylé et dolichostylé. Fig. 1. Nous nous sommes proposé (1) D’étudier, par des mensurations nombreuses, la morphologie de la fleur et Vhétérostylie de Pulmonaria officinalis L., pour en dégager des données numé- 400 Etude biométrique sur la Pulmonaire officinale riques précises sur le type moyen de chaque organe, sa fixité relative, et l’étendue de ses variations possibles. Fie. 1. Pulmonaria officinalis Gr. 2/1. (Vaprés Hildebrand, Botanische Zeitung, 13 janv. 1865). (2) De déterminer la nature des courbes, relatives 4 la variation de longueur des organes des deux types d’une fleur hétérostylée. (3) D’établir si, en des localités différentes, le type floral subit des modifica- tions de races orientées dans un sens déterminé, et si on retrouve le méme type moyen et la méme loi de fréquence. Cette derniere question, on le voit, présente un certain intérét au point de vue de la géographie botanique. C’est seulement a l’aide des études biométriques comparées, quil est possible de dégager, dune part I’étendue de la variation possible d’une espéce dans les diverses localités de sa station habituelle, d’autre part de déterminer dans quel sens la variation a une tendance a s’accentuer. Ces mesures biologiques ont en outre l’avantage de laisser des documents statistiques sur l’état dune espece qu’il peut étre intéressant d’étudier & nouveau plus tard, au point de vue de son évolution possible. N Avant d’aborder ce travail je tiens & reconnaitre combien j’apprécie ’honneur de le voir inséré en langue frangaise dans Biometrika. Je veux aussi rendre un hommage de reconnaissante gratitude et de remerciements A M. le Professeur W. F. R. Weldon. Non content de revoir mon manuscrit, mon savant confrére a bien voulu m’aider de sa critique et de sa collaboration précieuse dans la tache ingrate du calcul mathématique de nombreuses données numériques. Cest pour moi un devoir de le reconnaitre ici et de ’en remercier chaleureusement. Historique. En réalité, nous possédons bien peu d’études de biométrie florale. Deux auteurs, Darwin* et Hildebrandt, pourtant, & propos des Pulmonaires, ont été amenés & dire quelques mots sur les différences tlorales observées entre les fleurs brévistylées ou brachystylées et les fleurs du type dolichostylé ou brévistémoné. Mais ce qui préoccupait ces auteurs c’était la question de la fécondité relative des * Ch. Darwin, Des différentes formes des fleurs dans les plantes de la méme espéce, trad. Heckel, p. 110. Reinwald, 1878. + Hildebrand, Die Geschlechter-Vertheilung bei den Pflanzen, 1867, p. 37; Botanische Zeitung, 1865, 13 janvier, p. 13. Epmonp GAIN 401 deux types de fleurs, et aucune statistique, ni aucun graphique n’ont appuyé leurs observations sur les dimensions des organes floraux. Voici d’ailleurs les seules données signalées par eux : Chez Pulmonaria officinalis, le pistil de la forme dolichostylée, dit Darwin, est deux fois aussi long que celui de la forme brachystylée, et les étamines ditférent d'une maniére correspondante quoique inverse. Les grains polliniques sont différents dans les deux sortes. Ceux de la pre- miére forme sont 4 ceux de la seconde comme 78 est & 100 en longueur, 6 a 7 en épaisseur. La corolle est plus grande généralement dans les fleurs brachystylées (et c’est Pinverse chez Pulmonaria angustifolia). Hildebrand a ramassé dans le Siebengebirge 10 Pulmonaria officinalis de chaque sorte. Les 10 dolichostylées ou brévistémonées portaient 289 fleurs, les 10 brachystylées ou brévistylées en portaient 373. Hildebrand conclut de 1a que les sujets brachystylés produisent beaucoup plus de fleurs. La conclusion est basée comme on le voit sur un nombre tres petit d’observations. Darwin reconnait d’ailleurs que 10 plantes anglaises dolichostylées, examinées par lui, furent trés fécondes aprés fécondation illégitime, tandis que les 10 plantes semblables, récoltées en Allemagne par Hildebrand, restérent compleéte- ment stériles. Cette différence semble indiquer une certaine variabilité de la fertilité. Les plantes de Darwin cultivées en plein air ne montrérent aucune tendance a devenir isostylées, et & perdre leur propre caractére dolichostylé, comme cela ce présente souvent parfois sous linfluence de la culture, dans plusieurs espéces hétérostylées de Primula. Darwin signale la grande variété de longueur du pistil et des étamines de Primula angustifolia, et trouve que, chez cette plante, la distance entre les antheres et le stigmate n’est pas constante; d’une moyenne de 7 mensurations seulement il conclut que cette distance dans la forme dolichostylée est a cette de la forme opposée comme 100 est 4 69. Les longueurs relatives moyennes des pistils de ces deux formes seraient entre elles comme 100 est 4 56, et pourraient atteindre méme le rapport 4°°. Cette variation si accentuée fait soupgonner a Darwin un état de transition et une tendance de la plante & devenir dioique. D’autre part Hildebrand signale que Pulmonaria azurea vest point hétéro- stylée. Les quelques mensurations, signalées ci-dessus, semblaient démontrer que VPhétérostylie était le mieux fixée chez P. officinalis pour diminuer de régularité chez P. angustifolia et disparaitre chez P. azurea. Biometrika 111 51 402 Etude biomeétrique sur la Pulmonaire officinale Généralites. Prenons un nombre NV d’échantillons de fleurs de Pulmonaires. Supposons qu'il sagisse d’établir le type de fréquence et le type de longueur moyenne du style de ces fleurs. Nous mesurons les styles. Ayant porté sur l’axe des abcisses les longueurs en millimétres exprimant la taille, nous élevons, aux divers points, des ordonnées de hauteurs proportionnelles aux nombres d’individus correspondants. Lorsqu’on étudie comparativement des fleurs provenant de localités différentes il faut naturellement autant que possible prendre le méme nombre d’échantillons de chaque localité. Une restriction pourtant doit étre faite. Il y a souvent plus d’avantage & prendre le plus grand nombre possible. La variation de longueur du style n’est pas discontinue. Dans nos mensura- tions nous avons ordinairement pris comme unité le 4 millimetre. Vu le grand nombre d’échantillons @ mesurer, il ne pouvait étre question d’employer la loupe, il fallait done choisir une unité facile a lire a l’ceil nu avec une approximation suffsante. Mais, les abscisses ne croissent pas en réalité de 4 en 4 millimétres, mais bien de quantités infiniment petites, c’est-a-dire de # a «+ dz. En joignant le haut des ordonnées, le graphique que nous obtiendrons sera donc un polygone de variation (Pearson) qui tend seulement vers la courbe limite de ce polygone. Ainsi il y a intérét & prendre un nombre le plus grand possible dindividus afin d’esquisser le mieux possible les vrais contours du polygone théorique artificiellement obtenu qui doit renseigner sur la courbe. Pour donner une idée de l’approximation relative quwil est possible d’obtenir avec wn petit nombre de 25 exemplaires, nous donnons ci-apres (fig. 2a) une courbe tracée avec deux lots de 25 plantes et celle qu’on obtient avec 31 plantes dont on a déterminé la distance du stigmate a l’anthére. Ces plantes ont été récoltées dX des distances de 3 métres au moins, au hasard des rencontres. Une fleur de chaque pied a été mensurée. Plus le nombre des individus s’accroit, plus la courbe a une tendance & monter vers les ordonnées de grande fréquence, mais les parties latérales correspondant aux faibles fréquences restent partiellement indéterminées et s’étendent de plus en plus loin. La courbe A (31 pl.) est enveloppante vis-a-vis des deux autres Bet C. Elle ~s7 A A kd 'é id s’étend de aen g. La courbe B a les mémes valeurs extrémes enregistrées, mais la courbe ¢ commence seulement en b pour finir en g. Néanmoins, malgré les différences, ces trois courbes ont bien la méme allure, avec le méme type de plus grande fréquence placée en d, et avec les mémes inflexions générales en c et f II est vraisemblable que la courbe limite de ces polygones est une courbe binomiale normale n’ayant qu’un sommet principal S. Les deux sommets secondaires s’, s” ne se maintiennent pas quand on dispose de 200 mesures différentes. EpMonpD GAIN 403 Ainsi les graphiques obtenus, dans ce qui va suivre, doivent parfois étre inter- prétés par suite de linsuffisance relative du nombre des mesures enregistrées. : | a : | . Py 14 fee il if = 6 = | i I So cS ae & 4 + = amal 4b 2 3 7 * : 1 : — e + 3 4 > TIE - Wa / we \ , | LARS 0 1 WW 2 OF 8 383 4 4% 5 5F 6 6F 7F.8 : Longueur en Millimetres. H Gao | ee freeones Cf --g Fic. 2a. A. —+—-+— Courbe tracée avec 31 plantes. B. ———\— Courbe tracée avec 25 plantes. CO. eee Courbe tracée avec 25 autres plantes. Laxou. 381—25 plantes isolées de 3 métres (brévistémonées). Distance du stigmate 4 l’anthére. Méme en opérant avec 25 ou 30 échantillons seulement, il y a des polygones de fréquence qui sont souvent tres voisins de la courbe limite. L’allure générale du périmétre du polygone renseigne dans ce cas par sa régularité qui n’est évidem- ment pas effet du hasard. Nous l’avons vérifié plusieurs fois pratiquement en comparant deux graphiques obtenus par exemple avec 30 et 140 échantillons différents. Dans le cas des courbes polymorphes il y a parfois une certaine incertitude dans l’interprétation du polygone*, mais dans ce qui va suivre la nature de la courbe est généralement non douteuse, et nous n’avons pas rencontré de courbes de cette derniére catégorie. Le présent travail apportera donc une solution & la question suivante qui n’a pas encore été abordée je crois: Quelles sont les diverses courbes des variations de longueur des organes d’une fleur hétérostylée ? Lhétérostylie est en somme une question de longueurs relatives de deux organes. Le dispositif présente une importance physiologique établie par les recherches sur le croisement+; on peut penser que l’hétérostylie se maintient par suite de conditions particulieres dont on peut espérer lire l’existence dans les mesures biométriques. Avant d’entreprendre ces recherches je pensais, par analogie avec d'autres faits biologiques, qu’un dispositif comme lhétérostylie ne pouvait sans doute se * Ludwig, Bot. Centralblatt, 1893, 1895. C. B. Davenport, Statistical Methods. + Darwin, Fécondation croisée. Forme des fleurs. 51—2 404 Etude biométrique sur la Pulmonaire officinale maintenir que par suite d’une variation unilatérale. Je supposais que quelques unes des courbes, comme, par exemple, celle qui concerne la distance du stig- mate a l’anthere, auraient probablement l’ordonnée maximum & une extrémité de leur étendue, comme dans celles qui sont appelées, a tort par de Vries, demi- courbes Galtoniennes. Comme on le verra par la suite, cette hypothése était fausse*. Les graphiques sont formels a cet égard. Pour arriver & apprécier la fixité relative de Phétérostylie il faut calculer la valeur moyenne de chaque caractere floral, c’est-a-dire établir son type de longueur >(@) Pour un nombre WV d’échantillons, soit m les mesures en 4 millimétres, et 7 les nombres exprimant la fréquence de chaque mesure m, > (mn) ne En somme, Z est une moyenne arithmétique de toutes les longueurs observées. moyenne, et puis le carré moyen des déviations = ry La longueur moyenne sera L = D’autre part le type le plus fréquent a une longueur K qui est aussi carac- téristique des tendances de la race. Si done les deux longueurs Z et K sont différentes il faut tenir compte des deux pour apprécier la fixité du caractere. Un exemple graphique fait mieux comprendre cette conclusion: Soient A, B, C trois courbes de fréquence obtenues avec les styles de trois lots de Pulmonaires de trois localités différents : | | Nombre des Individus. Echelle de millimetres. Fie. 2b. Les courbes A et B enferment deux surfaces égales et symétriques par rapport aux axes de grande fréquence qui sont superposés en OS. Elles limitent des polygones de fréquence tres différents d’aspect. Le type théorique moyen reste le méme. * Ce n’est pas un cas particulier 4 la Pulmonaire. Nous publierons ultérieurement une étude biométrique sur la Primevére qui aboutit 4 cette méme conclusion. EpMoND GAIN 405 La race n’a pas varié de type. Il existe naturellement un nombre indéterminé de courbes de méme surface que A et B, et intermédiaires de forme, et auxquelles la conclusion ci-dessus s’applique aussi. Si la valeur moyenne de la race n’a pas varié, en A et 5, il n’est pourtant pas sans intérét d’enregistrer deux faits: (1) Dans la station B les individus sont peu variables et leur type de styles est concentré autour d’une longueur moyenne dont ils s’écartent peu ; (2) Dans la station A les individus ont une longueur des styles qui est tres variable et il y a en quelque sorte un affolement du type. Si celui-ci persiste il y a ici une sorte de race géographique différente de l’autre. Les courbes B et C enferment deux aires égales, et les polygones de fréquence sont identiques et superposables. Le type moyen est tres différent en Bet C. Il est passé de 5 & 84, soit une variation, de la taille de la race, qui est une augmen- tation de plus de 50 p. 100 de sa taille initiale. Dans une courbe établie 4 l’aide d’échantillons de localités différentes, il faut done examiner si, dans les divers lieux, l’ordonnée de plus grande fréquence est déplacée & gauche ou & droite. Dans le travail qui suit, on a cherché a définir le type de longueur moyenne théorique, obtenu a l’aide de mensurations nombreuses dont on prend la moyenne arithmétique. Ce type moyen peut ne pas étre le type de plus grande fréquence. Il ne peut s’en éloigner beaucoup, si la courbe est sensiblement du type des courbes binomiales normales, ou des courbes hyperbinomiales, c’est-a-dire mono- morphes, bilatérales et symétriques. Dans le cas d'une courbe parabinomiale, c’est-a-dire dont l’ordonnée de plus grande fréquence est rejetée d’une cdté, le type moyen est fixé par l’ordonnée qui divise le polygone de fréquence en deux parties égales, et cette ordonnée n’est jamais la méme que celle qui correspond au type le plus fréquent. Cette derniére est évidemment aussi caractéristique de la race que l’ordonnée du type moyen; son simple déplacement, sans déformation considérable de la courbe parabinomiale, est une indication certaine de la variation de la race. Pour construire la courbe qu’on pourra regarder comme représentant la limite théorique du polygone des observations, nous avons adopté la formule symétrique de Gauss, & cause de la symétrie de la plupart des polygones obtenus. Avec le nombre restreint d’échantillons de chaque sorte étudiés, il était inutile d’essayer les formules plus compliquées de Pearson*. Voici donc les quantités que nous avons calculées, pour représenter chaque polygone par Ja courbe exponentielle de Gauss, * Phil. Trans, 1895, et Biometrika, passim. 406 Etude biométrique sur la Pulmonaire officinale Nous devons d’abord calculer la valeur moyenne du caractére étudié; soit M,, My, etc., les diverses valeurs individuelles dans la série NV d’échantillons, nous avons, pour trouver JM, la valeur moyenne, _ =(m) M V Les valeurs de « dans la formule de Gauss sont les écarts individuels, c’est- a-dire les différences entre les mesures individuelles et la valeur moyenne de la série, ou les valeurs de (m—M). Puisque la valeur la plus grande de y est obtenue en mettant #=0 dans la formule, on voit que la valeur la plus fréquente de la série étudiée doit étre la valeur moyenne. Dans les cas ot la valeur moyenne ne se trouverait pas plus fréquente qu’aucune autre, on devrait employer Pune ou l’autre des formules asymétriques développées par Pearson (loc. cit.). Pour calculer la quantité ~, on doit calculer la somme des carrés des écarts du moyen, ou la valeur du et nous avons Selon la notation d Amann (Journal de Botanique, T. 13) on pourra écrire x {(m—MY} __, ye et suivant la notation de Pearson on écrira Q =o (index de variabilité). L’écart probable, la valeur P d’Amann, lécart quartile de Galton, se trouve facilement par la relation P=067450 = 0°4769p. Dans les tableaux insérés dans ce travail on a donné une importance peut-étre exagérée a l’étendue empirique de la variation, telle quelle résulte souvent d’un tres petit nombre d’observations. On a voulu ainsi simplement donner aux botanistes des renseignements concrets sur ce quon pouvait s’attendre a rencontrer dans des herborisations analogues aux ndétres. Mais nous n’oublions pas pour cela que cette étendue empirique de la variation ne doit pas étre considérée comme une caractéristique du mode de variation, parce qu'elle est trop exposée a étre modifiée par des causes accidentelles, différentes dans chaque série d observations. En d’autres termes la loi de variation n’est pas changée parce que les limites enregistrées apparaissent dissemblables dans deux prises successives d’échantillons*. Il y a lieu au contraire d’attacher de importance a létendue théorique de la variation telle quelle se déduit des propriétés caractéristiques de l’exponentielle ; et, chaque table de l’intégrale de la Probabilité (celle de Bertrand, par exemple, ou * Duneker, Biolog. Centralblatt, Bd. xvi. No. 15, S. 569. Epmonp GaIN 407 celle de Sheppard) nous montre que pour une valeur quelconque de w ou de o l’étendue de la variation tend toujours & grandir, quand le nombre des individus étudiés devient plus grand. Préléevement des fleurs. Chaque fleur a été prélevée sur une hampe différente. On sait que chaque hampe florale porte des fleurs du méme type morphologique: nous avons plusieurs fois contrdlé ce fait par des mesures précises. I] y a donc une sorte de caractéristique individuelle. Si, par exemple, la fleur bien épanouie, prise comme type, est du type a style exserte par rapport au calice; on peut constater le méme caractere chez les autres fleurs du méme pied. Cette constatation initiale nous a servi de base pour étendre considérablement la portée des statistiques faites. Si les fleurs d’un pied avaient eu des caractéris- tiques différentes, il eut fallu les mesurer toutes pour en dégager la notion de variabilité maximum. Comme chaque plante possede une moyenne de 138 a 15 fleurs, les mensurations eussent di étre, nécessairement, 13 a 15 fois plus nom- breuses pour donner la méme approximation que celle que nous avons obtenue. Le nombre des mesures qui servent de base a ce travail est de pres de 5000. Ces mesures ont été fournies par environ un millier de hampes florales. Prélévement des échantillons. On a employé trois méthodes différentes pour choisir les hampes florales qui devaient fournir chacune une fleur 4 la mensuration. 1’ méthode. Elle consiste & explorer une localité de surface limitée (par exemple, 200 a 500 metres carrés suivant la rareté) et & y prélever toutes les hampes florales sans exception. Si un rhizbme émet plusieurs hampes, celles-ci doivent présenter une grande ressemblance puisqu’elles proviennent d’une méme graine mere. Chaque individu est donc représenté dans la statistique par un nombre de hampes qui est variable. Cette méthode de prélévement présente en outre l’inconvénient suivant: Elle suppose que les types brévistylés et les types brévistémonés sont aussi prolifiques au point de vue du nombre des hampes. S'ils ne le sont pas il semble qu'il y ait la une cause qui altere la rigueur de la biométrie comparée des deux types. 2° méthode. On préléve comme précédemment, et dans le lot on prend, au hasard, seulement une partie des plantes. 3° méthode. On préléve les hampes sur un espace plus grand, en ne ramassant, au hasard, que des hampes espacées de deux ou trois metres de distance. De cette fagon on ne recueille qu’un échantillon de chaque individu issu d’une graine Toutes les hampes récoltées proviennent d’individus et de graines différentes. Nous avons dressé des graphiques qui permettent de conclure que les trois méthodes peuvent donner des résultats comparables. 408 Etude biométrique sur la Pulmonaire officinale La 3° méthode exige pourtant moins d’échantillons différents pour dégager la loi de variation de chaque organe. Elle est donc supérieure aux autres, et c’est celle que nous avons employée pour la biométrie comparée des Pulmonaires de 4 stations différentes. Pour distinguer sirement P. officinalis de Vespéce voisine, P. tuberosa (var. latifolia et var. angustifolia), le caractére qui a été choisi a été le suivant: Car- pelles miirs—aigus au sommet. La Pulmonaire a racines tubéreuses a, au con- traire, des carpelles arrondis au sommet. Cette derniére est d’ailleurs beaucoup moins commune que l’autre dans les bois du calcaire jurassique des environs de Nancy. Plan du travail. Voici l’ordre des questions abordées : 1. Influence de la taille de la plante sur les dimensions florales. (Plantes récoltées & Maxéville en 1902.) 2. Comparaisons biométriques entre les fleurs brévistémonées et les fleurs brévistylées d’une méme localité. (Maxéville, 1903, et Messein, 1903.) 3. Etude comparée des plantes récoltées 4 plusieurs reprises dans une localité, en 1902 et 1903 (Maxéville), en vue de voir si le climat annuel exerce une influence. 4. Etude comparée des plantes de quatre stations, récoltées la méme année dans des localités trés différentes d’exposition. (Maxéville, Messein, Laxou, Malzéville.) 5. Conclusions. I. INFLUENCE DE LA TAILLE DE LA PLANTE SUR LA VARIATION DE LA FLEUR. Le calice de la Pulmonaire officinale est, comme on le sait, gamosépale, et d’un aspect tres comparable dans les deux types brévistylé et brévistémoné. II est renflé et pourvu de cing lobes dont la hauteur est & peu prés de } ou + de la hauteur totale du calice. Les mensurations ont porté sur la hauteur totale du calice mesuré dans son axe de symétrie. Les lobes du calice sont de dimensions assez variables pour des calices de méme hauteur totale. Voici les deux types extrémes: Deux calices de 14 milli- métres de hauteur totale peuvent étre fendus de 6 ou de 3 millimétres seulement. Les dimensions extrémes de hauteur du calice sont de 8 et 17 millimétres. Le calice, notamment, plus que les autres parties de la fleur, semble devoir varier un peu suivant la vigueur des individus, comme le font les feuilles. EDMOND GAIN 409 Il est donc nécessaire de rechercher si, aux variations de taille et de vigueur des tiges, correspondent des variations de dimensions pour les diverses parties de la fleur hétérostylée. Nos mensurations ont porté sur 25 tres grandes plantes, et 25 tres petites, choisies dans une récolte de plusieurs centaines dindividus brévistémonés d'une localité. Les grandes tiges avaient 19 & 25 cm. de hauteur. Les petites tiges atteignaient seulement une hauteur de 8 a 15 cm. On a prélevé une fleur épanouie et bien développée dans Vinflorescence du sommet de la tige de chaque plante. Les tables de statistique I et II donnent les mesures enregistrées. Voyez figs. 7—12. TABLE LI. Mesures de 25 grandes plantes choisies pour leur grande taille (Mawéville, 1902). (Valeurs en millimétres.) 1 2 3 4 5 6 i 8 Distance du stig- | Hauteur du haut mate au bord du | des étamines au- Nombre de Hauteur Longueur calice. Style dessus de la base | Distance fleurs Hauteur | Hauteur | du stigmate | du style du Nos. | des tiges | du calice | au-dessus de | au-dessus j stigmate (cm.) (mm. ) la pees de Vovaire Ree ete TYE Du |alanthére) par Total See de Mu ag 1C | Corolle | calice infl. OE: 1 19 133 123 104 1 — 5 6 64 7+7 |=14 2 21 14% 134 be 1 _ 7 8 5+ =| 9,6,5| 20 3 20 134 123 103 1 = 6 7 54 6,9 | 15 4 20 10) 12 10 = 1 5 6 6 6, 6 12 i) 19 133 12 10 14 — 5 6 6 (his) 15 6 22 13 12 10 if — 7 8 4 6,10} 16 if 20 124 12 10 L 54 | 664 54 %16 || 18 8 20 123 114 93 1 — 6 7 4 7,12] 19 g) 19 135 113 9s 2 — 6 i 4h 6,9 15 10 20 12 wl 9 1 — 5) 6 5 8,11] 19 il 20 144 134 114 1 = i 8 54 7,9] 16 12 20 12 114 94 4 54 | 64 5 vee | 13 20 13 11 9 2 — 6 a 4 yy 13 1h 20 114 114 93 6 7 4} 6,9 | 15 15 25 12 13 ll = 1 5h | 6h 64 Gen eee: 16 20 11 11 9 = - 5s | 64 44 5,9-| 14 17 19 11 11 9 — a 5 6 5 8, 5 13 18 19 124 12 10 $ — 5 6 6 6, 8 14 19 23 114 12 10 = 4 i 8 A908 1 iy 20 23 12 12 10 a = 5s 63 5s 7,10) 17 21 19 12 114 9h 4 = 5 6 5&6 | 6,15] 21 22 23 144 We 10 24 = 6 7 5 5,6 | 11 23 20 12 124 104 " 63 | 7% 5 7,5 | 12 2 19 12 11 9 1 63 74 33 1 90 6 25 22 12 12 10 — — 6 i 5 6,11] 17 Vee o-oo 4s de | 911d |) Ok A a | B—7 | 168 | 84h.) —. 1-878 Biometrika 111 52 410 Etude biométrique sur la Pulmonaire officinale TABLE II. Mesures de 25 petites plantes choisies pour leur petite taille (Maxéville, 1902). (Valeurs en millimetres.) 1 2 3 4 5 6 ¢ 8 Distance du stig- . : Hauteur | Longueur | ™ate au bord du REA ee | Distance Nombre de Hauteur | Hauteur | du stigmate| du style calice. dessus de la base du fleurs Nos. | des tiges | du calice |au-dessus de| au-dessus Style | stigmate (cm.) (mm.) la pee du_ | de lovaire = a4 Vanthére 7 Inelus de} P*52"° | covolle | calice in, | Total ul 8 12 12 10 —_— = 3) 6 6 6+7 |=13 2 12 164 13 11 3h 64 73 54 6, 9 15 3 13 14 13 11 i — 6£ | 7 be 7, lOuh 17 4 13 1 133 113 24 a 8 53 lel 8 5 13 123 125 10% — — 6 7 Bs 8,8 | 16 6 11 12 11 9 1 —_— 5 6 5 7,8 15 Uf 15 15 14 12 1 64 74 63 9, 2 11 8 10 12 12 10 — -- 5 6 6 8,5 13 9 15 16 13 11 3 — 6 a 6 6, 1 a 10 13 124 103 84 2 — 53 63 4 ne 16 11 12 133 124 103 1 — 54 63 6 6, 9 15 a2 11 113 12 10 — 3 6 7 5 3.0 3 13 11 135 12 10 1} —- 6 7 5 6, 0 6 Lh 14 95 114 93 —_— 2 63 7% 4 6,7 13 15 13 12 12 10 — — 6 0 5 6, 7 13 16 13 124 12 10° 2 — 6 7 5 8,11) 19 Lif 14 13 123 103 3 a 8 44 Ue U 14 18 14 13 12% 104 1 = 6 | 7 5 Vesey || 0) 19 13 14 12 10 2 = 6 "i 5 7,19} 26 20 15 13 13 11 — 53 63 64 6, 9 15 41 14 103 11 9 — 4 6 i 4 7,10 17 22 14 144 133 114 1 — ul 8 6 5,9 14 23 14 114 13 11 — 14 63 74 63 Ue 8 15 2h 14 12 11 9 1 53 63 43 to 16 25 14 12 13 11 = — 6 u 6 6, 7 13 Varia | 815 |94—I6k| 11—14 | 84—12 | —3) & +91 | 57 | 6—8 | 4=6) [= —=ouina40 Pour comparer avec les plantes brévistémonées voici les mensurations de 2 grandes plantes brévistylées et de 2 petites brévistylées prises au hasard. (Nous n’avons pas cru nécessaire de faire a leur sujet un examen de 50 échantillons.) EpMoNnD GAIN TABLE III. 411 Plantes brévistylées choisies pour leur grande ow leur petite taille (Mawéville, 1902). (Valeurs en millimetres.) Pulmonaires brévistémoneées. 25 petites plantes (Mawxéville). | Hauteur du haut | Hauteur . . | des étamines au- F Hauteur | Hauteur | du stigmate | Longueur Distance — dessus de la base | Distance INombrerds des tiges | du calice | au-dessusde| du style | du stigmate _du nears (cm.) (mm. ) la base du | au-dessus | au bord du | , stigmate calice de lovaire calice | Dela Du a l’anthére corolle | calice Grandes plantes 25 13 oe 5 6 12 13 5 8+10=18 brévistylées 22 13 63 43 6} 12 15} 5} 8+ 9=17* Petites plantes 12 13 6 4 6 113 | 125 5s 74+6=13 brévistylées 12 12 a 5 5 12 13 5 7+9=16+ TABLE IV. Variations comparées de 25 grandes et de Catégories Grandes plantes hauteur =19—25 em. Petites plantes hauteur =8—15 cm. Proportion centésimale de styles exsertes par rapport au calice ... gistrés) calice ... Hauteur du stign styles égaux au calice styles inclus dans le calice 16 p. 100 ZO Ss 64s, 20 p. 100 24 =, 56g, Hauteur du calice (chiffres extrémes enre- nate au-dessus de la base du Longueur du style au-dessus de l’ovaire Distance du stigmate au bord du calice Hauteur du haut des étamines au-dessus de la base du calice ne Distance du stigmate 4 l’anthére Nombre de fleurs par inflorescences Nombre de fleurs par individu Nombre de fleurs pour 25 individus Nombre moyen de fleurs par individu * Soit 17:5 fleurs par plante. 11 4 143 millimétres kes ee) a galls . -2a4+1 ss, 648 5 34a 6S 5s 4 4 15 fleurs 11a2l , 378 7 15, 12 93 & 164 millimetres wo > S + Soit 14:5 fleurs par plante. 52—2 412 Etude biométrique sur la Pulmonaire. officinale TABLE V. P. officinalis (Maxéville 1902).—Plantes brévistémonées. Fig. 8. Hauteur totale du calice.—Nombre de plantes présentant les diverses hauteurs (pour 25 observations de chaque série). |9 9h 10| 104 11 23 12 | 123| 13| 135 14] 14% 15| 153 16 | 164 17| Millimétres | | Grandes plantes Se liee a |S | Nombre de (Table I, col. 2) laa gem eee alee ries 4 plantes Petites plantes | sll ay lls (Table TL, col 2 lees i 2\/6| 3 | Bo) /2o8 Woe) et ee ate ona . Hauteur du style au-dessus de Vovaire.—Fréquence relative pour 25 observations. Fig. 10. 8 |83 9 | 9% 10 10% 11| 114 12|124|13| — Millimdtres | Grandes plantes (Table I, col. 4) |—/}—|4|6|]9}] 3 }1) 2 ;—]|] — le Nombre de plantes Petites plantes (Table II, col. 4) | —| 1|3]/1)7] 4 |6] 2 |1)— \~ 3 Distance du stigmate au bord du calice.—Fréquence relative pour 25 observations. Fig. 9 bis. +3|+23|+2|423 +1|+4 0 - -1|-13|-2 ~2}|-s|-3} -4| Millimdtres Grandes plantes é F P Nombre de (Table I, col. 5) almealton’ Ma ee to a ae al | plantes Petites plantes a lh. = (Table II, col. 5) we oat te ea alice 9 9 ee ” Hauteur des étamines au-dessus de la base de la corolle.—Fréquence relative. Fig. 11. 4| | 5\ 5b [6] os] 7| 73] Millimetres | Grandes plantes (Table I, col. 6) }—}| — | 7| 5 | 7 | 2 | 4 | — | Nombre de plantes Petites plantes (Table II, col. 6) =| —|3| 4 6 | 3 | — 5 Distance du stigmate 4 lanthére.—Fréquence relative. Fig. 9. ” 3 | 3 | j | sy | 5 | 58 | 6 | 68 | 7 | v4 | Millimatres Grandes plantes (Table I, col. 7) |—| 1 )3] 4 |6] 6 |3] 2 |—]| — | Nombre de plantes Petites plantes (Table II, col.7) /—| —|3|2]7]5{|6] 2 |—| — Nombre de fleurs par inflorescences.—Fréquence relative, pour 25 observations. Fig. 12. Jo|z|2 slalsle|7 8|9|20| 11| 12 13] 14 15|16|17|18|19| 20| 21| 22 25 Grandes plantes! | : Belt | 51 inflo- (Table I, col. 8) ()~ | || bah aes Peet sk Nl ce cad catet mt fa a ceed ed Flesh ee | 25 Petites plantes - é : : ' 48 inflo- (Table IT, col. 8) 2|1/2)-/2| 9f15|6)7) 2/1 |-|-|-|-|-|-|-]1]-]-|-}j rescences EpmonD GAIN 413 Nombre de fleurs par individus.—Fréquence relative pour 25 observations. Fig. 7. 2 3|4 slel7|s8 9 10| 11 12 13) 14) 15 16| 17 18| 19| 20 | 21 | 22| 23) 24| 25| 26 | 27 | 28 | 29 | 30 reat als Hane | i; Grandes plantes | cE el oa Is 9 aad eee lle | ae lee (Table I, col. ast i ema ee ee ed eae ae | Pease eae 4 | ied Petites plantes 5 One erg ea | am ce pa ee ea | pee oF ee (Cable HT, ool 8}|-|2|~|~|2 ele 1 5|/2/5|3/|2 1 | he | | | Voici les conclusions ou les observations qu’on peut retirer de la comparaison entre les dimensions des fleurs des 25 grandes plantes et celles des 25 petites plantes. 1. Pour les dimensions du style et du calice, chez les grandes plantes le type semble plus concentré autour de la valeur moyenne (valeur plus grande de @ chez les petites plantes; voyez la Table VI). Ainsi, pour un méme nombre (25) d’échantillons de chaque sorte, c’est chez les petites plantes que nous avons rencontré, dans la localité considérée, les plus grands et les plus petits styles, les plus grands et les plus petits calices. extréme possible de la variabilité, puisque cette limite recule naturellement Par la suite du travail on verra, en effet, que les limites supérieures de la longueur du style ont été enregistrées de la fagon suivante : Nous n’avons pas ici d’ailleurs la limite lorsqu’on considére un nombre sans cesse croissant d’échantillons. Avec 50 observations (Maxéville, 1903) . 16°5 mm. a At3 . (Maxéville, 1902) 7 - i 2a0 be (Messein, 1908) 18 Fe » AT6 " (Maxéville, 1903) Lom 23 La chance de trouver un calice tres longueur du calice devient plus grande. chance de trouver un calice d’écart donné s’exprime par la valeur de la quantité o. long est d’autant plus petite que la La rapidité avec laquelle diminue la TABLE VI. Valeurs moyennes des caractéres, éudiées dans les plantes de grande taille et dans celles de petite taille. (Valeurs en millimetres.) Grandes plantes Petites plantes Caractére o o Moyenne| o | Un Moyenne| o ic Hauteur totale du calice see 12°52 | 1:044|0°209|} 12°78 | 1°582 | 0-316 Hauteur du style au-dessus de lovaire 9°94 | 0°683 | 07136 | 10°32 | 0°858 | 0:172 Distance du stigmate au bord du calice —0°60 | 0°927 | 07186 | —0°52 | 1-345 | 0-269 Hauteur des étamines au-dessus de la base | de la corolle Mer , 5°82 | 0°691 | 0-138 6°04 | 0°623 | 0-125 Distance du stigmate 4 Vanthére ... 5:10 | 0°707 | 07141 5°30 | 0°683 | 0°137 Nombre de fleurs par inflorescence 7°41 | 1°981 | 0-277 7°08 | 2°730 | 0°394 Nombre de fleurs par individu 15°12 2°658 | 0°266 | 13°60 | 4-499 | 0-450 414 Etude biométrique sur la Pulmonaire officinale Silon se bornait a l’examen de cette Table VI. on pourrait, il est vrai, croire & une petite différence du type chez les grandes et chez les petites plantes. On voit en effet que la valeur moyenne de longueur du style est de 9°94 mm. pour les grandes et 10°32 pour les petites: soit une différence de 0°38 mm. Mais ces valeurs sont sensiblement égales, et la différence apparait négligeable, lors- ; Pn 4G; a quon voit la grande valeur de la quantité TW dans chaque série. On remarque ainsi que l’étude d’un nombre d’échantillons beaucoup plus grand rapprocherait vraisemblablement ces valeurs moyennes, calculées avec 25 échantillons seulement de chaque sorte. Chez les petites plantes on rencontre les types de styles les plus inclus et les plus exsertes. Fig. 9 bis et Fig. 3. Pourtant le type moyen semble étre le méme. On trouve en effet pour 25 observations de chaque type: Grandes plantes Petites plantes Styles plus longs que le calice 4, 5 Styles égaux au calice 5 6 Styles plus petits que le calice 16 14 Mais il en résulte que les petites plantes ont un style qui a, par rapport au calice, une capacité de croissance plus grande que chez les grandes plantes. Dans les grandes comme dans les petites plantes il y a donc environ 2 d’incluses, ne 4 Sif Mee ee: 4 dexsertes, et 4 de types intermédiaires. 2. La distance du stigmate a l’anthere semble rester tres constante comme on le voit, aussi bien au point de vue des valeurs extrémes que de la longueur moyenne. Fig. 9 et Fig. 3. Le type le plus fréquent est le type 54. L’amplitude des variations constatées est de 4 & 61, soit 2°5 d’écart, c’est-a-dire de 1:25 au-dessus et au-dessous du type le plus fréquent. La courbe ici semble étre nettement symétrique. 3. Les grandes plantes ont plus de fleurs que les petites: © bo 5 grandes en ont 378, soit 15:1 par plante, 25 petites en ont 340, soit 136 par plante. \ Différence 38, environ 4 a {5 en plus. EpMonp GAIN 415 4. On voit de méme que chez les petites plantes le nombre de fleurs par individus et par inflorescences est moins constant. C’est chez les petites plantes qu’on trouve les individus et les inflorescences a fleurs les plus nombreuses et les moins nombreuses. Il y a 6 a7 fleurs par inflorescences et 13 4 15 par individus en général. Fig. 7. Grandes Plantes. Petites Plantes. ——OorTO eS ee Distance la Distance la Distance la Distance la plus grande. plus petite. plus grande, plus petite. spadne==ac> RY Types extrémes de distance entre Vanthére et le stigmate. Grandes Plantes. Petites Plantes. ee — OO Style le plus Style le plus Style le plus Style le plus inclus dans le calice. exserte du calice. inclus dans le calice. eaxserte du calice. KR t § H t H 1 ! ' i i ' ! H ' t H ; ‘ ' ‘ : ‘ | ' 1 ‘ ' ' ‘ : ' ' ; We-2-52% N SOCE E 10 Se ee Rapports de longucur entre le calice et le style. Millimétres. Fic. 3. Types extrémes des Tables I. et II. En résumé, malgré les variations individuelles de taille qu’il est facile de rencontrer, les types morphologiques des fleurs ne sont pas sensiblement modifies par la plus ow moins grande vigueur de la végétation. Nous pouvons constater des différences dans le nombre des fleurs plutét que des différences dans les dimensions des fleurs et dans les dimensions relatives des parties. 416 Kiude biomeétrique sur la Pulmonaire officinale HEF COMPARAISON ENTRE LES PLANTES BREVISTYLEES ET LES PLANTES BREVI- STEMONEES D'UNE LOCALITE. (Maxéville, 1903, et Messein, 1903.) A Maxéville nous avons fait une récolte de 120 pieds de chaque sorte et nous avons pris au hasard, dans les deux lots, 25 échantillons de plantes dolicho- stylées et 25 échantillons de plantes brachystylées. A Messein le nombre des plantes récoltées en une seule fois a été de 140 plantes brévistémonées et 95 plantes brévistylées. Les mensurations qui ont été plus nombreuses qu’a Maxéville (235 plantes au lieu de 50) sont relatives a trois caracteres seulement. Elles avaient pour but de vérifier quelques unes des con- clusions qu’on pouvait tirer & Maxéville d’un nombre de plantes plus restreint. Indépendamment d’ailleurs des résultats mentionnés aux Tables Nos. VII et IX, toutes les tables suivantes donnent aussi un grand nombre d’indications sur la méme question de comparaison. On trouvera ci-apres : (1) La Table No. VII des mensurations, et le résumé des variations. (2) La Table No. VIII des fréquences, tirées de la Table No. VIL. (3) Les graphiques exprimant les résultats de la Table No. VIII. Voyez Figs. 7, 12, et 13 4 18, p. 454. (4) La Table No. IX et les graphiques qui s’y rapportent (Messein). Voyez Figs. 19—22, p. 455. (5) Les variations comparées des fleurs brévistylées et brévistémonées. (6) Des documents sur la fréquence relative des deux types et sur leur floraison comparée, avec statistiques et graphiques. 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Résumant les fréquences de dimensions obtenues avec les plantes du Table VII. Figs. 13--18. Longueur du_ | Distance du stig- | Distance entre le | p; _, | Hauteur des éta- sipie | mateau bord du | bout delantitre mateaTanthere dela base dele | calico Longueur ie g Pa 8 = 3 a 3 n 3 n 3 millimetres 2 E is E = E 2 E 2 E 2 § a) g a 2 a 2 ca) a 2 a) 2 aa ia) a ~Q ia) ia) +3 —}/—-f;,—|;-—}]-]—]- —}|—|-—- one =— = =e — = = _— =—— — a —— —, ie ee ee es ae ees nn een ee pee +14 — 1 — — — — 7 = 4)|| 4 Pe 1 =e +4 1 2 — == = = = —_— — 0 =a) ee ee! 6 =) n a ee Bee ie 3 fb i. ee | a I oe lt eee pee ie 30 oo) i |) Se ee th 4) =e 8 2 = 3 ee ne a | 8 | 2 er en 3 aD Tes 1 =| Ss 2h |e 4 2 = 3 yi 3 | = 1 1 = 5 1 = 33 pa eae ee ee 3 1 3 3 —) i v an ee 3 ge 1 5 3 = pr es) ee 3 eS 5 3 4 = = altho 5 We Se) ee 6 | a | ee 5k Bey | ge 1 = 2 = 2 — | a 6 Ll 4 a i) gee 3 1 4 = i 64 = |= 5 a 2 okt | |, sees 7 Woes 3 Sie 1 eS 1 ==/ || 10") 2 7 ra el ee a eee wT 5 1. 8 ee te 1 Se ieee ee meet ee sR 2 || ans 8h Se ee | eee renee ee 1 — |e) ae 9 = 2 1 ee ee ee ee ale | 9 ee 2 = | feema|| eee ee | tee|eee 2 ys |) 10 = 6 als ares, heen eee eee i || 103 as 1 ed Bee Pl eee ul ees ee fees 3 = 1 = 11 = 3 =s i), & me 2 whe 2 = 114 = 7 ce | eee | Meee eo ye 3 |) ea 12 | ga ee ee ee 1 2 124 = 1 a ee ean ene ey eh ane 4 3 13 = 1 a ee ens ene er te) 4 13} a nn eis em ee ny ee eres S| 2 3 14 Ne a ae 7 4 Ur a ne ee ey ee ee eh ee 2 1 15 cd ce eed ae Ue aE a eee eee | et 3 rr a a i ee ea en se 1 16 oe rem ewe | ea ee er | a ace fe 2 16% — aa ee eee 2 419 EDMOND GAIN l dee |—l2\r1le!eletletictioti¢|/s|+ I a sag[Aystaoag 1d og -- | I I 2|6|9|IL| Ft] es/s8t| se] 6. | It] 42) e¢|t}1/—l|—}] 1] — | °° segucurpystagag or | ¥6 6 |4s| 9 |f2] 2 i9| 9 fo| ¢ |@| 1 i9| ¢ | 41 2 | 7 lo & r |e & \4e| ¢ |4e| 7+ ‘aolyvo Np pdoq nv ozvUISIS np sourysIT Tesh || eee lf Coe eed GOG el mOl Sol aed Sopp Aqstagag dost} —|—]|]—]| t]1] ti]el] 4 iet}asiet|os|st|/s |e |t | tl—|tl—l|—|-° sepuomeystasag = oo = = = ee a or | ¥6 | 6 is | 8 e114] §9 9 | ¥ oli] t ts | ¢ | te] a |ar| ir am) ‘QIAYJUB] BV oyvUsyys Np sourqsiqy deg |-| —-}|-} -]-}| -}-] -}]-} -]-] -}-]-]-|]-/-|-1/-|-|/¢lozltwloti9}] 1 l-le soaphqstagag dom) -| -}-| -|]-| -—|¢]-|61] tr ]32] of jge!et} it] e}4) -—|-| 1 /-|-—|-—|-|-|—-|-|-" sepuoutystasag oT fer| er rr| t fer | er Ser | 6T grr |r| For| or 56 | 6 is|s SalL fo |0 &e| ¢ Jer |r| fe |e ‘a[A4qs up anonsuo'T wdeg | -]-|] -]-] 3 le | & lat] ot {atl st jor] 2] el] ria] titi—-ilele sap[Aqstagag. opt} — |r| ti} tl ¢ fet] 9 lot] et {ts} zt }is| 6 }6] 2/1] t | ti —|-| sepaowmeystasag {gr| sr jar ar gor | 9 tor |or| tr] 1 fer | sr SeT | 6T grr| rz for | or| ¥6 6 | THM Ue STOISUOTAI ‘aol[vo Np sejo} anayneyy (006 ep snjd op eiquiou ne suonmeimsueut seo eutnsaa nb saouanhauf sap nva7qn2 2 JUSWIITNES STVUL ‘SagT[IeJap sUOYDUNsUaWw sap NneReTqQe} oT Tor sed suUOTUOP oU snou IJes9IqQe Inog) ‘SZ—GL ‘SOLA “SOGT “wmassayy—syvurofo “gq XI FIAVL ‘| of WwW 420 TABLE X. Etude biométrique sur la Pulmonaire officinale Variations comparées des plantes brévistylées et brévistemonées (Maxéville et Messein). Maxéville 1903 (Résumé du Tableau VIII) Messein 1903 (Résumé du Tableau IX) * Nous n’avons pas mesuré les dimensions des corolles. Catégories Brévistylé er : Brévistémonées révistylées | Brévistémonées | Brévistylées 25 plantes 25 plantes 95 plantes Bead eh 1D plantes anthéres styles anthéres styles styles ou anthéres ex- sertes du calice 24 p. 100 8 p. 100 — 9 p. 100 Proportion styles ouanthéres égaux centésimale de au calice 24 sy Cle; — Sirs) | styles ou anthéres in- clus dans le calice .. DOM 84S, — 83, Hauteur du calice* (chiffres extrémes) millimétres millimétres | millimétres|} millimétres enregistrés avec 25 échantillons 1034 16 12 a 163 10 a 163 10418 | Hauteur du stigmate au-dessus de la base du calice~ 6—94 11—15 53—8 83—15 Longueur du style au- -dessus de Povaire 4—"$ 9—13 35—6 6$—13 Hauteur du pistil au-dessus de la base du calice 6—93 11—15 — = Distance du stigmate au a bord du calice B=) +14 -3 33—9$ +35 4 — 63 Hauteur du haut des étamines au-dessus de la base du calice 103—14 73— aa = Distance du stigmate a Vanthdre 1—6 3—7 — — | Nombre des fleurs par inflorescences ... 3a11 1415 2a5 14 84 Nombre moyen de fleurs par inflores- cences ... ee moyenne 7, 1 | moyenne 6, 9 Nombre de fleurs par individu : 6A21 7 a 24 Nombre de fleurs pour 1000 individus 13554 13573 Nombre moyen de fleurs par individu 138, 55 13, 57 Elles sont d’ailleurs aussi trés variables quant a la hauteur du tube de la corolle et quant aux dimensions des lames des pétales. Epmonp GAIN 421 TABLE XI. 5 Comparaison entre les plantes de Mazéville (Table VIII.) et celles de Messein 1903 (Table IX.). Brévistémonées Brévistylées Caractére Maxéville Messein Maxéville Messein Moyenne o Moyenne o Moyenne o Moyenne o Longueur du style... ve ... | 10°82 |1°057|) 10°29 | 1142 5°36 | 0°742 5:03 | 0°499 Distance du stigmate 4 l’anthtre ... 4°82 | 1:028 4°85 | 1°195 3°20 | 1°394 3°48 | 1:437 Distance du stigmate au bord du calice ne seis oe wie 1°30 | 0°707 1°58 | 1°472 5°94 | 1°424 6°68 } 1°158 Hauteur du calice .... te ... | 14:00 | 1:°349| 13°90 | 1°465| 13°30 | 1°377] 13°73 | 1°370 Hauteur des étamines au-dessus de la corolle ... — soe ee 7:00 | 0:490 = = 11°56 | 0°993 — _- Distance entre le haut de Panthére et le haut du calice ... a soo || = lye} || 1eeiilZ! =— — —0°62 | 1°545 — — Chez les plantes brévistémonées il y a une ressemblance remarquable du type, dans les deux localités de Messein et Maxéville. Messein Maxéville 83 par 100 84 par 100 de styles inclus 8 “ 8 ri de styles affleurant au bord du calice 9 c 8 ” de styles exsertes. S’on représente par J la longueur du style (Fig. 4), et par d la distance du stigmate au bord du calice, il existe trois types de plantes qui réalisent les rapports de longueur suivants: 1>d, l=d, ld. | 12 a oe es) 422 Etude biométrique sur la Pulmonaire officinale En ce qui concerne la situation des anthéres voici ce qu’on observe 4 Maxéville: 24 p. 100 d’anthéres dépassent le calice. Calice a croissance limitée (trés fréquent) ou corolle & croissance exagérée (plus rare). 24 FP Ee effleurent le haut du calice. 52 ; " sont incluses dans le calice. Pour compléter la comparaison des plantes brévistylées et des plantes brévi- stémonées voici quelques chiffres: (a) sur leur fréquence relative, (6) sur leur floraison dans deux autres localités présentant une différence dans la nature du sol. a. Fréquence du type (p. 1000 plantes brévistylées) : A Malzéville A Essey sur calcaire jurassique sur le Lias (moyenne 4 prises d’échantillons) (1 prise d’échantillon) Plantes brévistylées 1000 1000 Plantes brévistémonées 936 767 Les plantes brévistylées paraissent donc plus nombreuses d’environ 74 44. A Nancy il en serait de méme pour Primula grandiflora. (D’aprés une de nos statistiques inédites.) Mais ce calcul présente une certaine incertitude puisqu’il est basé sur les observations d’une seule année. b. Floraison des Pulmonaires. Nombre des grappes florales par plante (par 100 plantes observées). Catégories de plantes | 1 grappe | 2 grappes | 3 grappes Nombre total de grappes Brévistémonées... 3 92 5 202 Brévistylées ise 18 77 5 187 Nombre de fleurs par grappes des divers ordres (par 1000 plantes). Chiffres calculés avec 40 & 50 plantes seulement de chaque type. Totaux Inflorescences ayant un : g Tae Ge Heine Ge 1\|2\)3) 4) 651] 6) 7 8 | 9 |10| 11 |12\13)| 14) 15| 16 Inflorescence | Fleurs pour par 1000 plantes | 1000 plantes Feat eee ees dest — —| 55 138) 193] 416/610) 138] 249 | 57 110 = 1966 | 13578 plantes brévistémonées | Nombre des grappes be 91 | 22|—| 91 182 320 | 523 | 136 | 182] 91) 136/68|22|—|22)/—| 1886 13554 brévistylées | Nombre de fleurs de la grappe terminale (par 1000 plantes). Nombre des fleurs Be 5 6 Vey oalo Sion aia eres 1s Nombre moyen par grappe terminale Nombre des plantes brévistémonées | — |} — | 55 | 361/388] 55 | 55] 53 | 33 | — | — Nombre des plantes brévistylées ... | —| 22 | 68 | 204] 408} 44 | 113] 47 | 28 | 44 | 2 EpMonD GAIN 423 Les trois tableaux précédents montrent bien qu’il ne semble pas y avoir entre les deux types d’autres particularités que celle-ci : Les plantes brévistémonées donnent un plus grand nombre d’inflorescences que les brévistylées et le nombre des fleurs n’est pas tres différent dans les deux cas. Mais cette conclusion est-elle générale? Nous avons cru devoir faire une autre statistique relative au nombre des fleurs afin de voir si la conclusion différente obtenue par Hildebrand ne se trouvait jamais justifiée. Voici la table de fréquence et le graphique, Fig. 5, relatif & une prise de 33 pieds, isolés de 3 métres, récoltés & Maxéville en 1903. (Plantes du 4° lot, Table XII.) )/ Lh aa ees ae eee ee aN Nombre des individus. (de) Tne Sena eayi Beene NGEE CECUANE NORGE ERR CP RPRCEL OEE TN 20 Nombre de fleurs par plante. Fic. 5. Nombre de fleurs par plante. Brévistylées M=Nombre moyen pour les Brévistémonées. Brévistémonées - - - - - M’= 53 ae i Brévistylées. Nombre des fleurs par individu. Nombre des fleurs 213|415/617|8|9}10)11)| 12 14) 15) 16) 17 | 18 | 19 Nombre | Nombre total moyen Nombre des individus 33 plantes brévistémonées |—|-|/2}-|1/-/-|5|/6 6,4]-|2)3])1)2/;1}]- 374 11:3 % brevistylées -22 JS |= |= || 2) 1) 0) a) ribo 7416) 6) 3) 2) — 452 13°7 Ce résultat pourrait sembler confirmer celui qu’a obtenu Hildebrand avec 10 plantes seulement de chaque sorte. Il ya environ 20°/, de fleurs en plus chez les Brévistylées récoltées dans cette localité des environs de Nancy. (Hildebrand avait trouvé 29 °/, pour celles qu’il avait observées en Allemagne.) D’autre part, dans une localité voisine de celle qui nous venons d’étudier, & Maxéville méme, nous avions trouvé un résultat tres différent; 13°5 fleurs par plante, pour chacun des deux types brévistylés et brévistémonés. (Voyez Fig. 7, et page 422: 13554 fleurs brévistylées et 13573 fleurs brévistémonées pour 1000 plantes de chaque sorte.) Nous pensons done qu'il n’y a pas leu d’admettre, comme une régle, que les plantes brévistylées sont plus riches en fleurs que les plantes brévistémonées. Il est comme on le voit possible de trouver des localités ou il en est tout autre- ment. D/ailleurs nous avons démontré plus haut que le nombre des fleurs dépend 424 Etude biométrique sur la Pulmonaire officinale en partie de la vigueur des plantes, puisque chez les plantes brévistémonées de grande taille le nombre moyen de fleurs par pied peut passer de 13°6 & 15°12, et méme plus, lorsqu’on s’adresse successivement & des plantes de taille de plus en plus grande. Définitivement nous concluons done tout autrement que ne I’a fait Hildebrand. Cet auteur ne disposait que d’un trop petit nombre d’échantillons, et ses conclusions ne pouvaient étre que tres approximatives avec 10 plantes seulement de chaque sorte. I] admettait donc, a tort croyons-nous, et avec lui Darwin aussi, que l’hétérostylie donne deux types d’inégale floraison et que les plantes brévistylées produisent plus de fleurs. Pour nous il n’en est rien: Les deux types brévistylés et brévistémonés pro- duisent, dans la région de Nancy, un nombre de fleurs variable, en rapport avec les conditions de végétation, mars non dépendant de Vhétérostylie. Le chiffre moyen est de 13 a 14 fleurs par plante et nous nous demandons comment Hildebrand a pu donner un chiffre moyen de 289 pour les Brévistémonées et 38°7 pour les Brévistylées. S’il n’y a pas d’erreur d’impression dans le mémoire, cet auteur aurait étudié un type de Pulmonaire officinale tres différent pour la floraison de celui qui se trouve en Lorraine. III. ETUDE COMPARKE DES PLANTES RECOLTKES DEUX ANNEES DE SUITE, A 5 REPRISES DIFFERENTES, DANS DES LOCALITES VOISINES (MAXEVILLE), ANNEES 1902 ET 1903. | En 19038, les 4 lots comprenaient au total 238 plantes de chaque sorte, ce qui correspond & 1904 mesures différentes. Nous avons pensé qu'il n’était pas urgent de donner un tableau général des 1904 mesures; comme nous l’avons fait précédemment pour la récolte de Messein, nous donnons seulement les tableaux de fréquence qui résument ces mesures. Néanmoins il nous a paru intéressant de donner les graphiques correspondant a chacun des lots, avant de donner les graphiques qui sont tracés avec les chiffres totaux. En 1902 le lot unique comprend 138 plantes brévistémonées et 35 brévistylées; leurs mesures ont été données. On trouvera done ci-apres : A. Table XII résumant les fréquences pour chacun des 4 lots de 100, 80, 25, 33 plantes; et donnant les nombres totaux pour l’ensemble des 238 plantes récoltées & Maxéville en 1903. B. Graphiques des lots 1, 2,3, 4. Voyez Figs. 283—36 et 183—18. C. Graphiques exprimant les résultats pour ensemble des 4 lots précédents (1903). Voyez Figs. 53—56. D. Tables XIII et XIV c, des mensurations de 138 plantes brévistémonées et des 35 plantes brévistylées récoltées en 1902 dans le méme endroit. E. Tables XIVa et XIVb de comparaison des plantes de 1902 et 1903. F. Graphiques donnant la comparaison des plantes de 1902 et 1908. Voyez Figs. 61—63 et Figs. 53 —56. sequel [ier | er jist | er | zr] ar | for or | %er| sr | 4! rr | ter! er | Ser | SEG [8407 9G UO NT | && a a av x | « ae s O8 - oc at OOT "** SOOTAYSTADIG “OT rol SOJULT SOIJOULTIIUL OP 9LGUIO NT - ——_ — — —<—<—______ —<—_—_—__—_______ mai — [ | 8&6 —_ | | & | 9 | GL | ST | 96 | 96 | 79 | GE | 96 | FL] F [%40} 91g ULO NT | a a eal Get re eg: Gera Mae | st ae 2) GS Sots Weak ie Lele Fist en M ey lage 9 = ees 08 ee ieee ee ee kG. 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U10 NT "SE ‘SL ‘83 ‘GS ‘SBI ‘ooITeo Np 9[ejo} IMeyneTY ‘saurs1oa $991970907 “(E0GT) saquavafip sasiud % ‘aqpaan py TIX ATAVL Biometrika 11 Etude biométrique sur la Pul le Una re office MONA 6 2 soqueyd | 9 [2404 VIG TION 66 6c (73 (73 (73 (73 SOIYQUAL [TUL Op IC UTHIO jy Ge 08 Oot soqur[ ToL Or 6 f. aA mic 3 89 al) w» if GY | 48 qin é mia ~ a ai So9TAIstAdIg “4OT sol ‘73 6 (73 aG ‘ce IT ‘Te ‘9g ‘SSI ‘ool[vo Np psoq ne ozyeUIsyYs Np souRAsSIC, (= 1 | | kOS | (al i ll | il | I 8 | GI | G | GE | GS | OF | FE} 9LT | 8} 4 6 |— 2 2 rs | | | “ «“ (He I I SAS 9 y 9 € T - i - aV GG = |, ea ae € GIS GREG: it |) ts Ly = . a€ 08 Lf Sse sal cd a Ver) Sag oD se Gam an Aap ae ce es = (3G oo. |- }e}/¢ |8 |6 | 0s/ et |et| 6 [9] % | T|—]o" septdastaptg “907 x1 souygie | %e|e|%12\%9| 9 | ie] ¢ |r| 7 | fe] | fe )@ | tr | 7 & | soaqourr[rut op a1qutoN BEG Se aC) Sal Sh AL SG RSs IS 6G iG HG G el Les [¥}0} 94q WO NT SS 2 el —|—1—| tT leje |—|s8 |e |e |r 11 : t® i ue Ce de ee eee eee ‘i “ f a | ican |e OTL 2 Go| ees G 8 | 41} 61 |Z 6 | G| G 1S | Sst | aaa | anes ae Sf ee 1 Ob gs) 06) GE 1S | SS 2 af SopmoutogstAgrey 407 sai, soqUuryg of | Y SOAJOULI[[LUL Op BIG UIO N FE ‘PL “6 ‘Gg “SSL ‘(panuyuoo)— TTX ATAVL ‘aA1QYJUB] BV OVVUISYS Np sourqsi(] Epmonp GAIN Mawxéville, 1903. Longueur relative du style par rapport au calice (Brévistémonées). Proportion par cent. De styles | De styles égaux | De styles inclus au calice exsertes 1° lot (lot total 100) 70 14 15 2 lot (lot total 80) ee 71 115} 14 3° Jot (25 plantes, parmi 120 84 8 8 4¢ lot (100 pieds isolés de 3™) 75 10 15 Moyennes des 4 chiftres 75 12 13 Longueur du style par rapport au calice (Brévistylées). Proportion par Longueur du style plus grande | que la distance au bord du calice l>d Eeale 4 la distance Lo Longueur du style plus petite que la distance au bord du calice hea) 1 lot 17 par 100 | 13 par 100 70 par 100 2¢ lot 10 5 13 os 76 5) Soloten ye ee S00 te 68, 4° lot (pieds isolés de 3™) 36 % 15 " 49 43 SS SSS Moyennes des 4 chiffres 24 10 66 427 cent. 428 Htude biométrique sur la Pulmonaire officinale TABLE XIII. Mazxéville (1902). Plantes brévistémonées (138 plantes). Brévistylées Brévistémonées (138 plantes) (35 plantes) | | | uo) 5 < sEo | | | 5 2 38 se | 32 | 328 | | = | gs | S8s Soto esse Be) 84 | 984 ee | Bo | 805 L H || a H D L H D set | ee | Bee = 35 A fas] 5 el 10 15 | -3 || 9 | 14 | -38 11 14} -I, | 5 Ge hs 7 Os 113 | 142 | -1 91 | 134 | -2 10 13 -1 5 16.) 9 15) =e 10 (see 9 | 115) -} 12h_| 15 -} 5 IB 3 WAP Ih 102 | 1344) —1 92 | 14 | -22 || 11 12 +1 4x | 14 ery li |} — 11 15. || =o 112 | 144] -1 10} 13 -} 5 123 | 54 15) | 234 9 1221) 1g) Or stele 11 124 +3 5 150s eal geal 10 13 | -1 || 10s} 138 | -3 12 16 -2 Wy als. 8) Te © Pe) aio IB FSi 113 | 16 | —22 || 12 15 al | iz |G 14] --2 10 13 | -1 103 | 18 | —3 10 14 —2 be |) osaiens 17 | ~3 12 fee les 13 | -2 11 15 —1 ZN ee | 14 TBS Paige® | = ik 15) =s 10 133 —4 Pe alees |G Teese it a 12 16 | -2 10 13 =a 5 AG ey, 133 | — 10 sealer he 9 132 | —14 || 10 14 =3 FE EY LG 13 | -1 93] 15 | -32 |] 12 16 | — 10} 114 +1 5 133 | 62 13 | —21 || 10 IB |) =i HOT cigs | 93 13 =F 5 1A ae a al 95 | 114 10° | 13°) =1 108 | 122 = 5 Bye 14 | -3 12 17 | +8 11 13° = 11 123 +4 ® | sy | G 13 | -1 ML) rise 9 13 | -2 9} 13 —2 ie Pe 144 | —14 |] 103] 14 | -14]} 112 | 142] -1 81 12 -1 | 5 1447 14 Qi || 12h | 142 | — Oy 8} 103 | 17 —-41 | 5 | 1292] 52 13) A ae eer el 133 | -3 uh 13 -1 6 154 | 7 2 9 | 122 | -1¢ |] 10 | 43 | -1 9 13 -2 qo | i | 6 TS | ia 13 | — 11 129) 9 13 -2 Ai 12 |G 112 | +2 11 ita 2) 12 132 | +2 93 | 134 =5 be | 1844/96 12 | +1 9 17% |-—22 || 10 14 | —2 10 12 = 5 134 | 63 14 | -4 || 10 14 2 10 134 | —14 |} 10% | 182 =i 4-| 132 0 74 1 1 11S | 14 es) ee eee 84 10} 5k | 132] 6 id I tee OU lee 10 ea 1is< |) 03 +4 ey 12) eal 10 | 112°] +3 12 16 | —23 8h 10 +i 6 14 6 120 | 11g | 154] -¢ 9 15 | —4 8i | 12 —-1i | 5 | 13 | 6 123 | —2 10 | 132] -18 |) ll 15 | —2 ||. 8% | 15 —44 | 42 | 15 | 82 17, | —4 11 14 | -1 11 By? 8 12 —2 6 | 142] 6% 16 | —32 93) 141] -3 9 15 | —4 10 12 sins 5 15 8 14 | =1 10$ | 138 | -$ 10 | 15 | -3 10 13 —4 5 1g) | @ 16 | -22 |] 124] 13h] +1 5A | 14 | 62 + | Amplitude de la variation. we || 88123/10817|+3 a- 43] 4—6 |12—16) 53 Epmonp GAIN Chez les plantes brévistémonées il y a 76 p. 100 de styles inclus. Ta ss 10_—SC—=,, de styles exsertes. de styles égaux au calice. 429 Nous placant au point de vue des renseignements botaniques faciles a vérifier, nous donnons ci-dessous quelques unes des dimensions observées. Elles peuvent étre retenues au point de vue de la botanique descriptive et comparative des Pulmonaires de stations différentes. E. TABLE XIVa. Comparaisons des plantes de 1902, et des plantes de 1903, @une méme localité (Maxéville). Maxéville Année 1902 Année 1903 Brévistémonées | Brévistémonées (1902) (1903) styles exsertes du calice 10 par 100 13 par 100 Proportion centésimale’ ,, égaux au calice eC; ie oc || WE 12, inclus dans le calice Ba LS Too ss ” chiftres extrémes enregistrés sur les échontillons observés ... Hauteur du calice 10417 mm. 10 4 19 mm. chiffre de grande fréquence : 132) 5 13 ou 14 ,, Hauteur du stigmate au-dessus de la base du calice ... » 9 10415 ,, : : Pee ; (chiffres extrémes observés 8—123 ,, 8—13 ,, Longueur du style au-dessus de l’ovaire ichiffre de grande fréquence i 10. : On re ._\chiffres extrémes +3a-44,, +28 —-4,, Distance du stigmate au bord du calice } ichiffre de grande fréquence es ae 2 1Ao ote ee 5 _, jchiffres extrémes ‘observés - 2—7t ,, Distance du stigmate & l’anthére chiffre de grande fréquence \ i 44 ou5, Brévistylées Brévistylées (1902) (1903) + — chiffres extrémes observés chiffre de grande fréquence ie Hauteur du stigmate au-dessus de la base du calice ... ; chiffres extrémes observés chiftre de grande fréquence chiffres extrémes observés chiffre de grande fréquence chiffres extrémes observés chiffre de grande fréquence Hauteur du calice Longueur du style au-dessus de l’ovaire Distance du stigmate au bord du calice Distance du stigmate & ’anthtre 124 16mm. We }) ” 82 4 173 mm. 14 ” 5AgL 3—7$ ” 5 ” ON= MG =o ” Lh7 5, L 430 Etude biométrique sur la Pulmonaire officinale Les chiffres ci-dessous offrent un intérét plus considérable au point de vue de étude mathématique de la variation : TABLE XIVb. Masxéville 1902 et 1903. Brévistémonées Brévistylées 1902 1903 1902 1903 | Moyen o Moyen o |Moyen o Moyen| o Hauteur totale du calice ... tee ...| 13°62 | 1°369 | 13°12) 1°377 | 13°87 | 0-897 | 13-04 | 1:474 Hauteur du style .., 3 ... | 10°37 | 1°029| 10°21 | 1:081} 5:07) 0°549) 4-99 | 0°700 Distance du stigmate & Vanthare: “6 — — — 3°84 | 1-070 Distance du stigmate au bord de la calice —1:26 | 1°305 | —0°92 | 1:159 | 6°80 | 0°920} 6:05 | 1°439 F. P. officinalis, Mawéville, 1902. Table XIV c. obtenw avec les chiffres mentionnés & la Table XITI. Hauteur totale du calice. Fig. 63. Dimensions en el 9 | 94 ae 124 13} ae 15 | 154 16| 163 17 \ 17% 18 | 183] 1 Plantes Brévistémonées .. 1| 5 |13| 6 |32] 19 Wik) lf &) 4 =e — |—| 138 Brévistylées — —|—j|1) 2) 6| 6 bs DN s4e2e4y 2 — |— 35 Longueur du style. Fig. 62. cael 3 33 4 | 44] 5 | 53] 6 63 7 \72| 8 83 | 104 Ue 12 | 124| 13 | 134 Plantes Brévistémonées ... | — | || 9.5 1810) 3 | aeulrosa lias ai) ae 188 Brévistylées —|4]2 55 | —|—|—]}]—|—]|— —|—|— Distance du stigmate au bord du calice. Fig. 61. F | Dimensions en mm. +33) 24/2\ 14 1|+3 iS —1) 14] 2 | 23\3| 33 4|4g|s 54| 6 | 64 7|7 8 sy 9 93 | Plantes Brévistémonées ... | — EE 115i) 8 rats 0 31 12/98) 7161246) 2) l=) soi) eae = | 138 Brévistylées PS SPST SLE VES 22) 212) 252) 2 ieee a) ol ae 35 Chez les plantes brévistémonées il y a 76 par 100 de styles inclus. 14 , de styles égaux au calice. 10 55 de styles exsertes. EpMonD GAIN 431 Conclusions relatives a& la fiaité du type pendant deux années successives. On voit en comparant les graphiques (Figs. 58—56 et Figs. 61—63) que les résultats sont tres semblables pour les deux années 1902 et 1903: C’est ainsi que le maximum de fréquence de la longueur des deux styles est sur les chiffres 5 et 10 dans les deux cas, et malgré le nombre faible des observations faites. La position relative des deux courbes pour la distance du stigmate & l’anthére est la méme en 1902 pour tous les lots. I] en est de méme pour la position des 2 maxima de fréquence de la distance du stigmate au bord du calice: ils sont en 1902 et 1993 sur — 1 chez les Brévisté- monées et + 6 chez les Brévistylées. Le maximum des fréquences de la hauteur du calice est aussi dans tous les cas aux environs de 13 a 14. On voit done que Tinfluence du climat de Vannée ne semble pas modifier les capacités de croissance des diverses parties de la fleur hétérostylée. IV. ETUDE COMPARKE DES PLANTES DE QUATRE STATIONS DIFFERENTES DES ENVIRONS DE NANCY. Nous avons récolté des plautes espacées de 3 metres environ, afin de ne mesurer que des pieds issus de graines différentes. Le nombre des plantes mesurées a été de 25 au moins pour chacune des stations de Laxou, Malzéville, Maxéville, Messein. Voici la série des documents mentionnés ci-apres : G. Tables XV, XVI, XVII, XVIII, donnant les mensurations des plantes de chacune des quatre localités. H. Tables XIX, XX, XXI, XXII. Fréquences relatives des diverses longueurs étudiées. I. Tables XXIII a et XXIII B. Variabilité comparative dans les quatre stations. J. Schémas représentant les types extrémes ou caractéristiques de chaque station. Voyez p. 451. K. Graphiques comparés, relatifs aux Tables XIX, XX, XXI, XXII. Voyez Figs. 37—48, Figs. 49—52, et Figs. 57—60, pp. 457—S. L. Des documents précédents nous pouvons conclure ensuite sur Les caractéres généraux des races géographiques observées, Les types moyens théoriques calculés, La variabilité et la fixité de l’hétérostylie chez la Pulmonaire. 432 Htude biometrique sur la Pulmonaire officinale G. TABLEAUX DES MENSURATIONS DES PLANTES DE QUATRE LOCALITES DIFFERENTES. Les pieds récoltés étaient situés & 3 metres de distance au moins. TABLE XV. Pulmonaires récoltées d& Laxou. (Année 1908.) Valeurs en millimétres. Brévistylées Brévistémonées 2 2 3 2 2 2. | 308 2 a] ge) 2 | 88 |ges\55| a, | e222] Be |.2 1282) saa a3 | 32 | 8 | se le¢q| ce) 28 | 28 || 2. g2 | 8 |Se8| ge 0] Se (lege S| ed] & | 92 [s88| 88| #8 | gel 3] 58 | = [eae] gf | #8 | ge g/ gg | g | #2 |ges| Be) 3 as | ¢| ge | 8 |see| BS | 3 a8 Ziel izie 3 B32 |e | sé s $2 || 2 Zz" | B |eSS| 8s 3 ie cece ae Elie olbe = a ) @ [ABE] A aS | 1; — 12 10 31h | 4} 15 81 || 1 | 73 | 23 8 133 —33 heel ih 9 Baul, oe RSP el) Vee eles 8h | 14% -4 Cele perues 9: | 3. | 42) 165 Pe = 7 | 4¢ | Of Ne i4s -3 4| 4 105 Si | Qh | 4 13 i 4 — 7% | 3 Bt 13$ -3 5 |10-14} 14 19" 1°35 Nee 16} 92 || 5 — | 7 3h 8h 133 —: 6), — 12 10 31] 42 141 8 6 |\2bis&7| 8 13 74 143 —5 7) = 105 8h | at] 4 12 6 7 ~ if 4 9 135 ~ 23 8} — 12 10 ee! 12 6 8 64 | 33 8 143 — 43 ON SS 91 | 32] 4 123 62 || 9 6 | 45] 9 14 —3 10| — 113 OL | 211° 5 13h | 6h ||} 10; — 6 | 3] 8s 14 —3} | — | Ww 10 Bye | aes) 16 9 || 12 64 | 3h] 8 12 -2 12| — 103 gh | ah] 4 13 7 |i? |» — Te es 9 13 —2 13| — | 103 84 | Qh] 4 13 7 || 13} — 6s | 43] 9 135 —23 U 113 OF 5) BB | ea ails 8h || 14} 2-138 | 6§] 3 7% | 105 -1 To) —— | 1 9 allie 14 7 || 15 8 6 | 6.) 0 15 ~ 16} — 11 9 23 | 4} 14 74 || 16 — 8 2 8 143 -— 43 i7| 9 113 OR 12.1 eG: ey re Soileee | 8 || 2 8 14 — 43 18 113 OF Pugh | 4 14 oe TES a 4 9 13 =2 19| — 11 9 | 22) 43 13 61 || 19 — 7| 4 93 143 —3 20; — 113 93 | 3 | 44] 13 63 || 20; — He ee 9 14 —3 21| — 11 9 12 5 16 9 || 21 — 7 34 84 14 —~3} 22 | 11 9 1d |= 13 BE || 225) 73 | 3 8k 123 =2) 23 |) == 11 9 Q | 5 12 ES UEeas Nh We 7 | 4k) OL ies -y 24) 3 iis 11 3 | 6 15 7 || 2 a 8 | 3$| 9s | 18 -h 25 124 | 102 | 32] 5 143 (ea 2 re ae 9 144 —3} : if 26 — 7s | 44). ~9 13 —2 ar 1 7 | 5 103 | 13% =i 28)|" Ad 7% | 34] 9 17 —6 29 7 | 3e | Se alls ~ 2 L0)e |e 6h | 5 93 135 —9 31 = 7% | 38 8% | 14 —3} Valeurs | 491-14] 81-19| 13-5 | 4-6 |112-161| 5-9 Valeurs | 628 | 13-6) 73-104 (10; "aoe extrémes 2 aa ed 4 7 22! aes extrémes 2 aoe EpmMonp GAIN 433 TABLE XVI. Pulmonaires récoltées a Maizéville. (Année 1903.) Les pieds récoltés étaient situés & 3 métres de distance au moins dans une station regardant le midi. Longueurs exprimées en millimétres. Brévistylées Brévistémonées P 2 | 82 |3e | 28] 5 | Se ¢ | gee] r — s Aa g 25 (28 Be | t a2 g ae = Sieh | le Z 23 a ge 3 =) Boe) a2 2 aa S vat 3 Besa aS 2 as a ae 5 i 22d Bo 3 38 3 ed 3 aes 39 3 38 & | 32 & seo |Sael'Sa | SS) fei) & | se bo | ese | ee 82 ge g $8 s so |Tok| SE] Le | ta g | os 3 cep | Be is 3 3 | 38 » | g@ |8a5| 82| 38 | gk il os | od » -|-838 | 8s gS 25 oe aed Z 22 ago tot es ae a ste 2 a23 pe 8 z8 2 oF 3 Sa 3 io as 3 a iS o8 m=) Ss An ae 5 a Rea Ie a ij=He |e | Se] ag | Bei a| a" | 8 | Bee) 8° | 25 Boles = 2 3 A || Ree A 1) — 12 10 | 3$] 42] 11 44 || 2} — | 6% | 43 9 14 —3 Ds 13 11 4 5 13 6 2) — | 6b | 54 10 12 = Sue, 19 12 10 2 6 14 | 6 52 |= 7% | 4 93 13 =14 El ie) 0 4 5 13 6 4/ — 7% | 5 103 14 ~—14 5| — 13 11 4 5 13 6 ne 7 5 10 124 -4 Gy 11g | 9%] 3 44] 114] 5 6| — | 6b | 3% 8 12 -2 7) — 12 10 33] 42} 11g] 5 ely 7 6 11 il5} — G | 12 10 3h]; 46] 12 | 5k i] 8] — 74 5s 11 144 —14 9 |20—80) 123] lod| 48) 4 | 15 9 || 9] — 7% | 4 10 14 2 10; — 13 isl Saale Te S21 200 6k | 5 93 12 =f ial || a= 11 9 g2 | At 8 | 12/12] 18 6 34 74 103 =i 135) 114 93 | 3h | 4 | 10 4 ||i2| — 74 4 gt 124 —1 ifs} || pees 124 | 10) 3$/ 5 | 4 3| 29 | 63 43 9 104 +4 | — 114 9s | 2 | 5k] 13 6s | 14) — 8h 34 10 12 = | 11g} 98] 3 | 48] UE] 5 |} ze; — 7% | 43 10 13 —1 16; — 12 10 3 5 12 | 5 || 16| 24 6 7 11 133 -t 17 | — 12 10°) 3 5 Tor) 5 | 27 | = 7 34 8h 13 — 24 8A 25 12 10 | 2 6 12h] 44 //18| — | 63 5 9 113 = FIPS es 12 10 | 38] 48] 128] 6 |} 19; — | 6$ | 3$ 8 11$ =i} BD |) = 11 9 | 2 5 11 Ame 202 —= | 8 4 10 12 = Qs 12 LOS 5 12 5 || 21 | 97 7 44 93 143 —3 | ae 11g | 9F| 3 | 43) 1383) 7 || 22) 23 7 3 8 12 =9 23 | — 13 11 44) 44 / 128 | 6 || 23) — | TE | 4B 10 14 2 | = 13 ul 5 4 13 eel a1 4 8 12 2 25| — 123 | los | 4 44 | 12 5 || 25 | — 7 6 11 123 aE Valeurs | : Valeurs 1 So ilisa Tene Coney extrémes | 11-18] 9-11 | 245 | 4-6 | 8-15 |13-9]| names | 8-88 | 3-7 | 7-11 | 103-143 |-38+3 Biometrika 111 55 434 (Les Htude biometrique sur la Pulmonaire officinale TABLE XVII. Pulmonaires récoltées & Maxéville. (Année 1903.) pieds récoltés étaient situés & 3 métres de distance au moins dans une station regardant le nord.) Longueurs exprimées en millimetres. Bréyistylées Brévistémonées g 2 5 2B 2 1) asia allem 2 P| ee | 3 | SS | gag (Zeeeb| 88 |e || #| gat S| gas | sa | 22) Be & | 88 iS ae | 88 |e*te4| 38 | Se | 2] sé = | o2 2) feces ae 2 |ee | & | s8 | gas lasses) 2 | 23 |i a | we | 2 | ead} Be | 2 38 ° 68 2 Se Smo |sse7 5 ao ilo Oa 2) 3 a3 da iS} RaQ 4 | 2 5 Bo | 2B |§°Re & ag || 4 4 eens | Se | 1s 28 gq j-at ja" (ee | la” | Ree eee 1| 64 11 9 3 4 94 33} 1) — 63] 5 9%) 11 +3 2} — | 1s 9} | 2% 5 13 6 | 2| — 7 | 4% 9% | 11 +4 aos 105 Si | 2 4 13 ees: | BL | 5 Bs | 12 —1} Meal 124 104 | 34 5 124 55 || 4] 50 7 3h gh 14 — 3% ‘fel ete | 9 24 44 11s | 5 || 5 7 | 3% 8% | 12 -14 6| — 12 10 3 5 13 6 || 6 |49&56| 75] 6§ | 12 14 — 7| — 12 10 24 5} 12 44 || 7] — 7 | 3% 83 | 12 —1} 8 114 93 | 25 5 12 5 gs| — 6 | 5 9 113} -3 9 12% 105 | 43 4 12} 1) 16h, 9 | 7 | 43 9% | 12% 1 10 | 52 11 94 | 33 4 13 Ta LOM. t= 6 | 4 st | 19$| —2 | — | 18 ud 4 5 14 fea ee |e 7% | 45 9 11 — 12); — | 12 10 3 5 13 6 J ||2 7 | 5s | 108 | 13 -4 13 | — | ll 9 2 5 12 re Wl 13an eB 64 | 5§ | 10 11 ar ieee 11 9 2 5 iol 4 || 4 8, | 46s) ol eae —14 15 | 51 113 93 | 1 6 14 6 || 18) — 8 | 5e |-11d | 14 -} i6| — | 11} 9% | 2 5} V4) toa) ee 7 | 4 9$ | 13 —i} 17 | 57 105 8. | 14 5 11 4 | i7| — 74 | 4% | 10 133 | —15 eS 1 9 2 5 123 | 5% || 18] 55 Ta aioe 8k | 14 —3$ 19 | — 13 11 4 5 12 5 || 19; — 63 | 53 | 10 12 — 20 | 62 12 10 2 6 144 | 63 || 20] 59 hee ee 9 15 —4 21| — | 14 12 5 5 13 6 22) — 7 | bem TOR [cid -13 22 114 9. | 3 44 Diet|) ae eee ee 7 5 10 14 -2 23 | 58 114 93 | 3} 4 3 | 7 || a) — 7) 5s | 11 13 — 2,/ — | 12 10 3 5 13 5k || 2 _ 7 | 43 93 | 133] -2 Og aa 103 ss | 1s 5 13 6 || 25} — 74 | 6 114 | 18 +3 Valeurs | 194-14] 8h-12 |14-44| 46 | 94-143] 33-7|| V@leurs | 533] 33 63|9}-19| 11-15 |-48 +1 extrémes 27 ace | ene 4 a Ba? ta = extrémes te | Sip pg elie = EpMmMonp GAIN TABLE XVIII. Pulmonaires récoltées a Messein. Les pieds récoltés étaient situés 4 3 métres au moins les uns des autres. (Année 1903.) Valeurs 435 en millimétres. Brévistylées Brévistémonées uw i FS § g | Be aa 3 el = = 223 2 2 5 3 Bo o f° | Ss8 | so] 8 BS || 3 ae 3 | Aas EE: fe ee © | 38-| = | 32 | 382) 38) #8 | 3B iS] 2] £ | sse| 3] 28 | st . s Sg ggo Ss S =) . - 5 aes 28 2 Li) = 114 93 | 23 5 Ws} 44] 2) — i 6 a 133 —4 2 3 il 4 5 13 6 | 2) — 64 | 4 84 | 104 $1 42 134 | 113] 5 4. | 12 6 2) = 6s | 6 10g | 123 JR |e 12 10 24 bE | 12h | 5 Hes 7 5 10 10 4D Cal 12 10 3e 4. | 124 | 6 |= i 4 9 11 — 6) | 123 | 103 | 33 Sean i 5 6) — 63 | 44 9 104 +43 71 — 12 10 3 5 13k | 63 ]| 7] 45 7 5 10 8 +2 &| — 11 9 2 5 11 4] &| — a 4 9 114 = Oj eee 11g] 95] 3 44 | 10h] 4 9} — Z 4 9 13 =o OE = 12 10 34 ae) Tle | 6 || 20) — 7 5 | 105 | 114 +1 ii 12 10 24 Beale Seal 2 Gall y fal) ea 7% | 6 | 11g | 18 +4 12.) — 12 10 4 ANNO ere 140 6 6 10 Hk +1 13 | 36-48] 11 9 3 4 10 7A ye Fs oa| ake 6 6 10 13 —1 Uh 12 10 24 bE | 11 Bee eae 7 34 sk | 113 =a 15 | — 11 9 a4 45] 10 34 || 15 | — 7 4 93 | 103 +1 16) — 12 10 3 5 14 rie (oe 6$ | 53 | 10 10 +2 17 113 93 | 23 5 123 | 534/17 | — 7 5} | 103 | 12 +3 18 | — 13 Ul 4 5 12 5 1s | = 64 | 53 9 143 — 33 19 123 | 103 | 34 5 m | 8 | 79| — | 7 | 4 92 | 11 +4 20 | 41 ll 9 4 6L | 124] 4 || 20} 33 8 be | 114 | 14 —i Ci) S| W2E | 10k | 22 | 6. | 13h) 53/27) — | 6 | 5f 9§ | 114 = Be 13 11 4, | 44] 135] 7 || 22| — 64 | 54 9 124 —14 23; — 133 | 114] 4$ 5 | 11k | 4] 28] -- . Ak gs | 14 —24 yee Se Hiei sae 5 134) 6025 7 4 sie 9 +20 25 114 94 | 3 44 | 11 41 |) 25 | — 7 5 10 Lie +3 26) — 12 10 33 46 | 104 | 4 | 26) — 74 | 43 9 11$ —4 27 | — ilu 9 24 46) 128] 6 | a7) — 7 | 46 | 10 145 —24 23 | — 13 11 34 be | 104 | 3 8 | — 7 3d 8$ | 104 rope AG. 1) 13 | 11 35) 5g | 15 | 73 || 29 al Ok. SP Or elo. —3 380 | — 13 1G 4 4i | 14 resi |e 63 | 44 9 ll = Sil 124 |~102 | 38 | °5 13 Cre — a 5 10 12 = BO) aa 114 93] 1 64] 11 2. 62>) 43 74 | 6 114 | 163 =3 33 | — 12 10 3 5 13 6 || 33) — 7 4 9 105 +4 Bh | es 124 | 103 | 34 5 134 | 63 || 34 |34-39| 7 3 8 12 =9 iy || 10 8 1 i 124 | 53 || 85 | — a 4h 93 94 +2 | 86) — 14 12 5 5 145) 74 || 36) — 7 Di 0 113 +3. | al 103 8h | 2 4 11 5 | 37 | — 7 6 11 114 +12 | Rus. 10-14| 8-12 | 4-5 | 4-64 | 10-15 | 24-8 pa 6-8 | 3-6 |8-114/8-16}]—-3}4+2 | 55—2 436 Htude biométrique sur la Pulmonaire officinale H. TABLEAUX DES FREQUENCES RELATIVES DES DIVERSES LONGUEURS ETUDIKES. TABLE XIX. Hauteur totale du calice. Figs. 49 a 52. Nombre de plantes présentant les diverses hauteurs. Laxou Malzéville Maxéville Messein - & a ® = 3 s 3 = a 3 | & g 8 g 2 Hauteurs > 3 es g = 3 es a en a 3 a Bo ae =a A 3s millimétres 5 a 5 A 455 g 5 ae : - | a |e) 8]e) & : aa) ia) ea) ica) Sur 25 | Sur 25+} Sur 31 | Sur 25 | Sur 25 | Sur 25 | Sur 25 | Sur 25¢) Sur 37 | Sur 25t| Sur 37 7% == = = az = a = Jes 8 = = = 1 = = = = — 1 1 84 = = == Bee 9 es = — 1 1 Is i _ _ == — 1 10 i a ae _ 3 3 2 2 104 = 1 1 = 2 = = 14 3 3 5 il 3 — 2 4 3 5 3 4 114 i a = 4 2 3 1 3 3 5 g* 12 3 1 1 4 Te 4 4 3 3 1 3 124 1 1 1 4 3 3 2 4 6* 2 2 13 6* 6 6 5* 4 9* 4 2 4 3 3 133 i 4 i 1 1 = 2 4 4 1 1 14 3 ‘D 5 1 4 2 7* 1 2 2 2 144 2 5 8* = 2 1 = a 1 1 2 15 4 1 1 1 — — 1 1 2 —_— 1 158 1 =). ee) = Se 16 ” = = fas a oe 164 1 — = — = 1 17 = 1 1 = = = a 17% = =e : = ite = 2a reat | 138 mam: 14}mm. | 13mm.) 12mm. 13mm.)14mm. 123mm. 113 mm. Type moyen (pour la station) 13? millimetres 123 millimétres 133 millimétres 12 millimétres + En ne tenant pas compte des six premiéres plantes de la série de 31 plantes brévistémonées (Laxou). { En prenant seulement les 25 premiéres plantes de la série de 37 plantes de Messein. * Astérisques, indiquant le plus fort chiffre de chaque colonne. Hauteur de létamine. Epmonp GAIN TABLE XIX bis. Figs. 37 a 40. Distance du haut de l’anthére au bas du calice. Hauteurs en millimétres Nombre de plantes présentant les diverses hauteurs Laxou Malzéville Maxéville Messein re) Brévistémonées toe CoO NVNVAADAN we ine | to~ta~re | | eae ares | | * Totaux bo or ww a Brévistylées le S _ J |e) eae | * | | | e | roroc~trexre| | * | | | rp wwonn| | | | | prowagaare | Totaux bo or bo or Oe) I 437 Moyennes (4°83) 438 Htude biométrique sur la Pulmonaire officinale TABLE XX. Hauteur du style et du stigmate au-dessus de Vovaire. Figs. 41—44. Nombre de plantes présentant les diverses tailles Longueurs en | millimétres du Laxou Malzéville | Maxéville Messein style et du stig- mate réunis Sur 25/Sur31| Sur 25 Sur 25 | Sur 25 | Sur 37 3k — — — -— -- — el 4 ge | — 3 4 2 3 2] 7 =s 10* 3 7 10 Pe 7 = 8 12* | 11* | 16* = | 53 1 = 1 4 3 5 a 6 2 — 3 2 it 1 ae res ae 2 2 4 = = as ee 1 2 1 a = 8 4 5 4 — ~ 1 sealigee 5 8 1 6* 2 3 | 9 OFF) aoe 2 3 1% VielO 8 | 9h 4 5 5 5 4 5 £ J 10 1 1 7* 4 6. ||| 10% % \ 10} 1 1 1 3 3 3 6 | 11 — = 4 1 1 2 a | 114 2 2 3 12 - 1 — — 12% — — — Laxou Malzéville Maxéville Messein Type le plus fréquent (Brévistylées 4 43 5 5 (moyenne de fréquence) {Brévistémonées 9 10 8% 10 13 143 133 15 Moyenne théorique calculée 4°64 4°74 4°94 52 4:95 ‘ % 886 877 9:52 9°72 9°74 9°70 (9-42) 439 EpMoND GAIN TABLE XXI. Figs. 45 a 48. Distance du stigmate au bord du calice. té : eaakresvanacacs | ||] ii iii} tt = SagUOULaySTAVIG = a | s Sr Whee Roce cero Viet eee a eH cm Om taller fae ie es) n Z o = 2 _ LIL IL LLL | par acmmntm acon | | | | aa sagTAystagig, = ed N ss Lt Lot Pelt | esse cs reaneieier | ea] || | nm wo 2 |soquompsupig ZF | | | [aavonte|jan| |i iii litt = n oD A a x A | segidystagag 5 VAL eS aD el isi esiestorcoxocen eos |) | Tila dl wm es a * * S| soquowmpystapig | 5 | | |nwwaviaa |] | | | | | dd id | | | +5 n N S a x 2 sop[Aqstagag s ll ITP lal | proaammman =| | mM 5 ‘ 30 x Re L111 | jamonbenoem tall il iii | SOQUOUI9STAII | i BS a % 5 Tala see -caceies ters [icon (elas tS| eat 11 4 n a septsystagig. | LT TTT LEE LT LL | [Levert op creo cre | mM =) fob) | “0 étudiés Sell eee |S aos | 2 2 ow ee x 3 sas/| 8,5 |s$H5™ B q ae iS g BS | ‘seu |a™ago|] $ 3 Ese Se a eo] Hee | 8 ee) ts. + ee eB 5B oot Bose aes) e) & | se Se | 2 | > a 2 5 5 fQ a ae ‘S ~Q a Laxou 74 | 6 | 7 14 11 10 13 144 | 17 174 Hauteur totale} Malzéville | 8 8 | 5 1 Oss | KO |) ils} 12 154} 15 du calice Maxéville | 6} | 6 | 5 1 9 103 | 13 14 15 153 Messein 95 | 6 | 93 1 94 7% | 124 | 113] 154] 17 Laxou 9 | 43] 3 4 | 10 5E | 11 7 144 | 83 Hauteur totale) Malzéville | 8 | 3 | 33 5 104 bs | 12 7 135 9° des étamines | Maxéville | 93 | 45] 35 | 43 10 5 114 7 14 | 83 Messein 8b | 34 | 3 5 103 53 | 12 7 14 85 Laxou 7413 | 4 5 34 7 4 9 64 | 103 Hauteur totale) Malzéville | 8 | 3 | 44 54 34 7 44 | 10 7 | lig du style et du | Maxéville | 9 3B 45 34 34 8 5 8h 63 | 124 stigmate Messein 8} | 33 | 4 4 35 Sly a) 9 i 12 5) Laxou 94 | 53 | 6 4 —-44 | -1 | -—7 | -3 |-10 -63 pence tos | Matséville, |105 | ft) 44) 4 | =1 | 41 | 6 | —2 |= 93 | —3f bord du calice | Maxéville | 9 45) 6 44 —-3 | +13) -6 | -145 /- 73] -4 Messein 11 63 | 63 6 -2 | +25] -6 — 8% 4 1 Laxou 5h | 4h | 5k] 1 i 1 a2] 32] sil 68 a Malzéville | 6 | 4 | 5 ie ee or ee oT Rain eet Reisathive) | Slexevilie | 6 14 | 4 24 1 By i) oe 43 5 7 Messein 63 | 53 | 4 Ly, — 23 | 3 44 | 54 63 | > Z . hi 7 Biometrika 111 56 Htude biometrique sur la Pulmonaire o le Cina 442 ——_= 02-28 | 110-1 |F1-2 | oF-ee| 2r6-0|z8-5 | ¥s-FS | 008-0 0-€ | O1-25 | 14L0 [48-3 |" cxQqqUE y oreMBQs np coueysIg 61-78 | 61E-1 |BE-9—| LG-GT | 818-0 |F9-9—| LL9S | BEET BE-G—- HL-9T | LOL-T |B’-L—| oot[vo np prog ne oyeMsys np aoueysiq LG-11 | PLS-0 |96-F | BIL | 99-0 |F6-F | OLTT| $9¢-0/28-r | 9421 | seG-0|F9.7 |" 7 a[X4s np epeq0y ameneRy Te | ¥88-0 [60-21 | 9-2 | 478-0 /89-11 | I-¢ | 129-0 21-21 | ZO-2 | 908.0 /8F-11 | “7 “7 sourureys sop e[ejo} «none py LB-TL | €88-T | LBB | €9-8 | 190-1 | FF-21 | LL-11 | BPE | OL-ZL | 6-6 | GLe-1|98-eL | 7 sorTeo Np eYe}0} aneqneHT | : Zoot} 2 | w |Zoor) 2 | w |2Zoot) » | w |Z oot) » | w 7 gupnye exqqoxe) wLEssaqy oTtanxeny omEAgz1eN noxey ‘soo[A4staorq soqurtg “q PLOT | L18-0|88-r | 91-81} 929-0927 | z9-02| ze6.0 |2e-r | 29-98 | 986-0 99-8 | 7° oaquguEy y oyemUByS up dourysIq — |@sr-t]9t-o-| — | ssz1fort-| — |6z0-t)or.t-| — | Z¢t-1 |¢6-2—| coyeo np prog ne ayes np ooueysiqd 10-6 | 18-0 |0L-6 |09-0L | T20-T/ZL-6 | 9201] F30-1/6¢-6 [SL | 89-0 /LL8 [7 7° —— opdqs np e7e703 anoqne TT 90-81 | £68-0/16-9 | es | 8F9-0/00-L |9e-8 | 29¢-0/96-9 |ZLL |GPSO TLL | 77 sourueys sop 97240} moqne yy 8¢-F1 | 64-1 9811 | F1-6 | 991-1 |F9-21 |OL-8 | OOT-T)F9-21 |ee-2 | 920-1 |LEL | * —sorTeo np ofeq0q anoyne Hy Ww Ww Ww Ww For) 2» | w |Zoor} » | w |Zoot) » | w |Zoor] » | w gipnyg axaqowavy Ulessoyy OT[TAPXBIL OTTTANZTV IL noxery “‘SOPUOUPYSTAPIG SoJURTG "WV ‘saquasafiup suoynjs augonh supp sanuaqqo sunajypa sap woswsndwog ‘€ TIXX WIdVe EpMonpD GAIN 443 TABLE XXIV. Distance du stigmate au bord du calice. | Laxou | Malzéville | Maxéville | Messein Styles inclus ... ... | 100 par 100 72 69 38 Styles égaux au calice 0 | 20 15 19 Styles ex. ... re 0 8 16 43 Le : | Longueur du style (l) relatiwement au calice (UV). U-—l=d. Sur 100 styles il y a Laxou Malzéville | Maxéville Messein ld 0 20 20 32 if Done, pour les brévistylées comme pour les brévistémonées le style a la plus aly grande capacité de croissance 4 Messein par rapport & la capacité de croissance du calice. L. CARACTERES GENERAUX DES RACES GEOGRAPHIQUES OBSERVEES. Si lon compare les polygones de fréquence obtenus avec 25 plantes d’une localité (Messein) et ceux qu’on obtient avec 37 plantes du méme lieu, on constate que les sommets et les limites latérales de ces polygones correspondent sensiblement aux mémes points de la ligne des abscisses. La méme conclusion est exacte pour les polygones obtenus 4 Maxéville avec les récoltes simultanées de 25 plantes et 100 plantes. Malgré la faiblesse relative du chiffre 25, il n’y a donc pas de causes d’erreurs suffisantes, pour nous interdire de tirer des conclusions relatives aux races géogra- phiques de la Pulmonaire des 4 localités comparées. Ces comparaisons portent sur les points suivants : 1. Hauteur totale du calice. 2. Distance du stigmate aw bord du calice. 3. Hauteur de Vétamine. 4. Distance du stigmate a& Vanthére. Si on compare soit les chiffres des Tables XXIII a et B soit les graphiques (Figs. 37—48 ; 49—52 ; 57—60) on voit tout de suite quil y a des variations assez accusées dans les quatre stations étudiées. Ce sont les plantes brévistémonées de Messein qui ont montré le calice le plus variable, avec tendance vers les petites tailles: la plus fréquente étant seulement dune longueur de 11 mill. 4. 56—2 444 Etude biométrique sur la Pulmonaire officinale Si l'on suppose que la grande capacité de croissance du calice correspond & une vigueur plus grande de la fleur on peut penser que les autres parties de la fleur seront peut-étre influencées dans le méme sens. D’autre part si la capacité de croissance du calice est faible cela peut provenir d’un arrét de développement de Yorgane. Dans cette hypothése un organe voisin, le style par exemple, pourrait bénéficier de cet arrét de développement et exagérer lui-méme sa propre capacité de croissance. Si on consulte la Table (XXIII B) on voit que, parmi les 4 types brévistylés, cest justement le type brévistylé Laxou qui a le calice du type moyen le plus grand tandis que ¢’est lui qui a le style du type moyen le plus petit. De méme, parmi les 4 types brévistémonés c’est le type brévistémoné Messein qui a sensiblement le style du type moyen le plus grand et le calice du type moyen le plus petit. Les chiffres de la Table XXIII B semblent bien démontrer ce fait d’ailleurs visible aussi sur les mensurations individuelles faites sur des centaines d’échan- tillons : La longueur du calice et la longueur du style sont deux quantités qui varient en sens inverse, aussi bien chez les fleurs brévistylées que chez les plantes brévistémonées, en passant dune race & une autre. I] était naturel de penser que cela entraine cette autre conclusion : Les types de styles les plus inclus appartiennent aux fleurs ayant les plus grands calices, et inversement les types de styles les plus exsertes appartiennent aux fleurs ayant les plus petits calices. I] en est ainsi dans beaucoup de cas, et la comparaison des types moyens est démonstrative a cet égard : Distance du stigmate au bord du calice. Pour le type de grande fréquence : | de chaque station Pour le type moyen Loealités | ae Difference Brévistylées | Brévistémonées | entre les | Brévistylées | Brévistémonées | Différence deux types | Laxou ...| —7 mill. —3 mill. 4 —7°22 — 2°95 4:27 Maxéville -6 , -1$, 4} — 5°64 -1:10 4°54 Malzéville} -6 ,, —2o0u0 4 ou 6 —5°32 —1:10 4°20 Messein...| —6_,, +4 ou 0 65 — 5°32 —0°'16 5°16 Il y a évidemment, & Laxou, tendance a la production d’une race a grand calice, a style court et trés inclus dans le calice ; tandis qu’é Messein on voit qu'il y a une tendance trés accentuée & la production d’une race a calice court et & style long exserte. Voyez Table XIV. Ceci d’ailleurs est contrélé aussi par les mensurations individuelles. Nous avons noté, en effet, que chez certaines fleurs il y a une sorte de nanisme floral, c’est-a-dire une réduction proportionnelle des diverses parties. EDMOND GAIN 445 On trouve donc ici une démonstration que le type géographique en formation est au moins partiellement fixé. On trouvera par exemple & Messein des fleurs a styles tres exsertes de deux sortes: 1* cas. Celles qui ont un calice plus court que la moyenne du type et qui ont un style plus long que la moyenne du type. C’est une race en formation, ne tenant peut-étre sa particularité que comme variation individuelle. 2° cas. Celles qui ont un calice plus grand et un style plus grand, ou bien encore un calice plus petit et un style plus petit, que la moyenne du type. Celles-l4 sont des races fixées, au moins partiellement: elle tiennent la particularité qui les caractérise, d’une influence héréditaire. Nous pouvons comprendre la formation de ces races en constatant que l’arrét de développement du calice entraine le plus grand développement du style ou inversement. On peut supposer que dans le bouton floral le temps qui sépare le début de la croissance des deux organes est un facteur important qui modifie leur capacité de croissance, et comme conséquence ameéne la formation de races spéciales. De méme pendant le grand développement de la fleur, au moment de son épanouissement il suffit d’une influence du milieu physique (pluie...température...) pour expliquer la variation des proportions relatives des deux organes; ceux-ci ne se trouvant pas 4 la méme période de leur évolution. Types moyens théoriques calculés (Moyennes arithmétiques). Conclusions relatives a la variabilité dans les quatre localités étudiées. 1. Le style a une capacité de croissance moyenne qui est plus forte et va en s’accroissant dans l’ordre suivant: Laxou, Malzéville, Messein, Maxéville. Soit 100 la capacité de croissance moyenne du style des brévistémonées & Laxou; elle sera 110°83 & Maxéville, soit 10°8°/, en plus. Soit 100 la capacité de croissance moyenne du style des brévistylées & Laxou ; elle sera 106°46 & Maxéville, soit 6°4°/, en plus. 2. Les tailles extrémes du style qui ont été observées sont plus grandes a Maxéville. Mais il est vrai que le nombre des échantillons observés a été plus grand quailleurs. L’accroissement se fait dans le méme ordre: Laxou, Malzéville, Messein, Maxéville, pour les Brévistémonées. Cest donc a Maxéville qu’on a trouvé le plus grand style et a Laxou qu’on a trouvé le plus petit. Il en est de méme pour les styles; ils correspondent aux plus grandes et aux plus petites étamines. 446 Etude biométrique sur la Pulmonaire officinale 3. Les tailles moyennes du calice sont au contraire plus grandes a Laxou (13:86 et 13°72). La variation semble se faire en sens inverse du style. Soit 100 la capacité de croissance moyenne du calice des brévistémonées a Laxou; elle sera 90°53 & Maxéville, soit 9°5 en moins; et 86 & Messein, soit 14°/, en moins. Soit 100 la capacité de croissance moyenne du calice des brévistylées & Laxou ; elle sera 89°86 & Maxéville, soit 10°2°/, en moins; et 88°72 a Messein, soit 11°3°/, en moins. 4. Le type moyen du calice est remarquablement fixé dans chaque station pour les deux types brévistylés et brévistémonés. Types moyens (calice) Types moyens (style) Brévistémonées Brévistylées Brévistémonées Brévistylées Laxou ws ig 13°72 mm. 13°86 mm. 8-77 mm. 4°64 mm. Malzéville ... a 12°64 ,, W210 ;, 9°52 ,, 4:82 ,, Messein .. uss 11°86 ,, 12:27 ;, 9:70 ,, 4:96 ,, Maxéville ... ae 12°64 ,, 12°44 ,, 9772) 5; 4:94 ,, La différence relativement plus accusée entre les deux chiffres 11:86 et 12°27 de Messein provient de ce fait que a Messein le calice des échantillons du type des brévistémonées a été trouvé tres variable dans les échantillons observés (8 a 16 mill.) tandis que le type des brévistylées est plus concentré autour du type moyen (10 a 15). Crest bien la ce qui explique la faiblesse du chiffre 11°8. Le chiffre 12:28 est tout-a-fait normal. 5. Le pistil a ordinairement une longueur un peu moindre que |’étamine du type inverse, surtout en ce qui concerne les pistils des Heurs brévistémonées : Types moyens théoriques Ee a) Différences entre le pistil et les étamines des types inverses Brévistémonées Brévistylées |! Kitamines et pistils de | Etamines et pistils de Pistil |Etamines| Pistil | Etamines grande taille petite taille Laxou 10°77 711 6°64 | 11°48 0°71, soit 6 °/, 0°47, soit 6°6 °/, Malzéville | 11°52 6:96 6°82 | 12°12 0°60 ,, 4:9°/, O14; Sco ae Messein 11:70 | 6-91 | 6:96 | 12-09 OP ae BRE 0:05: ,, On e/ Maxéville | 11°72 7 6°94 11°68 0°04 4, 0°3°/, 0:06 ,, 08 °/, Moyennes | 11°43 6°99 6°82 | 11°84 Epmonp GAIN 447 ) : : , ‘ Dans les’échantillons qui ont été passés en revue, et mesurés avec attention, le pistil dune fleur brévistylée et ’étamine d’une fleur brévistémonée d'une méme station sont ordinairement, assez rigoureusement, d’une méme taille moyenne. Le P| pistil d’une fleur brévistémonée et |’étamine d'une fleur brévistylée d'une méme station sont, seulement approximativement, de méme taille moyenne, I’étamine ? ’ étant ordinairement un peu plus grande, au maximum de +5. 6. La distance du stigmate a l’anthere est tres différente chez les brévisté- monées et chez les brévistylées. Elle est plus faible de 4 environ chez les brévistylées. C’est, comme on le voit pour P. officinalis une conclusion semblable a celle qui a été obtenue par Darwin avec 10 échantillons de P. angustifolia : Brévistémonées _—_ Brévistylées pane oe ae Laxou oes 366mm. | 2°84mm. | 0°82,sc0it28°/, 3°25 Malzéville ... | 4°52, | 3-30 ,, 1°20 ,, 35°/, 391 Messein... 4°88 ,, | 314 ,, 174 ,, 47°/, 4:01 Maxéville ... 4°76 ,, | 2°82 ,, 1:94 ,, 68°/, 3°79 | | : = ; : - Chiffre moyen 4°45 ,, | 3°02 ,, 1°42, soit 47 °/, 3°73 Si on représente par 100 la distance moyenne du stigmate a l’anthere chez les fleurs brévistylées, la distance est de 147 chez les brévistémonées, soit une différence de 47 p. 100. D’autre part cette différence est plus faible chez les deux types de la station de Laxou. Elle est plus forte chez les types de Messein et Malzéville, et atteint 68 °/, & Maxéville. Si on représente par 100 le chiffre de la moyenne des 2 types: 3°73, les valeurs correspondants des différentes stations sont : Laxou 87:1 Malzéville 105 Messein 107°5 Maxéville 101°6. Les stations de Messein et Laxou différent done de prés de 20 p. 100, soit 4, Variabilité et fiaité de Vhétérostylie de la Pulmonaire. Si lon veut apprécier la variabilité et la fivité relatives de Vespece, dans les quatre stations, il y a leu de ne pas s’en tenir & la comparaison des types de grande fréquence fournis par les graphiques. I] faut calculer le type moyen théorique, qui est obtenu en faisant la moyenne arithmétique des diverses longueurs observées. 448 Etude biométrique sur la Pulmonaire officinale Apres avoir vu défiler des tailles extrémes différentes, et de fréquen:e respective assez variable, on est surpris de constater, pour l’étamine et pour le pistil, le peu de différence présentée par les moyennes théoriques calculées, dont les chiffres figurent A la page 446. Hauteur de l’étamine au-dessus Hauteur du pistil au-dessus de la base du calice de la base du calice Brévistylées | Brévistémonées | Brévistylées | Brévistémonées Kcart des extrémes si a a8 5°6°/, 3°/, | ser tie Amplitude des variations extrémes ob-) servées par rapport au chiffre de 3a 4°/, Digs 3a 4°), 4—5°/, la moyenne générale nage Ae J Il ressort de ces chiffres (1) Que amplitude ordinaire de la variation est relativement faible. (2) Que l’étamine est moins variable de longueur que le style. (3) Que les fleurs brévistémonées semblent un peu moins variables que les fleurs brévistylées. La premiere conclusion explique pourquoi lhétérostylie peut se maintenir malgré la multiplicité des tailles observées, et malgré le fait de l’existence de petites races géographiques trés localisées. On peut supposer que si lhétérostylie a été perdue par certaines especes de pulmonaires c’est que, & un moment donné lamplitude de la variation moyenne théorique a été tres supérieure 4 10°/, et n’est pas rentrée ensuite dans les limites de ce chiffre. Darwin avait émis l’hypothese que certaines Pulmonaires présentaient peut étre une hétérostylie mal fixée. Ce cas particulier explique en outre que [évolution graduelle vers un type non hétérostylé semble ne pas eaister a Nancy. Pour que Vhétérostylie disparaisse chez un type hétérostylé habituellement, il ne suffit pas qu'une cause brusque affole le type, et le rende trés variable, il faut que le type moyen lui-méme soit tres modifié. Si lon étudie la variation de l’hétérostylie de la Pulmonaire on voit que la variabilité spécifique doit s’accuser par la variation de la position de axe de plus grande fréquence qui peut étre repoussée a droite ou a gauche. Il faut constater que la conclusion finale n’est pas celle que pourrait laisser entrevoir les mesures biométriques prises isolément sur quelques échantillons seulement : Lhétérostylie de Pulmonaria off: semble trés peu variable en tant que caractere fondamental de Vespéece. Elle se manifeste avec des modalités trés variées, mais elle est bien fixée, au moins dans les localités observées. La variation la plus importante observée dans les diverses stations consiste dans les différences relatives de développement du calice et du style: Jl ya en EDMOND GAIN 449 certains points de la station de Messein une race de Pulmonatre officinale a style trés euserte par rapport au calice et, au contraire, la station de Laxow offre une race @ style trés inclus. On peut dire de méme que certaines races tendent a présenter chez les deux types de fleurs une distance trés variable du stigmate a lV'anthére. Cette distance étant beaucoup plus grande chez les fleurs dolichostylées. CONCLUSIONS GENERALES. 1. Quelles que soient les variations individuelles de la taille de Pulmonaria officinalis, les types morphologiques et les dimensions des organes floraux ne sont pas modifiés par les variations de la taille des tiges. Table IV, page 411, et Table VI, page 413. La distance du stigmate a l’anthére, signalée par Darwin comme variable chez Pulmonaria angustifolia, est aussi tres variable chez P. officinalis; mais cette variation ne dépend pas de la taille des plantes. Fig. 3, page 415. Dune facon générale, chez les petites plantes les dimensions des organes floraux subissent des variations un peu plus grandes que chez les grandes plantes. Chez celles-ci le type est plus concentré autour des dimensions moyennes et fréquentes. 2. Les grandes tiges présentent un plus grand nombre de fleurs: soit, en moyenne, 1560 fleurs pour 100 grandes plantes, contre 1360 fleurs pour 100 petites plantes. Le nombre moyen des fleurs par individu n’est pas tres différent pour les plantes brachystylées, et les plantes dolichostylées : on trouve quelquefois, chez les premieres, un nombre un peu plus grand de fleurs (Fig. 5, page 423), mais Hildebrand a généralisé a tort qu’il en était toujours ainsi. Il y a des localités ou le nombre moyen de fleurs est tout & fait le méme pour les plantes brachystylées ou brévistylées et pour les plantes brévistémonées ou dolichostylées. Fig. 7 et Fig. 10, page 454. La floraison plus ou moins abondante ne semble done pas en rapport avec Phétérostylie. 3. Sion explore une surface de 1 ou 2 hectares des bois des environs de Nancy, en prenant toutes les Pulmonaires rencontrées, les plantes brévistylées paraissent plus nombreuses, d’environ {5 a 4, que les plantes dolichostylées ou brévistémonées. Mais ce calcul présente une certaine incertitude; le résultat obtenu dépend peut- étre de l’étendue prise comme unité de surface, ou méme de la derniére période du rythme météorologique. On peut admettre, en effet, que les deux types ne sont pas tout a fait dans les mémes conditions, pour résister, par exemple, a des pluies qui peuvent & un moment donné, produire sur les deux types une coulure inégalement défavorable. 4. Les Tables X et XI (pp. 420, 421) montrent trés nettement la comparaison des dimensions des fleurs brévistylées et des fleurs brévistémonées. Les différences Biometrika 111 57 450 Etude biométrique sur la Pulmonaire officinale sont peu nombreuses. Les deux types oscillent autour des mémes dimensions moyennes, et les chiffres extrémes observés dans une centaine d’échantillons sont assez peu différents. Jl y a pourtant une particularité tres intéressante & noter, cest linégalité de la distance entre le stigmate et l’anthére. Elle est chez les brévistylées plus faible d’au moins } de ce qu'elle est chez les brévistémonées. Dans certaines stations ces deux distances sont entre elles comme 100 est a 172. Pour la moyenne des chiffres de quatre stations des environs de Nancy, on trouve, pour les brévistylées une valeur moyenne de 302mm. et pour les brévistémonées 4°45mm., soit, par rapport au chiffre le plus faible des deux, 47 p. 100 en plus (voir page 447. Figs. 14, 55, 57 a 60). Il est curieux de constater l’absolue fixité de lhétérostylie avec un caractére aussi variable que celui que nous venons d’examiner: le libre croisement maintient la constance des dimensions moyennes du style et de |’étamine, sans réaliser la constance de la différence des longueurs de ces organes dans chaque fleur (voir page 446 et les graphiques, Figs. 57—60, 37—40, 41—44). 5. Linfluence du climat de l’année ne semble pas modifier la capacité de croissance moyenne, et les capacités de croissance extrémes des diverses parties de la fleur hétérostylée. Tables XIV a et XIV, pp. 424—29, et Figs. 61—63, 53—56. 6. Si on compare des Pulmonaires de quatre stations différentes (Laxou, Malzéville, Maxéville, Messein) on voit quil y a des différences assez accusées. Fig. 6, Tables XXIII A et B, pages 441—2. La longueur du calice et la longueur du style sont deux quantités qui varient en sens inverse aussi bien chez les plantes brévistylées que chez les plantes brévistémonées. Certaines stations, comme Messein par exemple, peuvent posséder des races de Pulmonaires & styles exsertes du calice, tandis que d’autres (Laxou) donnent des fleurs & styles profondément inclus dans le calice. I] est & remarquer d’ailleurs que les fleurs brévistylées de Messein présentent aussi des étamines moins incluses que celles de Laxou (voir page 451 les dessins des types moyens théoriques, et les types extrémes de ces deux localités). La distance du stigmate a l’anthére n’est pas la méme dans les diverses stations : pour les brévistémonées elle varie de 3°66 mm. a 480mm. ; pour les brévistylées elle varie de 2'74 4 3:34. Cela représente une différence qui, par rapport au chiffre le plus faible, peut atteindre 31°/, pour les premieres, et 21°/, pour les secondes, page 44:7. Ainsi nous pouvons conclure que dans chaque station il est possible de trouver des sortes de races géographiques locales orientées vers une modification spéciale des proportions des divers organes. Pour ce qui est du phénoméne de I’hétérostylie il constitue, chez Pulmonaria officinalis, un caractere specifique trés peu variable. Cette hétérostylie est plus ou moins accusée chez les divers individus, et nous avons méme trouvé une plante ot la distance du stigmate A l’anthére était presque Epmonp GAIN Brévi- Brévi- Brévistémonées Brévistylées Pee es oe Brévistémonées BES 2 rea Lavine Style le plus long: et Style le plus long Utes 1 Distances extrémes du Distances extrémes du | Lenguews J Longueurs le plus court le plus court Bay || Sac stigmate a l'anthére stigmate Qlanthére {moyenne et | moyenne et OyeD, eel minimum minimum du calice | du calice 3 =) S p 8 | ( 10 111213 141516 S 3 ‘= 8 3 5 0 17 18 27 2829 3031 32 '~— S wD ~ ail p p 33 34 434445 4647 48 SS = ‘= Ss S p 5 ! 49 50 596061 62 63 64 Fic. 6. stations étudiées. Millimétres Schémas er 2 ee extrémes ou Materia i: Pulmonaires pour les quatre (Voyez Tables XV, XVI, XVII, XVIII, pp. 432—435.) TIT cp [ Me | Ia 57—2 452 Etude biométrique sur la Pulmonaire officinale nulle*. Mais, malgré les types de fleurs si différents, les types moyens calculés sont d'une remarquable fixité pour les races des quatre localités étudiées (voir page 446). Et pourtant la loi de fréquence est légerement modifiée dans beaucoup de cas (voir les graphiques, 87 —52 et 57—60, pages 457—8). 7. L’ensemble du travail donne des renseignements sur la nature des courbes relatives & la variation de longueur des organes des deux types d’une fleur hétéro- stylée. Les graphiques 53 & 56, établis avec des chiffres suffisamment nombreux, et comparés aux autres graphiques du mémoire, permettent de schématiser les résultats en donnant les courbes qui synthétisent les nombreuses mensurations biométriques de ce travail. a. En ce qui concerne les longueurs du style et de V’étamine des deux types de fleurs, les courbes de fréquence de ces longueurs sont des courbes hyperbinomiales. Une certaine asymétrie pourtant se manifeste sur les courbes du style dont l’axe tend a étre rejeté vers la gauche. Fig. 53. Les sommets de grande fréquence sont plus surélevés pour les styles des fleurs brévistylées que pour les autres, Fig. 53; cest inverse pour les sommets de fréquence des étamines. Figs. 39 et 43, 38 et 42. Sur 1000 échantillons de plantes brévistémonées il y en a environ 450 présentant des étamines moyennes, et 275 présentant des styles moyens. Sur 1000 échantillons de plantes brévistylées on trouve environ 325 plantes a étamines moyennes, et 400 plantes a styles moyens. Si on ajoute deux millimetres pour la hauteur de l’ovaire, aux longueurs les plus fréquentes des styles, on obtient la hauteur des pistils les plus fréquents des deux types (7 et 11? mm.). Les hauteurs des étamines des types inverses sont justement aussi 7 et 113 pour les types les plus fréquents. Le “type théorique,” des Pulmonaires de Maxéville, vérifie exactement cette — relation. Les types des autres stations peuvent s’en écarter seulement au maxi- mum de 6°/, (Laxou), (voir page 446), et c'est généralement |’étamine qui est un peu plus grande que le style de la fleur inverse. Cette fixité assez remarquable du type moyen théorique de l’étamine et du pistil s’oppose & la variabilité si con- sidérable, signalée précédemment, pour les valeurs moyennes théoriques de la distance du stigmate a l’anthere. On voit, par les graphiques, que la longueur du pistil comme la longueur de ’étamine peuvent varier de 5 4 15 millimetres. Voyez aussi Tables XXIII A et B, pages 441—2. L’étamine longue et le style long ont plus de possibilité de variation (9 a 15 et 7 a14) que l’étamine courte et le style court (5 4 9 et 4 a 8). * Le présent travail n’en démontre pas moins qu’il n’existe pas & Nancy de ‘‘type général” de Pulmonaire ayant le style et les étamines de méme taille. Plusieurs auteurs francais admettent Vexistence de ce troisiéme type général. Il est possible que quelques types extrémes, analogues 4 celui qui est mentionné ici, aient éte observées. Mais existe-t-il une localité oti ce type est fixé? Epmonp GaINn 453 b. La distance du stigmate 4 lanthére est différente dans les deux types brachystylés et dolichostylés, et plus grande dans ce dernier, Fig. 55. Les deux courbes de fréquence sont binomiales, d’égale hauteur ; la distance de leurs axes de fréquence est de 0'8 & 2 millimétres, soit de 25 & 70°/, de la valeur totale. c. La distance du stigmate au calice est représentée par deux courbes binomiales normales, Fig. 56. La courbe des brévistémonées étant plus haute, avec axe de grande fréquence sur —1, c’est-d-dire que le stigmate est inclus dans le calice de 1 millimétre. La courbe des fleurs brévistylées est moins haute et par conséquent plus étalée. Elle indique une trés grande variabilité, depuis 0 jusque —12, cest-A-dire que le stigmate peut affleurer a la pointe des lobes du calice ou rester inclus de 12 millimétres. L’axe de*grande fréquence est sur — 6. d. La hauteur du calice est représentée par une seule courbe pour les deux types de fleurs. L’hétérostylie n’influence done pas les dimensions de cet organe, dailleurs tres variable. Fig. 54. La courbe est probablement binomiale avec une région a droite de l’axe de plus grande fréquence, qui est presque toujours irréguliere et tend a se surélever avec affaissement immédiat. C’est la seule des courbes qui soit moins précisée et moins certaine. Cette incertitude résulte peut-étre de ce fait que tous les lobes du calice ne sont pas toujours égaux, ce qui donne un flottement dans les mensurations. Dans ce cas en effet le chiffre exact 4 retenir serait la moyenne des 5 chiffres fournis par les 5 lobes. Or ce calcul n’était pas réalisable rapidement et n’a pas été fait. On prenait le chiffre le plus fort. Comme on le voit c’est dans les grandes tailles que survient la perturbation de la courbe. Or nous avons observé que les calices & dents inégales étaient surtout fréquents dans les calices tres développés. DVEXPLICATION DES GRAPHIQUES. Figs. 7, 12, 13 4 18. Réprésentation graphique des chiffres du Tabl. VIII. Maxéville, 3° lot, 1903, pp. 417—424; Comparaison des plantes brévistylées —— et des plantes brévistémonées - - - -. Figs. 8, 9, 9 bis (Distance du stigmate au bord du calice), 10, 11. Comparaison graphique entre les plantes de grande taille - - - - et les plantes de petite taille —— récoltées 4 Maxéville 1902. Toutes les plantes brévistémonées. Voyez Tabl. V, p. 412. Figs. 19—27. Réprésentation graphique des chiffres des Tabl. IX et XII. Voyez pp. 419, Messein, et 425, Maxéville, 1% lot, 1903. Figs. 28—36. Réprésentation graphique des chiffres du Tabl. XII. Voyez p. 425. Fig. 31 et Fig. 35, au lieu de inclu lisez exserte. Figs. 37—48. Réprésentation graphique de V’influence de la station. Figs. 37—40, Hauteur totale des étamines, p. 437; Figs. 41—44, Longueur du style, p. 438; Figs. 45--48, Distance du stigmate au bord du calice, p. 439; Figs. 46 et 47, aw liew de inclus lisez exsertes; Figs. 4952, Hauteur totale du calice, p. 436; Figs. 57—60, Distance du stigmate 4 l’anthére, p. 440. Figs. 53—63. Réprésentation graphique de Vinfluence du climat annuel. Figs. 53—56, Nombres totaux 4 Maxéville en 1903, p. 425; Figs. 61—63, Nombres totaux 4 Maxéville en 1902, p. 428, 454 Etude biométrique sur la Pulmonaire officinale 6 | | Nombre de fle RES ERASEes li See ; 5 omobre de fieurs ongueu HEI a fackrtey Cela JCC atta du style. Ag ON Hees S |e] salem ea y 0 | a a at ae BERNESE Ly | EAI AT PN CCEA EEN BEANE ANnee 10 — |—___ Hauteur du 74 BBSEee aac oH BS RE Sar Eee 5 SESGEE NEES EEE Aga CANE TTT TT Ty Bia [fim | fa | ce 5 FCCC wit ~ fH Distance du stigmate | i l'anthére. 0 12S NGeeas STAAL a 1 5 7 Fic. 10. Millimétres. Fic. 11. Nombre de fleurs par inflorescence. Millim@tres. Millimétres. The 12,” Comparaison graphique entre les plantes de grande taille (- - - - - ) et les plantes de petite taille (——) ré€coltées A Maxéville 1902. eo tes les payee brévistémonées (v oyez Eebl = or 9 8h | Distance du haut de l’anthére au haut du calice. s 2. PE AL BeBe seeee 4 [\\ Bug PCAC JSR BBE hae Phat pn eZ, ZA PEE EE SEE EE ATA | (RUNG eS RGR ECO TTT TTT Vive i 0 LP IW IV I PI Te ERBBEZ Boe ano =) f Milliamdtres, aie 13. Millimtres, ame 14. ascot femineTE] gaan a EEEEEEECEEEEEEEE CE ei aac 10 |_| Bo ERERV EERE Tee |_| | |] | fl BE [| | | Lil fil Li | [| if | la | Be Be fy 0 0 | | ee Tie Vis 10 14 Millimttres. Tia. 1B. Millimdtres, () u COE Eee! Du stigmate au a ee nc (|e hoedra ij em ia a i ROR | |_| |_| , i ea ea | wo | aH a a | TN ss AmeCeeE gt tt tt AT en TT \ 3 EERESoo vl} JD ER RESEeShReRaPeN 9 BIG eta LEEPER PEE CCA ERT 0 LITT IW NY d 1 eNonee Tie We Miliinetres onic 18. Réprésentation graphique des chiffres du Tabl. VIII. Plantes brévistylées — Plantes brévistémonées - - - - - - Un degré de léchelle verticale = un individu, —e S20 auteur d a calice. fo 15] Messein, EpMmonp GAIN istance du 455 stigmate au = (2) bord du calice. Messein of batt 9 10 11 Millimétres. 12, 13 #14. Fic. 19. Nombre des individus, Pulmonaires.|_| Messein.{_{ | . iS” REEL Distance du stigmate a Vanthere. jdus. oO =o a ieeeeeeueress fo) SEsSpenE 0 SemiGNZaNIG EARS 20. GR 8 Millimétres. Nombre des indiy 4 Fic. _ OA + 20 [ Haut. fa aieial calice. te 40 Messein. Maxeville, 1903 1° lot. 36 : 1903. a Longueur 15} — 330 du style. 3 as 4g 325) = B20 alo as = ag 2 Be E 5 Z, 5 a 4a ol alt BEEN ei 78 9) 10) Ay 12; 97S Milliméetres. Fic. 22. Sie OMRON GIR ZNRIGN Ans 1596p ar Longueur Millimétres. HiGew23. _ du style. Distance du seaas Maxéville, stigmate au 4 g80 1° lot. 15} bord du ; 3 1903. % ealice. ETF ' & | Maxévilley 7T fi a = Z| I lot. 20 e190) 1903. u H : ieesea ieee ttatt 2 = a t = 2 2 2 210 5 A g Z 0 i 3\ 4 5 43°42 #1 0 -1 -2 -3 -4 -5 Millimétres. Fic, 24. 9 Millimétres. Fie. 26. Distance du lai | ict , 14 stigmate a Brevistylees 13|Distance du w lanthére. 7 .12|stigmate au = Ei “ svisté Ses 3 11} bord du so | Maxeville, Brevistémoneées = 1 ¢ ASU) Teo (alm 7hclelulelllalniell ee “E10 calice. cl} 7 ats, 13) Ce = Voyez Be ee an Tabl. [IX et XIL-= 7 Ole s & 6 » | somo 5 24 & = 3 = = 2 ‘% a ae aN 0 eiarroaGe trys 0 -0.123456 789101119 Peano <3 Millimétres. Fic. 25 Millimetres. Fic. 27. 456 Etude biométrique sur la Pulmonaire officinale Hattour 30 totale au ; calice. |; S fe Pour comparer ee j = rt avec la fréquence = Sool de longueur du | = SAN a i yle - = ee SEE nan Ll] Hie eerie. vo oO os ERS Ref on | RZ) = ORES ae 2 oS n So : eb fo} = cabo lial a man eS ol LAY me p 9 10 11 #12 18 14 15 i 17 10 Millimétres. = a oe a a u calice. 2° TT TTT TART Distance : 7H z = Fie, 291 TAN I u stigmate a Sal a 2 ‘the o5 S| TPholin) olefin Ne om enene, Seem =o Sea elena Maxemile fa tt ST | Poa id J ° I = x CCEA 7 LIZIN a aa aN ene Es = eee eSkssSuas 10 11 12 . s : 3 of LAT TIT TTT INR Milliméetres. Z 2 3 4 7 8 wi10 Millimbtres ro IP = 8 See Eee hie= 30 aaa ese BRENEP ERS Eeeeweeee = got tt TT TT TT TLongueur du stylel || °F 5 SEES linheeee Mascrille, OD lot. iil 2 4 a BRR ESNSeeAe Ee a3 s BRERA BS Bo Ree it HEBGBEosoes g1 Soo Lt TTT REBREEEEEE) = Enns HEREEREEEee) 2 Eas | a ; co leh | a | | 3 2 HGS SHE ERE ENERAS SB), istance du ee ae Bee ee Aes Aa Rae stigmate au tae i |G } Bnew Z as) a ES \ = Ban Bes Ho aS = rp ZN ~ a rpc Gh WO nn. Em Ohm i mie el on = 4 Millimetres P 5 = pr Distance du A = stigmate au 3 aan Bord du 10, 8 calice. git tt At TTT T TTT tT tig. 36. | pote rt Lil Maxeville, 311 F DCIS eke sia aimbael oe toe “E10 u sty et = BinHe lel eel ogs z Boe ille, = +2 +1 O -1 -2 -3 -4 4 Millimétres. = _ Brév istylées — = Brevistémonées -- - - = Voyez Tabl. XIL. Millimétres. EpMonp GAIN 457 31 ae) Re 3 d= n oO 3 o I 2 & 5 a . 3 3 iS 10 oI iE 5 3 de a = 5 3 :: : 5 = : Z : 4 SunGEe 7 G.9F 10 11 12. 19. 14 915 Millimétres. a 3 B 42 > os 2 2 = = S sec (tall mo o oH o ine) ua 2 HH 2 5 g e HH Z, 6 jG, = 4 51/1 ALI a E at S 4 5 6 7 8 8 10 i 12 |e i Millimetres. BABE EES EEESEaN Se Gms 9° TORT MSeai4e 15 3 Millimétres ; mn 510, 31 Gel zs d= = 3 as] A= & & & 5 tre} og. oO o 3 =I a = 22 Se ° [TN ° a MillGnettes0 1 12 13 14 pao ar ae eT 12 H (ee 1 Het OMe es Indl Millimétres. . Sa Oe Sanne ee cua Uhcs Cee ence Longueur du style. Influence de la station. : de la station. F1c@.37-40 yGeadene g : 1G. 41- ae 3% : 2 = g|Styles inclus. | las} a7 47 os 26 . : Preeeeverer i]-5) 4 a o3 ia 52 aie BS = at NE fo} = 5, te 0 . a $2 2 0° 0 1 3 3 4 5 6 7 3 2 2 nie Millimétres. = el LiL TT Styles metus] as oa Malzeville, | A | TTT TTT | a Ear |_| pai 3 = HAA is 2 RH I = 2 lel 7 AA a) q 27 eB yg Sasol elu Omer su 4 1b) 6 7 =e -0 0 zs Millimétres. z Millimetres. Distance du stigmate au bord du calice. Fr¢.45-48 Influence de la station (voir Tableaux XV—XVIII). Plantes brévistémonées - - - - -- Plantes brevistylées — Biometrika m1 58 O=j=NWOFNDNWO 4 e , e e e 458 Etude biométrique sur la Pulmonaire officinale é 0g 8 STR i. 90 Longueur du style. EqG Tabl XIL g5 E ee BREPEERBOeeeooo vo = 33 e A DSSESSSBEE SIC oO £2 $e Z BeceS £1 dae 560 a oie: = 4 ele, ae as) 8 ~“ n 40 = =-2 | & = fi5 Ew a7 a SK & 56 Eee = 2) Rae oe: qe] nN me 4 0 Se Z io 55 oS ae Ee by (0 emer: Cy 13 «14 = g pL Pe aortas ra fe Millimetres. 3 = oars ‘28 ia aa 4 Lea sels) Hauteur du ee mean NA i VUTY TY [4] 3 _ =o i=} 1 . S hs ela) = a B 9 40 M1 10 49 14-1616 17 7, Os 8 10 11 12 19; 140d) 1eNnierioMmrom20 = Millimétres. ae #8 Millimétres. S7 30|Distance_ Fe Lee eo i 6 | | og) .du Puro tah [| 5 4 o6{sti es Ae $4 24) yord du <3 22 ; 22 | 20 calice Be 5 PY RT Tt, Eo VAN RE LT NANT 36 S7 8 9 10) 1 19°18, 14°15 46,4 a M : Bb is 319 5° 3 =8 as = + E5 a4, Millimétres. gd Zo Fic.53-56 Oe ee a Maxéville. 38 2 Ql O-1-2-3-4 en abl. : 2 5 oe Willimtres > Fia.61-63: sige as totaux 3 Maxéville £4 q . 1902. Tabl. XIIT. —€0 © 5 ff A) 5 mn 57 “=40 S6 5 at =30 Es 2 2 oy -§20 i £10 zo 5 2 me) eI z Zz ESERBSESSaeS Bi 9 JT ATA] | Messein.| 5 TEER a 5 a | aa ei i [a fa 3 3so_-_Lt TT tf |] ic.6 2! - o z=) *) “I =| ° Zz a 514 at 12 Bs H = Ea ae 3" 2 esi 2 5° 5 Br 2 Sale : 6 Ls 8&7 8 ocean illimétres. oa Distance du stigmate 4 4 PanthSte. ALTERS BETS ee f-Fis, Brévistémonées---- Brévistyléex STA10,9 102 sss 4 se Millimétres, MISCELLANEA. I. On the Correlation between Hair Colour and Eye Colour in Man. Iv seems desirable in view of the recent discussions on the relationship between coat pigment and eye colour in certain mammals to ascertain whether there exists any constant relationship between these characters in the case of man. material, wherein far greater numbers have been reduced to permilles. Eye Colour. I. Swedish Returns due to G. Retzius. Hair Colour. Hell Melist Braun Totals Blond Braun Schwarz Totals 667 288 45 Il. Prussian Returns due to R. Virchow. Hair Colour. Eye Colour. Blond | Braun | Schwarz | Brandroth 355 73 0 1 242 78 5 1 127 109 8 1 724 260 1133 3 I have been able to collect the following tabled 58—2 460 Miscellanea III. TJtalian Returns due to R. Livi. Hair Colour. Braun | Schwarz Totals Hell Melist Braun Eye Colour. Totals IV. Germano-Jewish Returns due to R. Virchow. Hair Colour. Blond | Braun | Schwarz} Brandroth | Totals — <= Blau... J 114 82 0 1 197 Tt | Grau a 113 11337/ 25 1 276 g | Braun ...] 100 333 92 2 527 pay & el Totals... By) 552 117 4 1000 V. Baden Returns due to O. Ammon. Hair Colour. Blond | Braun | Schwarz | Roth Totals 5 S| Hell 644 S Melist 229 D Braun 127 > a | Totals I have quoted the permille results in Tables I, III and V direct from Retzius and Fiirst’s Anthropologia Suecica, p. 155, and preserved their German terminology for describing hair and eye colours so that I may mark the fact that they consider the German classes to cover also the Italian-Swedish groupings. The original source of the Italian returns is R. Livi: Antropometria militare, Roma, 1898, and of the Baden, Otto Ammon: Zur Anthropologie der Badenser, 1899. Those for Prussian and Jewish children I have taken from the paper by Rudolf Virchow: Farbe der Haare und der Augen der Schulkinder, Archiv fiir Anthropologie, Bd. xvi. 1886, S. 468, etc. In IT 4,127,744 children were classified, and in IV, 74,146. The correlations were determined from these numbers before reducing to permilles. Miscellanea 461 VI. British Returns due to K. Pearson. Hair Colour. Fair Brown | Dark Totals s <= | Light 384 S Medium ... 403 | Dark 213 a & SS Totals... 1000 My data are from my observations on school children, in this case for boys only. I have put my categories ‘Dark’ and ‘Jet Black’ together as ‘Dark’ as the nearest equivalent to the continental ‘Schwarz’ possible under the circumstances. My three eye categories cannot be very different from the ‘ Hell,’ ‘ Melist’ and ‘Braun’ of Retzius’ tables, Their exacter definitions will be found in Biometrika, Vol. 111. p. 162. The importance of complete equivalence is, however, for our present purposes, not very great. We want to get the same number of reasonably definite groupings in each case. The six tables above each supply a 12-fold classification. From these tables the correlation between hair and eye colours was determined for me by Dr A. Lee using the method of mean square contingency,—a method which gives results inde- pendent of any scale order whatever*. We found Correlation between Hair and Eye Colours. Sweden (Conscripts) "2495 Prussia (Schoolboys and Schoolgirls) +2714 Italy (Conscripts) 3091 German Jews (Schoolboys and Schoolgirls) 3381 Baden (Conscripts) 3540 Great Britain (Schoolboys) "4203 Now these results seem to show that the correlation between hair and eye colours is by no means so close as has been hitherto supposed. Further it appears to be less in those districts which, whether light or dark, have a majority of one type. It is not improbable that the higher values in Baden and Great Britain are due to the effect of a greater mixture of local races, such local races not having interbred largely. In my opinion the results for the German Jews show that the population so classified is very far from being purely Semitic. If as I suspect the lesser values of the correlation occur in the relatively more homogeneous groups, then we might infer that increasing purity of race would mark a still slighter correlation between hair and eye pigment. In other words, if mankind originally consisted of several races each with a definite pure eye and pure hair colour, then the right statement is that the correlation between hair and eye colours was interracially unity or perfect, and ¢ntraracially zero. The point is of course one of terminology, provided the decreasing intraracial correlation with increasing racial purity be once established as a fact. But it is an important point of terminology, especially when pure races are crossed for hybridisation experiments. Is it correct to say that the correlation in white mice between eye pigment and coat colour is perfect? Since both characters are invariable, algebraically the correlation takes the indeterminate form 0/0. It is not unusual * Pearson: ‘‘Mathematical Contributions to the Theory of Evolution. XIII. On the Theory of Contingency and its Relation to Association and Normal Correlation.” Drapers’ Research Memoirs, Biometric Series, I. (Dulau and Co., Soho Square, London.) 462 Miscellanea to call it ‘perfect,’ but I think the statement must be reconsidered in the light of the suggestion made in this note that possibly increasing racial purity marks decreasing correlation. The ‘perfect’ correlation in the case of the white mice is really a sub-conscious transfer of the idea, based on experience of white and grey mice, of an interracial correlation coefficient equal to unity. It is one of the many points where caution is needful in passing from the old conception of correlation in the sense of Cuvier as an association of two attributes to the modern biometric notion as a relation between deviations. 1G 12, II. On the Correlation between Age and the Colour of Hair and Eyes in Man*. In recent work the resemblance of siblings in hair and eye colour has been used for measuring the intensity of collateral inheritance. In determining the correlation in pigmentation between siblings, allowance ought to be made for change of pigmentation with age supposing as in the case of man, we do not, as with greyhound puppies or thoroughbred yearlings, take the siblings at sensibly the same agest. It is usually stated that eye and especially hair colour are modified by age, but hitherto no quantitative measure of the change seems to have been published. It is the object of the present paper to determine measures of this kind. Prussian school children as given by Rudolf Virchow (‘“‘Gesammtbericht tiber die von der deutschen anthropologischen Gesellschaft veranlassten Erhebungen tiber die Farbe der Haut, der Haare und der Augen der Schulkinder in Deutschland,” Archiv fiir Anthropologie, Bd. xvi. 1886, S. 468-9) provided the following data. See Tables I and II. In these tables the so-called “andere Combinationen” were omitted as no ages were given; they are, however, very insignificant in total number. Using the method of mean square contingency, we have for children between 6 and 12 years of age: Correlation of Age and Hair pigmentation =:033. Correlation of Age and Eye pigmentation =-027. TABLE I. Age and Hair Colour, Prussian School Children. Hair Colour. Haare Blonde Braune Schwarze Brandrothe Age 6— 8 409,830 129,225 5,172 1,622 545,849 8—10 1,565,036 555,287 25,736 5,405 2,151,464 10—12 488,938 190,729 8,866 2,208 690,741 12—1}4 131,883 55,023 2,443 602 189,951 Totals 2,595,687 930,264 3,578,005 * T have put together the following results from Notes on this subject made by Dr Ginzo Uchida when working in my laboratory and placed by him at my disposal. K. P. + The allowance is easy to make, if the correlation between pigmentation and age is known. See Pearson: R. S. Proc. Vol. 71, pp. 289—294. Miscellanea TABLE II. Age and Eye Colour, Prussian School Children. Kye Colour. Augen Blaue Graue Braune Totals Age 6— 8 227,223 178,014 140,612 545,849 8—10 946,576 692,249 512,639 2,151,464 10—12 292,756 229,221 168,764 690,741 12—1}4 74,277 66,445 49,229 189,951 Totals 1,540,832 1,165,929 871,244 3,578,005 The children above 14 have been omitted because few in number they come from a selected class, while the above compose the whole child population in the elementary schools, It will be seen at once that the correlations are far lower than might have been anticipated. Indeed so low as to make no change of significance when we are dealing with the correlation of hair and eye colour in children, or with the degree of resemblance between siblings of 6 to 14 years of age *. Virchow’s data, however, combine the two sexes and it seemed desirable to consider the point for one sex only and possibly for a greater range of ages. Accordingly the following Tables were prepared from a portion of the sister-sister series of school data papers collected by Prof. Pearson. TABLE III. Age and Hair Colour, British Schoolgirls. Hair Colour. Fair Brown Jet Black | Totals 27 195 419 439 225 Totals * Pearson, Huxley Lecture. See Biometrika, Vol. m1. pp. 149—150., 464 Miscellanea TABLE IV. Age and Eye Colour, British Schoolgirls. Kye Colour*. Light | Medium} Dark | Totals 192 412 430 220 Totals 404 571 | 279 1254 From these Tables by the method of mean square contingency we have: Correlation between Age and Hair Colour ="158.: Correlation between Age and Eye Colour =:096. Thus by dealing with one sex only and going on to 19 years of age, we see that the corre- lations while still not large are yet sensibly increased. If we may compare the German and English material, we should say that there is little change in hair or eye colour with children under 14; by this we mean, not enough to influence the determination of pigmentation resem- blance of children of different ages. But after 14 there is even before 19 a more marked change, the correlations still, however, remaining low. This change is much more considerable in the case of hair than of eye colour, though sensible in both. Even thus the values of the collateral heredity coefficients, if we allowed for change of age, would hardly be influenced within the limits of their probable errors. It would be interesting to trace the change in the correlation for one sex and race for later ages, but the material does not appear to be available. There is a table “showing the colour of eyes and hair of both sexes at all ages of English and Welsh origin” in the Final Report of the Anthropometric Committee of the British Association (1883)+. But the classification is different from that used in our data. Moreover the results are classified first according to eye colour, and in the case of eyes of a ‘neutral’ colour, the hair colour does not appear to be distinguished. Thus it is impossible to base a correlation table of hair colour at different ages on the B.A. data, and no satisfactory comparison can be made with our present results. The only other material which is known to us is embodied in the Sozalanthropologische Studien of the late Dr W. Pfitzner of Strasburg, whose researches are in many respects both valuable and suggestive. But even where he deals with fairly numerous data}, certain limitations soon appear. Thus for the period from 5 to 20 years he examined only 164 girls, and it seems impossible to determine a correlation from such numbers. Moreover his figures are exclusively based on observations made on the corpse. He ought therefore to have ascertained as a pre- * Dr Uchida has omitted the ages 4 to 7 as of very small frequency. Tables for much larger numbers will be eventually published. Dr Uchida has not included the ‘blue’ schedules, prin- cipally infant schools, at all. Material is probably available for nearly 2,500 girls. K.P. + Report of the British Association, 1883, pp. 278-9. + Schwalbe’s Zeitschrift fiir Morphologie, Bd. 1. 8. 372. de Miscellanea 465 liminary whether the proportions of different hair colours in the case of those who die early and in hospitals are the same as those of healthy children in the population at large. On the basis of our statistics this is improbable. A selective death rate in the matter of pigmentation, and peculiar selection of subjects, vitiates largely, we believe, returns based upon post-mortem room observations. All that has been done with Pfitzner’s observations was to work out the Table for males from 0 to 75 years of age. This is given below. TABLE V. Correlation of Age and Hair Colour. Males, Lower Elsass. Hair Colour. | Blond | Braun Schwarz Totals Age 0—15 384 {83°8} | 74 {16-2} Of Oo} 458 15—30 } 122 {35-8} | 204 {59-8} 15} 4:4} 341 30—45 } 119 {28-0} | 261 {61-6} 44 110-4} 424 45—60 120 {24-6} 292 {60°6! 75 {15-4 487 60—75 58 {28°7} | 105 {52:0} 39 {19-3} 202 Totals 803 936 173 Using the method of mean square contingency we find: Correlation between Age and Hair Colour=°"451. Now if we were to trust this table we should have a very marked increase in black hair with increasing age, and this is the interpretation which Dr Pfitzner put upon results like this in his memoir. But a little consideration shows that this cannot be correct. Are we to say that there are no children with black hair in Lower Elsass, and that the 20 per cent. found among old persons is due to darkened pigmentation only? Prussia is lighter than Elsass but it contains ~ 18 per 1000 of such children. We should have expected at least eight or nine black-haired children in Pfitzner’s 458 under 15 years of age. Baden close to Elsass shows 18 per cent. of conscripts with black hair, while Pfitzner gives only 4:4 with black hair between 15 and 30! Pfitzner’s results, if attributed to age-effect, seem quite incompatible with what is known of the normal population for Elsass. They are, however, quite comprehensible if there be a positive correlation between fairness and disease in childhood. Now this is exactly what our British school children show: there ts a correlation between health and darkness of hair colour. Hence if we do not follow up individuals, noting their pigmentation at different ages, but simply correlate age of different individuals with hair colour, we are liable to exaggerate the correlation between age and pigmentation, and this will be especially the case, if we use hospital returns. Hence, it is probable that our neglect of a selective death rate, based upon the known correlation between general health and pigmentation, really emphasises the values found for correlation between pigmentation and age. Further, while it is probable that if we take adult life into account we should find this correlation increased—perhaps even to ‘2 or °25 —the value deduced from Pfitzner’s observations of ‘45 may be safely considered to mark in the first place a selective death rate, i.e. a correlation between fitness ¢7r childhood and dark pigmentation. Biometrika 111 59 466 Miscellanea In conclusion it may not be without interest to exhibit the results for age, hair and eye colours of British Schoolgirls from 7 to 19 in a single table : TABLE VI. Correlation of Age with Hair and Eye Colours. Hair Colour. Eyes Red Fair Brown Dark Totals Age: 710% Tight 4 {5°5} 52 {71:9} 17 {23:3} OO aa Medium 5 {6-4} 27 {34:6} 40 {51:3} 6{ 7-7} | 78} 192 Dark 1 {2-4} 6 414-6} 20 [48°8! 14 {34-2} | 41 10-18) Taeht 6 {4-1} | 92°5 {63-1} | 43-5 {29-4)| 5 4 Beat iia Medium 10 {5-6} | 57°5 {31-9} | 82 {45-6} | 30-5 {16-9} 180 412 Dark O10 }-| 12° {14-1} | 31--¥36:5} | 42. 447 es 18—16 | Light 4 {33} | 62 {51-7} | 45:5 {37-9} | 85 { 7-1} 120) Medinm | 8-5 {4:0! | 66-5 {31-1} | 103 {48-1} | 36 {16-8} | 214! 430 Dark 5 {5-2} 5-5 { 57} | 38 {39-6} | 47-5 {49-5} | 96 16—19 | Light 3a 31 {48-4} | 21-5 {33-6 8-5 {13-3} | 64 Medium | 2 {2-0} 34 {34°3! | 48 {48-5 | 15 {15-2} | 99} 290 Dark 1°5 {2-6} 45 {7-9} | 18 {31:6} | 33 {57-9} 57) Totals = 50 {4:2} | 450-5 {58-9} | 507-5 {81°5} | 246 { 5-4} | 1954 f Light 17 {4:2} | 237-5 {58-9} | 127-5 {31-5} | 22 { 5-4} 404 All Ages Medium | 25°5 {4°65} | 185 {32-4 | 273 (47-8! | 87°5 {15-3} 571 \| Dark 7:5 12-7} | 28 10-0} | 107 {38-4} | 136-5 {48-91 | 279 The numbers in curled brackets give the percentages of each hair colour of girls of a given age having a given eye colour. Examining this table it would seem doubtful, having regard to the paucity of individuals dealt with, whether we can assert significant changes in the percentages of medium-eyed girls having fair or brown hair at different ages. Nor would it be wise to insist that the changes of percentages in red-haired girls with light or dark eyes are significant. Red- haired girls with medium eyes seem to become continuously fewer with age; light-eyed girls with fair hair become significantly fewer, and brown-haired girls with light eyes more numerous. Dark-eyed girls with fair or brown hair become significantly fewer and dark-eyed girls with dark hair become more numerous, and probably light-eyed girls with dark hair also. The medium-eyed girls with dark hair (except in infancy?) remain much the same in percentage. Thus except in the case of red-haired girls those with medium eye colour change least; the fair-haired girls with light eyes tend to become brown or even dark, and the dark-eyed girls with fair or brown hair to become dark-haired. How far these changes are influenced by a relative death rate still remains to be determined. Occupation of Father. Miscellanea 467 III. On the Contingency between Occupation in the Case of Fathers and Sons. By EMILY PERRIN. It is a problem of some interest to determine how far ancestral bent and how far environ- mental conditions influence a man in his choice of occupation in life. The discussion of this problem has become feasible since the introduction of the new method of contingency into the statistical treatment of related variables*. By this method all questions of continuity and of scale in the variables are dispensed with. We fall back on the simplest and most fundamental of ideas—a measurement of the deviation from independent probability in the case of the two variable characters. The coefficient of contingency measures the degree of association or de- pendence between any two series and becomes more and more nearly the coefficient of correla- tion as the material approaches normality. In Professor Pearson’s memoir on Contingency he deals in Illustration D+ with my first statistics of occupational contingency. These covered 775 cases of occupation for father and son classified into 14 groups; the material was extracted from the Dictionary of National Biography. I have since doubled the number of extracted cases, and taken an additional 1550 from Who’s Who. I have kept the two materials quite distinct for comparative purposes. There are undoubtedly great differences in their character, although both sources of record are of course subject to selection, i.e. either father or son must have reached a moderate amount of distinction to be entered in either work. The following Tables give my material. TABLE I. Contingency between Occupations of Fathers and Sons (from Who's Who). Occupation of Son. ae | _ a) oa o>] ere! aI a | BS 2 | 4 olel, Svies ' Se i) a> | 2 | s/s] ¢ 2,8 tee 2S) el ag 12 S oO e > o an By “) Fal a 7D Pa Cc 3 Bi 3 g i ie S feat q ~ 4m = + nd bb 3 e fm} i Ra oS n oO a D x ral Oo ia a ag ro a y ag > = 4 oO im n =e! igen zy ei ae iS Be) q ca) 4 3 ca ota 1 YL a bb | oO “3 o | ss a | Ga ad q ea ) a) ~ S Pie xq a as] O 5 fo HB 4 Ay op) Arte od mee Teacher, Clerk, ) Civil Servant) w ww aD wo Crafts... = 2 1 1 : —| — 4 Divinity 58 | 138 52 — | 80 | — 5 | 42 | 53 5 15/10] 16 62 411 Agriculture — |— 1 }/—/] 2/1 ]/—-}—}] 8/—;—]—] 2 IL 10 Landownership | 42] 5 | 17 15 | — | 20 | 24 | 13] 10} 10) 15 | 380] 14 215 haw... 9 5 iks? — {11 }— | — | 40 |] 16 1/12) 1 Uf 8 123 Literature 1 5 1 a i) Ss | = 4/17/—/ 1)/—]-—- 2 333} Commerce 4 8 6 ——— | << TOM Os e383 3 1 2 17 116 Medicine 15 | 11 11 — 8 | — 9 9 3 I iese 1 3 5 109 Navy Ae wae 25 1 4 — 5 |] — 3 i 3 1 4/16 3 2 70 Politics & Court oe 3 1 3 1 | el elke — 26 Scholarship} P : re and Science § 2 2 ! = Totals 1550 * «Mathematical Contributions to the Theory of Evolution. XIII. On the Theory of Contingency andits Relation to Association and Normal Correlation.” By Karl Pearson, (Dulau & Co., London, 1904.) + Loe. cit. p. 32 et seq. 59—2 Occupation of Father. 468 Contingency between Occupations of Fathers and Sons ( from Dictionary Miscellanea TABLE II. of National Biography). Occupation of Son. | | we | Ex | Sa | >| 8 ta £181 2 | is | > n = <4 Gl 5S 4.)4) 32 / Si) ees |S Sel eae ahem "o's A & | So oe o | s BF < a Hio|s | CD fos] = 4 | Army ... 49 | — 8 -| — 5 | 2 6 Sa 4 3 Art) eee oak 2 | 105 1 1 3); — | — 2, 4} — — 1 Teacher, Clerk, | : : | Gc] Servant 2 | 22)| aU eine Wetby) etl sau| TONE hee | 2 Crafts ... if 91 1 14 7|/-—|— ya |) lat 5 3 | — Divinity 13 15) 6 Se al L | iva24. 5 | 20 8 Agriculture 2 4 4 4 6) 2 —— ih |) 1b 3 5 2 Landownership 23 3 7 — | 14| 8 § | 22) 9 1} 10) 12 Law G | S|. 10: || = | 10 =k Ontos) Losi edauleacaimes Literature 1 1 il -- 5} — | —} 47 11 1 2 1 Commerce 16 | 31 9 2 | 35| — | — | 16) 31 1°39 9 3 Medicine 2 fi 5. | 5 |e By = ore) |) —— Navy ... Sat hy} 3 2 | — 1 ee a ice Se 25 ks Politics & Court | 13 ) — 3 — A 2 9 Sh (|| = 2 3 Scholarship 2) 1) 90) 231). {Viva fol bret alee aero ea eee and Science § Totals Politics and Court) | mH ie ww RF BWONN OTR AT Scholarship and | Science It will be seen at once how the temporary official class which largely fills Who’s Who, crowding Army, Navy and Civil Service columns, finds a much smaller place in the record of national importance. On the other hand Literature represented by 155 fathers and 33 sons in Who's Who contributes 157 fathers and 33 sons to a random sample of the same number from the Dictionary. The relative distinction of Literature is thus the same in the present and the past. Other single entries will be found on comparison of some suggestiveness, but I do not stay over them here. Using Professor Pearson’s notation I find: § For Who’s Who (1550 cases) : Mean Square Contingency, @?= 1:285,868, Coefficient of Contingency, C,=°7500. For Dictionary of National Biography (1550 cases) : Mean Square Contingency, o?=1°413,601, Coefficient of Contingency, C,=°7653. Professor Pearson for my first Table of 775 entries from the Dictionary gives* Mean Square Contingency, @?=1:299,206, Coefficient of Contingency, C, = "6275. * Loe, cit. p. 34. ™ Miscellanea 469 But C,=V ¢?/(1+¢°), and thus in the last case we ought to have C,=°7517, and not °6275, which is due to an oversight in the arithmetic. Thus we see that the coefficient of contingency whether found from a sample of 775 or one of 1550 from the Dictionary has sensibly the same value, and this value is identical with one found with the same classification and the same number of cases from such an entirely different source as the annual Who’s Who. It seems clear that whether we take the present, or the long period of the past embraced by the Dictionary, the environmental influences which induce a man in this country to follow his father’s occupation must have remained very steady. The coefficient of contingency for parental inheritance will be like the coefficient of correlation about ‘5. I think, therefore, we may say that in the choice of a profession inherited taste counts for about 3 and environmental conditions for about 4. These numbers of 2 to 1 are somewhat less than the 3 to 1 given by Professor Pearson on the basis of the erroneous value °6275 cited above. It would be extremely interesting to compare these results for an old country like Great Britain with those for a new country like America. A priori we should expect to find a greater freedom from environmental influences, a greater choice in the son, and so a nearer approach to a pure inheritance of taste. IV. On a Convenient Means of Drawing Curves to Various Scales. By G. UDNY YULE, Newmarch Lecturer in Statistics, University College, London. Let an ordinary scale of equal parts, say inches, be engraved on the moving blade of a “clinograph,” or adjustable set square, the zero point of the scale being at the lower end. If the blade be set at an angle 6 to the horizontal, the vertical distances of the points 1, 2, 3... of the scale above a horizontal line X.VW drawn through the zero point, are evidently sin 6, 2sin 6, 3sin 6, etc. Hence if a curve be plotted to the base XY, with the scale maintained at this incli- nation, it will be drawn with a scale of which the unit is sin 6, where 6 may take any value we please from 0° to 90°. The plotting proceeds in the ordinary straightforward way. Supposing two ordinates to be plotted are 8°95, 7°63, the clinograph is slipped along the T-square until the 8-95 of the scale falls over the proper vertical, when the point is pricked off; the clinograph is again shifted till the 7°63 of the scale comes over the second vertical and its value is similarly marked, and so on. A scale of variable inclination thus becomes, for plotting purposes, a scale with a continuously variable unit. Such a scale is particularly convenient for plotting certain curves of given equation, e.g. the normal curves of errors, ve Y=9o @ 20%, ¥ being the ordinate at the mean, and o the standard deviation. In the ordinary way, the curve is plotted by the aid of tables giving the value of e~*’, the most complete tables being those of Mr W. F. Sheppard (Biometrika, Vol. 1. pp. 174—190). Intervals of, say, ith of the standard deviation are marked off along the base in either direction from the mean, ordinates erected at these points, and their magnitudes plotted from the tabular values multiplied by y. With the inclined scale this process may be considerably abbreviated. To divide the base, the T-square or straight-edge is turned round at right angles* to the base, a length, say J/S, equal to the standard deviation is plotted from the mean along WY, and the * Tf the adjustment be made as described below, any inclination will do. Hence it is of no consequence if the two edges of the drawing board are not at right-angles. 470 Miscellanea inclination of the scale is adjusted so that, when it moves along the T-square, the zero-point will pass over the mean J/ and the point 5 over the point S. The units of the scale will then give fifths of the standard deviation. Once the inclination has been adjusted, the T-square may be moved up or down if necessary to complete the plotting. The verticals are then drawn in, and the value of 7) marked oft on the central ordinate. The T-square being now placed parallel to the base, the scale and square are adjusted so that the zero point lies over the base and the point 1 7 10 over the top of y). The tabular values of e~*" then give the remaining ordinates directly from the scale readings. Even the trouble of extracting or reading the tabular values may however be eliminated, if a special scale be engraved, in which the distances of the divisions from the left-extremity are pro- portional to the ordinates e~#*". The inclination of the moving blade being once adjusted as above, the remaining ordinates are plotted direct from the divisions of the scale without interpolation, As a matter of practice I have thought it best for the scales to be made, as in fig. 2, with the joint like an ordinary carpenter’s rule, such a joint being stiffand wearing fairly well. The centre portion of each edge of the rule is bevelled for plotting, but the ends are left thick to prevent the rule slipping under the T-square or straight-edge. Four scales can be engraved on such a rule. Fic. 1. AB is a straight-edge or T-square. It is evident that the principle is applicable to a variety of curves, and I have had special scales engraved for plotting ellipses (the scale being given by equidistant ordinates in a quadrant of a circle), arcs of parabolas (such as are required in drawing parabolic girders, bending moment curves, etc.), curves of sines or cosines, and the normal curve of errors. The scales were made for me by A. G. Thornton, King Street West, Manchester. For statistical work, three plain scales of different units and divisions and a normal-curve scale form a convenient set. With the plain scales, curves of any sort are readily plotted with any desired ratio of length to breadth, e.g. for reproduction on a given page or lantern slide. Miscellanea 471 The idea of using a scale at a variable inclination is such a simple one, that it scarcely seems possible it can be novel, though new to me. Many ideas of considerable antiquity, e.g. “Gunter’s Lines,” come extremely close to it. The advantage, however, of the inclined scale, used direct on the drawing board, over the Gunter’s lines (scales divided on lines passing through the pivot of the carpenter’s rule), is very considerable in point of time, the use of dividers being avoided altogether. Fig.-2. V. Albinism in Sicily—A Correction. The abstract of Biometrika, Vol. 1. Pt. 1. contains this passage: “W. F. R. Weldon shows that the data from Sicily provided by Arcoleo are not in accordance with Mendelianism nor with the theory of gametic purity.” These words fairly give the purport of the article appearing at p. 107 of that number, over Professor Weldon’s initials. On looking into the matter I find that the more serious of the two considerations Professor Weldon adduces, namely, the production of two pigmented children as well as three albinos by two albino parents, rests on a mistake. His acquaintance with Arcoleo’s work is derived from Archivio per ’ Antropologia, t. 1871, but he apparently failed to notice that this was not an original communication. The original, from which the Archivio copied a part only, appears in Gazeta Clinica dello Spedale Civico di Palermo, F. 11. (1871). Here Arcoleo states explicitly that he never met with any case of an albino child being born to an albino parent. The following passages give his words*. “ Passando all’ albinismo della specie umana, si chiede: € anch’ esso ereditario? Per dirsi ereditario un vizio o un morbo, bisogna che si ripeta nei discendenti nel modo onde esiste negli ascendenti. Eppure in 24 famiglie da me esaminate, in nessuna ¢ preesistito un esempio di tal genere, nt nei 24 figli procreati dai cinque albini coniugati ve ne ha uno solo che richiami il tipo albino del padre o della madre. Parrebbe adunque che I’ albinismo nella specie umana non fosse affatto ereditario, &c.” * Pp. 12—13 of reprint. I cannot give the original pagination. 472 Miscellanea Again: “ Non essendo ancora dimostrato I’ albinismo ereditario nell’ uomo, si dimanderebbe sempre; quale.é la causa prossima che lo ingenera ?” Therefore the parents of family No. 7 were not as Professor Weldon states, both albinos, but both pigmented. The words which misled him, “Gli antenati furono tutti bianchissimi” plainly refer to “ the extraordinary fairness of many blonde persons, who were still slightly pigmented,” a phenomenon witnessed by Professor Weldon himself in Sicily. On the other hand this correction somewhat increases the discrepancy from Mendelian expectation to which Professor Weldon also calls attention. The families from supposed DR parents, as corrected, contained 86 pigmented, and 52 albinos, the Sassari being 103°5 and 34°5, a notable deficiency of normals. For several reasons I suspect that these numbers must be taxed before any deduction can be drawn with great confidence from the deficiency of normals; but it is by no means improbable that the deficiency does indicate some real complication, which indeed may on other grounds be already apprehended. When I had occasion to refer to albinism in Man I wrote as follows (P. Z. S., 19038, 11. p. 77) “Naturally we may inquire whether albinism in Man is not a similar recessive. Castle has given evidence pointing in this direction. The occurrence of albinism in the families of first cousins (see Day, Seligmann, &c.) is consistent with this view; but there are a few recorded cases of the occurrence of albinos in the offspring of albinos breeding with normal parents, where the hypo- thesis that the normal parent was DR is not at all easily admissible. No case of the union of two human albinos is known to me. The matter cannot here be further discussed, and the reader must refer to the literature, the most important paper being that of Cornaz.” These words seem to me to express very clearly the doubt I then felt (1903). It was surpris- ing to find them transformed by Professor Weldon into the statement that “the suggestion [that albinism in Man has a Mendelian behaviour] is considered probable by Bateson.” Never- theless after further experience, and especially after study of Arcoleo’s paper (previously known to me by title only) with its record of 5 families bred within the 2nd canonical degree of relationship, I now lean with some decision towards the view that albinism in Man will be shown to have a Mendelian inheritance, possibly, as I said above, with a complication. W. BATESON. 25 November, 1904. [I think Dr Arcoleo’s memoir hardly bears out in one respect the interpretation Mr Bateson puts upon it. Iam not clear what Dr Arcoleo means by the words cited by Mr Bateson at the bottom of p. 471. The emphasis may be on nel modo and di tal genere. They may refer to the special type and intensity of the albinism, for example in regard to defective vision and nystagmus. But I do not think it possible to interpret them in the sense of Mr Bateson: “Here Arcoleo states explicitly that he never met with any case of an albino child being born to an albino parent.” Dr Arcoleo states explicitly that the mother of the four albinos in Family No. 6 was “una albina di belle forme,” and the union (within the second canonical degree) arose from the desire on the part of the Cav. N. N. to have an albino daughter like her. If the Cavaliere was DD then the case is in favour of Professor Weldon ; if he was DR, then the result in this family, 4 albinotic and 7 pigmented offspring, was reasonably in accordance with the Mendelian expectation, which is 55+1. K. P.] CAMBRIDGE: PRINTED BY J. AND C. F. CLAY, AT THE UNIVERSITY PRESS. Abstract of Articles in Biometrika, Vol. III. Parts II. and III. March—July, 1904. (1) This double number contains two memoirs dealing with the selection of small variations. In the first Dr H. E. Crampton presents us with the first of his studies on variation and elimina- tion in Philosamia cynthia. He demonstrates that elimination actually does occur during pupal existence as well as at the time of metamorphosis. The individuals who successfully survive these conditions are in some respects structurally different and on the whole less variable than those that do not. Natural selection thus certainly exists for the material under con- sideration. According to Dr Crampton the selection must be considered as indirect, i.e. due to correlation, for it can hardly be considered, for example, that stouter antennae can be of service to the pupa, when it does not use them, and yet the less stout antennae are eliminated in the pupal stage. In short the test of fitness or untitness has reference to the physiological coordina- tion among the constituent elements of the whole organism, and does not necessarily depend upon the use advantage at a particular stage. In the second paper W. F. R. Weldon deals with the problem as to whether small variations in the form of the shell spiral in a race of Clauszlia exhibit sensible selection between the young and the adult stage. A previous investigation into another race of Clausilia had afforded strong evidence of such periodic selection. Contrary to his experience in the case of C. laminata, no evidence of selective elimination could be discovered in the shell characters investigated in C. itala. We are therefore compelled to conclude (i) either that the young were collected after the main selection had taken place or (ii) that the environment is so favourable that at present no selection is taking place. Taken in conjunction with Crampton’s results and the earlier work on C. laminata we rust assert that while selection of small variations certainly does take place in very different forms of life, it is not universally occurring in all species under every environ- ment in every period. (2) A second paper, On the Laws of Inheritance in Man, deals with the inheritance of the mental and moral characters and its relation to that of the physical. The method of the paper is the comparison of the intensity of likeness in mental and in physical characters in the case of brethren. The general conclusion is that the mental, moral and physical characters are inherited in sensibly the same manner. Whatever influence environment may have it does not serve to intensify the moral and mental resemblance of brethren beyond the physical resemblance. Nor do brethren in the case of physical characters less subject to environmental influence show less resemblance than in the case of physical characters which can be influenced by food and training. The bearing of this result on the problem of national degeneracy is emphasised. (3) W. R. Macdonell publishes the first memoir dealing with any considerable number of English skulls. The material, covering between 300 and 400 crania, with a high degree of proba- bility formed the contents of a London City plague pit of 1665. The measurements, 42 in number, are given and their biometric constants compared with those of allied European and unallied races. Normal and abnormal crania are illustrated by fifty plates ; it is hoped that the photo- graphs of special crania will serve as the beginning of a series to which reference may be made in describing abnormalities in future memoirs. The general results indicate that this series differs very widely from the German and French series, and from the English head as described by various modern writers. That the series, however, is typical at least of the 17th century Londoner is proved by comparison with a second series of London skulls. It is shown by some appended statistics that the most comparable data are those of the Long Barrow race [REREO; scattered up and down Europe. It would appear probable that that race has contributed largely to the London, if not to the whole English population, a conclusion which should serve to modify a good deal of historical and anthropological opinion. (4) The fourth memoir, a cooperative paper, deals with the colour inheritance of Greyhounds. The material consisted partly of schedules filled in by breeders, partly of data extracted from the Greyhound Stud-books. It was found quite impossible to neglect ancestral influence and no means of fitting the material into any Mendelian formula was apparent. The parental and grandparental correlations have sensibly the same intensity as for man and horse, and we may therefore reasonably suppose them to fit the geometrical law of decreasing intensity (Ancestral Law). The fraternal correlations for the data drawn from the stud-books agree well with the results for man and Basset Hound, but those drawn from the schedules are much higher, com- parable only with the fraternal correlations in the case of the thoroughbred horse. A number of special investigations were made to elucidate this difference, but the only solution that can be offered seems to be that the coat colours entered on the schedules were observed at a very early stage, and that the litter at this stage is more uniform than later, possibly after the shedding of the first coat. The Greyhound may be a confirmed “heterozygote,” but if so the memoir seems to show that any population of this character in man, horse, or dog obeys closely the ancestral law of decreasing correlation. (5) In the Miscellanea will be found an elementary proof of Sheppard’s formulae for correcting raw moments, and also approximate formulae for passing from the ordinates of frequency curves to the adjacent areas or sub-frequencies. CAMBRIDGE AT THE UNIVERSITY PRESS LONDON: C. J. CLAY AND SONS, AVE MARIA LANE and H. K. LEWIS, GOWER STREET NEW YORK: THE MACMILLAN COMPANY LEIPSIC: BROCKHAUS BOMBAY AND CALCUTTA: MACMILLAN AND CO., LIMITED. Yearly Subscriptions 30s. Price per Part 10s. Volumes I and II, now complete, 30s. each. Bound in Buckram, 34s. 6d. net each. * KARL PEARSON” es 5 ae ; 2. B. DAVENPORT . we : ‘CAMBRIDGE aS pi ce ‘AT THE UNIVERSITY PRESS © et ee LONDON: 6: aoe CLAY AND SONS; AVE ‘MARIA LANE : or fy AR H. ‘K. LEWIS, GOWER, STREET ny bas seat (NEW YORK! THE MACMILIAN COMPANY ees rae : Re a SKS _ LEIPSIO: BROCKHAUS nies ye cage Cae heeds ie oes | BOMBAY AND ‘CALCUTTA: “MACMILLAN AND 005 LIMITED. - 4 nee ; : “Entered. at the New ‘York Post, Office as Second cae Matter. EES * x The following papers, among other's, will. be issued in Vol. UI: . Experimental and Statistical Studies upon Lepidoptera. I. Variation and Elimination in Philosauria cynthia. By Henry E. CRAMPTON. A Third Study of the Variation and Correlation of the Human Skull, with special reference to 17th century: English Crania. By W. R. MACDONELL, ae A Second Study of Natural Selection in Clausilia lanunata Monracu. By. W. F. R. WELDON. On the Prediction of Cranial Coates from Circumferential "Measurements, By M. A, LEweEnz. On Inheritance in Man. II. Inheritance of the Paychical Characters. By Kari PEARSON. . Report on the Observations made on nm Shirley Poppies in the Summer of 1908, Soa, (Cooperative Study.) On the Influence of Season and Environment on the Roe rane and, Variation one the Lesser Celandine. (Sobnontare Study.) 4 x =) , ¥ THE FIRST NUMBER OF: THE — British Journal of Psychology EDITED BY eee WARD ann: W. H. R, RIVERS WITH THE COLLABORATION OF 1s Sar ae ea W. McDOUGALL. 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A Com- : _ parative Study of the Grey and White Matter, of the Motor-Cell Groups, and of the Spinal Accessory Nerve, in the Spinal Cord of the Porpoise (Phocena Communis). (Plates VI.—IX.) IL Wm. Waicut, ~~ _M.B., M.Se.; F.R.C.S. Skulls from the Round Barrows of Hast Yorkshire, (Plate X.) III. P.P. ~ Larraw, B.A. ‘The Varieties of the Os Calcis, (Plates XI.—XV.) IV. Tomas Lewis. Further Observations_on the Functions of the Spleen and other Hemolymph Glands. (Plate XVI.) V.° Prof. - G. Extior Suirn, M.A., M.D Note on an Exceptional Human Brain, presenting a Pithecoid. Abnor- _ mality of the Sylvian Region. VI. Prof. G. Hxurior Suita, M.D. Note on the Communication between the Musculo-spiral and Ulnar Nerves. VII. Prof. G. ELuor Suits, M.A., M.D. The Fossa Parieto-Occipitalis. VIII. J. Ernest Frazer, F.R.C.S. The Insertion of the Pyriformis and Obturator Internus, and Formation of the Posterior Circular Capsular Fibres and Upper Retinaculum.of Weitbrecht. TX. 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' Each number of MAN consists of 16 Imp. 8vo. pages, with illustrations in the text together with one full-page plate; and includes Original Articles, Notes, and Correspondence; Reviews and Summaries; Reports of Meetings ; and Descriptive Notices of the Acquisitions of Museums and Private Collections. Price, 1s. Monthly or 10s. per Annum prepaid. TO BE OBTAINED FROM THE ANTHROPOLOGICAL INSTITUTE, 3, Hanover Square, London W. AND THROUGH ALL BOOKSELLERS, CONTENTS. (All Rights reserved) : } ing I. Experimental and Statistical Studies upon Lepidoptera—I. Variation and Elimination in Philosamia cynthia. By HENRY EDWARD Aes Crampron, (With three Figures in text.) .