ANTHROPOMETRIC NOMENCLATURE : 11. THE INDICES O F H E A D HEIGllT T. D. STEWART Division, of Physical dnthropology, United States National M ~ L S B U ~ L , Waskington, District of Columbia I n part I of this series, dealing with the length-breadth or cephalic index, the reasons for reviewing the literature on this general subject are stated and need not be repeated here. The present part of this review is limited to the indices of height based on measurement of height from basion; and since basion cannot be used as a landmark on the living, it is further limited largely to the indices that apply to the skull. This restriction seems desirable because the auricular heights have not been extensively used, except of course in the living, and little effort has been expended upon the classification of the indices based thereon. Classifications of these latter indices are given by Martin ('28). Considering that the height indices attempt to express a single characteristic, that is, the relative height of the head, they are as a whole perhaps even more confused as regards basic measurements and classifkations than the cephalic index. Being not one, but at least three indices, with separate classifications for each, the array of names and figures is indeed bewildering. It is hoped that an understanding of the history of these classifications will aid in clearing up this confusion. As in the case of the cephalic index I shall review the history of the height indices chronologically and give a fairly full docixmentation. Because these indices have not been as fully discussed in the past as the cephalic index, there are fewer leads in the literature and a brief search cannot hope to uncover all the references to this subject. For this reason 23 24 T. D. STEWART I do not regard this review as being comprehensive, although I feel that it includes tbe main contributions. THE INDlCES O F THE SKULL 2P52. Anders Retzius, the originator of the terms dolichocephaly and brachycephaly, which today distinguish the major classes of the cephalic index, had a much broader conception of these terms than we do now. Tn a letter to Duvernoy dated 1852 (published 1864) Retzius defines his terminology by listing tlie most distinctive characteristics of the “ gentes dolichocephalae” and “gentes brachycephalae.” The fifth item in each list refers to height (pp. 118-119) : I n dolichocephaly “the height of the skull is ordinarily low ;” in brachycephalp “the height of the skull, compared with the length, is considerable.” Although thus manifesting an interest in skull height (measured incidentally from the anterior border of the foramen magnum to the highest part of the vault), Retzius does not seem to have stated definite ratios. 2859. Baer, who was greatly influenced by Retzius, and who published a remarkably modern-seeming anthropometric study of selected crania in 1859, was probably the first to express a length-height ratio (p. 248) : With the average skull of all human kind the simplest way to express this proportion is: Length to height, to breadth, as 1 ‘I p ‘ I 5 or1000 “ 750 ‘‘ €400, . . . .* Baer measured height from the plane of the foramen magnum to the vertex of the skull. 186‘3-1864. The English anthropologist Thurnam used the same method of measuring height as Baer and was probably one of the first to apply a terminology to the length-height inCiim erailium medium totius generjs huinani simplici hac proportione expriini pousit : Loiigitudo ad altitudincm, ad latitudinem, ut 1 I‘ 4 ” i! vel1OOO “ 750 ‘ I SOO,.. .... 25 THE IXDICES OF HEAD HEIGHT clex. Thus in describing his tables of measurements he says (1863-1864, p. 460) : The two remaining colunins, A and B, give the relative proportiosz of the breadth and height to the length, in which the latter is reduced to the coinmon module of 1.00. The first of these proportions, A, is the important one, called the “Cephalic Igtdes” by M. Broca; . . . . The other, B, in like manner, expresses in numbers the tendency to the depressed or platycephalic, or to the elevated or acrocephalic form. In the two columns, the low figures point to dolichocephalism and to platycephalism, the high figures to brachycephalism and to acrocephalism respectively ; whilst those of ineciium value represent a more regularly ovoid and more equally developed form of skull, both as respects length, breath and height, which may be defined as orthocephalism. The terms platycephaly and acrocephaly had been used prior to this in connection with pathological and artificially deformed skulls ; the term orthocephaly had been suggested by Welcker in 1862 to distinguish the midpart of the range of the cephalic index (see part I, p. 104). 1866. A new trend was initiated in 1866 when Davis pointed out in a review of van der Hoeven’s work on the skulls of Caroline Islanders that the series from this region stands out pretty distinctly from the rest of the skulls of human races hitherto known and described . . . . They are unusually long, unusually narrow, and, at the same time, very high, or tall . . . . to which we have applied the distinctive term high-narrow skulls, or hypsi-stenocephalic . . . (p. 55). We do not pretend to define what ought to be the exact value of hypsi-stenocephalic skulls in an^ arrangement of human crania, but have no hesitation in saying that they deserve a distinct place apart from all others (p. 57). . Welcker (1866) immediately seized upon this idea and amplified it. He called attention to the fact that the combination of dolichocephaly and high-headedness was contrary to Retzius’ pronouncement (see above) ;that apparently Retzius had considered only the relationship of length and height (lateral profile), whereas ‘a long skull could be high relative 26 T. D. STEWART to breadth (frontal and occipital profiles)2. In one table he listed the length-breadth and length-height indices of all available series from the most dolichocephalic to the most bracliycephalic, and thus showed the parallel increase in the lengthheight index3; in another table he reassembled these data geographically and ethnologically, from which he deduced the following five morphological types : Hypsistenocephaly - high and iiarrow Hypsibrachycephaly - high and broad Orthocephaly - medium high and medium broad Platystenocephaly - low and narroa Platyhrachj-cephaly - low and broad 1873. Although Welcker placed no boundaries to his groups, this deficiency was soon corrected by von Ihering (1873). Instead of using the length-height index, however, von Ihering substituted the breadth-height index, characterizing those inand those of 100 or inore dices below 100 as “platy~ephalic”~ *Aber welche Schadel iiennen wir hoeh’! Die von Davis als Paradigmen seiner Hypsistenocephalen abgebildeten Kopf e erscheiiien im Profilbilde (da j a auch c?ie Langsdurchmesser sehr gross sind) , wenn aucli nicht flach, doch keineswegs auffallend hoch. Wohl aber ist letzteres in der Frontal- und Occipitalansicht der Fall, und ich stimme Davis vollstandig bei, menii er jene Kopfe “Hochschadel ’ ’ nennt. Retzius beurtheilte die Srhadelhohe, \vie ich hierbei erinnern zu mussen glaube, nach dem Eindrucke, welchen die Schadel in der Profilbetrachtung machen, also naeh dem Langshohenindex, er naniite diejeiiigen Schadel hoch, deren Hohenindex gross ist. So richtig dies an sich scheint, so wird man zugeben miissen, dasv es mindestens eben so richtig ist, die Hohe iiach der Froiital- oder Occipitalansicht, also nach dem Breitenhohenindex (oder dem Verhaltniss des Breiten- zum Hohenindex) zu beurtheilen. Da, wie ich nachmeiseii werde, zwisclien Liings- und Hohendurchmesser ein weit constanteres Verhaltiiiss besteht, als zwischen Breiteiiund Hohendurchmesser, so zeigen sich die Hohenunterschiede in der Frontaloder Occipitalansicht i n einem vie1 ausgiebigeren Spiele, als in der Seitenansicht. Ieh ziehe darum den letzterwahnten Modus der Hohenbestiinmung entschieden vor und freue mich, hierin mit meinein verehrten Freuiide Davis zusammen zu treff ell. leh nenne mithiii in Nachfolgendem eineii Schadel hoeh, wenn der Hohendurchmesser, flach weiin der Breiteiidurcliiiiesser das grosseste Hauptmaass des Schadels nachst dem L5ngsdurchmesser ist (pp. 152-133). Shown also by Gaussin in 1865. ’Welcker had hesitated t o use this term because Vircliow had already applied it to a pathological deformity, but von Ihering ignores this. In 1874 Virchow suggested that the term “chainaecephalic” be substituted, since it would thus avoid this eoiinotation. 27 THE INDICES O F HEAD HEIGHT as “hypsicephalic.” I n this way he arrived at the followiiig classification (p. 162) : LT.-BR IXDEX UXDER 72 Br.-ht. index under 100 Br.-ht. index 100 and over Platpdolichocephaly Hypsidolichocephaly I LT.;BR. INDEX d2-79.9 Piatymesocephaly HFpsimesocephaly I LT.-BB. IXDEX 80 AND Ot‘Eli Platybrachycephaly Hypsibrachycephaly At this time several methods of measuring height were in vogue and were reviewed by von Ihering (pp. 158-161), but it is not clear to me which one he used as a basis f o r his classification of the breadth-height index5. Martin (’28, p. 650) attributes to Davis and Welcker a classification of the breadth-height index combining and expanding the terminology given above : Ultrabrrtchystenocephaly [sic] ......... Hyperbrachystenocephsly [sic] . . . . . . . . . Brachystenocephaly [sic] .............. Orthostenocephaly .................... Hypsisteiiccephaly .................... Hyperhypsistenocephal y ............... Ultrahypsistenoeephaly . . . . . . . . . . . . . . . . 89.9 and below 90.0- 94.9 95.0- 99.9 100.0-104.9 105.0-109.9 110.0-114.9 115.0 and above I have been unable to locate the references for this statement. Since Davis and Welcker did not use the breadth-height iiiclcs in their classification (see above) and since they were interested primarily in the relationship of the length-breadth and length-height indices, I have doubts as to the correctness of this attribution. Moreover, .the prefixes ultra and hyper were not introduced even f o r the cephalic index until 1885 (cf. part I, p. 120 et seq.) and Welcker’s publication of this date (Davis died in 1881) still deals with the length-height index. This about ends the efforts to relate the cephalic and height indices, although Flower stated in 1879 that The index of height [len@h-height] is not usually divided into special groups, as its chief interest lies in its relation to the breadth index [cephalic index], especially as to whether it is Slanouvrier (1885, p. 679) s a y thnt ton Ihering took n~asiiniim height froin the lowest point on the base. 28 T. D. STEWART greater or less. In the former case it may be called hypsicephalic, in the latter tapeinocephalic, though these terms are generally reserved for extreme variations in these’ directions (Ed. of 1907, pp. 419-420). Since Flower says that the terms hypsicephalic and tapeinocephalic are “generally reserved” for extreme cases, I infer that he means for pathologically deformed skulls. As far as I can discover he is the first to apply the name “tapeinocephalic” to one of the height index groups. 2875. In 1875 Broca proposed a general nomenclature for all indices except the cephalic and nasal (pp. 175-176) : The Fenera1 nomenclature can be reduced to three terms expressing the idea of a large, medium or small index. The root seme (from ohpa, s i p or index) is common to the three terms, and on combining it with the three adjectives pLyac, large, pkcoc, intermediate, and pix& small, one obtains the three words megaseme, mesoseme, microseme, applicable to the classification of all the indices6. His classification of the length-height and breadth-height indices, based upon basion-bregma height, is as follows (p. 179) : LENGTH-HEIGHT INDEX Microseme Mesosemc Megaseme ............ ............ ............ 71.99 and below 73 -74.99 -r 4o and above BRDADTH-HEIGHT INDEX 91.99 and below 93 -97.99 98 andabove In establishing the limits of each of these groups Broca followed two principles (p. 176) : I n the first place, one ought to conside\r that these divisions are made in order to facilitate the study and the comparison of races rather than individuals. It is not a question therefore of classifying the individual indices but the mean indices of rarious series. Consequently, when one proposes to classify tlie,de%reesof an index, it is necessary to determine the mean of this index in all races ; one finds that it attains its maximum, 11, in one particular race, and that it reaches its minimum, T,a nomenclature gBnBrale peut se rkduire B trois terines exprimant l’idCc d’un indice grand, moyen ou petit. Le radical sPtite (de u+a, signe ou indice) est coinmun aux trois terines, et en le combinant :ITW les adjectifs p’ynu, grand, plrni, intermGdiaire, et ,IU +. petit, on ohticnt les trois mots wiPgnsdme, me‘sos8mr. nt irroni me, applicablrs 8. In classification de tons les indices. THE INDICES O F HEAD HEIGHT 29 m, in another race. It is between these two figures that it is a question of determining three groups, by means of two divisions which will limit the intermediate group. I n the second place, as f a r as possible the differences expressed by the titles of three groups ought to be of nearly equal value. To obtain that one divides the difference 31-ni into three nearly equal parts. A division into three absolutely equal parts would almost necessarily cause the breaks to fall on fractional numbers, which would be very troublesome for the ineniory; there is therefore an advantage in breaking the series at whole numbers. The figures M and in being nearly always fractional numbers, one replaces them with the nearest whole numbers and thus their difference becomes a whole number. This difference is not always divisible by three; if it is not, one of the groups ought to be more restricted than the others, and preferably one will diminish the mesoseme group, because this group is usually that which includes the greatest number of races. Now, it is desirable, for the ease of descriptions, that the divisions of an index should serve a s often as possible to distinguish two races.’ ‘En premier lieu, on doit songer que ces divisions sont faites pour fnciliter I’btude et la comparaison des races bien plut6t que des individus. Ce lie sont donc pas les indices individuels qu ’il s ’agit de classer, mais les indices moyens des diverses series. P a r consequent, lorsqu’on ae propose de classer les degres d’un indice, il f a u t commencer par dbterminer la inoyenue de cet indice dans toutes lee r:ices; on trouve qu’elle atteint son maximum, M, dans une certaine race, et qu’elle descend B son minimum, m, dans une autre race. C’est entre ces deuv chiffres qu’il s’agit de determiner trois groupes, 5i l’aide de denx coupures qui limiteroiit le groupe intermediaire. En second lieu, il faut autant que possible que les differences expriinees par 1es titres de trois groupes soieitt a peu pr&s d’egale valeur. Pour cela, on divise la difference M-m en trois parties ? peu i prhs Cgales. Une division en trois parties absolument Bgales ferait toniber presque n6cessairement les coupures sur cles uoinbres fractionnaires, tr8s-ghants pour la memoire; il y a donc avantage i les fixer sur des iiombres entiers. Les chiffres M et ?it &ant presque toujours deu nonihres frsctionnaires, on les remplace par des nombres entiers les plus rapproeh6s et leur diffCrence devient ainsi un iiombre entier. Cette diffBreiice a ’est pas toujours divisible par trois; s i elle ne l ’ e ~ tpas, i l faut que l’un des groupes soit plus restreint que les autres, et on resserrera de prefBrence le groupe ni6so&me, parce que ce groupe est ordinairemelit celui qui coniprend le plus grand nombre de races. Or, il est desirable, pour la commodite des descriptions, que les coupures d ’un indice puissent servir le plus souvent possible 5 distiiiguer deux races. 30 T. D. STEWART Broca gives the ranges of the means of the length-height and breadth-height indices as 69-78 and 86-104, respectively. Applying the above principles to these figures it is quite apparent how Broca arrived at his classification. 1883. Broca's general nomenclature for these indices apparently was not, widely accepted, for within 10 years the Frankfort Agreement (Ranke, 1883) set forth a classification of the length-height index that combines the names suggested by Davis, Welcker and Virchow: Chamaecephaly (flat skulls) ......... 70.0 and below Orthocephaly ...................... Hypsicephaly (high skulls) .......... 70.1 -75.0 75.1 and above The Agreement specifies two methods of measuring height froin basion (vertical to the eye-ear plane or to bregma) but fails to state which applies to the index of this classification, although obviously attaching more importance to vertical height. The year after the Frankfort Agreement was published (1884) Turner provided still another classifleation of the length-height index based on basion-bregma height* : Tapeinocephaly .......... below 72 [71.9 and below] Metriocephaly ........... between 72 and 77 [72-771 Akrocephaly ............. above 77 [77.1 and above]' It will be recognized that this terminology combines names previously suggested by Thurman and Flower. The term metriocephalic is preferred . . . . because it expresses like the well known terms mesaticephalic and mesocephalic, a form intermediate between two extremes (~LTPIOC,moderate), whilst the word 6p8oc has no special relation to this intermediate index. Besides the term orthocephalic had previously been used by Prof. Welcher to express the breadth index [cephalic index] of a group of skulls intermediate between the dolichocephalic and brachycephalic (Footnote p. 5 ) . Duckworth repeats this in his textbook of 1904 (p. 261). Martin ( '38, p. 649) gives a different interpretation: X-71.9 72.0-76.9 77.0-x T H E INDICES O F HEAD H E I G H T 31 Topinard repeated Broca's classification lo in his famous textbook of 1885, but added the following interesting remarks (p. 682) : 1885. From the first in my Amtlzropology, I have manifested the little confidence that I have in these two indices [length-height, breadth-height]. Being given the approximate volume of the skull to which it is predestined by heredity, and aside from accidental influences during birth, the general form of the skull obeys a system of compensation. When its antero-posterior diameter increases, its vertical and transverse diameters tend to shrink, both at the same time o r one at a time. If there is antagonism between the great axis of the cranial ovoid and the two other axes that are perpendicular to it, there is antagonism then between the latter; when one yields, the other resists, all things being equal, although finally both yield. Such is the cause which prevents the vertical indices from expressing what one would wish. In the first index the exclusion of the transverse diameter from the comparison causes uneasiness; in the second, it is the [longitudinal diameter]. I have thought therefore that the mean between the two indices would give a better result than the one or the other separately, and I have given it the name of mixed index of height. The endeavor has responded only mQderately to my expectation. The means of the mixed index range from 77.7 to 89.111. lo It should be noted that Martin ( '28, p. 649) gives this classification with the Frankfort terminology. l' DBs l'abord, dans mon Anthropologie, j 'avais manifest6 le peu de confiance que m'inspiraient ces deus indices. La forme gBn6rale du criine, &ant donne le volume approsiinatif auquel ellc est pr6destin6e par hCr6dit6, en laissant de cGt6 Ies influences accidentelles sur 1'individu pendant la crossance, oMit L un systBme de compensation. Lorsque son diamBtre antCro-post6rieur s 'allonge, scs diamhtres vertical et transverse tendent B se r6tr6cir, les deus en m&me temps ou un seul B la fois. S 'il y a antagonisme entre le grand axe de 1'oroi'de criinien et 1es deus autres ases qui h i sont perpendiculaires, il y a antagonisme ensuite cntre eeux-ri ; lorsqu 'un cBde, 1'autre resiste, toutes choses Bgales, bien qu 'il arrive que tous les deux &dent. Telle est la cause qui emp6che les indices verticaux d 'exprimer ee qu'on roudrait. 1)ans lc premier indice, le diani?-tre transversc csclu de la compnraisoi~ g h e ; dam le second, c'est le diametre transverse [ant6ro-post&rieur?]. J 'avais donc pens6 que 1s moyenne entre les deus indices donnerait un meilleur resultat que l'un OLI l'autre s6parenient, et j e Itti avais donn6 le nom d 'indicc mizte d c hazitezir. L 'essai n 'a que m6diocrement r6pondu a nion attente. Les variations de I'indice mixte ont rlans les inoyennes de 77.7 A 89.1. 32 T. D. STEWABT 1890. A cursory search tlirough the subsequent literature reveals a few variations in these classifications : In 1890 Mies used a classification of the length-height index based on height taken from basion vertical to the eye-ear plane: Chamaeeephaly ............. 71.7 and below -76.7 Orthocephaly .............. 71.8 Hypsicephaly .............. 76.8 and above 1895. An entirely new terminology with different class ranges was used by von Torok in 1895 in classifying the breadth-height index (footnote, p. 286) : Eurycrany ................. 95.0 and below Mesoeurycrany ............. 95.1-100.0 Stenocrany ................ 100.1 and above’* I have not discovered what measurement of height is involved jn the index as here classified, although Martin (’28, p. 650) iiicludes this classification under the index formed from basion-bregma height. However, it would seem more likely that the vertical height was intended. 1914. The following classificatioiis of the length-height and breadth-height indices were given by Martiii in 1914 (repeated in the 1928 edition) without comment other than indicating that they are based on basion-bregma height (pp. 649-650) : LENGTH-HEXGHT IXDEX Chainnecephnly (better ehamaecrany) ........ Orthocephaly (better orthocrany) ............ Hypsicephaly (better hypsicrany) ............ 69.9 and below 70.0-74.9 75.0 and above BREADTH-HEIGHT INDEX Tapeinocephaly (better tapeinocrany) ........ 91.9 and below Metriocephaly (better metriocrany) ........... 92.0-97.9 Acrocephaly (better acrocrany) .............. 98.0 and above This classification of the breadth-height index is clearly a combination of Broca’s figures and Turner’s nonienclature. Martin ( ’28, p. 630) gives the class iange for stenocranp as 101.0-s. THE INDICES O F HEAD HEIGHT 33 Hooton ( ’30, pp. 46,48) has slightly altered the above class ranges of both indices for no apparent reason: LENQTH-HEIQRT INDEX Chaniaecephalp ............. 69.5 and below Orthocephaly .............. 69.6-74.5 Hypsicephaly .............. 74.6 and above BEFADTH-HEIIGHT INDEX ............ 91.5 and below Tapeinocephaly Metriocephaly ............. 91.6-97.5 Acrocephaly ............... 97.6 and above 2916. Finally, we may note that Hrdlicka (1916), like Manouvrier, has expressed dissatisfaction with the lengthheight and breadth-height indices as used separately : . . . . none of these [indices] are very satisfactory for showing the true value of this dimension [height], which on the one hand is proportionate to the size of the skull, and on the other stands in a more o r less compensatory relation with both the length and breadth of the vault. It has long been felt by the writer that some expression of the real relative value of the height measurement was required, and this need led him ultimately to compare it not with the very variable length or breadth of the skull, but with the mean of these two measurements. The resultant index, which may be called siniply the height index of the vault, gives us a new means of comparison and classification of the skull and promises to prove much more satisfactory than the two older indexes (p. 116). In another publication the same year ( ’16 a ) , dealing with the living, HrdliEka called this ratio the “mean height index,’’ which name he has used ever since. As will be shown later, he has not made a classification of this index13. It will be recognized, however, that HrdliEka ’s “mean height index” and Manouvrier ’s “mixed index’’ are essentially the same. Suminary. After an early period of trying to relate the length-height index to the cephalic (cranial) index in a special classification of racial groups, attention turned to the classification of the individual height indices. I n general there may be said to be three of these indices, the length-height, the The writer (Sten-art, ’40) has used the following subdivisions merely for purposes of analysis. s-80.4, 80.5-83.4, 83.5-x. 34 T. D. STEWABT breadth-height, and the mean height or mixed. Each of these indices in turn depends upon the definitions of the measurements entering into its formation. I n the classifications given above there are probably no variations in the measurement of length and breadth. Of the measurements of height from basion represented in these classifications there are at least two: to bregma, and vertical to the eye-ear plane. Although most of the authors do not explain their classifications, it may be assumed from the history of the cephalic index (see pt. I) that they have based them on the midpoint of the range for humanity. The variations listed above are summarized in table 1. TABLE 1 Comparison of classifications. INDEX BASED ON BAS:BREG. HT. -4Ut.hOr CLASS N A M E Length-height index: Chamaeerany (Microseme) I Broca and Turner i Martin i Hooton 1 Orthocrany ( Mesoseme) Broca Turner Martin Hooton I Broca Hypsicrany (Megaseme) INDEX BASED ON VERT. HT. FIWM BASION Class ranse Author Class range x-71.9 s-69.9 X-69.5 Ranke * Mies x-70.0 x-71.7 72.0-74.9 72 .O-7 7 .O 70.0-74.9 69.6-74.5 and Martin 75.0-x 74.6-x 77.1-x i Hooton i Turner Ranke Mies 70.1-75.0 71.8-76.7 Ranke Mies 75.1-r 76.8-r Breadth-height index : I Eroca and Hooton i Tapeinocrang (Mieroseme, eurycrany ) < Metriocrany (Mesoseme, mesoeurycrany ) Acrocrany (Megaseme, stenocranvl _ I and i Eroca Hooton i I and i Broea Hooton I i Martin x-91.9 X-91.5 Torok Martin 92.0-97.9 91.6-97.5 Torok Martin 98.0-s 97.6-x ToGk x-95.0 95.1-100.0 100.1-x These class names a r e now most generally used, but the names now used for the breadth-height index were originally suggested by Turner f o r the lengthheight index (see p. 30). Frankfort Agreement. T H E INDICES O F HEAD HEIGHT 33 T H E INDICES O F T H E HEAD Owing to the fact that there is no measure of height on the head comparable to basion-bregnia height on the skull, the indices of head height naturally are not comparable to those of skull height that we have been considering. I n this connection Martin ('28, p. 199) has pointed out the incorrect practice of those authors who use the classifications of the length-height index as designed for the skull for analyzing the index obtained from the head. Aside from the classifications given by Martin, based upon auricular height in the living, there does not appear to have been other efforts in this direction. In view of the general interest in HrdliEka's mean height index as applied to the skull, and in spite of the fact that it is not strictly comparable to that on the living head, it is desirable to present here his fuller views on this subject as expressed in his writings on the Old Americans ('25, pp. 170-171) : The reason for adopting this ratio [mean height index] rather than using the old height-length and height-breadth indices, should be obvious enough after what has been seen concerning the behavior of head length and breadth with changing cephalic index. As this index rises the length of the head decreases and the breadth increases in a closely compensatory manner, while the height remains but little affected. As a result we obtain a low or high height-length or heightbreadth index not as as indication of the relative height of the head, which is the point to be ascertained, but as a measure of the changing head length or breadth. The height-length and height-breadth indices of the head or skull are therefore unsuited for the purpose for which they were intended. But their mean is free from this disadvantage; it is a constant that is not affected or not affected materially by the changing breadth-length relations ; and contrasting the height with this constant gives a true index of the relative height of the skull or head. In showing the distribution of this index, the writer, as on other occasions, will not attempt any specific nomenclature and subdivision, which in time tend to assume unnatural and 36 T. D. STEWART more or less fetichistic value. The criteria by which any index or measurement must be judged primarily and above all, are its average, and its curve of distribution. DISCUSSION It is evident that less attention has been given to classification of the height indices than to that of the cephalic index. There has been only one general agreement (Frankfort) that included the classification of one of these indices (lengthheight) and even this classification is not given in Martin’s “Lehrbuch” ( ’28). The terminology of the classifications has become fairly well established as it relates to either length or breadth, but it is not restricted to a particular definition of height. I f this terminology is to be of full use, it should be exactly defined both as to the measurements involved and the class limits employed. Unless one of the present arbitrary classifications is adopted, it would be well to search for one that is more meaningful from the morphological standpoint;. The relative value of the various indices of height has been the subject of discussion ever since they came into use. Both the length-height and the breadth-height index have had their partisans, whereas many have given both or a mean of the two. Naturally, those who have been accustomed to use only the length-height or breadth-height index have been confused by and unable to interpret the mean height index. I n order to show how these three indices vary in extreme forms of the human skull, I have prepared table 2. The four populations here represented vary from dolichocrany (71.0) to brachycrany (82.9) and from chamae- or tapeiiiocrany (68.1, 84.9) to hypsi- or acrocrany (77.8, 101.5) ; there are combinations of narrow and high-headedness (New South Wales series), broad and high-headedness (Kentucky series) , narrow and low-headedness (Southern California Island series), and broad and low-headedness (Aleutian Island series). When subdivided according to the conventional classes of the cephalic index there is a tendency for the length-height index to increase as the cephalic index increases, whereas the 37 THE INDICES OF HEAD HEIGHT breadth-height index decreases. This is due to the compensatory changes in the dimensions. The mean height index occupies a position midway between the other two indices and reflects the ohanges in both; it is intermediate also in its range (see p. 31 f o r range of Topinard's mixed index). Many have recognized that there are disadvantages in considering either the length-height or breadth-height index alone. TABLE 2 Comparison of three indices of cranial height (basion-bregma). CBANIAL IhmEX (NO.) SERIES (author) New South Wales (HrdliEka, '28) Mean S. California I. (HrdliEka, '2i) Mean Kentucky (HrdliFlia, '27) Mean Aleutian Ii~lands (Hrdlicka, '24) Mean LT.-HT. INDEX M m N HT. RE.-HT INDFX INDEX X-69.9 70.0-74.9 75.0-79.9 (36) (51) (9) 69.8 72.0 76.3 71.0 (96) 71.5 (Ortho-) 83.6 (14) (25) (5) 66.6 673 69.2 71.3 73.7 (84) 1 79.2 78.2 78.4 78.6 68.1 (Chamae-) 78.5 70.0-74.9 75.0-79.9 80.0-84.9 (15) (41) (6) 76.5 78.0 i9.2 76.6 (62) 77.8 (Hypsi-) 75.0-79.9 80.0-84.9 85.0-1 (7) (32) (13) 70.2 70.2 70.0 82.9 (52) 70.2 (Ortho-) X-69.9 iO.0-74.9 75.0-79.9 80.0-84.9 (40) 100.8 (Acro-) 1 1 6:2 ? 1 92.3 (Metrio-) 104.1 88.2 I ? 4 \ T - 101.5 (Acro-) 89.8 ;%:86.4 75.1 81.0 76.9 84.9 (Tapeino-) Thus in the present example the Australians are quite lowheaded according to the length-height index (even cliamaecranic according to Broca's subdivisions) but quite highheaded (acrocranic) according to the breadth-height index. The mean height index indicates a moderately high head14. did not fully appreciate this point when I criticized Dixon's use of the length-height index (Stewart, '40)' but some of his findings mere probably dne t o this weakness of the single index. 38 T. 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