THICKNESS O F THE MALE WHITE CRANIIJM T. WINGATE TODD Hamann Museum of Comparative Anthropology and Anatomy, Western Reserve Universzty, Cleveland, Ohio THREE FIGURES AVERAGE CRANIAL THlCKNESS AND I T S RELATION TO AGE A study of the thickness of the cranium needs no introduction. Our information upon the subject is scanty in the extreme. Krause indeed makes the following statement : “Die Wandungsdicke betragt ca 15 mm. an der Protuberantia occipitalis externa ; am Schiideldach schwankt sie zwischen 5-7 mm. und sinkt auf 2 mm. an der Squama om. temporium.,’(2). More precise data are not available. It has long been held that in old age the cranium becomes thinner, although Henle (I) reminded his readers that Lucae (3) had questioned whether the diminishing weight of the skull in senility might not be associated with atrophy in the facial skeleton rather than with changes in the cranial bones. I n order to obtain more exact information on the thickness of the cranium and its relation t o age, I have taken measurements upon 448 male white crania of known age o r of age determined to within a year or two by methods which I have previously outlined, and I have subjected this material to a detailed examination the results of which I propose now to record. Each skull was set up on the Reserve Craniostat (5’6) in the Frankfort plane; the maximum glabellar length and auricular height were determined. ?Vith Plower’s craniometer the maximum breadth was obtained and the Eurya marked. The points involved in these measurements were penciled upon the cranium. The skull being already bisected, 245 THE ANATOMICAL RECORD, T O L . 27, NO. 5 246 T. WINGATE TODD it was easily unpinned and the two halves taken apart. The thickness of bone at each of the sites mentioned was then determined with a large Martin’s Tasterzirkel and recorded. In those skulls which had been opened at autopsy and therefore had had the calvarium removed instead of being bisected in the sagittal plane, the frontal thickness was obtained by Martin’s Koordinatenzirkel. All measurements were determined to the nearest quarter millimeter. The thickness at t Fig. 1 Age distribution of 445 male skulls used in the calculation of average cranial thickness. Note the peaks a t each decade and half decade. The threeyearly running average eliminates these irregularities. Ordinates refer t o years ; abscissae t o number of skulls. (By accident three of the 448 skulls are omitted in the figure.) the Euryon on right and left sides was averaged. Thus we obtained a series of determinations of thickness at the following sites : frontal area (glabella) including the frontal sinus, Opisthion, vertical point, Euryon. It is obvious that the thickness at the Opisthion is more serviceable than Krause’s measurement at the external occipital protuberance. My secretary, Miss Lindala, arranged the series in order of age and the three-yearly running average was ascertained. It is to be understood that all measurements were determined twice, that all figures have been checked and all calculations 247 THICKNESS O F MALE WHITE CRANIUM 7 -: OCClnTALiL - - - --- I I - 7- VERTEX 6- 4- EURYON I 1 1 1 I 4- I 1 & Fig. 2 Unsmoothed graphs of the running averages a t four cranial sites plotted on arithmetic grid. This figure is included in order to contrast its effectiveness with that of figure 3. Ordinates in years; abscissae in millimeters of thickness. Figure 2 presents the unsmoothed graphs of the running averages on arithmetic grid paper at each of the four sites chosen from nineteen to eight-two years. Thickness is recorded in millimeters. From twenty-nine to fifty-two years the graphs, except that of frontal thickness, possess a very smooth appearance. During this period the occipital thick ness is practically constant at approximately 6 mm.; thickness at the vertex increases slowly from 5.4 mm. to 6.0 mm. ; at the Euryon thickness increases from 2.9 mm. to 3.5 mm. Other studies which we have made convince us that the period from just under thirty years to just over fifty years 248 T. WINGATE TODD is the most stationary period in differentiation of the skeleton. We were not surprised, therefore, to find that cranial thickness during this period alters very slowly or not at all. We were also prepared to find a greater swinging of the graphs before and after this period of lull in cranial differentiation. It is noteworthy that oscillation of the graphs is more marked after fifty years than under thirty years. A glance at figure 1indicates that the cause for this appearance is not found in the comparative paucity of material; it is rather to be sought in a sporadic thickening of the cranium during later life. We find, then, no evidence of real diminution in thickness of the cranium with increasing age and share Lucae’s view of the causation of senile loss of skull weight. From a study of the age relationship in frontal thickness we note the extreme individual variability in dimensions of the frontal sinus and t,hat this sinus does not appreciably increase in dimensions during adult life. The average frontal thickness of the cranium is not far from 11.0 mm. The occipital thickness and vertex thickness are each nearly 6.0 mm. and the thickness at the Euryon approaches 4.0 mm. Disregarding age, these averages are found mathematically to be the following : Average thzckness Glabella, Opisthion, Vertex, Euryon, 11.26 5.73 5.88 3.56 mm. mm. mm. mm. There is a serious objection to plotting running averages on arithmetic grid: it gives no adequate idea of the percentage variations. I have therefore plotted the distribution upon arithlog grid and present the results as figure 3. We shall see later that by adding the coefficients of rariation for each of the four types of male white cranium shortly to be differentiated, and dividing the sum by four we obtain the following average coefficients of variation for each of the several sites of measurement in thickness : 249 THICKNESS O F MALE WHITE CRANIUM Glabella, 23.19 ; Opisthion, 29.53 ; Vertex, 21.78 ; Euryon, 29.28. Figure 3 gives at a glance a rough idea of the same result. It is obvious at once that the Opisthion and Euryon are the most variable areas of cranial thickness, and this is naturally clue to the erratic development of external body ridges at the 1 T 1 1 T. T T 1 1 1 T 1 1 FRoyru OCClPlTU VERTEX EURYON AGE 11 20 1 1 1 1 1 1 1 1 1 1 1 1 25 30 35 40 45 50 55 60 65 70 75 80 12.0 Fig. 3 Unsmoothed graphs of the running averages in cranial thickness plotted on arith-log grid t o demonstrate visually the relative percentage variability at each site. Compare these graphs with the figures in table 1. Ordinates refer to years ; abscissae to millimeters of thickness. former and to the marked local irregularity of endocranial bony surface at the latter site. Glabellar thickness, much to my surprise, shows no such large variability. Also there is no progressive increase in thickness shown on the graph. I therefore conclude that after early adult life there is no usual further encroachment by the frontal sinus. The very variable supra-orbital ridges of course do not figure in this measurement. Like the glabellar region, the area of the 250 T. WIPI’GATE TODD vertex is relatively less variable. But unlike the Glabella, the vertex shows a definite trend of increasing thickness on the graph. Allowing for irregularities, cranial thickness at the vertex does increase with age from early adult life up till about sixty years. Thereafter there is no definite decrease in thickness, the oscillation of the graph being accounted for by paucity of material. This increase in thickness related t o age may be observed in the curve of the Euryon and t o a slighter extent also in that of the Opisthion. It does not occur at the Glabella. There is, then, a small but definite inclination on the part of cranial thickness t o increase with age up to about sixty pears. No one of the curves exhibits a real tendency toward decrease in thickness after sixty. Consequently we must hold with Lucae that diminishing weight of the skull in senility, a phenomenon which undoubtedly occurs and is amply confirmed in studies to be published by my colleague, Doctor Ingalls, results from atrophy in the facial skeleton rather than from chaiiges in the cranial bones. The oscillation of these unsmoothed graphs demonstrates visually the utter impossibility of predicting the probable thickness of the cranium at any age and the error into which one may fall if one attempt to use mere cranial thickness as an age indicator. RELATION O F CRANIAL THICKNESS TO CRANIAL T Y P E It has been usual t o invoke the cephalic index as a rough method of distinguishing between cranial types. I n the course of our studies we have come to regard cephalic index as merely one of the compensatory methods by which cranial form is adapted to cerebral volume. The determining factors for cephalic index are to be sought primarily in the initial conformation of the cranial base. I believe that I have obtained a more precise method of subdividing crania into types -a method which will be fully presented upon another occasion. The fundamental principle of this subdivision is the relation between cerebral (or perhaps it were safer, at pres- THICKNESS O F MALE WHITE CRANIUM 251 ent, to say possible physiological brain) volume and cranial dimensions. By modifications of contour some crania accommodate a greater brain volume than others of the same linear dimensions. By this method I have segregated four cranial types which for essentially the same linear dimensions possess the following average possible physiological brain volumes. (For a discussion of the possible physiological lorain volume see 7.) a. 1307 cc. p. 1383 cc. y. 1449 cc. 6. 1501 cc. Industrial fluctuations and social upheavals following the war have provided an illuminating means of demonstrating the reactions of each of these types of individual to existing conditions of civilization. Closer investigation of the types demands an inquiry into the thickness of cranium characteristic of each. From 1917 to 1922, inclusive, our material includes the following numbers of male white skulls definitely allocated to each type : a, 38 ; P, 39 ; y, 43 ;6,49. From so slender a material it would be unwise to draw too far-reaching conclusions. Nevertheless, the sample provides a reasonable working test of the justification of our segregation. Niss Lindala has therefore calculated f o r me the means and variabilities in thickness f o r each type in this sample, and her results after being checked by myself are presented in the table below (table 1). There is apparently a diminishing scale of thickness in each dimension in the ascending series of crania from type a to type 6. The significance of this diminution must be considered, but first of all a glance at the variabilities is important. The coefficients of variability range between 18 and 34 per cent. This is a very high degree of variability and type of cranium has no real influence upon the variability. Without some comparison, however, it is impossible t o realize the unusual degree of this variability. From time to time there 252 T. WINGATE TODD have been gathered tables of variability in different bodily dimensions, but in these tables there is evident no significant order of variability. From a study of our own material I am led t o infer that the apparent chaos of such tables result,s from the very heterogeneous material utilized, the different methods employed by the several observers from whose investigations the figures are obtained, and the inadequacy and uncertain character of the material itself. Upon another occaTACLE 1 YEAN STANDARD D E V I A T I O N COEFFICIENT O F VARIATION a. Glabella.. . . . . . . . . . . . 11.8 -C .323 Opisthion . . . . . . . . . . . 6.1 f 2 2 9 Vertex . . . . . . . . . . . . . 6.2 2 .145 Euryon . . . . . . . . . . . . . 3.7 -1- .122 2.95 ? 2 2 8 2.10 f .162 1.33 k .lo3 1.12 & .087 23.00 -+- 2.052 34.43 C 2.962 21.45 2 1.726 30.27 C 2.553 p. Glabella ............ 11.5 -C .225 2.08 2 .159 1.45 2 .111 1.17 2 .089 1.23 2 .094 18.09 24.17 20.17 33.24 t 1.424 Opisthion . . . . . . . . . . . 6.0 i.l57 Vertex ............. 5.8 f .126 Euryon . . . . . . . . . . . . . 3.7 f 2 3 3 . . . . . . . . . . . . 11.0 -C .257 Opisthion . . . . . . . . . . . 5.7 f .178 Vertex . . . . . . . . . . . . . 5.9 -C .l50 Euryon . . . . . . . . . . . . . 3.5 2 .097 2.50 2 .182 1.73 2 .126 1.46 & .lo6 0.94 2 .068 22.73 30.35 24.75 26.86 C 1.736 C 2.406 ............ 9.8 -C .254 Opisthion . . . . . . . . . . . 4.9 -C .138 Vertex . . . . . . . . . . . . . 5.2 f .lo4 Euryon . . . . . . . . . . . . . 3.1 4 .080 2.64 iA80 1.43 i- .097 1.08 2 .074 0.83 4 .057 26.94 29.18 20.77 36.77 2 1.964 y. Glabella 6. Glabella -t 1.938 2 1.602 & 2.805 2 1.908 t 2.090 C 2.147 3- 1.472 4 1.952 sion it will be necessary to discuss fully the very definite order of variability shown by a material of known origin and ascertainable selection like that housed in this institution, and to formulate what may conveniently be defined as the laws of variability in anthropometry. I n order to emphasize this order of variability in a preliminary manner, I have drawn a p table 2 from the records of our investigations on the Reserve material. The standard of variability is that of standing height. This indicates roughly the variability of the body as an entity. Sitting height closely resembles it. Whereas the variability of the THICKNESS O F MALE WHITE C R A N I U X 253 body as a whole is not far from 3.5 per cent, the variability of major parts, leg and skull, f o r example, is between 4 and 5 per cent. Variability of segments of these major parts, namely, femur length and internal nasal length, is between 5 and 6 per cent. Upon such a basis of comparison we may infer that some real restraining influence is at work upon dimensions like epicondylar breadth of the femur and cranial breadth. Cranial capacity, as we are taught from a study TABLE 2 W e s t e r n Reserve material-Hamann Museum Coeficients of variation: W h i t e males NUIBER 100 100 100 100 100 167 167 167 50 30 167 45 49 43 43 14 DIMEKSlOb Standing height Sitting height Leg length (cristal h t ) Femur length R. (maximum) Femur epicondylar breadth R. Cranial length (R.R.) Cranial breadth Cranial auricular height Internal cranial length Internal nasal length Cranial capacity Dura volume Thickness cranium (vertex 8.) Thickness scalp length Thickness scalp breadth Thickness scalp auricular height COEFFICIENTS O F VARIATION 3.55 t- 0.146 3.77 t- 0.180 4.69 2 0.219 5.65 t 0.270 4.61 & 0.220 4.51 t- 0.166 3.93 & 0.117 4.14 2 0.152 3.79 2 0.25 5.30 2 0.36 8.45 t- 0.297 12.62 2 0.911 30.77 t 1.472 62.13 t 6.014 40.00 & 3.343 22.41 & 3.144 of cranial types, displays an expected fairly large degree of variability and, considering its small bulk, dura volume must be under some restraining influence. Scalp variabilities are unusually great, and these are discussed at length elsewhere(8). For reasons therein disclosed, 20 per cent is regarded as the typical scalp variability, and it is apparent from a consideration of table 1that scalp thickness and skull thickness are both of the same order of variability. At present, then, one would point out that our experience indicates the degree of variability shown by cranial thickness to be much greater than we should expect were there any 254 T. WIKGATE TODD true natural selection in cranial thickness. I consider that Nature is not greatly concerned over the mere thickness of the cranium, and we can never expect to predict this measurement with any real accuracy. It is plain, however, that the 6 type cranium stands somewhat apart from the others in its definitely thinner bone: it is less clumsily made and shows a higher grade of what the French have termed ‘perfectibilitk. ’ In order to demonstrate the difference in thickness between the types of skull, I have calculated the odds against the difference in the mean thicknesses of series a and series 6 being due merely to random sampling. The result of this investigation is given below. Odds against difference i n thzckness betweem a and 6 bezng t k e result of random sampling Glabella thickness, 962 t o Opisthion thickness, 408 to Vertex thickness, 13,279 t o Euryon thickness, 109 to 1 1 1 1 I n order to realize the significance of these figures we must bear in mind that statistically odds of 199 to 1 are regarded as good evidence of a real difference-a difference too great to be accounted f o r merely by the natural inadequacy of the sample to represent truly the entire population( 4). Another method of evaluation represents the difference between the means in terms of the standard deviation of this difference. If the difference is three times its standard deviation, the probability is great that there is a fundamental distinction between the two samples ; if the difference is three-and-a-half times its standard deviation, the probability amounts to a certainty. Now the differences between the means of the several dimensions in series a and series 6, each in terms of its standard deviation, are the following : At At At At Glabella, Opisthion, Vertex, Euryon, 3.28 3.03 3.79 2.78 THICKXESS O F MALE WHITE C R A N I U M 355 Hence by either method one legitimately concludes that between series a and series 6 there is a significant difference in thickness of the cranium except in the region of the Euryon. The difference is too small to be put to practical use in computing cranial capacity (or rather total possible physiological brain volume) in the living, but nevertheless it exists. It is also worthy of comment that the difference is most certain in the vertex, the site above all others where bone thickness is uncomplicated by confusing features present at each of the other locations, namely, in the glabellar area the frontal sinus, at the Opisthion external ridge development, and at the Euryon relatively large variations consequent upon modeling of the inner table upon temporal convolutions. I have already advanced the hypothesis that Nature is not greatly concerned over the precise thickness of the cranium, and yet I have demonstrated that there is a significant difference in thickness between type a and type 6 skulls. This apparent contradiction requires explanation. From other studies now in progress I contend that the a type cranium is in general a clumsily built, ill-filled brain case and fundamentally different from the cranium of the 6 type, although there are some crania originally probably of the 6 type which secondarily, as a result of pathological thickening, simulate specimens of the a type. Further discussion of this thesis is irrelevant here. The point which I desire to make is that thickness is a mere incident in the configuration of the cranium. The 6 type is a finer grade of cranium, more delicately and finely fashioned and better filled with brain. Hence actual cranial thickness is less in the 6 type than in the a type. But apart form this general modeling there is no evidence of an effort to control cranial thickness itself. We may observe this lack of control in the fact that there is no significant difference between a and 6 types in variability of thickness. 256 T. WINGdTE TODD SUMMARY 1. Average thickness in male white crania is given by the following figures : Glabellar area, 11.3 mm.; Opisthion, 5.7 mm. ; Vertex, 5.9 mm. ; Euryon, 3.6 mm. 2. Cranial thickness increases slightly with age up to about sixty years, but thereafter there is no real evidence of any normal change. 3. Cranial thickness is so variable that it appears unreasonable to imagine it under specific natural control as many dimensions seem t o be. It is so variable that one may not expect to predict it with a real degree of accuracy for any particular cranium. 4. Segregation of crania upon a basis of the relation of capacity to linear dimensions indicates at least four types of male white skulls, of which the most finely modeled and best-filled type has cranial walls significantly thinner except at the Euryon than those of the lowest type. 5. Cranial thickness is of the same order of variability as scalp thickness. LITERATURE CITED 1 HENLE, J. 1871 Handbueh der systematischen dnatomie des Menschen. Braunschweig, 3. Aufl., Bd. 1, Abt. 1, Knoehenlehre, S. 220. 2 KRAUSE,C. F. T. 1879 Handbuch der nienschlichen Anatomie. Hannover, 3. Aufl., Bd. 2, S. 55. 3 LUCAE 1861 Zur Morphologie der Rassenschadel. Frankfurt, Bd. 1, S. 7. (Ref. from Henle.) R. 1923 Medical biometry and statistics. Phila., p. 258. 4 PEARL, 5 TODD, T. W. 1923 Cranial capacity and linear dimensions in white and negro. Am. Journ. Phys. Anthropol., vol. 6, p. 148. 6 1923 Effeet of maceration and drying upon the linear dimensions of the green skull. Journ. Anat., vol. 57, p. 338. 7 1923 Dura volume in the male white skull. Anat. Rec., vol. 26, pp. 263-273. 8 TODD,T. W., AND KUENZEL,W. 1924 The thirkness of the scalp. Journ. Anat. (in press).

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