MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 179 



and the abnormal, because the occipital distortion is found in the skulls of so many of our Ameri- 

 can races, and because it is felt that its careful study by measurement may eventually prove of 

 great value in comparing the races. In some cases, however, separate tables have been arranged 

 for the apparently normal skulls, -which are designated as follows: Numbers H. 7, H. 12, H. 15, 

 H. 18, H. 19, H. 21, H. 23, H. 25, H. 26, H. 34, H. 30, H. 39, H. 40, H. 44, H. 54, H. 57. (See Tables 

 iv and v). 



$ 9. POSITION OF MAXIMUM OCCIPITAL POINT. 



A feature, probably the effect of occipital distortion, which is usual in these skulls is the ele- 

 vated position of the maximum occipital point. In 50 specimens in which the position of the 

 lambda may be determined, we find that the maximum occipital point lies above it in 10, and at it 

 or less than 5""" below it in 10 more. In other words, the maximum occipital point lies without 

 the occipital bone in 20 per cent of the specimens and is barely included in the latter in another 

 20 per cent. In 3 of the former 10 skulls the point is seen in the region of the obelion. In the 

 remaining 30 skulls, while it is found on the occipital bone, it is visually found high on it. In only 

 5 cases (10 per cent of all) does the point appear in the region of that usually ill-defined locality, 

 in these skulls, the inion. 



$ 10. THE LENGTH-BREADTH INDEX. 



The equality in this collection of the cephalic index of Broca to the length-breadth index of 

 the Frankfort agreement is remarkable and is due no doubt to the occipital flattening. The 

 maximum occipital point being unusually elevated by reason of the flattening ( 9), it often coin- 

 cides, or nearly coincides, with the posterior extremity of the German horizontal length, thus ap- 

 proximating the only factors of these two indices that differ. In 13* out of 47 cases these two 

 indices are exactly equal to one another; in one-half t of the 34 remaining cases the indices differ 

 less than one unit. According to this index the longest skull is again H. 23, and it is one of those 

 skulls in which both indices are alike. H. 46 is again the shortest skull, but its horizontal length 

 being shorter than its greatest length, we have the higher length-breadth index of 99.31. Accord- 

 ing to the "agreement " concerning this index, 3 skulls only are mesocephalic, 8 are brachycephalic, 

 and 36 are hyperbrachycephalic. The average, closely approximating that of the analogous ver- 

 tico-trausverse index, is 88.75, an extreme grade of brachycephaly. 



In 10 instances^ we have the confusing record of a vertico-transverse index higher than a 

 length-breadth index. This involves the paradox of a length greater than the maximum length. 

 A reference to measurements 6 and 7, in Table i, will show, furthermore, that such is our actual 

 entry in the cases where footnotes are referred to. This apparent inconsistency arises from the 

 following conditions: First, the occiputs of these skulls are so distorted that one side of them pro- 

 jects posteriorly beyond not only the other side but beyond any point in the posterior part of the 

 sagittal plane, so that the profile of the skull does not correspond in outline to a section in the 

 sagittal plane. Hence, second, the longest dimension parallel to the horizontal plane is not in the 

 sagittal plane. We do not, however, measure directly from the glabella to the most prominent 

 side of the occiput, which would give us an oblique measurement, but by means of the vertical 

 plates of Spengel's crauiometer we measure that which is a line parallel to the sagittal plane but 

 lying to one side of it. Imagining this line to be projected upon the sagittal plane, we reckon our 

 indices according to the accepted formula. We might have so modified the results or the modes 

 of measurement as to remove this discrepancy from the record, but we considered it more candid 

 as well as more scientific to give the results as originally determined. 



$ 11. THE VERTICAL INDICES. 



The occipital depression referred to not only directly shortens the antero-posterior diameter, 

 but increases the height and width of the skulls actually as well as comparatively. As a conse- 

 quence, no! only is the cephalic index very large throughout the group, but the vertical indices 

 are correspondingly exaggerated. 



* Nos. H. 3, H. 5, H. 6, H. 7, H. 11, H. 12, H. 14, H. 18, H. 23, H. 32, H. 44, H. 52, H. 55. 



t Nos. H. 0, II. KJ, H. 15, H. 16, H. 21, H. 25, H. 26, H. 27, H 34, 1 f. 35, H. 36, H. 37, H. 41, H. 42, H. 50, H. 53, H. 56. 



t Nos. H. 9, H. 19, H. 21, H. 25, H. 28, H. 40, H. 42, H. 53, H. 56, H. 57. i 



