MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 195 



NOTE ON THE MANNER OP TAKING THE GERMAN PROFILE ANGLE. 



This measurement is taken by Spengel's craniometer, an instrument of great accuracy but of rather limited 

 usefulness. A close description of its mechanism is too long to be given here ; for sudi \ve refer to Uarless's Lehrbuch 

 tier rittsliscken Anatomic, zweito Auflago, Stuttgart, 1876, pp. 506 et seq. 



It is sufficient for our purpose to say that, as regards the facial angle, the craniometer consists of a strong 

 metal table whereon the skull is placed vertex downwards with its right side facing toward the operator and adjusted 

 in the plane of the Frankfurt agreement; and of a goniometer in a plane vertical to that of the table. 



It is not often that the skull is sufficiently symmetrical to allow the four points, two supra-auricular and two 

 suborbital, of the required plane to be placed in the same level. It is practically impossible in cases where this 

 may be done to then find the points dc refers of the sagittal plane vertically one above another. As the goniometer 

 is vertical to the table which serves as a fixed point from which to determine the desired plane, it is evident that 

 in order to use it, the points in the sagittal plane must he vertically disposed. Therefore we place the skull so that 

 the alveolar point is exactly above the nasion while both are on the midline of the machine and face the goniometer. 

 Care is taken to see that some points in the posterior part of the sagittal plane are also in the midline. The skull 

 is then so adjusted that the supra-auricular and suborbital points of the right side, which, as stated, faces the operator, 

 are in the same horizontal plane. The goniometer is put in position and the angle is read. 



To sum up : The angle given in this report is, except in cases of skulls with the right side broken away, taken 

 with the skull in such a position that the sagittal plane is vertical and the right side of the Frankfurt piano is 

 horizontal. 



4 21. GNATHIC INDEX. 



Iii 39 cases we have been able to calculate the gnathic index of Busk and Flower, which is 

 found by multiplying the length of the basilo-alveolar radius by 100 and dividing the product by 

 the length of the basilo -nasal radius. The results are shown in Tables xxxvi, xxxvu, and xxxvm, 

 in which we find (according to Flower's classification) but two skulls that are prognathous (above 

 103). There are 10 mesognathous ^98 to 103) and the remaining 27 are orthognathous (98 and 

 below). The minimum of the series is 88.78 and the maximum 110.11. The average, 95.92, is 

 orthoguathous to a high degree and allows us, in respect to the character expressed by the gnathic 

 index, to class this people along with the highest European races.* 



Gosse states that one of the effects of the occipital deformation, such as these skulls exhibit 

 (tete deprlmce par derriHre), is to diminish the projection of the lower part of the face.t Possibly 

 we may thus explain the marked orthognathis-m of the Saladoaus. Nevertheless we fail to dis- 

 cover any direct relation between the facial angle and the occipital contour in this group. Exceed- 

 ingly flattened occiputs may be found as often among skulls having high as among those having 

 low indices, and the average index of the apparently normal skulls (94.10) is less than that of the 

 obviously flattened, when, as an inference from Gosse's proposition, we might expect it to be 

 higher. 



22. ALVEOLO-SUBNASAL PROGNATHISM. 



The important character of alveolo-subnasal prognathisni we have examined in 27 skulls, 

 according to the rules established by Topinard,J and we have tabulated the angle and the index 

 of this prognathisni with the vertical and horizontal measurements which constitute the factors of 

 the latter. (Tables XXXIX-XLII.) 



Skull II. 43 has the lowest index, 14.28, and the greatest angle, 82. Skull H. 57 (Plate L) 

 has the highest index, 61.53, and the smallest angle, 59. 



The average index of the series is 37.27 and the average angle 70.03. In the tables given 

 by Topinard Americans are not included. His average index of the Malays, 37.42, is nearest to 

 that of the Saladoans, and the factors of the index are much the same, the horizontal being 0.5 in 

 both races. The Malay angle, G9.7, though not the nearest to that of our collection, is but little 

 removed from it. The angle of the Polynesians. 70.8, and the angle of the Indo-Chinese, 70.1, 

 arc nearest to that of our collection. Angles of other Mongoloid races, 72.6 to 71.0, are slightly 

 higher, and consequently may be supposed to indicate some evolutionary advancement. His 

 highest average Caucasian angle of 81.8 is not as high as the highest Saladoan, and his lowest 

 average Namaquois of 58.2 is lower than the Saladoan lowest. 



"ToriNARD; up. tit., p. 94. 



t Essai sur les (Informations artificielles du crane, Paris, 1855, p. 68. 



t " Du prognathism alvcolo-sous-nasal." Revue d'unthropologie. Paris, Vol. I, 1872, p. 642 et scq. 



Op. cit., p. 668, and Eldinents d'authropologie, p. 888. 



