A CONTRIBUTION TO THE STUDY OF THE SCOTTISH SKULL. 409 



of dioptrographic tracings, and find that the angle varies in value from 84° to 94°, 

 with a mean value of 89*45° ; 19 of the specimens have an angle exactly 90° in value, 

 and 27 have an angle greater than 90°. In Buchner's complete series of 40 Tasmanian 

 skulls, including male and female, like the above Australian group, the zentrum angle 

 ranges in value from 85° to 94*5°, with a mean value of 89'6° ; 14 specimens have an 

 angle exactly 90°, and 9 are over 90° in value. 



Bolk (42), from an examination of 70 skulls (of which the race is not stated), has 

 found that the angle which the basion-bregma line forms with the glabella-lambda 

 line varies between 84° and 98°. The top of the variation curve lies at 90° (i.e. in 

 17 cases out of 70). He further states, however, that "the angle formed by the 

 basion-bregma and the glabella-inion lines is almost as constantly found at 112° 

 (14 cases out of 70)." In the present series of 100 the angle that occurred most 

 frequently between the last two lines was 107°, and it was found in fifteen instances. 

 The coefficient of variation of the angle was 2'95. 



Falkenburger (41 ), from an examination of a series of deformed Peruvian and 

 Mexican skulls, was able to convince himself that this perpendicular relationship of 

 the basion-bregma to the glabella-lambda line was prevalent also in such skulls ; the 

 variation of the angle occurring in these skulls was about equal to that found in series 

 of normal skulls. 



In the series of 100 Scottish skulls examined I find that the zentrum angle shows 

 a range of variation from 87° to 100°, with a mean angle of 92 '5° ; the angle most 

 frequently found is 91°, and it occurs 21 times. The coefficient of variation of the 

 angle is 2'79. The angle is 90° exactly in 11 per cent, of the skulls, 10 per cent, 

 only are under 90°, while the remainder, or 79 per cent., show an angle greater 

 than 90°. 



In the Tasmanian and Australian series, therefore, the tendency for the angle to 

 be less than 90° is marked, while in the Scottish series the tendency for the angle 

 to be over 90° is still more evident. A comparison of the coefficients of variation 

 shows that, as regards this angle, the Scottish skull is slightly more variable than 

 the Tasmanian. 



From an analysis of the measurements in my series of 100 skulls I find that the 

 magnitude of the angle at the zentrum may be considered to depend on several 

 variable factors : — 



1. The length of the glabella-bregma chord. 



2. The length of the glabella-basion chord. 



3. The size of the upper glabella angle. 



There is a very close relationship between the tendency towards increase in size 

 of the upper glabella angle and the tendency towards decrease in the zentrum angle. 

 The relative lengths of the glabella-bregma and glabella-basion chords have also a 

 close relationship with the size of the zentrum angle, a long glabella-bregma chord 

 associated with a short glabella-basion chord tending to increase the angle, and vice 



