OSTEOMETRY; THE MEASUREMENT OF THE BONES 



75 



length line, and the lines of length and breadth of the superior face. 

 Whether the angles which have their apices at n and pr are of especial 

 value is not known, but the third angle, the apex of which is at ba, is 

 already listed above, and serves to measure the length of the superior face. 

 B. The Cranial quadrilateral (n-b-l-ba). This figure, more than any 

 other, especially with the cranial base as one of its sides, serves to define 



i.int. 

 ' 



Fro. 28. Important angles shown on a sawn skull, illustrating an old method of study; 

 based upon several drawings of Topinard. Certain well-known lines are given their earlier 

 French nomenclature to facilitate the reading of French texts of the period of Broca and 

 Topinard. 



n-sphen-ba, the Sphenoidal angle of Welcker. 



n-ba, the cranio-basal length, the "cranial base line." 



n-ba-pr, the facial triangle of Vogt. 



n-ba-a, the facial triangle of Welcker. 



The naso-basal angles of Vogt and Welcker, respectively, were used by these two men. 

 Vogt used the angle n-ba-pr, and Welcker the angle n-ba-a. The two inions, external 

 and internal, are incidentally shown in this figure. 



the profile of the entire cranium. Thus far it is not known to have been 

 used, but from its appearance, embracing the entire cranial contour, it 



