CURVE OF SPEE IN MAMMALS 
191 
I am unable to suggest a satisfactory explanation for the absence 
of a similar relation between the "center angle" of the curve of Spee 
and the articular basio-nasal angle in the artiodactyla, or within 
the same species in the other orders. As a matter of fact, in a compli- 
cated structure like a skull, the anatomical relations which exist 
among the different parts are exceedingly complex, so that even the 
relation between the "center angle" of the curve and the articular 
basio-nasal angle may involve numerous factors which may be dif- 
ferent in the different skulls. Again, the fact that in the primates 
the skulls show a reciprocal relation between the degree of the "center 
angle" of the curve of Spee and of the articular basio-nasal angle, if 
the human case be omitted, while in artiodactyla such a relation is 
absent, might be explained by further tests, but in the present state 
of our knowledge even a provisional explanation seems futile. 
IX. RELATION BETWEEN THE FORM OF THE FOSSA MANDIBULARIS AND 
THE CURVE OF SPEE 
As to the relation of the form of the fossa to the curve of Spee, 
Spee has given his opinion in different places in his paper (1890). 
I have compiled, below, his various statements so far as these relate 
to my own studies: 
1. The development of the curve of Spee is dependent upon the 
presence of the tuberculum articulare. 
In other words, the curve of Spee does not exist on a skull which 
has no tuberculum articulare. 
2. In skulls possessing the curve of Spee, when the antero-posterior 
movement of the lower jaw takes place, the summits of the cusps of 
the bicuspids and molars of the lower jaw and the condyle move 
either on an arc of the same circle or on arcs of two circles which are 
homo-centric: the cusps on one circle, the condyle on the other. 
We may deduce from this that the steeper the path of the condyle 
of the lower jaw during antero-posterior movement, the shorter will 
be the radius of the cylinder-surface, or vice-versa. 
3. There is close relation between the curve of Spee and the sagittal 
movement of the jaw during mastication. 
That is to say, we cannot recognize the curve of Spee on any skuU 
which shows no sagittal movement of the jaw during mastication. 
