160 MASARU NAGAO 
less accurately correspond to the arc of a circle with its convexity down- 
wards. This curve varies in different individuals. If, in a skull with 
typical denture, it is continued in a projection of the jaw upon the vertical 
sagittal plane, it touches the anterior face of the articular surface of the 
condyle. This is the most ideal form. In the case of man, the center of 
this curve lies behind the crista lacrymalis posterior and on the line 
bisecting the horizontal plane passing through the orbit." 
The curve thus formed has been called "the curve of Spee" or "the 
compensating curve," and was considered by Spee to have important 
relations to the mechanism of mastication. 
Fick (1911) doubted the relation stated to exist between this curve 
and the movement of the lower jaw, but he did not give any evidence 
to substantiate his contention (see section viii). This view of Fick 
has, however, not been further examined by other investigators and 
the conclusion of Spee is therefore generally accepted in its entirety. 
Since the conclusion of Spee has a very important bearing on the 
mechanism of mastication, I thought it worth while to reinvestigate 
the curve of Spee and if possible to determine whether Fick's 
objection is in any way justified. 
As a first step an attempt was made to determine the nature of the 
curve shown by various mammals when the line is drawn touching 
the summits of the buccal cusps of the bicuspids and molars. From 
the curve thus obtained, the variations in the degree of the curvature 
shown by different species of mammals were determined for the pur- 
pose of a comparative anatomical study. At the same time, the 
degree of the inclination of the fossa, the gnathic index, dental index, 
and the angle between the line of articulation and basio-nasal line, 
were all measured directly on the skulls of many mammals, in order 
to determine whether any of these are related to the formation of 
the curve of Spee; indeed, Spee himself considers that the inclination 
of the fossa and the gnathic index have such a relation. Finally, 
using these data, the relation of this curve to the masticatory move- 
ments of the jaws is discussed. 
This work was begun in July, 1917, and completed in the earlier 
part of 1918 at The Wistar Institute of Anatomy and Biology. It 
gives me great pleasure to acknowledge my indebtedness to Dr. 
Greenman, Director of the Institute, for his generosity in permitting 
