172 
MASARU NAGAO 
same plane. To obtain the radius (r) from the constants a, /3, and 
y, the following formula was used: 
The radius (r) of the circle circumscribed about the triangle of area 
(/) equals a /3 7/ 4 /. But from Hero's formula: 
Area (/) = >J 5 Si Sz 
lis = A (a + ^ + 7), then 
Si = S — a 
3^ = 3-0 
S3 = S — y 
. ' . radius (r) = a, /3, 7 / 4 5" 5i S2 S3 
When the curved line did not touch the anterior face of the artic- 
ular surface of the condyle (K), as in the case of the muskrat or 
opossum, some other point than K was taken, and the length of the 
radius obtained from the triangle as in the previous cases, or directly 
by the use of compasses. 
The data obtained from these determinations are given in tables 
Tables 2 to 16 give, for each species, the values of a, /3, and y (meas- 
ured directly on the skull); the length of radius (calculated on a, 0 
and 7) ; the value of the "center angle" of the curve of Spee (calcu- 
lated on the radius), of the angle of inclination of the fossa (measured 
directly on the skull), and of the articular basio-nasal angle (measured 
directly on the skull); also the gnathic index and the dental index, 
both measured directly on the skull and calculated for each individual. 
The name of each species is given at the head of the table. The 
arrangement of individual records within each table was made ac- 
cording to the diminishing value of the "center angle" of the curve 
of Spee. The numbers entered were all rounded and the mean values 
for each measurement are averaged according to the columns. 
Table 17 gives for Primates the mean values of a,j8,and 7, the mean 
length of radius of the circle, the mean value of the "center angle" of 
the curve of Spee, the mean value of the inclination angle of the fossa, 
the mean value of the articular basio-nasal angle, and the mean values 
of the gnathic and dental indices for each species. The arrangement 
2 
2 to 18. 
