CURVE OF SPEE IN MAMMALS 
171 
arc. With this in mind, the number of degrees representing the 
angle which subtends a given length of the arc was determined by 
the following formula: 
where A represents the angle and r the radius. 
In the above formula the radius is given as the measure of the 
curvature and at the same time the length of the chord is given instead 
of the arc — the length of the chord being proportional to the length 
of the arc — and thus the former may be substituted for the latter. We 
may therefore consider that the angle A may be taken to represent 
both the length of the radius and the length of the arc. The angle 
A, called "the center angle," and its method of determination will 
now be presented. 
We have already stated that in the cylinder surface Ues the part 
of the circle which passes through each cusp of the bicuspids and 
molars and the middle point of the anterior face of the articular sur- 
face of the condyle. It is possible to determine the length of the 
radius of any given circle or arc from the three points taken on the 
circumference by means of the formula on page 172. The three 
points a, h, and K, from the buccal cusps of the bicuspids and molars 
and the middle point of the anterior face of the articular surface of 
the condyle, would be preferable, since the distances between adjacent 
points should be as great as possible for the sake of exact measure- 
ments. I have however chosen the point h instead of the point i, 
because the point i in the third molar is not only absent in some cases, 
but also shows great variation. Speaking more precisely, the mesio- 
buccal cusp in the most posterior molar was chosen for the present 
purpose instead of the disto-buccal cusp. For measuring the constants 
a (ah), /3 (hK) and y (aK) on the skull (fig 4), the directions which 
were given in the preceding section should always be followed. It 
must be emphasized here again that the circle, and the triangle which 
was formed connecting the three points, were both projected upon the 
Sin — = 
2 
Chord 
2r 
IV. DETERMINATION OF THE LENGTH OF RADIUS 
