100 Blake on the Teeth of Cog-Wheels. 
the velocities of their planes at the describing point shall be 
constantly equal, two curves will be traced on the planes of 
contact in the line of centres. Now sinne ed is equal to py: 
ad is equal to af: Therefore, in the progress of the mo- 
tion or action, the points c and d meet and coincide with 
each other at f, But it has been shown that these two points 
are equidistant from the point p. . Im the same manner it 
may be shown that any other points which are equidistant 
from p meet and coincide with each other. Therefore, in 
any given space of time, equal quantities of the two curves 
pe and pd pass through the point of contact p. Wherefore 
they roll upon each other without silding, and consequent- 
ly without friction. 
or.—By varying the relative velocities of the circles and 
describing point, an infinite variety of atripsic curves may 
uced, 
sHOL.—By a similar process of reasoning it may be 
shown, that no curves are atripsic, but such as are described, 
or are capable of being described in this manner. 
