280 Investigation of the Epicycloid. 
referred to this cause, since the actual amount of the resistance of the 
air at the velocity obtained from a one pound force, could not be 
known, unless we could perform the experiment first in vacuo, and 
then in the open air. But when we find that the higher velocities 
cause greater proportional losses, on the pivot of greater friction, the 
air having certainly greater effect there than at the lower velocities 
and a fortiori, greater still on the pivot of least friction, we are com- 
pelled to infer that the superior proportional loss must be due to the 
greater effect of friction at high velocities. 
It is evident that as the weight producing momentum in the wheel 
is increased, it must develope the cord in less time than when the 
smaller force is employed. But if the forces or weights employed 
for this purpose were greatly increased so as to bear a high propor- 
tion to the size and weight of the wheel, the times in which they 
would make their descent might approach very nearly to that by 
which they would descend by gravity alone ; and the limit to the 
increment of velocity in the wlicel when set in motion by weights, 
must obviously be found, when the surface of the axis over which the 
moving cord is applied, has attained the same velocity as that which 
gravity would give to any heavy falling body whether great of small, 
by traversing the same space through which the weights are caused 
small implies the loss of a corresponding quantity i the moving boay 
mation might soon be so near as to render the differene 
velocity due to gravity and that actually attained by t 
the axis at the moment the cord leaves it, wholly unappreciable. 
Se eee 
Anr. IV.—Investigation of the Epicycloid; by E. F. Joaxs™ of 
Middletown, Conn. 
1. If acircle, as AMK, (figs. 1 and 2,) remain fixed, and another 
circle ABF, -called the generating circle, be made to revolve ae 
its circumference, in the same plane with it, either externally of "i 
ternally, the line described by any point, as B, in the circ 
of the generating circle, from the time of its leaving the circu es 
ence of the fixed circle until it returns to it again, is called a oe 
epicycloid. 
