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 wheel 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 or small, 

 by traversing the same space through which the weights are caused 

 to descend. This velocity it can never absolutely attain, however 

 much the weight may be increased, or the wheel diminished, since 

 the communicating of momentum to any quantity of matter however 

 small implies the loss of a corresponding quantity in the moving body 

 which transfers it. But for all purposes of experiment, the approxi- 

 mation might soon be so near as to render the difference between the 

 velocity due to gravity and that actually attained by the surface of 

 the axis at the moment the cord leaves it, wholly unappreciable. 



Art. IV. — Investigation of the Epicycloid ; by E. F. Johnson, of 

 Middletown, Conn. 



1. If a circle, as AMK, (figs. 1 and 2,) remain fixed, and another 

 circle ABF, called the generating circle, be made to revolve upon 

 its circumference, in the same plane with it, either externally or in- 

 ternally, the line described by any point, as B, in the circumference 

 of the generating circle, from the time of its leaving the circumfer- 

 ence of the fixed circle until it returns to it again, is called a plane 

 epicycloid. 



