Wheel and Jlxle. 113 



192. It would seem, therefore, by having regard only to an 

 equilibrium, that we might diminish at pleasure the ratio of the 

 power to the weight, and make a force, however small, counter- 

 balance one however large, by means of the wheel and axle, 

 and such machines as depend upon the same principle. But if we 

 take into consideration their motion, and have respect also, as we 

 must, to the nature of the agents to be employed, we cannot aug- 

 ment the effect at pleasure. The ratio of the radius of the cyl- 

 inder to that of the wheel, is not arbitrary. It requires a par- 

 ticular adaptation to the purpose proposed, in order to produce 

 the greatest possible effect. 



Suppose, for example, that the agent applied to the arm E, Fig 99. 

 tends to move with a velocity w, a id that the force of which it 

 is capable, is raw, that is, equal to a known mass ra urged with 

 a velocity u. Let v be the velocity with which the point E 

 would be moved in virtue of the resistance of p ; then, if we call 

 jD the perpendicular distance of E from the axis, and tf that of 

 p from the axis, we shall obtain the velocity thatp would have, 

 by the proportion, 



since it is evident, that the point E and the point where the cord 

 touches the cylinder, would have velocities proportional to tLeir 

 distances from the axis. 



We must suppose, therefore, that at the instant when the 

 power comes to exert itself, the velocity u is composed of the 

 velocity i>, which actually takes place, and the velocity u i>, 

 which is destroyed ; and that at the same instant the weight p has 



the velocity -^-, which actually takes place, and the velocity -jr- 



in the contrary direction which is destroyed ; that is, the moving 

 force m (u v) must be in equilibrium with the mass p, urged 



with the force ? f) . Accordingly, 



whence 



muD* 



V m D* 



Meeh. 15 



