MECHANICS. 85 



consequence to find two numbers that will express 

 the ratio, not exactly, but more nearly, than can be 

 done by smaller numbers. The method of finding 

 such numbers, is explained in the Elements of Alge- 

 bra. See EULER, Elem. cTAlgebre, torn. IT. Addi- 

 tions, 19. ; also WOOD'S Algebra, 371. 



Of the Pulley. 



143. The pulley is a wheel moveable on an axis 

 with a groove cut in its circumference, round 

 which a cord passes. The axis of the pulley is 

 either fixed or moveable. When fixed, the pulley 

 gives no mechanical advantage, but serves merely 

 to change the direction of the power applied to the 

 cord which passes over it. When the axis of the 

 pulley is moveable, one end of the cord is made 

 fast to a fixed point ; the power is applied to the 

 other, and the weight hangs by the block in which 

 the axis of the pulley is fixed. By a single pulley 

 of this construction, a force is enabled to balance 

 another twice as great. 



Various combinations of pulleys give various degrees of 

 advantage ; but in every case there is an equilibrium, 

 when the spaces that would be passed over by the 

 power and the weight in the same time, are in the in- 

 verse ratio of their quantities. 



It is obvious, that the pulley is reducible to the lerer 

 of the second kind, or, still more directly, to the 

 >case, 128. of a body supported by two props. 



The 



