80 Statics. 



Application of the Principles of Equilibrium to the Machines 

 usually denominated Mechanical Powers. 



139. The general object of machines is to transmit the ac- 

 tion of forces. The end to be attained is not always to augment 

 the action of which the power employed is capable, when applied 

 directly to the mass to be moved, or resistance to be overcome. 

 Sometimes it is merely proposed to transmit this action in a de- 

 terminate direction. At other times the purpose to be answered is 

 to cause a body to describe spaces regulated upon certain condi- 

 tions, relative either to time or other circumstances, conditions 

 which do not always require that the force employed should 

 augment as it is transmitted. We have examples of this kind of 

 machinery in clocks, watches, orreries, &c. 



The number and nature of the machines vary according to 

 the object we have in view. But to be able to determine their 

 effects, it is not necessary to consider them all separately. How- 

 ever compounded and varied they may be, they are merely com- 

 binations of a certain very limited number of simple machines. 



We come now to make known the properties of these simple 

 machines. We shall afterward proceed to show how these pro- 

 perties are to be applied in estimating the effects of compound 

 machines. 



There are now usually reckoned seven simple machines, 

 namely, the rope machine, the lever, the pulley, the wheel and axle, 

 the inclined plane, the screw, and the wedge. 



These machines, being considered simply with respect to a 

 state of equilibrium, may be reduced to two, and indeed to one, 

 namely, the lever. But in the case of motion, the nature of each 

 leads to particular considerations, and requires a separate treat- 

 ment. 



Of the Rope Machine. 



1 40. We proceed on the supposition that the ropes or cord* 

 employed are perfectly flexible. It will be shown, however, m 



