THE LEVER AND WHEELWORK. 253 



WHEELWORK. 



When a lever is applied to raise a weight, or overcome a resistance, the 

 space through which it acts at any one time is small, and the work must be ac- 

 complished by a succession of short and intermitting efforts. In fig. 4, after 

 the weight has been raised from W to W', the lever must again return to its 

 first position, to repeat the action. During this return the motion of the weight 

 is suspended, and it will fall downward unless some provision be made to sus- 

 tain it. The common lever is, therefore, only used in cases where weights are 

 required to be raised through small spaces, and under these circumstances its 

 great simplicity strongly recommends it. But where a continuous motion is to 

 be produced, as in raising ore from the mine, or in weighing the anchor of a 

 vessel, some contrivance must, be adopted to remove the intermitting action of 

 the lever, and render it continual. The various forms given to the lever, with 

 a view to accomplish this, are generally denominated the wheel and axle. 



In fig. 10, A B is a horizontal axle, which rests in pivots at its extremities, 



Fig. 10. 



or is supported in gudgeons, and capable of revolving. Round this axis a rope 

 is coiled, which sustains the weight W. On the same axis a wheel, C, is 

 fixed, round which a rope is coiled in a contrary direction, to which is append- 

 ed the power P. The nroment of the power is found by multiplying it by the 

 radius of a wheel, and the moment of the weight by multiplying it by the radius 

 of its axle. If these moments be equal, the machine will be in equilibrium. 

 Whence it appears that the power of the machine is expressed by the* propor- 

 tion which the radius of the wheel bears to the radius of the axle ; or, what is 

 the same, of the diameter of the wheel to the diameter of the axle. This prin- 

 ciple is applicable to the wheel and axle in every variety of form under which 

 it can be presented. 



It is evident that, as the power descends continually, and the rope is uncoiled 

 from the wheel, the weight will be raised continually, the rope by which it is 

 suspended being at the same time coiled upon the axle. 



When the machine is in equilibrium, the forces of both the weight and power 

 are sustained by the axle, and distributed betwen its props, in the manner ex- 

 plained in fig. 7. 



When the machine is applied to raise a weight, the velocity with which the 

 power moves is as many times greater than that with which the weight rises, as 

 the weight itself is greater than the power. This is a principle which has already 

 been noticed, and which is common to all machines whatsoever. It may hence 

 be proved that, in the elevation of the weight, a quantity of power is expended 

 equal to that which would be necessary to elevate the weight if the power were 

 immediately applied to it, without the intervention of any machine. This has 

 been explained in the case of the lever, and may be explained in the present 

 instance in nearly the same words. 



