THE LEVER AND WHEELWORK. 



In one revolution of the machine the length of rope uncoiled from the wheel 

 is equal to the circumference of the wheel, and through this space the power 

 must therefore move. At the same time the length of rope coiled upon the axle 

 is equal to the circumference of the axle, and through this space the weight 

 must be raised. The spaces, therefore, through which the power and weight 

 move in the same time, are in the proportion of the circumferences of the 

 wheel and axle ; but these circumferences are in the same proportion as 

 their diameters. Therefore the velocity of the power will bear to the 

 velocity of the weight the same proportion as the diameter of the wheel bears 

 to the diameter of the axle, or, what is the same, as the weight bears to the 

 power. % 



We have here omitted the consideration of the thickness of the rope. When 

 this is considered, the force must be conceived as acting in the direction of the 

 centre of the rope, and therefore the thickness of the rope which supports the 

 power ought to be added to the diameter of the wheel, and the thickness of the 

 rope which supports the weight to the diameter of the axle. It is the more 

 necessary to attend to this circumstance, as the strength of the rope necessary 

 to support the weight causes its thickness to bear a considerable proportion to 

 the diameter of the axle ; while the rope which sustains the power not requir- 

 ing the same strength, and being applied to a larger circle, bears a very incon- 

 siderable proportion to its diameter. 



In numerous forms of the wheel and axle, the weight or resistance is applied 

 by a rope coiled upon the axle ; but the manner in which the power is applied 

 is very various, and not often by means of a rope. The circumference of a 

 wheel sometimes carries projecting pins, as represented in fig. 10, to which 

 the hand is applied to turn the machine. An instance of this occurs in the 

 wheel used in the steerage of a vessel. 



In the common windlass the power is applied by means of a winch, which is 

 a rectangular lever, as represented in fig. 11. The arm B C of the winch 



Fig. 11. 



represents the radius of the wheel, and the power is applied to C D at right 

 angles to B C. 



In some cases no wheel is attached to the axle ; but it is pierced with holes 

 directed toward its centre, in which long levers are incessantly inserted, and a 

 continuous action produced by several men working at the same time ; so that, 

 while some are transferring the levers from hole to hole, others are working 

 the windlass. 



The axle is sometimes placed in a vertical position, the wheel or levers 

 being moved horizontally. The capstan is an example of this : a vertical axis 

 is fixed in the deck of the ship ; the circumference is pierced with holes pre- 

 sented toward its centre. These holes receive long levers, as represented in 

 fig. 12. The men who work the capstan walk continually round the axle, 

 pressing forward the levers near their extremities. 



