66 PRACTICAL LESSONS IN SCIENCE. 



ings, and on shipboard for raising the anchor or drawing the 

 ship to the dock, is a vertical wheel and axle. 



Sometimes the wheel and axle appears in a modified form as 

 when they are on separate axes and connected by belts, cogs or 

 friction, in which case equilibrium is obtained by using the ratio 

 of the circumferences or the radii as above. In the case of a com- 

 pound wheel and axle there will be equilibrium when the power 

 multiplied by the product of the radii of the wheels equals the 

 weight multiplied by the product of the radii of the axles. 



A pulley is a grooved wheel, turning freely on an axis, over 

 which runs a rope, to which the power and the weight are 

 attached. The frame of the pulley is the block and the pulley 

 may be fixed or movable. It is a lever of the first class having 

 equal arms. No force, or motion is gained by the use of a single 

 pulley, yet it is one of the most useful of the simple machines. By 

 its aid the sails of ships are adjusted, objects may be moved to 

 places otherwise inaccessible, and by the use of a horse or man 

 working on the ground, objects can be raised to the highest 

 elevations. 



In the case of a single pulley or group of pulleys with a single 

 rope, power multiplied into the vertical distance it moves equals 

 the weight into the vertical distance it moves. If the weight 

 is supported by one branch of the rope, power and weight are 

 equal. If the weight is supported by two branches of the rope, 

 as the weight rises both branches shorten and the power moves 

 twice as far as the weight, in which case power would equal 

 weight divided by two, so in a general way power equals weight 

 divided by the number of ropes supporting it. 



In the case of movable pulleys 

 with separate supporting ropes the 

 equation is: power equals weight, 

 divided by the power of two, whose 

 index is the number of pulleys. 

 A Fig. 8. C Any sloping surface may be used 



as a simple machine called an incline plane (See Fig. 8.) AB 

 represents the incline plane; BC the height of the plane; AC the 



