XXVI 



INTRODUCTION TO MECHANICS. 



for the sails are raised up the masts by the sailors on deck from the 

 change of direction which the pulley effects ; and the labour is faci- 

 litated by the mechanical power of a combination of pulleys. Pullies 

 are frequently connected, as described inj%. 32, both for nautical and 

 a variety of other purposes; but in whatever manner pulleys are con- 

 nected by a single string the mechanical power is the same in its 

 principle. 



The third mechanical power is the wheel and axle. Let us suppose 

 (fig. 33) the weight W to be a bucket of water in a well, which is to be 

 raised by winding the rope, to which it is attached, round the axle : if this 



Fig. 32. 



Fig. 33. 



be done without a wheel to turn the axle, no mechanical assistance is 

 received. The axle without a wheel is as impotent as a single fixed 

 pulley, or a lever, whose fulcrum is in the centre ; but add the wheel to 

 the axle, and you will immediately find the bucket is raised with much 

 less difficulty. The axle acts the part of the shorter arm of the lever, the 

 wheel that of the longer arm. The velocity of the circumference of the 

 wheel is as much greater than that of the axle, as it is further from the 

 centre of motion ; for the wheel describes a large circle in the same space 



Fig. 34. 



of time that the axle describes a small 

 one, therefore the power is increased 

 in the same proportion as the circum- 

 ference of the wheel is greater than 

 that of the axle. If the velocity of the 

 wheel were twelve times greater than 

 that of the axle, a power nearly twelve 

 times less than the weight of the bucket 

 would be able to raise it. Instead 

 of a wheel there is commonly attached 

 to the axle only a crooked handle, 

 which answers the same purpose 

 (Jig. 34). For the branch of the handle 

 A, which is united to the axle, repre- 

 sents the spoke of a wheel, and is as 

 effectuaFas an entire wheel ; the other branch, B, affords no mechanical 

 aid, merely serving as a handle ,to turn the wheel. Wheels are a very 



