44 MECHAXICS. 



together with the height to be raised. For instance, it 

 requires twice the force to raise two pounds as to raise 

 one pound, three times the force to raise three pounds, 

 and so forth. Also, twice as great a force is needed to 

 elevate any weight two feet as one foot, or three times as 

 great for three feet, and so on. Again, combining these 

 together, four times as great a force is required to raise 

 two pounds to a height of two feet as to raise one pound 

 only one foot ; eight times as great for four feet, and so 

 on. This holds true, no matter by what kind of ma- 

 chinery it is accomplished. Now this may all seem very 

 simple, but it serves to explain many difficult questions in 

 relation to the real power possessed by all machines. 



Take another example. Suppose that one wishes to 

 raise a weight of 1000 pounds to a height of one foot. If 

 his strength is equal to only 100 pounds, the weight 

 would be ten times too heavy for him. He might, there- 

 fore, divide it into ten equal j^arts of 100 pounds each. 

 Raising each part separately the required height of one 

 foot would be the same as raising one of them ten feet 

 higb. The weight is lessened ten times, but the distance 

 is increased ten times. But there are some bodies, as, for 

 example, blocks of stone or sticks of timber, which can not 

 well be divided into parts in actual practice. He there- 

 fore resorts to a machine or mechanical power, through 

 which the same result is accomplished by raising the 

 whole weight in one mass with his single strength ; but in 

 this case as well as the other, the moving force which he 

 applies must pass through ten times the space 6f the 

 weight. We arrive, therefore, at the general rule, that the 

 distance moved by the weight is as much less than that 

 moved by the power as the power is less than the weight. 

 This rule is termed by some writers the " rule of virtual 

 velocities,^'' virtual meaning not apparent or actual, but 

 according to the real effect, because the increase in 

 the velocity of the power makes up for increase in the size 



