40 MECHANIC POWERS. 



cogs of the wheel ; here it is plain, that the winch 

 and trundle would make ten revolutions for one of 

 the wheel A B and its axis C D on which the rope 

 K winds in raising the weight W ; and the winch 

 being no longer than the sum of the semi-dia- 

 meters of the great axle and rope, the trundle 

 could have no more power on the wheel than a 

 man could have by pulling it round by the edge, 

 because the winch would have no greater velocity 

 than the edge of the wheel has, which we here 

 suppose to be ten times as great as the velocity of 

 the rising weight ; so that, in this case, the power 

 gained would be as is 10 to 1. But if the length 

 of the winch be 13 inches, the power gained will be 

 as 20 to 1 ; if 19-£- inches (which is long enough 

 for any man to work by), the power gained will be 

 as 30 to 1 ; that is, a man could raise 30 times as 

 much by such an engine, as he could do by his 

 natural strength without it, because the velocity 

 of the handle of the winch would be 30 times as 

 great as the velocity of the rising weight ; the 

 absolute force of any engine being in proportion 

 of the velocity of the power, to the velocity of the 

 weight raised by it. But then, just as much power 

 or advantage as is gained by the engine, so much 

 time is lost in working it ; which is common in all 

 mechanical cases whatever. 



In this sort of machines, it is requisite to have a 

 ratchet wheel on the end of the axle C, with a 

 catch to fall into its teeth j which will at any time 

 support the weight, and keep it from descending, 

 if the person who turns the handle should, through 

 inadvertency or carelessness, quit his hold while 

 the weight is raising. By this means, the danger 

 is prevented which might otherwise happen by the 

 running down of the weight when left at liberty. 



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