62 FERGUSON'S LECTURES. 



turned by a winch ; which will make the power of the 

 engine to exceed the power of the man who works it, as 

 much as the number of revolutions of the winch exceed 

 those of the axle D, when multiplied by the excess of 

 the length of the winch above the length of the semi- 

 diameter of the axle, added to the semidiameter or half 

 thickness of the rope K, by which the weight is drawn 

 up. Thus, suppose the diameter of the rope and axle 

 taken together, to be 13 inches, and consequently, half 

 their diameters to be 61 inches ; so that the weight W 

 will hang at 6 inches perpendicular distance from below 

 the center of the axle. Now, let us suppose the wheel 

 A B, which is fixed on the axle, to have 80 cogs, and 

 to be turned by means of a winch six inches long, fixed 

 on the axis of a trundle of eight staves or rounds, work- 

 ing in the cogs of the wheel. Here it is plain, that the 

 winch and trundle would make 10 revolutions for one of 

 the wheel A B, and its axis D, on which the rope K 

 winds in raising the weight W; and the winch being no 

 longer than the sum of the semidiameters 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 10 to 1. But if the length of the winch be 

 12 itches, the power gained will be as 20 to 1 : if 18 

 inches (which is long enough for any man to work by) 

 the power gained would 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 to the velocity 

 of the power to the velocity of the weight raised by it. 



