38 MECHANIC POWERS. 



wheel, and is more powerful, in proportion to the 

 largeness of the circle it describes, compared with 

 the diameter of the axis. 



When the parts of the axis differ in thickness, 

 and weights are suspended at the different parts, 

 they may be sustained by one and the same power 

 applied to the circumference of the wheel, pro- 

 vided the product arising from the multiplication 

 of the power into the diameter of the wheel, be 

 equal to the sum of the products arising from the 

 multiplication of the several weights into the dia- 

 meters of those parts of the axis from which they 

 are suspended. 



In considering the theory of the wheel and axis, 

 we have supposed the rope that goes round the 

 axis to have no sensible thickness ; but, as in 

 practice this cannot be the case, if it be a thick 

 rope, or if there be several folds of it round the 

 axis, we must measure to the middle of the outside 

 rope, to obtain the diameter of the axis ; for the 

 distance of the weight from the centre is increased 

 by the coiling up of the rope. 



If teeth be cut in the circumference of a wheel, 

 and if they work in the teeth of another wheel of 

 the same size as Plate 2. fig. 3. it is evident that 

 both the wheels will revolve in the same time; and 

 the weight appended to the axis of the w T heel B 

 will be raised in the same time as if the axis had 

 been fixed to the wheel A. But if the teeth of 

 the second wheel be made to work in teeth made in 

 the axis of the first, as at fig. 4., since every part of 

 the circumference of the second wheel is applied 

 successively to the circumference of the axle of 

 the first, and since the former is much greater than 

 the latter, it is evident that the first wheel must go 

 round as many times more than the second, as the 



