Chap. 7.] fbs Wheel and Axle. 75 



Hence it follows, that to elevate a weight by means 

 of this machine, it is required that the power P fhould 

 be to the weight G, as the radius of the cylinder hg, 

 is to the lever h P j or, which amounts to the fame, as 

 the radius of the cylinder is to the radius of any wheel 

 or handle by which it may be turned. If in a ftate of 

 equilibrium the power is lefs than the weight, and that 

 in the proportion of the radius of the cylinder to that 

 of the handle which turns it, fo in a (late of motion the 

 power has more velocity than the weight, and that in 

 proportion as the radius of the handle or wheel that turns 

 it is to that of the cylinder. This rule fuppofes that the 

 power is always perpendidular to the radius by which it 

 acts; for the direction of the weight is always perpendi- 

 cular to the radius of the cylinder, fince the cord that 

 fuftains it is always a tangent to its circumference. 



In great efforts, ' as it is necefTary that the arms of 

 the lever of power Ihould be very long; when there- 

 fore it is extremely inconvenient to make them fo, and 

 when to multiply the number of them would weaken 

 the head of the cylinder too much, it has been the 

 practice to unite the extremities of the radii or cogs by 

 a circumference, and form a kind of wheel to which 

 other cogs are adapted, by which it is turned by men ; 

 as may be feen in the wheels ufed at quarries and for 

 cranes (fig. 8.) 



The capjtan is a real windlafs, and it differs only 

 in the pofition of the cylinder, which is vertical, where ^ 

 as in the windlafs it is horizontal. The manner of a 

 power acting upon a refiftance or burden, by means 

 of a wheel and axle or windlafs, is entirely applicable 

 to the capftan, but the latter is more advantageous. 

 Capftans are often fixed in fliips, to raife anchors or 

 other burdens to which cables are fattened, \s hich are 

 rolled or coiled upon the cylinder. 



It 



