98 THE WHEEL AND AXLE. 



arm, there will be an exchange of intensity of power for 

 velocity or time. In treating of the wheel and axle, unless 

 otherwise specified, reference is made to the former or usual 

 arrangement. 



182. Formulas for Wheel and Axle. The 

 law and formula for the lever apply here : 



P : W : : WF : PF, or, P : W : : r : R, 



the radii of the wheel and of the axle respectively being 

 represented by R and r. But it is a geometrical truth 

 that in any two circles, the ratio of their radii is the same 

 as the ratio of their diameters or circumferences. Hence 

 =n these ratios may be substituted for 



n __, r-r the ratio between the radii of the 



cJy u mm. L =, 



wheel and axle; or, 



P : W : : r : R. 

 P : W : : cl : D. 



FIG. 48. P : W :: c : C. 



183. Law of Wheel and Axle. TJie power 

 multiplied by the radius, diameter or circum- 

 ference of the wheel equals the weight multiplied 

 by the corresponding dimension of the axle. 



Note. If the radius of the axle be made the pow v er-arm, the for- 

 mulas will be as follows : 



P : W : : WF : PF, or, P : W : : D : d . 



184. Various Forms of Wheel and Axle. 



The wheel and axle appears in various forms. It is not 

 necessary that an entire wheel be present, a single spoke 

 or radius being sufficient for the application of the power, 



