Wheel and Axle. Ill 



that is, in the wheel and axle the power is to the weight, as the radius 

 of the cylinder to the radius of the wheel. 



187. If the weight/) be attached at some point B in the plane 

 of the wheel, in such a manner, that the perpendicular IB upon 

 its direction shall be equal to the radius of the cylinder, we may 

 consider AIB as an angular lever the fulcrum of which is at the 

 centre /; and in order to an equilibrium, we must have 159 



q : p : : El : AI, 



that is, the ratio between the power and the weight would be the 

 same as the above. Therefore the action of the power is trans- 

 mitted to the weight by means of the wheel and axle, in ihe same 

 manner as if the power and the weight were in the same plane. 



188. It is not the same, however, with respect to the force 

 exerted against the supports. This varies according to the dis- 

 tance of the plane BDL from the plane of the wheel. In order Fig.lOL 

 to determine what it is, we decompose the power q, considered 



as applied at parallel to A q, into two forces parallel to A q, 

 and passing through F and F. We decompose likewise the S5 

 power /?, considered as applied at /, into two forces parallel 

 to p D, and passing through F and F. By this means each 

 support will be urged by two forces, the magnitude and direc- 

 tions of which will be known. It will be easy, therefore, to re- 

 duce these forces, in the case of each support, to a single one of 

 a known magnitude and direction. 



This method of finding the forces exerted against the two sup- 

 ports, is founded upon the fact, that the two forces & and p reduce 

 themselves to one which acts at /. If we conceive this decompos- 

 ed into two forces parallel to the direction & and/?, and applied in /, 

 they will have simply the values of & and jo. Accordingly, (1.) 

 we may regard/? as applied at 7; (2.) The force ar, considered as 

 applied at /, and the force r applied at G, cannot but have for 

 a resultant the force q, by which they are produced, as we have 

 seen above ; moreover this resultant passes through E, since 



G7 : GE : : GB : GA : : q : *. 



189. If the power, instead of being applied in the direction 



of a tangent to the wheel, acted by means of the arms EE, and i<x>' 



