17'. T.I '-. 



Let tlio plane of the" paper be the plane in which the 



act, and also be 

 perpendicular to the axis, 

 of which C is the pm- 

 'ii, and about which 

 the lever can move ; -1 . /> 

 the points of application 

 of the forces P, W\ a, ft 

 the angles which the d 

 tions of the forces make 

 with any straight line aCb 

 drawn through C on the 

 paper. Let R be the pres- 

 sure on the fulcrum, and 6 the angle which it makes 

 witli the straight line a Cb; then if we apply a force R 

 in the direction CR, we may suppose the fulcrum re- 

 moved, and the body to be held in equilibrium by the 

 forces P, W, .//. 



We shall resolve these forces in directions parallel and 

 perpendicular to aCb\ and also take their moments about (7; 

 then by Art. 57 we have the following equations : 



Pcosa- JTcos-72cos0 = (1), 



Psina+ W&inft-Rsm = (:>), 



and P. CD- W. CE=Q (3), 



CD and CE being drawn perpendicular to the directions of 

 Pand W. 



Those three equations determine the ratio of P to IT wlion 

 there is equilibrium ; and the magnitude and direction of the 

 pressure on the fulcrum. 



For equation (3) gives 



P_ _ CE _ perpendicular on direction of IT 

 W ~~ CD~ perpendicular on direction of 1'" 



> by transposing the last terms of (1) and (2), we have 

 R cos 6 = Pcos a - IFcos , 

 R sin 6 = Psin a 4- TFsin ft. 



