134 Static** 



and hence 



** 



X FL : X FM, 



that is, since -- = 



u : v :: FL : FM; 

 from which we obtain as before, 



q : p : : FL : FM. 



. 10 _ 231. In the wheel and axle, when motion commences, the 

 points of application of the power and resistance describe similar 

 arcs, or arcs of the same number of degrees, the one upon the 

 circumference of the wheel, and the other upon that of the axle. 

 The directions of the forces are tangents to these arcs, whose 

 lengths are to each other as the radii IB, /^, of the axle and 

 wheel ; in this machine, therefore, we have 



: v : : IB : 1A, 

 and accordingly 



q : p : : IB : IA< 



232. In the pulley, if, while the weight p describes in rising 

 ^ l> 95 ' a space equal to w, each of the two cords which meet at the 

 moveable pulley, is shortened by the same quantity w, the cord 

 to which is suspended the power 9, will be lengthened by a 

 quantity equal to 2tf, which will consequently be the space 

 passed through by q in its descent. Taking, therefore, v = 2 w, 

 w.e shall have, in the case of an equilibrium, 



q : p : : u : v, 

 :: 1 : 2; 



or generally, the cords being parallel, 

 q :p :: 1 ; n, 



n denoting the number of cords that meet at the moveable 

 pulley. 



I will take, as the last example, the assemblage of pulleys, 

 represented in figure 87. If the power <?, in descending, pass 

 over a space v, the point JV will be elevated by a quantity 



