106 Statics. 



the sails of a vessel, by attaching it to one of the corners as rep- 

 resented in figure 86. 



Fig. 87. 179. If, therefore, the weight p is sustained by the power 5, 

 by means of several moveable pulleys, embraced each by a rope, 

 one extremity of which is attached to a fixed point, and the other 

 to the block of a pulley, the ratio of the power to the weight will 

 be that of the product of the radii of all the moveable pulleys to 

 the product of the chords of the arcs embraced by the ropes. 



Indeed if we call , p, the forces exerted at the centres of the 

 pulleys JV, JW, which are at the same time the tensions respective- 

 ly of the two ropes attached to the centres of N and M\ R, R/, R", 

 being the radii, and c, c', c", the chords of the arcs embraced 

 178. by the ropes in the several pulleys .AT, .A/, L, we shall have 



q : s : : R : c, 

 -a : (> : : R' : c', 

 9 : p : : R" : c" ; 



Alg.226. whence, by taking the product of the corresponding terms, 



(}&(> : -srQp :: RR'R" : c c'c", 

 or 



q : p : : RR'R" : c c f c" ; 



that is, when the cords are parallel, which gives 



c = 2 R, c' == 2 R 7 , c" * 2 R", 



q : p : : RR'R" : 2 R X 2 R' X 2 R", 



: : 1 : 2 X 2 X 2; 



in other words, the power is to the weight as unity to the num- 

 ber 2 raised to the power denoted by the number of moveable 

 pulleys. With three pulleys, for example, the power would sus- 

 tain a force eight times as great. 



130. But this arrangement of pulleys is not the most conven- 

 ient. It is more common to employ one of the forms represented 

 in figures 88, 89, 90, 91, 92, in which all the pulleys, both fixed 

 and moveable, are embraced by the same rope. Moreover all 

 the fixed pulleys are attached to one block, and all the moveable 

 pulleys to another. Sometimes the centres are distributed upon 

 different points of the same block as in figures 88, 89, 90, 91. 



