cos. * X cos. /3 X cos. y &c. where , /3, y, &c. are the angles which the 

 string's make with the direction in which the weight acts in each case. 



6. In a system of n pullies each hanging by a separate string, where the 

 strings are attached to the weight, P : W : : 1 .' 2 n 1. 



Cor. Supposing the weight of each pulley a, then the part of the 

 weight sustained by the pullies a X (2 n n 1) ; and .*. W 

 (2 n 1) P + (2 n n 1) a. 



PULLEY, on the ascent or descent of bodies over. 



1. If two bodies P and Q are connected by a string and hung over a 

 fixed pulley, the accelerating force, supposing P the heaviest, is g X 



P-Q 



-. Substitute this for F in the formulae for the rectilinear descent 



Xg*. 



of bodies ( see Motion) and we get 



2. If two bodies P and Q are connected to- 

 gether by a cord going over a fixed pulley, and 

 one of them Q descends down an inclined 

 plane, we have the moving force of Q = Q X 



TT 



=r- ; hence the moving force of Q when con- 



nected with P = -^ P = 



QH PL 



O H P T 



~~ j and accelerating force 



irx- 



LX 



If P draws up Q, accelerating force = g X , which may 



L X " " 

 be substituted for F as in the last Art. 



Let both bodies P and Q move upon inclined 

 planes, whose lengths are L and I respectively, 

 and having a common altitude H, and let Q be 

 .the descending body ; then moving force of > 



219 



