104 Statics. 



pulley should be equally stretched, and thus mutually destroy 

 each other. The second condition is derived from the first in 

 the following manner ; 



. 176. From the tension of the two parts of the rope which 



passes over the pulley, there results an effort upon the body of 



the machine which may be determined by taking in the direc- 



Fig. 83, ti ns f tne r P es ? beginning at their point of meeting, I A, IB, equal 



83, 84. to each other, and forming the parallelogram IADB, in which 



the diagonal ID represents the force exerted upon the body of 



the machine, I A being considered as representing the tension of 



the rope Op or OG. Now since IT, 70, are tangents, and 



IB = IA, 



it will be seen that ID produced would pass through the centre 

 F of the pulley. Therefore, if the body of the pulley is not 

 firmly fixed, ID cannot be destroyed, except the obstacle, what- 

 ever it be, which is to prevent the motion of the body of the 

 pulley, is situated in some point of the line IF, extending from the 

 centre F to the point of meeting of the two ropes. Thus, if the 

 pulley is destined to turn in a block FG, fixed to some point G 

 without, and admitting of a motion about G, an equilibrium will 

 Flg ' 8 ' not take place except when the block has the direction FL 



In like manner, if the body of the pulley, being embraced by 

 a rope fixed to the point G, is moveable, there will not be an 

 Fig. 84. equilibrium, except the effort applied at the centre F, or to the 

 fixed block at this centre, is exerted in such a direction as to 

 bisect the angle formed by the two parts of the rope OG, Tq 

 and is at the same time to the tension of OG, T q, 



:: ID : IA : IB. 



177. It is now easy to find the ratio of the tension of each 

 part of the rope that passes round the pulley, to the force exert- 

 ed upon the body of the pulley, and consequently to the force of 

 which the moveable pulley is capable. The tension of each part 

 ' of the rope being represented by 1A or its equal IB, the effort 

 which is exerted upon the body of the pulley, will be expressed 

 by ID. But in the triangle IAD 



