Stiffness of Cords. 1 59 



ness of cords, agrees nearly with this law ; but all the experi- 

 ments that have been made upon this subject have not hitherto 

 agreed so perfectly with the theory as might be wished. 



255. We shall now illustrate the foregoing principles by an 

 example. For this purpose, let us suppose the common radius 

 of the pulley to be 2 inches, that of the axle j of the same quanti-f<; g4 go 

 ty, and the diameter of the cords to be | of an inch. Let us 

 take, moreover, the result of experiments on this subject, namely, 

 that a cord of half an inch diameter, loaded with 120 lb , and pass- 

 ing over a pulley of f of an' inch, occasions, by its stiffness, a 

 resistance of 8 lb . 



This being established, the weighty being 400 lb , as in article 

 242, the branches 1 and 2 will be loaded, both on account of 

 this weight and the force added to q to overcome the friction, by 

 a force equal to 209 lb , 6. Multiplying, therefore, this weight by 

 % of an inch, the diameter of the cord, and dividing by 2 inches, 

 the radius common to all the pulleys ; multiplying also the weight 

 120 lb , used in our experiment, by , the diameter of the cord, 

 and dividing by f , the radius of the pulley, in the experiment in 

 question ; we shall have for the results, 34, 93, and 40. Now 

 in order to obtain the force required by the stiffness of the cord 

 1, 2, which passes beneath the moveable pulley, we must use 

 this proportion, 



40 : 34, 93 : : 8 lb : 6, 99 or 7 lb nearly ; 



this fourth term is the quantity which it would be necessary to 

 add to the tension of the cord 2, if the lower pulley were fixed ; 

 but since it is moveable, which diminishes the tension by |, as 

 we shall see below, we have only 3 lb , 5 to be added to 109 lb , 6, 

 by which this cord is already stretched ; the whole tension will 

 thus be 113 lb , 1. 



We have seen that on account of friction, the tension of the 242i 

 cord 3 ought to be equal to 1 20 lb , 7 ; therefore the whole force 

 by which the cord 2, 3, which passes over the fixed block, is 

 extended, is 1 13, 1 -f- 120, 7 on 233 lb , 8. Multiplying this force 

 as above, by , and dividing by 2, we shall have 38,97. Seeking 

 as before the value of the stiffness of the cord 2, 3, which passes 

 ever the fixed block, we shall have the proportion, 



