ON THE FUNDAMENTAL PHOPERTY OF THE LEVER. 2g5 



Let the fulcru my* be-now removed, and let a weight E, of 

 1. pound, act upwards at the point/"; the eqivlibrium will 

 still continue ; but the weight E, of 1 pound, acting up- 

 wards aty, is equivalent to a weight G of 1 pound, actin* 

 downwards at B. Remove, therefore, the weight E, and 

 suspend the weight G from B ; then, since the equilibrium 

 is still preserved after these two substitutions, v/e have a 

 weight C, of one pound, acting at the extremity of the arm 

 AF, in equilibrio with the weights D and G, which together 

 make two pounds, acting at the extremity of the arm FB. 

 But FA is'to FB as 2 i)S to one ; therefore an equilibrium 

 takes place, when the weights are reciprocally proportional 

 to the arms, in the particular cas-e when the arms are as 2 to 

 1. By making Yf successively double, triple, &c. of FB, 

 it may in like manner be shuvvn, that, in these cases, the pro- 

 position holds tru'e. 



Prop. II. If two forces, acting at the extremities of the two P'op- ^^' 

 arms of a Iccer, and at equal angles to the arms, are in equi- 

 librio, they will be reciprocally proportional to the lengths of 

 the arms to which they are applied. 



Let AB, CD (fig. 2,) he two levers in contact at AB, and Demonstrated. 

 forming one straight line, A BCD. Bisect AB in /, and 

 CD in 9, and from the extremities A, B, suspend equal 

 weights pi, m, and from the extremities C, D, equal weights 

 K, n, so that wJtwrrCD : AB. If the two levers are now sup- 

 ported on the fulcray, qi, they will both be in equilibrio, and 

 will ftill form one straight line, the fulcrum^ being loaded 

 with a weightrzS m, and the fulcrum 9 with a weight— 2 h. 

 Let us now suppose the extremities B, C, of the levers to 

 adhere, and form one inflexible line AD ; and let an in- 

 verted fulcrum F be placed at the point of junction. The 

 equilibrium of the whole will evidently continue, and the 

 fulcray, (p, will be loaded as before. Remove the fulcra^, 

 9, and substitute in their place the weights 2 m, 2 w, acting 

 upwards, and equal to the load which they respectively sup- 

 port: The equilibrium will still continue. Now, instead of 

 the force m acting downwards at B, substitute an equal and 

 opposite force m', acting upwards at A, and instead of the 

 forcji » acting downwards at C, substitute an equal and op- 



posite 



