Leder. 101 



Let a = 24 inches, p = 20 pounds, q = 4 pounds, s = -^ of 

 a pound ; we shall have, 



2 +' 4.24 24 + 96 

 - 



that is, the fulcrum F, in order that there may be an equilibrium, 

 must be placed 4 T 8 inches from the extremity B ; whereas by 

 neglecting the weight of the lever, we should have 



q a 96 A . . 



x = = .-. = 4 inches. 



p + q 24 



If, on the other hand, the point B and the point F were given, 

 and it were proposed to find the point D where the force q, sup- 

 posed to be known as well as />, must be applied to produce an 

 equilibrium ; designating BF by 6, and BD by y, the equation 

 of the moments, becomes ' 



p b = s y (-|- y 6) -f- q (y 6) 

 = \ sy 2 syb + qy qb; 



(2 q 2 s 6) y _. 2^ 

 * s 



and 





_ s 6 9 V(q s b) 2 + (2 p b + 2 q 6) s 



s 



The positive value of t/ in this result gives the distance BD in 

 figure 78, and the negative value gives the distance BD in figure 

 79, the distance BF being supposed without gravity. 



If we would have the distance or length y at which the 

 weight of the part FD would of itself be sufficient to counterbal- 

 ance the weight p, we should put q = 0, which reduces the above 

 result to 



= 



y = 



