100 Statics. 



one direction, must be equal to the sum of the moments of those which 

 tend to turn it in the opposite direction ; which may be expressed 

 generally, by taking with contrary signs the moments of the forces 

 which tend to turn the lever in opposite directions, and saying, 

 that the sum of the moments must be zero. 



173. According] jr, all that we have said with respect tq the 

 63 value and direction of the resultant, is applicable here to the 

 determination of the force exerted against the fulcrum, and the 

 position of this point, whatever be the number of powers. 



Fig 78. 174. Knowing, for example, the twoweightsp and ^together with 

 the length and weight BD of the lever, if we would determine 

 the fulcrum JP, upon which the whole would remain in equilibri- 

 um, we should consider the weight of the lever as a new force r, 

 applied at the centre of gravity G of the lever, and it would be 

 necessary that the moment of p with respect to the unknown 

 point F should be equal to the sum of the moments of r and ^, 

 taken with respect to the same unknown point F. 



Let the lever BD be straight, and of a uniform magnitude 

 and specific gravity ; and, bearing in mind, that on account of 

 the directions of the forces being parallel, instead of the per- 

 pendiculars jPL, FK) FM, we may employ the parts BF, FG, 

 FD, which have the same ratio to each other, we shall have 



p x BF = r X FG + q X FD. 



Let a be the length of the lever, a; the distance BF-, we shall 

 have, 



BG = I a, FG = -J a x, FD = a x. 



Let s be the specific gravity of the lever, or, in other v.ords, the 

 weight of each inch in length of this lever; a and a; being also 

 counted in inchts ; s a will be the whole weight r. We have 

 accordingly, 



p x = s a ( J a x) + q (a x), 

 = -I sa 2 sax -f- q a q x, 

 from which we obtain 



x = ii^!_JL a 

 p + s a -f q 



