

Composition and Decomposition of Forces. 31 



AF parallel to the direction of p; and having assumed this 

 line as the direction of one of the components, we take arbit^ari- 

 ly for the value of this component any quantity p smaller than 

 p, if it is proposed that the two components should act on oppo- 

 site sides of the force p ; the second component q must in this case 

 be equal to p p ; and in order to find its position, it is only 

 -necessary, having drawn any straight line CBA, to take in AB 

 produced the part J5C, such as to give the proportion 



q : p :: AB : BC; 



then through the point C we draw /C, parallel to EB, and this 

 will be the direction of the force q. 



But if the two component forces are required to be on the 

 same side (in which case they will be directed opposite ways), 

 then we take for p any quantity, whether greater or less than p, 

 and if it be greater it will be directed the same way with p, and 

 if less, it will have a contrary direction with respect to p. Hav- 

 ing drawn a line AF parallel to EB, as the direction of p, we take 

 upon any assumed line BAG the point C, such as will give 



p porp p : p :: AB : AC ; 



and C will be the point through which the force q must pass par- 

 allel to the given force p; and the point C will be beyond A with 

 respect to , when p \$ greater than p ; and it will be between A 

 and B, when p is less than p. 



56. Since what we have now said of the force p with respect 

 to the components />, </, may evidently be applied to each of 

 these latter forces, it will be seen how we may substitute for any 

 single force, as many others as we please, the directions of which 

 are parallel. 



Of Moments and their Use in the Composition and Decomposition of 



Forces. 



57. The propositions we have established, are sufficient for 

 the composition and decomposition of forces, whatever be 

 their magnitudes and directions, provided they act in the same 

 plane. But the different kinds of motion which we have to con- 

 sider, require more simple and more expeditious means for de- 

 termining the resultant of forces, and its direction* 



