Composition and Decomposition of Forces. 25 



the parallelogram, we may infer generally that any two forces 

 which unite in the same point are always in the same plane 

 with their resultant. 



Of the Composition and Decomposition of Forces. 



42. Not only is it possible, by the principle above establish- 

 ed, to reduce two concurring forces to one, and to decompose 

 one into two others ; but we can in general reduce to a single 

 force, as many o.ther forces as we please, when they are in the 

 same plane, or when they unite at the same point ; and recipro- 

 cally, we can decompose one or several forces into as many other 

 forces as we please. 



43. But before we proceed to explain this, we must observe 

 that when a force p acts upon a body either by pushing or by Fig. 7. 

 drawing it, it is of no consequence at what point of the direction 



of this force we suppose the action to be applied. For example, 

 let the force p be exerted upon the body m by means of a rod 

 inflexible and without mass, or by a thread inextensible and 

 without mass, it is the same thing, whether the force p be applied 

 at the point .B, or at the point C, or whether it be of such a nature * 

 as to admit of being exerted at any point Z), on the other side of 

 the body. So long as its action is employed in the same direc- 

 tion, the effect will be the same. Distance can have no influ- 

 ence, except so far as the action of the power transmits itself by 

 the aid of some instrument, as a Lever or a cord, the matter of 

 which would partake of the action of the power, all which in- 

 struments we at present leave out of consideration. 



Thus, if two forces p and </, exerted in the same plane, ac- Fig. 8. 

 cording to the lines EC, DB, draw or push a body by the two 

 points E, Z), this body is urged in the same manner as it would 

 be, if the two forces were both employed at their point of meet- 

 ing A, the directions being supposed to remain unchanged. . 



This being premised, we proceed to the consideration of the 

 composition and decomposition of forces. 



44. Let there be four forces, jt>, </, r, ^ directed in the man- Fig. 9. 

 ner represented in the figure,* and all in the same plane. Let us 



* The direction of a force is indicated by the .figure of an 

 arrow. 



Mech. 4 



