48 ELEMENTS OF SCIENCE 



computed by this rule, and, inversely, any single force 

 may be considered as resolved into any number of forces 

 of which such single force would be the resultant. The 

 former process is called the composition and the latter 

 the resolution of forces, and both processes are most 

 frequently employed in the science of mechanics. 



In a system of balanced or statical forces, each is exactly 

 equal and opposite to the resultant of all the rest, as is 

 shown in a proposition known as the Polygon of Forces. 



Let us suppose that five forces are all acting at (from) 



FIG. 6. 



the point P, while their respective directions and in- 

 tensities, are represented by the five lines PF 1 , PF 2 , PF 3 , 

 PF 4 , and PF 5 , passing from those letters to P. Construct- 

 ing a parallelogram whereof PF 1 and PF' 2 are two sides, 

 the line PC will be their diagonal and resultant. Next 

 taking this resultant and the next force PF 3 as two sides 

 of another parallelogram, we find that PD will be their re- 

 sultant, and therefore the resultant of all the three forces. 

 Finally taking this latter resultant and constructing a 

 parallelogram from it and the fourth force, we find 



