1 04.] 



PARALLEL FORCES. 



59 



III. Parallel Forces. 



104. Resultant of Two Parallel Forces. The graphical con- 

 struction of the resultant (Art. 85) fails in the case of parallel 

 forces. 



As an expedient, we may resolve one of the two given forces 

 into two components and then combine these successively 

 with the other force. Thus, resolving P (Fig. 22) into P' and 

 P" along the lines I and II respectively, we may compound P" 

 with Q, and their resultant (acting along III) with P'. The 

 resolution of P into two arbitrary components P', P" is best 

 done in a separate diagram, the force polygon, by taking i 2 equal 

 and parallel to P, and drawing from any arbitrary point O, 



Fig. 22. 



called the pole, Oi, O2, which will represent the components 

 P f , P" in magnitude and direction. Then drawing 2 3 equal 

 and parallel to Q, we find O$ as the resultant of P" and Q. 



The whole operation of finding the resultant R of two paral- 

 lel forces P, Q is therefore as follows. First construct \hzforce 

 polygon by making I 2 equal and parallel to P, 23 equal and par- 

 allel to Q ; 13 gives the magnitude and direction of the 

 resultant R. Then assume a pole O and draw O I, O 2, O$. 

 Now construct the so-called funicular polygon (or equilibrium 

 polygon) by drawing in the original figure a line I parallel to O\ 

 intersecting P say in/; through p a line II parallel to O2 in- 





