42 



LOCATION OF RESULTANT. 



Art. 36 



36. Location of Resultant. The resultant of P 1? P 2 , P 3 , and 



P 4 is easily located in 

 the space diagram 

 Fig. 27; for the re- 

 sultant of P x and P 2 

 must pass through m 

 and be parallel to R r 

 in Fig. 26 (c); the 

 resultant of 1^ and 

 P 3 must pass through 

 n and be parallel to 



R 2 in Fig. 26 (c) ; and the resultant of R 2 and P 4 , which is the 

 resultant of all the given forces in this case, must pass through o 

 parallel to R or ea ; m no p is the resultant polygon. If a force 

 equal to E is applied in the line op, there will be complete equi- 

 librium. // it is applied parallel to op, as in qr, the resultant 

 is a couple, because E is equal to R. If it is applied at an angle 

 to op, the force polygon will not close and there will be neither 

 equilibrium of translation nor of rotation. 



When the forces are parallel, or when the intersections m, 

 n, .0 fall beyond the drawing, this method of locating the resultant 

 fails. A method which is applicable in all cases will now be given. 



37. The String Polygon. In Fig. 28 there are four nearly 

 parallel forces. The force polygon gives the equilibrant E, or 



\ 



Fig. 28. 



the resultant R, in amount and direction. But to find the 

 location of E or R in the space diagram it is necessary to 

 resort to what is known as the string polygon, because the 

 forces are so nearly parallel that their intersections will not 



