20 FORCES IN THE SAME PLANE. [oil ^P. H. 



the strain in c d, we have only to follow round the force poly- 

 gon iii the direction of the forces, and then refer to the forco 

 diagram. Thus Fig. 9, at c, P! S and S t act, and are in equi- 

 librium. The corresponding closed figure is given in the force 

 polygon (a). S acts away from c, PI acts downwards from 1. 

 Continuing this direction we find S x acting from 1 towards C. 

 Reversing this direction (Art. 4), we find that the resultant 

 which replaces S and P t acts from C to 1. Referring now to 

 the force diagram (&), and transferring this direction to the 

 point <?, we find this resultant acts to pull c away from d or 

 contrary to the direction of the force 1 C which replaces S 2 and 

 P 2 . The strain in c d is therefore tension. 



A much better way of arriving at the same result is to con- 

 sider the triangle c b d as a jointed frame which holds in equi- 

 librium the forces P t P 2 and R^. Then the strains in any two 

 pieces c d, c b, meeting at a point, are in equilibrium with the 

 force or forces acting at that point. 



Wo have then the force P x acting at apex c, decomposed tnto 

 strains along c b and c d (Art. 5) represented by C and 1 C in 

 the force polygon. All three are in equilibrium. P t acts 

 down. Follow down then from to 1 from 1 to C and C to 0. 

 Refer back now to apex c of the frame and transfer these 

 directions. The strain in c d acts away from the apex c and is 

 therefore in tension, while the piece c b would be in compres- 

 sion, since the direction of C is towards apex c. 



See also " practical applications " of the preceding chapter 

 for illustrations of this. In the same way follow round 1 C 

 Fig. 10 (a) and refer to (b) and S is in tension.'] 



2O. Case of a Couple. In Article 18 we remarked that the 

 pole can always be chosen in such a position as to give S and 

 83 intersecting within desired limits, provided that S and 83 or 

 the point and 2 do not coincide. This case however actually 

 happens, with a pair of equal and opposite forces that is, with 

 a couple. 



Thus in Fig. 1 1, PI. 3, we have two equal and opposite forces 

 PI, Pa- 



The force polygon closes : therefore the resultant is zero. 

 S and Sj are parallel, hence their point of intersection in the 

 equilibrium polygon is infinitely distant. By changing the 

 position of the pole, we see that S and 83 may take any posi- 

 tions in the plane. 



