CHAP. H.] DIFFERENT POINTS OF APPLICATION. 19 



resultant upon the components, are to each other inversely as the 

 components. Regarding any point of the resultant as a centre 

 of moments, the moments of the forces then are equal, and of 

 course the forces themselves are inversely as their lever arms. 



19. Equilibrium Polygon. If we consider the forces P t 

 P 2 , Figs. 8, 9. and 10, held in equilibrium by their components 

 C 0, 1 C, and 2 C, C 1, which act parallel to the lines S Si 

 and S 2 ; then regarding the line S t or c d as part of the mate- 

 rial plane in which the forces act, C 1 and 1 C balance one 

 another, and cause either tension or compression in c d. Sup- 

 pose the resultant R is to act so as to cause equilibrium, or 

 prevent the motion of the plane due to P! and P 2 . Then R 

 must act upwards in Figs. 8 and 9, and downwards from 2 to 

 in Fig. 10. In Figs. 8 and 9 then, S and S 2 act away from 

 c and d (Art. 4), and in Fig. 10 towards c and d. Following 

 round the force polygon, we find in the first two cases c d in 

 tension, in the last c d in compression. 



In the first two cases, the points of application c and d of S 

 P! and S 2 P 2 if connected by a string stretched between c 

 and d will be perfectly fixed and motionless ; while in the lat- 

 ter case, the string must be replaced by a strut. In case of 

 three or more forces the polygon or broken line which we thus 

 obtain, by choosing a pole, drawing lines to the beginning and 

 end of the forces in the force polygon, and then parallels tc 

 these lines intersecting the lines of direction of the forces in the 

 force diagram, we call the " string " or "funicular polygon" 

 or the " strut polygon" according as the forces act to cause 

 tension or compression along these lines. We can apply to 

 both cases the general designation of polygon of equilibrium or 

 " equilibrium polygon"* The perpendicular let fall from the 

 pole C upon the direction of the resultant in the force polygon. 

 we call the "pole distance " and shall always designate it by 

 H. The straight line joining the points c and d, or the begin- 

 ning and end of the equilibrium polygon, we call the "strut" 

 or " tie line " or generally the " closing line " and designate it 

 by Ii. The convenience and application of these terms and 

 conceptions will soon appear. In the present case of only two 

 forces, the equilibrium polygon becomes a straight line and 

 coincides with L, or c d. 



[NOTE. We repeat that in order to determine the quality of 



* The term u equilibrium polygon" is preferred to "funicular," as it ex- 

 presses the idea generally, without implying either tension or compression 

 alone, in the sides. 



