and Diagrams of Forces. 259 



When the conditions are fulfilled, the pieces of the frame can 

 support forces, but in such a way that a small disfigurement of 

 the frame may produce infinitely great forces in some of the 

 pieces, or may throw the frame into a loose condition at once. 



The conditions, however, of the possibility of determining the 

 ratios of the forces in a frame are not coextensive with those of 

 finding a figure perfectly reciprocal to the frame. The condition 

 of determinate forces is e = 2s— 2 • 



the condition of reciprocal figures is that every line belongs to 

 two polygons only, and e = s + /"— 2. 



In fig. 7 we have six points connected by ten lines in such a 

 way that the forces are all determinate ; but since the line L is 

 a side of three triangles, we cannot draw a reciprocal figure, for 

 we should have to draw a straight line / with three ends. 



If we attempt to draw the reciprocal figure as in fig. VII., we 

 shall find that, in order to represent the reciprocals of all the lines 

 of fig. 7 and fix their relations, we must repeat two of them, as 

 h and e by h 1 and e, so as to form a parallelogram. Fig. VII. is 

 then a complete representation of the relations of the force which 

 would produce equilibrium in fig. 7 ; but it is redundant by the 

 repetition of h and e, and the two figures are not reciprocal. 



FiR. 7. 



Fie. VII. 



S 2 



