BOW'S METHOD OF DRAWING DIAGRAMS IN GRAPHICAL STATICS. 497 



The stresses in the corresponding pieces of fig. 1 and fig. 3 are all equal if 

 they are equal in any pair of them. 



If in the frames represented in fig. 1 and fig. 3, we consider that the 

 pieces OS and TP cross one another at V without intersecting, we have six 

 points 0, P, Q, R, S, T joined by nine lines. Now in general if p points in 

 a plane are joined by 2p 3 lines the figure is simply stiff, that is to say 

 the form of the figure is determined by the lengths of the lines, and there are 

 no necessary relations between the lengths of the lines. 



But in Peaucellier's linkage the length of any line, as OT, is determined 

 when those of the other eight are given. For if a is the length of a side 

 of the rhombus, b the length of either arm OR or OS, c the length of either 

 arm TP or TQ, then if OT=d, 



Hence if any one of the nine pieces of the linkage be removed, the motion 

 of the remaining eight will be the same as before, and a given stress in any 

 one of the nine will produce stresses in each of the other eight which are 

 determinate in magnitude when the configuration of the linkage is given, though 

 they alter during the motion of the linkage. 



VOL. II. 



63 



