496 BOW'S MOTHOD OP DRAWING DIAGRAMS IN GRAPHICAL STATICS. 



These three forces, if in equilibrium, must meet in some point T. We 

 may therefore suppose them to be stresses in three new pieces OT, QT, ST, 

 which will complete the frame. 



Lei us suppose that both and T are outside the rhombus, and that 

 OS intersect* PT in the point V, and let us apply Bow's method to construct 

 the diagram of stress reciprocal to this frame. 



If we letter the areas as follows, putting 



A for the rhombus PRQS, 

 B for the triangle PSV, 

 C for the triangle OTV, 

 D for the quadrilateral ORPV, 

 E for the quadrilateral QSVT, 

 and F for the space outside the frame, 



then, in the diagram of stress, the stresses of the four sides of the rhombus 

 will meet in A, and since the opposite sides of the rhombus are parallel, the 

 lines EA and AD will be in one straight line, and the lines BA and AF 

 will also be in a straight line. 



Also since in the frame the pieces OR and OS are equal, the angles 

 ORP, PSV are equal, and the corresponding angles FDA, ABE must be equal, 

 and therefore the quadrilateral BEFD can be inscribed in a circle, and therefore 

 the angles FEA, DBA are equal, and the corresponding angles in the frame 

 TQS, SPY are equal, and therefore PT is equal to QT. 



If; therefore, is in one diagonal of the rhombus, T must be in the 

 other diagonal. 



The diagram of stress is completed by drawing EC parallel to BD, and 

 DC parallel to BE, and joining FC. 



This diagram therefore consists of a parallelogram BDCE, a diagonal ED, 

 a point F in the circle passing through FBD, and four lines drawn from F 

 to the angles of the parallelogram. 



If we now begin with the diagram of stress, and proceed to construct a 

 frame reciprocal to it, the form of the frame will be different according to the 

 cyclical direction in which the sides of the rhombus PRQS are lettered. If 

 in the one case we have the points and T both outside the rhombus as 

 in fig. 1, in the other and T will both be within the rhombus as in fig. 3. 



