518 ON RECIPROCAL FIGURES AND DIAGRAMS OF FORCES. 



The quadrilateral DEGF corresponds to the point of quadruple concourse 



The pentagon ACKLH corresponds to the meeting of the five lines acfdh. 



In drawing the reciprocal of fig. 2, it is best to begin with a point of triple 

 concourse. The reciprocal triangle of this point being drawn, determines three 

 lines of the new figure. If the other extremities of any of the lines meeting 

 in this point are points of triple concourse, we may in the same way deter- 

 mine more lines, two at a time. In drawing these lines, we have only to 

 remember that those lines which in the first figure form a polygon, start from 

 one point in the reciprocal figure. In this way we may proceed as long as 

 we can always determine all the lines except two of each successive polygon. 



The case represented in figs. 3 and III. is an instance of a pair of reci- 

 procal figures fulfilling the conditions of possibility and determinateness, but 



Fig. III. 



Fig. 3. 



presenting a slight difficulty in drawing by the foregoing rule. Each figure has 

 here eight points and eight polygons ; but after we have drawn the lines s, 

 n, o, k, r, we cannot proceed with the figure simply by drawing the last two 

 lines of polygons, because the next polygons to be drawn are quadrilaterals, and 

 we have only one side of each given. The easiest way to proceed is to produce 

 abed till they form a quadrilateral, then to draw a subsidiary figure similar to 

 tlmpq, with abed similarly situated, and then to reduce the latter figure to 

 such a scale and position that a, 6, c, d coincide in both figures. 



