254 



Prof. Maxwell on Reciprocal Figures 



The five triangles ADB, EBC, GJK, IJL, HIF corre- 

 spond to five points of triple concourse, a d b, ebc, gj k, ij I, h if. 



The quadrilateral D E G F corresponds to the point of qua- 

 druple concourse degf. 



The pentagon ACRLH corresponds to the meeting of the 

 five lines acklh. 



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 determine 

 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 in- 

 stance of a pair of reci- 

 procal figures fulfilling the 

 conditions of possibility 

 and determinateness, but 

 presenting a slight diffi- 

 culty in drawing by the 

 foregoing rule. Each fi- 

 gure has here eight points 

 and eight polygons ; but 

 after we have drawn the 

 lines s, n> o, k, r, we can- 

 not proceed with the figure 

 simply by drawing the last 

 two lines of polygons, 

 because the next polygons 

 to be drawn are quadrilate- 

 rals, 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 1 1 mp q, with 

 abed similarly situated, 

 and then to reduce the 

 latter figure to such a scale 

 and position that a, b, c } d 

 coincide in both figures. 



Fig. 3. 



Fig. III. 



