Roever — Geometrical Constructions of Lines of Force. 211 



of parallelism the point of intersection is below A A, and the 

 part marked 2 is traced. This part necessarily has the same 

 asymptote as part 1. The point A on part 2 is reached when 

 the line AP makes an angle it with A A, and then the line 

 AP is tangent to part 2 at A. On further rotation the part 3 

 of a loop is traced. The point A on this loop is reached 



when AP makes an angle it with AO, and then AP is tan- 

 gent to part 3 at A. Next the part 4 of the loop below A A 

 is traced; the point A is reached when AP again coincides 

 with A A, and then AP is tangent to part 4 at A. Next 

 part 5, which approaches asymptote II, is traced. After this 

 second position of parallelism part 6 is traced, then part 7, 

 and so on in the order indicated by the numbers. Any two 

 consecutive asymptotes, as for instance III and IV, are not, 

 in general, adjacent. 



The equation of the curve in Fig. 5 is 



5 20 



8ft) Ou>' — 8 T"5 7T — -q ""a 



