Eoever — Geometrical Constructions of Lines of Force. 213 

 To investigate the curve for tangents at A put for the 



1'' tangent w' = 



in which n^ is an integer. For the n^ tangent equation (1) 

 becomes 



tn' 



in which w, is the special value of <o when line AP coincides 

 with A A. Equation (19) shows that the angle between the 

 tangents at A to two consecutively formed parts of the curve 



Vfi IT 



is . Thus, in Fig-. 5, the angle between the tangents at 



in 



A to parts 1 and 2, or to parts 3 and 4, is — = -vr. - is 



7)1 6 m 



the angle between two adjacent tangents at A, and m is equal 



to the number of tangents at A. 



To investigate the curve for tangents at A put for the 



in which n^ is an integer. For the n,*'' tangent equation (1) 

 becomes 



mm ,^^ 



«;=_—7a + — (n„— 1) TT (20), 



in which (o\ is the special value of «' when line AP coincides 



with AA . Equation (20) shows that the angle at A 



111, 

 between two loops, consecutively formed, is — ir. In this 



m 



expression mir is the angle swept through by the rotating line 



AP before a position of parallelism coincides with a pre- 



