Roever — Geometrical Constructions of Lines of Force. 227 

 for the 2°^ 



to' = (o + TTy or trav a = trav w + «, 



for the n"', 



co' = 0) -f (n — 1) TT, or trav m = trav «o + (?* — \) s. 

 Then, for the n"* position of parallelism 



m . m 



—, ; versin a r- 



m -{■ m m + m 



trav a>^ = , , versin a — , _ > (w — 1) «-(42), 



which is analogous to equation (21). 



To investigate the curve for tangents at A^ put for the 



!•* tangent «' = 0, or trav a> — 0, 



2"^ *« (a' = TT, or trav m = 5, 



n^^ ti Q,' = (Hj — 1 ) TT, or trav od' = (n^ — 1) s. 



Then, for the n^**' tangent at A 



trav cot = versin a — — (n^ — 1 ) s (43), 



m 



which is analogous to equation (22). 



To investigate the curve for tangents at A'y put for the 



!■* tangent w = 0, or trav o> = 0, 



2°* ** a> = TT, or trav g> = s, 



n.^ *' ft) = (»2 — 1) TT, or trav m = (n^ — 1) «• 



Then, for the n^"* tangent at A' 



trav m't = — versin a — — (n„ — 1) s. . (44), 

 m' m' 



which is analogous to equation (23). 



