Boever — Geometrical Constructions of Lines of Force. 227 

 for the 2°"^, 



&)' = w + TT, or trav &)' = trav &> + s, 



for the n"^, 



&)' = ft) + (71 — 1) TT, or trav w' = trav w + (?i — 1) s. 



Then, for the n'*' }30sition of parallelism 



trav «» = . versin a ; > (n — 1) s.(42), 



711 + m m + m 



which is analogous to equation (21). 



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



1"' tangent &>' = 0, or trav w' = 0, 



2"* t< jy' = TT, or trav &>' = s, 



w^ << 0)' = (ii^ — 1) TT, or trav &>' = (Wj — 1) s. 



Then, for the n^*^ tangent at A 



trav (Ot = versin a — — {n^ — 1) s {^^)» 



m 



which is analogous to equation (22). 



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



1** tangent w = 0, or trav co = 0, 



2°* '* ft) = TT, or trav co = s, 



n.^ " (o = {n.^ — 1) TT, or trav co = (n^ — 1) s. 



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



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



which is analogous to equation (23). 



