Boever — Geometrical Constructions of Lines of Force. 227 

 for the 2 nd , 



co' = (o + 7T, or trav co = trav co -+- s, 



for the n th , 



&>' = co + (n — 1) 7r, or trav co' = fr'av <y + (»i — 1) s. 

 Then, for the n th position of parallelism 



m . m' , i \ / /» o \ 



trav co n = ; versin a : > {n — l; s.(4^), 



u m + m m + m 



which is analogous to equation (21). 



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



1 st tangent co' = 0, or trav co' = 0, 



2 nd " co' = 7T, or trav co = s, 



n^ " ©' = (Wj — 1) 7T, or trav co' = (n x — 1) 5. 



Then, for the n^ tangent at A 



trav co t = versin a — — (n l — 1 ) s (43), 



m 



which is analogous to equation (22). 



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



1 st tangent co = 0, or trav co = 0, 



2 nd " co = 77-, or trav co = s, 



n* " co = (n 2 — 1) 77-, or trav co = (n 2 — 1) s. 



Then, for the n., th tangent at A' 



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

 in' m' 



which is analogous to equation (23). 



