226 Trans. Acad, Sci. of St. Louis. 



They further show, that 



the difference in irav (used as an angular function) 

 between the angles made with A' AX by two adjacent 



5 



tangents at A is 



m 



the difference in trav between the angles made with 



__ s 



A' AX by two adjacent tangents at A' is — r, 



m 



the difference in trav between the angles made with 

 A' AX by two adjacent asymptotes is 



m 



m 



Fig. 10. 



O'l 



In Fig. 10, where ??z = 4 and — m' = — 1 



the number of tangents at A is 



A' 



** *' asymptotes 



m = 4, 



m' = 1, 



m — m' = 3. 



In order to investigate the curve represented by equation 

 (38) for asymptotes, put for the first position of parallelism 



oo' = ft), or irav to' = ti'av co, 



