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



They further show, that 



the difference in trav (used as an angular function) 

 between the angles made with A' AX by two adjacent 



tangents at A is — , 

 m 



the difference in trav between the angles made with 



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



m! 



the difference in trav between the angles made with 



s 



A' AX by two adjacent asymptotes is 



m — m 



Fig. 10- 



O' 



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



the number of tangents at A is m = 4, 



" " " " A'" m' = 1, 



" " " asymptotes «« m — m' = 3. 



In order to investigate the curve represented by equation 

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



&>' = g), or trav co' = trav <o, 



