228 Trans. Acad. Sci. of St. Louis. 



Equations (42), (43), and (44) show, in a manner similar to 

 that shown in case (a), that 



the number of branches passing through A is m, 

 " " «' branches passing through A is m , 

 44 " " asymptotes is m + w,' > 



the difference in irav between the angles made with 



A AX by two adjacent tangeuts 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 ^.'^4 X 

 by two adjacent asymptotes is — — — -. 



In Fig. 9, where m = 4 and m! = 1, 



the number of tangents at A is m = 4, 

 " " " «« " A is m — 1, 

 «« " " asymptotes is w + m' = 5. 



Issued June 30, 1896. 



