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 7n', 

 '♦ " " asymptotes is m + 7n', 



the difference in trav between the angles made with 



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



m 



the difference in (rav between the angles made with^'^-X" 



o 



by two adjacent tangents at ^' is — , 



the difference in trav between the angles made vfithA'AX 



by two adjacent asymptotes is 



S 



m + m' 

 In Fig. 9, where m = 4 and m' = I, 



the number of tangents at A is m = 4, 

 *< " " asymptotes is m + m' = 5. 

 Issued June 30, 1896. 



