298 Trans. Acad. iSci. of St. Louis. 



or if we consider the equation ira (x 2 — x 2 ) = mtrav g> put 

 for the 



1 st asymptote trav a> = 

 2 nd " trav w = 2 



n* " trav &) = (n a — 1) 2 



then from the above equation 



x a * = 2(n a — 1) — + * 2 (48), 



ira 



in which x a is the distance from to the n* a h asymptote. For 

 n = 1 equation (47) becomes the same as equation (40). 



For n a = equation (48) becomes x a 2 = — — + x 2 . The 



7T<T 



dashed curve (Fig. 7) is a portion of the complete curve of 

 which the limiting line is a part. For a = equation (47) 



ay) 



becomes x' a = 2n a and for x = equation (48) becomes 



ira 



m 



x' a = 2 (n a — 1 ) — , in which x' a is the distance from to the 

 ira 



n* a h asymptote of the dashed curve. 



A comparison of case (b) with case (a) will show a complete 



analogy of the corresponding equations. 



Issued January 19, 1897. 



