S9^ Trans. Acad. JSci. of St. Louis. 



or if we consider the equation Tra (x^ — x^^) = wtrav oo put 

 for the 



1"* asymptote trav a = 

 2""* " trav CO = 2 



n^^ " trav w = (n^ — 1)2 



then from the above equation 



m 



xj = 2in,-l) -^ + V (48), 



7r<7 



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

 ria = I equation (47) becomes the same as equation (40). 



For w„ = equation (48) becomes x^^ = — — + x^^. The 



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

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



becomes x'^ = 2n^ — and for Xq = equation (48) becomes 



ira 



m 



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



TTff 



n^ asj'^mptote of the dashed curve. 



A comparison of case (6) with case (a) will show a complete 

 analogy of the corresponding equations. 



Issued January 19,1897. 



