152 RELATIONS BETWEEN SEVERAL PLACES IN ORBIT. [BOOK I. 



we obtain 



which expressions entirely coincide with those given in article 107, if a is there 

 changed into a. 



Finally, these series, as well for the ellipse as the hyperbola, are eminently 

 suited to practical use, when a or a possesses a very great value, that is, where the 

 conic section resembles very nearly the parabola. In such a case, the methods 

 previously discussed (articles 85-105) might be employed for the solution of the 

 problem : but as, in our judgment, they do not furnish the brevity of the solution 

 given above, we do not dwell upon the further explanation of this method. 



