SECT. 3.J PLACES IN ORBIT. 135 



99. 



We retain, in the HYPERBOLA also, the symbols p, v, v ,f, F, r, r , t with the 

 same meaning, but instead of the major semiaxis a, which is here negative, we 

 shall write a ; we shall put the eccentricity e = ( r in the same manner as 

 above, article 21, etc. The auxiliary quantity there represented by u, we shall 



f 



put for the first place = , for the second = Cc. whence it is readily inferred 

 that c is always greater than 1, but that it differs less from one, other things 

 being equal, in proportion as the two given places are less distant from each 

 other. Of the equations developed in article 21, we transfer here the sixth and 

 seventh slightly changed in form, 



[2] 



[3] 



[4] 



From these result directly the following : 

 [5] faF=ka(0-. 



[6] sin/=a(e i 



[7] 



[8] 



Again, by equation X. article 21, we have 



r , O . 



