( 32:, ) 



ZV < 2n — 1 



holds; for small value of n, e.g. ra = l,5, /" would have to be 



. 8 



< , which has certainly been lound in observations; hut for larger 

 9 



9 

 values of //, e.g. // = 5. /- would have lo he < which will, most likeh , 



25 



not be the case. So if n is large for a not too small value of /', 

 the ellipse (d') will also possess points for which 8 X and c, is positive, 

 and the possibility that it intersects the I s ' parabola, is not excluded. 

 At given / 3 we might find the limit for the value of n, at which 



it is still possible thai =0and =0 do not intersect, by de- 



1 ,/.,■'-' rfu a J 



termining the relation which must exist between /'- and n for the 

 ellipse to touch the first parabola. But this would lead to lengthy 

 calculations, which we shall omit here. We will, however, examine 

 more closely some properties of the ellipse. 



1. Determination of the centre. 



From /'(O == and ƒ'(*=,) = or 2n + a x -f rrr-^ = 21' i >r (1 -f e,) 

 and 2n + e 1 + n*s, = 21* (i + *,) follows (1 -f- ejx — n* (1 + e t ) M , 

 from which follows thai the line 0' M (fig. 37) makes an angle 



a' 



p' 



Fig. 37. 



