PART II. POLAR MAGNETIC PHENOMENA AND TERRELLA EXPERIMENTS. CHAP. VI. 697 



If 



ie one root is positive, and the other negative; and at the same time the velocity is hyperbolic, so that 

 ic particle retires indefinitely. 

 If, on the contrary, 



oth the roots will be positive. Let us call the smallest r v , and the largest r a . Then 



-/i Qtt + r a v-} -j" + ( rv 



Hence we obtain 



__ 



r 







at is to say, the particle will move in an ellipse, of which the perihelion is just on the boundary-circle. 

 The eccentricity will be 



_ 2r 



e _ r r 2 " rv " 



r u r p 



If we substitute as before 



e obtain 



v*\ r, vl 



L' ^ 1 _ 2 + -5 1 = 1 2?z 



/" \ H / jtl 



We have, however (cf. p. 683), 



r d consequently 



r kn + 2 ~ kn + 2 / - 2 ' 

 vien we put, as before, 



As / may be as great as may be desired, the eccentricity may be as small as may be desired. 

 . the same time n must have greater values. Thus at a great distance from the globe, the orbit will 

 b almost circular. 



135. We have discussed above the problem of the mouvement of an electrically charged particle 

 aaut a magnetic and gravitating sphere, when the particle is ejected in the plane of the magnetic 

 ejator, and thus always remains there. We saw that there were boundary-circles towards which the 



