1082 CHARLIER, ON PERIODIC ORBITS. 



It follows from the values of the roots of the equation for 

 X that all curves of the families a, h and c are unstable. The 

 Orbits d and e in the vicinity of L^ and i^ are, on the con- 

 trary, stable, owing to the fact that all the values of A- in 

 these points are real and negative. A small body, moving in 

 a periodic orbit of the family d or e and exposed to sraall 

 disturbances from a foreign body, will describe a curve, the co- 

 ordinates of which may be regarded as composed of the co- 

 ordinates of the two ellipses (/ and e. 



