^'i.\fr. COXTF.Ml'OR.INY .ll>r.l.\\-f.S /\ I'llVSICS-IX (^f) 



precession of the entire system .ilxuil the (iirectioii of the iii.iL;iieiii- 

 lielil at the fre(Hieiir\- 



^i. = (Il lirmc (48) 



In other words, ll>e motion of the electron or electrons is, when re 

 terred to a coordinate system revolving about the direction of the 

 tield with frequency ell -iir tm\ the same as without tin- lield it would 

 l)e, when referretl to a stationary' cjordinate system. 



If the tieUl h.ippens to be normal to the plane of an elli()tical orl)it 

 being described by an electron about a nucleus, the ellipse will be 

 transformed into a rosette. If the field is neither exactly normal nor 

 exactly parallel to the plane of the ellipse, this plane may be imaj;ined 

 to swing around the direction of the field (around the line through the 

 nucleus parallel to the tield) like a precessing top, carr\-ing the orbit 

 with it. 



These statements are inexact if the rate of [^recession so calculated 

 is not quite small in comparison with the rate of revolution of the 

 electron. 



Jo. Motion of an Electron in a Field Compounded of an Inverse-square 

 Central Electric Field and an Uniform Electric Field 



This problem may be regarded as the limiting case of a more general 

 problem phrased as follows: to determine the motion of a particle 

 attracted by two fixed points according to the inverse-square law. 

 Imagine one of the fixed points to recede to infinity, its attracting- 

 power meanwhile rising at the proper rate to keep the field in the 

 region of the other at a finite value; and you ha\e the case described 

 in the sub-title above. Jacobi soKed the general problem a century 

 or so ago. 



The motion is difficult to realize and impossible to describe in words, 

 and seems also to be impossible to represent by any adequate two- 

 dimensional sketch. The electron makes circuits around the line 

 through the nucleus parallel to the uniform field, and in each circuit 

 it describes a cur\-e which is very nearly an ellipse; but the con- 

 secutve loops, as in the case of Fig. 3, do not coincide; furthermore, 

 they are not alike in shape, and they are not plane. The electron 

 winds around and around through the volume of what I am tempted 

 to call a doughnut, surrounding the aforesaid line as its axis; and in 

 the course of time its path fills up the doughnut "everywhere dense," 

 as the path of the electron in Fig. 3 woukl fill up the interior of the 

 dashed circle. 



