Geometrical Electron Optics 9 



If the electron has initially started from the axis, or if it has 

 started anywhere outside tJie magnetic field with zero or negli- 

 gible velocity, which is almost always the case, the constant at 

 the right side of equation (4) becomes zero, and we have 



mvt ^ -A, or 



hnvc = ^ — ^A- (5) 



s , Zmc- 



This means that the kinetic energy corresponding to the tan- 

 gential, i.e., rotational motion of the electron has a potential of 

 its own. Let us now combine this with the energy equation 



where v^ is the velocity in the meridian plane. Subtracting the 

 two equations we obtain 



i;»7V= = <'(<#. -2^A2) (7) 



which shows that the motion in the meridian plane can be de- 

 rived from a potential 



U = (/) — :^A2 (8) 



This shall be called the equivalent electrostatic potential of 

 the magnetic lens. It is also valid for any combination of electric 

 and magnetic fields."^ 



* On the problem of replacing Glaser's general refractive index by 

 simpler expressions if a second integral of the dynamical equations is 

 known, cf. Opatowski.^ The equivalent potential appears to have been 

 first used by C. Stoermer, Ann. Physik, 16, 685 (1933), and also by 

 L. Brillouin,' in 1941, in a less general form. 



