420 



electron that Hies into tliis bag can nevei' leave it across llie snrface 

 which it will perhaps not reach at all. Indeed, it may be that, 

 before the velocity is exhausted, its direction comes to be tangential 

 to a surface <o ;= const., characteiized by a value of oj smaller than 

 the one given by (15). It seems probable that in such a case the 

 electron, after having moved in the bag for a certain length of time, 

 will leave i( through the opening, but it is difficult to make sure 

 of this. ') 



§ 8. In Whittakkk's model the ring R is made up of the poles, 

 of equal signs, of a numl)er of magnets arranged along radii of the 

 ciicle and having their opposite |)oles at or near the centre. It might 

 seen» at first sight that in a structure of this kind the magnets can 

 be replaced by perfectly conducting solenoids carrying pre-existent 

 electric currents, so that we can do without magnetic charges. 



In reality, however, no satisfactory model can be obtained in this 

 wa}'. This is seen most easily when the electron is supposed to 

 move along the axis X. In the magnetic field due to this motion 

 the lines of force are circles around the axis, and therefore the force 

 acting on an element of current at a point F, is directed along a 

 line lying in the plane P A'. For such a force the moment with 

 respect to ^Y is zero; consequently, neither a solenoid nor a system 

 of solenoids can be acted on by a couple tending to produce a 

 rotation about X. 



Thus it would seem that the hypothesis of "magnetism" existing 

 independently of electric cun-ents is quite essential in Whittakek's 

 model. I need not speak at length of the reasons for which such an 

 assumption is not to be readily admitted. Let it be remarked only 

 that the equations (1)— (6), though forming a consistent system, do 

 not allow us to establish variation theorems of the kind of Hamilton's 

 principle. In this principle we are concerned with the difference 

 between the potential and the kinetic energy, so that, in the equations, 

 the two energies do not occur in the same way. Now, if there are 

 only electric charges, we can, as is well known, arrive at an equation 

 of the Hamiltonian form, in which ^d* takes the place of the 

 potential and hYC that of the kinetic energy. If there are only magnetic 

 charges, there is a similar formula, in which, however, the electric 



1) An interesting discussion of this question has been given (Phil. Mag. 44, 1922, 

 p. 777) by Mr. B. B Baker, wo has considered the case of an electron not moving 

 along the axis of the ring, without, however, taking into account the forces that 

 may arise from the existence of a magnetic field. 



