( 481 ) 



way of' motion for an electron niovino- with 5;>, when the external 

 force is suddenly sujipressed. The same applies to an electron moving 

 \\ith t»; if the motion is accelerated, and so if a force acts on the 

 electron, and if this force is suddenly suppressed, the equation (Fa) 

 cannot be satisfied in any way. This is because the momentary 

 disappearance of the external force is an impossible supposition. 

 Even an infinite acceleration would not satisfy equation {Va). The 

 internal force namely depends only on the former motion of the 

 electron, and not on the velocitv or the acceleration at the moment 



itself. Sommerfkld's conclusion that a motion with — =: x does not 



require an external force holds only if the initial velocity is i\ and 

 is nothing else but a statement in other words of the fact that the 

 force acting on an electron whose velocity is at the moment i mo- 

 mentarily — i. e, w ith intinite acceleration — brought from v> to 2}, is 

 zero at the moment /. If however we begin with a constant velocity 

 35j, and change the velocity at the moment t suddenly to 2?,, then 

 the force is not zero at the moment t, though the acceleration be 

 infinite, but it has ihat value which corresponds with a constant 

 velocity ^\. 



It may however be asked what will liapi)en, if the force acting 

 on an electron Avith 25 does not suddenly decrease to zero, but 

 ffraduallv. Sommf,rfkt,d savs about this case onlv that the sudden fall 

 to r, which he expects from a sudden suppression of the force, will 

 make room for a gradual fall. But as his expectation concerning 

 the case of a sudden suppression of the force appeared to be inac- 

 curate, we might suppose that also this expectation will appear not 

 to be satisfied. The more so because Sommkrfeld found a negative 

 value for the electric mass of an electron moving with 25. We might 

 therefore expect that a decrease of the force would cause an 

 acceleration. This, however, is not the case, and here we see how risky 

 it is to introduce the conception of mass in Ihe theory of the motion 

 of electrons, to which it is essentially strange. 



The negative mass, which Sommkkfeld ascribes to the electron 

 means nothing else, bnt that in order to move with a given ^^ the 

 electron requires a greater force when in the active interval the 

 velocity was on an average greater than 2>i, a smaller force when 

 it was less. By active interval is meant the time during which the 

 electron emitted the fieldforces, which at the moment f act on the 

 electron. The greater the velocity during the active interval, the 

 greater the force, and inversely the smaller the \elocity the smaller 



