104 LORENTZ— ON POSITIVE AND NEGATIVE ELECTRONS [April 17, 



in Opposite directions with equal velocities, Clausius could free him- 

 self from this restriction, and could even suppose one of the elec- 

 tricities to have no motion at all. 



These questions, after having for a time lost much of their in- 

 terest by the universal spreading of Maxwell's ideas, have again 

 sprung up, and have even become of fundamental importance in 

 the modern theory of electrons. I should therefore like to call 

 attention to them for a few moments, hoping the subject will be 

 thought suitable on the present occasion, because it is somewhat 

 like the old question whether one had to assume Franklin's single 

 fluid or a positive and a negative electricity. 



In order to show the connection I may observe that we can 

 never wholly escape from the dualism, the notion of two things with 

 opposite properties, that is forced upon our minds as soon as we come 

 to study phenomena. Indeed, while recognizing but one electricity, 

 the unitarian theory invested ordinary matter with the properties of 

 the missing fluid. It was obliged to assume the existence of a 

 mutual repulsion, not only between the particles of electricity, but 

 also between those of matter and to add to these forces an attraction 

 between a particle of matter and one of electricity. This is not very 

 different from a two-fluids theory; it is even practically equivalent 

 to it, if one of the two fluids is supposed to be permanently fixed to 

 the ponderable matter. After all, we shall have to choose, not, 

 strictly speaking, between one or two electricities, but between one or 

 two movable electricities, in modern terms, between one or two kinds 

 of movable electrons. 



I shall confine myself to the case of metallic bodies and I shall 

 first speak of a phenomenon which at first sight might seem sufli- 

 cient to lead us to a decision. 



Let us consider a very thin rectangular sheet of metal, traversed 

 in the direction of its length, say from left to right, by an electric 

 .current, and placed in a magnetic field whose lines of force are per- 

 pendicular to the sheet. Let us first suppose the current to consist of 

 a flow of positive electrons, towards the right-hand side, of course. 

 Then, by a well-known rule, each of these electrons will be acted on 

 by a force due to the magnetic field and perpendicular both to the 

 lines of force and to the current. This force will tend to drive the 



