4 Mr. J. J. Thomson on the Magnetic Effects 



and a mechanical force equal to 



da 7 dh dc 7 db 



e I- h dt +9 dt- h di> 



if the electrified bodies are at rest. 



The first of these corresponds to the well-known expression 

 for the electromotive force on a conductor moving in a 

 magnetic field ; the second is the mechanical force on a 



current in a magnetic field plus the term 9~t,~^-t.' 



We can deduce an important consequence of the assump- 

 tion, if we consider the case of the aether moving with uniform 

 velocity between two parallel planes charged, the one with posi- 

 tive, the other with negative electricity. 





If v is the velocity of the aether, h the electric displacement 

 at right angles to the planes, the magnetic force between the 

 planes will be parallel to a, and equal to —4z7rvh ; or if a is 

 the surface-density of the electrification on the planes — 4:7rvcr, 

 the magnetic force vanishes except between the planes, so that 

 on crossing the positively ' electrified surface there is an in- 

 crease in the magnetic force parallel to x equal to 4o7rcrv. Thus 

 the charged surface acts like a current sheet of intensity — av, 

 but — v is the velocity of the plane relatively to the aether ; so 

 that a charged surface moving with velocity v relatively to the 

 sether must act like a current sheet of intensity av. 



We will now proceed to apply these results to some special 

 cases. Let us suppose that we have a charged sphere moving 

 along the axis of z with the velocity w w and that it sets the 

 aether around it in motion in the same way as an incom- 

 pressible fluid is set in motion by a solid sphere of the same 

 radius moving through it with the same velocity. If a is 

 the radius of the sphere, 



=i 



u= 



w a s 



d 2 1 



v = ^w n a 3 - 



d 2 1 



2 ^ dydzr* 

 d d 2 1 



