at Low Pressures. 
261 
as perfect absorbers of the ions and they must consequently take 
up a negative charge in the same way as the glass walls of the 
tube. This is no doubt the explanation of the disturbance which 
the electrodes produce in the discharge. Near the walls of the 
tube the luminosity appears to be less intense than at the centre 
of the tube, but this appearance is probably partly due to the 
greater thickness of glass through which the discharge near the 
walls is seen. 
The fact that the Hall effect was found to be proportional to 
the magnetic field and independent of the current shows that the 
charges which the walls of the tube and the electrodes no doubt 
take up are too small to influence the measurements made. For 
since the mean value of n is proportional to the current and (as is 
shown below) the ratio of n at E to n at E f is independent of the 
current, hence the difference between n at E and n at E' must be 
proportional to the current, so that increasing the current ought 
to have increased the difference between the charges on the two 
electrodes necessary to make the numbers of positive and negative 
ions striking then equal, if these charges had been appreciable. 
According to these considerations the smaller the currents used 
the more reliable the results obtained should be, and this is 
exactly what was found experimentally to be the case. 
When the magnetic field is being applied it is easy to see that 
the luminosity increases in intensity as one passes horizontally 
from one side of the tube to the other. 
The above theory of the Hall effect shows that this should be 
the case, for we have 
f.g=n (Z + k lH X), 
K 2 dn 
k» ’ dz 
= n (— Z 4 - k 2 HX). 
Putting ^ ^ = B and adding these equations give 
K 2 
2 / 3 ^ = nHX{k 1 + k i ). 
Hence 
log n = 
HX 
2/3 
(&x + k 2 ) z + A . . 
For a tube of square cross section with its sides respectively 
parallel and perpendicular to the magnetic field and sides of 
length a, 
( a • 
I = a I idz } 
J o 
where I is the total current through the tube. 
