(31/ 
( 433 ) 
, = . . 
q^R.—R,) 
(f drops out). 
Substituting (30) in (31) we find 
^ _ HI ( Q -R,) (Ri~ q) 
2 mi p a (R x — R 2 ) 
Since the discharge in the experiments under consideration had 
the form of a small column, and since the values of the field Hare 
mentioned for one peculiar value of r (viz. r = 1.34 cm.) we may 
use the formula (32) putting p 1 = p, = p = 1.34. In the apparatus 
of Wilson and Martyn R x was equal to 1.505 cm. and R , to 1.16 cm. 
The value of ij is independent of the pressure. Say for nitrogen 
t] ~ 0.0002. In one of the experiments made with nitrogen the value 
of I was between 0.001 and 0.003 (el. magn. unities) and the 
intensity of the magnetic field was 41. 
Substituting these values in (32), we find that the angular velocity 
with which the gas moved in that experiment, supposing it to be 
the same as if the discharge had the form of a complete cylinder, 
must have been between 1.6 and 4.7. As to the observed angular 
velocity of the discharge, it was 2 jt . 9.5 or about 60. 
In the same way we find by substituting numerical values be¬ 
longing to other experiments that the angular velocity of the gas 
was always much inferior to that of the discharge itself. 
The general expression of the angular velocity of the discharge 
for r = ^ is after (1) 
<2 
So the proportion of the two angular velocities is found 
» ~ n " (q-RMR-Q) ‘ I' ' 
(34) 
t ( 9l * — p 3 *) X, a being the specific conductivity, 
q(R-R 2 ) 
a>~-c> lk * ( 9x '-QS) (Q-R t ) <*,-*) * 
This proportion increases as 9l — p 2 diminishes. 
(35) 
$ 2. The same formulae (28) and (33) are applicable to the case 
of an electrolyte, instead of a gas, filling the space between the 
flinders C x and C t . 
In that case the discharge will not be limited to a thin hollow 
cylinder, but will fill the whole space between the cylinders C t and 
