{ 4.w ) 
Let to be the angular velocity of the gas when the stationary 
state is reached. 
If two cylinders with radius r and r -{- dr resp. are so situated 
that r and p 2 ]> r -f dr, whence it follows that there is no 
current through the space which they include, the moments of the 
friction in the gas on the surfaces of these two cylinders will be 
equal and opposite in the stationary state. 
If v = ear is the velocity, and ^ the coefficient of friction, these 
moments per unit of length measured in a direction parallel to the 
axis, are resp. 
— r* . rj ^ . . . ... ( 4 ) 
dr 
+ a*'fr + drf 
r dv\ 
^dr) r +dr 
Since they are in equilibrium 
dv 
— r 9 T + (*• + drf 
dr 
^1 = 0, 
^drjr+dr 
( 5 ) 
( 6 ) 
2co + + 
The solution of this equation is 
The friction at the cylindrical surfaces bounding the gas is assume 
to be so great that the angular velocity there is zero. 
We have therefore outside the space occupied by the discharge 
and inside that space 
(10) 
b, and b 2 being constants. 
If however the radii r and r -|- dr are smaller than p, and 
than p„ the moment Hrdi acts on the gas between the 
with radii r and r -f- dr, on account of the current flowing t e 
This moment can be written in the form 
. . (H) 
