148 REPORT—1885. 
of coaxial cylinders. In v. Helmholtz’s experiments bb was rotated 
between the poles of a powerful electromagnet. The plates c, ¢ were 
connected with a commutator, which put them to earth when the rotating 
piece was in the position A, and to the plates of a Kohlrausch condenser 
when it was in the position B. Now suppose there is a difference of 
potential between b and c; suppose, for clearness, that > is at a higher 
potential than c, then when the rotating piece is in the position A the 
positive electricity goes to earth, and the negative is left to go to the 
Kohlrausch condenser, when the rotating piece gets to the position B. 
The change in this condenser was measured by a quadrant electrometer. 
y. Helmholtz found that the needle of the electrometer was deflected when 
the piece bb was rotating. Since everything is symmetrical about the 
axis of rotation, there would be no difference of potential between the 
oer eater eae 
4 
O b Oa 5 
Cc 
plates b and c, according to the potential law, if we neglect the action of 
the dielectric. According to Ampére’s law there will be a difference of 
potential between b and c equal to Oaw, where a is the radius of the rotat- 
ing piece, w its angular velocity, and © the vector potential along the 
direction of motion of the disc. According to the dielectric theory there 
will also be the same difference of potential between ) and ¢ if we sup- 
pose that there is no discontinuity in the motion. We shall suppose that, 
instead of the velocity changing abruptly from wa to zero as we pass 
from the rotating conductor to the dielectric, there is a layer of the 
dielectric next to the conductor in which the change of velocity is very 
rapid, one side of the layer moving with the velocity wa, the other side 
being at rest. Then, using the same notation as before, we have— 
_, dy _,de_d dx dy aH 
A Al wenn meet aie Wi 
., ab ded dzx dy at 
ide dt ° di dy y at la aoa ; 
Integrating across the thin layer of the dielectric, in which the velocity 
is changing rapidly, we see that the difference of potential between b 
and ¢ equals 
da dy 
H 
dt aie dt os 
dz 
dt’ 
where da /dt, dy/dt, dz/dt are the velocities of a point on the boundary 
Fr 
i i, 
ae ee 
