146 REPORT—1885. 
battery the condenser will charge up and there will be radial currents of 
electricity in the plates; the current passing through the solenoid will 
produce a magnetic force which will, if Ampeére’s theory be true, act on 
the radial currents in the plate of the condenser and set it in rotation. 
Schiller found that this effect was too small to be observed, so he modi- 
fied the experiment in the following way. Let us suppose that we have 
the two plates of the condenser rigidly attached to their axis and placed 
in a field symmetrical about its axis, in which the vertical component 
of the magnetic force is not uniform. Then if a current be sent through 
the upper plate, down through the axis, and out at the lower plate, the 
couple tending to twist the lower plate will not be equal and opposite to 
that tending to twist the upper one, as the magnetic force is not equal at 
the two plates, and thus the condenser will be set in rotation. Con- 
versely, if the condenser be set in rotation in the magnetic field, and two 
electrodes of a galvanometer be connected with its axis, then if Ampére’s 
theory be true there will be an electromotive force acting round the 
galvanometer circuit, which will produce a current, and this current 
could be much more easily detected than the rotation in the first form of 
the experiment. Schiller calculated the deflection which he ought to get 
if Ampére’s theory were true, and found that he could easily detect it if 
it existed; as he was not able to see any deflection, we must conclude 
that Ampére’s theory is not the true one. 
It is easy to see that, according to the potential theory, there would 
be no current in the galvanometer ; for, as everything is symmetrical about 
the axis, the potential is not altered by the rotation. The following 
calculation will show that, according to the dielectric theories, there should 
be no current through the galvanometer. 
For if a,b,c are the components of magnetic induction, F, G, H 
those of the vector potential, X, Y, Z those of the electromotive force, 
then 
K pe plated porous Heh, 
dt dt dx dé dt dt 
diz da ad da dy ca 
Y= ¢—— 6 -5——ahe 7 + H—}: 
sj eaglh ai agence Ree 
Suppose the condenser is rotating with an angular velocity w about 
the axis of Z; then the E.M.F. arising from one plate is, if R be its radius, 
R 
daz ch 
—(ps Gt) 
o| ert (F has a)? 
/0 
T dee dy _ .RO 
Now F - + G ai oRO, 
where © is the component of the vector potential along the direction 
of motion of a point on the circumference of the plate of the condenser. 
—e 
But the line integral of the vector potential round any curve equals — 
the number of lines of magnetic force passing through it, so that, since — 
the field is symmetrical, 
R 
Qn | cr dr = 27 RO. 
}0 
