384 H. A. Rowland—Magnetic Effect of Electric Convection. 
V-V' 
es 27(B—p) (2) 
V—V’ being the difference of potential between the disc and 
the outside plates, 6 the thickness of the disc and B the whole 
distance apart of the outside plates. The excess on the edge 
was (Maxwell’s Electricity, Art. 196, Eq. 18), 
BC 4 
E=2(V—V’) xB) log, (2 cos 3B) (3) 
where C is the radius of the disc. 
x= eee '_(o+@)dedy _ 
— D Aeryply (a2 2:2 4yt)t 
perme Om (b-+-2)VC?2—(b-x)? 
© IS 04y (a? a?) Va? + C2 —b2 — 26a" 
where a is the distance of the needle from the disc and } that 
from the axis; N is the number of revolutions of the disc per 
second and v=28,800,000,000 centimeters per second according 
to Maxwell’s determination. The above integral can be. ob- 
tained exactly by elliptic integrals, but as it introduces a great 
variety of complete and incomplete elliptic integrals of all three 
orders, we shal] do best by expanding as follows: 
_t2No 
4aNo 
X= Pa" (A, FAL +A; + he), (4) 
C-—b C+) M 
A,=20( are tan arg -+- are tan mE ) — a log, N’ 
M 
A,=—S( (648) log, 5: gare 20), 
. M 
A= ; —4Cs-+ (3s?-+-2sb+-a?) log, N 
4Cb 
+-(582+-36"b--at(s42) Joe | &e, &e., 
2 C2—f2 
M>=a?-+(C+6)?, N=a?+(C—2)2, 
