344 
PROFESSOR C. NIVEN ON THE INDUCTION OF ELECTRIC 
the term is therefore altered in intensity in the ratio M' : 1 and the azimuth increased 
by the angle O'. If we put 
jj~=M 2 e~ 2i *, 
we can easily prove that 
where also 
W=—^—=- 
P+l 
sill 3 , 7T 
- • v-n’ d = - + tan 
sin 3 + cos 3 2 
-i 
M sin 3 
K 
tan 23 = 
imnc 
M 4 =/c 4 + 
The action of the solid will therefore be the reverse of the original magnetisation 
and M' is a proper fraction. 
The coefficients 33 are found by considering the value of P 0 when z= 0 ; call it 
Z 0 . Then as we have found 
1 r r 30 r 30 
Z 0 =-t\ cos m(<f>— kcIk3 m {kp)\ Z' 0 J M (Kp')p'dp'. . . . (15) 
ir J o J o •' o 
Plate of jinite or infinitesimal thickness. 
§ 17. For the case of a plate bounded by two parallel planes at distance b apart, 
we may satisfy all the conditions by taking the same general forms for the vector 
potentials and for the currents in the sheet: and the characteristic equation for the 
determination of P will remain the same as before. If we suppose the inducing 
magnetism distributed on the positive side of the plate, we may express P 0 within the 
plate as a series of terms of the form 
Ae^J m (Kp)e K ~, 
the origin being in the axis of revolution, and on the positive surface of the plate. 
The forms for the vector potential due to the currents are all given by taking for P a 
series of terms of the type 
i. In the substance of plate — Ae^J,, l (Kp)e K: fie 1 " 14, 
ii. Outside the plate, 2 positive, e^J^np) Ce~ K " 
iii. Outside, 2 negative, e im4, J fnp). I)c +K “ 
where 
