318 
PROF. H. M. MACDONALD ON THE EFFECT PRODUCED BY 
and 
^2 
( 1 
1 
2/y = 
VOM 
PM/J 
RM, 
where X is the wave-length of the oscillations and M is the foot of the perpendicular 
from R on OP. 
When the point P is outside the tangent cone from O to the surface and near to 
the tangent cone and at a distance from O greater than OR it appears that the focal 
lines as determined above are situated one of them close to the surface of the 
obstacle and the other near to the source, hence the same analysis applies as in the 
immediately preceding case, and the components of the magnetic force at P due to 
the assumed surface distribution are given by 
Oi^ = -La', 13^ = -L/3', yo = 0, 
where 
da, 
and in the integral in the denominator the limits are indefinitely extended, while in 
the integral in the numerator the upper limit is — where denotes the perpen¬ 
dicular from Pt on OP. Evaluating the above, the value of L is given by 
r ~~ ic ^ 
J — 00 J 7 /,^ 
where 
Mij — 
r2 
/ 1 
1 \1 
Lx 
PM/J 
V2. 
RM, 
and therefore the principal parts of the components of the magnetic force at the 
point P outside the tangent cone and near to it are given by 
a = (l-L)a', /3 = (l-L)/3', y = 0, 
where L has the value given above. 
Considering now a point P on the surface of the obstacle near to the curve ot 
contact of the tangent cone and on the side of the surface remote from 0 it appears 
that the principal parts of the components of the magnetic force due to the oscillator 
and the assumed surface distribution are La', Lj3', 0, and there will be a corresponding- 
tangential electric force involving the factor L, therefore the surface condition is not 
satisfied at such points ; the same result holds for points near the curve of contact on 
the side of the surface next 0. It is therefore now necessary to determine Avhat the 
effect of the electric current distribution on the surface which woidd reduce this 
unbalanced electric force to zero is. Taking first the case of a point P inside the 
tangent cone on the side of the surface of the obstacle remote from O and near to 
the boundary of the cone, with the same notation as above, the components of 
