336 
PROF. H. M. MACDONALD ON THE EFFECT PRODUCED BY 
be the principal parts of the components of the actual magnetic force at P in these 
directions, then P being at a distance along the surface from the curve of contact of 
higher order than p {Kp)~'‘\ the principal part of the component of the magnetic force 
in the plane of OP and the normal to the surface at P which is due to the oscillator 
and the actual distribution on the part of the surface inside the tangent cone from 0 
and nearest to 0 is LM'i, and the principal part of the corresponding component of 
the magnetic force due to* the local distribution at P is eMi/(l + e), where 
e = {k' + LK cos (j))/{K'—LK cos cj)), and (f) is the acute angle between the normal at P 
and OP. 
Therefore 
Ml = eMi/(l+e)+LM'i, 
that is 
Similarly 
where 
Ml = (l + P)LM'i. 
M, = (l + e')LM'„ 
e' = [k' cos <^ + t/c)/(/c' cos <P — lk), 
and the principal parts of the components of the electric force at P can be similarly 
obtained. When k is small compared with 47rV/o-, k' is approximately given by 
k' = K:i(l+t), where ki = the modulus of 1 + e, is greater than 2, and the 
modulus of 1+e' is greater than 2 provided cos (f) is greater than kI2ki ; therefore at a 
point P on the part of the surface next the oscillator the amplitude of the tangential 
magnetic force is greater than iii the case of a perfectly conducting obstacle, and at a 
point on the j^art of the surface of the obstacle remote from the oscillator the tan¬ 
gential magnetic force is greater than in the case of a perfectly conducting obstacle, 
provided cos (j) is greater than The same results hold for the components of the 
electric force normal to the surface of the obstacle. 
It appears from the foregoing investigations that at a point P inside the boundary 
of the geometrical shadow formed by any opacjue obstacle the principal parts of the 
components of the electric and magnetic forces are 
LX', LY', LZ', La', L;8', Ly', 
where X', Y', Z', a', y8', y' are the principal parts of the components ot the electric 
and magnetic forces at the point P due to the oscillator, when the point P is at a 
distance measured along OP from the surface of the obstacle of a higher order than 
p {kp)~^^\ that when the obstacle is perfectly absorbing the principal parts of the 
components of the electric and magnetic forces at a point P on the surface of the 
obstacle inside the boundary of the geometrical shadow have the above values, that 
when the obstacle is perfectly conducting the ratio of the electric force normal to the 
surface at the point P on it to the electric force normal to the surface of a perfectly 
absorbing obstacle occupying the same space at the same point on it is 2, and that 
