334 
PROF. H. M. MACDONALD ON THE EFFECT PRODUCED BY 
it the principal parts of the components of the electric and magnetic forces at the 
point P are 
LX', LY', LZ', La', L/3', L/, 
where 
J -u„ 
and 7<o has the same meaning as above. 
An Imperfectly Conducting Obstacle. 
When the obstacle is an imperfectly conducting body the conditions to be satisfied 
at the surface of the obstacle are that the components of the electric and magnetic 
forces tangential to the surface are continuous. The electric and magnetic current 
distributions to be placed on the surface to eifect this can be obtained from the 
following considerations. At a point on the surface of the obstacle not near to the 
point where the axis of the oscillator meets it the incident waves may be treated as if 
they were plane waves; let Mi and Mg be the components of the magnetic force in 
the incident waves tangential to the surface. Mi being in the plane of incidence and 
Ms perpendicular to it, and let Ei and Es be the components of the electric force in 
the incident waves tangential to the surface, Ei being in the plane of incidence and 
Es perpendicular to it, then, if (f) is the acute angle between the direction of the 
incident waves and the normal to the surface at a point Q on it, writing 
where 
e = (/c'+iK' cos (f))f[K'—LK cos (f)), 
e' = (k' cos (j) + LK)/[K' cos <j) — iK)C 
k'“ = sin^ (f) + 4i7rLKVjcr, 
and O' is the specific resistance of the obstacle, the electric current distribution to be 
placed on the surface has components 
Ms( 1+€'), Ml (1+6), 
and the magnetic current distribution to be placed on the surface has components 
Es(1-6), Ei(1-6'). 
The effect of this distribution can be immediately obtained from the previous 
calculations by superposing the two distributions 
2M2e', 2Mie, 
and the two distributions 
M 2 (1-6'), El (1-6'); Ml (1-6), E,{l-e); 
the first two involve the same calculation as in the case of the perfectly conducting 
* The general value of e' is (47rV/o- + k' sec ~ which has the approximate value in the 
text -when the wave-length A of the oscillations is great compared with (t/Y. 
