AN OBSTACLE ON A TRAIN OF ELECTRIC WAVES. 
335 
obstacle, and the second two involve the same calculation as in the case of the 
perfectly absorbing obstacle, hence, at points inside the tangent cone from the 
oscillator to the surface of the obstacle, the principal parts of the components of the 
electric and magnetic forces vanish when the point is not near to the boundary of the 
geometrical shadow, at a point P outside the boundary of the geometrical shadow 
and not near to it, the principal parts of the components of the electric and magnetic 
forces in the reflected waves at P are given by multiplying the components due to 
2 M 2 at Q in the case of perfect reflection by e' and the components due to 2M, at Q 
by e, where OQ, QP make equal angles with the normal at Q to the surface. When 
the point P is inside the tangent cone and near to the boundary of the geometrical 
shadow, the distribution 2 M 2 e' gives the corresponding components multiplied of 
— (1—L)e' and the distribution M 2 (l—e'), Ei(l—e') the corresponding components 
multiplied by — (1—L) (1—e'), that is these two distributions give the corresponding 
components multiplied by — {1 — L) and the other two distributions give the corre¬ 
sponding components multiplied by — (1—L); therefore the principal parts of the 
components of the electric and magnetic forces at the point P due to the oscillator 
and to the assumed distribution on the surface are 
LX', LY', LZ', La', L^', Ly', 
where X', Y', Z', a', ^8', y' are the principal parts of the components of the electric 
and magnetic forces due to the oscillator at the point P and L has the value deflned 
above. It may be verified as in the case of the perfect conductor that the boundary 
conditions at points on the surface of the obstacle not near to the curve of contact of 
the tangent cone from the oscillator are satisfied by this assumed distribution on the 
surface. It also follows from the investigation for the case of the perfectly conducting 
obstacle that the principal parts of the components of the electric and magnetic forces 
at a point P inside the boundary of the geometrical shadow are given by 
LX', LY', LZ', La', Ly8', Ly', 
provided P is at a distance from the surface of the obstacle which is of an order 
higher than p [Kp)~'^^ and the perpendicular distance of OP from the point R on the 
curve of contact of the tangent cone from O to the surface is of the same or higher 
order than p [Kp)~'^\ where p is the radius of curvature of the normal section of the 
surface through OR. The principal parts of the components of the electric and 
magnetic forces at points on the surface of the obstacle near the curve of contact but 
at a distance along the surface from it of higher order than p {Kp)~'^^ can be determined 
as follows. Let M'l, M'y be the principal parts of the components of the magnetic 
force due to the oscillator tangential to the surface at the point P on it inside the 
boundary of the geometrical shadow, M'j being in the plane containing OP and the 
normal to the surface at P, and M '2 perpendicular to this plane. Further, let Mj, M 2 
