AN OBSTACLE ON A TEAIN OF ELECTEIC WAVES. 
337 
when the obstacle is imperfectly conducting this ratio is greater than 2,* but 
decreases as the distance along the surface of the point P from the edge of the 
shadow increases when the magnetic force in the incident waves is perpendicular to 
the plane of incidence. 
The same methods as have been applied in the foregoing can be used to solve the 
problem of the case of a transparent obstacle; it is convenient in this case to treat 
separately the components of the electric and magnetic forces tangential to the 
surface in and perpendicular to the plane of incidence. 
[October 17 .—The investigation given above of the effect of a perfectly absorbing obstacle assumes that 
the electric and magnetic forces on the surface change abruptly at the curve of contact of the tangent 
cone from the point O to the surface. When the creeping effect at the edge is taken into account, the 
quantity L gives the ratio of the forces at a point P inside the geometrical shadow to the forces at that 
point due to the oscillator alone, only if the point P is subject to the same restrictions as in the case of 
the perfectly conducting obstacle, that the distance of the point P along OP from the surface of the 
obstacle is of higher order than p {npY^I^ and that OM is of higher order than p (Kpj'Va. The theorem, 
that the electric force normal to the surface of the obstacle at a point on it when the obstacle is perfectly 
conducting has double the value it has when the obstacle is perfectly absorbing, can be established 
generally as follows: Lot E and i\I be the electric and magnetic forces in the incident waves tangential 
to the surface of the obstacle at a point on it. If the surface is perfectly conducting there is an electric 
current distribution 2Moj on it and a zero magnetic current distribution, and if the obstacle is incapable 
of supporting magnetic force there is a zero electric current distribution on it and a magnetic current 
distribution 2En)'; the superposition of these two distributions gives the solution for the case when the 
obstacle is perfectly absorbing and the electric and magnetic forces in the incident waves tangential to the 
surface at a point on it are 2E, 2M. Hence the electric current distribution on the surface of the 
obstacle when it is perfectly absorbing is Moj, and when it is perfectly conducting 2Moj, the electric and 
magnetic forces in the incident waves tangential to the surface being E, M ; and therefore the magnetic 
force tangential to the surface and the electric force normal to the surface of the obstacle when it is 
perfectly conducting have each double the value they have when the obstacle is perfectly absorbing. 
Similar reasoning applies to the case of the imperfectly conducting obstacle, the ratio in this case being 
1 + € for the component of magnetic force tangential to the surface in the plane of incidence and 1 + e' for 
the component perpendicular to the plane of incidence.] 
* For the case of waves of the wave-lengths used in wireless telegraphy, the conducting body being the 
sea, the value of this ratio at a distance of 150 miles is not greater than 2'06 and decreases as the distance 
increases. 
2 X 
VOL. CCXIl.-A. 
